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PUBLICATIONS

NBS Technical Note 1209

MARKET: A Modelfor Analyzing

the Production, Trammissbn, and

Distribution ofNatural Gas

Christoph Witzgall and Patsy B. Saunders

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No. 1209

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M he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The ^

Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

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Gaithersburg, MD 20899. ^Some divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithersburg, MD.
RATIONAL BUPP""

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NBS Technical Note 1209

MARKET: A Modelfor Analyzing

the Production, Transmission, and

Distribution ofNatural Gas

Christoph Witzgall Sponsored by:

Patsy B. Saunders Analysis and Forecasting Branch

Reserves and Natural Gas Division Operations Research Division U.S. Department of Energy

Center for Applied Mathematics Washington, D.C. 20461

National Engineering Laboratory

National Bureau of Standards Gaithersburg, MD 20899

Issued April 1985

/ \f \

U.S. Department of Conuneroe Malcolm Baldiige, Secretary National Bureau of Standards

Ernest Ambler, Director
National Bureau of Standards U.S. Government Printing Office For sale by the Superintendent Technical Note 1209 Washington: 1985 of Documents,

Natl. Bur. Stand. (U.S.) U.S. Government Printing Office, Tech. Note 1209, Washington, DC 20402

162 pages (Apr. 1985)

CODEN: NBTNAE
Abstract

This report describes the MARKET submodel, one of three that combine to

form the Gas Analysis Modeling System (GAMS). GAMS was developed for use by

the Energy Information Administration of the U.S. Department of Energy. It

provides a tool for analyzing the regional effects on the domestic natural gas

market of various policies for regulating the price of natural gas at the

wellhead. MARKET is concerned with the production of gas reserves and the

transmission and distribution of gas to consumers. It solves a network

equilibration problem to arrive at estimates of production quantities and

prices.

Keywords: demand, deregulation, energy model, equilibration, gas

distribution, gas production, gas transmission, natural gas,

network, pipeline, policy modeling, simulation, supply

iii
Acknowledgements

R.E.Schofer, together with the authors, was a charter member of the NBS

project team and was Instrumental in the design of the MARKET model and in the

Identification of Its data sources. He was later joined by A.D.Davles and

L.S.Joel. All three researchers were coauthors, along with the present

authors, of a comprehensive letter report to EIA upon which this report is

largely based. The authors also acknowledge the assistance provided by

J.Bernal in designing and implementing procedures to Insure smooth interfaces

between the MARKET model and various data sources. We appreciate the support

of R. H.F.Jackson during the design of the equilibration process. We thank

R.E. Chapman for his review and Implementation of the pipeline and distributor

tariff submodels, which have been designed by J.-^.Guldmann. Finally, we are grateful for the long hours spent by S.Cohen and B .M .Mariner-Volpe of the EIA

while assisting us in the implementation of the MARKET model.

iv
Table of Contents

Page

CHAPTER 1 : Introduction 1

CHAPTER 2 : Background and Model Overview 4

2.1 The national natural gas Industry 4

2.2 Characteristic features of the natural

gas market 13

2.3 Federal regulations of natural gas commerce 14

2.3.1 The NGPA 14

2.3.2 Rate determination 15

2 .4 Model purpose and scope 16

2.5 Data sources 18

2.6 Model overview 19

2.7 Model sensitivities 24

2.8 What can a model achieve? 27

CHAPTER 3: Conceptual Description of the MARKET Model 30

3.1 The general setting of GAMS 30

3.2 The role of the MARKET model in GAMS 31

3.3 The base network of supply patterns 32

3.3.1 Definition of the base network 33

3.3.2 Structure of the base network 36

3.3.3 Quantities associated with the

base network 37

3.4 Primary supplies and pipeline systems 38

3.4.1 Pipeline systems and system networks 39

3.4.2 Consumption patterns at M-nodes 40

3.5 Supply at the pipegate 42

3.5.1 Production profiles and supply curves 43

3.5.2 Analysis of production profiles 47

3.6 Demand at the burnertlp 51

3.6.1 Illustrating local demand curve generation.. 51

3.6.2 The regional demand compatibility condition. 53

3.6.3 Cut-off prices 56

3.7 Tariffs 56

3.7.1 Expected flows and peak day volumes 58

3.7.2 Outline of the distribution tariff module .. 59

3.8 Storage 62

3.9 The concept of equilibration 63

3.9.1 Definition of equilibrium 64

3.9.2 Transformation and combination of

demand curves 67

CHAPTER 4: Procedural Description of the MARKET Model 70

4.1 Modeling the base year 70

4.1.1 Initial system flows 70

4.1.2 Initial system price levels 72

4.1.3 Adjusting for storage costs 75

4.2 Equilibration 77

4.2.1 Bipartitlon 78

4.2.2 Committed Flows 79
Page

4.2.3 Feasibility Check 80

4.2.3.1 Flow generation and

normalization 82

4.2.3.2 Determining price levels 83

4.2.4 Negative flows and negative prices 84

4.2.5 Post-equilibration wrap-up 86

4.3 Updating secondary prices and flows 88

4.4 Estimation of storage requirements 90

4.5 Demand projection 91

4.6 Diagram of the MARKET model 92

4.6.1 Input phase 92

4.6.2 Base year modeling 93

4.6.3 Post base year modeling 94

4.6.4 Set up demand projection table 95

4.6.5 Project system demand 96

CHAPTER 5: Network Representation of the Gas Supply System 97

5.1 Phase I: Network Generation 97

5.2 Phase II: Processing Additional Data ....113

5.3 GENNET Output 115

NOTES 120

REFERENCES 157

VI
CHAPTER 1

Introduction

In the Spring of 1981, the Operations Research Division of the National

Bureau of Standards (NBS) was contacted by the Department of Energy's Energy

Information Administration (EIA) to explore NBS participation in the

development of a mathematical model representing the major economic aspects of

the natural gas market in the U.S. and their interrelationships. A need for

such a model was perceived because of a rising conviction in Congress and the

Administration that changes in the regulatory structure of the natural gas

market, particularly at the production end of it, were becoming necessary.

This regulatory structure is dominated by the Natural Gas Policy Act (NGPA) of

1978.

In the ensuing months, NBS conducted an intensive discussion with EIA

staff, in particular Dr. Richard P. O'Neill, about the requirements to be met

by such a model, its general structure, and the availability of supporting

data. NBS eventually concentrated on marketing aspects, formulating a network

equilibrium model and developing a solution procedure for it.

By the Fall of 1981, a first general specification of Gas Analysis

Modeling System (GAMS) had evolved, with NBS efforts now focused on the

Implementation of MARKET, one of three major components of the GAMS system.

The other two components are PROLOG and BID. PROLOG, developed at EIA, is

concerned with the exploration and development of natural gas reserves in

response to expected profitability, capital resources, and the availability of

drilling rigs and other equipment. Finding rates applied to levels of

exploratory drilling yield natural gas reserves which are offered for sale to

pipeline companies. BID, developed by Professor Charles Mylander of the U.S.

Naval Academy, simulates the process by which competing pipeline companies bid

for the reserves offered by producers. The actual price bid by each pipeline

company is based on the estimated production schedule and price of reserves currently dedicated to the pipeline company and the estimated price and

quantity of gas that can be marketed over the next several years. Reserves

are awarded on the basis of prices. When bid prices exceed ceiling prices, reserves are awarded according to historical market shares modified by bid

prices. MARKET, developed at the National Bureau of Standards (NBS), serves three major functions. First, it establishes a consistent set of base year

data describing commercial relationships among pipeline companies,

distributors, and end-use markets or consumers. Second, it provides

information relevant to the BID model by estimating the quantity of gas that

could be sold to distributors and end-users during the next several years at

various wellhead price levels. Third, given the average wellhead price and

maximum production available from each source of reserves awarded to a pipeline company, MARKET estimates the actual quantity and average price of

gas sold by simulating the transmission and distribution of gas to end users. The reserves available from each source are then reduced according to the

volume of gas sold.
NBS was also faced with providing a realistic representation of the

network of supply relationships between pipeline companies and distribution

companies, and with establishing bench-marks for burner-tip demand in the base

year. It was found that the form EIA-50 contained information from which such

a network could be generated for input into the MARKET model. This task

turned out to be too extensive to be handled manually. The task of generating

the network of supply relationships from form EIA-50 and supplemental data

was therefore automated, giving rise to the procedure GENNET, which operates

on a stand-alone basis. The first version of GENNET was completed in January

1982, and it was modified repeatedly until Fall 1982.

The MARKET model is conceptually independent of GENNET and will accept

any network generated — manually or by computer — so that it meets the

generic input requirements of MARKET.

Debugging of MARKET started in January 1982, and the first complete runs

of GAMS involving the entire network were obtained in Spring 1982. The

assistance of Mr. Samuel Cohen of EIA was crucial for this achievement. A

period of testing, adaptation and modification was followed by the first set

of production runs in October 1982. The results of these runs provided

important insight but in their details were not yet fully compatible with

several known aspects of the natural gas market, so that further adjustments

as well as further specification of legislative scenarios were needed before

conclusive production runs could be conducted. At that time, it was decided

that broader participation in these additional steps was desirable, and that

staff from Brookhaven National Laboratory (BNL), particularly Mr. Mark Minasi,

Dr. Steven Wade, and Mr. Bradford Wing should join NBS in efforts of upgrading

and maintaining the MARKET model, with Ms. Barbara Mariner-Volpe as coordinator. Definitive production runs were made at the end of April 1983.

Their results formed the cornerstone of the EIA publication: The Natural Gas

Market through 1990; Part IV; An Analysis of the NGPA and Several

Alternatives (DOE-EIA-0366, May 1983).

Subsequently, efforts to upgrade and to include new options were continued by both BNL and NBS. One major new development involved the

integration of the GAMS system with the EIA's Integrated Future Forecasting

System (IFFS). In August 1984, EIA issued a first set of documentary reports:

Model Documentation of the Gas Analysis Modeling System; Volume I: Model

Overview (DOE-EIA-0450/1) ; Volume II ; Model Methodology (DOE-EIA-0450/2);

Volume III ; Software and Data Documentation and User's Guide

(DOE-EIA-0450/3).

It is clear from this short history of the GAMS model, that there is no "final" version. At best there are certain "frozen" versions, which represent

various stages of development and various specific scenarios that EIA was called upon to analyze at particular points in time. Indeed, GAMS is fairly

typical for large modeling efforts of this kind in that it represents a collection of adaptable interrelating submodels rather than a single

monolithic package. Nevertheless, the characteristic features and the

structural basis of GAMS have remained unchanged to a remarkable degree.
The purpose and the scope of the present report must be seen in this

context. That purpose is to outline the major concepts and assumptions of the

MARKET model as developed by NBS . For additional details of implementation as well as information about alternative assumptions and particular stages of the

model evolution, the reader is referred to an extensive set of Notes at the

end of the report

.

