Federal Energy Regulatory Commission Staff Report •February 4, 2005 1

Principles for Efficient and Reliable Reactive Power Supply and Consumption

Table of Contents

Preface .......................................................................................................................... 2

Executive Summary ...................................................................................................... 3

Chapter 1 – Introduction:

What Is Reactive Power and Why Are We Concerned About It? ................................ 17

Chapter 2 – Physical Characteristics and Costs of Reactive Power in AC Systems .... 25

Chapter 3 – History of Reactive Power Pricing............................................................ 45

Chapter 4 – International Reactive Power Markets ................................................. 59

Chapter 5 – Existing Reactive Power Issues ................................................................ 65

Chapter 6 – Pricing and Procurement Options for Reactive Power ............................. 85

Chapter 7 – Conclusions, Recommendations and Questions ...................................... 105

Glossary ..................................................................................................................... 117

Appendix A – Literature Review of Reactive Power Markets.................................... 123

Appendix B – Generators ........................................................................................... 131

Appendix C – Transmission ........................................................................................ 144

Appendix D – System Operator .................................................................................. 160

Appendix E – Electric Plants in Service ....................................................................... 174

FEDERAL ENERGY REGULATORY COMMISSION

Staff Report • Docket No. AD05-1-000 • February 4, 2005

888 First Street, N.E. Washington, D.C. 20426
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Principles for Efficient and Reliable Reactive Power Supply and Consumption

Preface

In August 2003, there was a widespread power outage that affected 50 million people in the

United States and Canada. As a result of the April 2004 report and recommendations of the

U.S.-Canada Power System Outage Task Force and an increased number of filings for

reactive power compensation at the Commission, Chairman Pat Wood III formed an

interoffice staff team to develop principles for efficient and reliable reactive power supply

and consumption.

The team consisted of Richard O’Neill (team lead), Mary Cain, David Mead, Derek Bandera,

David Withnell, Zolaikha Salihi, Dharmendra Sharma, Emily Bartholomew, Giuseppe Fina,

Harry Singh, Kumar Agarwal, Tomohisa Koyama and Victor Coulter. John Jennrich served

as editor. Judy Eastwood served as graphic artist.

Brendan Kirby, John Kueck, Chris Mak, Frank Macedo, Ross Baldick, Bill Stewart. Marija

Ilic, Jamie Weber, Oscar Muñoz, Bruce Poole, Gary Nakarado, Saeed Farrokhpay, Thanh

Luong, LaChelle Brooks, Thomas Dautel, Kevin Kelly, James Ballard, Vis Tekumalla and

Joe McClelland, among others, provided helpful comments and contributions.

Over several months, team members consulted representatives of the American Public Power

Association, Edison Electric Institute, Electric Power Supply Association, Institute of Electrical

and Electronics Engineers, National Association of Regulatory Utility Commissioners, North

American Electric Reliability Council, regional transmission organizations and various

equipment manufacturers.

This report contains analyses, presentations and conclusions that may be based on or derived

from the data sources cited, but do not necessarily reflect the positions or recommendations

of the data providers.

The team appreciates the many contributions it has received. Any errors are those of the

interoffice staff.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 3

Principles for Efficient and Reliable Reactive Power Supply and Consumption

Almost all bulk electric power in the United States is generated, transported and

consumed in an alternating current (AC) network. Elements of AC systems

produce and consume two kinds of power: real power (measured in watts) and

reactive power (measured in volt-amperes reactive, or var). Real power accomplishes

useful work (e.g., running motors and lighting lamps). Reactive power supports the

voltages that must be controlled for system reliability.

EXECUTIVE SUMMARY

Principles for Efficient and Reliable Reactive Power

Supply and Consumption

Reactive power supply is essential for reliably operating the electric

transmission system. Inadequate reactive power has led to voltage collapses

and has been a major cause of several recent major power outages

worldwide. And while the August 2003 blackout in the United States and

Canada was not due to a voltage collapse as that term has been traditionally

used, the final report of the U.S.-Canada Power System Outage Task Force

(April 2004) said that “insufficient reactive power was an issue in the

blackout.” Dynamic capacitive reactive power supplies were exhausted in

the period leading up to the blackout.

Sound regulatory policies are necessary to ensure an adequate supply of

reactive power at reasonable cost. The rules for procuring reactive power

can affect whether adequate reactive power supply is available, as well as

whether the supply is procured efficiently from the most reliable and lowestcost sources. This is readily apparent in the large portions of the United

States where the grid is operated by independent system operators (ISOs);

these operators do not own generation and transmission facilities for
4 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Principles for Efficient and Reliable Reactive Power Supply and Consumption

producing and consuming reactive power, and therefore must procure reactive power from

others. But procurement rules also affect other parts of the United States where vertically

integrated utilities operate the grid, because reactive power capability also is available

from independent companies. Sound policy would ensure that system operators – whether

they are independent or vertically integrated – have adequate reactive power supplies to

choose from and at the lowest reasonable cost.

Not only is reactive power necessary to operate the transmission system reliably, but it can

also substantially improve the efficiency with which real power is delivered to customers.

Increasing reactive power production at certain locations (usually near a load center) can

sometimes alleviate transmission constraints and allow cheaper real power to be delivered

into a load pocket. Regulatory policies can substantially affect whether reactive power is

supplied so as to provide these economic benefits.

There are several problems and concerns regarding the current procurement practices and

pricing policies for reactive power:

1. Discriminatory compensation.

a. Transmission-based suppliers of reactive power capability receive compensation,

yet many generation-based suppliers are not compensated for reactive power

capability that aids in system reliability.

b. Independent generation resources may not always be compensated for providing

reactive power support to the grid in areas where other generators affiliated with

vertically integrated transmission owners receive cost-of-service payments for

providing similar service, despite the Commission’s policy requiring comparability.

2. Rigid but imprecise interconnection standards that are insensitive to local needs.

Interconnection standards generally require a standardized generation power factor for

new generation. But local needs often vary from the standards. Some locations may have

higher reactive power needs than the standard, while other locations may have smaller

needs. Moreover, the standards are imprecise in important respects. For example, the

standards do not specify on which side of the step-up transformer, and exactly how, the

power factor is to be measured.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 5

Principles for Efficient and Reliable Reactive Power Supply and Consumption

3. Lack of transparency and consistency in planning and procurement.

The reactive power planning standards and procurement processes are not transparent.

Alternative solutions to provide needed reactive power capability may be available, but

currently these options might not be adequately considered.

4. Poor financial incentives to provide or consume reactive power.

a. Many market participants that could provide additional reactive power capability

to the system have little incentive to do so. Price signals that could encourage

additional investment are limited.

b. In many cases load response and load-side investment could reduce the need for

reactive power capability in the system, but incentives to encourage efficient

participation by load are limited.

5. Poor incentives for some system operators to procure reactive power and reactive

power capability at least cost.

System operators outside of regional transmission organizations (RTOs) and ISOs that are

regulated transmission owners may lack the incentives to consider all available sources of

reactive power. That is because cost-of-service regulation generally rewards capital

investment, even when purchasing from a third party would be a less costly alternative.

6. Failure of system operators to adjust reactive power instructions so as to fully optimize

the dispatch.

Often, a range of reactive power production levels would fully meet the reliability

requirements of a transmission system. However, system operators typically choose the

level that meets specified guidelines, even though other levels within the range would allow

the demands for real power to be met at a lower total cost. A related issue is that the

software for implementing such reactive power optimization is not currently available.

The purpose of this paper is to begin a discussion about the proper regulatory policy toward

reactive power pricing and market design. First, it examines the physical characteristics

and costs of producing reactive power. Second, it reviews the history of reactive power

pricing at the Commission and briefly discusses current practices in other countries. Finally,

it develops pricing principles and examines market designs for reactive power. The paper
6 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Principles for Efficient and Reliable Reactive Power Supply and Consumption

also includes appendices that address the more technical issues in modeling reactive power

market design. To address the six problems and concerns identified above, the paper makes

four broad recommendations:

1. Reactive power reliability needs should be assessed locally, based on clear national

standards.

2. These needs should be procured in an efficient and reliable manner.

3. Those who benefit from the reactive power should be charged for it.

4. All providers of reactive power should be paid, and on a nondiscriminatory basis.

It may also be helpful to clarify what this paper does not do. It does not advocate an

unregulated market for reactive power, since market power problems could be widespread

in reactive power supply. It does not advocate a national prescribed approach to reactive

power needs. It does not intrude on the responsibilities of the North American Electric

Reliability Council (NERC). It does not advocate a specific technology approach; it is

technology neutral. And it does not advocate abrogating existing contracts.

Physical characteristics and costs. Reactive power may be supplied by several different

sources, including transmission equipment (such as capacitors, reactors, static var

compensators and static compensators), generators and synchronous condensers. Reactive

power does not travel over long distances at high line loadings due to significant losses on

the wires. Thus, reactive power usually must be procured from suppliers near where it is

needed. This factor limits the geographic scope of the reactive power market and, thus, the

number of suppliers that can provide reactive power and the amount of competition at any

place and time, at least in the short term before other suppliers can enter the market.

But while competition may be limited in reactive power markets, there may be at least

some existing alternative sources of reactive power supply in many locations, and new

sources may be able to enter the market over the longer term. The goal should be to

develop rules that ensure that adequate supplies of reactive power (including reactive

reserves) are available in all locations to ensure that operation of the grid is reliable and

efficient and that reactive power is procured at least cost over the short and long run. As

we discuss below, transparent and nondiscriminatory markets and prices for reactive power

have the potential to promote this goal.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 7

Principles for Efficient and Reliable Reactive Power Supply and Consumption

Generally, reactive power support is divided into two categories: static and dynamic. Static

reactive power is produced from equipment that, when connected to the system, cannot

quickly change the reactive power level as long as the voltage level remains constant, and

its reactive power production level drops when the voltage level drops. Capacitors and

inductors supply and consume static reactive power. Dynamic reactive power is produced

from equipment that can quickly change the Mvar level independent of the voltage level.

Thus, the equipment can increase its reactive power production level when voltage drops

and prevent a voltage collapse. Static var compensators, synchronous condensers and

generators provide dynamic reactive power.

Both the variable and fixed costs of producing static reactive power are much lower than

those of producing dynamic reactive power. If cost were the only issue, a transmission

provider at any instant in time would use static reactive power equipment first in procuring

reactive power, and use the dynamic equipment only after the static equipment had been

fully used. However, two factors force transmission providers at times to use more expensive

dynamic reactive power sources in place of cheaper sources. First, the lowest cost sources

cannot always produce reactive power as reliably as necessary. Static power equipment

does not produce reactive power as reliably as dynamic power equipment because the

transmission equipment’s production depends on voltage and, thus, its ability to produce

declines when voltage declines. Second, because reactive power does not travel far (due to

significant transmission losses), it usually must be produced near the location where it is

needed. Thus, expensive reactive power sources must sometimes be purchased even if

cheaper sources are idle because the expensive source is more reliable and/or is near the

location needing the reactive power, while the cheaper sources cannot get the reactive

power to where it is needed.

A generator’s cost of producing reactive power can sometimes include opportunity costs

associated with forgone real power production. Opportunity costs arise because there can

be a trade-off between the amount of reactive power and real power that a generator can

produce. When a generator is operating at certain limits, a generator can increase its

production or consumption of reactive power only by reducing its production of real power.

As a result, producing additional reactive power results in reduced revenues associated

with reduced real-power production.
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Principles for Efficient and Reliable Reactive Power Supply and Consumption

The history of reactive power pricing at the Commission. The recent history of reactive

power pricing begins with the Commission’s Order No. 888, its Open Access Rule, issued in

April 1996. In that order, the Commission concluded that “reactive supply and voltage

control from generation sources” is one of six ancillary services that transmission providers

must include in an open access transmission tariff. The Commission noted that there are

two ways of supplying reactive power and controlling voltage: (1) installing facilities as

part of the transmission system and (2) using generation facilities. The Commission concluded

that the costs of the first would be recovered as part of the cost of basic transmission

service and, thus, would not be a separate ancillary service. The second (using generation

facilities) would be considered a separate ancillary service and must be unbundled from

basic transmission service. In the absence of proof that the generation seller lacks market

power in providing reactive power, rates for this ancillary service should be cost-based and

established as price caps, from which transmission providers may offer a discount.

In Opinion No. 440, the Commission approved a method presented by American Electric

Power Service Corp. (AEP) for generators to recover costs for reactive power. AEP identified

three components of a generation plant related to the production of reactive power: (1) the

generator and its exciter, (2) accessory electric equipment that supports the operation of

the generator-exciter, and (3) the remaining total production investment required to provide

real power and operate the exciter. Because these plant items produce both real and reactive

power, AEP developed an allocation factor to sort the annual revenue requirements of

these components between real and reactive power production. The factor for allocating

to reactive power is Mvar2

 /MVA2 , where Mvar is megavolt amperes reactive and MVA is

megavolt amperes. Subsequently, the Commission indicated that all generators that have

actual cost data should use this AEP method in seeking reactive power cost recovery.

In its recent Generation Interconnection Rule, Order No. 2003, the Commission concluded

that an interconnection customer should not be compensated for reactive power when

operating within its established power factor range. (Under Order No. 2003, the required

power factor range is 0.95 leading [consuming] and 0.95 lagging [supplying], but the

transmission provider may establish a different power factor range.) However, the

transmission provider must compensate the interconnection customer for reactive power

during an emergency. In Order No. 2003-A, the Commission clarified that if a transmission
Federal Energy Regulatory Commission Staff Report •February 4, 2005 9

Principles for Efficient and Reliable Reactive Power Supply and Consumption

provider pays its own or its affiliated generators for reactive power within the established

range, it must also pay the interconnection customer.

ISOs and RTOs use a variety of methods to compensate generators for reactive power.

Most pay generators their allocated revenue requirement or some other form of capacity

payment. In addition, some ISOs and RTOs pay a generator for its lost opportunity costs

when producing reactive power requires a reduction in real power output. Finally, some

ISOs and RTOs impose penalties on generators for failing to provide reactive power, while

others don’t impose penalties.

International experience. In several countries where the system operator does not own

generation facilities, the system operator compensates generators that provide reactive

power. These countries include England and Wales, Australia, India, Belgium, the

Netherlands and certain provinces of Canada. Sweden follows a different policy. Reactive

power in Sweden is supplied by generators on a mandatory basis, and there is no

compensation. In the province of Alberta, Canada, generators are penalized for failing to

produce or absorb reactive power, and in Argentina, such penalties are imposed not only

on generators, but also on transmission operators, distribution operators and large loads.

Finally, in Japan, Tokyo Electric Power Co. gives its retail customers a financial incentive

to improve their power factors through discounts of the base rate.

Market design issues. As noted above, reactive power can be produced from either static

or dynamic sources. Static sources are typically transmission equipment, such as capacitors.

Historically, the costs of static sources are included in the revenue requirement of the

transmission owner (TO), and, thus, are recovered in the TO’s cost-of-service rates from its

customers. By contrast, dynamic sources are typically generation equipment, including

generators capable of producing both real and reactive power, and synchronous condensers,

which produce only reactive power. This generation equipment may be owned either by

TOs or independent entities. There are competing views about whether or how such

generators should be compensated for reactive power.

Should generators be compensated? One view is that generators should not be compensated

for reactive power, at least within specified limits. Under this view, generators should be
10 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Principles for Efficient and Reliable Reactive Power Supply and Consumption

required to have a specified minimum capability to produce reactive power as a condition

of interconnecting to the grid, and they should bear the costs of maintaining this capability

as well as the costs of producing reactive power from this minimum capability.

This paper takes a different view. We conclude that market participants should be

compensated for the reactive power that they provide, in order to ensure an adequate,

reliable, and efficient supply of reactive power. That is because it is unlikely that an operator

will offer to supply reactive power unless it expects to recover its costs and earn a profit.

Of course, many generators are able to earn revenue from sources other than reactive

power – such as from sales of real power. Thus, much generation investment would continue

to be made even if generators are not paid for providing reactive power. However, failing

to pay generators for reactive power could reduce the amount of generation investment,

because revenue from real power sales and other sources, by themselves, may not be

sufficient for some projects to cover the project’s costs and return a profit. In addition,

paying generators may help retain reactive power capability where it is needed. Failing to

pay for reactive power could also reduce the amount of reactive power capability installed

in new generation equipment. That is because developers may elect not to add reactive

capability beyond the minimum requirements if they are not going to receive any additional

revenue from doing so. Also, paying suppliers for reactive power production requested by

the system operator will create incentives for the suppliers to follow the system operator’s

instructions.

Compensating operators for providing reactive power and reactive power capability could

also encourage system operators to make good economic decisions within the bounds

established by reliability. If suppliers must be paid for reactive power capability, system

operators should have a greater incentive to procure reactive power from the lowest cost

sources and to avoid procuring excessive reactive power capability in generation pockets

where it is not needed.

Comparable compensation for all generators. A related issue is whether all generators

should be paid for reactive power. In some control areas that are not operated by ISOs or

RTOs, generators owned by the transmission provider are paid for reactive power while

other generators are not. We conclude that such discrimination is poor public policy and
Federal Energy Regulatory Commission Staff Report •February 4, 2005 11

Principles for Efficient and Reliable Reactive Power Supply and Consumption

could be considered undue discrimination under the Federal Power Act. We think that the

Commission’s general policy favoring comparability should apply in the reactive power

context. That is, independent generators should be eligible for the same compensation for

reactive power as a generator owned or affiliated with the transmission provider providing

comparable service

However, the level of compensation should depend on the needs of the system. In areas

where additional capability and production are needed, prices should be sufficient to

encourage additional investment and supply. Conversely, in areas with significant excess

capability, lower prices are appropriate so as not to burden customers with excessive costs

or to encourage additional investment that is not needed.

Compensation for static versus dynamic reactive power. Another issue is whether owners

of static and dynamic sources of reactive power should receive the same compensation.

We conclude that the reactive power capability from static sources is less valuable than

from dynamic sources, because dynamic sources can adjust their production or consumption

of reactive power much more quickly as needed to maintain voltage and prevent a voltage

collapse. Thus, reactive power capability from dynamic sources is a different product than

the capability from static sources, and the market price for dynamic capability at a given

location and time may often be higher than the market price for static capability. However,

reactive power that is actually produced or consumed at a given location and time has the

same value whether it is provided by a static or dynamic source. Thus, if reactive power is

bought and sold in real time, the price faced by all reactive power providers at a given

location and time should be the same, regardless of the source. This recommendation is

consistent with the pricing policies for real power, where fast-responding units providing

operating reserves for real power are paid more than slow-responding operating reserves,

while all real power produced at a given location and time is paid the same price.

Pricing options. There are two general ways to compensate generators for providing

reactive power. One way is the capacity payment option, in which the generator is paid in

advance for the capability of producing or consuming reactive power. The payment could

be made through a bilateral contract or through a generally applicable tariff provision.

Once the generator is paid, it could be obligated to produce or consume reactive power up
12 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Principles for Efficient and Reliable Reactive Power Supply and Consumption

to the limits of its commitment without further compensation when instructed by the system

operator. To ensure that the generator follows instructions in real time, the generator

could face penalties for failing to produce or consume when instructed. Currently, this is

the most common method for compensating reactive power providers.

The other way is the real-time price option, in which the generator is paid in real-time for

the reactive power that it actually produces or consumes. Under this option, the generator

is paid only for what it produces or consumes, but it pays no penalty for failing to produce

when instructed.

It is also possible to combine some of the features of each of these options. For example, a

generator might receive a capacity payment in advance in exchange for the obligation to

produce or consume reactive power within a specified power factor range upon instruction

by the system operator, but might also receive a spot price for producing or consuming

additional reactive power beyond the specified range.

Under the capacity payment option, there are at least four methods for determining the

capacity payment:

1. A cost-based payment – based either on the current (AEP) method, or other costbased methods.

2. Capacity market payment. A generator’s installed capacity obligation would include

an obligation to provide reactive power within a specified power factor range and

the generator’s compensation would be bundled in with its capacity payment.

3. Prices determined through auction. The ISO or RTO could hold an auction for

reactive power capability and the winners of the auction would receive the applicable

market clearing price.

4. Pay nothing – based on the view that each generator should be obligated to provide

reactive power as a condition of interconnecting with the grid.

Under the real-time pricing option, there are at least four methods for determining the spot

price:
Federal Energy Regulatory Commission Staff Report •February 4, 2005 13

Principles for Efficient and Reliable Reactive Power Supply and Consumption

1. Pay nothing – at least for reactive power produced within a specified power factor

range. This option may be most appealing when the generator has received a

capacity payment in advance for the capability to produce within the specified

range.

2. Unit-specific opportunity costs. Pay a generator for the unit-specific opportunity

cost it incurs due to reduced real power production, either for any reactive power

produced or, alternatively, only for reactive power produced outside a specified

power factor range underlying any capacity payment that the generator received

in advance.

3. Market clearing prices determined through auction. Determine real time prices

based on a spot market auction for reactive power. In the auction, all accepted

bidders at a location could receive the same market-clearing price based on the

highest accepted bid. One issue for the auction is whether reactive power prices (i)

are calculated directly or (ii) are derived from the implicit opportunity costs associated

with real power prices and the supplier’s real-power energy bids. Under the direct

pricing approach, reactive power sellers would submit price bids for supplying (or

consuming) specific amounts of reactive power, and the reactive power price at any

location and time would be the highest accepted price bid. Under the derived

approach, reactive power suppliers would submit price bids for supplying real power

as well as information indicating the trade-off between supplying various amounts

of real and reactive power. However, the supplier would not submit a specific price

bid for producing reactive power. From the submitted information, the ISO or RTO

would calculate the implicit opportunity cost (i.e., the forgone real-power revenue

associated with supplying or consuming reactive power) incurred by each supplier.

The price for reactive power in the auction would be calculated based on these

derived opportunity costs.

4. Prices (or a pricing formula) announced in advance. This method is currently used

in the United Kingdom and India.

Choosing among the pricing options. Choosing among the options depends on the goals

and objectives. We think that a well-designed pricing mechanism can help achieve at least

two important goals. The first is to encourage efficient and reliable investment in
14 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Principles for Efficient and Reliable Reactive Power Supply and Consumption

infrastructure needed to produce reactive power and maintain the reliability of the

transmission system. The second is to encourage efficient production and consumption of

reactive power from the existing infrastructure, taking into account the opportunity costs

of competing uses of resources, so as to keep rates low.

We have concerns about whether the current methods of procuring and compensating for

reactive power promote these goals. For example, current rules treat generators differently

from other providers of reactive power. Owners of transmission equipment that provide

static reactive power capability receive cost-of-service payments through a routine filing

process. However, owners of generators are sometimes expected to provide reactive power

capability within established ranges without compensation, as a condition of interconnection

to the grid. In addition, the regulatory process often makes it harder for independent

generators than for owners of generators that are affiliated with vertically integrated

transmission owners to receive compensation for their reactive power capability through

routine regulatory filings. Interconnection requirements to provide capability for reactive

power provide no compensation in certain locations and this arrangement blunts the incentive

to provide this capability. The Commission should review the current AEP methodology

of Opinion No. 440 for determining payments for reactive power capability, especially

with regard to its effect on investment incentives. Further, the Commission should streamline

the process for filing and collecting Opinion No. 440 rates by independent generators. The

regulatory process that independent generators must follow in order to receive compensation

is much more burdensome and time-consuming than that for affiliated generators.

Streamlining the process for independent generators – so as to make the regulatory process

the same for affiliated and independent generators – would remedy this problem.

Spot markets for reactive power. Forward contract markets can allow market participants

to lock in trades in advance and hedge risk. Developing bid-based reactive power spot

markets, operated by ISOs and RTOs, can allow participants to adjust their forward positions

as market conditions change, making it less risky to enter into forward contracts. In addition,

spot markets can help facilitate meeting demand with the lowest-cost resources that are

available in real time. Spot pricing devoid of market power provides signals to improve the

efficiency of the system. For example, we have been told of market participants with shunt

capacitors that do not dispatch them properly. We suggest price signals can help do the
Federal Energy Regulatory Commission Staff Report •February 4, 2005 15

Principles for Efficient and Reliable Reactive Power Supply and Consumption

job. Examples presented in this paper and some preliminary research suggest that a fuller

consideration of reactive power in real time spot markets in conjunction with real power

markets may have the potential to reduce the total costs of meeting load substantially.

However, the idea of a bid-based reactive power spot market is new and we believe it is too

soon to implement one. Simulation and experimentation are needed to understand the

effects of alternative auction market designs. In addition, the software and other costs of

developing a reactive power auction market should be understood. For the present, while

spot auction markets are being further studied, we recommend paying real-time prices for

actual reactive power production based on the provider’s own opportunity cost or based on

administratively determined prices announced in advance, in order to encourage suppliers

to produce reactive power where it is needed.

Addressing market power. As noted earlier, many suppliers of reactive power have market

power because the number of reactive power suppliers at any location is often very small.

Thus, regulatory policies need to be in place to restrict the ability of reactive power suppliers

to exercise market power. This paper does not reach a conclusion about how best to the

mitigate market power of reactive power providers. Several options should be considered.

We mention two options here, but others may also be available. Of course, the traditional

method at the Commission for limiting the exercise of market power has been cost-ofservice regulation. While the cost-of-service option should be considered, it is not the only

available option, and it may not be the best option. Cost-of-service regulation can blunt

incentives for suppliers to minimize their costs; cost reductions don’t increase profits, but

instead reduce the supplier’s revenues. Another option is the procedure used in ISO spot

markets for real power – that is, to cap the suppliers’ bids while allowing all accepted

suppliers to receive a market clearing price in the spot market that reflects the highest

accepted bid. This option may provide incentives for the supplier to reduce its costs, especially

if the supplier does not always set the market clearing price. Cost reductions would not

always reduce revenues, and thus, could increase profits.

In the future, however, market power in reactive power markets could be a smaller problem

because entry and exit could become easier. With the advent of new technology, equipment

that supplies reactive power now comes in smaller increments and can be made mobile
16 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Principles for Efficient and Reliable Reactive Power Supply and Consumption

(e.g., truck mounted). These characteristics could allow new suppliers to enter and exit

different market locations quickly and for considerably less investment and sunk costs.

Current entry rules are a barrier to this technology, however. We need a discussion of how

this affects the Commission’s policy on market design.

Concluding thoughts. This paper is intended to begin a discussion of regulatory policies

affecting reactive power. Any changes in policy resulting from this discussion are likely to

take some time to implement, and some changes are likely to be made more easily and

quickly than others. For example, policies that promote comparability are likely to be

more easily made, and we recommend working to implement them in the near term. These

policies include (1) clarifying the requirements and compensation rules for providing reactive

power, as well as the definitions underlying these requirements and rules, (2) creating

incentives that encourage desired behavior, (3) streamlining the process for compensating

independent generators for reactive power capability and provision to make the process

comparable to that for affiliated generators, and (4) making reactive power procurement

and compensation more transparent, for example by calculating and publishing reactive

power production, consumption and prices on a comparable basis to real power. Other

policy changes involve more complex issues, and will require more time to consider. Policy

changes that involve a complete market redesign will thus need to be implemented over the

longer term. The ultimate goal should be an integrated set of co-optimized markets with

bilateral markets relatively free from federal regulation. This goal requires research, software

development, education and testing, and is likely to require 5 to 10 years to fully implement.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 17

CHAPTER 1

INTRODUCTION

What Is Reactive Power And Why Are We Concerned About It?

What is reactive power? Almost all bulk electric power is generated,

transported and consumed in alternating current (AC) networks.

Elements of AC systems supply (or produce) and consume (or absorb or

lose) two kinds of power: real power and reactive. Real power accomplishes

useful work (e.g., runs motors and lights lamps). Reactive power supports

the voltages that must be controlled for system reliability.

In an AC electrical system, voltage and current pulsate (described

mathematically by sine waves) at the system frequency (in North America

this is 60 Hertz, or 60 times per second). Voltage is a measure of the potential

energy per electric charge, and current is a measure of the average velocity

at which electrons are moving. Voltage (measured in volts) is analogous to

pressure in a water or gas system, while current (measured in amperes) is

analogous to the velocity of fluid flow – water or gas.

Although AC voltage and current pulsate at the same frequency, they peak

at different times. Power is the algebraic product of voltage and current.

Over a cycle, power has an average value, called real power, measured in

volt-amperes, or watts. There is also a portion of power with zero average

value that is called reactive power, measured in volt-amperes reactive, or

vars. The total power is called apparent power, measured in volt-amperes,

or VA.

Reactive power has zero average value because it pulsates up and down,

averaging to zero; reactive power is measured as the maximum of the

pulsating power over a cycle. Reactive power can be positive or negative,

depending on whether current peaks before or after voltage. By convention,

reactive power, like real power, is positive when it is “supplied” and negative

when it is “consumed.” Consuming reactive power lowers voltage

magnitudes, while supplying reactive power increases voltage magnitudes.

An analogy for describing reactive power is a person on a trampoline. While

walking across the trampoline, the person will bounce up and down. The

bouncing is caused by an exchange of stored energy between the trampoline

springs and the Earth’s gravitational field. Similarly, reactive power in an

electric transmission system is just the pulsating transfer of stored energy
18 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Introduction: What is Reactive Power and Why Are We Concerned About It?

between various kinds of electrical components in the system.

Because voltage and current are pulsating, the power on a transmission line

also pulsates. In a transmission system, this pulsating transfer of stored

energy results in a loss of power called line losses. In the trampoline analogy,

the person’s “real” power goes into moving horizontally across the

trampoline, while “reactive” power keeps the person standing on the

trampoline as it bounces. The effort the person expends to keep standing

during bouncing results in no net forward motion, but is necessary to walk

across the trampoline. The motion from the trampoline bouncing is always

perpendicular to the direction the person is walking; this is called being in

quadrature. Similarly, real and reactive power are also in quadrature (90

degrees out of phase) and hence the letter Q is commonly used to designate

reactive power. Real power is commonly designated as P.

Reactive power takes up space on transmission lines. Here reactive power

is like the head on a beer because it takes up space in the glass leaving less

room for the real beer. For a transmission line, the square of the real power

plus the square of the reactive power must be less than the square of the

thermal capacity (measured in volt-amperes) of the line. When thermal

capacity is exceeded significantly for a long time, the line will sag, possibly

into vegetation, causing a short circuit, or anneal, resulting in structural

damage. Real power losses in transmission lines are proportional to the

current in the line. Because power is the algebraic product of voltage and

current, the same power at high voltages has a lower current, and hence,

has lower losses. Power is transmitted over long distances at a high voltage,

up to 765,000 volts, while the power at a wall outlet in the United States is

only 110 volts.

Reactive power is difficult to transport. At high loadings, relative losses of

reactive power on transmission lines are often significantly greater than

relative real power losses. Reactive power consumption or losses can increase

significantly with the distance transported. Losses in transmission lead to

the expression that reactive power does not travel well. When there is not

enough reactive power supplied locally, it must be supplied remotely, causing

larger currents and voltage drops along the path.

The main advantage of AC electric power is that the voltage level can be
Federal Energy Regulatory Commission Staff Report •February 4, 2005 19

changed with transformers, which are iron cores wrapped in wire. A current

flowing in a wire induces a magnetic field around the wire; a time-varying

current induces a changing magnetic field. If a coil of wire is placed in a

changing magnetic field, a voltage is induced in the coil. The changing

current in a coil will also induce voltages in other coils in the magnetic field.

This is how transformers change the voltage level of AC power. The number

of wires on each side of the transformer core determines the voltage level at

that side.

The Need for Reactive Power. Voltage control (keeping voltage within

defined limits) in an electric power system is important for proper operation

of electric power equipment to prevent damage such as overheating of

generators and motors, to reduce transmission losses and to maintain the

ability of the system to withstand disturbances and prevent voltage collapse.

In general terms, decreasing reactive power causes voltages to fall, while

increasing reactive power causes voltages to rise. A voltage collapse occurs

when the system is trying to serve much more load than the voltage can

support.

Inadequate reactive power supply lowers voltage; as voltage drops, current

must increase to maintain the power supplied, causing the lines to consume

more reactive power and the voltage to drop further. If current increases

too much, transmission lines trip, or go off-line, overloading other lines and

potentially causing cascading failures. If voltage drops too low, some

generators will automatically disconnect to protect themselves. Voltage

collapse occurs when an increase in load or loss of generation or transmission

facilities causes dropping voltage, which causes a further reduction in reactive

power from capacitors and line charging, and still further voltage reductions.

If the declines continue, these voltage reductions cause additional elements

to trip, leading to further reduction in voltage and loss of load. The result is

a progressive and uncontrollable decline in voltage, all because the power

system is unable to provide the reactive power required to supply the reactive

power demand.

Reactive power needs are a critical part of the planning process. Supplychain management, the name often given to the manufacturingtransportation-storage-consumption process, is usually measured in days,

Introduction: What is Reactive Power and Why Are We Concerned About It?
20 Principles for Efficient and Reliable Reactive Power Supply and Consumption

weeks or months for most industries. For electricity this process takes less

than a second – the ultimate just-in-time system. If there is a disruption in

the system, corrective action is called for in seconds or minutes. As a result,

the system must be planned so that it can respond to contingencies. Auctions

can be employed to satisfy the procurement needs of the planning process.

Reactive power needs are determined in the planning process, which is part

engineering, part economics and part judgment. The engineering analysis

requires running large, complex mathematical computer models of the electric

system. The economic analysis requires putting costs or bids into the models

to determine how to achieve an efficient, reliable system. The judgment

arises due to the large number of modeling choices, expert assumptions and

approximations that often are necessary.

Reactive Power and Blackouts. Inadequate reactive power leading to voltage

collapse has been a causal factor in major power outages worldwide. Voltage

collapse occurred in the United States in the blackouts of July 2, 1996, and

August 10, 1996, on the West Coast. Voltage collapse also factored in the

blackouts of December 19, 1978, in France; July 23, 1987, in Tokyo; March

13, 1989, in Québec; August 28, 2003, in London; September 23, 2003, in

Sweden and Denmark; and September 28, 2003, in Italy.

While the August 14, 2003, blackout in the United States and Canada was

not due to a voltage collapse as that term has been traditionally used by

power system engineers, the Task Force Final Report said that “insufficient

reactive power was an issue in the blackout.”1 The report also cites

“overestimation of dynamic reactive output of system generators”2 as a

common factor among major outages in the United States. Due to difficulties

modeling dynamic generator output, the amount of dynamic reactive output

from generators has been less than expected, worsening voltage problems

and resultant power outages. Recommendation 23 of the blackout report,

“Strengthen reactive power and voltage control practices in all NERC

regions,” states: “The task force also recommends that FERC and

appropriate authorities in Canada require all tariffs or contracts for the

sale of generation to include provisions specifying that the generators can

be called upon to provide or increase reactive power output if needed for

reliability purposes, and that the generators will be paid for any lost sales

1

 U.S.-Canada Power System

Outage Task Force, Final

Report on the August 14,

2003, Blackout in the United

States and Canada: Causes

and Recommendations, April

2004, 18.

2

 Outage Task Force Final

Report, 107.

Introduction: What is Reactive Power and Why Are We Concerned About It?
Federal Energy Regulatory Commission Staff Report •February 4, 2005 21

attributable to a required increase in the production of reactive power.”

Many devices contribute to a system’s reactive power and voltage profile.

Generators can supply and consume reactive power. For a fixed amount of

energy input, the generator can, by changing control settings, supply real

and reactive power subject to the conservation of energy and the equipment

capability. Capacitors, also called condensers, supply reactive power. A

transmission line, due to its physical characteristics, supplies reactive power

under light loading and consumes it under heavy loading. Power system

voltages are controlled through the supply and consumption of reactive

power. Devices called relays sense overloads and send a signal to a circuit

breaker to remove the asset from the network.

Market Design for Reactive Power. For almost a century, electricity policy

and practice were geared to the vertically integrated utility. Tradeoffs

between generation and transmission investments were largely internal

company decisions and, for the most part, out of the public view. Reactive

power investment costs were included in rate base and redispatch costs were

placed in fuel adjustments clauses and recovered from customers. While the

Public Utility Regulatory Policies Act of 1978 (PURPA) required utilities to

buy power from qualifying third-party generators, PURPA did not specifically

address the purchase of reactive power. With the introduction of independent

power producers (IPPs) and merchant transmission, we need to reexamine

the role of who supplies and consumes reactive power and who is responsible

to pay and be paid for reactive power.

When the industry consisted of mostly vertically integrated utilities, the

planning process was often shrouded in engineering, mathematics and

modeling jargon, making it difficult for many to understand. Reactive power

requirements were opaque. With the advent of independent system operators

(ISOs) and regional transmission organizations (RTOs), the process has

become less opaque.

Unlike the cost of real power, for generators, most of the costs of reactive

power are sunk investment costs. Therefore, decisions made today will affect

the industry for years to come. Some argue that providing reactive power

for free is good citizenship or good utility practice. In the era of the vertically

Introduction: What is Reactive Power and Why Are We Concerned About It?
22 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Introduction: What is Reactive Power and Why Are We Concerned About It?

integrated utility, good citizenship was accompanied by cost recovery. Now,

IPPs have no rate base or fuel adjustments clauses, but the costs are still

incurred. In some ISOs, IPPs are paid a demand charge for certain reactive

power capability and lost-opportunity costs if they need to reduce real power

output. Proper real time price signals and capability payments would provide

incentives to enhance both reliability and the efficiency in the short term.

Efficient competition is a way to achieve efficiency and reduce costs to

consumers. Efficient competition is difficult to achieve, but competition

merely for the sake of competition is just sport. Due to innovation and

technological progress, the optimal industry structure and mode of regulation

may need to change. As regulated markets move from franchised monopolies

toward competition, regulation needs to move from direct price regulation

to market rules. Competitive markets require a competitive market design.

In some markets, little more than basic contract and property rights laws

and their enforcement are necessary. In electricity markets, the value to

society of continuous high-quality electric power makes additional market

rules necessary. As Nobel Prize winning economist Ronald Coase stated:

“All exchanges regulate in great detail the activities of those who

trade in these markets ... these exchanges are often used by economists

as examples of a perfect competition ... It suggests ... that for anything

approaching perfect competition to exist, an intricate system of rules

and regulations would be normally needed. Economists observing

the regulations of the exchange often assume that they represent an

attempt to exercise monopoly power and to aim to restrain

competition. ... An alternative explanation for these regulations: that

they exist in order to reduce transaction costs ... Those operating in

these markets have to depend, therefore, on the legal system of the

State.”3

Put differently, efficient market design does not just happen spontaneously.

It is the result of a process that includes full discussion, learning and informed

judgments by all affected and responsible parties.

Many argue that both transmission and reactive power are public goods.

This is an oversimplification. When a transmission line is congested, the line

3

 R.H. Coase, The Firm, the

Market and the Law,

Chicago (University of

Chicago Press, 1988), 1-31.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 23

Introduction: What is Reactive Power and Why Are We Concerned About It?

no longer has a public good characterization. The electric system is replete

with externalities and assets that are both substitutes and complements,

which can change based on system conditions. Some argue that scale

economies limit the ability of competition to achieve efficiency, but

redundancy required by reliability contingency considerations limit the use

of possible scale economies. Reactive power supply or consumption can

incur opportunity costs when generators must reduce real power output to

supply reactive power. Reactive power is consumed by transmission lines

when highly loaded.

To function efficiently, markets should be complete. That is, for all scarce

services, compensation must be received by the suppliers and be paid for by

the consumers. Otherwise, supply and investment signals are muted,

shortages can develop and curtailments become necessary. This holds true

for reactive power. Sellers should be paid a market price or rate for reactive

power that they supply so as to avoid shortages. Buyers should pay the

market price or rate. Due to the system design, customers often cannot be

disconnected from the system in time to avoid a blackout. Therefore, the

capability to serve them may need to be purchased in advance. Complete

pricing may include both commodity and capacity markets due to lumpiness

in investments, system contingencies and lack of demand response.

Without complete pricing, market participants must mark up the remaining

priced products in hopes of compensation for the loss of complete pricing.

This does not always result in efficient decisions. Further, because correct

incentives do not exist, the system operator (SO) may need to resort to

command and control to obtain necessary nonpriced resources. Investment

decisions may be distorted and market monitoring problems may arise.