The document is organized into four chapters and an appendix consisting

of a set of notes. Chapter 2 provides the background setting and an overview

of the model for the nonspecialist reader. It attempts to convey the nature

of the analytic requirements, which GAMS in general and MARKET in particular

are designed to address, and to discuss the model structure vis-a-vis these

requirements. The subsequent more comprehensive description of MARKET is then

split into two parts: Chapter 3 features the key concepts of the model

individually, whereas Chapter 4 treats their interrelationships and the

procedural techniques employed in the model. Chapter 5 describes the GENNET

procedure for generating the representation of the supply network which

underlies MARKET.

A letter report, GAMS /MARKET; A Model for Analyzing the Production , Transmission, and Distribution of Natural Gas , was transmitted to EIA in May

1983. The present report relies heavily on the material contained in that

letter report which is more detailed and documentation oriented, but does not

deal with some of the more recent developments.
CHAPTER 2

Background and Model Overview

In this chapter, we examine the aspects of natural gas commerce which are

to be modeled- We then specify requirements for such a model, discuss

available data, and provide a brief overview of the MARKETT model. We close

with an examination of the expectations which surround mathematical models

like GAMS.

2.1 The national natural gas industry

Not until the 1930's did the use of natural gas begin on a significant

commercial scale. During the two decades following World War II, natural gas

proceeded to replace manufactured gas almost entirely as the Nation's gas fuel

and to open vast new markets as a residential and commercial heating and

cooling agent, as industrial boiler fuel and feed stock, and as a resource for

generating electric energy. For a comprehensive as well as entertaining

treatise on the development of the natural gas market in our country, we refer

to an article by B. Commoner [6].

This development was put into motion by the evolution of an extensive and

intricate system of gas pipelines . The majority of the large pipelines

originate in the area encompassed by Texas, Lousiana and their neighboring

States. They service distant major population and industrial centers such as New England, the Upper Midwest, and California. A newer development is the

influx of Canadian Gas into the Pacific States and the Great Lakes Region. A

trans-Canadian pipeline making Alaskan gas available to the lower 48 states is

still on the planning boards. Beyond this, the construction of new pipeline

mileage has apparently peaked, and only few major pipeline extensions are anticipated.

The pipelines are operated by pipeline companies (see Table 2.1).

Typically, these companies buy their gas from gas -producing companies on the

basis of long term price-binding contractual agreements. These represent

agreements by individual producers to offer their whole production for sale to one particular pipeline company, respectively, usually for the entire

production periods of the facilities in question. The agreements also

stipulate how sales prices are to be set and recalculated over time.

The pipeline company then sells and transmits the gas to distribution

companies , which sell and distribute the gas locally to end-users. The latter

are generally divided into four end-use sectors , residential, commercial,

industrial and electric utilities, with different rates charged according to

sector. Consumption data are usually reported broken down by these sectors.
To denote the major stations through which gas passes on its way to the

end-user, the terms wellhead , pipegate , citygate and burnertip are frequently

employed. The gas enters the pipegate, the start of the pipeline proper,

after it has been gathered from the wellhead and processed to remove liquids

and impurities. A considerable amount of plant and lease fuel , typically

around 5-8%, is needed to power gathering and processing facilities, and is

consumed on the spot by various parties involved in the production process.

The citygate is the point at which the gas becomes the property of the

distribution company, and the burnertip is the point of actual consumption

(see Figure 2.1). On their journey from pipegate to citygate, shipments will

suffer transmission losses , mainly due to the use of parts of these shipments

as pipeline fuel , that is, gas to power compressor stations. During

distribution, gas will be lost by leakage or be otherwise unaccounted for.

Volume of natural gas is usually measured at 14.73 psia and SO^F. A

frequently used unit is the "Mcf" (= 1000 cubic feet). Energy content of

delivered natural gas varies between 950 and 1250 Btu (= British thermal unit)

per cubic foot with 1020 Btu adopted frequently as a nominal value. The

abbreviations "BBtu" and "Quad" are used for billions and quadrillions of Btu,

respectively. In this report, we use the terms volume and quantity

interchangeably for shipments of gas, regardless of whether these shipments

are measured by volume or energy content.

Both pipeline and distribution companies are considered public utilities,

that is, they are permitted to recover all costs, but are not permitted to

profit beyond an agreed upon return on the securities issued by them. Posted

rates, or tariffs , are therefore subject to review and approval by public

agencies. Prices charged by interstate pipeline companies are monitored by

the Federal Energy Regulatory Commission (FERC), and those of intrastate

pipelines and distribution companies by the Public Utility Commissions in

their respective States.

From the regulatory point of view, there is an important distinction

between the interstate and the intrastate market for natural gas. The

interstate market is formed by pipeline companies which engage in the

transmission and selling of natural gas across state lines, and also by those

producers whose gas reserves are contractually dedicated for sale to such

interstate pipelines. The intrastate market is then defined by exclusion as those production and transmission facilities which are not part of the

interstate market.

The above description of the natural gas industry is, of course,

oversimplified. First of all, not all gas transmitted by a pipeline is owned

by that pipeline: there are many transactions in which a pipeline company

transmits gas owned by some other party. The tariffs for such transmission

services are again posted and subject to approval by public agencies.
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The distinction between pipeline companies and distribution companies is

not as clear-cut as one might wish. A typical distribution company (see Table

2.3) like Washington Gas Light may have transmission facilities crossing state

lines, and therefore could be considered legally an interstate pipeline. Some

distributors like Pacific Gas and Electric may own transmission facilities

comparable in size to those of major pipeline companies and may be the main

suppliers of other sizeable distributors. On the other hand, pipeline

companies may sell directly to end-users in the industrial as well as in the

residential sectors. Sales of this kind to major industrial customers are typically nonjurisdictional, i.e., subject to less stringent tariff control by

the FERC. The same distribution company may furthermore sell - at different

rates - in more than one State, Washington Gas Light being again a prime

example.

Distribution companies are, in general, concerned with local

distribution. Their numbers of customers are typically large, and most

customers are end-users. Pipeline companies transmit large quantities of gas over long distances. They gather gas from many production facilities, channel

it into large single pipelines, and sell to a relatively small number of

customers, mostly for resale rather than end-use. Distributors are state

regulated; interstate pipelines are federally regulated. Distribution

companies tend to be older corporate units than pipeline companies, going back

to the days of coal gas: in some cases the old wooden pipes are still in use*

Frequently, a distribution company supplies both gas and electricity, whereas

pipeline companies deal typically with only one energy source, namely natural

gas. Classification becomes difficult for companies like Mountain Fuel and

Kansas-Nebraska. These are relatively young companies serving large sparsely

populated areas which often spread over state lines. While distributing

directly to residential as well as Industrial end-users, they operate large

transmission facilities and withdraw gas from dedicated reserves. These

companies thus have the characteristics both of distributors and of medium

sized interstate pipeline companies.

Last but not least, there is a large degree of vertical integration of

corporations across production, transmission and distribution. Many pipeline

companies and even some distributors own gas reserves directly or via

subsidiaries. Many distribution companies are subsidiaries of a pipeline

company. For example, the distribution companies Columbia of Ohio, Columbia

of West Virginia, and Columbia of Pennsylvania are wholly owned subsidiaries

of the Columbia Gas Pipeline Company. On the other hand, Washington Gas

Light, a distributor, owns gas reserves in Wyoming.

A significant portion of the natural gas withdrawn consists of direct

sales by producers to end-users; or it is producer-used , that is, it will be

directly utilized other than as plant and lease fuel by its producer, usually

a large industrial facility, without involving any second party. In the

latter case, there are no actual sales involved, although prices may be

formally reported for tax purposes.
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12
2.2 Characteristic features of the natural gas market

For our purposes, the salient feature of the natural gas market is the

relationship between the pipeline company as buyer and the gas producer as seller. As was mentioned above, this relationship is based on long range

contractual agreements which dedicate the production from specified reserves

to a particular pipeline company. This commitment of an individual producer

to a particular pipeline company is due to the need for a physical hook-up

between the wellhead and the pipegate. The pipeline company thus acts as a monopsony: it is the only available buyer from all those gas reserves to

which it has access. In this situation, the contractual agreements serve a dual purpose: they set price levels or price formulas over the anticipated

period of production, and they protect the producer by establishing production

levels which the pipeline mist absorb. These contract clauses commonly take

the form of take-or-pay provisions. In their strictest form these provisions

stipulate that the buyer is required to pay for a certain percentage of the

available production regardless of whether he actually withdraws this amount.

A similar contractual rigidity and price levels tied to world oil prices

govern most import agreements.

Since increased demand causes increased production of gas from expensive

sources, one might expect a market characterized by "diseconomy of scale",

that is, unit prices rising with increasing demand. Due to take-or-pay

provisions, however, average wellhead prices tend to fall rather than rise

with increasing demand. Therefore, and because of fixed tariff requirements

(see Section 2.3.2), the natural gas market is dominated by economy of scale

effects.

Another important characteristic of the natural gas market is its

seasonal pattern. Gas demand in the residential and the commercial sectors is

considerably higher in the heating season, approximately October through

March, than during the remainder of the year. On the other hand, for physical

and financial reasons, gas production proceeds at an essentially even pace.

This leads to production in excess of demand during the nonheating season. Vast underground storage facilities are then used to store excess gas for

consumption during the heating season. Underground storage facilities may be

owned or leased by distribution companies as well as by pipeline companies.

The need for storage can be reduced by smoothing demand. This is

accomplished, particularly in Southwestern States, by electric utility

companies using gas as generator fuel during the summer months to supply

additional electricity needed for air conditioning. Alternatively, customers

able to use fuels that can be stored locally, such as oil or coal, are induced

by reduced rates to use gas mainly during periods of excess availability. If

not enough gas is stored during the summer, then shortages might be caused,

for instance, by unexpectedly inclement weather conditions. In this case,

certain industrial customers may be curtailed , meaning that residential and

commercial market sectors are given priority for the available gas.

13
2.3 Federal regulation of natural gas commerce

Federal regulation of the natural gas industry began with the passage of

the Natural Gas Act of 1938 (NGA, Public Law 75-688). It addressed the

interstate market only, spelling out the rules for monitoring tariffs,

providing the foundation for what was subsequently interpreted as the

authority of the FERC to establish ceiling prices at the wellhead (Phillips

decision 1954) and to require proof of sufficiency of the reserves available

to a pipeline company in order to meet anticipated end-user demand for a specified number of years. Over the succeeding four decades, the NGA was followed by numerous laws and regulations affecting all aspects of the natural

gas industry. The most comprehensive of these laws is the Natural Gas

Policy Act of 1978 (NGPA, Public law 95-621), which evolved after more than

eighteen months of Congressional debate.