Reactive power – supplied and consumed by generation, load and

transmission – is ubiquitous in AC electric systems. The supply and demand

of reactive power is the dominant controller of voltage in many locations.

Reactive power capability requires both fixed and sunk cost investment.

Reactive power supply has cost tradeoffs. Like real power reserves, reactive

power reserves have different qualities. Some of these differences include

speed and continuity of response and response capability when voltage is

decreasing.
24 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Introduction: What is Reactive Power and Why Are We Concerned About It?

Like real power, a portfolio of reactive power sources may be optimal. The

highest valued reactive power comes from generators that have almost

instantaneous response that is not a direct function of a voltage. Reactive

power from capacitors has a slow response and declines with the square of

the voltage.

Competition in generation makes it important to consider the development

of complementary markets for reactive power. Some argue that reactive

power is cheap. Economic analysis of reactive power is often dismissed using

phrases reminiscent of the 1950s claim for nuclear power as “too cheap to

meter,”4

 yet reactive power is not costless and is critical to system reliability.

Sufficient reactive power is critical to avoiding an extremely costly system

collapse, but the cost of avoiding a blackout is difficult to calculate. The

transfer characteristics of reactive power makes the topology for reactive

power markets small relative to real power markets, raising market power

concerns, but market entry by many devices that can supply and consume

reactive power increase the potential number of market participants.

The remainder of the paper reviews the physical characteristics of the devices

and costs of supplying reactive power; reviews the history of reactive power

pricing at the Commission and internationally; provides an economic analysis

of reactive power pricing and pricing options for reactive power; and

provides conclusions, recommendations and questions for the Commission’s

future approach to reactive power markets. Several appendices are included

to examine in technical detail the literature, investment incentives, market

design and options discussed in the main body of the paper.

4

 Lewis L. Strauss,

chairman, Atomic Energy

Commission, before the

National Association of

Science Writers, New York

Times, September 17, 1954,

5.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 25

CHAPTER 2 Physical Characteristics and Costs of Reactive Power in AC Systems

Physical Characteristics and Costs of Reactive Power in AC Systems

Reactive power is an inherent part of the generation, transmission and

distribution of electricity. Inductance and capacitance are inherent

properties of the electric power system elements such as transmission lines,

transformers and capacitors. Inductance consumes reactive power and

capacitance supplies reactive power. Most of the electric power loads are

inductive in nature. Induction motors and transformers consume reactive

power. Common examples of applications of induction motors include air

conditioners, household appliances, mining, industrial equipment and

manufacturing processes. Underground and overhead transmission lines

have inductance and capacitance, and can either supply reactive power or

consume reactive power depending on the line loading. Generators can

supply or consume reactive power within limits.

Reactive power needs to be managed or compensated in a way to ensure

sufficient amounts are being produced to meet demand and so that the electric

power system can run efficiently. Significant problems (e.g., abnormal

voltages and system instability) can occur if reactive power is not properly

managed. Capacitors, which supply reactive power, can be switched into a

system in real-time to compensate for the reactive power consumed by the

electric power system during periods of heavy loading. Similarly, inductors,

which consume reactive power, are added to compensate for the reactive

power supplied by the electric power system during periods of light loading.

These devices are installed throughout the electric power system to maintain

an acceptable voltage profile for a secure and efficient power system

operation. Generators can also provide or absorb reactive power. Reactive

power compensation can be either static (e.g. capacitors or inductors) or

dynamic (e.g. generators) in nature.

Physical Characteristics. Reactive power compensation can be well managed

under predictable changes in load demands and generation balances,

scheduled generation and transmission outages and contingencies that are

within the operating criteria. A key characteristic of reactive power demand

is the magnitude and speed at which it changes over time. Due to the varying

nature of loads, reactive power requirements, both supplying and consuming,

can change significantly (and sometimes unpredictably) during the day at

the same location.
26 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Physical Characteristics and Costs of Reactive Power in AC Systems

5

 Data from PowerWorld

software, compiled from

NERC and FERC filings.

Generally, reactive power support is divided into two categories: static and

dynamic. Capacitors and inductors (or reactors) supply and consume static

reactive power, respectively. These are called static devices since they have

no active control of the reactive power output in response to the system

voltage. Synchronous generators, synchronous condensers, Flexible AC

Transmission Systems (FACTS) including static var compensators (SVC),

static compensators (STATCOM), and Dynamic Var (D-var) are considered

as dynamic reactive power devices capable of changing their output

according to pre-set limits in response to the changing system voltages.

Synchronous Generators. Most generators connected to the electricity grid

are synchronous generators, meaning that they operate synchronously at

the same electrical frequency. Generator settings can be adjusted to produce

combinations of real power and reactive power. When the generator

increases its reactive power output, its real power capability may need to

be reduced if the generator reaches its limits; a discussion of generator

capability limits appears at the end of this chapter. Reactive power supply

from generators requires a minimal additional amount of fuel or real power

from the network. The cost of a generator depends on the capacity, fuel

type and voltage level. The reactive power capacity for a generator is

determined by thermal limits. Thermal limits are determined by the thermal

properties of the materials in the generator; if the generator overheats,

insulation will degrade and its parts may be damaged. Because the reactive

power constraints in generators are thermal and equipment takes some time

to heat to the point of degradation, generators are designed to provide

significantly increased amounts of reactive power output for short periods.

A generator can increase or decrease reactive power output smoothly and

almost instantaneously within its designed capabilities. Generators have a

longer response time if the real power output needs to be adjusted or the

generator is offline; the generator ramp rate and startup time will determine

how quickly the generator can adjust its reactive power output in these

situations. Generators have high maintenance costs due to their moving

mechanical parts and cooling systems. There are about 10,000 synchronous

generators in North America with a combined maximum reactive power

capacity of 600,000 Mvar5 and maximum real power capacity of

approximately 900,000 MW (but due to generator constraints discussed
Federal Energy Regulatory Commission Staff Report •February 4, 2005 27

Physical Characteristics and Costs of Reactive Power in AC Systems

6 Energy Information

Administration (EIA),

Electric Power Annual

(2003), Chapter 2, Table

2.1, Existing Net Summer

Capacity by Energy Source

and Producer Type, 1991

through 2002, at http://

www.eia.doe.gov/cneaf/

electricity/epa/epat2p1.html

later in this chapter, these maximum capacities are not simultaneously

available).6

Figure 1: Synchronous Gener onous Generator Leaving the Factory

Source: Photo Courtesy of Hitachi

Distributed Generation. Distributed generators are small power sources

including microturbines, fuel cells and engine generators connected to lowervoltage electric distribution systems. They may be owned by utilities or by

customers, and are often owned by large industrial plants. Distributed

generators have the same reactive power characteristics as large generators

– they produce dynamic reactive power and the amount of reactive power

does not necessarily decrease when voltage decreases. The reactive power

output can be quickly adjusted within the generator operating limits, but

will require more time if the generator needs to be started or its real power

output needs to be adjusted. The major advantage of distributed generators

is that they provide reactive power capability locally, often at the site of

large loads, reducing reactive power losses in transmission lines.7

7

 J.D. Kueck, B.J. Kirby,

L.M. Tolbert and D.T. Rizy,

“Tapping Distributed Energy

Resources,” Public Utilities

Fortnightly, September 2004,

46-51.
28 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Physical Characteristics and Costs of Reactive Power in AC Systems

Wind Generators. Wind is naturally intermittent and therefore must be

approached by planners and system operators differently than conventional

thermal and hydroelectric generation. The variable and largely

uncontrollable nature of wind generation introduces new challenges into

the control of the power system. Integration of a continually fluctuating,

uncontrolled generation resource such as wind impacts the control systems

in all time frames. Consequently, the operational and scheduling systems

must adjust generating patterns to accommodate the variability in the wind

in order to maintain the same level of system reliability. These adjustments

are necessary to ensure that sufficient generation is available to meet the

control area load and interchange schedules on the various control time

frames.

In addition, some wind facilities – especially older facilities – can have

asynchronous (induction) generator designs that do not supply reactive

power, but may actually draw reactive power from the system. However,

newer models can provide reactive power and are designed with a selectable

power factor ranging from 0.90 lagging to 0.95 leading. For these new

generators, the power factor is settable at each Wind Turbine Generator

(WTG) or by the plant SCADA system for the whole farm. Dynamic var

control, commonly called Dvar, can be supplied to control the wind plant’s

power factor, or voltage. Dvar systems can optimize local system conditions

to improve plant reliability and availability. Dvar can be customized to

meet the local utility demands. Equipment with Dvar capabilities is more

expensive but has better var control capabilities. Many WTGs currently

operating or in storage ready for sale do not have this capability. However,

for large wind farms located away from load on a weak grid, the Dvar

capabilities will most probably be required to meet reliability and stability

requirements.

Synchronous Condensers. Synchronous condensers are synchronous machines

that are specially built to supply only reactive power. Synchronous generators

that are not economic to operate can be modified into synchronous condenser

operation. The conversion costs are typically in the $2 million to $3 million

range. Synchronous condensers consume approximately 3% of the machine

power rating in real power from the network. Synchronous condensers have

similar response times and high maintenance costs of generators. In North
Federal Energy Regulatory Commission Staff Report •February 4, 2005 29

Physical Characteristics and Costs of Reactive Power in AC Systems

America, most synchronous condensers connected to the transmission system

are retired fossil or nuclear power plant AC machines that have been

converted. Some hydro generators can operate as synchronous condensers.

Supervar. Supervar machines are rotating machines, much like motors and

generators, that use high temperature superconductor technology. They

serve as reactive power “shock absorbers” for the grid, dynamically

generating or absorbing reactive power, depending on the voltage level of

the transmission system. Supervar machines use standard synchronous

condenser frames and stator coils mated with new, power-dense rotor coils

made from High Temperature Superconducting (HTS) wire. The result is a

synchronous condenser that is more efficient than conventional machines -

without the typically high rotor maintenance costs. Supervar machines are

specifically designed for continuous, steady-state dynamic var support while

having multiples of their rated output in reserve for transient problems. The

HTS rotor enables these machines to provide up to eight times their rated

capacity for short periods. Supervar machines can also serve as lower cost

replacements for old, polluting inner city reliability-must-run (RMR)

generating facilities that are required to operate in order to maintain system

reliability and voltage support. There is one prototype Supervar installation

in the US.8

Transformers. Generators and synchronous condensers operate at voltages

lower than transmission system voltages and are connected to high voltage

transmission lines through generator step-up transformers. Transformers

are electromagnetic devices that convert power from one voltage level to

another; they are inductive devices and therefore consume reactive power.

Transformers are also used throughout the power network to change voltage

from high transmission levels to lower distribution levels.

Transformer Taps. Large power transformers are generally equipped with

“voltage tap changers,” sometimes called “taps,” with tap settings to control

the voltages either on the primary or secondary sides of the transformer by

changing the amount and direction of reactive power flow through the

transformers. Tap changers do not consume or supply reactive power; taps

force voltage on one side of the transformer up, at the expense of lowering

the voltage on the other side. Taps can be thought of as pumping reactive

8 American Superconductor,

www.amsuper.com.
30 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Physical Characteristics and Costs of Reactive Power in AC Systems

power from one side of the transformer to the other to regulate voltage.

Transformer taps can be controlled automatically based on local system

conditions, or manually. The insulators and contacts used in tap changers

are subject to high currents and deteriorate over time; they must be replaced

about every 15 years. On-load tap changers can change the tap position

while the transformer is energized. Tap changers generally have 32 steps

and each step can move within several seconds, depending on the design

and system requirements. Adding a tap changer to a transformer when it is

initially designed and built is a relatively small cost in comparison to the

cost of the transformer. The North American electric power system has

about 8,000 tap-changing transformers, and 15,000 fixed tap transformers.9

Figure 2: Transformer ansformer

9

 Data from PowerWorld

software, compiled from

NERC and FERC filings.

Source: Photo courtesy of Siemens
Federal Energy Regulatory Commission Staff Report •February 4, 2005 31

Physical Characteristics and Costs of Reactive Power in AC Systems

Phase Shifting Transformers. Phase Shifting Transformers (PSTs), also called

Phase Angle Regulators (PARs), allow system operators to control real power

flow. Phase shifting transformers have taps that control the phase angle

difference across the transformer. Increasing the phase angle difference

across a transformer has the effect of increasing the impedance of the line,

which will reduce the amount of real power on the line (power flows distribute

among lines according to the relative impedances of the lines). Phase shifting

transformers are usually installed to control real power flow, especially along

parallel paths. Phase shifting transformers are also a useful tool for reactive

power control. Controlling the real power flow along a line allows for

control of the reactive power consumed or produced by the line. Costs of

phase shifting transformers are similar to costs of regular transformers.

Transmission Lines. Electric transmission lines have both capacitive and

inductive properties. The line capacitance supplies reactive power and the

line inductance consumes reactive power. At a loading known as surge

impedance loading (SIL), the reactive power supplied by the line capacitance

equals the reactive power consumed by the line inductance, meaning that

the line provides exactly the amount of Mvar needed to support its voltage.

Lines loaded above SIL consume reactive power, while lines loaded below

SIL supply reactive power. The amount of reactive power consumed by a

line is related to the current flowing on the line or the voltage drop along the

line; the amount of reactive power supplied by a line is related to the line

voltage. An ideal line with zero resistance (zero real power losses) that is

loaded at its surge impedance loading will have the same voltage at both

ends because it is not supplying or consuming reactive power. Figure 3

shows that the consumption of reactive power by transmission lines increases

with the square of current. Thus, when it is critically needed during large

power transfers, reactive power is the most difficult to transport. When

reactive losses are negative, the line is supplying reactive power; when they

are positive, it is consuming reactive power.
32 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Physical Characteristics and Costs of Reactive Power in AC Systems

Figure 3: Transmission Line Real and Reactive Power Losses

vs. Line Loading

Source: B. Kirby and E. Hirst 1997, Ancillary-Service Details: Voltage Control, ORNL/

CON-453, Oak Ridge National Laboratory, Oak Ridge, Tenn., December 1997.

High voltage DC transmission lines. High voltage DC transmission lines

(HVDC) transmit power via DC (direct current). They normally consist of

two converter terminals connected by a DC transmission line and in some

applications, multi-terminal HVDC with interconnected DC transmission

lines. The converter terminals consist of electronic converters, converter

transformers, filters and capacitors to convert power from AC to DC and

from DC to AC. In addition to voltage conversion, the converters are capable

of controlling the amount of power flows and direction over the DC

transmission line.

Because DC transmission lines are transmitting power at zero hertz, the

reactive power consumption on the line is zero. The converters require

reactive power for the conversion process typically in the range of 40% of

the power rating of each of the converter terminals. Therefore, for a 1,000-
Federal Energy Regulatory Commission Staff Report •February 4, 2005 33

Physical Characteristics and Costs of Reactive Power in AC Systems

MW HVDC transmission, 400 Mvar is typically required at each terminal.

The reactive power is required to compensate for the reactive power

consumption in the converter transformers and to maintain an acceptable

AC voltage level on the AC side of the converter terminals. Much of this

reactive power requirement is provided by shunt capacitors and filters, which

are required to filter out or reduce the harmonic currents resulting from AC

waveform chopping in the AC-DC and DC-AC conversion processes.

Therefore, a properly designed HVDC system is essentially self-sufficient

in reactive power. Due to its inherently fast electronic control, it is also

capable of supporting the AC terminal voltages by controlling the DC power

flow over the line and consequently the reactive power consumption in the

converter transformers.

Traditional HVDC and transmission is installed for special applications such

as long distance power transmission (e.g., hydro or coal-by-wire) and

submarine power transmission. Back-to-Back DC and HVDC Light are

specific types of HVDC systems. HVDC Light uses new cable and converter

technologies and is economical at lower power levels than traditional

HVDC.10 Back-to-Back DC is used for asynchronous connection of two

AC systems with different system characteristics that cannot be connected

via AC ties (Eastern United States to Québec, Eastern United States to

Western United States and Eastern and Western United States to the ERCOT

part of Texas are examples).

Switched Shunt Capacitors. During heavy load periods, switched shunt

capacitors are utilized to provide voltage support by injecting reactive power

to the power system. Switched shunt capacitors are connected to the system

through mechanical switches or circuit breakers and their real power losses

are very small. Reactive power output from capacitors is proportional to

the square of the voltage. This can be a problem during a contingency or a

depressed voltage condition; as the voltage falls, the reactive power supplied

by the capacitors decreases according to the square of the voltage, causing

voltage to fall further.

Capacitor banks are sets of capacitors that are installed in a substation.

The capacitors in a bank are switched in blocks. Switched capacitors cannot

smoothly adjust their reactive power output because they rely on mechanical

10 www.abb.com.
34 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Physical Characteristics and Costs of Reactive Power in AC Systems

switches and take several cycles (less than one second) to operate. When

capacitors are switched out, they must be discharged before reconnection,

normally with discharge time ranging from two to fifteen minutes. In special

applications requiring switching-out and fast reconnection, the capacitor

banks are equipped with fast discharge reactors that will discharge the

capacitors in about 120 milliseconds (ms), thus enabling them to be

reconnected to provide voltage support to the power system. Capacitor

banks range from $1 million for 50 Mvar at 115 kV to $5 million for 200

Mvar at 500 kV; adding additional capacitors costs $500,000 or more,

depending on the voltage and the Mvar added.11 Capacitor banks and

switches have relatively low maintenance costs. There are approximately

5,000 switched shunt capacitors in the North American power system, with

about 170,000 Mvar of capacity.12

Series Capacitors. Series compensation is based on controlled insertion and

removal of series capacitors in AC transmission lines. Series capacitors

provide reactive power to the power system according to the square of the

line current – the higher the line current, the more reactive power support.

Due to characteristics of the impedance of a series capacitor compared to

that of the line impedance, a series compensated transmission line is

electrically reduced to a shorter distance, thereby increasing its transfer

capability. In some situations, series capacitors can excite low-frequency

oscillations, which can damage turbine-generator shafts. Series capacitors

have similar costs to shunt capacitors, and are used on long transmission

lines, especially in the western United States.

Flexible AC Transmission Systems (FACTS). FACTS are technologies that

increase flexibility of transmission systems by allowing control of power

flows and increasing stability limits of transmission lines. FACTS devices

can be installed in a substation, requiring less space and permitting than

additional transmission lines. There are several varieties of FACTS devices.

Some of the FACTS devices for reactive power management are static var

compensators (SVC), static synchronous compensators (STATCOM),

dynamic var (D-var) and distributed superconducting magnetic energy

storage (D-SMES).

Static Var Compensators. Static var compensators (SVCs) are basically

11 Cost data from EIA,

“Upgrading Transmission

Capacity for Wholesale

Trade,” March 2002, at

http://www.eia.doe.gov/

cneaf/pubs_html/

feat_trans_capacity/

w_sale.html.

12 Data from PowerWorld

software, compiled from

NERC and FERC filings.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 35

Physical Characteristics and Costs of Reactive Power in AC Systems

shunt capacitors or shunt reactors connected to the system via power

electronic switches called thyristors to control the voltage by supplying or

consuming system reactive power. Similar to capacitors, the reactive output

of an SVC varies according to the square of the connected bus voltage.

Static Compensator. A Static Compensator (STATCOM) provides voltage

support and control to the system similar to a synchronous condenser, without

the spinning inertia, and therefore is superior to SVCs or capacitors in

mitigating voltage instability leading to system collapse. It is basically a

Voltage Source Converter (VSC), using power electronic switches called

IGBTs (insulated gate bipolar transistors) to convert a DC voltage input

into a 3-phase voltage at 60 hertz with the additional capabilities of fast

control of the phase angle and amplitude. Therefore, reactive output from a

STATCOM is independent of system voltage.

Both SVCs and STATCOMs are controlled by microprocessors that

automatically regulate bus voltages within a defined band. SVCs are usually

large installations in substations and STATCOMs take up slightly less space

in the substation. Once installed, they do not require fuel inputs but do use

a small amount of electricity from the network. In the 115-230 kV range,

SVCs typically operate in ranges of 0-100 Mvar inductive and 100-200 Mvar

capacitive, and cost $5 million to $10 million. At higher voltages, SVCs

range from 300 Mvar inductive to 500 Mvar capacitive, and cost $10 million

to $15 million.13 Smaller SVCs can change output in a few milliseconds.

Larger SVCs can make small changes quickly, but may take a few seconds

to make larger changes. Output from SVCs can be varied continuously –

they do not require the discharge time needed for switched capacitor banks.

There are more than 30 SVCs installed in the United States, ranging from

30 Mvar to 650 Mvar each.14

STATCOMs are more compact than SVCs, requiring less space in a

substation. SVC and STATCOM maintenance costs are higher than

capacitor banks, but much less than generators. STATCOMs are installed

at seven sites in the United States, ranging between 30 Mvar and 100 Mvar

each.

13 Cost estimates provided

by ABB, e-mail from Eric

John, employee of ABB, to

FERC’s Mary Cain, dated

July 20, 2004.

14 ABB SVC projects

worldwide, available at

www.abb.com.
36 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Physical Characteristics and Costs of Reactive Power in AC Systems

Figure 4: Installation of Mobile SVC

Source: Photo Courtesy of Areva Transmission and Distribution

Relocatable SVCs consist of modules that can be transported with normal

transportation equipment (truck, train, boat). They take up to a few weeks

to install, depending on the location. They need concrete platforms and

some of the modules need to be bolted into the concrete. Moving the modules
Federal Energy Regulatory Commission Staff Report •February 4, 2005 37

Physical Characteristics and Costs of Reactive Power in AC Systems

from the transportation vehicle to the cement platform is done with a crane

or similar equipment. The modules have prefabricated cables and buswork

for easy interconnection. Currently, relocatable SVCs are being used in

Japan, Switzerland, Australia and the United Kingdom.

D-var (Dynamic Var). D-var voltage regulation systems dynamically

regulate voltage levels on power transmission grids and in industrial facilities;

D-var is a type of STATCOM. D-var dynamic voltage regulation systems

detect and instantaneously compensate for voltage disturbances by injecting

leading or lagging reactive power to the part of the grid to which the D-var

is connected. The amount of reactive power delivered per unit varies

typically from 1 Mvar to 8 Mvar continuous, with near instantaneous reactive

power output up to 24 Mvar per unit. There are currently 22 installations

of D-var systems in North America.15

D-var voltage regulation systems are scalable and mobile, characteristics

that allow utilities to install them in their power grid at locations that need

the greatest amount of reactive power support. D-var dynamic voltage

regulation system components can be configured inside a standard truck

trailer that can be moved to substations for optimized var support throughout

a power grid or placed in a standard enclosure for more permanent siting at

a substation. D-var systems provide dynamic var support for transmission

grids that experience voltage sags, which are typically caused by high

concentrations of inductive loads, usually in industrial manufacturing

centers, or from weaker portions of the transmission grid, typically in remote

areas or at the end of radial transmission lines.

D-var systems also are suited to address the need for dynamic var support

at wind farms. Because of the remote locations of most large wind farms,

the power they generate must often be delivered a long distance to the ultimate

customer on a relatively weak utility transmission grid. A D-var system is

ideally suited to mitigating voltage irregularities at the point of

interconnection between the wind farm and the grid. D-var systems can be

integrated with low cost capacitor banks to provide an extremely costeffective solution for large wind farms. For instance, a small (8 MVA) Dvar device combined with a number of medium voltage capacitor banks is

sufficient to solve most of the voltage problems associated with wind farms.

15 American Superconductor,

www.amsuper.com.
38 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Physical Characteristics and Costs of Reactive Power in AC Systems

Distributed SMES, or D-SMES. A superconducting magnetic energy storage

(SMES) system is a device for storing and instantaneously discharging large

quantities of power. These systems have been in use for several years to

solve voltage stability and power quality problems for large industrial

customers. A distributed-SMES (D-SMES) system is a new application of

proven SMES technology that enables utilities to improve system reliability

and transfer capacity.

D-SMES is a shunt-connected Flexible AC Transmission (FACTS) device

designed to increase grid stability, improve power transfer and increase

reliability. Unlike other FACTS devices, D-SMES injects real power as well

as dynamic reactive power to more quickly compensate for disturbances on

the utility grid. Fast response time prevents motor stalling, the principal

cause of voltage collapse. D-SMES devices can be transported on standard

truck trailers, with one 250-kW system per trailer. The inverters provide up

to 2.3 times nominal instantaneous over-current capability and can also be

configured for continuous var support. Each 250-kW trailer operates

independently, improving reliability. Six D-SMES systems are installed in

the midwest United States.16

Costs. Differences in effectiveness and costs of the different devices dictate

that reactive power generally is provided by a mix of static and dynamic

devices. The cost of reactive power service depends upon the choice of

equipment. The costs of satisfying static reactive power demands are much

lower than those of satisfying dynamic reactive power demands. While

capital costs tend to dominate, the costs of providing reactive power also

include generator fuel costs, operating expenses and the opportunity costs

from not generating real power. The capital costs of static sources of reactive

power, such as capacitors, are orders of magnitude lower than the capital

costs of dynamic sources, such as generators, SVCs and synchronous

condensers. Table 1 shows the speed, voltage support and costs for the

different sources of reactive powers and does not include transformer tap

changers. The ability to support voltage means the ability to produce

reactive power when voltage is falling. The availability of voltage support

indicates how quickly a device can change its reactive power supply or consumption.

Disruption is low for devices that can smoothly change reactive power output

and high for devices that cannot change reactive power output smoothly.

16 American Superconductor,

www.amsuper.com.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 39

Physical Characteristics and Costs of Reactive Power in AC Systems

Table 1: Characteristics of acteristics of Voltage-Contr oltage-Control Equipment ol Equipment

Equipment 

type 

Speed of 

response Voltage Support Costs 

 Ability Availability Disruption Capital 

(per 

kvar) 

Operating Opportunity 

Generator Fast Excellent, 

additional shortterm capacity 

Low Low Difficult 

to 

separate 

High Yes 

Synchronous 

Condenser 

Fast Excellent, 

additional shortterm capacity 

Low Low $30-35 High No 

Capacitor Slow Poor, drops with 

V2

High High $8-10 Very low No 

Static Var 

Compensator 

Fast Poor, drops with 

V2

High Low $45-50 Moderate No 

STATCOM Fast Fair, drops with 

V 

High Low $50-55 Moderate No 

Distributed 

Generation 

Fast Fair, drops with 

V 

Low Low Difficult 

to 

separate 

High Yes 

Source: Modified from B. Kirby and E. Hirst, Ancillary-Service Details: Voltage Control,

ORNL/CON-453, Oak Ridge National Laboratory, Oak Ridge, Tenn., December 1977.

Generator Reactive Power Capability. An electricity generator has two

parts. The armature, also known as the stator, is the stationary part of the

generator. It is a large cylinder, with slots running lengthwise on the inside.

Coils of wire go through the slots. The field, also known as the rotor, is an

electromagnet that rotates inside the stator.

Figure 5 shows a generator stator with a rotor inside (the rotor is sticking

out farther than usual for illustrative purposes). In fast generators, the rotor

is made of solid steel; slots are cut into its surface and coils of wire are

wound through the slots. The generator shaft is a rod through the center of

the rotor, and this is connected to the prime mover, which can be a steam,

combustion, wind or hydroelectric turbine. When the turbine spins, the

generator rotor spins, and the spinning magnet of the rotor induces an electric

field in the stator wires. The stator is connected to electrical equipment that

transfers electrical power from the generator to the power system. The

stator and rotor are enclosed, and air or compressed hydrogen cools the

generator inside the enclosure; some generators have water pipes installed

on the stator for additional cooling.
40 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Physical Characteristics and Costs of Reactive Power in AC Systems

Figure 5: Generator Stator and Rotor Generator Stator and Rotor

Source: Photo courtesy of General Electric Co.

A generator’s output capabilities depend on the thermal limits of various

parts of the generator and on system stability limits. Thermal limits are

physical limits of materials such as copper, iron and insulation; if the generator

overheats, insulation begins to degrade and over time this could result in

equipment damage. Increasing real power output of a generator heats up

the armature. Increasing reactive power output heats up the field windings

and the armature. To supply reactive power, the generator must increase

the magnetic field to raise the voltage it is supplying to the power system;

this means increasing the current in the field windings, which is limited by

the thermal properties of the metal and insulation. The field current is

supplied by the generator exciter, which is a DC power supply connected to

the generator. The field current can be quickly adjusted by automatic control

or with a dial to change the reactive power supplied or consumed by the

generator. Stability limits are determined by the ability of the power system

to accept delivery of power from the connected generator under a defined

set of system conditions including recognized contingencies. All generators

connected to a power system operate at the same electrical frequency; if a

generator loses synchronism with the rest of the system, it will trip offline to

protect itself.

Current and voltage are both time-varying quantities in sinusoid waveform;

when current lags voltage, it reaches its peak after the voltage, and when

current leads voltage, it peaks before the voltage.

Stator

Rotor
Federal Energy Regulatory Commission Staff Report •February 4, 2005 41

Physical Characteristics and Costs of Reactive Power in AC Systems

Figure 6 shows current and voltage waveforms. The blue squares represent

a voltage waveform. The red solid line is current in phase with the voltage.

The green dotted line is current leading voltage by 45 degrees, and the purple

dashed line is current lagging voltage by 45 degrees. Phase angle is a quantity

that indicates the difference in time of peaks of sinusoid waveforms; the

phase angle difference between the blue and green waveforms is 45 degrees.

Power factor is a measure of real power in relation to reactive power;

mathematically, it is defined as the cosine of the phase angle between voltage

and current. When the power factor is leading, the current phase angle is

greater than the voltage phase angle; when the power factor is lagging, the

current phase angle is smaller than the voltage phase angle. Capacitors

supply reactive power and have leading power factors, while inductors

consume reactive power and have lagging power factors. The convention

for generators is the reverse. When the generator is supplying reactive

power, it has a lagging power factor and its mode of operation is referred to

as overexcited. When a generator consumes reactive power, it has a leading

power factor region and is underexcited.

Figure 6: Voltage and curr oltage and current waveforms

Source: FERC staff
42 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Physical Characteristics and Costs of Reactive Power in AC Systems

Figure 7 is an example of a generator capability set, or curve. Due to the

shape of the boundary, it is referred to as a D-curve. It has three components,

labeled field heating limit, armature heating limit and core-end heating limit.

The conductors on the armature are connected at the ends, and the core end

(or end region) refers to these end connections. The generator prime mover

is the turbine connected to the generator; the size of the turbine determines

the prime mover limit. The prime mover is generally designed with less

capacity than the electric generator. Because generators are almost always

supplying or consuming some amount of reactive power to support system

voltage, a turbine capable of delivering all of the mechanical power the

generator can convert to electricity would be underutilized. The generator

and turbine are separate pieces of equipment and may be upgraded

independently; upgrading to a turbine with greater mechanical power output

may extend the turbine constraint closer to the boundary of the D-curve.

Figure 7: Generator Capability Curve

Source: B. Kirby and E. Hirst 1997, Ancillary-Service Details: Voltage Control, ORNL/

CON-453, Oak Ridge National Laboratory, Oak Ridge, Tenn., December 1997.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 43

Physical Characteristics and Costs of Reactive Power in AC Systems

The capability-set limits are thermal limits for different parts of the generator.

If the generator output approaches these limits, an alarm will notify the

generator operator of the problem; if the operator does not bring the

generator back to a safe operating point, the generator’s protection scheme

(relays, circuit breakers, fuses) will operate, resulting in disconnection of

the generator from the network; finally, if the protection equipment fails

and the operator does not act in time, the generator will overheat, potentially

causing equipment damage. Because generators are expensive, generator

operators generally will not operate the generator in a way that risks

damaging the equipment and losing revenue during repair. At the edges of

the D-curve, the opportunity cost of extending generator real or reactive

power supply amounts to the millions of dollars that would be needed to

replace damaged generator equipment and lost revenue during repair. The

characteristics of the generator step-up transformer that connects the

generator to the electric transmission system, as well as operational policies

of the transmission system, may impose further limits on generator output.

Generator capability may be extended by the coolant used in the generator.

A more efficient coolant allows the generator to dissipate more heat, thereby

extending thermal limits. Most large generators are cooled with hydrogen;

increasing the hydrogen pressure cools the generator equipment more

effectively, increasing the generator’s capability.

Figure 8 shows a hydrogen-cooled generator. The blue curve in Figure 9 is

an example of a capability curve with different hydrogen pressures.

Compressed hydrogen cools the generator three to four times as much as

air, and water cools a generator 50 times as much as air. Water cooling is

used only for large generators (300 megavolt amperes [MVA] or higher)

because of the high cost of adding a water cooling system, which circulates

water through pipes in the generator stator. Hydrogen cooling systems

circulate hydrogen gas inside a case surrounding the entire generator. Some

large generators have both water cooling pipes and hydrogen gas cooling.
44 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Physical Characteristics and Costs of Reactive Power in AC Systems

Figure 8: Hydrogen-Cooled Generator Hydrogen-Cooled Generator

Source: Photo courtesy of Hitachi

Figure 9: Generator Capability Curves at Different Generator Capability Curves at Different

Hydrogen Pressures

Source: Modified from B. Kirby and E. Hirst 1997, Ancillary-Service Details: Voltage Control,

ORNL/CON-453, Oak Ridge National Laboratory, Oak Ridge, Tenn., December 1997.

REAL-POWER OUTPUT (MW)

REACTIVE POWER (MVAR)

Overexcited

Supplying MVA

R

Underexcited

Consuming MVA

R

Operation with increased hydrogen 

pressure (added cooling)

Normal operation
Federal Energy Regulatory Commission Staff Report •February 4, 2005 45

CHAPTER 3 History of Reactive Power Pricing

History of Reactive Power Pricing

Historically, utilities designed transmission rates based on the costs of a

plant booked to the transmission function. With regard to reactive

power, transmission-only customers were assigned costs for reactive power

support. Rate designs varied according to reactive power use or adjustments

to a transmission customer’s real power demand or energy consumption

according to the customer’s power factor. Reactive power then was related

to the reliable operation of the transmission system and most utilities imposed

penalties or rewards upon large customers whose power factor was below

or above a threshold or trigger power factor. Furthermore, reactive power

costs were embedded inside a “deadband.”17

 In 1990, in Northern States Power Company,

18 the Commission found for

the first time that a separate charge for reactive power was not inherently

unjust and unreasonable. In a subsequent case again involving Northern

States Power Co., the Commission set procedures by which utilities were to

set unbundled wholesale prices for reactive power service.

Specifically, the Commission stated that:

Northern States will be required to consolidate the total cost of all reactive

power sources in the development of a proposed reactive power charge.

. . . the utility will be required to identify the actual costs of the portion of

the generator used in the production of reactive power. Northern States

will also be required to identify and omit from the calculation of the base

transmission rate the cost of transmission equipment dedicated to the

production of reactive power. In this manner, the total costs associated

with reactive power supply will be consolidated for the development of a

single charge for this service, in recognition of the fact that reactive

power is supplied by many sources throughout a utility’s system. Based

on the general methodology described above, Northern States will be

free to propose either an average or an incremental rate design in a

particular case. As always, the burden of proof will be on the utility to

justify its proposed rate.19

Against this background, this chapter explores the evolution of the

Commission’s pricing policies for reactive power.

17 A deadband is a range of

activity that does not incur

extra charges and is used to

simplify rate design.

18 Opinion No. 383, 53

FERC ¶ 61,027 at

61,107, reh’g denied, 53

FERC ¶ 61,306 (1990).

19 Northern States Power

Company (Minnesota and

Wisconsin), 64 FERC ¶

61,324 at 63,386 (1993),

reh’g denied, 74 FERC ¶

61,106 (1996).
46 Principles for Efficient and Reliable Reactive Power Supply and Consumption

History of Reactive Power Pricing

Order No. 888

In Order No. 888,20 issued in 1996, the Commission concluded that six

ancillary services, including “reactive supply and voltage control from

generation sources service” (reactive power), must be included in an open

access transmission tariff.21 The Commission found that reactive power is

necessary to the provision of basic transmission service within every control

area. It explained that although a customer is required to take reactive

power from the transmission provider or control area operator, a customer

may reduce the charge for this service to the extent it can reduce its

requirement for reactive power.22

The Commission further explained that there are two ways of supplying

reactive power and controlling voltage: (1) installation of facilities, usually

capacitors, as part of the transmission system; and (2) use of generating

facilities. The Commission said that it would consider the costs of the first

to be part of the cost of basic transmission service and, as such, would not

be a separate ancillary service. As to the use of generating facilities, the

Commission explained that this service must be unbundled from basic

transmission service and would be considered a separate ancillary service.

Because the transmission provider must provide at least some reactive power

from generation sources and because the transmission customer has the

ability to affect the amount of reactive supply required,23 the Commission

required that reactive power must be offered as a discrete service and, to

the extent feasible, charged for on the basis of the amount required. The

Commission further stated that it would consider ancillary services rate

proposals on a case-by-case basis.

With respect to the pricing of ancillary services, the Commission offered

the following guidance: (1) ancillary service rates should be unbundled

from rates for basic transmission service; (2) the fact that Commission has

authorized a utility to sell wholesale power at market-based rates does not

mean that it has authorized the utility to sell ancillary services at marketbased rates; (3) in the absence of a demonstration that the seller does not

have market power in such services, rates for ancillary services should be

cost-based and established as price caps, from which transmission providers

20 Promoting Wholesale

Competition Through Open

Access Nondiscriminatory

Transmission Services by

Public Utilities and Recovery

of Stranded Costs by Public

Utilities and Transmitting

Utilities, Order No. 888,

FERC Stats. & Regs.

Regulations Preambles

January 1991-June 1996 ¶

31,036 at 31,705-06 and

31,716-17 (1996), Order

No. 888-A, FERC Stats. &

Regs., Regulations Preambles

July 1996-December 2000 ¶

31,048 (1997), order on

reh’g, Order No. 888-B, 81

FERC ¶ 61,248 (1997),

order on reh’g, Order No.

888-C, 82 FERC ¶ 61,046

(1998), aff’d in relevant part

sub nom. Transmission

Access Policy Study Group v.

FERC, 225 F.3d 667 (D.C.

Cir. 2000), aff’d sub nom.

New York v. FERC, 535 U.S.

1 (2002).

21 Order No. 888 at 31,705.

The pro forma open access

transmission tariff (OATT)

includes six schedules that set

forth the details pertaining to

each ancillary service. The

details concerning reactive

power are included in Schedule

2 of the pro forma OATT.

Order No. 888 at 31,960.

22 In this regard, the

Commission recognized that

the ability to reduce reactive

power requirements will be

affected by the location and

operating capabilities of the

generator. It asserted that any

arrangement for the customer

to self-supply a portion of

reactive supply should be

specified in the transmission

customer’s service agreement

with the transmission provider.

(See next page for sidenote 23)
Federal Energy Regulatory Commission Staff Report •February 4, 2005 47

History of Reactive Power Pricing

may offer a discount to reflect cost variations or to match rates available

from any third party; (4) the amount of each ancillary service that the

customer must purchase, self-supply or otherwise procure must be readily

determined from the transmission provider’s tariff and comparable to the

obligations to which the transmission provider itself is subject (transmission

provider must take ancillary services for its own wholesale transmission

under its own tariff); and (5) the location and characteristics of a customer’s

loads and generation resources may affect the level of ancillary service costs

incurred by the transmission provider (rates and billing units should reflect

these characteristics to the extent practicable).24

Further, the Commission stated that:

[s]eparation of reactive supply and voltage control from basic

transmission service also may contribute to the development of a

competitive market for such service if technology or industry changes

result in improved ability to measure the reactive power needs of

individual transmission customers or the ability to supply reactive supply

from more distant sources.25

In Order No. 888-A, the Commission agreed to modify Schedule 2 to refer

to generating facilities that are under the control of the control area operator

instead of in the control area. The Commission emphasized that the control

area operator must be able to control the dispatch of reactive power wherever

it is located. It further stated that the transmission customer’s service

agreement should specify the generating resources made available by the

transmission customer that provide reactive support. The Commission also

agreed to modify Schedule 2 to allow a transmission customer to supply at

least part of the reactive power service it requires through self-provision or

purchases from generating facilities under the control of the control area

operator. The Commission added that the transmission customer’s service

agreement should specify all reactive supply arrangements. The Commission

denied a request that customer-owned generation facilities that are available

to supply reactive power should automatically receive a credit. Finally, the

Commission recognized that reactive power does not travel well and

indicated that it would not require that the supply of reactive power be on a

gridwide or regionwide basis because reactive power must be supplied near

the point of need.26

24 Order No. 888 at 31,720-

21. The Commission

further stated that revenues

a transmission provider

receives from providing

ancillary services must be

recorded by type of service

in Account 447, Sales for

Resale, or Account 456,

Other Electric Revenues, as

appropriate.