2.3.1 The NGPA

A main purpose of the NGPA was to facilitate the decontrol of natural gas

prices at the wellhead in a manner which would not disrupt existing markets.

In particular, the NGPA was intended to provide a price structure which would

gradually escalate some wellhead prices to parity with crude oil prices, and

thereby provide a smooth transition to a limited decontrol in 1985. Here

parity is obviously understood in terms of Btu content. The lawmakers were particularly concerned with the possibility of a sudden large increase in gas

prices should a gap exist between crude oil prices and natural gas prices at

the time of decontrol. Such a price "fly-up" may conceivably occur under such

circumstances in spite of long range contractual agreements between producers

and pipelines because of the existence of pricing clauses or "favored nation"

clauses in such agreements, or because of legal ("force majeure") and

commercial pressure for renegotiations.

The price escalation factors specified in the NGPA were based on the

assumption that the 1985 crude oil price would amount to about $15 per barrel.

The crude oil price, however, has risen much faster and, as a result, the NGPA

has not been sufficient to narrow the gap between oil and gas prices

effectively.

In order to formulate its decontrol scheme, the NGPA defines several

categories of natural gas depending on their mode of production. These

NGPA-categories are referred to by their corresponding section numbers in the

NGPA: 102-109. Roughly speaking, category 102 ("new gas") refers to wells

drilled after 1977 and sufficiently distant (2.5 miles) from, or sufficiently

deeper (1,000 feet) than a previously established reservoir, but not below

15,000 feet. Category 103 ("not so new gas") contains wells drilled after

1977, but not well enough separated from previously established reservoirs.

Category 104 ("old interstate gas") encompasses all reserves dedicated to

interstate commerce prior to 1978. Categories 105 and 106 refer to "old

intrastate gas", the difference between the two being whether the gas is

produced under an original or renegotiated ("rolled over") contract.

14
Category 107 ("high cost") gas includes new wells which are very deep (below

15,000 feet). Category 108 ("stripper wells") is made up of slowly producing

wells mainly found in Appalachia, and Category 109 covers all the remaining

types of gas. Categories other than 104,105,106 will contain reserves that

have not yet been contractually committed to a specific buyer. Eventually

such reserves will enter either the interstate or the intrastate market.

Under the NGPA most new gas (category 102) is scheduled for deregulation

by 1985, as are parts of categories 103, 105 and 106. The remaining portion

of category 103 is to be deregulated by 1987. The very cheap old gas in

category 104 is not considered for deregulation and its price is not permitted

to rise faster than inflation.

The NGPA also contains incremental pricing provisions, namely mechanisms

for pipeline companies to pass on certain price increases at the wellhead

without requiring a rate hearing by the FERC. These provisions contain

special clauses protecting the residential and commercial markets by requiring

industrial "boilers" to absorb, within specified limits, a comparatively

larger portion of such price increases. Full NGPA ceiling prices were originally denied to production from reserves owned directly, i.e. not via

subsidiary, by an interstate pipeline company. In such cases, the FERC

maintained the old NGA position that prices at the wellhead were to be

calculated on a cos t-of -service basis. That position was overturned by the

U.S. Court of Appeals for the 5th Circuit (Mid-Lousiana 1981). The

Mid-Lousiana decision's biggest impact is on the El Paso Natural Gas Company,

which obtains about 15% of its production from directly owned reserves.

2.3.2 Rate determination

The rate schedules under which transmission and distribution companies

collect their revenues differ widely in their structures. Interstate

transmission tariffs are monitored by the FERC and follow schemes whose

salient features are a monthly so called demand charge , which is "fixed", that

is, it has to be paid regardless of the quantity purchased, and a so called

commodity charge , which is "variable", that is, a per unit cost. The demand

charge for each customer is calculated from a posted demand rate by

multiplying it with maximum expected peak demand, for instance, in terms of

largest daily delivery during the year. Such a maximum expected peak demand

is stated by the customer, and it limits the peak delivery to which the

customer is entitled under this rate schedule. In addition, a rate schedule

may stipulate minimum sales, seasonal surcharges, and so on. Pipeline

companies covering large distances may distinguish up to seven, but more usually two or three, different rate zones. Besides so called "general

service schedules", pipeline companies offer separate rate schedules for

various special purposes and for direct sales to end-users.

The rate schedules of distribution companies reflect the differences in

guidelines issued by public utility commissions in different states.

Furthermore, separate rate schedules have to be provided for the individual

end-use sectors. For a discussion of distributor rate schedules see [2].

15
All methods for determining the actual tariff numbers within a rate

schedule are, regardless of all other differences, based on the same principle, namely recovery of expenses. Typically, a rate base is determined

for the year in question. This rate base consists essentially of the cost of

total plant (at purchase prices) plus working capital for the year minus

accumulated depreciation and minus accumulated deferred income taxes. The

costs of capitalization of the rate base and of dividends to stockholders

determine the required return for the year. This required return together

with the cost of purchased gas, operating and maintainance expenses,

depreciation expenses and taxes constitutes the total cost of service , which

is to be compensated by tariffs. The cost of service is divided into a "fixed" part and a "variable" part, the latter consisting of the unit cost of

purchased gas and a portion of the operating and maintainance expenses. In

the case of interstate gas pipeline companies, the FERC limits what fraction

of the fixed cost of service can be recovered through (fixed) demand charges.

The most recent decision (United Formula, 1973) sets a limit of 25% for all

interstate gas pipeline companies. Thus at least 75% of the fixed costs of

service, together with all variable costs of service, must be recovered through

(variable) commodity charges.

The presence of fixed charges generates an immediate economy of scale at

the citygate and at the burnertip. A less immediate but stronger economy of

scale effect is due to the relative constancy of the rate base and therefore of

the fixed costs of service: if sales decrease then tariffs must increase to recover this fixed cost of service. These effects reinforce the economy of

scale effects that result from take-or-pay provision at the wellhead.

2 .4 Model purpose and scope

In view of the persistent gap between gas and oil prices, important

questions arise about the prospect, size and timing of price "fly-up" caused by

deregulation of natural gas production prices as stipulated in the NGPA. At

the heart of these questions is the need to understand the consequences of

different deregulation options in order to analyze the potential effects on all

parties. Specifically, the analyst wants to consider deregulation measures of

the following form: (i) some NGPA categories originally not slated for

deregulation will now be subject to deregulation; (ii) the deregulation date of a particular NGPA category will be changed; (iii) the escalation of price

limits for particular NGPA categories will be accelerated or retarded.

The following questions will have to be addressed: What would be the

regional price and consumption figures for natural gas at the burnertip during

the 1980's under various category-specific deregulation assumptions? How would

the reserve position and category mix change for major pipeline companies, and

what impact would this change have on the supply situation for the particular

regions served by these companies? In this section, we will address the

question of what general structural specifications a mathematical model like

the GAMS model would have to meet in order to aid in analysing such questions.

16
The immediate Impact of the changes caused by deregulation measures is on the wellhead prices which are paid by the pipeline companies to their

producers. Individual pipelines will be affected differently, because their reserves contain different proportions of NGPA categories. These reserve differences translate into price and consumption impacts at the burnertip,

which differ by region and end-use sector. Furthermore, the exploration

patterns will change with the economic attractiveness of the various

production categories, and one might expect pronounced regional differences in

what categories of gas are considered worth exploring for. This is because the

market position of the individual pipelines which are supplied by a particular

production region may vary from production region to production region.

These considerations indicate the "resolution", i.e., the degree of

detail, needed in the model and in the supporting data. In particular, the

following requirements should be met:

(A) The major conduits of supply represented by the major pipelines and

pipeline aggregates, as well as the major distributors and distributor

aggregates along with their supply relationships, must be identifiable items

within the model.

(B) All consumption must be traceable through the system from wellhead to

burnertip. By this we mean that, at each way-station, the incoming quantity

is accounted for in terms of outgoing quantities and predicted transmission

and distribution losses. The available reserves have to be reduced by the

amounts of gas withdrawn from these reserves.

(C) Funds payed for incoming and received for outgoing gas transactions

must be balanced, taking tariffs into account, so that effects of price

changes at the wellhead on prices at the burnertip can be predicted. This

balance is a bookkeeping balance it does not preclude profits or losses.

(D) The reserves of a pipeline need to be distinguished according to

their NGPA category as well as other information — historical, physical and

contractual — necessary to establish reserve-production ratios and to

formulate the wellhead price changes due to deregulation.

(E) Demand elasticities must be available, for instance through exogenous

specifications, by user sector for each distribution point that is represented

in the model and for each study year.

(F) Tariffs for pipeline companies and distributors should be modeled in

such a fashion that effects of economy of scale resulting from fixed costs and

nearly constant rate bases can be observed.

The requirements (A) through (F) are necessary to establish a causal

relationship between selective price changes at the wellhead and subsequent

changes in consumption at the burnertip. The requirements (A) and (D) are also necessary to provide a framework for the modeling of the acquisition, by

individual pipelines or pipeline aggregates, of newly discovered reserves.

(B) and (C) are needed to establish tight arithmetic connections between

volumes and prices at the wellhead on one side and at the burnertip on the

other.

17
2.5 Data sources

The GAMS model has been designed and implemented to meet the requirements

outlined in the previous section. The question then arises whether the

necessary data are available for its support. We proceed to describe the

major data sources at hand.

First, all interstate gas pipeline companies are required to report their

annual sales to each client by volume and price. These data are part of

Form FERC-2 , which is a comprehensive annual report of all transactions of a pipeline company. Form FERC-2 has recently become available in computer

readable form.

Next, all sellers of natural gas for end-use, that is, all distribution

companies, but also some pipelines and producers, have to respond to

Form EIA-5Q . This form, intended for assessing alternative fuel demand due to

natural gas curtailments, asks for monthly sales broken down by end-use

sectors, the number of customers in each end-use sector, a list of suppliers

by name together with the annual quantity they supplied, and a list by name of

their major nonresidential customers. The information is compiled annually in

computer readable form and covers the period from April 1 until March 31.

Mandatory since 1980, production and consumption data are collected on a calendar year basis by Form EIA-176 . This form also reports "amounts

unaccounted for", that is, gas lost for various reasons by companies selling

for end-use. In addition, Form EIA-176 contains information about

producer-used gas, which is not available from Form EIA-50.

All domestic operators of oil and gas wells report their estimated oil

and gas reserves annually on Form EIA-23 . Similarly, the interstate pipeline

companies report on the status of their dedicated reserves and of commitments

by other pipeline companies on Form FERC-15 , the natural gas companies ' annual

report on gas supply.

Detailed figures about the purchases of interstate pipelines from gas

well operators, covering both volumes and prices as well as indicating NGPA

categories , are available in the form of Purchased Gas Adjustment (PGA)

filings . These are required to be filed by interstate pipeline companies,

under the incremental pricing provisions of the NGPA, whenever a company

applies for an adjustment of its posted gas prices in response to price

increases at the wellhead.

The tariffs posted by the major interstate gas pipeline companies are listed semiannually by H. Zinder and Associates in their Summary of Rate

Schedules of Natural Gas Pipeline Companies [4] . More detailed information on these tariffs can be extracted from rate hearing depositions with the FERC.

Every year, the American Gas Association (AGA) publishes an extensive and

valuable summary of statistics, mainly at the state level, called GAS FACTS

[1]. Also, the EIA provides annually a comprehensive statistical overview of

natural gas commerce in the United States based on Form EIA-176. Its

publication, the Natural Gas Annual (NGA) (DOE-EIA-0131) , covers the

18
production, interstate movements, storage, and consumption of natural gas. An

excellent guide to data collections by the Federal Government available in

1980 and a concise discussion of the underlying issues are provided by the EIA

report, A Review of Requirements for Natural Gas Data (DOE-EIA-0624) , of

December 1980.

While the available information is copious on volumes, it is rather

sparse on prices, especially burnertip prices other than state averages.

Additional difficulties are due to the fact that many of the above data sources are restricted to interstate commerce. Nevertheless, a data base

supporting the GAMS model has been assembled successfully.

It should be noted that this data base refers essentially to a single

year, the "base year" 1980. This is because key data sources have been

available only recently in a form that is useful to the model. Indeed,

several months are usually needed to compile and edit the data collections of

the previous year, and post 1980 data were therefore not available during the

design phase of the model. Nor were earlier data representative, since 1980 was the first year reflecting the full impact of the the NGPA.

This poses a peculiar challenge to the modeler: instead of being able to

extrapolate past temporal trends, he has to rely essentially on "snap-shot"

information about a single base year and to create future temporal trends from

it. This is achieved by referring to given time-dependent demand curves for

individual regional end-use sectors during the forecast period. Such demand

curves indicate the annual quantity of natural gas consumed at a particular

market and in a particular year as a function of the average annual unit

price. Using models outside the GAMS system and without NBS assistance, EIA

has been able to create the basic information from which such individual

demand curves can be derived. The parameters of these demand curves are the

main temporal inputs available.

2.6 Overview of the MARKET model

The GAMS model explores the impact of policy decisions on natural gas

cost and consumption by year, end-use sector, and demand region as well as on the discovery, acquisition and production patterns of the natural gas reserves. The GAMS system consists mainly of three models called PROLOG, BID

and MARKET (see Figure 2.4). PROLOG models the exploration and development of reserves.

BID awards the resulting reserve additions to individual pipeline

companies on the basis of a simulated bidding process and it informs MARKET

accordingly. Once a reserve belonging to a particular gas producing company

has been awarded — or rather dedicated — to a particular pipeline company,

it is assumed that gas from this reserve may be sold to this pipeline company

only and that any request by the pipeline company within the production

capability of the producer will be met at prices agreed upon at the outset.

This does not mean, that these prices will not change (in constant dollars) on

19
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20
a yearly basis, but rather that price changes are also agreed upon in advance,

possibly conditional to the occurrence of certain events. Price renegotiations can be specified in GAMS as part of a deregulation scenario. It should

be noted that GAMS is the first model to represent the entire national gas

market in a way designed to distinguish the process of committing gas reserves from the process of purchasing gas at the wellhead.

The main task of the MARKETT model is to determine annual consumption

volumes and their prices by region (both "Census" and "DOE") and end-use

sector (see Figure 2.5). It does so by economic equilibration based on a comprehensive network of national supply patterns , encompassing all

significant pipeline companies and distributors. This network is generated by

a stand-alone computer program called GENNET . GENNET extracts most of the

information for this task, including the connectivities which determine the

structure of the network, from Form EIA-50.

In the first modeled year, the base year, MARKET establishes a baseline

of volumes, prices, and related quantities. For subsequent years, it

generally equilibrates between demand at the burnertip and supply at the

pipegate, taking into account transmission and distribution losses (including

compressor fuel), add-on tariffs (that is, charges for transmission and

distribution expenses), and storage. There is a specific supply curve for

each "pipeline system" and a specific demand curve for each "market".

Pipeline systems represent either a single major pipeline company or a combination of smaller ones. Markets typically consist of all customers of a distributor that are in the same end-use sector.

The demand curves are essentially exogenous input. They indicate how

much gas a market is potentially able to absorb at any given average price

during the year in question. Some of the parameters of the demand curve reflect the market performance during the previous year. Prices of

alternative fuels, in particular residual ("Number 6") fuel oil, are used to

provide cut-off prices for various markets, that is, gas prices above which

gas is replaced by an alternative energy source, and below which gas would be

the preferred fuel.

A supply curve indicates the annual average unit price as a function of

the annual purchase from reserves dedicated to a particular pipeline system.

It is determined, as outlined below, from the full amounts that could be

produced from each of the individual "reserve blocks", their take-or-pay

ratios and their posted wellhead prices. The full amounts that could, but do

not have to, be produced in a particular year are calculated from "production

profiles", which essentially express possible production rates as a function

of the maturity of the reserves in question. Production profiles for the base

year are an EIA developed input. For subsequent years, reserve additions with

specified production profiles are generated within GAMS by PROLOG.

The way in which the annual production is spread over the available reserves determines the average wellhead price: the more that is taken from

cheaper reserves instead of expensive ones, the lower the price. The

withdrawal strategy thus determines the supply curve. Once the actual annual

21
purchase at the pipegate has been calculated by MARKET, either in the process

of establishing the base year flow or in the process of equilibration, then

this amount is actually withdrawn according to the above strategy. The

amounts remaining in each individual reserve are recorded for reference by

other components of GAMS.

When using MARKET, the analyst can choose from two alternative withdrawal

strategies. The "minimum cost-take" strategy minimizes the average purchase

price after having satisfied the take-or-pay provisions. Under the "rateable

take" strategy, the take-or-pay provisions are again satisfied first, and then

a fixed percentage of the remaining deliverable gas in each reserve block is

withdrawn.

What happens in the model if there is not enough demand to pass the

take-or-pay thresholds? Under both of the above options, a fixed percentage

of the take-or-pay minimum in each reserve block is withdrawn and the price is

determined accordingly. That is, if a shortfall occurs in the model, the

theoretically ensuing penalties are not fully assessed. This is done because

for the purpose of equilibration only those wellhead costs that can be passed

through to the consumer at the burnertip should be considered. In the absence

of meaningful precedents for large defaults, the position was taken that there

are regulatory obstacles to passing significant take-or-pay penalties on to

the end-user. It was also assumed that the impact of large take-or-pay

penalties would be blunted by individual renegotiation.

The burnertip price is determined by adding tariff increments for

transmission and distribution to the wellhead price after making allowances

for plant and lease fuel. Transmission and distribution (add-on) tariffs are modeled separately. For transmission tariffs, base year averages are determined from rate hearing depositions at the FERC. These base year

transmission tariffs, which consist of demand rates (fixed) and commodity

charges (variable), may be escalated by a constant factor in each subsequent

year. For distributors, general relationships between the quantities of sales

and the number of customers on one side, and rate bases on the other, were empirically developed for this project by J.-M. Guldmann of Ohio State

University [3] . These relationships are used for estimating distribution

tariffs.

The burnertip prices determine - via the demand curves -the amount to be

produced while, on the other hand, this amount determines the well-head price

which in turn determines the burnertip price. It is this kind of circular

definition that is resolved by the equilibration process, which is discussed

extensively in Chapters 3 and 4.

The solution of this large equilibration problem is made possible by a decomposition scheme in which MARKET selects a "primary" supplier for each

distribution company so that each distributor is nominally associated with

a single pipeline system. The equilibration process then matches each

individual supply curve against a well defined set of associated demand

22
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23
curves. Some sales, particularly those between the resulting subnetworks, are considered "secondary" and serve as boundary conditions for the equilibration.

The secondary volumes and prices are updated in a separate process at the end

of the model year based on the arbitrary assumption of equal cost shares among

suppliers of an individual distributor. By this we mean that, in the presence

of several suppliers to a distributor, the ratios of their sales values remain

constant from one year to the next.

To some extent, incoming secondary quantities may be thought of as take-or-pay obligations, and indeed there are many examples where the

secondary supplier does supply a distributor on a take-or-pay basis. The

reason, however, for honoring secondary transactions first is fundamentally

that their estimates have been completed at previous time step in the model

process, and that the equilibration is designed to proceed under fixed side

conditions.

At the end of each model year, the MARKET model develops estimates which

enable it to respond to repeated queries by BID about how much gas a particular pipeline company will be able to absorb in a given future year at a given price. Here "future" means after the year for which the model has just

completed its forecast. The BID model utilizes the responses to these queries

for developing the bidding posture of the pipeline company in question. These

demand projections can be thought of as a "model within a model" in that they

try to represent processes invoked by actual pipeline companies when they

estimate their sales potential (see Figure 2.6) for various "price tracks"

covering future years.

The MARKET model is designed around the present framework of natural gas commerce: a distributor supplies captive end-users and buys from one or more pipeline companies and possibly from other distributors; a pipeline company

buys from other pipeline companies but mainly from committed producers. The

MARKET model ignores vertical integration. Most deregulation scenarios can be

modeled within this framework, except the scenario in which all pipeline

companies are transformed into common carriers. While working within the

above framework, the MARKET model does not attempt to address the effects of

deregulation on the financial position of corporations involved in natural gas commerce.

2 .7 Model sensitivities

To which quantities and assumptions is the MARKET model sensitive?

Numerical model results clearly depend on the structure of the supply network,

the available reserves and their categories in the base year, burnertip

consumption and prices in the base year, the specified demand elasticities,

parameters for tariff estimation, the bidding procedures in BID, drilling

equipment data in PROLOG, just to name a few. The assumed level and price of

Canadian imports may critically affect the quantity of gas used by electrical

utilities in California, and so on. Those model conclusions, however, which

are based on comparing several GAMS runs with each other, will depend on many

such quantities only in a minor way as long as the general structure of the

natural gas market is reasonably well represented. This point will be

discussed further in the next section.