25 Order No. 888 at 31,707

n.359.

26 Order 888-A at 30,228-29.

(sidenote 23 from page 46)

23 For example, the

Commission noted that

transmission customerswho

control generating units

equipped with automatic

voltage control equipment

can use those units to

respond to local voltage

requirements and thus

reduce a portion of the

reactive power requirements

associated with their

transaction. The

Commission also noted that

transmission customers can

minimize the reactive power

demands that they impose on

the transmission system by

maintaining a high power

factor at their delivery points.
48 Principles for Efficient and Reliable Reactive Power Supply and Consumption

History of Reactive Power Pricing

In Order No. 888-B, the Commission rejected an argument that “under the

control of the control area operator” refers only to generators with automatic

voltage control. It clarified that what is under the control of the control

area operator is the reactive production and absorption capability of the

generator and not the generator’s ability to produce real power. The

Commission clarified that “simply supplying some duplicative ancillary

services . . . in ways that do not reduce the ancillary services costs of the

transmission provider or that are not coordinated with the control area

operator does not qualify for a reduced charge.”27

Post-Order No. 888 Cases

Opinion Nos. 416 and 440. Soon after the issuance of Order No. 888, the

Commission was presented with the issue of how to calculate a generatorsupplied reactive power charge. Two significant opinions, Opinion Nos.

41628 and 440,29 set forth the foundation for the Commission’s resolution of

this issue.

In Opinion No. 416, the Commission found that a reactive power charge in

a situation in which the transmitting utility delivers power from generation

located on its own system is consistent with Order No. 888 and is appropriate.

However, the Commission rejected Southern Company Services Inc.’s

proposed reactive power charge as unjust and unreasonable, and adopted

an alternative methodology for determining a reactive power charge.

The Commission recognized that the failure to provide the correct amount

of reactive power at various points on the transmission system can cause

deviations from desired voltage levels and disruption in the flow of power

on the system. The Commission noted that Southern’s proposed reactive

power charge at issue was intended to recoup the costs associated with

using its generators to supply or absorb reactive power.

To quantify the incremental reactive power impact of the proposed

transactions on the Southern system, Southern performed load-flow studies

to determine the amount of additional reactive power supplied by Southern’s

generators to support the agreements at issue. To design the reactive power

charge, Southern identified six generating components involved in the

27 Order No. 888-B at

62,094.

28 Southern Company

Services Inc., Opinion No.

416, 80 FERC ¶ 61,318

(1997), reh’g denied,

Opinion No. 416-A, 82

FERC ¶ 61,168 (1998).

29 American Electric Power

Service Corp., Opinion No.

440, 88 FERC ¶ 61,141

(1999).
Federal Energy Regulatory Commission Staff Report •February 4, 2005 49

History of Reactive Power Pricing

production of reactive power: (1) the exciter; (2) the exciter cooling system;

(3) generator stator; (4) rotor; (5) turbine assembly; and (6) step-up

transformer. Southern assigned 100 percent of the cost of the exciter and

the exciter cooling system to the reactive power charge and allocated the

cost of the remaining items between real and reactive power based on a

relationship of real and reactive power to apparent power, the nameplate

power factor.30 Southern then determined the cost of real power capacity

and energy losses associated with the additional reactive power demand

and divided the sum of the real and reactive power costs by the total amount

of real power involved and levelized the reactive power charge over the

contract term to produce a fixed annual reactive power charge.

The Commission determined that Southern’s load-flow studies were not an

appropriate measure of cost causation on the Southern system. The

Commission explained that it would not allow the use of incremental costing

for generator-supplied vars when the transmission charge (as well as the

cost of transmission-related vars) is developed on a rolled-in basis.

The Commission found that a reactive power charge calculated by

determining the annual cost of generator-supplied reactive power capability

on the Southern system and dividing this cost by Southern’s annual system

peak load to be a reasonable approach. The Commission also rejected

Southern’s proposed heating loss component because Southern had not

explained why the energy costs associated with the heating loss component

are not already recovered through Southern’s fuel adjustment clause.

The Commission further found that Southern’s formula for allocating the

costs of the generator stator, rotor and step-up transformer to be reasonable.

With respect to the exciter system, the Commission determined that Southern

should not be permitted to allocate the entire costs of these generator

components to the reactive power charge, but should allocate these costs

between real and reactive power in the same manner as the other costs

described above. The Commission also rejected the inclusion of any turbine

costs in the reactive power charge. It stated that “in contrast to other

components that produce both real and reactive power, turbines produce

only real power.”31

30 Apparent Power2 = Real

Power2

 + Reactive Power2.

31 Opinion No. 416 at

62,091.
50 Principles for Efficient and Reliable Reactive Power Supply and Consumption

History of Reactive Power Pricing

The Commission’s rejection of heating loss and turbine costs was appealed

to the U.S. Court of Appeals for the District of Columbia. The court remanded

to the Commission the turbine assembly costs for reconsideration and stated

that the Commission should allow a recalculation of heating loss costs and

should reconsider whether all heating loss costs are recovered.32

In Opinion No. 440, the Commission approved a methodology presented by

American Electric Power Service Corp. (AEP) for generators to recover costs

for reactive power. AEP identified three components of production plant

that are directly related to the production of vars: (1) the generator and its

exciter; (2) accessory electric equipment that supports the operation of the

generator-exciter; and (3) the remaining total production investment required

to provide real power and operate the exciter. Because these plant items

produce real and reactive power, AEP developed an allocation factor33 to

segregate the reactive production function from the real power production

function. AEP based this allocation factor on the capability of a generator

to produce vars, where this capability is measured at the generator terminals.

Once the plant investment associated with reactive power production is

determined, AEP applied an annual carrying charge to these costs to

determine an annual revenue requirement.

Subsequently, in WPS Westwood Generation LLC,

34 the Commission

standardized the methodology for reactive power compensation by

indicating that all generators seeking reactive power recovery that have

actual cost data and support should use the method employed in Opinion

No. 440, i.e., the AEP methodology.

Revenue Requirement Filings by Generators. After Opinion No. 440, but

prior to WPS Westwood, the Commission accepted a proposal by PJM35

that revenue requirements of generation owners that are not transmission

owners be included in the charges for reactive power and that reactive powerrelated revenues be allocated to all generation owners. As a result, many

independent generators in PJM began to file rate schedules, under section

205, specifying their revenue requirements for providing cost-based reactive

power. These filings generally followed the AEP methodology, i.e., inclusion

of the fixed capacity component discussed above, but also included other

components. The trend began with the Commission’s acceptance of a filing

by FPL Energy MH50 LP.36 In its filing, FPL Energy included not only the

32 Alabama Power Co. v.

FERC, 220 F.3d 595 at 600-

01 (D.C. Cir. 2000).

33 AEP used the formula

Mvar2 / MVA2 to determine

the allocation factor.

34 101 FERC ¶ 61,290 at

62,167 (2002) (WPS

Westwood).

35 PJM Interconnection LLC,

Docket No. ER00-3327-

000, September 25, 2000

(unpublished letter order).

36 FPL Energy MH50 LP, 96

FERC ¶ 61,035 (2001).
Federal Energy Regulatory Commission Staff Report •February 4, 2005 51

History of Reactive Power Pricing

fixed capability component in its revenue requirement, but also a heating

losses component and a lost opportunity costs component. Subsequent filings

that included a heating losses component37 and often a lost opportunity costs

component38 were mostly accepted by delegated authority.39 Recently, the

FPL Energy model was adopted by generators in the Midwest ISO territory

that filed rate schedules for reactive power,40 and by generators seeking

37 Generally, heating losses

are described as significant

losses through ohm heating

associated with the armature

winding and field winding

of the generator. There are

also heating losses through

the generator step-up

transformer.

38 Lost opportunity costs are

generally described as costs

incurred in the event that a

control area operator calls

on a generator to curtail its

real power output in order

to provide reactive power. In

other words, the

opportunity cost is equal to

the value of the reduced real

power sale that resulted from

increased reactive power

provided to the control area

operator.

39 See, e.g., Liberty Electric

Power LLC, Docket Nos.

ER03-88-000 and ER03-88-

001 ) (unpublished delegated

letter order issued December

30, 2002); Handsome Lake

Energy LLC, Docket No

ER02-771-000 (unpublished

delegated letter order issued

March 8, 2002); Bethlehem

Steel Corp., Docket No.

ER02-1894-000

(unpublished delegated letter

order issued June 25, 2002);

Sunbury Generation LLC,

Docket No. ER02-2362-000

(unpublished delegated letter

order issued October 22,

2002)

40 See Troy Energy, LLC,

105 FERC ¶ 61,250 (2003)

(Troy Energy); Orion Power

MidWest L.P., 107 FERC ¶

61,216 (2004).

compensation under interconnection agreements with transmission owners.41

The Commission has recently ordered hearing procedures for many of these

filings from generators seeking to recover reactive power costs.42 Because

these filings have been made by nonutility generators, the Commission

generally has allowed them to use proxy figures for their return on equity

and overall rate of return based on the return on equity and overall rate of

Electrical Generator Electrical Generator

41 See, e.g., Tenaska Virginia

Partners LP, 107 FERC ¶

61,207 (2004).

42 See, e.g., Duke Lee Energy,

LLC, 107 FERC ¶ 61,200

(2004); Troy Energy.

Source: FERC image library
52 Principles for Efficient and Reliable Reactive Power Supply and Consumption

History of Reactive Power Pricing

return percentages accepted by the Commission for the transmission owner

to which they are interconnected.43

Other Compensation Issues With Generators. The Commission has stated

that a generator need not be compensated for providing reactive power

within its design limits and that providing reactive power within design

limitations is not providing an ancillary service; it is simply ensuring that a

generator lives up to its obligations.44

In addition, the Commission has stated that a transmission owner is not

required to provide compensation to generators for reactive power if the

generator is not under the control of the control area operator.45 However,

the Commission has found that to the extent a transmission owner is

compensating an affiliate-owned generator for providing reactive power, it

must also compensate other generators that provide reactive support to that

system.46

Also, the Commission has stated that a transmission owner should have the

right to call upon a generator to start up its generator, if possible, to provide

reactive power during an emergency condition, but that the transmission

owner should reimburse the generator for its out-of-pocket costs to start up

its facility.47 The Commission also stated that “if [a generator] refuses to

supply reactive power in an emergency condition when it is able to do so,

[the generator] should pay the costs that result from that refusal.”48

Further, the Commission has stated that where the transmission provider

requests a generator to increase or decrease reactive power output beyond

that which the generator is required to provide, the generator must be

compensated by the transmission provider.49 The Commission has stated

that generators are free to file ancillary service schedules to provide for

compensation.

As to the reactive power that a generator has to provide, the Commission

has found that it is just and reasonable for a generator to be required to

provide equipment, at its own cost, to meet its reactive power obligations in

order to interconnect to a transmission provider’s system.50

43 Many of these filings

usually cite to City of Vernon,

93 FERC ¶ 61,103 (2000),

reh’g denied, 94 FERC ¶

61,148 (2001) and New

England Power Pool, 92

FERC ¶ 61,020 at 61,041

(2000) where the Commission

accepted the use of such

proxies in other contexts.

44 Michigan Electric

Transmission Co., 96 FERC

¶ 61,214 at 61,906 (2001),

citing Consumers Energy

Company, 93 FERC ¶

61,339 at 62,154 (2001),

order on reh’g, 94 FERC ¶

61,230 at 61,834 (2001).

45 Otter Tail Power Co., 99

FERC ¶ 61,019 at 61,092

(2002).

46 Michigan Electric

Transmission Co., 97 FERC

¶ 61,187 at 61,853 (2001).

47 American Transmission

Systems Inc., 97 FERC ¶

61,273 at 62,162 (2001).

See also Cambridge Electric

Light Co., 96 FERC ¶

61,205 at 61.875-76 (2001)

(“Since the transmission

provider is responsible for

the reliability of the system

and any liability that might

accrue due to a loss of

reliability, we believe that it

is in the best position to

determine when a generator

should be disconnected,

either permanently or

temporarily.”).

48 American Transmission; at

62,162; to date, the

Commission has not

addressed what these costs

might be.

49 Detroit Edison Co., 95

FERC ¶ 61,415 at 62,538

(2001).

50 Consumers Energy Co., 94

FERC ¶ 61,230 at 61,834

(2001).
Federal Energy Regulatory Commission Staff Report •February 4, 2005 53

History of Reactive Power Pricing

With regard to qualifying facilities (QF) and whether they can be

compensated for providing reactive power, the Commission has dismissed

such filings because rates that QFs charge for reactive power are not subject

to Commission review under section 205.51

Transmission Customers. In Order No. 888, the Commission abandoned

the approach of having a ceiling rate of 1 mil per kWh ($1/MWh) for a

package of three ancillary services, including reactive power. However,

pre-Order No. 888 tariffs of many utilities use 1 mil per kWh as the rate for

this ancillary services package. Figure 3.1 presents a sample of reactive

power rates on file at the Commission.

Figure 3.1: Examples of Reactive Power Char er Charges in Tariffs

Reactive Power Charges in OATT Schedule 2 for Selected Utilities

COMPANY NAME ($/Kw-MONTH)

Duke Energy $0.2000

Tucson Electric Power Company $0.1610

Nevada Power Company $0.1580

Black Hills Power $0.1203

Dominion Virginia Power $0.1100

Florida Power Corporation $0.1100

Florida Power and Light $0.1008

Sierra Pacific Power Company $0.1000

Southwestern Public Service Company $0.0940

Northern States Power $0.0930

Carolina Power and Light Company $0.0888

Bonneville Power Administration $0.0670

Public Service Company of New Mexico $0.0500

El Paso Electric Company $0.0440

Portland General Electric Company $0.0384

Public Service Company of Colorado $0.0312

Puget Sound Energy $0.0060

Arizona Public Service Company No Charge

Idaho Power Company No Charge

PacifiCorp No Charge

Source: Current OATTs on file with the Commission.

51 See Pine Bluff Energy

LLC, 104 FERC ¶ 61,227

at P 13 (2003); Carville

Energy LLC, 104 FERC ¶

61,252 at P 11 (2003).
54 Principles for Efficient and Reliable Reactive Power Supply and Consumption

History of Reactive Power Pricing

Service agreements can provide that transmission customers will supply

their own reactive power and voltage control service.52 As was explained

in Order No. 888, although the pro forma tariff states that the transmission

provider must provide and the transmission customer must take reactive

power and voltage control service, the amount taken from the transmission

provider would be net of any amount furnished by the customer.53 This

would be reflected in the service agreement that addresses the amount of

ancillary services the customer is purchasing from the transmission provider.

The Commission has also stated that requests for reactive power credits

must be specific and supported by a demonstration of exactly how much

reactive power the customer will supply.54

The Commission has stated that the costs of generator step-up transformers

(GSU) should be assigned directly to its related generating unit, not rolled

into transmission rates.55

Order No. 2003. In Order No 2003,56 the Commission emphasized that an

interconnection customer “should not be compensated for reactive power

when operating its generating facility within the established power factor

range, since it is only meeting its obligation.” However, the Commission

required the transmission provider or RTO/ISO to compensate the

interconnection customer for real and reactive power or other emergency

condition services that the interconnection customer provides to support

the transmission system during an emergency situation. In Order No. 2003,

the Commission also stated that the “Interconnection customer shall design

the Large Generating Facility to maintain a composite power delivery at

continuous rated power output at the point of interconnection at a power

factor within the range of 0.95 leading (producing) to 0.95 lagging

(absorbing), unless transmission provider has established different

requirements that apply to all generators in the control area on a comparable

basis.”57

In Order No. 2003-A, the Commission clarified that if the transmission

provider pays its own or its affiliated generators for reactive power within

the established range, it must also pay the interconnection customer.58

52 Atlantic City Electric Co.,

77 FERC ¶ 61,144 at

61,537 n.22 (1996).

53 Order No. 888 at 31,715-

17 (1996).

54 See, e.g., Delmarva Power

& Light Co., 78 FERC ¶

61,060 at 61,220 (1997);

Alliant Services Inc., 84

FERC ¶ 61,252 at 62,250

(1998).

55 Maine Public Service Co.,

Opinion No. 434, 85 FERC

¶ 61,412 at 62,566 (1998).

56 Standardization of

Generator Interconnection

Agreements and Procedures,

Order No. 2003, 68 Fed.

Reg. 49,845 (Aug. 19,

2003), FERC Stats. & Regs.,

Regulations Preambles ¶

31,146 at P 21 (2003)

(Order No. 2003), order on

reh’g, Order No. 2003-A, 69

Fed. Reg. 15,932 (March 26,

2004), FERC Stats. & Regs.,

Regulations Preambles ¶

31,160 (2004) (Order No.

2003-A), order on reh’g,

109 FERC 61,287 (2004)

(Order No. 2003-B).

57 Order No. 2003, section

9.6.1. See also Florida

Power & Light Co., 108

FERC ¶ 61,239 (2004).

58 Order No. 2003-A, 416.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 55

History of Reactive Power Pricing

In the rehearing requests to Order No. 2003-A, generators requested the

Commission to clearly establish and enforce the principle that interconnection

customers have a right to be compensated for providing reactive power

both within and outside the bandwidth regardless of the compensation

arrangements that may exist between the transmission provider and its

affiliate. In Order No. 2003-B, the Commission clarified that Order 2003-A

does not prejudge how the interconnection customer is to be compensated

for providing reactive power. It notes that such payments are to be provided

under a filed rate schedule unless service is provided under a Commissionapproved RTO or ISO tariff.59

Reactive Power and RTOs and ISOs

PJM Interconnection LLC, New York Independent System Operator Inc.

(NYISO), ISO-New England Inc. (ISO-NE), Midwest Independent

Transmission System Operator Inc. (Midwest ISO), California Independent

System Operator Corporation (CAISO) and Southwest Power Pool Inc. (SPP)

use a variety of methods to compensate generators for reactive power and

to charge customers for the provisions of reactive power.

Compensation to Generators. With the exception of CAISO, the RTO/ISOs

provide compensation to generators for providing reactive power under

Schedule 2 of their tariffs.

Under PJM’s Schedule 2, PJM compensates all generators (affiliates of

vertically integrated utilities and IPPs) with a payment equal to the generation

owner’s monthly revenue requirement as accepted or approved by the

Commission. In order to qualify for Schedule 2 compensation, generators

have to be under the control of the control area operator and be operated to

produce or absorb reactive power. PJM also provides lost opportunity cost

payments when there is a reduction in real power output. The other ISOs

that use Schedule 2 generally compensate generators in a similar fashion

albeit with some slight variations.

Midwest ISO’s Schedule 2 compensates generators owned by transmission

59 Order No. 2003-B at P

120.
56 Principles for Efficient and Reliable Reactive Power Supply and Consumption

History of Reactive Power Pricing

owners for providing reactive power, but provides no mechanism to

compensate IPPs for providing this service. The rates for reactive power

are based on the control area operator rates on file with the Commission

and are paid where the load is located, i.e., on a zonal basis, while loads

located outside Midwest ISO are charged an average systemwide rate.

Midwest ISO’s compensation for reactive power is a pass-through of the

revenues collected by individual control area operators providing the service.

Also, Midwest ISO does not provide for lost opportunity costs.

NYISO’s Schedule 2 provides compensation for all generators that provide

reactive power. However, generators owned by utilities are compensated

differently from nonutility generators operating under power purchase

agreements. Moreover, generators owned by utilities are also compensated

differently based on whether they are under contract to supply installed

capacity.Generators that provide voltage support service receive an equal

annual payment from a pool that consists of the total costs incurred by all

generators, in that year, that provide voltage support service. The NYISO

outlines these payments in its 2004 Voltage Support Service Rate Schedule.

The rate for the generators in 2004 is derived by dividing the annual 2002

program cost ($61 million) by the 2002 generation capacity expected (15,570

Mvar), which provides a compensation rate of $3,919/Mvar per year.

NYISO also provides for lost opportunity costs and penalties for failing to

provide reactive power. In order to qualify for compensation under NYISO’s

Schedule 2, a generator has to pass a capability test performed by NYISO.

ISO-NE’s Schedule 2 compensates generators for providing reactive power

based on four components: (1) capacity cost; (2) lost opportunity cost; (3)

cost of energy consumed; and (4) cost of energy produced. ISO-NE does

not provide penalties for a generator’s failure to provide reactive power. In

order to qualify for compensation under ISO-NE’s Schedule 2, a generator

must be in the ISO-NE market system and provide measurable voltage

support.

SPP’s compensation for reactive power is a pass-through of the revenues
Federal Energy Regulatory Commission Staff Report •February 4, 2005 57

History of Reactive Power Pricing

collected by individual control area operators.

While CAISO does not have a Schedule 2 in its tariff, the CAISO tariff

states that generators receive no compensation for operating within a

specified power factor range. If the CAISO requires additional reactive

power, it procures this either through reliability must-run (RMR) contracts

or, if no other sources are available, by instructing a generator to move its

reactive power output outside its mandatory range. Only if the generator

must reduce its real power in order to comply with such an instruction will

it be compensated, i.e., lost opportunity costs.

Power Factor Range. As discussed above, Order No. 2003 established that

an interconnection customer can receive compensation for providing reactive

power when its generator provides reactive power outside of the power

factor range of 0.95 leading (producing) and 0.95 lagging (absorbing), or

the power factor range established by the transmission provider. PJM requires

a power factor range of 0.95 leading and 0.90 lagging. CAISO also has the

same requirement for generators that do not operate under reliability must

run agreements. All participating generators in CAISO that do operate

under such agreements, however, are required to operate within the power

factor range specified in their agreements.

Reactive Power Testing. Midwest ISO, NYISO and ISO-NE have established

their own power factor criteria requirements. Testing requirements vary.

The NYISO requires that generators perform a reactive capability test once

a year to determine how much they can provide for the ISO. In ISO-NE all

generators must initially conduct a full lagging reactive power demonstration

test. The test is repeated every five years to determine leading and lagging

reactive power capability. SPP does not have specific requirements in place,

but is seeking to develop RTO-wide criteria for generators. Until the criteria

are set, generators in SPP negotiate with individual control areas to provide

services based on their reactive power capability. Similar to SPP, in Midwest

ISO individual control areas negotiate with generators to fulfill the need for

reactive power in their regions.
58 Principles for Efficient and Reliable Reactive Power Supply and Consumption

History of Reactive Power Pricing

Reactive Power Charges for Transmission Customers. The charges that

transmission customers pay for reactive power are included in the ISO/RTO

specific Schedule 2. When a transmission customer requests to purchase

reactive power from PJM, NYISO or ISO-NE, charges are based on the

monthly charges incurred. SPP and Midwest ISO do not have a formula

rate but pass through reactive power charges from the control area operator.

Under the CAISO tariff, scheduling coordinators (transmission customers)

are billed for the costs incurred under the RMR contracts.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 59

CHAPTER 4

International Reactive Power Markets

There are several market designs throughout the world for reactive power

that have developed in the recent past. The mechanisms include

requirements, contracts and real-time prices. In this chapter we describe the

market designs for reactive power in several Canadian provinces and several

countries.

Reactive Power Markets in Canada. In Canada each province determines

its own electricity policy and hence, regulatory practices as they relate to

the provision and compensation for reactive power. Ontario and Alberta

have independent system operators.

In Ontario, all generators of more than 10 MW connected to the grid

controlled by the Independent Electric System Operator (IESO – formerly

the Independent Electric Market Operator, or IMO) are required by the

market rules to have the capability of supplying at their terminals reactive

power in the range of 90% lagging (injecting into the system) and 95%

leading (absorbing from the system) based on the rated real power at rated

voltage. The generators must be capable of operating continuously at full

output within +/- 5% of the generator’s rated terminal voltage. The generators

are not required to operate continuously outside this voltage range to satisfy

reactive power requirements.

Generators who have signed ancillary service contracts for reactive support

and voltage control are compensated for the incremental costs from energy

losses incurred by running at non-unity power factor or costs of running as

synchronous condensers at the IESO’s request. They are also compensated

for their lost profits if directed to provide reactive capability outside the

market rule requirement range.

Shunt reactive compensation, primarily switched capacitors or reactors, is

installed by the transmission owner(s) to meet the forecast reactive power

requirements as part of their transmission investment programs.

In Alberta, generators may be penalized if they are not capable of producing

or absorbing reactive power within a 0.90 lagging and 0.95 leading power

factor range. These penalties can constrain MW output for a specific period
60 Principles for Efficient and Reliable Reactive Power Supply and Consumption

International Reactive Power Markets

(e.g., six months). In transmission constrained areas where generators

provide “transmission must run” service, the contracts include compensation

for reactive power.

In Manitoba, generators are compensated when they provide reactive power

capability outside of the normal range specified in the Transmission System

Interconnection Requirements. The compensation mechanism is defined in

the interconnection tariff and is based on generators verifiable costs to provide

the extra reactive power.

In Québec and British Columbia, the Open Access Transmission Tariff treats

reactive support and voltage control as an ancillary service. The cost of

providing this service is recovered from the transmission customer and paid

to the suppliers. Beyond this there are neither incentives nor penalties for

the provision of reactive power.

Reactive Power Markets in Europe. In Great Britain, in the early 1990s,

after privatization and corporate unbundling of generation, transmission

and distribution, the England-Wales market started with a cost-reflective

(cost-based) approach to paying generators for reactive power. Since the

mid-1990s, a market-oriented approach to reactive power has evolved.

Generators with a capacity greater than 50 MW are required to have a

0.95 leading power factor to a 0.85 lagging power factor capability at the

high voltage side of the generator step-up transformer. After extensive

consultation with market participants, metering and monitoring rules were

established and new dispatch rules were developed.

The National Grid Co. (NGC), which is both the system operator and the

transmission owner, sends the generator a dispatch signal consisting of the

amounts of real power and reactive power within a range of the required

generator capability. A generator can accept a default payment for reactive

power of approximately $2.40/Mvarh leading or lagging, or as an

alternative, the generator may offer contracts with a minimum term of one

year. The offer consists of three parts: a synchronized capability price in £/

Mvar, an availability capability price in £/Mvar and a utilization price in £/

Mvarh. The grid company assesses the offer, historical performance and

effectiveness of each generator against its locational forecast needs in about
Federal Energy Regulatory Commission Staff Report •February 4, 2005 61

International Reactive Power Markets

20 electrical zones to decide which offers to accept. This provides generators

incentives to offer capability beyond the requirements, lowering investment

requirements for the transmission system.

The NGC has financial incentives to keep congestion low. Since 1990 the

company increased its transmission reactive power capacity from about

3,000 Mvars to about 19,000 Mvars of mechanically switched capacitors,

9,000 Mvars of SVCs and 4,000 Mvars of Quadrature Boosters (similar to

phase shifters) in 2004. Some of the SVCs can be relocated by truck in about

eights months. In contrast to conventional approaches, NGC relocates some

of the transmission assets in order to target areas in need of relief. Twenty

percent of the reactive power supplied is from generators.60 Since 1993,

through a combination of contracting with generators, operational

improvements, improved forecasting and investments in transmission, NGC

has reduced congestion costs, as defined by the regulator, by 90%.61

In Sweden, most of the generation (primarily hydro) is located in the north

while the transmission system carries the power to the south where most of

the load is located. Reactive power, which is supplied mostly in the south, is

supplied on a mandatory basis and there is no compensation. The goal is to

keep reactive power flow on the transmission system close to zero, especially

at certain interfaces. Some large generators are seldom used for voltage

control and are operated at a constant reactive power output. Hydro and

thermal units are required to maintain a capability to inject reactive power

of one third the amount of active power injection (a power factor of

approximately 0.90). Network operators use as much static reactive power

as possible.62

In the Netherlands, the network companies have local reactive power

requirements. These companies purchase reactive power locally through

bilateral contracts with generators or through exchange with other network

companies. Generators contracted for the reactive power service are paid

for their reactive power capacity only. No payment is made for reactive

power supplied.63

The Belgian Independent System Operator has a transmission tariff for

reactive power and voltage regulation that has a small charge per Mwh for

60 Julian Cox, National

Grid Co., presentation to

FERC staff, October 25,

2004.

61 S. Oren, G. Gross and F.

Alvarado, “Alternative

Business Models for

Transmission System

Investment and Operations,”

2002, http://

www.eh.doe.gov/ntgs/

gridstudy/MAIN_3.PDF, 10.

62 John D. Kueck, Brendan J.

Kirby, Leon M. Tolbert and

D. Tom Rizy, Voltage

Regulation with Distributed

Energy Resources (DER),

Oak Ridge National

Laboratory, Oak Ridge,

Tenn., draft, received

November 4, 2004.

63 J. Zhong, and K.

Bhattacharya, “Reactive Power

Management in Deregulated

Electricity Markets - A

Review,” IEEE Power

Engineering Society Winter

Meeting, 27-31 Jan. 2002,

pp. 1287-1292.
62 Principles for Efficient and Reliable Reactive Power Supply and Consumption

International Reactive Power Markets

a specified power factor range and a much higher charge outside of this

range. In the power factor range 0.95 leading to 0.95 lagging, for power

greater than 10% of the contracted real power, the reactive power charge

varies with voltage of the point of interconnection to the transmission

network. In the transmission network the charge is 0.21 Euro/MWh ($US

0.27). At the network side of transformers into the medium voltage

distribution network, the tariff is 0.23 Euro/MWh ($US 0.31). For reactive

power outside the 0.95 leading/lagging power factor range, the charge is 6

Euro/Mvarh ($US 7.83). When the real power is less than 10% of the

contracted amount, the lower charge applies for reactive power up to 32.9%

of the real power, and the 6 Euro/Mvarh charge applies if reactive power is

above 32.9% of 10% of the contracted amounts.64

Reactive Power Markets in Other Countries. The Australian ISO provides

reactive power compensation to generators and synchronous condensers.

For the generators there are mandatory capabilities (0.9 lagging and 0.93

leading) and compensation for accepted offers of higher capabilities. The

providers receive an availability payment, an enabling payment when

dispatched and a compensation payment when their generators are

restrained from operating according to market conditions. The voltage

control sequence is generally as follows: capacitors and SVCs are switched

on; reactive power is provided from generators where real power output is

not constrained; in specific areas, synchronous compensators are called from

a merit order depending on price; real power generation is constrained;

and, lastly, market trades are curtailed.65

In India, the state electricity boards (similar to load serving entities) were

drawing large amounts of reactive power from the EHV grid, causing 20%

voltage drops on the 400-kV system, avoidable transmission losses and

considerable reactive power from generators. The Indian regulator put a 4

paise/kvarh (approximately $1/Mvarh) price (buy and sell) on reactive

power when the voltage dropped below 97% of nominal. In off-peak periods

the charge is reversed when the voltage goes above 103%. All low voltage

problems have now vanished.66

In Japan, Tokyo Electric Power Company (TEPCO) gives their retail

customers the financial incentive to improve their power factor. It comes in

64 ELIA System Operator S.A.

Tariffs 01-01-2005 – 31-03-

2005, Table 8: Tarif du

réglage de la tension et de la

puissance réactive (Tariff for

voltage regulation and for

reactive power), 21 December

2004, available at http://

www.creg.be/pdf/Tarifs/E/

ESOFR-01012005-

31032005.pdf

65 John D. Kueck, Brendan J.

Kirby, Leon M. Tolbert and D.

Tom Rizy, “Voltage Regulation

with Distributed Energy

Resources (DER),” Oak Ridge

National Laboratory, Oak

Ridge, Tenn., draft, received

November 4, 2004, and J.

Zhong, and K. Bhattacharya,

“Reactive Power Management

in Deregulated Electricity

Markets – A Review,” IEEE

Power Engineering Society

Winter Meeting, January 27-

31, 2002, 1287-1292.

66 Fax from Bhanu Bhushan,

employee of the Indian

National Grid Co., to Mark

Lively, October 14, 2004 and

email from Sushial Soonee,

employee of the Indian

National Grid Co., to Mark

Lively dated October 20,

2004.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 63

International Reactive Power Markets

the form of a discount of the base rate. The discount is based on the customer’s

power factor. The electricity rate is a two part tariff: Base Rate + Electricity

Rate, where

Base Rate = (Unit Price [Yen/kW])*(Contract kW)*(1.85-Power Factor)

Electricity Rate = (Unit Price [Yen/kWh])*Total Usage [kWh]

Unit Price for Base Rate is about US10$/kW and Unit Price for Electricity

Rate is about US10¢/kWh. This program results in load installing equipment

to increase its power factor and hence, reduce the base rate. Under this

tariff the average customer power factor is 0.99.67

In Argentina, generators, transmission operators, distribution operators, and

large loads have obligations to serve reactive power. Generators are required

to produce and consume reactive power within the limits of their capability

curves (D-curves). Transmission operators are required to maintain voltages

within +/-3% for 500 kV and +/-5% for 220 kV and 132 kV. There are two

levels of sanctions for failure to comply with the requirements. If the outage

67 TEPCO presentation to

FERC staff, TEPCO’s Practice

of Voltage & Reactive

Management, January 19,

2005.
64 Principles for Efficient and Reliable Reactive Power Supply and Consumption

is announced in advance, there is a reactive power charge. There is an

additional penalty if the outage is unannounced. Additionally, if an

uncommitted generation unit is dispatched as a result of a reactive power

shortage, the parties responsible for the shortage must pay the generator its

startup costs. The penalty for an announced generator outage is the

operations and maintenance cost of substitute equipment and a reactive

power charge of Argentine $0.45/Mvarh ($0.15 US). If a generator outage

is expected to last for more than one season, the generator may elect to

install capacitors or reactors, as appropriate, to avoid the penalty charge.

If an outage is announced a day or a week in advance, the penalty charge is

Argentine $4.50/Mvarh ($1.50 US). If the outage is not announced in

advance, the penalty charge applies for all hours the generator is in service

or on reserve for the season. Generators that do not comply with reactive

power requirements may be denied access to the system. The penalty system

for transmission operators is similar to that of generators, with penalties

charged per Mvar and based on the conceptual hourly compensation for

lost load. Distribution operators and large loads are charged similar to

generators, based on the replacement equipment operation and maintenance

costs.68

68 Argentina. Energy Secretary.

Resolution SE 0106/2002.

Official Bulletin no 29.899,

May 16, 2002, pp. 8-10.

“ANEXO 4: CONTROL DE

TENSION Y DESPACHO DE

POTENCIA REACTIVA”,

(Appendix 4: Control of

voltage and dispatch of

reactive power), available at

http://www.enre.gov.ar/web/

bibliotd.NSF/

04256380006cf0060425636f00508108/

57abd18e0397241403256bbb

0044b849?OpenDocument
Federal Energy Regulatory Commission Staff Report •February 4, 2005 65

CHAPTER 5 Existing Reactive Power Issues

Existing Reactive Power Issues

The existing reactive power market framework originates from the

historically vertically integrated approach to electricity generation,

transmission and distribution based on the view that the industry was a

natural monopoly and subsequent regulatory policy changes to require open

access. This chapter details some of the existing issues and potential problems

with existing approaches to reactive power pricing and procurement.

Because reactive power can be supplied or consumed by most assets in the

electrical system, a comprehensive look should be made regarding the current

incentives that exist to encourage reliable, efficient investment choices among

generation, transmission and load. There are several problems and concerns

regarding the current procurement practices and pricing policies for reactive

power. These include a lack of transparent planning standards,

noncompetitive procurement, discriminatory compensation policies, rigid

interconnection standards that may not meet local needs and poor real-time

incentives for production, consumption and dispatch.

Planning and Design for Reactive Power Issues

Existing system designs rely on both detailed system studies and engineering

rules of thumb or good utility practice for new generation requirements

regarding reactive power capabilities. System operators and regulators

require the supply of reactive power within specified power factors, or

operational bands, for interconnection. Outside of the specified power

factors, generators may be paid opportunity costs for the supply of additional

reactive power in independent system operator (ISO) markets. When the

supply of available reactive power resources is deemed deficient, system

operators rely on the system planning process to identify the investments

needed to satisfy the system’s reactive power needs.

1. Transparent and Consistent Reactive Power Planning Standards.

Consistent and transparent planning standards for the overall reactive power

system needs do not exist. Guidelines for dynamic and static reactive power

requirements on the transmission system can differ from one system to

another. The lack of such standards is a source of concern because of the

public good characteristics of reliability. Reactive power is needed to ensure

reliability, but because reliability is a public good, the harm from procuring
66 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Existing Reactive Power Issues

inadequate reactive power capability is not fully borne by a given

transmission provider. As a result, transmission providers may not have the

incentive to procure adequate reactive power capability. Consistent,

enforced national planning standards might help to address this issue. In

addition, the process used by many transmission providers, especially those

outside of regional transmission organizations (RTOs) and independent

system organizations (ISOs), for identifying potential system needs and

developing alternative solutions is not transparent. As a result, it is difficult

for the public to determine whether transmission providers procure reactive

power and reactive power capability from the lowest-cost sources.

NERC, the North American Electric Reliability Council, sets reliability

standards for system operations and planning and monitors compliance with

these standards.69 Each control area has a reliability coordinator who has

the responsibility of conducting reliability planning analysis and monitoring

reliability in operations; this may be the system operator, the control area

operator or a separate entity. NERC Operating Manual Policy 9, “Reliability

Coordinator Procedures,” states that reliability coordinators are responsible

for next-day planning, including reactive reserves, having situational

awareness of reactive reserves and communicating problems with reactive

reserves to control area operators, transmission operating entities and other

reliability coordinators in real-time. NERC Planning Standard I.A, Table 1

lists the required system performance for loss of load under increasingly

severe contingencies. Not providing enough reactive power to meet these

standards is a violation, but there are currently no strong penalties for

violating NERC standards. NERC has a new operating standard for Voltage

and Reactive Control, proposed to take effect in April 2005. This standard

requires transmission owners to maintain voltages within established limits,

to maintain reactive reserves to keep voltages within acceptable limits

following a single contingency and that transmission operators be able to

direct the operation of devices necessary to regulate transmission voltage

and reactive flow. The standard also requires generators to keep transmission

operators informed of generator reactive power capabilities and generator

voltage regulation equipment status.

Although standards exist, they are not specific. Because of the lack of clear

standards for reactive power reserve requirements and because a transmission

69 NERC Version 0 Reliability

Standards – Operating

Standards, Standard VAR001-0 – Voltage and Reactive

Control, NERC, October 25,

2004, available at

http://www.nerc.com/~filez/

standards/Version-0-RF.html.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 67

Existing Reactive Power Issues

provider may not bear the full reliability costs of inadequate reactive reserves,

transmission providers may procure insufficient reactive power reserves.

Of course, cost-of-service regulation may tend to offset the incentive to underprocure reactive power capability, because a transmission owner could

increase its return by adding equipment providing reactive power capability

to its rate base. However, these incentives to add equipment reactive power

capability are largely negated in those cases where states have imposed

rate freezes and regulatory disincentives for additional investment, since

the costs and return from investing in additional resources cannot be

recovered from customers.

2. Noncompetitive Procurement of Reactive Power Needs. In addition to

the lack of transparent standards for reactive power needs existing as a

barrier to efficient supply of reactive power, the regulatory processes may

provide incentives for system operators not to adequately consider all

available alternatives in the procurement of reactive power capacity.

Reactive power continues to be procured primarily as a cost-of-service

product. The cost-of-service model generally rewards capital investment,

but not necessarily efficient contracting with nonaffiliated sources. If a

vertically integrated utility buys power at a lower cost than can be produced

internally, there is little or no reward. If the same capacity is built at a

higher cost and put in the rate base, the vertically integrated utility is usually

rewarded with a risk-adjusted return on equity that is often disproportionately

high compared to the risk. The result is often inefficient and more expensive

rate base investments. Historically, utilities have resisted buying power

from third parties (other than affiliates), arguing that such purchases are

incompatible with system reliability.