24
FOR EACH PIPELINE

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portion of the MARKET model

25
The question of sensitivity really aims at the possibility of more disconcerting phenomena: are there parameters to which the model is sensitive

in an unstable fashion so that small changes in such input parameters lead to

large swings in output responses. Among the input items which may indeed cause such an instability in MARKET are discontinuous demand curves. By this we mean demand curves which specify a large demand at prices up to a particular cut-off

price and, say, zero demand for any price that exceeds, however minimally, the

cut-off price (see Section 3.6.3). Such discontinuities or cliffs in a demand curve may cause unstable behavior, provided some modeled burnertip prices end

up close to a cut-off price. It is obvious that in such a case a very small

change in any one of a multitude of model parameters may cause the burnertip

price to increase just enough to push the demand "over the cliff", that is, cause a previously hefty demand to suddenly disappear. Similarly, a small

parameter change somewhere in the model may trigger a price decrease which is

small but sufficient to activate a hitherto latent demand.

This potential instability does not invalidate the MARKET model. On the

contrary, it may be germane to actual market behavior and may thus provide

valuable insight. Also, the instability need not always be realized, since the

results are often sufficiently far away from cliffs that small parameter

changes will have only commensurate effects. The purpose of a particular

analysis should determine the extent to which the analyst chooses to build

potential instabilities into his demand curves. It also helps if the

instabilities are dispersed over a large network.

In many models, instability is caused by oscillatory behavior . Again,

this may be a bona fide representation of real phenomena. In fact,

determining whether oscillatory behavior develops, and its amplitude, may be a main purpose of a model. However, when or where a peak occurs in an oscillatory process tends to be sensitive to small changes in input parameters

and assumptions. In designing the MARKET model, the authors have attempted to

avoid oscillatory behavior as much as possible. However, oscillatory effects

may be caused by a combination of cliffs in demand curves and tariff responses

to past demand levels.

A third kind of sensitivity is caused by what may be called switches . In

this case, small changes in the first year of a multiple year model may result

in a different setting of a switch and accordingly set the model on different

time paths leading to a large discrepancy of results in later years. Such a switch mechanism in a model may again represent the reality of the situation

to be modeled (e.g., bandwagon effects), but unrecognized switch situations

may jeopardize model results. MARKET does not contain intentional switches.

An undesirable switch situation may arise for excessively large, so called,

"lag exponents" in the demand specifications, and is discussed in a note to

Section 3.6.

26
2.8 What can a mathematical model achieve?

The mathematical models we are talking about make statements about the

future development of an extremely complex system, In the present Instance,

the natural gas Industry in the United States. The description of such a system typically requires a large data base, and Involves a huge amount of

calculation In which these data are transformed and related to each other in

order to derive certain indicative quantities. In this enterprise, the

computer is a necessary ally, so much so that mathematical models often are identified with particular collections of computer programs whose output is

considered as the result of the model.

The claim that future behavior of a complex system can be predicted in

this fashion needs examination. What a model can do is to single out certain

perceived trends, propose mathematical relationships between them, and

determine the consequences of these assumptions. These consequences should

indeed be valid estimates of future behavior provided the postulated trends

continue intact over the forecast period, and the assumptions representing the

modeler's perceptions of those trends and their relationships were essentially

correct. The first condition cannot be verified: unexpected developments

cannot be ruled out. At best, a model can predict what might happen assuming

that some selected present trends and relationships continue or be subject to

anticipated changes. This is not a problem. Indeed such information is

extremely valuable to any decision maker. Actuarial models of mortality, for

instance, are indispensable to various Industries in spite of the realization

that the detailed results of these models often have been invalidated by the occurrence of catastrophes. The problem is rather that of verifying the

remaining condition, namely, that the assumptions which govern the underlying

trends and their Interrelationships were perceived and represented correctly.

This is a formidable task under the best of circumstances, and may well not be

practical as an a priori exercise. In such situations, the analyst must rely on skill and intuition to assess the assumptions on which the mathematical

model is based and to detect discrepancies in the model output. Model

assumptions can be further tested by sensitivity analyses and through

experimentation with modified assumptions. For mature models, the experience

of past model applications might provide guidance in interpreting more recent

model results.

An Important class of model assumptions represent idealizations , that is,

conceptually compelling relationships which would hold exactly were it not for

minor and less clear-cut effects militating against them. The physicists*

model of free fall is a case in point. Here the effects of air resistance,

air currents and the changing distance from Earth are ignored. It is

important to explore idealized behavior. Even if an idealization turns out to

be untenable, the actual behavior of a system is often best understood in

terms of deviation from idealized behavior. Accepted patterns of Idealization

support the analyst's understanding of a model and provide a vantage point for

the comparison of different models. The MARKET model is built on several

idealizations. The concept of economic equilibrium is a major one of these.

27
This concept represents an idealization because the time-lags involved in

arriving at an equilibrium are ignored. Most cost optimizations are idealizations because in real life cost minimization may not be the only

decision criterion, and even if it were, cost minimization decisions in the

real world may have to be based on information that is less complete than the

model assumes. Ignoring effects arising from vertical integration within the

natural gas industry constitutes yet another idealization.

Not all model assumptions are idealizations. Many represent undisputed

facts. Others express the modeler's intuitive selection of a process intended

to exhibit the same qualitative behavior as some particular feature in the real

world. Such assumptions are often called exogenous assumptions and carry with

them an element of arbitrariness. An example of such an essentially arbitrary

exogenous assumption is the equal cost shares assumption for alternate

suppliers in MARKET. Other exogenous assumptions are scenario specifications , e.g., the development of world oil prices. These assumptions, mostly about

quantities rather than relationships, specify the hypothetical situations to be

analyzed by the model.

Certain assumptions are simplifications adopted to facilitate the solution

of a problem. Their justification is the expectation that the errors which are introduced by these simplifications are sufficiently small. A typical

simplification is the decomposition in MARKET of the base network of supply

patterns into subnetworks served by single "primary" suppliers, with supplies

between different such subnetworks considered "secondary" and estimated in a less detailed fashion. Like most large models, GAMS resorts to judgmental

assumptions where the modeler's information is limited with respect to some minor aspect of the model, or where certain model quantities have to be

arbitrarily constrained to lie within the perceived limits of model validity.

Judgemental assumptions are a priori perceived as having only inconsequential

effects on the results of the model; otherwise they would be classified as exogenous assumptions. Simplifications and judgmental assumptions may act as indicators for areas for further research and model improvement.

Some judgemental assumptions in MARKET are prompted by a particular set

of model data and may have to be changed if the model were to switch to a different data set. Several model runs are usually needed to stabilize model

performance and to detect internal data inconsistencies. This holds in

particular for the large network of gas supply patterns representing, for the

purposes of the model, the entire national gas industry. While this network

is automatically generated offline by GENNET , this is done with the

expectation of subsequent adjustments by the analyst. It would have been

possible to automate most of those adjustments, but to do so would not have

been an effective use of available resources at the time.

Based on the scope and extent of the underlying exogenous and judgmental

assumptions, the use of a mathematical model in an analysis needs to be

qualified. Unlike for the classical statistical models, confidence statements

concerning the forecasts of policy evaluation models such as GAMS usually

cannot be given. Concerning the value in using such models, the position

taken is that a model "forecast" represents one among several plausible

28
developments, differing in their underlying assumptions, for which the impact

of hypothetical trend-breaking events such as deregulation is to be assessed.

It is expected that the size and the direction of the impact can be gauged

differentially with a higher degree of confidence than that accorded to the

model forecast itself. Experience with mathematical models by and large tends

to support this expectation. It can also be verified to some extent by

examining the impacts of trend breaking events on alternative plausible

forecasts, that is, forecasts based on different exogenous assumptions

specifying model relationships.

It would be a mistake to ignore some important benefits which accrue from

the process of modeling in itself. This process cannot help but increase

understanding of the subject area by forcing a systematic investigation of and

experimentation with the assumptions upon which present understanding is

based. This may lead to increased insight through reevaluation of these

assumptions. A further benefit lies in the implicit data analysis performed

by a model. This analysis may pinpoint inconsistencies and errors in data

sets as well as semantic differences among separate data sources. If a model

is executed at regular time intervals, then the analyst can develop his

intuitive judgment of the relationships between the model results and the real

world. In this case, the model acts as a powerful "indicator" of trends and

events. A mathematical model may be the only way to do justice to a complex

and substantive data base.

29
aiAPTER 3

Conceptual Description of the MARKET Model

In this chapter, we describe the major building blocks of the MARKET

model: the network structure, supply at the wellhead, demand at the

burnertip, tariffs and storage. In the next chapter, we will discuss the

model processes which are based on these building blocks.

The description of the model will consist, for the most part, of

introducing the major variables of the model and of stating in terms of these

variables the assumptions with which we attempt to reflect aspects of the real

world. The latter have been outlined in Chapter 2. Statements about model

variables usually represent model assumptions rather than factual statements,

and are therefore not always expressly identified as assumptions.

3.1 The general setting of the GAMS model

The purpose of the GAMS model is to explore the impact of alternative

policy decisions on (i) natural gas cost and consunq)tion by year, end-use

sector and demand region; ii) depletion of existing reserves; iii) exploration

and acquisition of new reserves.

The GAMS model is a recursive simulation model with econometric and

linear programming components. The model "simulates" in that it creates a fairly detailed facsimile of the natural gas industry, and in that it is built

largely on cause-and-ef feet relationships among the components of the

industry. The degree of explicitness necessary to address the major questions

facing the analyst was discussed in the previous chapter. The simulation is

"recursive", because it begins with a baseline of historical data and modeled

quantities for the base year , and derives new values for these quantities for

the next year by referring to the values in the base year. The quantities

modeled for each subsequent year are calculated analogously using those of the

previous year.

All internal financial statements are in constant dollars , that is, base

year dollars. For most recent scenarios, the base year has been 1980, while

all model years covered the period 1980-1990. Certain demand estimation

procedures, however, extend beyond the model years to a horizon year , say,

1995 ( Note 1 ). Some model values refer to the year prior to the base year.

In the absence of a specific convincing policy-relevant alternative

hypothesis, the judgemental assumption is made that there are no major changes

in weather conditions , or more precisely, that in all years up to the horizon

the weather conditions will be equivalent to those during the base year.

The natural gas industry conducts its operation under the influence of

multiple state and federal regulations. This tends to limit the effect of

particular corporate structures on its mode of operation. Intricacies of

corporate structures are beyond the scope of the model. Consequently, GAMS

30
ignores vertical integration , that is, it assumes producers, pipeline

conq>anies and distributors to be separate corporate units, each Independently

pursuing its own corporate interests.

In what follows, pipeline systems are the model elements which buy and

transport natural gas, selling it subsequently to client distribution

companies. Reserve blocks , representing the producer function, are aggregates

of reserves which are treated as units by the GAMS model. The reserves in the same reserve block are of a single NGPA category and share other properties of a physical, contractual or historical nature.

3.2 The Role of the MARKET model in GAMS

As pointed out before, GAMS consists of three models: PROLOG,

representing exploration, discovery and development of reserves; BID,

representing commitment of these reserves to pipeline systems; and MARKET,

representing production, transmission, distribution and consumption of natural

gas. The GAMS driver calls these models in the above sequence once for each

model year. The results of the BID model impact the MARKET model directly and

vice versa, whereas there is no such direct impact on PROLOG. In some cases, we will therefore refer to an interaction with BID , instead of using the more correct but less informative term "interaction with the GAMS driver".

There are two instances of interaction between BID and MARKET. In the

first instance, information for each reserve block, including newly acquired

ones about its current level of production capability, take-or-pay provisions

and price of gas is transmitted from BID to MARKET at the beginning of each

model year. During the model year, MARKET then equilibrates supplies and

demands to determine the amount consuToed at the burnertip and the amount which

has to be produced in order to support this consumption. This annual

production is allocated to specific reserve blocks, and the quantities of gas

contained in these reserve blocks are accordingly reduced. The quantities

remaining in each particular reserve block are reported back to BID at the end

of the model year. Thus BID is kept apprised of how much gas each pipeline

system can draw upon in the future. All reserve information has been adjusted

prior to being passed to MARKET to reflect processing and the removal of plant

and lease fuel.

In the second instance of interaction, BID queries MARKET repeatedly on how much gas a pipeline system would be able to absorb, and would

correspondingly purchase at the pipegate from dedicated reserves, in a given

future year for a specified average purchase price at the pipegate. Here the

term "future" is used in terms of the model: the "present" year is the latest

year for which the MARKET model has completed its forecast; the future years

are those years which follow, up to the horizon. BID uses the above

information when it models the bidding for new reserves.

These marketability estimates required by BID are derived by applying an abbreviated version of that part of MARKET which is invoked annually to

execute the regular forecasts. Each year, MARKET constructs a demand

projection table , whose rows correspond to a specified number of consecutive

31
future years (the look-ahead period), whose colunes correspond to price

tracks , and whose values are the maximum amounts of gas which might be

purchased from dedicated reserves at each given price in each given year by

the pipeline system for which the table is being set up. The prices increase

from left to right in each row. The values in each individual row are sample

points for a projected pipegate demand curve which is typically monotonically

nonincreasing. The values in individual columns, however, need not change

monotonically over the future years ( Note 2 ).

The queries from BID are handled as a table look-up procedure, with

interpolation for in-between prices and default conventions for prices which

fall outside the grid ( Note 3 ). However, BID tailors the grid prices to each

individual pipeline system in such a fashion that most look-up prices can be

expected to lie inside the grid. The recursive nature of MARKET requires that

each year can be analyzed only after the previous years have been analyzed.

The same is true for the abbreviated version of MARKET which is used to

estimate maximum purchases for future years. The demand projection table is

therefore constructed column by column, each application of the abbreviated

MARKET procedure building on the results from the previously modeled year.

The main reason for abbreviating the demand projection portion of MARKET

is that the projections for future years are carried out separately for

individual pipeline systems and, therefore, cannot model the actions and

reactions of other pipeline systems. To some extent, this may be thought of as reflecting the fact that, in real life, the leadership of a pipeline

company must plan and bid on the basis of limited information about the plans

of other pipeline companies.

Because of the abbreviated modeling and because of the maximum sales

assumptions during previous years, the values in the demand projection table are speculative: it is not guaranteed that, when the actual modeling process

reaches the year of the projection, the modeled pipegate prices and quantities

lie precisely on the projected pipegate demand curve. This of course is not an inconsistency of the model, because the "actual" future-year values depend

on decisions yet to be made (i.e. simulated) by BID.

3.3 The base network of supply patterns

MARKET requires a representation of the national natural gas transmission

and distribution system by a collection of networks. These networks are a major input into the model. Networks generated by the GENNET program in

separate runs have been used in production runs. The most prominent network

in this collection is the base network . It represents all significant sales

relationships between pipeline and distribution companies, but does not cover

sales to end users. Essentially, the base network represents each company by

a node , and links two nodes by an arc whenever one of the corresponding

companies supplies the other. In general, an arc has an origin node and a destination node which differs from the origin node. Some arcs, however, may

have only a destination node. In this fashion, a formal network or "graph" is

defined. These formal networks represent relationships between their nodes,

but do not necessarily correspond to physical layouts.

32
Pipeline companies transport not only their own gas, but also — for a fee — gas that belongs to other companies. Since gas from various sources

cannot be distinguished once it enters the pipeline, this amounts to a swap of

gas shipments. Transactions of this kind are not distinguished in the base

network. The latter represents sales regardless of whose pipelines were used

for the actual delivery. This design decision is based on the observation

that pipeline companies treat transportation fees paid to other companies as a general operating cost to be compensated through generally posted tariffs.

Thus a distributor who receives direct delivery through the pipeline operated

by the supplier and another distributor delivery to whom requires the

transportation services of an additional pipeline company will be charged the same tariffs, other things like rate zones being equal.

In what follows, a formal definition of the base network will be followed

by a brief discussion of its generation principle and its associated model

quantities. Whenever possible the name used in the model's computer code for

a model quantity is provided in parentheses along with this quantity when it

is first mentioned.

3.3.1. Definition of the base network

The base network is a network representation of sales and does not

attempt to portray the physical network of pipelines. The gas sold by a particular pipeline company to a distributor need not be physically delivered

using facilities of this pipeline company: it may well be transported by some other pipeline to its destination. The model also does not consider capacity

limitations for transmission. Figures 3.1 and 3.2 illustrate the distinction

between the network of physical pipelines and the network of sales.

In Figure 3.1, we picture two distinct pipeline companies. Pipeline

company Pj sells to four distribution companies: Di , D2 , D3, D4 . However,

its physical facilities are disconnected: one piece serves Dj, D2, D4, while

a separate piece connects D3 to pipeline company P2. The latter sells to

distribution companies D4 and D5. It does not sell to distributor D3, but

agrees to provide transportation between the two separate facilities owned by

Pi. The existing sales relationships are schematically characterized by

Figure 3.2, with distributor D4 being supplied by both pipelines.

Accordingly, the base network contains two kinds of nodes, pipeline nodes

or P-nodes and distributor nodes or D-nodes . Each D-node must be supplied by

at least one node. D-nodes may not supply P-nodes. However, P-nodes may

supply other P-nodes and D-nodes may supply other D-nodes.

33
Gas

TT777 Pipeline P^ Pipeline P2

Figure 3.1: Physical layout of pipelines

Figure 3.2: Network of sales patterns for Figure 3.1

34
In the present network, groups of actual pipeline companies are combined

Into single pipeline systems. This aggregation is accomplished by representing

each actual pipeline company in such a pipeline system by a P-node and

connecting them to a single artlflcally introduced P-node (Figure 3.3). The

latter will serve as what will be later defined as a "root node" (Note 4).

Root

node

mrn

Reserves

Figure 3.3; Rooted pipeline cluster

35
3.3.2. Structure of the base network

We turn to the question of determining the existing supply patterns. In

recent applications, this information was obtained from Form EIA-50. On that

form, companies report their monthly burnertip sales according to end-use

sectors, but not their sales for resale. In addition, the above companies

report their suppliers, and it is this information which defines the sales

patterns. NBS has developed GENNET, a stand alone computer program that

automatically generates a base network from Form EIA-50 computerized files

( Note 5 ). This procedure is described in Chapter 5. At this point, we describe

a few features of GENNET which are helpful to the general understanding of the

structure of the base network.

A number of mostly small suppliers listed on Form EIA-50 belong to the

intrastate market, and are accounted for as follows: if a supplier is not

found on an analyst-supplied list of interstate pipeline companies, then these

supplies are associated with the state in which delivery is taken, and are considered as originating from a model-generated "intrastate pipeline company",

which is characterized by an exogenously selected cluster of states. Such a model-generated intrastate pipeline company can contain small interstate

pipeline companies as well as actual intrastate pipeline companies, and should

therefore not be confused with the latter. The model generated intrastate

pipeline companies are represented in the network by P-nodes just like the

interstate pipeline companies, and they are treated like the latter throughout

the model.

Direct sales of natural gas by pipeline companies to end-users are also

reported on Form EIA-50, as are direct sales by producers to end-users. The

latter sales are treated as direct sales by one of the model-generated

intrastate pipeline companies. In order to maintain a model convention that

all end-users are supplied from D-nodes, the GENNET program includes

artificial D-nodes in the base network, attaching them to P-nodes to play the

role of intermediary distribution companies selling whatever is actually sold

directly by the pipeline companies in question.

In any given State, direct sales by pipeline companies to end-users, if

present, typically follow one of two patterns: (i) the pipeline company sells

to one or a few large industrial customers or electric utilities; (ii) the

pipeline company functions as a distribution company serving substantial

numbers of residential and commercial customers in the given State. In both

cases, GENNET introduces artificial intermediary D-nodes into the base

network. In the first case, the D-node is marked as a direct sales D-node (or

"pseudo" D-node in Section 5.1) in the network generated by GENNET, and MARKET

will treat these special D-nodes differently during tariff and price

calculations (see Sections 3.7 and 4.1.2). In the second case, however, the

artificially generated D-nodes ("generic" D-nodes in Section 5.1) are not

distinguished from the genuine ones and are treated like the latter throughout

the MARKET model.

36
There are other occasions in which GENNET creates D-nodes that do not

correspond exactly to distribution companies listed in Form EIA-50

compilations. For instance, a multi-state distribution company will be broken

down into its state components, each represented by a separate D-node. Also,

in a later version of GENNET, the analyst has the option of aggregating all

those distributors within a State whose sales fall below a specified threshold

on a statewide basis and representing them by a single D-node. None of these

artifically generated D-nodes are specifically identified as such and are consequently treated by MARKET as if they were genuine.

Included in the base network are some arcs without origin node, which we call outer arcs , and whose destinations are typically P-nodes. Their purpose

is to accommodate imports and Alaskan gas ( Note 6 ) by providing the analyst

with a mechanism for specifying individual exogenous prices and volumes on a year by year basis for those outer arcs he chooses to activate. To aid the

analyst, GENNET prints a directory of the outer arcs it has set up.

3.3.3 Quantities associated with the base network

Almost every arc of the base network represents a transaction that

occurred during the base year and is expected to occur again during the model

years. We call such arcs proper arcs . Exceptions are: (i) arcs which have

been added to connect P-nodes for the purpose of pipeline system

representation, such as arcs emanating from the root node in a rooted cluster;

(ii) outer arcs, i.e., import and Alaskan arcs. In fact, none of the P-to-P

arcs are proper in the current network, although more advanced versions of the

network may have proper P-to-P arcs representing stable sales between pipeline

companies. Such sales are currently handled by reallocating some of the

dedicated reserves.