Once the system operator can identify and define the reactive power products

that are needed to maintain system reliability, an opportunity for all suppliers

to meet those needs should be made available. Those that supply reactive

power products should be paid for the reactive power services provided.

For instance, smaller mobile sources of reactive power can be placed to

meet incremental system needs at times in which large traditional investments

can be economically postponed while maintaining reliability. Some have

argued that these resources are ignored because the system operator has

little incentive to use available tools that may reduce the ability of the operator
68 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Existing Reactive Power Issues

to place additional assets in rate base.

3. Discriminatory Payments to Reactive Power Generation Sources. Some

generation resources that provide reactive power capacity to the grid are

not compensated while others that provide similar service receive cost-ofservice payments. In non-RTO markets, payments for reactive power to

generation resources are often limited to affiliate resources. The argument

against nonaffiliate payment is based on the planning process of the

transmission owner. The transmission owner claims that nonaffiliated

resources are not part of the transmission planning process and the reactive

power obligations are needed primarily to maintain the reliability of the

existing system and do not provide any additional system-wide benefit.

Further, determinations of public convenience and necessity generally do

not address reactive power needs specifically. The process to determine the

validity of such claim against systemwide needs or benefits is not transparent

and has the potential for abuse. The payment of affiliate generation resources

for reactive power capability, while denying nonaffiliate suppliers that

provide useful and needed reactive power capability to the system is

discriminatory. Payments for reactive power capability are not being made

in a comparable manner to the suppliers that provide similar service under

such regime.

Under Order 888, transmission service generally contains a charge for the

supply of reactive power. A question arises as to whether unaffiliated

generation is adequately compensated for both its reactive power capability

and its supply of reactive power to the system. Comparability is required

by a transmission owner toward its own and other interconnected generation.

The ISO issues and pricing are relevant in the non-ISO markets along with

this comparability requirement.

Several issues arise regarding which generation units should be eligible for

reactive power payments. An argument is sometimes made that generation

developed as part of “the system-planning process” should be eligible for

reactive power compensation, while unaffiliated projects provide no such

value to the system. New generation resources are required to provide

reactive power by the Large Generator Interconnection Procedures. Further,

as transmission owners continue to purchase unaffiliated facilities, there
Federal Energy Regulatory Commission Staff Report •February 4, 2005 69

Existing Reactive Power Issues

exists the possibility that these investments receive reactive power

compensation whereas the former unaffiliated suppliers were rejected for

such compensation.

4. Appropriateness of Existing Payment Structure for Generation Supply.

Chapter 3 reviewed the history of reactive power pricing. The compensation

to generators has been based on a formulaic approach that may have little

relationship to the costs associated with the supply of reactive power

capability and real time supply. For instance, the allocation factor used in

the AEP methodology does not directly relate to the incremental investment

cost in providing reactive capability or supply. Methods that attempt to

allocate the fixed investment costs of a generator among the joint products

that it produced (i.e., real and reactive power) inherently have some degree

of arbitrariness. While this may have been appropriate in the cost-based

paradigm it may need to be reexamined under a market-based approach.

Such a re-examination is especially appropriate when eligibility for such

payments may be determined, in part, by market participants and potentially

provide an unfair competitive advantage.

Investment that results in reactive power capability by generation resources

is driven by interconnection requirements, historical inertia and potential

cost recovery for capacity. There is little interaction between the actual

system need or value of reactive power capability and its supply by

independent generation resources. For instance, there appears to be little

empirical rigor to support the existing standards of interconnecting generation

power factor requirements. Additionally, cost-of-service methodologies and

payments for reactive power capability may have little relationship to the

value of reactive power capability to the transmission system. Generators

in some markets are uniformly provided a payment based on capital cost to

supply reactive power based on the Opinion 440 (American Electric Power

Inc., or AEP) Methodology. The Opinion 440 methodology provides a

regulatory formula that allocates a portion of fixed costs that are paid by

the transmission system customers. The requirements and costs that result

have little or no relationship to the need for this capability. Some locations

may have higher reactive power needs, and mechanisms to promote

additional investment in reactive power capability may be applicable in those

areas.
70 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Existing Reactive Power Issues

Alternative market solutions to provide needed reactive power capability

may be available, but these options are not being adequately considered

under the approaches currently pursued. Allowing the system operators’

identified reactive power needs to be procured and paid for through more

appropriate mechanisms should encourage more efficient supply of the

resources needed to support the network operation.

5. Lack of Compensation to All Suppliers of Useful Reactive Capability.

While transmission-based suppliers of reactive capability receive

compensation, many generation-based suppliers are not compensated for

reactive power capability that aids in system reliability. Compensating all

market participants for the value of reactive power that they provide should

encourage an adequate and efficient supply of reactive power. This is

particularly true for generation resources that are relied upon to provide

dynamic reactive power reserves. That is because it is unlikely that an

entity will invest in and offer to supply reactive power capability unless it

expects to recover its costs and earn a profit. Of course, many generators

are able to earn revenues from sources other than reactive power - such as

from sales of real power. Thus, much generation investment would continue

to be made even if generators are not paid for providing reactive power

capability. However, failing to pay generators for reactive power could

reduce the amount of generation investment, particularly in areas where

reactive power capability is very valuable to the system. That is, some

efficient generation investment might not be built or might retire early

without reactive power payments because revenues from real power sales

and other sources, by themselves, would not be sufficient to cover the project’s

costs and return a profit. Failing to pay for reactive power supplied by

generation resources also could reduce the amount of reactive power

capability installed in new generation equipment. Developers may elect

not to add reactive capability beyond the minimum requirements if they are

not going to receive any additional revenue from doing so.

6. Rigid but Imprecise Generation Interconnection Standards.

Interconnection standards generally require a standardized generation power

factor for new generation. While these standards provide independent

criteria for generation interconnection, local needs can vary from the

standards. Some locations may have higher reactive power needs than the
Federal Energy Regulatory Commission Staff Report •February 4, 2005 71

Existing Reactive Power Issues

standard, while other locations may have smaller needs.

The existing interconnection standards are imprecise in two important

respects. The standards do not specify on which side of the step-up

transformer the power factor is to be measured. Secondly, there is no

standard for exactly how the power factor is to be measured.

Real-Time Reactive Power Demand Issues

Reactive power is required by two types of customers. First and primarily,

reactive power is needed by the system operator to maintain voltage levels

and ensure the reliability of the transmission network. Second, reactive

power is supplied and consumed in varying amounts by most market

participants. The combination of the system operator’s need for maintaining

system reliability and reactive power consumption by real power load

determines the total system reactive power needs. Reactive power is defined

in Order 888 as an ancillary service. As such, market participants often

pay for reactive power through the applicable transmission service tariff.

1. System Operator Real-Time Reactive Power Needs. Reactive power is

used to maintain the voltages in the network and is used by electricity

customers, known as load, by power generation and by transmission owners.

The system operator determines the voltage levels of the system to maintain

reliability and promote efficient use of the system. Determining system

needs for reactive power at any given time is a combination of the power

system configuration; system operator decisions regarding voltage levels;

the consumption of reactive power by load, transmission and generation;

the consumption of real power by load; and the location of real-power supply.

Reactive power reserves are needed by the system to prevent voltage

collapse. While reactive power supply from transmission elements is useful

in reliably providing needed reactive power supply in most times, it is less

useful providing reactive power supply in critical times when reactive power

is needed to prevent voltage collapse. At these times, reactive power from

generators and synchronous condensers are needed to provide critical

supplies of dynamic reactive power. This reactive power capability will

generally go unused but is deemed critical to ensure the long-run reliability
72 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Existing Reactive Power Issues

of the transmission network. It follows that the presence of this reactive

power capacity and supply is critical in maintaining system reliability and

might be viewed as a distinct product.

A system’s real-time reactive power supply needs are, in part, determined

by the voltage schedule provided by the system operator. System operators

have flexibility in determining the voltage schedule across the system. These

choices are not fixed and changes may increase or decrease the reliability

and economic performance of the system. To date these decisions and the

factors that drive the decision may vary considerably among system

operators. The system operator, by adjusting voltage schedules can adjust

the required supply of reactive power. Further, the system operator’s

scheduling decisions will also determine the availability of reactive power

reserve capability.

At times, there may be insufficient supply of reactive power to maintain a

desired voltage level and the system will be operated at a lower level of

reliability. Similarly, a system operator may encounter a situation where

the reactive power supply is available, but only at the cost of backing down

needed real power supplies. In these cases, the system operator can either

curtail real load or run at slightly lower voltage levels. A system operator

may choose at times to run at slightly lower voltage levels rather than curtail

real load. Thus, there can be a tradeoff between maintaining a specific

reliability level and procuring reactive power at the cost of serving real

power load. Similarly, the system operator has a choice between relying

heavily on dynamic reactive power from generators or using nongenerator

reactive power resources and saving dynamic generator capability as reserves

in case of a system emergency.

Unlike real power reserves, which have a specific reserve margin requirement

in each region of the country, there is no clearly defined requirement for

reactive power reserves. Instead, the planning authority for each control

area runs contingency analysis and voltage stability studies to ensure that

the system has acceptable voltages in the operating state and following any

unexpected events. Planning techniques vary across the country; in some

regions voltage is a major concern and is studied extensively, while in other

areas voltage problems rarely arise. System operators monitor real-time
Federal Energy Regulatory Commission Staff Report •February 4, 2005 73

Existing Reactive Power Issues

voltages and use reactive power resources to correct voltage problems.

Because reactive power needs vary widely by location and system conditions

and since reactive power must be supplied locally, there could be numerous

reactive power zones, each with different requirements for static and dynamic

reserves.

2. Reactive Power Needs by Real Power Customers. A system’s reactive

power supply needs are also determined by the reactive power consumption

by load. Reactive power consumption by load can differ by load type. For

instance, some industrial market participants are large reactive power

consumers. The use of reactive power by load is often identified through

the load’s power factor. In some areas, market participants with low power

factors (and thus increasing the overall need for reactive power) are required

to make additional payments (often referred to as power factor penalties)

intended to compensate for the additional reactive power capability needed

to serve the market participant. In other cases, such market participants

are required to make additional investment in reactive power supply by the

market participant. Identifying those entities responsible for the need for

reactive power is an important aspect in evaluating reactive power pricing

policy.70 In this case, reactive power consumption by load should be measured

to the extent that it is cost effective to spur efficient reactive power capacity

investment and consumption decisions.

In many cases load response and load-side investment can reduce the need

for reactive power capability in the system. For instance, peak real power

loads due to high temperature are due primarily to increased air-conditioning

needs. Many air-conditioning units consume reactive power, thereby

increasing the reactive needs of the system concurrently. The joint

consumption of real and reactive power by these market participants has a

greater impact on the system than the consumption of real power by high

power factor uses. Incentives to encourage efficient load-side participation

to avoid additional investment in transmission and reactive power capability

may be under-developed.

3. Reactive Power Consumption by Transmission. Reactive power also is

consumed and produced by transmission equipment, but identifying the entity

responsible for the reactive power need is more complex than measuring

70 A basic economic

principle, whether in cost

allocation or market design,

requires those causing costs

to pay them; likewise, those

incurring the costs should

be compensated. The

determination of efficient

reactive power prices should

reflect the marginal costs of

reactive power service.

Otherwise, there are

subsidies and poor to bad

incentives to behave

efficiently and an increased

probability of system

failure.
74 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Existing Reactive Power Issues

consumption by load. Even if no real power customer consumes reactive

power, the system requires supply for voltage support and to cover the

reactive power consumption that occur within the transmission system.

Reactive power needs for the system depend on the location of the real

power supplies and real load. Due to significant reactive power consumption

over heavily loaded transmission lines, generation resources that are located

long distances from load create greater reactive power needs than resources

located near loads. System operators will be the purchasers of the reactive

power and will pass those costs to transmission customers.

4. Pricing Reactive Power to Transmission Customers. All transmission

customers benefit from reliable operation of the system. System reliability

– and thus a significant portion of the system’s reactive power needs – is a

public good. The pricing of a public good to its market participants is a

difficult problem. Efficient pricing requires that market participants reveal

their valuation of the public good, which in this case is system reliability.

One simple rule is that those who do not benefit from a public good should

not need to pay for it. This is true when the good is local in nature and only

benefits a subgroup of market participants. Pricing should strive to charge

those who benefit in rough proportion to the amount they benefit.

A difficult challenge is to determine which market participants increase the

need for reactive power and which proportionally benefit. These market

participants should be targeted to pay for the systemwide reactive power

needs. Further, a significant portion of theses costs are associated with

reactive power consumption within the system. One possible approach would

be to identify the transmission customers responsible for the reactive power

consumption that occur over transmission elements to maintain system

reliability. When real power is supplied closer to load, less reactive power

will be needed by the system. Distant power sources may require greater

supplies of reactive power. Thus, under certain system conditions it may be

appropriate that long distance transmission customers should be responsible

for the costs of providing the additional reactive power needs of the system.

Also, the real power load may be distant from the real power needs, so

simply targeting load in the areas requiring reactive power may not be

appropriate.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 75

Existing Reactive Power Issues

Real-Time Reactive Power Supply Issues

Reactive power capacity can be supplied through transmission as well as

generation (including distributed generation) investment. The purchasers

of reactive power are primarily limited to system operators who pass the

costs through to transmission customers. Some real power customers may

also procure reactive power resources to meet their own reactive power

needs and/or obligations imposed by the system operator.

Generation and some transmission products may provide dynamic reactive

power. Other traditional transmission products used to supply reactive

power provide static reactive power. The primary costs in developing reactive

power capacity are capital investment costs and form the basis for much of

the long run marginal cost of reactive power. The variable costs associated

with reactive power supply come from real power losses due to heating and

opportunity costs for generators that result from forgone real power sales.

The marginal operating cost of providing reactive power from within a

generator’s capability curve (D-curve) and from some transmission sources

(such as capacitors) is near zero.

1. Real-Time Cost Structure. System planning has historically attempted to

ensure that sufficient reactive power is available. As a result, there is a

further likelihood that surplus reactive power capability will be available to

the system at most times. This surplus reactive power capability is analogous

to the surplus real power capability that is intended to maintain a reliability

standard. Given the reactive power capability required to maintain reliability

on a planning basis, it is not unlikely that the marginal cost of reactive

power supply during most periods will be at or near zero. As a result, realtime market prices under competitive conditions at most times may be very

low, and thus pure spot pricing may not be sufficient to cover all investments

costs.

The investment cost structure for many transmission and generation-based

reactive power solutions could be “lumpy.” If an installed capacitor bank

fully relieves a reactive power problem and were to set the reactive power

price in a given location during most hours, the capacitor’s full costs are
76 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Existing Reactive Power Issues

unlikely to be recovered over time unless prices are sufficiently high when

prices are not zero.71 And if real-time reactive power prices are not

compensatory, investment in capacity to provide reactive power is likely to

be inadequate over the long term without a capacity requirement for reactive

power capability. Whether marginal-cost pricing for reactive power is fully

compensatory is an empirical question that depends on the knowledge of

reactive power prices.

2. Real-Time Compensation Structure. In today’s pricing environment, many

generators are not paid for reactive power produced within certain operating

bands and may be paid lost opportunity costs outside the bands.

Interconnection requirements to provide capability for products that receive

no compensation in the market provide little positive incentive to supply the

desired product. Aside from the mandatory direction from the ISO or

regulator there is no market incentive to encourage the supply of reactive

power at any specific time. Such obligations on suppliers may discourage

efficient maintenance or result in less than desired availability of supply.

Under such a policy based on mandates, the supplier’s goal is to minimize

the cost of compliance. Minimizing the cost of compliance may differ from

both minimizing the cost of production and maximizing efficient use of

resources to meet market participant needs. Additionally, mandatory supply

obligations relying on penalties for noncompliance require enforcement and

information by the obligator. Finally, the costs associated with mandatory

supply are not always apparent, thus making efficient decisions regarding

competing supply less likely. There is little incentive to choose or identify a

lower cost alternative.

3. Local Supply Market Power. Market power could exist in the supply of

reactive power. Suppliers of reactive power are likely to have significant

market power because reactive power is difficult to move over long distances

due to the consumption of reactive power by the transmission lines. Power

traveling over longer transmission lines at high loadings results in a higher

percentage of reactive power losses to real power losses. As a result, fewer

suppliers are ordinarily available to provide the reactive power needed at

any individual location. Some type of regulation or market power mitigation

may be needed to prevent reactive power prices from reflecting an exercise

of market power if suppliers are given the opportunity to place supply bids.

71 The characteristics of the

capacitor investment may

make it a “lumpy”

investment. The efficient

investment size may eliminate

the reactive power shortage

in most periods.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 77

Existing Reactive Power Issues

4. Incentives to Increase Real Power Transfer Capability. The locational

supply of reactive power can at times increase the available flow, or transfer

capability, for real power between two points. Since reactive power and

real power in combination congest the transmission system, increased reactive

supply in the right locations can increase the transfer capability for real

power. Existing pricing systems give no incentive to supply additional

reactive power that may allow low priced real power to displace more

expensive real power sources. This is particularly true if any increased

supply of reactive power requires a reduction in real power output. Because

the generator is generally only compensated for real power sales there is

little incentive to provide additional reactive power even if it increases

efficiency and lowers the total system costs.

5. Locational Siting Incentives. Reactive power pricing should encourage

efficient locational siting of new generation. New generation siting decisions

are often based on real power prices and incentives. New real-power

generation that displaces existing real-power resources may place an

increased burden on the system’s need for reactive power due to its location

on the network. Alternatively, new generation might choose locations that

reduce system reactive power needs if the reactive power pricing incentives

are apparent. Because reactive power losses in transmission lines are very

high, generators near loads can supply reactive power with much lower

losses than generators located long distances from loads. The system’s

reactive power needs and costs might be addressed through improved pricing

mechanisms that encourage siting decisions that are consistent with the

system’s reliability needs.

Locational investment incentives from reactive power losses differ from the

incentives from real power losses in existing regions with locational pricing.

Suppliers in regions that have locational marginal pricing including marginal

loss pricing inherently incorporate real power losses in their siting and

dispatch decisions. Real power suppliers receive and real power market

participants pay the marginal value of real energy at a given location. Under

full locational pricing (with marginal loss pricing) a generator that increases

the real-power losses on the system does in fact receive a negative signal of

this cost through a lower locational price. Similarly, a generator that reduces

the real-power losses will see the positive value.
78 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Existing Reactive Power Issues

6. Market Power by Reactive Purchasers. Market power by the system

operator could also be a problem for some sellers of reactive power. Because

reactive power needs are primarily identified and determined by the system

operator, there may be an incentive to procure reactive power from resources

that are affiliated with or provide a financial benefit to the system operator.

These might include the discriminatory procurement of reactive power from

generation resources and the development of rate-based transmission

upgrades despite available alternatives. Additionally, the system operators

may be able to exhibit monopsony power on reactive power suppliers and

procure existing reactive power supplies at prices that do not signal or

encourage needed investment.

7. Guaranteed Cost Recovery for Some Suppliers. Finally, market solutions

may be undermined by the potential for cost-based investment directed by

the system operators. If costly investments in reactive power capability

come from the market without cost recovery guarantees, there may be limited

assurances that the system operators might not subsequently purchase other

sources of competing supply such as capacitors that are put into the

transmission rate base. These risks discourage non-rate-based investment

and bilateral contracting for needed resources.

Reactive Power Dispatch Example

The following simplified two-node model illustrates some of the potential

benefits that come from efficiently dispatching reactive power above the

required power factor constraints. In the example, using the full reactive

capability of local generation units in a transmission constrained area can

increase the transmission of real power into the constrained area lowering

system costs by 20-30 percent. If the generator is not compensated in some

manner, there is no incentive to provide the additional reactive power. In

fact, the example shows a case in which there is less need for the local

generator’s real power when the local generator increases its reactive power

output, illustrating the potential disincentive for generation resources within

a transmission constrained area to provide useful reactive capability.

The example is solely for illustrative purposes and is not based on any actual

dispatch example. The model shows the limitations of current pricing designs
Federal Energy Regulatory Commission Staff Report •February 4, 2005 79

Existing Reactive Power Issues

that ignore the incentives to supply reactive power in the market.

Additionally, the model illustrates the effect on costs of system operator

decisions regarding voltage target levels. This example is meant to illustrate

dispatch changes in steady-state situations, and does not take into

consideration the implications of increasing reserves, such as adding

capacitor banks. In reality, decisions to expand capacity by investing in

other devices need to be considered.

The two-node model has one load, located at Bus A, with both real and

reactive components. Real and reactive generation resources are located

at both Bus A and Bus B. The real power capacity of Generator A is 500

MW. At maximum real output, Generator A is limited to a reactive power

production of 150 Mvar by its physical constraints; however, at lower real

output levels reactive power can be increased as defined by its D-curve

constraints, i.e., 400 Mvar at 50 MW. In this example, the reactive power

constraints are approximated by a linear function. The cost of real power

production by Generator A is constant at $80 per MWh, and the cost of

producing reactive power is $0 per Mvarh, which ignores the small cost of

losses in the generator. The real power load at Bus A is 1,000 MW and

reactive power load is 500 Mvar.

The production of real and reactive power by Generator B, located at Bus

B, is assumed to be unconstrained. The cost of real power production by

Generator B is constant at $10 per MWh, and the cost of reactive power

production is $0 per Mvarh. A transmission line with a thermal capacity of

1,000 MVA connects Bus A and Bus B. Other line parameters are shown in

the figures below. In the figures, the one transmission line is represented by

two flows: The larger, green arrows on the upper line represent the direction

and magnitude of real power flow in MW; the smaller, blue arrows on the

lower line represent the direction and magnitude of reactive power flow in

Mvar.

In Case 1 the system operator dispatches the system incorporating the limiting

reactive power supply constraint of 150 Mvar from Generator A using

PowerWorld software. PowerWorld, the simulation software used to

generate these examples, uses real power controls to obtain an optimal

solution. PowerWorld does not currently co-optimize reactive and real
80 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Existing Reactive Power Issues

power, and it does not consider a cost for producing reactive power. This is

true in other commercial power flow software packages as well; the reason

is that the reactive power optimization is nonconvex, and requires more

complicated optimization tools. The marginal cost of reactive power shown

in the examples is calculated from the change in real power losses from

increasing the reactive power demand; it does not include the higher

opportunity cost of backing off real power production subject to the D-curve

constraint.

By restricting reactive power production by Generator A to 150 Mvar or

less, the least cost system dispatch cost is $20,647 per hour. Generator A

produces 144.9 MW of real power and its full 150 Mvar of reactive power.

Generator B produces 905.8 MW and 423.8 Mvar. A total of 1,050.7 MW

is produced, of which 50.7 MW, or 4.8 percent of total real power, is consumed

as losses over the transmission line. Generator B produces 573.8 Mvar of

reactive power, of which 73.78 Mvar, or 12.9 percent, is consumed as losses

over the transmission line. The transmission line is operating at full capacity,

carrying 1,000 MVA from Bus B. Although the target per-unit voltage levels

at buses A and B are both 1 per unit (pu), given the other constraints in the

model, the PowerWorld software calculates the actual voltages to be 0.91

pu and 1.00 pu for Bus A and Bus B, respectively. The model was unable to

achieve the target voltage level of 1.0 pu at Bus A and still respect the

transmission line limit and reactive power requirement for Generator A.

Clearly, Generator B can supply the real power to the system at a lower

production cost than A, and we would prefer to dispatch more of its capacity.

However, because the transmission line is congested no additional real or

reactive power can flow from B to A. More specifically, the transmission

line is loaded at 1,000 MVA at Bus B, meaning the constraint is binding at

that point and no more power can be injected. At Bus A, the load on the

transmission line is 935 MVA. Increasing reactive power production by

Generator A will reduce the need to use Generator B to supply reactive

power to Load A, and decrease the amount of reactive power necessary at B

on the transmission line. Reducing reactive power flow on the transmission

line allows increased transmission of cheaper real power from Generator B

to Load A.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 81

Existing Reactive Power Issues

Case 1

MW 

Mvar 

Source: Derived from PowerWorld

In an environment where there is no reactive power pricing, Generator A

has no incentive to increase its reactive power supply because doing so will

decrease the amount of real power it will get paid for. In fact, if Generator

A were operating at a point on the limit of its D-curve, increasing reactive

power output would actually reduce the generator’s revenue because it would

sell less real power, unless it was paid for the supply of reactive power.

Therefore, higher total system costs can occur than if reactive power

production were compensated.

If the ISO has the flexibility to dispatch Generator A at any feasible point

within it D-curve or if generators were given location-based incentives for

producing reactive power, a more cost-effective dispatch is available, as

shown in Case 2. System costs for this case drop as Generator A increases

its production of reactive power, reducing the need for transporting it from

Generator B, and frees up transmission line capacity for increased real power

flow from Generator B to Load A. Generator A increases its reactive power

production to 390.5 Mvar, and reduces it real power production to 67 MW,

an operating point which lies on its D-curve, approximated as a linear

function in the software and illustrated below in Figure 1. Generator B
82 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Existing Reactive Power Issues

increases its real power output to 983.2 MW and decreases its reactive

power to 181.9 Mvar. Because it is now providing more real power than

Generator B, and because its production costs are cheaper than Generator

B, the system cost is reduced by $4,551/h, or 22 percent, to $15,196/hr. The

per-unit voltage level at Bus A increases to 0.94 pu, which is still below, but

closer to, the target voltage of 1.00 pu. This is because, again, there are

other system constraints that must be enforced. Losses over the line decrease

for both real and reactive power; the line consumes 50.3 MW and 72.4

Mvar.

Case 2

MW 

Mvar 

Source: Derived from PowerWorld

It is interesting to note what happens to the revenue of Generator A. Going

from Case 1 to Case 2, Generator A produces more reactive power to allow

more real power production from Generator B, thus reducing system costs.

At the same time, Generator A is forced to back down its production of real

power by 67 MW not only because it is being displaced by Generator B, but

also because it is forced to comply with its operating constraints. Lost revenue

as a result of this decreased real power output is (67 MW) x ($80/MWh) =

$5,360/hr, in this example. If Generator A is not compensated for reactive

power production, there is no incentive for it to back down real power.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 83

Existing Reactive Power Issues

Figure 1. Generator A D-Curve and Operating Points, Case 1 and 2

Source: FERC Staff

The marginal price of reactive power is shown to be $13.13 per Mvarh.

This is the increase in system cost as a result of increasing demand for reactive

power by 1 Mvar at Bus A. If demand for reactive power is actually increased

to 501 Mvar, the following changes take place: Generator B produces 0.2

MW more of real power in order to free-up capacity on the transmission

line. Generator A produces 0.3 MW less of real power – less is needed as a

result of the increased real power production at Bus B – but injects more

reactive power to supply the increased load at Bus B. The new real power

dispatch causes a change in system cost; the increase of 0.2 MW at Generator

A costs $16, and the decrease of 0.3 MW at Generator B reduces cost by

$3. The total change in system cost is $13 (within rounding), the marginal

cost of reactive power at Bus A .

Why doesn’t Generator A produce its full 400 Mvar? Presumably, this would

further increase line capacity available for cheap real power from Generator

B and reduce the system cost further. The reason for this is the transmission
84 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Existing Reactive Power Issues

line constraint. If Generator A is forced to produce 400 Mvar, its real power

production falls to 50 MW, and 1002.1 MW is required from Generator B

since losses or consumption in transmission are about 50 MW. However,

some reactive power is still needed from Generator B, and in order to fulfill

both real and reactive load at Bus A the transmission line will become

overloaded. The only way to relieve the congestion, and still respect the

physical limits of the generator, is to increase real power and decrease reactive

power production at Generator A, moving along the D-curve until the

constraint is alleviated. Incidentally, this is the same reasoning behind the

system response to increased reactive power demand at Bus A, discussed

above. The increased demand is not supplied by Generator A because that

would require a reduction in real power, requiring in turn an increase of

real flow from Bus B to Bus A, which would overload the transmission line.

Voltage targets defined by the system operator have an impact on system

dispatch and costs as well. Case 3 allows the target voltage level to rise to

1.05 pu at Bus B and, as a result of system response, reduces costs relative

to Case 2 by $581, an additional 4 percent, to $14,615. An additional benefit

of loosening the voltage requirement at Bus B is that the voltage level at bus

A rises to .99 pu. The system operator can effectively place a value on

system reliability by choosing at what cost it is willing to adjust its desired

voltage levels.

Case 3

MW 

Mvar 

Source: Derived from PowerWorld
Federal Energy Regulatory Commission Staff Report •February 4, 2005 85

CHAPTER 6 Pricing and Procurement Options for Reactive Power

Pricing and Procurement Options for Reactive Power

After the reliability needs of the system have been determined, the goal

of reactive power pricing and procurement should be to encourage

two efficient outcomes. First, it should encourage efficient and reliable

investment in the infrastructure needed to maintain the reliability of the

transmission system. Second, it should provide incentives for the reliable

and efficient production and consumption of reactive power from the existing

available infrastructure, taking into account the opportunity costs of the

provision of competing uses of the available resources (such as real power

and operating reserves). Additionally, it is important that any pricing system

allows the system operator real-time control over reactive power resources.

While pricing rules should complement the reliability needs of the system, in

some situations, the system operator may need to adjust reactive power

resources, applying out of market dispatch instructions during system

emergencies.

In both independent system operator (ISO) and non-ISO markets, reactive

power capability is paid on a cost-of-service basis to transmission suppliers.

Transmission elements that supply reactive power generally have their costs

rolled into transmission charges or into the regulated retail rate structure.

Generation suppliers are paid for reactive power through reliability-mustrun (RMR) contracts, cost-based payments or not at all. In some ISO and

non-ISO markets, generators have reactive power obligations based on their

interconnection and/or participating generator agreements with the system

operator. These generators have reactive power obligations and are required

to supply reactive power with out additional compensation.

To maintain the reliability of the system, real-time reactive power supply is

needed as well as reactive power capacity to serve as reserves. We review

three different approaches to pricing the supply of reactive power capability

and real-time reactive power supply. To procure needed reserves and supply

of reactive power, the pricing approaches can be applied comparably for

transmission, generation and load.
86 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Pricing and Procurement Options for Reactive Power

1. Cost-of-service payments

a. Uniformly to all suppliers

b. To those suppliers that fulfill an identified system need

2. Prices from a forward auction process

3. No payment to generation or load sources, payments to transmission

sources

To price the real-time supply of reactive power sources, we review four

possible approaches.

1. No payment for supply within a required bandwidth or capability

level

2. Payment of lost opportunity costs (such as forgone real-power sales)

3. Locationally specific market clearing prices based on either on bids

or opportunity costs

4. Fixed price schedule developed in advance

a. Uniform price

b. Unit-specific basis

General Pricing Principles and Regulatory Intervention

1. Efficient Investment and Regulatory Intervention. The decision to make

a private investment, or for the government to make or force an investment

or to otherwise intervene in the market, is typically based on a cost-benefit

analysis. For private firms, the cost-benefit analysis becomes an expected

profitability and risk analysis. In a private enterprise economy, government

intervention should come only in anticipation of or after a significant market

failure. A market failure is said to occur when the market outcomes deviate

from efficient outcomes.

When a market cannot be efficient without government regulation, it is

considered a market failure. Regulatory or other government interventions

offer potential solutions to market failures, which can result from the effects

of externalities, public goods, market power and information imperfections.

Reactive power markets today are the product of the regulatory framework

based on the perceived economies of scale and scope of the electric utility

industry.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 87

Pricing and Procurement Options for Reactive Power

Externalities occur when the actions of market participants are not priced

into the market. If left to itself, the market will supply less of a public good

than desirable and more of a product with negative externalities than

desirable. Examples of public goods are roads, local police, clean air, national

security and electric reliability.

Market power can also lead to inefficient market outcomes. Market power

occurs when market participants can influence the price. Market power

occurs naturally if there are economies of scale or scope. Market power is

exercised by sellers when less of a good is produced to drive up the market

price. Market power is exercised by buyers when less of a good is purchased

to drive down the market price. Market power also is created when the

government awards a monopoly franchise that legally prohibits competition

as in the case of system operators and utilities. In many markets, reactive

power is supplied, in effect, by franchise monopolies.

Information asymmetries can also lead to market failure. Information

asymmetries occur when all market participants do not have the same

information. When the access to market information is controlled by a market

participant, inefficient outcomes can arise. Information asymmetries are

corrected by ISOs via the information it publishes on public Web sites. For

a vertically integrated utility, affiliate rules are a weak “second best”

approach to avoiding information asymmetries. Market participants need

good information to make efficient decisions. Information concerning reactive

power is typically either not calculated or not disseminated widely. There is

very little public information regarding the specific needs for and deployment

of reactive power.

2. Efficient Regulation Criteria. When significant market failures occur, the

government or coalitions of market participants often intervene with

additional rules, market designs or investments to move the market back to

more efficient outcomes. In futures and stock markets, the exchanges make

rules overseen by the U.S. Securities and Exchange Commission (SEC) and

the Commodities Futures and Trading Commission (CFTC). In wholesale

electricity markets, the FERC both makes the rules and oversees the market

rules.
88 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Pricing and Procurement Options for Reactive Power

Public investment should be made at the lowest efficient cost. Procurement

auctions and competitive contracts are used to procure the needs at the

lowest cost. Auctions are prominent in highway construction and defense

procurement. Regulated franchised monopolies are also used to make

investments. Competitive hiring is used for personnel needs.

Public investment must be paid for. Public goods can have locational

dimensions. One pricing principle is that those who benefit pay in proportion

to the benefit. For example, one difference between local police and national

defense is who pays. Local police and other first responders are usually

paid for by the local community, but national defense is paid for by the

entire country from general federal tax revenues. It is also common in the

United States to have multistate regional organizations for activities such

as water or transportation management. For electricity, ISOs and regional

transmission organizations (RTOs) fill that niche between purely local or

state organizations and the federal government.

Generally, private firms have little ability or incentive to correct market

failures. Traditionally, the market power of franchised monopolies was

mitigated by cost-of-service pricing. When formerly franchised monopolies

are exposed to competition, cost-of-service pricing often breaks down

revealing higher prices than the competition creates, which in turn gives

rise to stranded costs.

For externalities and public goods, the market design should result in prices

through which those benefiting are paying for the public good and those

causing externalities pay for the damage caused. Pollution externalities are

often priced by taxes on pollutants (also known as Pigouvian taxes) or in

cap-and-trade markets, e.g., SO2

 and NOX, where the government decides

the level of pollution and monitors for compliance. In these markets, market

participants are allowed to create or purchase and store pollution credits

for future use.When roads or other transportation systems become congested,

they lose their public good quality.

When market failures are addressed through regulatory market rules and

requirements - especially with minimal intervention - residual competition

can provide an opportunity for efficient market outcomes.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 89

Pricing and Procurement Options for Reactive Power

3. Market Rules and Regulation to Simulate Efficient Outcomes. In the

absence of externalities, competitive markets result in an efficient allocation

of resources. Perfectly competitive markets are characterized by a large

number of small buyers and sellers. None of the individual actions by market

participants can impact the price. All market participants have perfect

information in competitive markets as well as no barriers to entry and exit.

The prices that result from these markets are determined at the level at

which supply meets demand, and move instantaneously to maintain this

equilibrium balance.

In regulating reactive power markets, an important question is whether

reactive power prices should include the characteristics of prices in

competitive markets, which encourage efficient outcomes. These

characteristics arise naturally in competitive markets because of market

pressures, without imposition from government regulation. In markets that

are not structurally competitive, market designs such as auctions are used

to obtain desired outcomes. In electricity markets, two desired outcomes

are efficiency and reliability.

There are three key characteristics of competitive markets:

First, prices in competitive markets tend to reflect sellers’ marginal costs.

Such prices send desirable signals to market participants. This characteristic

helps ensure that the efficient amount of output is produced and consumed.

That is, output is produced only when the product’s value to market

participants at least matches the cost of producing the incremental output.

During shortage periods (also identified as scarcity situations that may

include unplanned outages), competitive prices will be determined by the

marginal customers’ value of consumption, meaning that competitive prices

are set by the demand curve when the supply runs low. At these times,

prices will exceed the marginal cost of production, but reflect the marginal

value on the load side.

By contrast, prices in noncompetitive markets can exceed the marginal cost

during nonscarcity conditions. The higher noncompetitive prices reduce

demand that could have been met at a cost less than the value to consumers.

In markets without significant market power, competition keeps prices near

marginal cost, because if prices rise above the marginal cost of the most
90 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Pricing and Procurement Options for Reactive Power

expensive supplier needed, sellers with spare capacity below the price will

offer their spare output to the market and thereby reduce the price.

Second, in a competitive market, all sellers (at any given time and place)

receive the same price for the same product. This feature ensures that the

demand is met by the lowest-cost producers. Any seller whose costs exceed

the price would face pressure to exit the market. Competition keeps prices

the same to all market participants. No seller would willingly sell below the

market-clearing price and no buyer would willingly pay more than the

market-clearing price. However, where sellers face economies of scale or

scope, price discrimination among buyers may be necessary in order to allow

efficient sellers to recover their costs and give buyers the lowest overall

costs.

Finally, long-term contract prices tend to reflect expected future real time

market prices. If contract prices were significantly higher than expected

real time prices, market participants would refuse to sign contracts because

they would expect lower costs in the real time market. Conversely, if contract

prices were lower than expected real time prices, load-serving entities (LSEs)

would abandon real time purchases in favor of the lower contract price.

Decisions to enter into long-term contracts also include the risk tolerance of

buyers and sellers.

There are at least two ways to compensate reactive power providers. One

way is to pay them in advance for their reactive power capability (capacity).

This is the typical way that most providers are compensated currently. The

pricing options for the short-run supply of reactive capability are discussed

below in this chapter. To complement or supplement compensation for

reactive power supply capacity there may be useful reasons to price realtime reactive power supply particularly for generation resources that can

provide reactive power. The pricing options for the short-run supply of

reactive power are discussed following the capacity options in this chapter.

While it is possible to rely on only one of these ways, the methods are not

mutually exclusive, and indeed there may be benefits to using both methods.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 91

Pricing and Procurement Options for Reactive Power

Options for Pricing Reactive Power Capacity

Once the reliability coordinator or planning authority has identified the

reliability need, there are several approaches to pricing the supply of reactive

power capacity that meets this need. The pricing alternatives for reactive

power supply may be applied locationally to all sources of reactive power,

such as generation, distributed generation, capacitors and FACTS. The

pricing rules potentially may be applied differently to differing supply

resources based on their operating and supply characteristics. Further,

differing options may be used to compensate differing capacity supply types.

For instance, static and dynamic reactive power capacity may be priced

differently.

There are additional options regarding the time frame in which reactive

power capacity should be procured. One approach to procurement would

incorporate the reactive power planning process and procure needed capacity

on a long-term basis based on forward planning criteria. Another approach

could shorten the time frame and allow shorter term procurement periods

such as an annual procurement. Differing approaches may also be taken

with regard to static versus dynamic reactive power supplies.

A reactive capacity requirement framework for reactive power supply that

parallels existing ISO (real power) capacity markets may be useful in

developing adequate reactive power capacity. The current ISO (real power)

capacity requirements exist to ensure that adequate generation resources

are available in the system to maintain a desired level of reliability. The

capacity product is intended, in part, to provide a market mechanism for

sufficient investment in generation resources that will be used in a limited

number of hours in a given year, but are needed for reliability on a planning

basis. In the absence of the capacity product, revenues may be insufficient

for fixed cost recovery (absent the exercise of market power). This is not

generally viewed as a desirable market feature and does not ensure a desirable

level of reliability. Dynamic reactive power capacity serves a similar purpose.

Investments in dynamic reactive power capacity serve a valuable reliability

role in the system operation. Yet, the system operator may rarely need to

dispatch the dynamic reactive power resource, thus the capacity requirement
92 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Pricing and Procurement Options for Reactive Power

framework can provide a transparent mechanism to ensure that adequate

reactive capability is available to maintain system reliability.

1. Cost-Based Capacity Payment. A cost-of-service compensation package

can be developed to compensate suppliers for available reactive power

capacity. Reactive power suppliers would be obligated to make their reactive

power capacity available to the system operator in exchange for the

payment.

There are two primary approaches in deciding which suppliers are eligible

for the cost-of-service capacity payment. First, all suppliers of reactive

power capacity could be eligible to receive payment from the system operator.

Second, the system operator could pay only those suppliers that it identifies

as providing needed reactive power capability to the system.

The first option, a blanket cost-of-service payment for all available reactive

power capacity, may not result in reactive power capacity investments being

targeted to areas that need it. Because the compensation for reactive power

capacity is not closely related to the need for the capacity, there may be

overinvestment in areas that do not require additional reactive power and

underinvestment in areas that are in need. However, this approach avoids

questions regarding inequitable treatment among market suppliers

particularly generators. Some potential reactive power suppliers argue that

decisions of need by system operators are not made in a fair, least-cost and

nondiscriminatory manner.

The second, cost-based approach would be to have the system operator

procure all reactive power capacity needs through cost-of-service payments.

This approach would require a clear needs assessment. This approach gives

the system operator the ability to target its needs and avoid the costs of

procuring resources above the system needs. The cost-of-service

arrangements could be made on an annual basis, as is done in some areas

through RMR contracts to supply reactive power. Alternatively, the payment

structure could be over the life of the asset as is traditionally done for

transmission source of reactive power. However, this approach by the system

operator may have the ability to give preferential access to these cost-based

payments to select suppliers. In this case mechanisms to incent efficient and
Federal Energy Regulatory Commission Staff Report •February 4, 2005 93

Pricing and Procurement Options for Reactive Power

non-discriminatory procurement are needed. It is important to allow all

solutions to compete to provide the least cost solution to the identified need.

2. Explicit Payment for Reactive Power Capacity through Systemwide

Forward Procurement. The system operator could hold an auction for reactive

power capacity in which suppliers would be compensated for a commitment

to make reactive power capacity available to the system. This payment

would be for a physical call option on the capacity, and the actual supply

would either be without further compensation or among the options outlined

later in this chapter. This approach allows competition among generation

and transmission elements to supply reactive power needs.

Requirements would likely be set locally, based on the needs determined by

the system operator. This would allow prices to reflect the locational value

of reactive power capacity and avoid paying for excess capacity in areas

that do not need it. The length of the procurement term may differ based on

an evaluation of the market characteristics and competitive alternatives.

For instance, if efficient alternatives can compete to fulfill the need with

relatively low capital costs or with mobile infrastructure (such as mobile

SVCs) a shorter term procurement period may be advantageous. However,

if significant barriers to entry exist for entry a longer term procurement

period may be most effective. In instances where locational market power

exists, cost based offers could be required to prevent the exercise of market

power.

The forward procurement of reactive capability could be part of an overall

forward resource adequacy procurement process. PJM is in the process of

developing a proposal that would procure capacity obligations in advance

through a forward auction. The proposal currently includes operational

constraints that must be met as part of the auction’s solution. Suppliers

would be paid a premium for providing operational flexibility to the system

if the auction determines that a premium payment is needed. Reactive power

capacity needs could also be built into this type of framework to ensure

adequate procurement of reactive power capability in advance. Prices would

be low or even zero if there existed excess supplies of the operational

capability, and would rise when the capability was in shorter supply. The

forward procurement would allow the opportunity for existing participants
94 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Pricing and Procurement Options for Reactive Power

to incorporate incremental future investment opportunities into their bids

and allow new investment to compete as well.

3. Pay Nothing to Generators; Pay Cost-of-Service/Forward Procurement

for Transmission Solutions. Finally, we could rely on regulatory mandates

on all generators to supply reactive power without further compensation

and rely solely on cost-of-service transmission procurement by the system

operator. Under this option there would be an obligation by generation

resources to supply reactive power through a generation interconnection

agreement or some other capacity obligation. Transmission solutions to

meet reactive power needs could either be procured through cost of service

investment or forward market based procurement.

For systems that have installed capacity (ICAP) requirements, the obligation

to hold reactive power capability or to supply reactive power can be part of

the generators’ obligation as a capacity supplier. No supplemental payment

for reactive capacity would be made. This mechanism will result in

investment to jointly supply the real and reactive capacity needs. Generation,

transmission and load can participate to meet these requirements. The costs

of this investment will be passed through via capacity prices. Locational

requirements for real and reactive power may not be coincident, however.

Reactive power tends to be more location specific and the locational capacity

needs for real power will not necessarily ensure that locational needs for

reactive power are met. Therefore, capacity needs for real and reactive

power may be most efficiently procured separately.

Ultimately, under this option, the new generation may be designed with

only minimum reactive power capability and will result in a need to over

invest in transmission assets even when generation based solutions would

be less costly. Further, generation resources that could provide valuable

reactive capability to a local area will have no incentive to incorporate this

value into its locational investment decision and may choose to locate in a

less costly area that has lower reactive need.

Under each of the three options, penalty mechanisms for nonperformance

will need to exist and will need to be adequately enforceable. Reactive

power suppliers would be expected to supply reactive power at the instruction
Federal Energy Regulatory Commission Staff Report •February 4, 2005 95

Pricing and Procurement Options for Reactive Power

of the system operator for the benefit of the system. While nearly all market

participants are adversely impacted by a system collapse, the short term

incentives to supply real power (which receives compensation) rather than

reactive power could lead to inadequate reactive power supply in times in

which there is an opportunity cost to reactive power supply. Additionally,

lack of compensation real-time mechanisms may lead to reduced maintenance

incentives that adversely affect a unit’s ability to supply reactive power

when it is needed most.

Real-Time Pricing of Reactive Power

There are several approaches to pricing the short-run supply of reactive

power in ISO markets. These pricing options may replace or complement

the revenues from supply of reactive power capacity described in section C.

The pricing alternatives for reactive power supply may be applied locationally

to all sources of reactive power, including generation, distributed generation,

capacitors, FACTS and others.

1. Background. Currently, very little reactive power procured in real-time

receives any payment. Rather, transmission providers and system operators

procure reactive power from a combination of owned assets and generators

that are required to provide reactive power as a condition of their

interconnection to a grid. To the extent that suppliers are compensated for

reactive power in real-time, it occurs in some ISOs that pay generators for

their individual lost opportunity costs when supplying reactive power. Realtime prices and compensation for reactive power should reflect real-time

costs incurred with the actual supply of and opportunity costs of supplying

needed reactive power, not market power.

Pricing reactive power supply in real-time is generally more complex than

paying for capacity. Approaches to reactive power pricing must take into

account the benefits and the costs of each method. Simple pricing rules,

such as not paying for real-time reactive power supply are the least complex

to implement, but may not lead to efficient reactive power investment

decisions and dispatch. However, more complex approaches may introduce

technical challenges and bring with it the need for additional market power

mitigation rules to achieve the potential efficiency gains. Additionally, more
96 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Pricing and Procurement Options for Reactive Power

complex real-time solutions will require additional software development,

well defined reactive power standards, and significant policy discussion

before the possibility of implementation.

Benefits of Spot Compensation. There is often more than one source for

obtaining reactive power at a given place and time, and some market

participants can adjust their consumption of reactive power. Establishing a

real-time reactive power price reflecting the market’s locational marginal

cost could encourage efficient decisions by market participants. It would

encourage the lowest-cost suppliers to provide the reactive power. It would

also encourage consumers of reactive power to evaluate their net

consumption of reactive power, consuming it when the price is worth the

value and reducing their consumption when the price is higher than the

value.72

Reactive power equipment, especially static equipment such as capacitors,

cannot switch instantaneously. Frequent switching of such equipment

increases wear and tear and reduces the lifetime of the equipment. Realtime pricing systems for reactive power could need to take this into account,

with factors similar to minimum up and down times used in generator

commitment for ISO power markets.

Marginal Cost Pricing in Real-time. Marginal-cost pricing may not

compensate suppliers for the full cost of reactive power (including capital

costs) over the long run. In fact, the prices of real-time reactive power

supply during most times may be close to zero. To supplement real-time

revenues a payment such as those detailed above would likely still be needed

to ensure adequate investment.

The marginal cost of providing reactive power from within a generator’s

capability curve (D-curve) is near zero. However, the suppliers’ capital

costs may be significant. Similarly, installed transmission resources (such

as capacitors) have minimal costs beyond the initial capital expenditures.

Under both cases real-time prices that reflected the operating costs would

be at or near zero. The suppliers’ full costs are unlikely to be recovered

over time unless the prices were sufficiently high at times when prices were

positive.73 If reactive power prices are not compensatory in total, investment

72 Practically speaking, load

that consumes measurable

reactive power would

typically correct this problem

with the installation of

capacitors. Once installed,

these units would provide the

consumer with its reactive

power needs. The system

operator could turn off such

devices if lower voltage levels

were desired.

73 The characteristics of the

capacitor investment may

make it a lumpy investment.

The efficient investment size

may eliminate the reactive

power shortage in most

periods.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 97

Pricing and Procurement Options for Reactive Power

in capacity to provide reactive power is likely to be inadequate over the

long term. An available approach is to use a real-time procurement and

pricing to complement a capacity based procurement for reactive power.

The capacity market would in this case be the primary vehicle for fixed cost

recovery, while the spot revenues would cover any short-term operating

costs and potentially provide contributions to fixed costs.

Market Power, Bidding Constraints. Competitive markets are composed

of buyers and sellers that are unable to control prices. This assumption does

not necessarily hold in the supply of reactive power. Suppliers of reactive

power may have significant market power at times because reactive power

is difficult to move over long distances during heavy line loading due to the

consumption of reactive power by the transmission lines. Additionally, at

high loadings, power traveling over transmission lines results in greater

relative reactive power losses than relative real power losses, further limiting

the ability to use distant resources to supply reactive power. As a result,

fewer suppliers are ordinarily available to provide the reactive power needed

at any individual location, particularly in peak loading periods. However,

the narrow geographic definition of a reactive power market may be offset

by the potential additional suppliers. For instance, generation, transmission

and load can all install devices that produce and consume reactive power.

Nevertheless, regulation or market power mitigation may be needed to

prevent reactive power prices from reflecting an exercise of market power.

Forward Procurement and Hedging. Many products and services - including

real power - are bought and sold in both real-time and forward contract

markets. Forward contract markets allow market participants to lock in

trades in advance and hedge risk; real-time markets allow participants to

adjust their forward positions as market conditions change, making it less

risky to enter into forward contracts. Importantly, real-time markets for

real power help facilitate reliably meeting demand with the lowest-cost

resources that are available in real time. Resources committed to supply

under contract may be more expensive than other resources available in

real time. The real-time market allows expensive contract resources to

transfer their responsibilities to lower-cost resources, allowing both resources

to benefit. Also, open real-time markets operated by ISOs provide transparent

real-time prices that help provide a point of reference in negotiating contract
98 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Pricing and Procurement Options for Reactive Power

prices. Real-time markets could potentially provide similar benefits for

procuring reactive power until the forward markets stabilize.

To mitigate suppliers’ reactive market power, mitigation mechanisms could

be in place to ensure that suppliers’ bids reflected their marginal costs

(including opportunity costs). For instance, supply offers within a generator’s

capability curve could be restricted to a level near zero because no significant

opportunity costs exist in the supply of reactive power. Bids for reactive

power outside this range could be restricted to opportunity costs based on

the physical attributes of the unit’s capability curve (for more detail see

appendices B and D). Under this approach cost of service transmission

elements would also offer reactive capability at incremental costs (for more

detail see appendices C and D). The result would be prices that reflect the

marginal cost of delivering real and reactive power to each location.

Because the system operator is the primary procurer of reactive power, it is

likely to have monopsony power and the ability to affect the price.

Additionally, the system operator may also be a competing market

participant in the generation or transmission reactive power supply

resources. However, much of the real-time needs should be an automated

feature based on the system operator’s dispatch software and, thus, not

likely to be subject to manipulation by the system operator. Auditing of the

system inputs and parameters may, however, be necessary in situations where

the operator is a market participant. Clear, transparent and nondiscriminatory

procurement rules would be needed to overcome this conflict.

Transaction, Hardware and Software System Costs. The transaction and

investment costs associated with the development of a locational real-time

pricing differ by option. For instance, it is possible that the transaction

costs associated with the development of a locational real-time market for

reactive power supply that parallels existing real-time energy markets may

outweigh the potential benefits. It may be argued that the associated

software and hardware costs for implementation, together with the software

and hardware costs of the mitigation procedures and the staff costs of market

monitoring, outweigh the efficiency gains. Whether this is or is not true is

an open question and worthy of further investigation as reactive power

policies are developed.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 99

Pricing and Procurement Options for Reactive Power

2. Payment Options For Real-Time Supply Obligation. There are several

approaches to pricing the short-run supply of reactive power. These pricing

options may replace or complement the revenues from supply of reactive

power capacity described above. The pricing alternatives for reactive power

supply may be applied locationally to all sources of reactive power, including

generation, distributed generation, capacitors, FACTS and others.

No Payment for Production within Bandwidth/Physical Rating. One

approach is to mandate that reactive power be supplied within a fixed range

at no additional cost. This generally corresponds with the existing practices

where reactive power capability may be paid for, but real-time reactive

power supply is not compensated.

System operators would have the ability to dispatch running generation

units to supply reactive power within the bandwidth without further

compensation. Revenue to support the investment would come from the

pricing of reactive power capacity or expected infra-marginal energy sales

that contribute to a supplier’s fixed cost (in the case of generation sources).

For transmission elements such as capacitors and FACTS devices, the required

supply bandwidth could simply correspond with the physical rating of the

element. The system operator would have control over the elements and

use them to meet the system voltage needs. The transmission facilities would

receive no additional compensation based on their use. Again, as for

generation resources, the capital cost recovery would be generated from

the pricing of reactive power capacity.

For generation, the bandwidth requirement may be based on the capacity

sold in advance or based on an administratively determined fixed range

measured at the high side of the step up transformer. The fixed range could

be based on a universal generator power factor or a fixed percentage of the

unit’s maximum output. If this fixed range is within the generator’s nameplate

power factor, the incremental cost to the generator will generally be limited

to losses as there will be little or no forgone real energy output. Under this

approach, a generator with a nameplate power factor lower than the

requirement may incur significant lost opportunity costs due to reductions

of real power output in order to meet its obligation to supply reactive power.
100 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Pricing and Procurement Options for Reactive Power

This approach would allow a generator to evaluate its investment in the

infrastructure needs to supply reactive power. For instance, a supplier may

choose an oversized turbine to maximize the real power output of the

generator at a unity power factor. However, in operation this configuration

may expose the supplier to higher opportunity costs to supply reactive power

as it may have to back down real power supply to meet its reactive power

supply obligation. In this case, it will not be in the generator’s financial

interest to follow dispatch instructions absent an ex-post penalty structure

and may not be the most economical way of achieving the desired result.

Further, backing down real power output in peak periods may be

problematic.

Investment to increase reactive power capability by generation resources

would be determined jointly by the payment structure for reactive power

capacity and the expected trade-offs between increased capital expenditures

to relax the D-curve constraints and lost energy sales from required reactive

power supply.

This pricing approach would also be consistent with a contract with RMR

resources74 that are paid a cost-of-service rate for the supply of reactive

power capacity and receive no specific revenues associated with the quantity

of reactive power supplied.

While the system operator could procure reactive power from suppliers at

no charge within the band, opportunity cost payments for reactive power

would be needed at a minimum for supplies outside of the band.

Overall, this approach requires little development of additional software

and minimal settlement costs because most participants will not receive

payment. Real-time market power concerns are also not of significance,

however, the potential for physical withholding remains. Lack of payment

could result in reduced maintenance incentives and lead to inefficient

investment decisions.

Opportunity Cost Payments. A second approach to pricing reactive power

would pay lost opportunity cost for supplying reactive power. For

transmission elements this price is at or near zero and as a result they would

74 Reliability-must-run

(RMR) units have

traditionally been units that

do not receive sufficient

revenues through the

markets to remain profitable

but are needed to maintain

the reliability of the system.

Often these units have

market power, but are

prevented from the exercise

of market power through

mitigation rules. Inadequate

market pricing mechanisms

can prevent adequate

revenues from the market for

these specific units. RMR

contracts between the system

operator and the RMR

generator ensure adequate

revenues and cost recovery,

but fail to send a signal to

the market in cases where

new infrastructure is needed.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 101

Pricing and Procurement Options for Reactive Power

receive little or no payment. Generation resources may, however, experience

real-time opportunity costs in supplying reactive power in real time. Most

ISOs have such payment mechanisms in their tariff. To date, this tool has

not been widely used in those areas that have such mechanisms.

Any supply of reactive power that resulted in reduced real output would be

compensated based on profits forgone from the real power sale lost based

on the D-curve constraint. This approach might result in differing payments

to suppliers offering the same quality of reactive power because payment

would be based on each supplier’s own unique lost opportunity cost of forgone

energy sales. Such an approach will not encourage investment in the

infrastructure needed by generators to supply reactive power because there

may be no contribution to fixed costs from reactive power sales. Investment

would likely only come as a result of interconnection obligations or through

payments for reactive power capacity. In fact, an existing unit may have an

incentive to increase the turbine size to increase the capacity of real power

output at the expense of the unit’s power factor. If there is no compensation

or obligation to provide reactive capability then there is no incentive for the

generation owner to provide the reactive power service that avoids any

opportunity cost of real power.

Market Clearing Prices. Another approach would be to pay all suppliers

the applicable market clearing price analogous to locational payments for

real power. This approach could be applied to both generation and

transmission sources of reactive power. Revenue collected from cost-ofservice reactive power supplies could be credited back to the applicable

customers.

In this case, suppliers will have the incentive to voluntarily invest in reactive

power capability because the market clearing mechanism could provide some

fixed cost recovery for investment in reactive power capability. This market

design could also accommodate the demand, or load, side. Because all

reactive power would be priced reactive power, potentially large revenue

transfers are possible as suppliers receive payment for all reactive power

supply. With real-time prices come incentives to make investments (e.g., in

capacitors) to hedge these prices; however, because the price may be zero

most of the time such needed investment and hedging may only occur after
102 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Pricing and Procurement Options for Reactive Power

a shortage condition becomes apparent. Reactive power would be paid for

to support the reactive power use of the transmission system and load.

The process could be viewed as an extension of the traditional co-optimization

of real power and operating reserves, which results in dispatch instructions

that are consistent with the pricing signals. For instance, a supplier of

ancillary services receives a price from the market that takes into account

any lost opportunity cost of not supplying energy and thus has the incentive

to supply the reserves rather than energy. Similar pricing can occur for

reactive power. The price could be established in either of two ways.

i. Bid-Based

Suppliers could bid reactive power prices and quantities into the market

and receive a market clearing price for the quantity supplied. Because

real and reactive power are jointly produced, the structure of these bids

could be complex. Because the D-curve determines the feasible set of

real and reactive power production, separate independent price quantity

bids for real and reactive power are likely to lead to infeasible or

inefficient dispatch instruction. Merchant transmission elements could

also offer reactive services under this approach.

ii. Based on Highest Opportunity Costs

This approach would allow suppliers to be paid a price based on the

highest opportunity costs of those participants supplying reactive power

to the market while meeting the system needs at lowest total (bid) cost.

As mentioned above, the cost to supply reactive power by most

transmission elements is zero and as such would generally be restricted

to bids at or near zero under this approach.

Because real and reactive power are jointly produced by generation sources,

their bids would be composed of a real power supply curve and the applicable

capability curve (D-curve). More detail on this is contained in the technical

appendices. Suppliers will have the incentive to voluntarily invest in reactive

power capability because the market clearing mechanism could provide fixedcost recovery. Those responsible for reactive power consumption, both enduse and transmission-related, should pay for the supply.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 103

Pricing and Procurement Options for Reactive Power

A more sophisticated alternative might even allow bids for reactive power

supply outside of the standard D-curve operating parameters to meet system

needs during scarcity situations. Such supply bids could compensate

generators for additional wear and tear on the unit for supplies outside of

the standard operating bounds of the unit. This might be particularly useful

in emergency conditions to maintain reliability and avoid voltage collapse.

Allowing market clearing prices also could support bids by load and

transmission suppliers. This may provide increased reliability during critical

times. For instance, a transmission owner may be willing to incur the

additional maintenance costs of running equipment beyond normal operating

parameters for a period of time in exchange for the additional compensation

from the reactive power market. Additionally, load response resources could

also benefit from such pricing. For instance, reduced air-conditioning load

during peak periods can provide valuable relief to a system’s reactive power needs.

Developing software to allow efficient pricing of reactive power in real

time could be a barrier to developing a real-time market. Additional software

development will be needed to implement an approach that simultaneously

optimizes real power, reactive power and voltage levels. However, it is

unclear whether the benefits of such development would warrant the

investment costs in terms of software development and market complexity.

The opportunities for short-run efficiency gains from the system, however,

are difficult to deny. The development of software for improved reliability

and pricing tools are joint costs. The market and reliability needs are driven

from the same underlying system constraints. Software development taking

both needs into account can provide market participants with lower total

system costs and provide more benefit than allowing the software for both

needs to be developed independently.

Administratively Determined Prices or Pricing Formula Announced in

Advance. Another method is to pay generators a predetermined price for

the reactive power, or a price based on a predetermined formula. This method

is currently used in several countries. These administratively determined

prices may include unit-specific cost-of-service payments based on a common

rate formula. They may also be location specific or may feature a uniform

systemwide price for supply.
104 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Pricing and Procurement Options for Reactive Power

This approach would provide an incentive for reactive power suppliers to

be available to the extent that the payment exceeded the marginal costs of

supply. However, it is possible that when the system is most stressed, the

opportunity costs are likely to be the highest. Thus, the incentive to supply

reactive power may not be there when it is needed most. Further, in normal

operating periods, prices significantly different than actual operating costs

can lead to inefficient dispatch and higher customer costs.

Pricing Options Summary

As noted, there at least two ways to compensate reactive power providers.

One way is to pay them in advance for their reactive power capability

(capacity) based on reliability needs. A second way is to pay them in real

time for their actual reactive power production and reserves. While it is

possible to rely on only one of these ways, the methods are not mutually

exclusive and, indeed, there may be benefits to using both methods. Each of

the approaches has its own particular advantages as well as drawbacks.

For instance, the pricing options that may show the most promise in terms

of market efficiency may have the highest administrative costs and introduce

complexity that is unacceptable to some market participants. Some of the

simpler and more traditional approaches to reactive power procurement

and pricing have some undesired incentives that lead to inefficient investment

due to poor market signals or the lack of an independent system operator.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 105

CHAPTER 7 Conclusions, Recommendations and Questions

Conclusions, Recommendations and Questions

Conclusions and Recommendations

Reactive power is important for the reliable operation of the bulk power

system. The value of reactive power is primarily for reliability, but it

can also allow additional transfer of real power. The value of reactive power

is highly locational, but this is not fully reflected in the Commission’s rate or

market designs. The optimal approach to reactive power market design

and reliability involves and links generation, transmission and load.

Earlier in the paper, in the Executive Summary and at the beginning of

Chapter 5, we identified six problems and concerns regarding the current

procurement practices and pricing policies for reactive power. We make

four broad recommendations to address these problems and concerns:

1. Reactive power reliability needs should be assessed locally, based on

clear national standards.

2. These needs should be procured in an efficient and reliable manner.

3. Those who benefit from the reactive power should be charged for it.

4. All providers of reactive power should be paid, and on a

nondiscriminatory basis.

Below, we discuss in more detail our recommendations to address these

problems and concerns.

1. Discriminatory compensation.

a. Transmission-based suppliers of reactive capability receive compensation,

yet many generation-based suppliers are not compensated for reactive

power capability that aids in system reliability.

b. Independent generation resources may not always be compensated

for providing reactive power support to the grid in areas where other

generators affiliated with vertically integrated transmission owners

receive cost-of-service payments for providing similar service, despite

the Commission’s policy requiring comparability.

Recommendation: All providers of reactive power, including owners of

transmission equipment, independent generators, and generators owned or
106 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Conclusions, Recommendations and Questions

affiliated with the transmission provider, should be paid on a

nondiscriminatory basis. In some control areas, generators owned by the

transmission provider are paid for reactive power while other generators

are not. Such discrimination is poor public policy and could be considered

to be undue discrimination under the Federal Power Act. Comparability

has been a bedrock principle of open access and competitive market

development. The Commission’s general policy favoring comparability

should apply in the reactive power context. Pricing and market design should

be independent of ownership. Thus, independent generators should be eligible

for the same compensation for reactive power as generators owned or

affiliated with the transmission provider providing comparable service.

Otherwise, the transmission provider’s generation will have an unfair

commercial advantage, independent power producers will have less incentive

to enter the market (even when they have lower costs) and the costs of

producing reactive power will be higher than necessary. Of course,

compensation should be based on the system’s needs for reactive power.

Order No. 888 was implemented when the merchant generation sector was

relatively small. In light of the Large Generator Interconnection Rule, the

Commission should review the methodology of Opinion No. 440 and, in

particular, its effect on investment incentives. Further, the Commission should

streamline the process for filing and collecting Opinion No. 440 rates to

eliminate the greater regulatory burden imposed on independent generators

for receiving reactive power compensation, relative to affiliated generators.

With the advent of new technology, equipment that supplies reactive power

comes in smaller increments and can be made mobile, e.g., truck mounted.

These characteristics allow for temporary or permanent solutions for

considerably less investment and lower sunk costs. Current entry rules are

a barrier to this technology. However, if this barrier were removed, market

power in reactive power markets could be a far smaller problem because

entry and exit could become much easier. We need a discussion of how this

affects the Commission’s policy on market design in general and for

transmission in particular.

2. Rigid but imprecise interconnection standards that are insensitive to local

needs. Interconnection standards generally require a standardized
Federal Energy Regulatory Commission Staff Report •February 4, 2005 107

Conclusions, Recommendations and Questions

generation power factor for new generation. But local needs often vary from

the standards. Some locations may have higher reactive power needs than

the standard, while other locations may have smaller needs. Moreover, the

standards are imprecise in important respects. For example, the standards

do not specify on which side of the step-up transformer, and exactly how,

the power factor is to be measured.

Recommendation: Clear and precise interconnection standards should be

developed that are sensitive to local needs, but that comply with generally

applicable national reliability standards.

3. Lack of transparency and consistency in planning and procurement. The

reactive power planning standards and procurement processes are not

transparent. Alternative solutions to provide needed reactive power

capability may be available, but currently these options might not be

adequately considered.

Recommendation: Current rules and definitions have different

interpretations and need to be more fully developed to avoid disputes and

poor investment decisions. For example, there appears to be no unambiguous

definition of the power factor requirement. Further, the power factor

requirement does not translate into the amount of reactive power that should

or could be available. “Good utility practice” is often invoked as the design

criteria for reactive power, but “good utility practice” is not well defined

and in most cases has not evolved at the same pace as the market. Full

discussion of the meaning of “good utility practice” for future reactive power

requirements is needed. Good citizenship and rules should not be the sole

approach to investment in reactive power capability.

Currently, system planning for reactive power and procuring reactive power

for reliability are less transparent than they could be. Transparency and

better documentation in system planning are needed to demystify the process

of planning for reactive power capability. Reactive power supply and

consumption, as well as prices, should be publicly reported. Marginal prices

are a simple calculation after the optimal power flow is calculated. They

are not costly to calculate and publish.
108 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Conclusions, Recommendations and Questions

4. Poor financial incentives to provide or consume reactive power.

a. Many market participants that could provide additional reactive power

capability to the system have little incentive to do so. Price signals that

could encourage additional investment are limited.

b. In many cases load response and load-side investment could reduce the

need for reactive power capability in the system, but incentives to

encourage efficient participation by load are limited.

Recommendation. The market design should align financial compensation

and incentives with desired outcomes to ensure that adequate reactive power

is available and produced in the right locations in order to maintain reliability

and meet load at the lowest reasonable cost. Some have a different view –

that independent generators should be obligated to provide a specified

minimum capability to produce reactive power without compensation as a

condition of interconnecting to the grid, but we think that this view will not

encourage optimal investment and production of reactive power. If

independent generators aren’t paid for providing reactive power capability,

some may elect not to enter the market, and some existing generators may

elect to retire sooner than if payments were made. Suppliers of reactive

power should be compensated for providing reactive power and reactive

power capability. Similarly, once capability payments are received, capability

tests for reactive power should be a routine part of reliability procedures

and penalties should be assessed for test failures. For the present, while

longer term options are being further studied, we recommend considering a

policy of paying market participants for the reactive power that they produce

on the system operator’s instruction based either on the unit’s own opportunity

cost or on an administratively determined price or price formula announced

in advance. Further, we recommend considering a policy of charging

consumers for consuming reactive power from the transmission system. Such

payments and charges would encourage market participants to produce or

consume reactive power where it is needed.

The market rules should allow greater compensation for reactive power

capability having greater quality and value, just as they do for real power

operating reserves. For example, reactive power capability from dynamic

sources is more valuable than from static sources, because dynamic sources

can adjust their production or consumption of reactive power much more
Federal Energy Regulatory Commission Staff Report •February 4, 2005 109

Conclusions, Recommendations and Questions

quickly when needed to maintain voltage and, thus, prevent a voltage

collapse. Thus, reactive capability from dynamic sources should be paid

more than capability from static sources at the same location. This is

consistent with the policy of paying higher prices for faster-response (and

thus, higher quality) operating reserves for real power. For example, 10-

minute spinning reserves are generally more valuable – and are generally

paid more – than 30-minute nonspinning reserves at the same location and

time because the former can respond to dispatch instruction more quickly

than the latter. However, reactive power that is actually produced or

consumed at a given location and time has the same value whether it is

provided by a static or dynamic source. Thus, the price faced by all reactive

power providers in a spot market at a given location and time should be the

same, regardless of the source. This policy is consistent with the approach

followed in spot auction markets for real power in ISO markets, where all

suppliers at a given location and time are paid the same price for their real

power production.

5. Poor incentives for some system operators to procure reactive power and

reactive power capability at least cost. System operators outside of RTOs

and ISOs that are regulated transmission owners may lack the incentives to

consider all available sources of reactive power. That is because cost-ofservice regulation generally rewards capital investment, even when

purchasing from a third party would be a less costly alternative.

Recommendation: The Commission should pay careful attention to ensure

that transmission providers procure reactive power supply and capability

at least cost, and that the rates charged by the transmission provider reflect

such least-cost procurement.

6. Failure of system operators to adjust reactive power instructions so as to

fully optimize the dispatch. Often, a range of reactive power production

levels would fully meet the reliability requirements of a transmission system.

However, system operators typically choose the level that meets specified

guidelines, even though other levels within the range would allow the demands

for real power to be met at a lower total cost. A related issue is that the

software for implementing such reactive power optimization is not currently

available.
110 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Conclusions, Recommendations and Questions

Recommendation: System operators should begin the process of developing

the capability for determining how to adjust reactive power levels so as to

fully optimize the dispatch. Part of this process would involve charging or

paying market participants for reactive power on a real-time basis. Complete,

efficient market design for reactive power could reduce overall costs

substantially. Some preliminary simulations reported in this paper suggest

that a fuller consideration of reactive power in real time spot markets in

conjunction with real power markets may have the potential to reduce the

total costs of meeting load. By not properly pricing reactive power, we may

be missing opportunities to further increase reliability and efficiency. Fully

incorporating reactive power in the dispatch decision through a bid-based

reactive power market is a relatively new idea, and we believe it is too soon

to implement one. This design needs a full and open discussion and some

empirical observation before additional steps are taken. Simulation and

experimentation are needed to better understand the effects of alternative

auction market designs for reactive power. The appendices attempt to lay

the groundwork for such a discussion. In addition, the software and other

costs of developing a reactive power auction market should be understood.

There is much speculation and little empirical knowledge of the value of

reactive power or what spot market prices for reactive power would be if

there were jointly optimized day-ahead and real-time markets for reactive

power. To provide better information on these values, RTOs and ISOs should

calculate reactive power marginal values (or prices) and post them on the

same basis as real power prices.

Short-term versus long-term reform. This paper is intended to begin a

discussion of regulatory policies affecting reactive power. Any changes in

policy resulting from this discussion are likely to take some time to implement.

Some changes are likely to be made more easily and quickly than others.

For example, policies that promote comparability are likely to be more easily

made, and we recommend working to implement them in the near term.

These policies include (1) clarifying the requirements and compensation rules

for providing reactive power, as well as the definitions underlying these

requirements and rules, (2) creating incentives that encourage desired

behavior, (3) streamlining the process for compensating independent
Federal Energy Regulatory Commission Staff Report •February 4, 2005 111

Conclusions, Recommendations and Questions

generators for reactive power capability and provision to make the process

comparable to that for affiliated generators and (4) making reactive power

procurement and compensation more transparent, for example by calculating

and publishing reactive power production, consumption and prices on a

comparable basis to real power. Other policy changes involve more complex

issues, and will require more time to consider. Policy changes that involve a

complete market redesign will thus need to be implemented over the longer

term. The ultimate goal should be an integrated set of co-optimized markets

with bilateral markets relatively free from federal regulation. This goal

requires research, software development, education and testing, and is likely

to require 5 to 10 years to fully implement.

Questions

We intend this paper to stimulate a public discussion about the proper

regulatory policy toward reactive power pricing and market design. To

help advance this dialogue, we invite public comment on the questions below.

General

Should transmission providers report the value of real and reactive

power on their systems? Would this help make better locational

investment decisions?

By not properly pricing reactive power, are we missing opportunities

to further increase reliability and efficiency?

Should reactive power reserves be differentiated by quality as are

real power reserves? Should dynamic reactive power be differentiated

from static reactive power?

What are the relationships and differences among standard

transmission assets, e.g., capacitors, FACTS devices and generators

in reactive power supplied? Where do FACTS fit in? What is the

effect of different outage rates?

How, what and when are dispatch signals for reactive power sent to

market participants?
112 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Conclusions, Recommendations and Questions

Should the general approach to voltage scheduling be reexamined to

improve reliability and efficiency?

Should generators be required to supply an identified range of

reactive power without compensation?

Reliability and Engineering

System Planning

How are reactive power reserves determined? How are reactive

power reserves quantified?

Do we have enough reactive power capability in our generators to

meet the reliability needs of our power system? If so, how do we

know?

What should the static reactive power capabilities (or reserves) be?

What should the dynamic reactive power capabilities be? What

should the reactive power capabilities be used for?

Should reactive power reserve requirements be locational and/or

better defined like real power reserves?

Should reactive power reserves be procured competitively?

Are there optimal design characteristics with respect to reactive

power for generators, transmission and load? If so, how are they

derived? Or, do they depend on system characteristics? If so, how

are they derived?

For Generation

What is “good utility practice” for reactive power supply and reserves

from generators?

What reactive power capabilities, if any, should be required of

generators without compensation?
Federal Energy Regulatory Commission Staff Report •February 4, 2005 113

Conclusions, Recommendations and Questions

Is a generic power factor requirement the best approach to reactive

power capabilities or should it be based on system requirements?

Are the interconnection standards with respect to reactive power

capability clear? Is it clear what it means to have a 0.95 power factor

requirement in the Large Generator Interconnection Procedures

(LGIP)?

Should the power factor requirement for generators be measured at

the high or the low side of the step-up transformer?

Should there be the reactive power requirements for non-synchronous

generators (wind, solar)? If so what?

What is the role of distributed generation in providing reactive power?

What are the options for reactive power output as a function of

investment in generator design?

Does it make economic sense to oversize the generator or the turbine?

Should required reactive power capability differ based on location

on the system? For instance, should we allow generators distant from

load to have less capability?

What are the advantages of supplying dynamic reactive power locally

from distributed energy resources (DER)?

For Transmission

Should there be interconnection standards with respect to merchant

transmission?

Can thermal transmission constraints be relieved by supplying or

consuming reactive power? If so, how and to what extent?

Can nonthermal transmission constraints be relieved by supplying

or consuming reactive power? If so, how and to what extent?
114 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Conclusions, Recommendations and Questions

Systems Operators

How are voltage schedules determined? Who decides? What are the

criteria? Are they optimized? Are generators required to operate at

a given power factor, or are they required to maintain a specified

voltage? Are generation costs incorporated into voltage schedule

decisions?

Should the approach to voltage management and scheduling be reexamined? How does voltage scheduling affect economic operations?

Should there be incentives for voltage management?

Should system operators take transmission lines out of service to

balance reactive power?

What instructions or signals (prices, real power, reactive power,

voltage, frequency) does the system operator send to generators,

transmission and load? (In particular, for reactive power)

What information does the system operator have on generator

capabilities and how is it used?

Under what circumstances might a generator be required to reduce

real power output due to a shortage of reactive power?

Are phase shifters set to get optimal system performance? If so, how?

Are D-curve parameters of each generator available to the control

area or system operator?

Costs, Pricing and Markets

Costs

What are the cost differences among reactive power from capacitors,

FACTS and generators?

What is the incremental investment cost for generator reactive power

capability? 
Federal Energy Regulatory Commission Staff Report •February 4, 2005 115

Conclusions, Recommendations and Questions

Order No. 888 Rate Design

Are independent power suppliers being compensated comparably to

the generation supplied that is owned by transmission owners?

Can the capital costs of reactive power capability be effectively

unbundled? Should reactive power pricing be unbundled? If so, how?

Does Opinion No. 440 properly encourage efficient reactive power

capabilities? If so, how? If not, how should it be changed?

How can we streamline the Opinion No. 440 process for establishing

rates?

How does the reactive power capability of existing and

interconnecting independent power producers impact system

reliability?

RTO Markets

What software advances are needed for efficient and reliable reactive

power markets?

Should reactive power capability requirements be locational and

procured in capacity markets?

How are generator capabilities used in the ISO/RTO markets?

How should merchant generators and transmission be compensated

for the capability to provide reactive power?

How should distributed energy resources (DER) be compensated for

supplying dynamic reactive power?

How should reactive power rates and markets be designed in RTOs?

Should there be different prices for reactive power produced by static

and dynamic sources?

Are there incentives for generation, transmission and load to increase
116 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Conclusions, Recommendations and Questions

their capability, e.g., by increased cooling where needed? If not, why

not?

Should reactive power be paid opportunity cost compensation based

on the real power price?

Should a separate reactive power capacity market be developed? If

so, what should the capacity supply obligation time frame be? Daily?

Monthly? Annually?

Should there be different types of payments or markets for reactive

power from different sources (generators, capacitors, SVC,

STATCOM, synchronous condensers, etc)?

What are the computational impediments to including reactive power

in the day-ahead and real-time markets?

What are the noncomputational impediments to including reactive

power in the day-ahead and real-time markets?

What kind of market power mitigation would be needed?

What is the magnitude of reactive power value (price) relative to

real prices?

What is the volatility of reactive value (price) compared to real

power?

How would a reactive power market reflect the high opportunity

cost of insufficient reactive power (i.e., a cascading blackout)? Is

the market suspended for emergency situations?
Federal Energy Regulatory Commission Staff Report •February 4, 2005 117

Glossary Glossary of Terms

Alternating Current (AC): An electric current

that periodically reverses its direction. In North

America, an electric current that reverses

direction 120 times per second, thus pulsating

60 times a second. Each pulse equals one cycle.

Armature: The part of the generator in which

an electric field is induced (for large

synchronous generators it is the stator, a

cylinder with coils of wire around it).

Capacitance: A property of electric circuits that

supplies reactive power.

Capacitor Bank: A group of switched

capacitors.

Circuit Breaker: A switch used to connect

components of an electric transmission network.

Competition, perfect: An ideal market structure

characterized by a large number of small firms,

identical products sold by all firms, freedom of

entry into and exit out of the industry, and

perfect knowledge of prices and technology.

Competition, imperfect: A market structure

characterized by two or more sellers and buyers

that fail to match the criteria of perfect

competition with one or more buyers or sellers

having a perceptible influence on price.

Complete Pricing: A situation in which the

supplier is paid for all goods and services

provided and the customer pays for all goods

and services consumed.

Consumption: The use of a product or service

(such as reactive power).

Contingency: An outage of a line, transformer,

or generator. Power systems planners study

major contingencies so that the system can

operate through likely contingencies without a

blackout.