With each proper arc, GENNET associates an annual transaction quantity or flow (QUANA) and its corresponding unit sales price (PRCEA) averaged over the

base-year. These volumes are inputs for the base year, along with the base

network specifications, and are updated annually by the model. Arcs which are not proper will not have flows or prices associated with them as inputs, since

they do not correspond to transactions listed on Form EIA-50. GENNET also

associates with each arc a transmission loss (RTMLA) estimate. These loss

rates are either inputs or, optionally, calculated on the basis of

transportation mileage ( Note 7 ). Once entered or calculated, they remain

unchanged.

Due to transmission loss, the transaction quantity at the origin of an arc is necessarily greater than that at the destination. If not otherwise

stated, flow specifications are understood to apply at the destination

throughout the model.

For each node of the base network we input a storage capacity (QSTOW) and an associated annual storage loss (RSTLW) estimate. Both are held constant in

the model. Storage capacity refers to large underground storage facilities,

not the short term storage devices used mainly by distribution companies.

37
This storage capacity does not represent the capacity of storage owned and

operated by the company in question, but rather the capacity typically

available for storage of the company's ovm gas, regardless of whether the

facilities are owned or leased. See Sections 3.8 and 4.4 for further

information on how the MARKET model handles storage.

The only geographical information in the base network concerns distributors: it identifies a home State (XLOCW) for each D-node. As was mentioned before in this section, distribution companies that sell in more than one state are split into one component for each state and each of these

components is represented by a D-node, provided this component distributor is

large enough to meet the size criteria of GENNETT (see Chapter 5).

Finally, a tariff indicator (UTILA) has been attached by GENNEI to an

arc. Its purpose is to indicate whether a tariff for this arc is to be

specified directly. If the indicator is positive, it will point to a tariff

scheme consisting of a demand rate (PDEMU) and a commodity mark-up (PCOMU).

The meaning of these quantities will be explained in Section 3.7. Along with

the tariff scheme, a mileage estimate (GDSTU) is provided to MARKET to be used

optionally for calculating the transmission loss along the arc in question

( Note 7 ). If the tariff indicator is zero, then there are no tariffs and

mileage estimates, and if it is negative it indicates a direct sales D-node.

For these cases, tariffs are not provided directly but are determined in

MARKET as described in Sections 3.7 and 4.13.

3.4 Primary supplies and pipeline systems

The distributors are now partitioned into groups associated with distinct

pipeline systems. To this end, for each D-node and some P-nodes,

respectively, a single arc terminating at this node is selected as a node's

primary arc or predecessor arc . The origins of the predecessor arcs are called predecessor nodes . Conversely, there are successor nodes .

In the case of D-nodes, we select as the incoming primary arc the one that delivers the largest supply in the base year. The designation will

remain unchanged during later model years, even though the model does not assure that these primary supplies remain dominant. Since every D-node is

supplied from at least one node in the base network (see Section 3.3.1), each

D-node has a (unique) predecessor.

In the case of P-nodes, predecessor arcs are selected so as to indicate

that these nodes represent portions of a pipeline or a pipeline system. For

instance, in rooted pipeline clusters such as the one illustrated in Figure

3.3, the arcs connecting the root node on the left with the P-nodes on the

right would be predecessor arcs of the latter. The predecessor arcs of

P-nodes are typically not proper arcs and have therefore no volumes of gas

associated with them at the outset. The choice of the predecessors of P-nodes

is therefore not based on dominance of supplies.

38
Nodes without predecessors are necessarily P-nodes and are called

root nodes * All arcs in the base network which are not primary arcs are called secondary .

The methodology of the MARKET model is based on the assumption that the

transactions designated as primary transactions in the MARKET model cover a major portion of the natural gas market. The MARKET model is considerably

less detailed in its estimation of secondary transactions than of primary

transactions. The basic assumption of primary dominance is well satisfied

considering the current base network as a whole: including imports, secondary

transactions of the P-D and D-D kind between different pipeline systems

account for less than 15% of total volume ( Note 8 ). However, there are a few

locations in the base network at which the effect of secondary transactions is

relatively more pronounced than in the network as a whole. In Section 4.1.1 we will describe some measures that can be taken to mitigate potential adverse

effects of local secondary dominance. See Section 6.4 for a discussion of the

issues concerning the division of base network arcs into primary and secondary

ones

.

3.4.1 Pipeline systems and system networks

Consider the predecessor of a particular node, then the predecessor of

the predecessor, and so on. This repeated selection of predecessors must

either terminate at a root node or go on forever in a cycle. In the latter

case, we consider the predecessor assignment faulty. The network generator

GENNET provides a noncyclic predecessor assignment (See Chapter 5).

The term "pipeline system" can now be completely defined. In the base

network, each node is either a root node or the successor, direct or indirect,

of a single root node. Each root node then defines a unique system of P-nodes

and D-nodes, all of which are connected by a sequence of primary arcs to this

particular root node. This is what we call a "pipeline system". In the

model, it will act like a single pipeline company serving a set of client

distributors as their main supplier.

Between one and six market nodes or M-nodes are attached to each Dnode. Each of these markets consists of all customers of this particular

distributor which meet one of the following criteria:

Residential

Commercial

Utilities without residual fuel oil capability

Industrial without residual fuel oil capability

Utilities with residual fuel oil capability (switching subsector)

Industrial with residual fuel oil capability (switching subsector)

In other words, the two end-use sectors "industrial" and "utilities" are further subdivided into end-use subsectors by their ability to switch to

residual ("Number 6") fuel oil as their alternate energy source. This ability

renders these markets particularly sensitive to price increases, which is one reason why they are treated separately. Other reasons are differences in

curtailment priority and consumption patterns ( Note 9 ).

39
With each pipeline system, we now associate a system network consisting

of P-nodes and D-nodes connected by primary arcs with additional M-nodes

attached to the distributors. In each system network, each node but the root

node has a unique predecessor whereas the root has none. A graph with this

property is known as a "rooted tree" provided it is connected, as is the case here. Each node in the base network appears in precisely one system network.

The predecessors of M-nodes are D-nodes, the predecessors of D-nodes are either D-nodes or P-nodes, and, if they exist, the predecessors of P-nodes are P-nodes. Each P-node must have at least one primary successor that is not a direct sales D-node. This latter property is needed for price level

calculations described in Section 4.1.2.

Figure 3.4 illustrates the relationship between two system networks and a

base network. Here the rooted cluster method (Figure 3.3) was used to

represent pipeline systems of more than one pipeline company. Solid lines

Indicate arcs in the system networks. Heavy lines indicate arcs in the base

network, the broken ones refering to secondary arcs. Pj and P4 are the root

nodes. All arcs in the base network are proper (recall this term's definition

in Section 3.3.3) except the outer arc terminating at P2 and the two arcs originating at Pi. The latter two arcs are not proper if Pi, P2 and P3 form a rooted cluster with Pi an artificially introduced root node. P-to-P secondary

arcs like the one from P4 to P2 are a feature of a more advanced network

design. In the current network, such arcs are not present.

As in the base network, the system network connectivities are input to

the model. This input has to be compatible with the base network and the

predecessor assignment for the latter. The network generator GENNET

automatically generates the system networks along with the base network In a compatible fashion. Currently there are 17 pipeline systems, of which five

represent commerce which is predominantly intrastate.

The distinction between primary and secondary supply transactions, and

the resulting concept of a pipeline system, is a major design concept of the

model. It brings about a dramatic simplification of the model solution by

permitting most model processess to be carried out for one pipeline system at

a time, with secondary information being updated only once every model year

( Note 10 ).

3.4.2. Consumption patterns at M-nodes

For each D-node, the MARKET model requires customer and monthly

consumption figures by end-use sector in the base-year. These quantities are part of the system network data, which are a major input currently generated

by GENNET. More recent versions of MARKET provide a benchmarking capability

which adjusts these input data in order to ensure compatibility with NGA data

in the base year (Note 11)

.

40
^Primary in base network — Secondary In base network — Other system arcs

Figure 3.4: Schematic example of a gas supply network, consisting

of a base network (heavy lines) supplemented by the

market nodes.

41
For each M-node, there is a known base year consumption (QBASV) and a base year customer count (ZBASV). These quantities are part of the pipeline

system specifications that are prepared by GENNET and are taken directly from

Form EIA-50. The same source yields, for each M-node, a heating factor

(RHTGV) and a loadf actor (RLODV). These were derived from the Form EIA-50

monthly consumption data. The heating factors are used to represent

seasonality of demand. They are defined as the ratios of heating season

(October through March) consumption to total annual consumption at each

M-node. The estimates for loadf actors are used by the model for tariff

calculations. They represent the ratio of peak day consumption to average

daily consumption over the year. "Monthly" loadf actors obtained by dividing

the peak month consumption by the average monthly consumption over the year

are read into GENNET and transmitted to MARKET, which then transforms these

monthly loadfactors into "daily" loadfactors by multiplication with an analyst

provided loadf actor transformation ratio . AGA, acting on an inquiry by NBS,

has reported in a private communication results of a data analysis which

support the assumption that a loadf actor transformation ratio of 1.5

represents a reasonable approximation to the relationship between "monthly"

and "daily" loadfactors, and this value is consequently used in MARKET

( Notes 12, 13 ).

With each M-node, the model associates distribution losses measured

between the citygate and the burnertip. These include compressor fuel,

company usage, leakage and otherwise unaccounted for losses. At present,

there is no input mechanism for these distribution losses. The model will

estimate corresponding loss factors very roughly in the course of establishing

system flows for the base year (see Section 4.1.1). For system nodes other

than M-nodes and with the exception of the root node, the transmission loss on the primary inflow has already been determined, namely for the corresponding

arc in the base network (Section 3.3.3). This loss quantity can therefore be

transferred from the base network to the system network ( Note 14 ). When there

is no need to be specific, we will refer to both transmission and distribution

losses as system transmission losses (RTMLV) or just transmission losses .

3.5 Supply at the pipegate

At the beginning of each model year, starting with the base year, the BID

model presents MARKET with a list of reserve blocks . These include reserves available at the start of the mDdeling process as well as - after the base

year - newly discovered and acquired reserves provided by PROLOG and BID. For

each of these reserve blocks, BID specifies the pipeline system the reserve block is dedicated to, the amount of remaining reserves (QRRSK), the unit reserve price (PSUPK), the take-or-pay percentage (RTOPK) , as well as productivity information. The take-or-pay percentage is the percentage of the

full annual production capability from a reserve block for which the pipeline

system will have to pay regardless of whether delivery is taken of that

amount. We assume for the purposes of the model that all take-or-pay

provisions are in this simplified form.