Core End: The ends of the generator armature;

the ends of the armature overheat before the

rest of the armature when a generator is

consuming reactive power.

Cost, fixed: A cost that does not vary with the

amount of output produced. However, in

contrast to a sunk cost, the cost can be entirely

avoided if no output is produced. For example,

the cost of equipment is often a fixed cost in

that the same equipment cost is incurred

regardless of how much output is produced

from the equipment. However, the equipment

cost could be avoided by not purchasing the

equipment, and thus, not producing any output.

In addition, the equipment cost would be fixed

but not sunk if the purchased equipment could

be sold after it is purchased (and thus, the

equipment cost would be avoided after the sale)

if the owner no longer wishes to produce

output.

Cost, sunk: A cost that (1) does not vary with

the amount of output produced, and (2) cannot

be avoided even if no output is produced. For

example, if a piece of equipment has been

purchased and has no value to anyone other

than the present owner, the cost of the

equipment is a sunk cost, because the owner

could not sell the equipment in order to avoid

the equipment cost in the future.

Glossary of Terms
118 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Glossary of Terms

D-Curve: The set of curves defining the real

and reactive power capacities of a generator;

also known as the generator capability curve,

or generator capability set. The curves are

shaped like a capital letter D, hence the name

D-curve.

Direct Current (DC): An electric current that

flows in only one direction.

Distributed Generator: A small generator

connected to an electric distribution system.

Dynamic Var (D-var): A voltage regulation

system manufactured by American

Superconductor, used for reactive power

support and classified as a FACTS device.

Efficiency: As a term in economics, efficiency

is a state in which resources are used in a way

that produces the maximum economic value to

members of society.

Exciter: The part of a synchronous generator

that provides the field current. It can be a DC

motor connected to the field of the generator,

or an electronic DC power supply.

Externality: The effect of a purchase or use

decision by one set of parties on others who did

not have a choice and whose interests were not

taken into account. In a free market, an

inefficient amount, too much or too little of the

good, will be consumed from the point of view

of society.

Field: The part of the generator that induces an

electric field in the armature (for large

synchronous generators it is the rotor, a

spinning electromagnet)

Filter: A device to minimize oscillations at

certain frequencies in the transmission system.

Filters are installed with switching devices such

as FACTS and HVDC to mitigate the effects of

high-frequency switching on the transmission

system.

Flexible Alternating Current Transmission

System (FACTS): FACTS devices are

technologies that increase flexibility of

transmission systems by allowing control of

power flows and increasing stability limits of

transmission lines. There are several varieties

of FACTS devices, including SVCs,

STATCOMs and D-vars.

Fuel Adjustment Clause: A clause in the tariff

of a utility subject to cost-based regulation that

allows the utility to quickly adjust its prices

when its fuel costs change, so that the utility

exactly recovers its fuel costs.

Generator Capability Set: The set of curves that

define a generator’s real and reactive power

capability. (See D-curve)

Generator Step-Up Transformer: The

transformer that converts low voltage power

from a generator to high voltage power, and

connects the generator to the high voltage

transmission system.

Good, private: A good which possesses two

properties: (1) excludability (also referred in this

context as rivalry) - cannot be consumed by

everybody since consumption by one person

reduces or excludes consumption by another,

and (2) depletability (it is finite).

Good, public: A good which possesses two

properties: 1) it is non-rivalrous, meaning that

its benefits do not exhibit scarcity from an

individual point of view; once it has been
Federal Energy Regulatory Commission Staff Report •February 4, 2005 119

Glossary of Terms

produced, each person can benefit from it

without diminishing anyone else’s enjoyment 2)

it is non-excludable, meaning that once it has

been created, it is impossible to prevent people

from gaining access to the good.

High Temperature Superconducting (HTS):

Cables and wires made of superconducting

materials, cooled with liquid hydrogen or

nitrogen, operated at relatively high

temperatures of up to -320 degrees Fahrenheit,

in comparison to superconducting materials

that operate at near absolute zero, or -457

degrees Fahrenheit.

High Voltage DC (HVDC): High voltage DC

transmission lines have AC-DC and DC-AC

converters at each end and transmit power

using direct current. The converter stations can

be independently set to supply or consume

reactive power, and the lines do not supply or

consume reactive power since they are

transmitting dc power.

Independent System Operator (ISO): The

operator of a transmission system that is

independent of market participants. The

Commission’s Order No. 888 established eleven

principles for qualifying for ISO status,

including that (1) its governance be fair and nondiscriminatory, (2) the ISO and its employees

have no financial interest in any market

participant, (3) it provide open access to the

transmission system at non-pancaked rates

under a single tariff applicable to all users, (4)

it has primary responsibility for ensuring shortterm reliability of grid operations, (5) it has

control over the operation of interconnected

transmission facilities within its region, (6) it

identifies and takes operational actions to

relieve constraints on its system, (7) it has

appropriate incentives for efficient

management and administration and procures

services in an open competitive market, (8) its

transmission and ancillary service pricing

policies promote efficient use of and investment

in generation, transmission and consumption,

(9) it makes transmission system information

publicly available via an electronic information

network, (10) it develops mechanisms to

coordinate with neighboring control areas, and

(11) it establishes an ADR process to resolve

disputes.

Inductance: A property of electric circuits that

consumes reactive power.

Installed capacity (ICAP): The capacity of a

generation or demand-side resource that meets

certain requirements established under the

tariffs or operating agreements of certain ISOs

and that load serving entities within the ISO’s

control area must procure. The requirements

typically include bidding into the ISO’s spot

markets, curtailing energy exports during

emergencies within the ISO’s control area in

order to make the capacity’s energy available

to the ISO’s control area, and being available

(and thus, not on a planned or forced outage)

during a specified portion of the year.

Insulated Gate Bipolar Transistor (IGBT): A

newer type of semiconductor based electronic

switch used in high voltage applications.

kVA: A measure of apparent power equal to

1,000 volt-amperes.

kvar: A measure of reactive power equal to

1,000 reactive volt-amperes.

kvarh: A measure of reactive energy equal to

1,000 reactive volt-ampere hours.
120 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Glossary of Terms

kW: A measure of real power equal to 1,000

watts.

kWh: A measure of real energy equal to 1,000

watt-hours.

Lagging Power Factor: When the current phase

angle is smaller than the voltage phase angle,

the current lags the voltage, and the power

factor is lagging.

Leading Power Factor: When the current phase

angle is larger than the voltage phase angle,

the current leads the voltage, and the power

factor is leading.

Load: The amount of electric energy delivered

to customers on a system.

Large Generator Interconnection Procedures

(LGIP): Standard procedures for

interconnecting large generators with

transmission facilities that the Commission

required all public utilities that own, control or

operate transmission facilities to file, in Order

No. 2003, issued on July 24, 2003.

Marginal Cost: The additional cost incurred to

provide a small additional increment of a

product or service, such as electric energy.

Market Power: The ability of a market

participant to change the market price away

from the competitive level by withholding from

the market. Market power can be held by either

a seller or a buyer. For a seller, market power is

the ability to increase the market price above

the competitive level by withholding supply from

the market. For a buyer, market power is the

ability to lower the market price below the

competitive level by reducing its purchases (i.e.,

by withholding demand from the market).

Monopoly: Market structure in which only a

single market participant supplies a good or a

service.

Monopsony: Market structure in which only a

single market participant is a buyer of a good

or a service.

MVA: A measure of apparent power equal to

one million volt-amperes.

Mvar: A measure of reactive power equal to

one million reactive volt-amperes.

Mvarh: A measure of reactive energy equal to

one million reactive volt-ampere hours.

MW: A measure of real power equal to one

million watts.

MWh: A measure of real energy equal to one

million watt-hours.

Optimal Power Flow (OPF): An optimization

problem that solves real and reactive power

dispatch at minimum cost, subject to system

constraints.

Overexcited: The generator operating mode

where the generator is supplying reactive

power.

Power Factor (PF): (1) The ratio of real power

to apparent power, also the cosine of the phase

angle between line current and voltage (2) A

measure of real power in relation to reactive

power. A high power factor means that

relatively more actually useful power is being

taken or produced relative to the amount of

reactive power. A lower power factor means

that there is relatively more reactive power

taken than real power.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 121

Glossary of Terms

Power Factor, capability or design: The range

of power factors in which the generator is

designed to operate. Although not formally

defined, it is commonly understood to be the

range of power factor determined by the

generator’s maximum supply and consumption

of reactive power when the generator outputs

rated real power, at the operating limit of the

turbine. Alternatively, a point on the D-curve

where significant decrease in real power is

necessary to produce additional reactive power.

Power Factor, nameplate: The power factor at

the points on the capability curve of the

generator where the stator constraint intersects

the field current constraint.

Power Factor, operating: The power factor

(ratio of real power to apparent power)

produced or consumed at a point in time when

the generator is operating.

Prime Mover: The part of the generator that

moves the rotor, a water, steam or gas turbine

for electric power generators.

Qualifying Facility: A cogeneration or small

power production facility that qualifies under

FERC’s regulations and PURPA to sell electric

energy and capacity to a utility at the utility’s

avoided cost. A cogeneration power production

facility produces electricity and useful heat or

steam used for industrial, commercial, heating

or cooling purposes. A small power production

facility has a capacity less than 80 MW, with a

primary energy source of biomass, waste,

geothermal, or renewable resources (including

hydro).

Reactive Power: The portion of power that

establishes and maintains electric and magnetic

fields in AC equipment. Reactive power is

necessary for transporting AC power over

transmission lines, and for operating magnetic

equipment, including rotating machinery and

transformers.

Regional Transmission Organization (RTO):

Entity responsible for the operation of the

transmission network under Order 2000.

Minimum characteristics of an RTO include (1)

independence from market participants, (2)

appropriate scope and regional configuration,

(3) operational authority for all facilities under

the RTO’s control, and (4) exclusive authority

to maintain short-term reliability. The minimum

functions of an RTO are (1) tariff

administration and design, (2) congestion

management, (3) parallel path flow, (4)

ancillary services, (5) OASIS with Total

Transmission Capability (TTC) and Available

Transmission Capability (ATC), (6) market

monitoring, (7) planning and expansion, and (8)

interregional coordination.

Rotor: The rotating part of the generator.

Second Best (Second Best Efficient): The

preferred allocation of goods and services or

set of allocations that does not achieve an

efficient allocation. When only a limited number

of policy tools are available, second best

allocations generally maximize a social welfare

function.

Static Compensator (STATCOM): A FACTS

device similar to an SVC, but using switches

called Insulated Gate Bipolar Transistors

(IGBTs) to supply or consume reactive power

without capacitors and inductors.

Static Var Compensator (SVC): A FACTS

device consisting of electronic switches called

thyristors connected to capacitors and inductors
122 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Glossary of Terms

that can supply or consume reactive power.

Stator: The stationary part of a generator.

Supervisory Control and Data Acquisition

(SCADA): The system of meters and

communication equipment that sends status

information of electric power system equipment

to control centers.

Supply: The willingness of producers to sell a

given amount of goods and services for a price

at a particular time.

Surge Impedance Loading (SIL): Transmission

line loading when the reactive power supplied

by line capacitance equals the reactive power

consumed by line inductance.

Switched Shunt Capacitor: A capacitor

connected to a transmission line through a

switch.

Synchronous Condenser: An electric generator

not connected to a turbine that supplies or

consumes reactive power without supplying real

power.

Synchronous Generator: An electric machine

that runs in synchronism, at the same frequency,

as other machines on a network to produce real

and reactive power.

System Operator (SO): The entity that operates

the system. It gives the dispatch orders to

generators, transmission and load. A system

operator is independent when it has no financial

interest in the electricity assets.

Supervar: A synchronous condenser with high

temperature superconducting cables for

improved efficiency.

Thermal Limit: An operating limit determined

by thermal limits of materials in a device.

Thyristor: A type of semiconductor based

electronic switch.

Transmission Operator (TO): The entity that

operates transmission. It executes dispatch

orders from the SO.

Transformer Tap: Electronic switches that

adjust the amount of reactive power and

voltage on one side of the transformer by

changing reactive power and voltage on the

other side.

Turbine: Rotary engine in which the kinetic

energy of a moving fluid (water, steam or gas)

is converted into mechanical energy by causing

a bladed rotor to rotate.

Underexcited: The generator operating mode

where the generator is consuming reactive

power.

Var: Volt-ampere-reactive; var is a measure of

reactive power. By comparison, real power is

measured in watts.

Voltage Collapse: A dynamic phenomenon in

power systems where voltage in the network

becomes unstable, generators trip off line, and

blackouts occur.
Federal Energy Regulatory Commission Staff Report •February 4, 2005 123

Appendix A Appendix A -Literature Review of Reactive Power Markets

During the era of vertically integrated

utilities, reactive power was viewed

strictly as an engineering issue, something to

be built sufficiently into the system in a

centralized way. Studies conducted before

restructuring focused on whether reactive

power and other alternating current

characteristics were being represented correctly

in engineering calculations, such as contingency

models and distribution factors. (Ilic-Spong and

Phadke, 1986; Lee and Chen, 1992; see endmatter references for complete identification of

these and other references in the text). Other

engineering research was beginning to explore

the role reactive power controls had in

increasing the functioning of the grid, perhaps

in obviating (or at least postponing) some

system upgrades to generation and

transmission. (Ilic, 1991)

Beginning in the early 1980’s, researchers were

beginning to think about alternate ways of

pricing electricity to achieve specific objective,

such as maximal social welfare or system

reliability. Caramanis et. al. (1982) presented

a “new concept” in electricity pricing, a method

which evolved into what is now known as

locational pricing. In this work, it was suggested

that a market for electricity can efficiently set

location-specific prices based on instantaneous

supply and demand that promote consumption

patterns that benefit the transmission system.

Implementing separate prices for real and

reactive power would produce the most efficient

pricing outcomes, even though the authors

assert that the price of reactive power will often

be insignificant compared to real power prices.

The calculations for real power from this

seminal work were expanded upon by

Schweppe et. al. (1987); however, this later work

does not discuss reactive power. Although some

of the early economic publications mention

reactive power or various schemes for voltage

control, and indicate separate prices might be

desirable, none rigorously consider the

implications of reactive power prices or

mechanisms for setting these prices. (Outhred

and Schweppe, 1980)

In the early 1990s, with the restructuring of the

industry eminent, researchers began looking

more seriously at pricing both real and reactive

power in an economically efficient way. The

new emphasis on markets for electricity created

a new focus on reactive power pricing in the

literature: whether it was important, how it

should be done, what would be the resulting

prices. Baughman and Siddiqi (1991) presented

an early argument that because the physics of

real and reactive power are so closely tied,

simultaneous pricing of real and reactive power

would be important to the development of

electricity markets and that in the presence of

voltage constraints, reactive power prices can

be extremely high.

In 1993, Hogan made the claim that because

they do not include the effect of reactive power,

DC load models are not sufficient to determine

real power prices of systems with voltage

constraints, and that the price of reactive power

is not negligible and does not have a simplistic

Literature Review of Reactive Power Markets
124 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Appendix A -Literature Review of Reactive Power Markets

relationship to real power. He presented a

three-node example that showed marginal

reactive power prices soaring to equal those of

real power. Because there was no simple

relationship between real and reactive power,

and because reactive power prices can be

significant, Hogan argued that electricity

markets need explicitly to include prices for

reactive power.

This argument was countered in 1994 by Kahn

and Baldick, who showed that Hogan’s example

system was artificially constrained - that one

of the generators was not allowed to produce

more reactive power when it could have done

so. When the test system was re-dispatched in

a more efficient way, the price of reactive power

(in the presence of voltage constraints) dropped

again to be a fraction of the real power price.

The conclusion was that with appropriate

centralized planning, the cost of providing

enough reactive power to a system is negligible,

and this need for centralized planning was used

to argue for regional transmission groups.

After the Hogan-Kahn-Baldick debate, it

became accepted that reactive power

management had to adapt in this new,

restructured era. Now in addition to effecting

grid security, reactive power and voltage control

played a part in determining market efficiency

(Ilic and Yu, 1999). Much of the research that

followed focused on alternative ways to manage

and dispatch reactive power in the future,

including whether desirable system voltage

profiles exist and how could they be determined.

There was also increased production of

technical and nontechnical (Sauer, 2003) papers

discussing reactive power, presumably because

a wider audience – wider than just the

engineering community – needed to know what

it was, how it worked and why it was

important. Kirby and Hirst (1997) discussed the

role of transmission in voltage control,

characteristics of voltage control equipment and

strategies for voltage control management.

Several years later another report came out that

described reactive power balance, reactive

power and transmission and black-start

techniques, generator reactive capability

(comparing actual performance with

manufacturer name plate characteristics) and

the importance of optimizing transformer tap

positions for producing and absorbing reactive

power (Adibi, 2000). Alvarado et. al. (2003)

produced a comprehensive literature and

market review of reactive power pricing

strategies intended to help the Transmission

Administrator of Alberta, Ltd., make a

determination of how to handle reactive power

in their system. This study, while making no

specific recommendations for Alberta, outlined

possible areas of action for improving

investment and dispatch decisions, among

others.

Some of the more technical papers to emerge

at this time focused on the implications of

inductive load (Meliopoulos et. al., 1999),

advances in over excitation region control and

generator behavior in this region (Murdoch et.

al., 2001), and the importance of determining

critical buses for voltage stability, rather than

market concentration, to combat market power

(Zambroni de Souza et. al., 2001). Ilic et. al.

(2004) presented a technical analysis of

limitations of DC power flows to adequately

represent the effects of reactive power and
Federal Energy Regulatory Commission Staff Report •February 4, 2005 125

Appendix A -Literature Review of Reactive Power Markets

generator reactive power limits. The paper

examines differences in LMPs resulting from DC

OPF and an AC OPF with reactive power

limitations, and attributes these differences to

allocating line capacity to reactive power in the

AC OPF case.

In looking to the future of markets and policy,

two general areas of research developed. One

examines decentralized incentives for reactive

power capacity and dispatch, how optimal

power flows (OPFs) can be modified to

incorporate reactive power costs, and what

price signals would best capture the incentives

for building capacity and ensuring performance.

The other focuses on the role of centralized

planning and control of reactive power planning

and production in the era of restructured

electricity markets.

Two case studies were published in 1995 that

represent the two sides of this new research.

Both described methods for dispatching reactive

power, but one paper described a centralized

reactive power management program, which

serves to ensure that efficient amounts of

reactive power support are supplied by the

transmission and distribution system. It also

described how to meet unexpected reactive

power demand with generators (Nedwick et.

al., 1995). The other paper explained reactive

power dispatch based on two complimentary

OPF calculations, one minimizing cost to obtain

economic benefits, and the other minimizing the

amount of “control action” – the number of

physical controls that change – in order to

maintain physical practicality (Dandachi et. al.,

1995). Neither paper advocated pure market

economics or centralized control, but each

placed greater emphasis on one or the other,

and this is how most of the debate has been

framed since the mid-1990s.

In the following few years, researchers studied

the new role of system operators in relation to

reactive power and what function centralized

planning and control should have. An integrated

method for capacity planning was proposed

based on OPF iterations, determining the best

location and size of capacitor banks on a system

(Chattopadhyay et. al., 1995). The Reactive

Services Working Group at PJM proposed

several short- and long-term strategies for

combining centralized requirements and

planning with decentralized bidding for capacity

projects, along with a two-part tariff to

encourage capacity and performance (PJM,

2001). Nobile and Bose (2002) suggested

creating Voltage Control Areas (VCA) as a

strategy for controlling voltage by blending

centralized and decentralized control. Voltage

set-points are determined by the VCA system

operator, but decisions about dispatch to meet

these set-points are based on economic bids and

long-term contracts.

Meanwhile, several reports were published that

examined the implication of using different

objective functions in traditional OPF

algorithms to optimize reactive power dispatch.

These objectives included minimizing network

losses, minimizing the movement of

transmission devices (like transformer taps),

maximizing social welfare and minimizing total

costs (including implicit costs like changing

transformer taps) (El-Keib and Ma, 1997;

Weber et. al., 1998; Choi et. al., 1998; Lamont

and Fu, 1999). These reports also looked at the
126 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Appendix A -Literature Review of Reactive Power Markets

possibility of pricing reactive reserves, the cost

of outages or reactive power curtailments and

a responsive demand-side. One report

attempted to internalize all aspects of the power

system – all traditional OPF constraints as well

as load frequency control, harmonic distortions

and emission rates – into one set of prices in

order to create a truly efficient market with

minimal need for centralized planning or

control (Baughman et al., 1997, two parts).

Because these studies used different test systems

and different algorithms to compute reactive

power prices it is difficult to compare resulting

prices directly. That said, the magnitude of

reactive power prices generally falls within the

range of about one-tenth to one-half of real

power prices, with larger ratios occurring

because of voltage constraints, peak loading

conditions or loads with low power factors.

Although they no longer soar to the original

Hogan levels, they are “significant,” the

authors state, in providing appropriate market

signals (Siddiqi and Baughman, 1995; El-Keib

and Ma, 1997; Weber et al., 1998; Choi et al.,

1998).

Suggested strategies for pricing reactive power

have evolved over the last 10 years from

simplistic pricing methods – making reactive

power production a noncompensated generator

obligation, or basing the price on the level of

real power output – to more complicated

incentive structures. Initially, reactive power

was considered almost too cheap to meter and

should simply be the obligation of generators

to provide, at least within their capability curve

(Chattopadhyay et al., 1995; Hao and

Papalexopoulos, 1997). Compensating

generators for opportunity cost, the loss of real

power revenue when ramping down real power

and ramping up reactive, has since become

widely accepted (Sauer et al. 2001; Hao, 2003).

The Federal Energy Regulatory Commission

(FERC) in 1995 published its Notice of Proposed

Rulemaking directing that independent power

producers generating real power should be

required to provide some amount of reactive

power. These generators should be compensated

in a way comparable to traditional utility

producers, and the price for reactive power

should be based on the unbundled price of

producing reactive power. Partly as a response

to this, Kirsch and Singh (1995) explained how

the reactive power pricing method suggested

by FERC will result in prices that are either too

high or too low. Alvarado et al. (1996) identified

several problems with the way reactive power

was being priced in real U.S. markets at the

time, such as only localized demand was being

priced, there were inconsistent assumptions

about cost and there was no differentiation

between the price of static reactive power

(cheaper, provided by capacitor banks and other

transmission facilities) and dynamic reactive

power (more expensive, provided mainly by

generators).

To fix these problems, researchers began

looking into alternative, more sophisticated

ways to determine prices. The relationship

between real power flow and reactive power

indicates it would be desirable to compensate

reactive power producers for reactive power

production allows more real power flow. ElKeib and Ma (1997) suggested that dispatching

reactive power based on minimizing losses on
Federal Energy Regulatory Commission Staff Report •February 4, 2005 127

Appendix A -Literature Review of Reactive Power Markets

a system will compensate generators for

producing reactive power even when operating

within acceptable voltage limits, production

that is typically uncompensated. The difference

between supplying static and dynamic reactive

power has also been widely discussed, and

many advocate explicitly differentiated pricing

for these two services (Alvarado, 1996; PJM,

2001). Many authors recognize the difference

between encouraging investment in reactive

power capability and inducing its production.

A way to approach this distinction is with a

two-part tariff, compensating both reactive

capacity and performance (Chattopadhyay

et.al., 1995; Hao and Papalexopoulos 1997;

Kirby and Hirst, 1997; PJM 2001). Several of

these publications describe the need for longterm contracts in markets for reactive power

as a preventative measure against exercise of

market power (Kirsch and Singh, 1995;

Alvarado et. al., 1996; Nobile and Bose, 2002).

Another way to potentially use markets to value

voltage regulation is to let market participants

bid their desired level of voltage tolerance into

the market. In this way, market participants can

implicitly communicate their value for voltage,

voltage regulation and reactive power. An

additional benefit of recognizing different

voltage needs is that relaxing voltage tolerances

can improve the optimality of an OPF solution;

incorporating voltage values as decision

variables in an OPF calculation has the potential

to reduce system costs. Exploration of this topic

has only begun, but initial findings indicate that

it is a promising area of research (Kim et. al.

2004).

At this point, there is no single widely accepted

strategy for determining or encouraging

appropriate investment in reactive power

capability and production, but researchers from

multiple disciplines (engineering, economics,

policy) are expanding their knowledge of this

subject and continuing to add to the dialogue.

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128 Principles for Efficient and Reliable Reactive Power Supply and Consumption

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Federal Energy Regulatory Commission Staff Report •February 4, 2005 129

Appendix A -Literature Review of Reactive Power Markets

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Reactive Power Support,” IEEE Transactions

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August 1999.

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the 1990s,” IEEE Transactions on Power

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1995.

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for Voltage Control in a Competitive Ancillary

Service Market,” 14th PSCC, Sevilla, Session

20, Paper 4, June 2002.

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of Supply Pricing for Electric Power Systems,”

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Gross, Fernando Alvarado, Schmuel Oren and

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Services in Electricity Markets: Costing and

Pricing of Ancillary Services Project Final

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Center (PSERC) Publication 00-08, May 2001.

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Power Systems Engineering Research Center,

Department of Electrical and Computer
130 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Appendix A -Literature Review of Reactive Power Markets

Engineering, University of Illinois at UrbanaChampaign, September 16, 2003.

F.C. Schweppe, M.C. Caramanis, R.D. Tabors,

and R.E. Bohn, Spot Pricing of Electricity,

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“Reliability Differentiated Pricing of Spinning

Reserve,” IEEE Transactions on Power

Systems, Vol. 10, No. 3, pp.1211-1218, August

1995.

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Sauer, and Christopher L. DeMarco, “A

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Power,” Proceedings of the Hawaii

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Conference on System Sciences, 2001.
An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Federal Energy Regulatory Commission Staff Report • February 4, 2005 131

Appendix B 

n this appendix, we will start a discussion to explore future pricing of reactive power from 

generation. We examine the incentives for efficient investment and operations decisions 

through price and quantity signals from the system operator to synchronous generators. We 

examine the generator operator (GO) as a price taker avoiding the complications of gaming 

strategies, and, thereby, we ignore market power issues here because they complicate the 

discussion and can be addressed through mitigation. We focus on the cost and profits of 

producing real and reactive power from synchronous generators. The analysis focuses on steadystate operations with minor and temporary excursions into disequilibrium. A more complete 

discussion must include a full discussion of reliability in general and transient and dynamic 

stability in particular. The analysis for motors, the consumers of real and reactive power, is 

essentially the same. For simplicity of exposition we simplify the representation of some other 

characteristics and products. 

A generator can be viewed as a multiproduct firm. Among the joint products that the generator 

offers are real power, real power reserves, reactive power and reactive power reserves. The 

investment and operating decisions are made based on market rules and expected revenues from 

the products it sells. The life of a generator starts with the investment decision. The decision to 

build a generator occurs if the expected discounted revenues from all services exceed the costs 

including a risk adjusted return on investment. There are many design decisions that determine 

the costs of building and operating the generator. In turn the market design and design decisions 

determine the revenues streams. Here we will pay special attention to the reactive power design 

capabilities, but they are intimately intertwined with the overall design. 

In these appendices the approach taken is indifferent to whether the system operator is 

independent or a vertically integrated utility. If the system operator is independent, it must 

monitor and mitigate market power and the asset owner/operators have a greater incentive to be 

efficient. If the system operator is a vertically integrated utility, the prices become transfer prices 

for internal transactions and the efficiency incentives are usually blunted by the overall 

regulatory scheme. 

Currently, most generators are given schedules that include the quantity of real power produced, 

a voltage and a range in which each must be kept to avoid incurring financial penalties. Some 

system operators send prices along with the real power and voltage. Occasionally, the system 

operator asks for additional amounts of reactive power. Schedules may be set daily, but may vary 

in intervals of minutes or seconds. Most equipment has automatic controls to maintain the 

prescribed ranges. 

I 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 132

The Investment Decision. Generator investment decisions determine its range of operation and 

are driven by technology, interconnection rules, market rules, the market design and the prices 

that result. The preference is that the generator design be the result of efficient market signals. 

Many parameters describe the generator. For example, more expensive cooling equipment allows 

higher levels of sustained reactive power output before serious equipment damage. An incentive 

for this can come from a price signal for reactive power. To describe the investment decision we 

start by defining some of the design parameters. Let 

Pmin, Pmax be the minimum and maximum rated real power output, respectively, in MW Qmin, 

Qmax be the minimum and maximum rated reactive power output, respectively, in Mvar (the 

same units as MW), Prrmax be the maximum rated ramp rate for real power output, in MW/sec, 

Qrrmax be the maximum rated ramp rate for reactive power output, in MW/sec, HR be the heat 

rate in MMBtu/MWh. 

We will assume the ramp rates up and down are equal and the heat rate is uniform over the 

operating range. The capital costs are: 

C(Pmin, Pmax, Qmin,Qmax, Prrmax, Qrrmax, HR). 

In general, as Pmax increases, C increases (∂C/∂Pmax = C’ > 0), but the average capital costs 

(C/Pmax) decline then eventually increase with increasing Pmax. Differentiating average costs with 

respect to Pmax: 

∂(C/Pmax)/∂Pmax = (∂C/∂Pmax)/Pmax - C/(Pmax)

2 = (Pmax ∂C/∂Pmax-C)/(Pmax)2

. 

Average capital costs reaches its minimum at a capacity Pmax = Pmax* satisfying 

∂(C/Pmax)/∂Pmax = 0 or 

 

∂C/∂Pmax = C’(Pmax*) = C(Pmax*)/Pmax*

That is, for Pmax up to Pmax* , C’ > C/ Pmax while, for Pmax > Pmax*, the average costs increase with 

increasing Pmax. 

Also, as Qmax increases , C increases (∂C/∂Qmax > 0), but the average capital costs (C/Qmax) 

decline with increasing Qmax up to some level Qmax* where the average costs increase with 

increasing Qmax. For practical purposes, Qrrmax is generally large enough that it is almost never a 

binding constraint and is not a significant component of capital costs. Thus, we will drop it from 

further analysis. 

The turbine is often designed to the smallest Pmin possible. For a steam boiler, Pmin will most 

likely be determined by steam operating constraints. A high value of Pmin makes the generator 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 133

less flexible, results in high start-up and no-load costs and, therefore, less valuable as an asset. 

Qmin and Qmax are determined by the overall design and the cooling equipment in the generator. 

Prrmax is limited by thermal and mechanical stress and stability. For fossil fuel generators since 

the fuel costs are a large part of total costs and the expected asset life of 20 years or more, the 

heat rate (HR) is usually designed to the most efficient technology. In the past 20 years the heat 

rate for gas generators has improved from 12,000 to 6,000 MMBtu/MWh. Over the life of the 

generator these characteristics can change, as components are replaced and upgraded with new 

equipment. For example, when a turbine is replaced the real power capability can increase, 

changing the operating characteristics. 

In designing generating plants, for a given turbine size, the other equipment (the exciter, 

alternator, voltage regulator, step-up transformer) can be sized larger for greater production of 

reactive power when at the same real power output. If the other equipment is fixed, the turbine 

can be sized or resized in an overhaul, moving the turbine constraint closer to the boundary of 

the generator’s D-curve, discussed in more detail later in this appendix. The market design 

compensation scheme will, in part, determine the future configuration of IPP generators. 

One approach to determining these cost differences is to ask for bids or “quotes” for different 

levels of capability from the manufacturer. Instead of formal quotes, the choice of parameters is 

often achieved through discussion and negotiation with the equipment vendors. 

The investment decision requires revenue forecasts from a portfolio of contracts and projected 

spot market profits. The decision becomes to invest if: 

C(Pmin, Pmax, Qmin,Qmax, Prrmax, Qrrmax, HR) < ∑t dt[πt(pt, Pt, Qt) + CPt] 

 

where dt is the discount factor, pt is a vector of the expected market prices after entry, Pt, Qt are 

vector of the expected market quantities after entry (Lower case p denotes a price and upper 

case P denotes real power.), πt are the spot market profits for period t and CPt are the contract 

payments net of spot market revenues in period t. 

Contract payments can be from sale of future output commitments and/or rate base demand 

charges. 

Although not necessarily required, central forward markets can create contractual commitments 

to supply reserves of both real and reactive power that minimizes the costs of maintaining 

reliability. With mobile technologies, entry decisions have shorter time horizons. Some devices 

can be installed and relocated in less than a year. Other technologies can be installed within an 

auction with a longer time horizon of the procurement. Market participants could offer 

equipment without a precommitment of installation. Reserves markets can be characterized as 

stochastic variations of optimal dispatch auctions. 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 134

In competitive markets, generators are designed through parameter choices to maximize total 

profits equal to operating profits plus contract payments minus capital costs: 

Max ∑t dt[πt(pt, Pt, Qt) + CPt] - C(Pmin, Pmax, Qmin,Qmax, Prrmax, Qrrmax, HR). 

When risk and uncertainty are introduced, a more complex stochastic analysis involving real 

options is necessary, but this topic is beyond the scope of this appendix. 

Over time, generator design and manufacturing will move to the most profitable design. If the 

market design omits paying for certain desirable characteristics, such as reactive power, they will 

tend to be undersupplied. When these decisions result in sunk capital, we may have to live with 

them for years or decades. In efficient competitive markets, the most profitable design will be the 

design most beneficial to society, within the framework of the market rules. 

Operating Constraints. The economic operation of a generator requires that it operate within 

certain constraints to avoid outages and serious equipment damage. These constraints are 

determined by the physical design of the generator, the materials it is made of, the size of the 

components, etc. The input to a synchronous generator is an energy source, e.g., hot gasses, air, 

steam or water that turns a turbine. 

Synchronous generators supply complex power. Power entering the network from a synchronous 

generator has real and reactive power components. We start with a voltage source E (complex 

numbers are bold and real numbers are in light face type): 

E = ZGI + V

 

where E is the internal generated voltage of the machine, ZG = R + (-1)1/2Xd, R is the resistance, 

Xd is the synchronous reactance, I is the complex current (I* is the complex conjugate of I, i.e., 

I(I*/|I|2

) = 1),and V is the complex voltage.

The complex power from the generator is: 

S = VI* = V(E-V)*/ZG* 

Since R is usually much smaller than Xd, we can assume R = 0, then 

 P = VEsin(δ)/Xd 

 Q = V(Ecos(δ) – V)/Xd

 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 135

where δ is the torque angle of the machine equal to the difference in phase angle between E and

V, P is the real power output of the generator and Q is the reactive power output of the generator, 

Since sin2

(δ) + cos2(δ) = 1, 

 (PXd /VE)2 + ((Q Xd + V2

)/VE)2 = 1 or 

 P2 + (Q + V2

/Xd)

2 = (VE/Xd)2 

If the maximum design capability of the field current equipment occurs at Emax then the field 

current constraint of the D-curve becomes: 

 P2

 + (Q + V2/Xd)

2 ≤ (VEmax/Xd)2 

When additional real power is needed, the steam valve (for a steam turbine) is opened, the torque 

increases, the rotor speeds up and the frequency increases. This increase in real power must be 

met by an increase in load or decrease in other generation in order to keep the frequency in an 

acceptable range, and supply and demand on the system in balance. If V, E, Xd remain constant, 

the power angle must be increased and Q will decrease. 

If the voltage regulator setting is increased, E increases. If V, δ, Xd remain constant, the Q will 

increase. If voltage and reactance are held constant, 

∂P/∂E = Vsin(δ)/Xd

∂Q/∂E = Vcos(δ)/Xd 

Operating Costs. We will assume that in the time period t fuel costs are constant. The operating 

costs in time period t are 

 ct(Pt,Qt, PRdwn, PRup, QRdwn, QRup; Pmin, Pmax, Qmin,Qmax, Prrmax, HR, cft, qft, csup) = cftqft + csup

where cft is the fuel and variable O&M costs in $/fuel unit qft is the quantity of fuel in fuel units, 

csup is the unit start-up costs, if the generator is running, csup= 0. Pt is the real power output of the 

generator, PRdwn and PRup are real power reserves in the up and down directions, Qt is the 

reactive power output of the generator, QRdwn and QRup are reactive power reserves in the up and 

down directions. 

The quality of real power reserves is often specified in terms of the ramp rate constraints. For 

example, the maximum change in real power output by a generator in ten minutes is the 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 136

maximum ten-minute reserve quantity. Comparable ramp rates for reactive power are effectively 

unlimited. 

 Dropping the fixed parameters to simplify, and defining losses as l(Pt,Qt ): 

ct(Pt,Qt, PRdwn, PRup, QRdwn, QRup ) = cftqft + csup

 Subject to the production possibilities set defined as 

Fuel input 

Pt ≤ qft/HR – l(Pt,Qt )λMW (1) 

Real power capacity 

Pmin + PRdwn ≤ Pt ≤ Pmax - PRup λPmin, λPmax 

(2, 3) 

Reactive power capacity 

Qmin + QRdwn ≤ Qt ≤ Qmax - QRup λQmin, λQmax 

 (4, 5) 

Ramp rate 

Pt ≤ Pt-1 ± Prrmax λPRD, λPRU (6, 7) 

rotor/field current 

(Pt – Pf)

2

 + (Qt - Qf)

2 ≤ (Sf)2 λf (8) 

stator/armature current 

(Pt)

2

 + (Qt)

2 ≤ (Sa)2 λa (9) 

under excitation/armature core end 

(Pt - Pu)

2

 + (Qt - Qu)

2 ≤ (Su)2 λu (10) 

Miscellaneous 

Qt ≤ biPt + ai λi for i = 11,..., n 

(11, ... n) 

where (Pi ,Qi) is the center of a circle with radius Si for i = f, u,λMW is the marginal value of the 

thermal power input to the generator, losses are l(Pt, Qt) = f(If

2

Rf, Ia

2

Ra ), λ = (λMW, λPmin, λPmax, 

λQmin, λQmax, λPRD, λPRU, λf, λa, λu, λ11, ..., λn) is a vector of marginal values (dual variables or 

Lagrange multipliers). 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 137

The last set of constraints is a catch-all category that includes the stability limit of the voltage 

regulator, voltage limits, generator terminal voltage limits and the prime mover operating limits. 

They can be reasonably approximated by linear inequalities. (See reference [1].) 

Power Input. Equation (1) is the thermal power conversion equation for complex power. It can 

be approximated by a set of piecewise linear constraints represented by chords of the circle. 

Losses. Losses result from currents occuring in several circuits, all of which increase fuel 

consumption and wear on the generator. The rotor field current losses are If

2

Rf; the stator field 

current losses are Ia

2

Ra. The heating induced by I2R increases the temperature in the wires. High 

temperatures over sustained periods can cause equipment damage, but can be reduced with 

additional cooling in the generator. Other losses from eddy currents and friction are usually 

ignored in steady-state models; however, they are often significant in the damping constants for 

dynamic models. 

Operating Reserves. An operating reserve is capacity held off the market to respond to one or 

more system contingencies. Operating reserves should be determined and priced simultaneously 

in auctions or power systems optimizations. Reserves capability is mostly determined by 

investment decisions and can be procured in forward markets, if necessary. Since, in this section 

of the appendix, we are not focusing on reserves, for ease of presentation, we will incorporate 

reserves into Pmin, Pmax, Qmin, and Qmax. The cost function now becomes ct(Pt,Qt), and the 

constraints in equations (2, 3) and (4, 5) become Pmin ≤ Pt ≤ Pmax, and Qmin ≤ Qt ≤ Qmax, 

respectively. 

Efficient Operations. Efficient operations require that the generator produce the optimal output 

at least cost. This is true for both a vertically integrated utility and ISO markets. In a vertically 

integrated utility, the dual variables or Lagrange multipliers from the optimal power flow model 

are equivalent to the market clearing prices from the ISO. The operating or spot market profits in 

time period t are 

πt(pt, Pt, Qt,) = pPtPt + pQtQt - ct(Pt,Qt) 

where pPt is the price of real power, and pQt is the price of reactive power. 

 

Lower case p denotes a price and upper case P denotes real power. 

In normal operations P is positive, but Q can be both positive and negative. A negative price 

signals the need for negative amounts (absorption) of reactive power. The resulting revenues, 

pQtQ, are nonnegative. 

 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 138

The D-curve. The constraints, (8), (9) and (10), form the D-curve, or generation capability 

curve, that partially defines the boundary of the PQ possibilities set. Respecting these constraints 

prevents damage from overheating, but they can be violated for short periods of time without 

significant damage. This allows for fast adjustments in reactive power output. The field current 

constraint is centered at (0, -V2

/Xd) where Xd is the direct axis synchronous reactance with radius 

VEmax/Xd. They can be conservatively represented by the chords on the circles at the intersection 

points as follows and shown in Figure B1: 

Figure B1. Linear Approximations of the Generator Capability Curve

REAL-POWER OUTPUT (MW)

REACTIVE POWER (MVAR)

Overexcited

Supplying MVA

R

Underexcited

Consuming MVA

R

Underexcitation Limit 

Linear Approximation

Armature Heating Limit 

Linear Approximation

Field Heating Limit 

Linear Approximation

Source: Modified from B. Kirby and E. Hirst 1997, Ancillary-Service Details: VoltageControl, 

ORNL/CON-453, Oak Ridge National Laboratory, Oak Ridge, Tenn., December 1997.

linear approximation to the field current constraint: Qt ≤ bfPt +af 

linear approximation to the armature current constraint: Qt ≤ baPt + aa 

linear approximation to the under excitation constraint: Qt ≤ buPt + au 

If a generator is operating on the turbine constraint, the marginal cost of producing reactive 

power is essentially zero. When a generator is not on the turbine constraint and is on another 

constraint, the locational price of reactive power is the opportunity cost of backing down real 

power. The b coefficients define the tradeoff between real and reactive power on the boundary of 

the constraint set and 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 139

 f

a

u

0, if not on the boundary

b , if field current constraint is binding

b , if armature current constraint is binding

b , if under excitation constraint is binding

t

t

Q

P

⎛ ⎞ ⎜ ⎟ ∂ = ∂

⎝ ⎠

The slope bf is typically about -.7, ba is typically about -5 and bu is typically about .4. When 

operating inside the D-curve, the marginal cost of producing reactive power is essentially zero 

or, more precisely, related to the marginal cost of losses in the generator. On the armature 

constraint, large increases of reactive power are available for very little decrease in real power 

defined on a unit basis by bf. (The armature constraint could be split in two linear constraints, 

each terminating at Qt = 0.) On the field current constraint, reactive power can be increased by a 

unit by decreasing real power by ba. On the under excitation constraint, reactive power can be 

increased by a unit by decreasing real power by bu. There is often a constraint for a voltage 

regulator with a slope of about .1. 

If the windings have additional cooling capability, the parameters of the D-curve become 

variable. Assuming the b parameters are constant, the first order approximation is 

 ai = f(cooling temperature in the windings), a is a vector of ai’s and 

 ci(ai) is the costs of changing ai. 

Therefore, the cost of adjusting the D-curve constraints is ci(ai). 

Soft Constraints. In emergencies, equipment may be operated beyond rated, nominal or steadystate limits for short periods of time. As formulated, the production possibilities set is composed 

of ‘hard’ constraints. To ‘soften’ the constraint, let Pmaxr be the rated capacity and make Pmax a 

variable with the following entry in the cost function: 

 cP(Pmax) is proportional to (Pmax/Pmaxr)

m

 

For m large, cP(Pmax) is close to 0 when 0 < Pmax < Pmaxr and cP(Pmax) increases quickly when Pmax

becomes larger than Pmaxr. The function, cP(Pmax), can be much more detailed, but for this 

discussion the simple polynomial will suffice. This can be closely approximated by a piecewise 

linear function. 

Taking into account operating reserve simplifications, variable cooling and soft 

constraints, the cost function becomes 

 c(Pt, Qt, ai, Pmax) = c(Pt, Qt) + ∑ici(ai) + cP(Pmax). 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 140

This cost function has been described as a ‘hockey stick’ curve because it is very steep beyond 

Pmaxr and as ai gets large. A similar ‘penalty’ approach can be used to soften other constraints. 

Profit Maximization or Cost Minimization. For time period t, given prices, p, (we drop the 

subscript, t, to ease the presentation) and remembering that we are ignoring reserves, to 

maximize profits, we form the Lagrangean: 

 L(P, Q, u, λ) = p(P, Q) - c(P, Q, u) - λMW(P -qf/HR + l(P, Q)) - λK(P, Q, u) 

where u is a vector of control or decision variables, e.g., a, Pmax, and qf, and K(P, Q, u) ≤ 0 is the 

linearized production possibilities set defined by: 

 Pmin ≤ P ≤ Pmax

 Qmin ≤ Q ≤ Qmax 

 P ≤ P-1 ± Prrmax 

 Q ≤ biP + ai for i = 8,..., n 

where P-1 is previous period real output. 

λ = (λPmin, λPmax, λQmin, λQmax, λPRD, λPRU, λ8 , ..., λn) 

λMW , λ ≥ 0. 

The generator maximizes profits by maximizing its Lagrangean. The optimality conditions 

include 

∂L/∂qf = -cf +λMW/HR = 0 or λMW = cfHR. 

The value of an additional MW is the heat rate times the cost of fuel. 

For optimal real power, 

∂L/∂P = pP - λMW(1 + ∂l/∂P) + λPmin - λPmax + λPRD - λPRU + ∑i λibi = 0. 

Solving for pP, the component parts of the real power price are: 

 pP = λMW(1 + ∂l/∂P) - λPmin + λPmax - λPRD + λPRU - ∑i λibi 

 When the generator operates at capacity and is not being used for reserves or on the D 

boundaries, 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 141

 pP = λMW(1 + ∂l/∂P) + λPmax = cfHR(1 + ∂l/∂P) + λPmax

The price is a composite of the fuel cost, heat rate losses and the value of additional capacity. 

If a constraint in K(P, Q, u) ≤ 0 is not binding, the associated λi is 0. Except under unusual 

conditions, only one or two of the λ’s are nonzero. For λPmin and λPmax, both cannot 

simultaneously be greater than 0. For λPRD and λPRU, both cannot simultaneously be greater than 0. 

 

Similarly, for optimal reactive power, 

∂L/∂Q = pQ - λMW∂l/∂Q + λQmin - λQmax + λQRD - λQRU + ∑i λibi = 0 

Solving for pQ, the component parts of the reactive power price are: 

 pQ = λMW∂l/∂Q - λQmin + λQmax - λQRD + λQRU - ∑i λi 

When the generator is not being used for reserves or on the D-curve boundaries, the price is a 

function of the losses and the price for reserves: 

 pQ = λMW∂l/∂Q - λQRD + λQRU

Except under unusual conditions, only one or two of the λ’s are nonzero. For λQmin and λQmax, 

both cannot simultaneously be greater than 0. For λQRD and λQRU, both cannot simultaneously be 

greater than 0. 

Prices can be positive or negative. For generators, the real power price is (almost always) 

positive, but the reactive power can be positive or negative. When pQ is negative and Q is 

negative, the payment is positive: the generator is being paid to absorb reactive power to hold 

voltage down. This might occur in light loading conditions if the transmission lines and 

capacitors could not be switched out to reduce reactive power production elsewhere. 

If output (P, Q) is not on the boundary of the augmented (variably cooled) 'D - curve' then λi = 0, 

i = 8,..., n. If (P, Q) is on the boundary then typically only one λi can be greater than 0. But the 

boundary can be moved at a cost and 

∂L/∂ai = ∂ci(ai)/∂ai - λi = 0, for i = l, ..., n. 

∂L/∂Pmax = m((Pmax)

m-1/(Pmaxr)m - λPmax = 0. 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 142

To simplify the analysis of the real/reactive tradeoffs, we will assume that the first eight 

constraints of K(P, Q, u) ≤ 0 are not binding, then 

λPmin = λPmax = λQmin = λQmax = λPRD = λPRU = 0 

If output (P,Q) is not on the boundary of the D-curve, 

 pP = λMW(1 + ∂l/∂P) 

 pQ = λMW∂l/∂Q 

If one λi > 0, i = 1,...,n 

 pP = λMW(1 + ∂l/∂P) - λibi 

 pQ = λMW∂l/∂Q + λi 

System Dispatch. In an ISO market or vertically integrated utility, a generator sends a bid or 

cost function in the form of the cost function along with its operating constraints. Also, the 

generator must run or spin at the system frequency (60 cycles per seconds in North America). 

The SO also requires generation, load and transmission operators to operate to maintain bus 

voltages within a certain range. This is often called the dead band or zone. The system operator 

(SO) optimizes the system and returns one of the following signals to the generator, (P, V), (pP, 

P, V) or (P, V, Q), depending on the market design. 

Using pQ as the signal for Q can be ambiguous because a large range of reactive power can often 

be produced at a cost close to zero. Therefore, a (pP, pQ) signal is generally unacceptable and 

should have quantities associated with the prices of reactive power. There are often penalties for 

operating outside the prescribed quantity range; in an ISO this penalty is often a function of the 

bus or nodal price. A safe but possibly redundant signal would be (P, V, Q, pP, pQ) where (P, V, 

Q) should be an optimal solution to the generator’s bid function. 

Multipart Contracts or Tariffs. If investments are lumpy and cost recovery or profitability in 

the spot markets is risky, multipart tariffs or contracts may be employed to lower risk and 

address lumpy investments. An efficient multipart tariff requires one or more demand charges for 

capacity that recovers capital costs not recovered in the spot market. The demand charge can be 

considered a real option payment to ensure the capability is available when needed. Because 

investment in reactive power is a joint cost with real power capacity, the proper demand charge 

for reactive power is hard to establish. This is particularly difficult when real power is 

compensated through market prices. When compensation for reactive power capacity is properly 

recovered, the commodity rate of opportunity costs would be compensatory. 
Appendix B - An Engineering and Economic Analysis of Real and Reactive Power 

from Synchronous Generators 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 143

Opportunity Costs. Let (P1, Q1) be the dispatch at the required level of reactive power and pP1 is 

the price of real power under the dispatch. Also, let (P2, Q2) be the dispatch after a redispatch 

beyond the required level of reactive power and pP2 is what the price of real power with the 

redispatch. 

 Profits1 = pP1P1 - c(P1,Q1) 

 Profits2 = pP2P2 - c(P2,Q2) 

 Opportunity costs = Profits2 - Profits1 = pP2P2 - c(P2,Q2) – (pP1P1 - c(P1,Q1)) 

If b(P,Q) is the bid function, 

 Apparent opportunity costs = pP2P2 - b(P2,Q2) – (pP1P1 - b(P1,Q1)) 

If the generator must dispatch real power down, in order to meet reactive power requirements, 

then P2 < P1, usually pP2 > pP1 and b(P2,Q2) < b(P1,Q1). Apparent opportunity costs are 

necessarily usually positive. 

Summary. This appendix examined the investment and operating decisions of generation market 

participants with particular focus on reactive power and the trade-offs with real power. it also has 

laid the ground for bidding in the auctions in Appendix D.

References:

1. M. M. Adibi, “Reactive Power Consideration,” Electric Power Research Institute, 2000. 

2. Arthur R. Bergen and Vijay Vittal, Power System Analysis, 2nd Ed., Prentice Hall, 2000. 

3. Charles A. Gross, Power System Analysis, Wiley, New York, 1979. 

4. David Luenberger, Optimization by Vector Space Methods, Wiley, New York, 1969. 

 

5. Oliv Mangasarian, Nonlinear Programming, McGraw-Hill, New York, 1969. 
Federal Energy Regulatory Commission Staff Report • February 4, 2005 144

Appendix C 

An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements 

n this appendix, we examine the investment and operating decisions of a transmission 

owner/operator (TO) based on the cost of supplying and consuming real and reactive power 

from transmission elements in a market with active transmission participation. Currently, TOs do 

not participate in electricity markets in the way generators or loads do because they are not in a 

position to modify the operation of their equipment based on economic signals or prices. 

Exposing TOs to price signals could result in improved capital investment decisions, as well as 

operating decisions which could improve the performance of the entire grid. Transmission 

elements include lines, capacitors, reactors, FACTS devices and transformers. The TO can 

operate a single transmission element or a traditional control area. Here, we examine the TO’s 

incentives to invest in, supply, transport and consume real and reactive power in a reliable and 

efficient manner when they play an active role in the market. 

The TO may be different from the system operator. If the system operator is financially 

independent from the owners of the electric assets, it is called an Independent System Operator 

(ISO). In this appendix, the approach taken is indifferent to whether the system operator is 

independent or a vertically integrated utility. If the system operator is independent, it must 

operate under a market design that gives incentives to the asset owner/operators to be efficient. If 

the system operator is a vertically integrated utility, the prices become transfer prices for internal 

transactions with efficiency incentives blunted by the overall regulatory scheme. We examine the 

TO as an entity or function separate from the system operator. 

We examine the TO as a price taker, avoiding the complications of gaming strategies. Gaming 

strategies are dampened through competition and mitigation of market power in the system 

operator’s auction markets. The TO takes signals from the system operator and its investments in 

transmission assets are determined by profits (or the return on the investment). 

The TO operates a transmission system by connecting and disconnecting transmission elements 

to and from the network, and by changing the phase angle, transformer tap setting, capacitance, 

inductance, resistance and impedance. Modern technical equipment can change some parameter 

settings in less than a cycle (i.e., less than 1/60 of a second) or so and can sustain repeated 

changes over successive cycles, but at additional capital and operating costs compared to 

conventional mechanical switching, which typically takes several cycles or more to operate and 

cannot sustain multiple successive changes. 

Transmission elements can, in principle, compete under the market design to transport power 

first by designing and, after construction, changing the physical properties of the 

transmission elements to perform a more valuable service. If there is a price difference between 

I 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 145

nodes, there usually are adjustments that can be made to improve efficiency. For example, by 

changing the resistance, reactance or capacitance of the transmission element the amount of real 

and reactive power flowing on the element can be changed to improve efficiency and reliability. 

These changes typically require expenditure and, consequently, the fundamental goal is to set 

incentives so that efficient changes are made, both in operations and in capital investments. 

The analysis focuses on steady-state operations with minor and temporary excursions into 

disequilibrium. For simplicity of exposition we simplify the representation of some 

characteristics. 

Active Transmission Market Participants. Today, in most ISO spot markets, transmission 

owners are mostly economically passive. That is, they usually do not change their device 

parameters in response to short-term economic conditions. The lack of active transmission 

market participation dulls the incentives of transmission owners for optimal investment and 

degrades potential system performance. Active transmission market participants subject to 

equipment, reliability and economic constraints should be a part of optimal system operation. 

There are some current practices that treat transmission elements as not completely static. Today 

some capacitors are switched in and out by the TO on instructions from the system operator. 

Some equipment can be truck mounted and is therefore mobile. In light load, transmission lines 

are opened to better balance reactive power. In some markets, phase shifters are optimally 

dispatched in the day-ahead market; in others they are set as a result of a political debate or in 

near-emergency conditions. These examples illustrate a slow movement toward incorporating 

active transmission participation in electricity markets, but there are still many more 

opportunities for transmission participation that could be available through active market 

participation. 

Investment Decisions. The carrying capacity of transmission lines is based on thermal, voltage 

and stability limits. These limits include surviving large disturbances or contingencies. Short 

lines (less than 50 miles) are usually limited by thermal capacity. Intermediate length lines (50 to 

200 miles) are often voltage limited. Longer lines are often stability limited. Steady state stability 

limits are specified by the maximum allowed phase angle differences. 

To examine the investment decision for a transmission element, we must describe the investment 

parameters. Let: 

 MVAmax be the rated thermal capacity, 

τ be the transformer tap ratio, α be the transformer phase shift, 

 R be the resistance, X be the reactance, and Bcap be the shunt susceptance. 

 The capital costs of a transmission line are a function of these parameters: 

 C(MVAmax , R, X, Bcap, α, τ, length) 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 146

In general, capital costs increase with MVAmax (∂C/∂MVAmax > 0), but the average capital costs 

per unit of rated thermal capacity (C/MVAmax) decline with increasing MVAmax. For higher 

capacity lines with operating voltages above 200 kV, the decline in average capital costs are 

small when all costs, including right-of-way and substation costs, are included. For additional 

information see reference [9]. 

Average capital costs may in some cases reach a minimum then increase. Differentiating average 

costs with respect to MVAmax: 

∂(C/MVAmax)/∂MVAmax = (∂C/∂MVAmax)/MVAmax - C/(MVAmax)

2 

 = (MVAmax ∂C/∂MVAmax-C)/(MVAmax)

2 

∂(C/MVAmax)/∂MVAmax reaches its minimum at MVAmax = MVAmax* satisfying 

∂(C/MVAmax)/∂MVAmax = 0 or 

 

∂C/∂MVAmax = C’(MVAmax*) = C(MVAmax*)/MVAmax*

That is, where average costs equal marginal costs. For MVAmax up to MVAmax*, C’ < C/ MVAmax

while for MVAmax > MVAmax* the average costs increase with increasing MVAmax. 

In general, capital costs also increase with decreasing resistance (∂C/∂R < 0). For very large 

capital expenditures like superconductors, resistance can be lowered to near zero with 

superconducting technology. However, with superconductors there is an energy expenditure to 

maintain the superconducting state, which is analogous to losses but with a different dependence 

on flow. In general, capital costs increase with decreasing impedance (∂C/∂X < 0). The ability to 

change transformer tap ratios or the existence of phase shifter settings add to the flexibility to 

respond to market signals. One approach to determining these cost differences is to ask for bids 

with different levels of capability. 

The investment decision requires revenue forecasts from a portfolio of contracts and projected 

spot market profits. The decision is to invest if: 

 C(MVAmax , R, X, Bcap, α, τ, length) < ∑t dt[πt(pt, Pt, Qt, TRMt) + CPt] 

 

where dt is the discount factor, pt is a vector of the projected market prices after entry, (Pt, Qt) are 

vector of the projected market quantities after entry (Lower case p denotes a price and upper case 

P denotes real power.), TRMt is the transmission reliability margin in time period t that can be 

differentiated by direction, πt are the spot market profits for period t and CPt are the contract 

payments net of spot market revenues in period t. Contract payments can be from selling pointto-point transmission rights and flowgate rights and/or rate base demand charges. 

Although not necessarily required, forward markets can create contractual commitments to 

supply reserves, both real and reactive. With mobile technologies, some devices can be installed 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 147

in less than a year or the time horizon of the procurement. Market participants could offer 

equipment without a precommitment of installation. Reserves markets can be characterized as 

stochastic variations of optimal dispatch auctions. This issue will be discussed in appendix D. 

For profit oriented investors, transmission is designed to maximize total profits equal to 

operating profits plus contract payments minus capital costs: 

 Max ∑t dt[πt(pt, Pt, Qt, TRMt) + CPt] - C(MVAmax , R, X, Bcap, α, τ, length). 

When lumpiness, risk and uncertainty are introduced, a more discrete complex stochastic 

analysis involving real options is appropriate for a complete analysis, but this topic is beyond the 

scope of this appendix. 

Over time, transmission asset design and manufacturing will move to the most profitable design. 

For example, more expensive better performing equipment will not be employed unless it is 

profitable. If the market design omits paying for certain desirable characteristics, they will tend 

to be undersupplied. Requiring certain characteristics without paying for them has poor 

incentives and could distort other markets. When these decisions result in sunk capital, we may 

have to live with them for years or decades. In efficient competitive markets, the most profitable 

design will be the design most beneficial to society, within the framework of the market rules. 

Next we examine profits and efficient operations in the short term markets. 

Steady State Flow Equations for Transmission. The operation of an asset must obey the 

physical laws. We describe the operating constraints and the influence on parameter choice on 

output in this section. A generic transmission line can be defined in the Figure C1 below: 

Figure C1: Generic Transmission Line

Rk

1:τkexp(αk√-1)

Pijk

Vi

Bcapik

Xk

Bcapjk

Vj

θi θj

Qijk

Pjik

Qjik
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 148

Shunt conductance in the model is omitted for clarity and since it is usually negligible. The basic 

equation for defining the real power flow along line k from bus i = I(k) towards bus j = J(k) is: 

 Pijk = Gk[(Vi)

2

 - (ViVj/τk)cos(θi - θj + αk)] - Bk(ViVj/τk)sin(θi - θj + αk) 

 

 Pjik = Gk[(Vj/τk)

2

 - (ViVj/τk)cos(θj - θi – αk)] - Bk(ViVj/τk)sin(θj - θi – αk)

 where: 

θi is the phase angle of the voltage at bus i and θij = θi - θj

 Vi is the voltage magnitude at bus i (Vi = Vj/τk + ik (Rk + (-1)1/2Xk )), 

τk is the ideal transformer tap ratio on line k 

αk is the ideal transformer phase shift on line k 

 Gk and Bk are line parameters determined by the resistance and reactance of the 

 line k. The parameters Gk and Bk, called conductance and susceptance 

 respectively, are determined from the resistance, Rk, and the reactance, Xk, of line k: 

 Gk = Rk/(Rk

2

 + Xk

2

) and Bk = -Xk/(Rk

2

 + Xk

2

). 

 I and J are index sets of the end buses for transmission element k. The end busses of line 

 k are specified by the sets I and J. 

To examine the contribution to profit, we need to examine the marginal performance of the 

equipment. To examine the transmission response to changes in control parameters, for ease of 

presentation, we will assume all functions are continuously differentiable. Discrete changes can 

be introduced with integer valued variables but it brings additional notational complexity which 

will be omitted here. For additional information see reference [4]. 

The partial derivatives of conductance and susceptance with respect to resistance and reactance 

are: 

∂Bk/∂Rk = -∂Gk/∂Xk = 2RkXk/(Rk

2

 + Xk

2

)

2 

∂Gk/∂Rk = ∂Bk/∂Xk = (Xk

2

 - Rk

2

)/(Rk

2

 + Xk

2

)

2

Prior to investment the element parameter choices, particularly that of resistance, can be highly 

variable. Once the element is constructed the options for varying the parameters are more 

limited. 

The partial derivatives of real power with respect to the phase angle and the voltage at bus i are: 

∂Pijk/∂θij = ∂Pijk/∂αk = (ViVj/τk)(Gk sin(θij+αk) - Bkcos(θij+αk)) 

 

∂Pijk/∂Vi = Gk(2Vi - (Vj/τk)cos(θij + αk)) - Bk(Vj/τk)sin(θij+ αk)). 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 149

 

The partial derivatives of real power with respect to conductance and susceptance are: 

∂Pijk/∂Gk = Vi

2

 - (ViVj/tk)cos(θij + αk) 

 

∂Pijk/∂Bk = -(ViVj/tk)sin(θij+ αk). 

For -π/2 ≤ θ ≤ π/2, -1 ≤ sin(θ) ≤ 1 and 0 ≤ cos(θ) ≤ 1. Since cos(θij + αk) < 1, if Vi > Vj/τk then 

∂Pijk/∂Gk > 0. If sin(θij+ αk) > 0 then ∂Pijk/∂Bk < 0. If sin(θij+ αk) < 0 then ∂Pijk/∂Bk > 0. 

The partial derivatives of real power with respect to resistance and reactance are: 

∂Pijk/∂Rk = (∂Pijk/∂Gk)(∂Gk/∂Rk) + (∂Pijk/∂Bk)(∂Bk/∂Rk) = 

 [(Xk

2 - Rk2

)(Vi

2

 - (ViVj/τk)cos(θij + αk)) - 2RkXk(ViVj/τk)sin(θij+ αk)]/(Rk

2

 + Xk

2

)

2

. 

∂Pijk/∂Xk =(∂Pijk/∂Gk)(∂Gk/∂Xk) + (∂Pijk/∂Bk)(∂Bk/∂Xk) = 

 [-2RkXk(Vi

2

 - (ViVj/τk)cos(θij + αk)) - (Xk

2

 - Rk

2

)(ViVj/τk)sin(θij+ αk))]/(Rk

2

 + Xk

2

)

2

Since ∂Pijk/∂Gk > 0, if Rk << Xk then ∂Pijk/∂Rk > 0, but the increase in flow due to an increase in 

Rk is accounted almost entirely by an increase in losses; that is, delivered power decreases with 

increasing Rk . (See the expression for partial derivative of losses, below.) 

We often make simplifying assumptions to get a better intuitive feel of the behavior of system 

parameters. If Vi ≈ Vj/τk , 

 

∂Pijk/∂θij = ∂Pijk/∂αk ≈ (Vi)

2

(Gk sin(θij+αk) - Bkcos(θij+αk)) 

∂Pijk/∂Vi ≈ Vi[Gk (2 - cos(θij+αk)) - Bksin(θij+αk)] 

If θij is close to 0 then sin(θ) ≈ θ and cos(θ) ≈ 1. In addition if Vi ≈ Vj/τk, and Rk << Xk then 

Gk ≈ 0 and Bk ≈ -1/Xk. 

∂Pijk/∂θij = ∂Pijk/∂αk ≈ Vi

2

/Xk

∂Pijk/∂Vi ≈ 0 

∂Pijk/∂Rk ≈ (Vi

2

 - (ViVj/τk))/Xk

2 ≈ 0 

∂Pijk/∂Xk ≈ -θijVi

2

/Xk

2

. 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 150

When the assumptions are not met the approximations may not be very useful and they may lead 

to poor results. 

The basic equation for defining the reactive power flow along line k from bus i = I(k) towards 

bus j = J(k) is: 

 Qijk = -Bk[Vi

2

 - (ViVj/τk)cos(θij + αk)] - Gk(ViVj/τk)sin(θij + αk) - Vi

2

Bcapik 

 Qjik = -Bk[(Vj/τk)

2

 - (ViVj/τk)cos(θji - αk)] - Gk(ViVj/τk)sin(θji - αk) - (Vj/τk)

2

B capjk 

where Bcapik and Bcapjk are the shunt susceptances at each end of the line representing the line 

charging capacitance of line k. Each term is equal to half the total line charging susceptance of 

the line. 

The partial derivatives of reactive power with respect to the phase angle and the voltage at bus i 

are: 

∂Qijk/∂θij = ∂Qijk/∂αk = -(ViVj/τk)(Bksin(θij+αk) - Gkcos(θij+αk)) 

∂Qijk/∂Vi = -Bk[2Vi - (Vj/τk)cos(θij + αk)] - Gk(Vj/τk)sin(θij + αk) - 2ViBcapik 

The partial derivatives of reactive power with respect to conductance and susceptance are: 

∂Qijk/∂Gk = -(ViVj/τk)sin(θij+αk) 

∂Qijk/∂Bk = -(Vi

2

 - (ViVj/τk)cos(θij+αk)) 

The partial derivatives of reactive power with respect to resistance and impedance are: 

 

∂Qijk/∂Rk = (∂Qijk/∂Gk)(∂Gk/∂Rk) + (∂Qijk/∂Bk)(∂Bk/∂Rk) = 

 = -∂Bk/∂Rk[Vi

2

 - (ViVj/τk)cos(θij+αk)] - ∂Gk/∂Rk(ViVj/τk)sin(θij+αk)] 

 = -{2RkXk[Vi

2

-(ViVj/τk)cos(θij+αk)] + [(Xk

2 - Rk2

)(ViVj/τk)sin(θij+αk)]}/(Rk

2

 + Xk

2

)

2

 

∂Qijk/∂Xk =(∂Qijk/∂Gk)(∂Gk/∂Xk) + (∂Qijk/∂Bk)(∂Bk/∂Xk) = 

 = -∂Bk/∂Xk[Vi

2

 - (ViVj/τk)cos(θij+αk)] - ∂Gk/∂Xk(ViVj/τk)sin(θij+αk)] 

 = -{(Xk

2 - Rk2

)[Vi

2

-(ViVj/τk)cos(θij+αk)] - 2RkXk (ViVj/τk)sin(θij+αk)}/(Rk

2

 + Xk

2

)

2

 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 151

If Vi ≈ Vj/τk , we have 

∂Qijk/∂θij = ∂Qijk/∂αk = -(Vi)

2

(Bksin(θij+αk) + Gkcos(θij+αk)) 

∂Qijk/∂Vi = -Vi{Bk[2- cos(θij+αk)] + Gksin(θij+αk) + 2Bcapik}. 

∂Qijk/∂Rk = -Vi

2

{2RkXk[1-cos(θij+αk)] + [(Xk

2 - Rk2

)sin(θij+αk)]}/(Rk

2

+Xk

2

)

2

 

∂Qijk/∂Xk = -Vi

2

{(Xk

2 - Rk2

)[1-cos(θij+αk)] - [2RkXk sin(θij+αk)]}/(Rk

2

+Xk

2

)

2

 

If θij +αk is close to 0, Vi ≈ Vj/τk, and Rk << Xk, we have 

∂Qijk/∂θij ≈ 0 

∂Qijk/∂Vi ≈ -2Vi(Bk + Bcapik) 

∂Qijk/∂Rk ≈ 0 

∂Qijk/∂Xk ≈ 0. 

Transmission Losses. Although often ignored for computational and presentational simplicity, 

losses can be a significant factor in system economics. This is especially true for reactive power 

losses. Transmission losses are essentially the power consumed/absorbed by the transmission 

asset, and dissipated as heat, as it performs its function of moving or transforming power. For 

real power, losses (or consumption) for transmission element k are: 

lPk (θ, V, t, α) = Pijk + Pjik = Gk[Vi

2

 + (Vj/τk)

2

 - 2(ViVj/τk)cos(θij + αk)] 

The partial derivatives of real power losses with respect to voltage and phase angle are: 

∂lPk /∂Vi = 2Gk[Vi - (Vj/τk)cos(θij + αk)]. 

∂lPk /∂θij = ∂lPk /∂αk = 2Gk (ViVj/τk)sin(θij + αk). 

If we assume Vi > Vj/τk, an increase in the high-end voltage increases real losses, but the flow is 

increased by an even greater amount. If θij + αk > 0, an increase in phase angle increases real 

losses, but again the flow also increases. 

The partial derivative of real power losses with respect to conductance is: 

∂lPk /∂Gk = Vi

2

 + (Vj/τk)

2

 - 2(ViVj/τk)cos(θij + αk) 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 152

Since cos(θij + αk) < 1, if Vj/τk < Vi then ∂lPk /∂Gk > 0 and an increase in conductance increases 

losses. 

Since ∂lPk /∂Bk = 0, the partial derivatives of real power losses with respect to resistance and 

reactance are: 

∂lPk /∂Rk = (∂lPk /∂Gk)(∂Gk/∂Rk) = 

 (Xk

2 - Rk2

) [Vi

2

 + (Vj/τk)

2

 - 2(ViVj/τk)cos(θij + αk)]/(Rk

2

 + Xk

2

)

2

. 

If Xk > Rk then ∂lPk /∂Rk > 0. 

∂lPk /∂Xk = (∂lPk /∂Gk)(∂Gk /∂Xk) 

 =(-2XkRk)[(Vi)

2

 + (Vj/τk)

2

 - 2(ViVj/τk)cos(θi - θj + αk)]/(Rk

2

 + Xk

2

)

2 

Real losses increase as the resistance, voltage difference and phase angle difference increase. For 

a transmission line, if Xk >> Rk (as is usually the case), then Gk ≈ 0 and lPk (θ, V, τ, α) ≈ 0. If the 

transmission element is a line, as its length increases, the resistance, Rk, increases, Xk increases 

and losses increase. Resistance and reactance are design parameters and, in some more expensive 

devices, can be varied in operation. As voltage gets higher, in general, Rk /Xk decreases. 

 For reactive power losses (or consumption) are: 

lQk (θ, V, t, α) = Qijk + Qjik 

 = -Bk[Vi

2

 + (Vj/τk)

2

 - 2(ViVj/τk)cos(θi - θj + αk)] - Vi

2

Bcapik - (Vj /τk)

2

Bcapjk 

The partial derivative of reactive power losses with respect to voltage is: 

 

∂lQk /∂Vi = -2Bk[Vi - (Vj/τk)cos(θi - θj + αk)] - 2Bcapik 

If Vi is sufficiently larger than Vj/τk then an increase in voltage at the high voltage end increases 

reactive losses (but would also tend to increase voltage at the low voltage end, countervailing 

this effect.) If Vi ≈ Vj/τk then increasing voltage decreases (net) reactive losses. 

The partial derivative of reactive power losses with respect to phase angle is: 

∂lQk /∂θij = ∂lQk /∂αk = -2Bk(ViVj/τk)sin(θi - θj + αk)] 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 153

If sin(θi - θj + αk) > 0 then an increase in the phase angle increases reactive losses. 

The partial derivative of reactive power losses with respect to susceptance is: 

∂lQk /∂Bk = -((Vi)

2

 + (Vj/τk)

2

 - 2(ViVj/τk)cos(θi - θj + αk)). 

Since cos(θi - θj + αk) < 1 then ∂lQk /∂Bk < 0. 

Since ∂lQk /∂Gk = 0, the partial derivatives of reactive power losses with respect to resistance and 

reactance are: 

∂lQk /∂Rk = (∂lQk /∂Bk)(∂Bk /∂Rk) 

 =(-2XkRk)[(Vi)

2

 + (Vj/τk)

2

 - 2(ViVj/τk)cos(θi - θj + αk)]/(Rk

2

 + Xk

2

)

2 

∂lQk /∂Xk = (∂lQk /∂Bk)(∂Bk /∂Xk) 

 =(-Xk

2

 + Rk

2

)[(Vi)

2

 + (Vj/τk)

2

 - 2(ViVj/τk)cos(θi - θj + αk)]/(Rk

2

 + Xk

2

)

2 

Reactive power losses decrease with increasing susceptance, Bk, increase with the phase angle 

difference, voltage differences and can be offset with additional capacitor capacity. 

 If Vi ≈ Vj/τk, 

lQk (θ, V, τ, α) = Vi

2

{-2Bk [1 - cos(θi - θj + αk)] - Bcapik - Bcapjk}. 

 When -2Bk[1 - cos(θi - θj+ αk)] = Bcapik + Bcapjk, lQk = 0. 

The point at which lQk = 0 is called the surge impedance loading. It is easy to see how a 

capacitor can offset reactive power losses. Capacitors are often installed in banks and deployed 

as needed. As the phase angle moves away from 0, reactive losses (or consumption) increase. 

If Xk >> Rk (as is usually the case), then Bk ≈ -1/Xk and lQk (θ, V, τ, α) is usually non-zero. If the 

transmission element is a line, as it gets longer, the resistance, Rk, increases, Xk increases and 

losses increase. As nominal voltage class gets higher, in general, Rk / Xk decreases. 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 154

If θij + αk ≈ 0 and Vi ≈ Vj/τk , 

∂lQk /∂Vi = -2Bk [Vi - (Vj/τk)cos(θij+ αk)] – 2 ViBcapik] ≈ -2ViBcapik

∂lQk /∂θij ≈ -2Bk(ViVj/τk)(θij+ αk) 

∂lQk /∂Rk =-2Rk [Vi - (Vj/τk)cos(θij+ αk)] - 2 Vi Bcapik]/ Xk

3

 ≈ 0 

∂lQk /∂Xk = -[(Vi)

2

 + (Vj/τk)

2

 - 2(ViVj/τk)]/Xk

2 ≈ 0 

If Xk >> Rk, Bk >> Gk then reactive losses are much greater than real losses: 

lQk (θ, V, τ, α) >> lPk (θ, V, τ, α). 

Operating Costs. Although we will examine a single transmission element, this analysis can be 

extended to more than two buses by presenting prices and quantities at the priced buses or nodes. 

We will further assume that in the time period t the physical depreciation and operating costs are 

essentially negligible. We have the following constraints. 

Conservation of Energy:

 Pijk + Pjik - lPk = 0 λP (1) 

 Qijk + Qjik - lQk = 0 λQ (2) 

where λP is value of another unit of real power transferred and 

 λQ is value of another unit of reactive power transferred.

Thermal Limits: If the thermal limit, in MVA, is MVAmax, then: 

 [(Pijk)

2

+(Qijk)

2

]

1/2 + TRM - MVAmax ≤ 0 λMVAi (3i). 

 [(Pjik)

2

+(Qjik)

2

]

1/2 + TRM - MVAmax ≤ 0 λMVAj (3j). 

 where λMVAi is the value of another unit of thermal capacity at bus i. 

The thermal limit is often simplified to Pijk + TRM - MWmax ≤ 0 where MWmax is adjusted in 

magnitude to account for the simplification. An approximation can be derived from the first 

order Taylor series expansion, 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 155

 bPijkPijk+bQijkQijk + TRM - MVAmax ≤ 0 

where bPijk/bQijk is the tradeoff between real and reactive power when the element is at its 

limit and MVAmax is the adjusted capacity including the constant terms of the linearization (an 

alternative approach would be to supply a piecewise linear function as an approximation to the 

quadratic function.). 

Miscellaneous Surrogate Constraints. Some other constraints can be formulated as: 

 Pijk - MWh ≤ 0 λh (h = 5,..., n) 

 

 where λ = (λP, λQ, λMVA, λh) is a vector of marginal values (dual variables 

 or Lagrange multipliers). 

Power Inputs, Outputs and Losses. Real losses are induced by current in a line and are equal to 

I

2

R. An increase in current increases the temperature in the wires. High temperatures can cause 

equipment damage. 

Operating Reserves. Transmission reserves should be determined and priced simultaneously in 

auctions or power systems optimizations. 

Efficient Operations. Efficient operations require that the TO produce the optimal output at 

least cost. In many cases once an asset is in-service the operation is passive. This is true for both 

a vertically integrated utility and ISO markets. In a vertically integrated utility, the dual variables 

or Lagrange multipliers from the optimal power flow model are transfer prices. In an ISO, the 

Lagrange multipliers are the prices. The revenues in time period t are 

 pt(Pt, Qt, TRMt , MVAt

max , Rt, Xt, τt , αt , Bcapt)’ 

 where pt = (pPti, pPtj, pQti, pQtj, pTRMt, pMVAt, pRt, pXt, pτt , pαt , pBcapt ) is a price vector, 

 pPti, pPtj is the price of real power buses i and j in time period t, 

 pQti, pQtj is the price of reactive power buses i and j in time period t, 

 pTRMt is the price of transmission margin in time period t, ... 

Revenues depend on the bus prices and the amount of real and reactive power injected or 

withdrawn at each bus. 

Soft Constraints. In emergencies, equipment is often operated beyond rated, nominal or steadystate limits for short periods of time. As formulated, the production possibilities set is composed 

of hard constraints. To soften the constraint, we introduce MVAmax as a real time parameter 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 156

variable. If MVAmaxr is the rated capacity, we can make MVAmax a variable with the following 

entry in the cost function: 

 cMVA(MVAmax) = (MVAmax /MVAmaxr)

m 

For m large and MVAmax < MVAmaxr, cMVA(MVAmax) is close to 0. For m large and MVAmax > 

MVAmaxr, cMVA(MVAmax) increases quickly when MVAmax becomes larger than MVAmaxr. The 

function, cMVA(MVAmax), can be much more detailed, but for this discussion the 

polynomial will suffice. This can be closely approximated by a piecewise linear function. This 

type of cost function has been described as a ‘hockey stick’ curve because it is very steep beyond 

MVAmaxr. In a multi-period setting, the amount of time an asset can be operated beyond its rating 

can be specified similarly to the way that downtime is modeled for generators. This process can 

be used to soften other constraints. 

If the asset has additional cooling capability, the thermal capacity of the asset becomes variable. 

 MVAmaxr = f(cooling temperature, wind speed) and 

 cc(MVAmaxr) is the costs of changing MVAmaxr

 Now, the cost function becomes 

 cMVA(MVAmax, MVAmaxr) = (MVAmax/MVAmaxr)

m + cc(MVAmaxr). 

Profit Maximization or Cost Minimization. For time period t, given prices, p, (we drop the 

subscript, t, to ease the presentation) and ignoring losses, we form the Lagrangean: the TO 

maximizes profits by solving the Lagrangean optimization: 

 L(P, Q, TRM, MVAmax, R, X, α, τ, Bcap, λ) = 

 p(P, Q, TRM, MVAmax, R, X, α, τ, Bcap) - cMVA(MVAmax, MVAmaxr) 

 - λK(Pi, Pj, Qi, Qj, TRM, MVAmax, R, X, α, τ, Bcap) 

 where K(Pi, Pj, Qi, Qj, TRM, MVAmax, R, X, α, τ, Bcap) ≤ 0 can be represented as: 

 

 Pijk + Pjik - lPk = 0 λP (1) 

 Qijk + Qjik - lQk = 0 λQ (2) 

 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 157

bPijkPijk+bQijkQijk + TRM - MVAmax ≤ 0 λMVAi (3i). 

 bPjikPjik+bQjikQjik + TRM - MVAmax ≤ 0 λMVAj (3j) 

 Pijk - MWh

 ≤ 0 λh (5,..., n) 

 

 where λ = (λP, λQ, λMVAi, λMVAj, λh) is a vector of marginal values (dual variables 

 or Lagrange multipliers). 

Prices and quantities for real and reactive power (λP, λQ) can be positive or negative. When pQ is 

negative and Q is negative, the payment is positive. If a constraint is not binding, the associated 

λh is 0. When Karush-Kuhn-Tucker conditions (see [4] and [5]) are satisfied, there is a solution 

to the problem. We now find the maximum of the Lagrangean. The optimality conditions include 

choosing the optimal parameter settings of MVAmax, R, X, α, τ, Bcap to satisfy: (since it is not 

needed, we drop the subscribe k) 

∂L/∂Pij = pPij - ∑h λh∂Kh/∂Pij = 0 or 

 pPij = λP(1+∂Pji/∂Pij - ∂lP/∂Pij) + λMVAibPij + ∑h λh 

∂L/∂Qij = pQij - ∑h λh∂Kh/∂Qij = 0 or 

 pQij = λQ(1+∂Qji/∂Qij - ∂lQ/∂Qij) + λMVAibQij 

∂L/∂MVAmax = pMVAmax -∂c/∂MVAmax - ∑h λh∂Kh/∂MVAmax = 0 or 

 pMVAmax = ∂c/∂MVAmax + λMVAi + λMVAj 

 

∂L/∂X = pX - ∑h λh∂Kh/∂X = 0 or 

 pX = λP(∂Pij/∂X+∂Pji/∂X - ∂lP/∂X) + λQ(∂Qij/∂X+∂Qji/∂X - ∂lQ/∂X) 

∂L/∂R = pR - ∑h λh∂Kh/∂X = 0 or 

 pR = λP(∂Pij/∂R+∂Pji/∂R - ∂lP/∂R) + λQ(∂Qij/∂R+∂Qji/∂R - ∂lQ/∂R) 

∂L/∂τ = pτ -∂c/∂τ - ∑h λh∂Kh/∂τ or 

 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 158

pτ = λP(∂Pij/∂τ+∂Pji/∂τ - ∂lP/∂τ) + λQ(∂Qij/∂τ +∂Qji/∂τ - ∂lQ/∂τ) 

∂L/∂α = pα - ∑h λh∂Kh/∂α = 0. or 

 pα = λP(∂Pij/∂α+∂Pji/∂α - ∂lP/∂α) + λQ(∂Qij/∂α +∂Qji/∂α - ∂lQ/∂α) 

∂L/∂Bcapi = pBcap - ∑h λh∂Kh/∂Bcapi = 0.

 pBcapi = λQ(∂Qij/∂Bcapi - ∂lQ/∂Bcapi ) 

This optimization depends on variable control over a variety of parameters, many of which are 

not currently variable, including line limits, resistance and reactance. 

Summary. This appendix examined the investment and operating decisions of active 

transmission market participants. Its intention is to stimulate discussion of introducing active 

transmission participation into the market. 
Appendix C -An Engineering and Economic Analysis of Real and Reactive Power 

from Transmission Elements

Principles for Efficient and Reliable Reactive Power Supply and Consumption 159

References:

1. Arthur R. Bergen and Vijay Vittal, Power System Analysis, 2nd Ed., Prentice Hall, 2000. 

2. Charles A. Gross, Power System Analysis, Wiley, New York, 1979. 

3. William W. Hogan, “Financial Transmission Right Formulations,” Harvard University, 

March 31, 2002, submitted to FERC in RM01-12-000. 

4. David Luenberger, Optimization by Vector Space Methods, Wiley, New York, 1969. 

5. Oliv Mangasarian, Nonlinear Programming, McGraw-Hill, New York, 1969. 

6. Richard O’Neill, Ross Baldick, Udi Helman, Michael H. Rothkopf and William Stewart 

Jr., “Dispatchable Transmission in RTO Markets,” IEEE Transactions on Power Systems, 

to appear. 

7. R.P. O’Neill, U. Helman, B.F. Hobbs, W.R. Stewart and M.H. Rothkopf, “A Joint Energy 

and Transmission Rights Auction: Proposal and Properties,” IEEE Transactions on 

Power Systems, 17(4), November 2002, 1058-1067. 

8. Richard P. O’Neill, Paul M. Sotkiewicz, Benjamin F. Hobbs, Michael H. Rothkopf and 

William R. Stewart Jr., “Efficient Market-Clearing Prices in Markets with 

Nonconvexities,” European Journal of Operational Research, Vol. 164/1, 269-285. 

9. Krishnan Dixit and Ross Baldick, “An Empirical Study of the Economies of Scale in AC 

Transmission Line Construction Costs,” December 2003. 
Federal Energy Regulatory Commission Staff Report • February 4, 2005 160

Appendix D 

An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

he system operator’s job is to efficiently plan and operate the system using the constrained 

assets along with associated bids or costs. In this appendix, the system operator neither owns 

nor operates electric assets, but gives signals or messages to generators, transmission 

owner/operators and load that define how the system should be operated. We also assume that 

the information system is noiseless and has accurate system measurement, e.g., revenue quality 

meters but make comments on potential noise problems. The system operator can be considered 

an ISO or a separate function in a vertically integrated utility. The system operator’s investments 

are in software, hardware and personnel, and responsibilities include reliability planning and 

operation. 

In these appendices the approach taken is indifferent to whether the system operator is 

independent or a vertically integrated utility. If the system operator is independent, it must 

monitor and mitigate market power of market participants. Through market design, the electric 

asset owner/operators should have profit incentives to be efficient. Large firms often simulate 

competition internally by using transfer pricing between functional units like system operation, 

generation operation and transmission operation. If the system operator is a vertically integrated 

utility, the prices become transfer prices for internal transactions, but the efficiency incentives 

are usually blunted by the overall regulatory scheme. 

Electricity is unusual in that when a generating or transmission unit is lost and prices go up, 

demand response is minimal and, in extreme cases, load must be removed from the system to 

prevent wide-spread system collapse. Because of the low level of demand response, and need for 

carefully balanced generation and load, networks tend to be designed conservatively. Wood and 

Wollenberg state, “Networks are designed with large capacity margins so that the elements tend 

to be loaded conservatively.” (See reference [7].) To enforce this conservative loading and 

maintain grid performance, the system employs three types of constraints: thermal, voltage, and 

stability. Thermal constraints arise from overheating of equipment leading to damage and poor 

performance. Voltage is controlled by supplying and consuming reactive power. Stability 

limitations are part art form based on experience and selected simulations. As computation speed 

increases, software improves and costs decrease, more analysis can be performed both closer to 

real time and in forward planning leading to greater efficiency and reliability. 

The state of the power system is defined by voltage and phase angles at system nodes. Here we 

ask the optimal AC power flow (AC OPF) software to find the optimum output in terms of P and 

Q. This includes optimal voltage schedules and settings of transformer taps, switched capacitors 

and FACTS devices. The system operator’s management of reactive resources involves 

equipment capability and actual delivery. That is, the system operator must have control over 

T 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 161

enough reactive power capability to produce and absorb reactive power in response to the timevarying and location-specific requirements of the system to control voltage efficiently. An AC 

constrained optimal-power-flow analysis can determine the reactive power dispatch that 

maximizes benefits to the system. 

In a competitive environment, determination of who has provided what service will be more 

important. Basing generation schedules or payment on claimed capability may not be adequate. 

The actual reactive power output from a generator may not match the manufacturer’s capability 

specifications. Adjustment of tap settings on the step-up (and other) transformers, adjustment of 

station service voltage levels, and recalibrating and setting alarms and meters (and sometimes 

replacing meters) are often needed to increase the actual reactive power output. 

Today, ISOs run centralized capacity, transmission rights, day-ahead and real-time markets for 

real power. These auctions can be extended to include reactive power. Again the approach taken 

in this appendix is indifferent between a vertically integrated utility and an ISO. In a capacity 

market auction we can no longer neglect the discrete nature of investment choices, but the 

auction process no longer has tight time windows to be completed like the DAM and RTM. Here 

we outline a capacity auction for reactive power. 

Computational and Modeling Issues. Some argue that a full AC model would be 

computationally burdensome. Significant computer hardware advances and advances in market 

software design, driven by market design changes, e.g., PJM, NYISO and ISO-NE, have been 

made in the last decade. In 1996, a 300-node network market model in New Zealand was the 

state of the art. Currently, a 30,000-node model with greater network detail is being solved faster 

than the 300-node model in 1996. As yet, there is no production software the can perform a full 

AC constrained optimal-power. 

Problems, once considered practically unsolvable, are now solved in several minutes. These 

advances allow a convergence of reliability and market software. The limiting factor seems to be 

data quality (garbage in, garbage out). Even with all these advances, reactive power and voltage 

control is still a challenge. Robust optimal solutions to a security constrained AC OPF that 

includes reactive power and voltage control are still elusive and require more research and 

development.

To date, reactive power management in bulk power systems has been based on establishing preand post-contingency voltage limits. Generators are given voltage schedules. Control devices, 

such as transformer taps, shunt capacitors/reactors and generator voltages, are set to maintain 

voltages within the limits, using a variety of manual and local automatic control. Many controls 

can be adjusted at most a few times in a day. 

Reactive power limits are also managed implicitly via surrogate transmission limits. Thermal 

limits are de-rated to account for reactive power flows. Interface limits are often surrogate 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 162

constraints associated with voltage, voltage drop, and voltage stability. Must-run units are 

identified through off-line studies. Because these approaches do not base limits on actual reactive 

power values and are updated infrequently, they often necessitate large and imprecise safety 

margins that can reduce the utilization for the power system. 

Today, the standard market operation system package does not include reactive power as part of 

the co-optimization of real power with reserves. The real and reactive controls are 

mathematically cross-coupled. In the ideal OPF formulation, real and reactive controls are 

considered simultaneously subject to all constraints with a single cost objective function. 

Intertemporal constraints need to be modeled similar to the approach to generator unit 

commitment. To date convergence and formulation problems have prevented usable engineering 

solutions. Currently, active and reactive power controls are optimized separately leading to 

suboptimal solutions. 

We need to bring more science into what is still seen by many as an engineering art form. A 

modular and flexible approach to modeling the problem will allow less expensive incorporation 

of the necessary algorithms for co-optimizing with reactive power. To support better software 

development, data quality needs improvement. ISO New England is currently engaged in 

projects to evaluate sensitivities during system congestion and the difference between proxybased voltage constraints and explicit modeling in the OPF. 

Conservation of Complex Power Balancing Equations. The power flow at each bus in a 

network must obey the conservation of power laws. For simplicity we assume one generator or 

load at each bus. For real power at each bus i and each connecting transmission element k , the 

conservation of real power yields: 

 HPi(Pi,V,θ, u) = Pi - ∑k Pijk = 0, 

 where Pijk = Gk[Vi

2

 - (ViVj/τk)cos(θi - θj + αk)] - Bk(ViVj/τk)sin(θi - θj + αk), the real power 

flow from bus i to bus j on transmission element k. If i is not a terminal bus for k, Gk = Bk = Pijk

= 0. 

For reactive power at each bus i, conservation of reactive power yields: 

 HQi(Qi,V,θ, u) = Qi - ∑k Qijk = 0,

where Qijk = -Bk[Vi

2

 - (ViVj/τk)cos(θi - θj + αk)] - Gk(ViVj/τk)sin(θi - θj + αk) - Vi

2

Bcapik, 

the reactive power flow from bus i to bus j on transmission element k. If i is not a terminal bus 

for k, Gk = Bk = Qijk = 0. 

 Bus 0 is defined as the swing, slack or reference bus and we define 2n independent bus 

balancing equations in vector form: 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 163

 HP(P,V,θ, u) = (HP1(P1,V,θ, u),..., HPn (Pn,V,θ, u)) = 0. 

 HQ(Q,V,θ, u) = (HQ1(Q1,V,θ, u),..., HQn(Qn,V,θ, u)) = 0. 

 

We define the Jacobian matrices of partial derivatives as: 

 J11 = [∂Pi/∂θj]ij J12 = [∂Pi/∂Vj]ij J21 = [∂Qi/∂θj]ij J22 = [∂Qi/∂Vj]ij 

 where i, j = 1,..., n and [ ]ij is the entry for ith row and jth column. 

For i ≠ j, 

∂Pi/∂θj = -∑k {(ViVj/τk)[Gksin(θi - θj + αk) - Bkcos(θi - θj + αk)]}; 

∂Pi/∂Vj = -∑k {(Vi/τk)[Gkcos(θi - θj + αk) + Bksin(θi - θj + αk)]}; 

∂Qi/∂θj = ∑k {(ViVj/τk)[Gkcos(θi - θj + αk) + Bksin(θi - θj + αk)]}; and 

∂Qi/∂Vj = ∑k {(Vi/τk)[-Gksin(θi - θj + αk) + Bkcos(θi - θj + αk)]}. 

Also, 

∂Pi/∂θi = ∑k {(ViVj/τk)[Gksin(θi - θj + αk) - Bkcos(θi - θj + αk)]}; 

∂Pi/∂Vi = ∑k {Gk[2Vi - (Vj/τk)cos(θi - θj + αk)] - Bk(Vj/τk)sin(θi - θj + αk)}; 

∂Qi/∂θi = -∑k { (ViVj/ τk)[Gkcos(θi - θj + αk) + Bksin(θi - θj + αk)]}; and 

∂Qi/∂Vi = -∑k {Bk[2Vi - (Vj/τk)cos(θi - θj + αk)] + Gk(Vj/τk)sin(θi - θj + αk)] + 2ViBcapik.}. 

In each the summation over k must be taken over the appropriate transmission elements. 

Decoupling the Power Flow. To solve these equations simplifications are often made based on 

actual system operations. If we assume Rk << Xk, then Gk << Bk. We assume no shunt reactances 

to ground and no shunts to ground from autotransformers. If we assume no phase shifting 

transformers, then αk = 0. Additionally, we assume, θi - θj ≈ 0 and τk = 1, the simplifications 

yield: 

 HPi (Pi,V, θ, u) ≈ Pi - ∑k Gk[Vi

2

 - ViVj] + ∑k BkViVj(θi - θj ) ≈ 0, i = 0, 1,..., n 

 HQi (Qi,V, θ, u) ≈ Qi + ∑kBk [Vi

2

 - ViVj] + ∑k GkViVj(θi - θj ) ≈ 0, i = 0, 1,..., n 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 164

∂Pi/∂Vj ≈ -∑k Vi[Gk + Bk(θi - θj ) ] ≈ 0, 

 where the sum includes all elements k connecting i and j, 

 

∂Qi/∂θj ≈ ∑k (ViVj)[Gk ] ≈ 0, 

 where the sum includes all elements k connecting i and j, 

For i ≠ j, 

∂Pi/∂θj ≈ ViVj∑k Bk and let Bij = Vj∑k Bk, 

 where the sum includes all elements k connecting i and j 

∂Qi/∂Vj ≈ Vi∑k Bk, and let Bij = ∑k Bk, 

 where the sum includes all elements k connecting i and j. 

Also, 

∂Pi/∂θi ≈ -Vi∑j Vj∑k Bk and let Bii =-∑j Vj∑k Bk, 

 where the sum includes all elements k connecting to i for each j. 

∂Qi/∂Vi ≈ -Vi∑k Bk and Bii = -∑k Bk, 

 where the sum includes all elements k connecting to i for each j. 

Let ∆P/V = (∆P1 /V1,..., ∆Pn /Vn), ∆Q/V = (∆Q1 /V1,..., ∆Qn /Vn), ∆V = (∆V1,..., ∆Vn), 

∆θ = (∆θ1,..., ∆θn) and B = [Bij]ij, we obtain the DC power flow model: 

∆P/V = B∆θ 

As can be seen the DC model assumes constant voltage and is blind to reactive power, but is 

easier to solve than the AC model. Voltage constraints are approximated with proxy thermal 

constraints. 

The decoupled AC model is: 

 

∆P/V = B∆θ and ∆Q/V = B∆V 

 

The system is solved by fixing voltages solving the DC equations, then solving the reactive 

equations and iterating between the two sets of equations to achieve the best result. Both DC 

model and the iterative model approaches arose out of a need to simplify the computation. As 

hardware advances are made, computational constraints are less important, although these 

approximations may still be useful in solving the coupled equations rapidly. The remaining 

challenge is to find an optimal solution to the highly nonconvex AC optimization problem. More 

work needs to be done to improve the optimization techniques. 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 165

Voltage Limits. Voltage limits, based on results of system studies, are assigned to buses in order 

to maintain grid stability. : 

 Vi

min ≤ Vi ≤ Vimax λVimin, λVimax i = 1,..., n 

If Vi = Vi

max or Vi = Vimin, the dual variable can be different from zero. In the computer 

algorithms, equality constraints are approximate. Software requires acceptable tolerances for 

zero. All constraints are, in effect, inequality constraints. Instead of constraints like Vi

min ≤ Vi ≤

Vi

max , a cost of voltage deviation could be added to the objective function to represent the 

possibility, yet high cost of, voltage deviations. The function should have steep slopes when 

approaching limits. For example, dropping the subscript i, let 

 V – vmax+ + vmax- = Vmax with vmax+

, vmax- ≥ 0, 

 V - vmin+ + vmin- = Vmin; vmin+

, v

min- ≥ 0, and 

 cV(V; Vmin, Vmax) = (vmax+)

m + (vmin-)m. 

the variable, vmax+ , measures the excursion outside the ‘deadband’ or target range on the high 

voltage side and the variable, vmin-, measures the excursion outside the ‘deadband’ or target range 

on the low voltage side. 

In an optimization if V > Vmax, v

max+ > 0, then vmax- = vmin+

 = v

min- = 0. If V < Vmin

, v

min- > 0, then 

vmax- = v

min+

 = vmax- = 0. If Vmin < V < Vmax, v

max+

 = v

min- = 0, then cV(V; Vmin, Vmax) = 0. The 

magnitude of m sends a price signal for ‘violating’ the hard constraint, Vmin ≤ V ≤ Vmax. The 

marginal cost is 

∂cV/∂V = m(vmax+)

m-1 + m(vmin-)m-1. 

If V is outside the range [Vmin, Vmax], the cV(V; Vmin, Vmax) increases rapidly depending on m. 

The function, cV(V; Vmin, Vmax), could be interpreted as an insurance premium for voltage 

collapse that is a function of where the system operates. An analogous construct can be used for 

frequency, but we omit it here to avoid additional notation. Certain loads may want even smaller 

tolerances on voltages. They could submit bids with smaller tolerances. 

The AC Optimal Power Flow Auction. The system operator acts as an auctioneer by taking 

bids from market participants. Each generator submits a bid of the form: 

 bGi(P, Q, uGi) subject to operating constraints, KGi(P, Q, uGi) ≤ 0 where uGi is a vector of 

control variables for i = 1,..., I 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 166

Each transmission operator submits a bid of the form: 

 bTk(P, Q, uTk) subject to operating constraints, KTk(P, Q, uTk) ≤ 0, where uTk is a vector of 

control variables for k = 1,..., K. 

With some loss in approximation, both bids can be required to be linear mixed-integer in both 

the bid function and the constraint function. We have purposely created bid parameters for 

transmission that were previously considered fixed. FACTS technology, in particular, enables 

these parameters to be varied. The bus chosen for the market transaction can be limited to a 

subset of buses or nodes that can be aggregated for the convenience of financial trading. In 

practical terms the system operator has a representation of both generation and transmission bid 

and constraint functions, and changes are submitted periodically. 

The system operator solves the following AC optimal power flow problem that may include 

some mitigation of the bids: 

 Max W(P,Q,u) = ∑i bGi(P,Q,uGi) + ∑k bTk(P,Q,uTk) - ∑i cVi(Vi; Vi

min, Vimax) 

 subject to 

 KG(P,Q,u) ≤ 0, μG 

 KT(P,Q,u) ≤ 0 μTk 

 HP (P,V,θ, u) = 0, λP

 HQ(Q,V,θ, u) = 0, λQ. 

 where KG(P,Q,u) = (KG1(P,Q,u1), ..., KGn(P,Q,un)), μG = (μG1 ,..., μGn), 

 KT(P,Q,u) = (KT1(P,Q,u1), ..., KTn(P,Q,un)), μT = (μT1 ,..., μTn) 

 HP (P,V,θ) = (HP1(P1,V,θ),..., HPn (Pn,V,θ)), λP

 HQ(Q,V,θ) = (HQ1(Q1,V,θ),..., HQn(Qn,V,θ)), λQ. 

If the problem is formulated as a mixed-integer nonlinear program, we can allow discrete system 

changes like generation start-up, breaker status and phase shifter settings. (See references [6], [7] 

and [8].) To avoid making the problem overly complex, we will continue with only continuous 

variables. 

To solve AC optimal power flow auction problem, we define the Lagrangean function as 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 167

 Max L(P, Q, u, λ, μ) = 

 W(P,Q,u) - μGKG(P,Q,u) - μTKT(P,Q,u) - λPHP (P,V,θ) - λQHQ(Q,V,θ) 

The optimal solution must satisfy certain Karush-Kuhn-Tucker conditions (see [4] and [5]), that 

include: 

 ∇W(P,Q,u) - μG∇KG(P,Q,uG) - μT∇KT(P,Q,uT) - λP∇HP (P,V,θ) - λQ∇HQ(Q,V,θ) = 0. 

 

 μGKG(P,Q,uG) = 0, 

 μTKT(P,Q,uT) = 0 

 HP(P,V,θ) = 0 

 HQ(Q,V,θ) = 0. 

Let P*, Q*, u*, μG*, μT*, λP*, λQ* = argmax {L(P, Q, u, λ, μ), μ ≥ 0}. 

 where λPi is the optimal real power price at bus i, 

 λQi is the optimal reactive power price at bus i, 

 μTk is the optimal price vector for components of transmission element k, 

 μGi is the optimal constraint value vector for generator i. 

The partial derivative of the objective function is usually the derivative of the cost or bid 

function. The Lagrange multipliers, μ, give the value of a marginal unit of the constraint and λ is 

the value of relaxing the conservation of power equations. 

For real power at bus i, 

∂L/∂Pi = ∂W/∂Pi - μ∂K/∂Pi - λ∂H/∂Pi = 0 

Since ∂HPi/∂Pi = 1 and ∂W/∂Pi = ∂ci/∂Pi , 

 pPi = λPi = ∂ci/∂Pi + μ∂K/∂Pi + ∑j ≠ i λj∂H/∂Pi 

For reactive power at bus i, 

∂L/∂Qi = ∂W/∂Qi - μ∂K/∂Qi - λ∂H/∂Qi = 0 

Since ∂HQi/∂Qi = 1 and neglecting losses ∂ci/∂Pi = 0, 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 168

 pQi = λQi = μ∂K/∂Qi + ∑j ≠ i λj∂H/∂Qi 

For voltage at bus i, 

 ∂L/∂Vi = -∂c/∂Vi - μ∂K/∂Vi - λ∂H/∂Vi = 0 

 pVi = ∂c/∂Vi + μ∂K/∂Vi + λ∂H/∂Vi 

For reactance of transmission element k, 

 ∂L/∂Xk = ∂W/∂Xk - μ∂K/∂Xk - λ∂H/Xk = 0 

 pXk = ∂c/∂Xk + μ∂K/∂Xk + λ∂H/∂Xk 

For transformer tap of transmission element k, 

 ∂L/∂τk = ∂W/∂τk - μ∂K/∂τk - λ∂H/τk = 0 

 pτk = ∂c/∂τ + ∑i λi∂Hi/∂τ + μ∂K/∂τk + λ∂H/∂τk 

For shunt capacitor of transmission element k, 

 ∂L/∂Bcapk = ∂W/∂Bcapk - μ∂K/∂Bcapk - λ∂H/Bcapk = 0 

 pBcapk = ∂c/∂Bcap + μ∂K/∂Bcapk + λ∂H/∂Bcapk 

For the thermal capacity of transmission element k, 

∂L/∂MVAk

max = 0 

For the phase shifter of transmission element k, 

∂L/∂α = -∂c/∂α - ∑i λi∂Hi/∂α = 0.

System Dispatch. In an ISO market or vertically integrated utility today, the transmission 

operators are essentially passive as market participants, with some minor active participation. 

Capacitors are switched in and out by the system operator. In some markets, e.g., Britain, the 

capacitors are mobile. In light load, transmission lines are opened to better balance reactive 

power. In some markets phase shifters are optimally dispatched. In others they are set as a result 

of a political debate. The system operator optimizes the system and returns one of the following: 

MVAmax, R, X, α, Bcap, depending on the controls to the TO and on the market design. In 

general, however, transmission characteristics are not changed optimally in real time. 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 169

In the reactive power market here, the system operator receives bids or cost functions in the form 

of the cost function along with its operating constraints from all market participants. The system 

operator optimizes the system and returns one of the following signals to market participants, (P, 

V), (pP, P, V) or (P, V, Q), depending on the market design. When pQ is at or near zero, the 

resulting signal for Q is ambiguous so the (pP, pQ) signal is generally unacceptable. A safe but 

redundant signal would be (P, V, Q, p) where (P, V, Q) should be an optimal solution to the 

system operator’s problem and p is a vector of complete prices. Currently both OATT and ISO 

tariffs have penalties for not responding to quantity instructions. In ISOs the penalties are a 

function of the market prices. Consequently full quantity and price information may be necessary 

for market participants to make efficient decentralized decisions. 

The above market model presents an ambitious market design to include reactive power. It is not 

necessary to implement all at once. Decisions on relative impact of additions to the market 

design should be made on a regional basis depending on the needs of the market and reliability. 

The Planning Process or Forward Procurement Auctions. In the planning process or 

procurement auction, the system operator has different time horizon from hours ahead to a year 

or more. Planning activities in a vertically integrated utility require costs estimates and operating 

constraints from the generation and transmission operators. Procurement auctions are run by 

independent system operators and function by having the system operator take bids from market 

participants. Some auctions for capacity only and not for forward power. In these auctions 

constraints and rights may be defined differently. Capacity for contingencies may only be needed 

for short periods of time. In these cases thermal constraints can be relaxed. Active participation 

in these markets can be avoided with bilateral contracts, but contracts must be accounted for in 

the reliability constraints.

 

 Each generator submits a bid that includes an offer for a new investment, UGit, in period t, 

capital cost, C(UGit), of the form: 

 bGi(P, Q, ui) - wGitC(UGit) 

 where bGi(P, Q, ui) is the offer/cost of operating the assets. The variable wGit is a binary 

decision variable, representing a “yes” or “no” investment decision. The bid is subject to vector 

constraints: 

 KGit(uGit, wGit, UGit) = uGit - UGitwGit ≤ 0, wGit ∈ {0,1} for i =N+1,..., N + Nnew 

 where Nnew is the number of newly proposed generation investments. 

These constraints are added to KGit(P, Q, uGit) ≤ 0, the existing operating constraints and 

constraints are modified for the new investment proposals. 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 170

Each transmission operator submits a bid that includes offers for a new investment, UTkt, in 

period t at capital cost, C(UTkt), of the form: 

 bTk(P, Q, uTk) – wTktC(UTkt) 

 where bTkt(P, Q, uTkt) is the offer/ cost of operating the assets. The variable wTkt is a 

binary decision variable representing a “yes” or “no” investment decision. The bid is subject to 

vector constraints 

 KTkt(uTkt, wTkt, UTkt) = uTkt - UTktwTkt ≤ 0, wTkt ∈ { 0,1} for k =K+1,..., K + Knew 

 where Knew is the number of newly proposed transmission investments. 

These constraints are added to KTkt(P, Q, uTkt) ≤ 0, the existing operating constraints and 

constraints are modified for the new investment proposals. 

We call KTkt(uTkt, wTkt, UTkt) = uTkt - UTktwTkt ≤ 0, wTkt ∈ {0,1}, the topology function since the 

setting of the wTkt defines the network. The wTkt variables are circuit breakers in dispatch 

markets. They collectively determine the topology of the network. In a planning model or 

forward markets, a circuit breaker becomes an investment option. 

The system operator operates as an auctioneer by taking bids from market participants and 

solving a contingent AC optimal power flow. The system operator chooses a discrete set of 

contingencies or events that satisfy the reliability criteria for the system, e.g., N-1 contingencies. 

A probability, ρω, is assigned to each mutually exclusive event ω where 0 ≤ ρω ≤ 1 and 1 - ∑ω ρω

is the probability of a system failure, e.g., 24 hours of system failures in 10 years (24/10*365*24 

= .00027). An event, ω, would be a failure (forced outage) of a large generator or a transmission 

element. 

After possible mitigation of the bids, the system operator solves the following AC optimal power 

flow problem: 

 Max Wt(P,Q,u) = 

∑t dt{∑ω ρω[∑i bGi(Pω

,Qω, uGiω)+∑k bTk(Pω,Qω, uTkω) - ∑i cVi(Vit

ω

; Vit

minω, Vitmaxω

)]} 

 subject to 

 KGi(P1

ω

, Q1

ω

, u1

ω

,... , Ptmaxω, Qtmaxω, utmaxω)

ω ≤ 0, μG

ω

 for ω ∈ Ω 

 KTk(P1

ω

, Q1

ω

, u1

ω

,... , Ptmaxω, Qtmaxω, utmaxω)

ω

 ≤ 0 μT

ω

 for ω ∈ Ω 

 HPt(Pt

ω

,Vt

ω

,θt

ω

)

ω

 = 0, λPt

ω

 for ω ∈ Ω and t. 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 171

 HQt(Qt

ω

,Vt

ω

,θt

ω

)

ω

 = 0, λQtω for ω ∈ Ω and t. 

 

 where dt is the discount factor and tmax is the time horizon. 

The problem is formulated as a mixed-integer nonlinear program. It requires that the system 

survive each contingency, ω ∫ Ω. Since the problem is stochastic, we can calculate expected 

future prices: pPt = λPt =∑ω ρωλPt

ω

 and pQt = λQt =∑ω ρωλQtω. 

Unfortunately, this problem is a large security constrained AC OPF that presents a significant 

computational challenge, but as a forward auction the time available to solve the problem can be 

measured in days. 

To solve the AC optimal power flow investment auction problem, we define the Lagrangean 

function and we solve the optimization problem in the same manner as before. Of course, any 

winning bid would be guaranteed its bid costs as a payment, but as a market clearing price 

auction modified for two-part or multi-part pricing, more efficient compensation is possible. 

Where entry competition is not feasible, bids may need to be mitigated. 

The auction or planning process can be designed as an iterative process. After each round market 

participants submit new bids to provide capacity and/or energy until the auction stops by rule or 

stops producing benefits. These auctions need additional rules to ensure good results. 

A Possible Market Design Market. In this section we present a straw man proposal as a means 

of departure from current market design to stimulate discussion. The SO takes bids from 

generation, transmission, and load. Since the market is usually lumpy, non-convex and has low 

demand elasticity, market power mitigation and scarcity pricing may be necessary. The SO 

solves the reliability constrained AC OPF with scarcity pricing and calculates quantities (and 

prices if desired) for dispatch signals. 

The market settlement would pay each market participant the product of bus price and quantity 

supplied by market participants. Other products like reserves are priced on a similar basis where 

the ‘bus’ may be an aggregated bus for each reserve category based on flow studies. An 

aggregate bus is an ex ante properly electrically aggregated bus that represents a region of 

similar electric properties. Examples include aggregations based on emergence ratings or 

reactive power capabilities. This is in contrast to a hub that is an ex post aggregation of prices. 

Since Pi - ∑k Pijk = 0 and Qi - ∑k Qijk = 0, pPi(Pi - ∑k Pijk = 0) and pQi(Qi - ∑k Qijk = 0). The market 

is revenue adequate. If the bids are ‘convex’, revenue adequacy is obvious (for more details see 

references 8 and 9). If bids reflect marginal opportunity costs, the market result is efficient and 

what would result if the market is competitive. 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 172

The market settlement would also guarantee bid costs for suppliers and not charge any buyer 

more than they offered to pay. If the bids are not ‘convex’, a two-part tariff or settlement scheme 

may be necessary (for more details see references 10 and 11). If the ACOPF objection function is 

greater than zero, there is enough valued offered by buyers to compensate all offers accepted 

offers by the sellers. Cooperative game theory allocations have been proposed as an approach to 

dividing up the benefits and assigning costs, but in general, there is no single fully incentive 

compatible method for the second part of the tariff. 

Bus prices are truly opportunity costs prices. This means that the incremental value to the market 

is for small changes at the bus for that time period. These prices do not give an investment signal 

unless the prices would persist into the future. As we have seen in the past, this is speculative 

In a forward auction market with a reasonably long horizon, many market participants or 

potential market participants and open entry, the market is efficient and competitive. Open entry 

requires access to sites and right-of-way by all market participants. Each market participant has 

the option of bilateral contracting that will depend on the transactions costs of using or not using 

a central market mechanism. 

An iterative auction process for long-term rights would look more like an IRP process with 

competition to build the new assets. 

Summary. This appendix examined the investment and operating decisions for planning by a 

vertically integrated utility or auction markets operated by the independent system operator. For 

many enhancements in software the issue is the relative tradeoffs with other enhancements. Low 

probability events like blackouts are difficult to assess in a cost benefit analysis. Its intention is 

to stimulate discussion of planning, investment and dispatch markets for real and reactive power. 
Appendix D -An Engineering and Economic Analysis of a System Operator’s 

Real and Reactive Power Planning and Markets 

Principles for Efficient and Reliable Reactive Power Supply and Consumption 173

References: 

1. Arthur R. Bergen and Vijay Vittal, Power System Analysis, 2nd Ed., Prentice Hall, 2000. 

2. M. C. Caramanis, R. E. Bohn and F. C. Schweppe, “Optimal Spot Pricing: Theory and 

Practice,” IEEE Transactions on Power Apparatus and Systems, Vol. 101, No. 9, September 

1982. 

3. Charles A. Gross, Power System Analysis, Wiley, New York, 1979. 

4. David Luenberger, Optimization by Vector Space Methods, Wiley, New York, 1969. 

 

5. Oliv Mangasarian, Nonlinear Programming, McGraw-Hill, New York, 1969. 

6. William W. Hogan, “Financial Transmission Right Formulations,” Harvard University, 

March 31, 2002, submitted to FERC in RM01-12-000. 

7. Richard O’Neill, Ross Baldick, Udi Helman, Michael H. Rothkopf and William Stewart Jr., 

“Dispatchable Transmission in RTO Markets,” IEEE Transactions on Power Systems, to appear. 

8. R.P. O’Neill, U. Helman, B.F. Hobbs, W.R. Stewart and M.H. Rothkopf, "The Joint Energy 

and Transmission Rights Auction: A General Framework for RTO Market Designs," Working 

Paper, Office of Markets, Tariffs and Rates, Federal Energy Regulatory Commission, July 31, 

2001, http://business.wm.edu/william.stewart/Energy/energy_market_economics.htm 

 

9. R.P. O’Neill, U. Helman, B.F. Hobbs, W.R. Stewart and M.H. Rothkopf, AA Joint Energy 

and Transmission Rights Auction: Proposal and Properties, @ IEEE Trans. Power Systems, 17(4), 

November 2002, 1058-1067. 

10. Richard P. O’Neill, Paul M. Sotkiewicz, Benjamin F. Hobbs, Michael H. Rothkopf and 

William R. Stewart Jr., “Efficient Market-Clearing Prices in Markets with Nonconvexities,” 

European Journal of Operational Research, Vol. 164/1, 269-285. 

11. Richard P. O’Neill, Ross Baldick, Wedad Elmaghraby, Michael H. Rothkopf, and William 

R. Stewart, Jr., “Finding Two-Part Tariffs that Support Efficient Equilibria 

in Non-Convex Markets,” August 2004, 

http://business.wm.edu/william.stewart/Energy/energy_market_economics.htm. 

12. A. J. Wood and B. F. Wollenberg, Power Generation Operation and Control, 2nd Ed., John 

Wiley and Sons, New York, January 1996. 
174 Principles for Efficient and Reliable Reactive Power Supply and Consumption

Appendix E Appendix E -Electric Plants in Service (2003)

Source: Form 1 Database

Accounts U.S. Dollars

(310) Land and Land Rights 610,596,947

(311) Structures and Improvements 15,183,125,395

(312) Boiler Plant Equipment 63,984,610,251

(313) Engines and Engine-Driven Generators 118,645,023

(314) Turbogenerator Units 18,138,116,901

(315) Accessory Electric Equipment 7,747,563,668

(316) Misc. Power Plant Equipment 2,031,368,371

(317) Asset Retirement Costs for Steam Production 256,278,453

TOTAL: Steam Production Plants 108,070,305,009

(320) Land and Land Rights 189,393,277

(321) Structures and Improvements 20,634,123,933

(322) Reactor Plant Equipment 30,382,418,886

(323) Turbogenerator Units 9,375,167,934

(324) Accessory Electric Equipment 9,626,506,240

(325) Misc. Power Plant Equipment 4,151,263,843

(326) Asset Retirement Costs for Nuclear Production 3,700,054,774

TOTAL: Nuclear Production Plants 78,058,928,887

(330) Land and Land Rights 499,961,476

(331) Structures and Improvements 2,072,478,124

(332) Reservoirs, Dams, and Waterways 6,352,487,660

(333) Water Wheels, Turbines, and Generators 2,979,902,854

(334) Accessory Electric Equipment 824,581,003

(335) Misc. Power Plant Equipment 255,842,689

(336) Roads, Railroads, and Bridges 190,436,253

(337) Asset Retirement Costs for Hydraulic Production 15,725,473

TOTAL: Hydraulic Production Plants 13,191,415,532

(340) Land and Land Rights 120,149,148

(341) Structures and Improvements 1,933,732,229

(342) Fuel Holders, Products, and Accessories 1,163,672,943

(343) Prime Movers 8,215,313,643

(344) Generators 7,639,307,657

(345) Accessory Electric Equipment 1,600,073,967

(346) Misc. Power Plant Equipment 220,264,209

TOTAL: Other Production Plants 20,892,513,796

Electric Plants in Service (2003)

(Accounts 101, 102, 103 and 106)
Federal Energy Regulatory Commission Staff Report •February 4, 2005 175

Appendix E -Electric Plants in Service (2003)

 Accounts U.S. Dollars

 TurboGen Accounts

314 18,138,116,901

323 9,375,167,934

333 2,979,902,854

344 7,639,307,657

Total 38,132,495,346

Accessory Electric Equipment Accounts

315 7,747,563,668

324 9,626,506,240

334 824,581,003

345 1,600,073,967

Total 19,798,724,878

All Production Plant Accounts 310-346

Steam 108,070,305,009

Nuclear 78,058,928,887

Hydro 13,191,415,532

Other 20,892,513,796

Total 220,213,163,224

Total costs of Turbogenerator 38,132,495,346

Percentage of Cost allocated to Generator and Exciter 24%*

Cost of Gen+Exciter 9,151,798,883

Total costs of Accessory Electric Equipment 19,798,724,878

Percentage allocated to VAR production 10%*

Cost of Accessory elctric equipment - watt/var production 1,979,872,488

Total (Gen+Exciter+Accessory electric equip) 11,131,671,371

Percentage allocated to Reactive Power 21%*

Investment in Reactive Power Production 2,337,650,988

Production Plants - (Gen+Exciter+Accessory Electric equip) 209,081,491,853

Percentage of real power reqd to produce reactive power 0.15%*

Investment in Reactive Power Production 313,622,238

Total Investment in Reactive Power Production 2,651,273,226

Percentage allocated to reactive power production 1.2%

*These percentages were used in American Electric Power Service Corp., 88 FERC P61, 141 (1999)

Application of AEP Methodology to all the respondents of Form-1 Application of AEP Methodology to all the respondents of Form-1