42
After MARKET has determined the amount to be withdrawn from each reserve

block, it makes the corresponding updates in the list of reserve blocks and

hands the updated list back to BID. MARKET also reports to BID, for each

individual pipeline system, the total remaining reserves prior to this year's

production. This and the above described exchange of information between

MARKET and BID constitute the first instance of interaction between MARKET and

BID as mentioned in Section 3.2.

For the base year, GAMS derives its reserve estimates mainly from Form

EIA-23 data ( Notes 15,30 ). EIA has sampled contracts between pipeline

companies and gas producers to estimate take-or-pay percentages for these

initial reserves.

3.5.1 Production profiles and supply curves

The model has to determine the potential annual production capability of

each reserve block for a current model year or, in other words, how much can

be maximally produced from a specific reserve block over the course of the

year. This amount is a fraction of the total reserves contained in the block,

and arises from the latter by division with a potential reserve-production

ratio . This reserve-production ratio is not constant but changes over the

productive period of the reserve block. For this reason, the BID model

specifies - and passes on to MARKET - a (potential) production profile rather

than a fixed reserve-production ratio to describe the production capability of a reserve block at its present state of development.

In general, one can distinguish three separate production phases. The

development phase begins with the start of production and is characterized by

rising productivity due to additional extraction equipment. The constant

phase is reached when productivity is limited mainly by capacity of the

gathering system. The decline phase sets in when the reserve nears exhaustion

and gas pressure drops to the point where withdrawal rates fall below the

limit set by the gathering system. GAMS assumes that the (full marginal)

production rate increases linearly during the development phase, remains

constant during the constant phase, and decreases exponentially during the

decline phase. This results in a production profile of the form shown in

Figure 3.5.

The production profile expresses the production rate as a function of

time. This functional relationship, however, is only valid if production

proceeds at full potential. If this is not the case, then gas pressure, for

instance, may not drop as fast as implied by the production profile. In order

to describe the effects of curtailing production, the model assumes that the

production rate depends only on the amount previously produced. More

precisely, given the amount previously produced, the model determines the time

at, which this amount could have been produced without any curtailments of

production. We call this point in time the production time as opposed to real

time. The integral over the profile function between the production time and

43
the production time plus one year then represents the production capability of

the reserve block during the year in question (see Figure 3.5). This

calculation is repeated each year.

O^->

c

o

o

3D

O

&> CL

Available annual

production

v^ 1

Previouslys

produced \

\ \ 1.\ \ \ \ r 1982

^

T r 1987

1 ^

1992

Time

t

Production

time

Figure 3.5: Schematic production profile

Once the potential production quantities are knovm for the reserve blocks

of a pipeline system, a supply curve can be determined for the pipeline

system. Essentially, this supply curve relates the annual production quantity

from all reserve blocks dedicated to the pipeline system to an annual average

unit price. To determine a price for the amount to be withdrawn, a withdrawal

strategy has to be specified. As was mentioned before, the MARKET model gives

44
the analyst a choice between two EIA-specif led withdrawal strategies: minimum

cost-take and rateable take . These options are not selectively applied: once

a withdrawal strategy has been selected, it is applied every time during the

model run.

As its name implies, the minimum cost-take strategy minimizes the supply

price. First gas is withdrawn from each reserve block up to its take-or-pay

threshold. After all take-or-pay provisions have thus been satisfied, the

left-over demand is then allocated starting with the cheapest reserve block

and proceeding in order of increasing prices. The gas currently available in

each reserve block is used up before proceeding to the next reserve block

until withdrawal is complete. The total amount to be withdrawn thus determines

the individual amounts to be withdrawn from each reserve block, and thereby

the average unit price for the total. In the case of take-or-pay shortfall,

that is, if the total amount to be withdrawn is insufficient to cover all

take-or-pay obligations, the withdrawal price is set arbitrarily to the

average price of the total minimum take-or-pay production. In this case, the same percentage of the take-or-pay limit is withdrawn from each reserve block.

Conceptually, this amounts to creating a single reserve block combining the

take-or-pay portions from all reserve blocks. Figure 3.6 illustrates the form

of supply curves that result from adopting this withdrawal strategy. Note,

that this supply curve is in terms of average prices per unit of production.

A supply curve in terms of marginal prices would take the form of a step

function and thus would not be continuous. For a detailed discussion of the

mathematical form of the supply curve under the minimum cost-take option see Note 16.

Average unit

liprice (to be

passed on to

consumer)

Region of

take-or-pay shortfall

Quantity

withdrawn

Figure 3.6: Schematic supply curve for minimum cost-take

45
The rateable take strategy proceeds In the same fashion up to the

take-or-pay threshold. Thereafter, however. It withdraws at the same rate

from all remaining sources ( Note 17 ) » For instance, if the remaining demand were half of the remaining supply, then one half of each of its remaining

deliverability would be withdrawn from each reserve block. The price then

becomes the average price of the remaining available supplies after

take-or-pay provisions have been satisfied. The supply curve is thus equal to

the supply curve which would result from two conceptual reserve blocks (See

Figure 3.7). For the rateable take strategy to work, it is important that

expensive reserves have high take-or-pay ratios compared to the less expensive

ones; otherwise, prices will be cheaper if take-or-pay provisions are violated.

Average unit price to

be passed on to consumer

Region of takeor-pay shortfall

Quantity

withdrawn

Figure 3.7: Schematic supply curve for rateable take

46
In justification of the arbitrary price used in case of a take-or-pay

shortfall, we present the following arguments. We are in effect considering

only that portion of the supply price at the pipegate which can be expected to

affect the price at the burnertip. When the formally calculated supply price

rises steeply because of take-or-pay shortfall — it rises to infinity as the

purchased quantity approaches zero — then it becomes doubtful whether this

price will be allowed to be passed on to the consumer, although there appear

to have been too few precedents for a regulatory policy to emerge. We also

expect that contract renegotiations would ensue if large take-or-pay

shortfalls were inevitable.

3.5.2 Analysis of production profiles

A production profile of the kind described above is determined by five

profile parameters:

Ti = start of production (TLINK)

T2 = start of constant phase (TCONK)

T3 = start of decline phase (TDCLK)

*imax ,~ maximum production rate (QRTEK)

Qres = total original reserves (QORSK)

In addition, we introduce as a sixth profile parameter the reserve-production

ratio during the phase of exponential decline

Tg = decline phase reserve-production ratio [years]

This parameter indicates how long it would take from the beginning of the

decline phase to exhaust the resources of the reserve block if production were

to be sustained at the maximum production rate Qmax (Figure 3.8). Thus Te can

Production

Rate

Time

Figure 3.8: Role of profile parameters

47
be calculated from the quantity of reserves available during the decline

phase. This amount, in turn, is found by subtracting the production during the

previous two phases

max [^) ^max • (V"^2^*

from the total original reserves Qrgg. The parameter Tg is recalculated in

each model year in this fashion. Using Tg, the profile function q(T) can be

expressed in the form

r

q(T)

^max

T-Ti

T2-T1

T3-T ^^P(-^)

for T < Ti

for Ti < T < T2

for T2 < T < T3

for T3 < T

The main computational task that faces MARKET concerning the modeling of

supplies is to calculate the full production capability Qfull of the reserve block during a given year. This calculation requires determining the point in

time Tprod such that full production up to this time would have yielded the

historical production Qhist from the time the reserve block has been

activated. More precisely, Qhist is the amount withdrawn from the reserve block in the course of modeling up to the present model year, and it is

calculated as the difference between the originally available reserve Qres ^^d

the remaining reserves Qrem*

Qhist ~ Qres ~ Qrem*

Both the original and the remaining reserves are provided by BID as part of

the reserve block information. This determines the state of development of

the reserve block and consequently the present production capability. In

order to determine Tpj-od ^^ express the full production prior to a given time

as a function of that time (see Figure 3.9)

48
Q(T) = / q(t)dt .

where

<res / q(t)dt ,

and then find the inverse T(Q) of the above function in order to determine

the production tine

Vod - T(Qhist)«

The latter then yields the full production capability for the current year

(see Figure 3.9):

Qfull = QCTprod + 1) - Q(Tprod)«

A Cumulative quantity withdrawn

Production time

"'^prod

Actual time

T

Original

reserves

Historical

production

Figure 3.9: Cutnulative production from a reserve block, as a function of

time: Q = Q(T)

49
In what follows, we will provide formulas for these calculations. Let

T2

Q(T2) = / q(t)dt = qnjax * ^2-Ti

2

T3

Q(T3) = / q(t)dt = Q(T2) + qmax-(T3-T2) = qmax' T3 _ Tl+T2_

2

be the quantities produced up to the breakpoints T2 and T3, respectively.

reader confirms readily that

To for T < Tj

The

Q(T) = ^max

(T~Ti)

2(T2-Ti)

for T| < T < T2

Q(T2) + (T-T2) = T - T1+T2 for T2 < T < T3

qmax 2

Q(T3) + Tg *(l - exp [I^zLJ) for T3 < T,

^max Te /

and that consequently

r T, + n

2(T2-Ti)Q

T(Q) =

*lmax

T2 + Q-Q(T2)

<lmax

T3 - Te-log f

1 - Q-Q(T3)

)

qmax ^e

for < Q < Q(T2)

for Q(T2) < Q < Q(T3)

for Q(T3) < Q < Qres.

These are the formulas used by MARKET for the calculation of the annual

production capability.

Note that the above formulas remain valid if Tj = T2 , T2 = T3, or both. In these cases the profiles will assume the shapes indicated in

Figure 3.10 ( Note 18 ).

50
Ti=T, T2=T: Ti = To=T.

Figure 3.10: Special cases of production profiles

3.6 Denvand at the burnertip

The MARKET model establishes for each M-node an individual local demand curve . The reader may recall that each M-node is associated with a unique

end-use sector and a unique distributor. Each M-node represents the total

market of this distributor in that end-use sector or subsector (see Section

3.4.1). The demand curves are based — as are the supply curves (see Section

3*5.1) —, on average rather than marginal prices ( Note 19 ).

Demand information is analyst supplied and in essence exogenous to MARKET.

However » the analyst is required to supply demand curves only for each of 10

DDE-specified demand regions see (Figure 3.11). From these regional demand curves — one for each end-use sector and each model year —, the local demand

curves are generated automatically. The MARKET model also has the capability

to generate future demand curves if the analyst so desires. This capability is

based on the input of regional reference volumes (QRRSIY, ORCMIY, ORINIY,

ORUTIY) and regional reference prices (PRRSIY, PRCMIY, PRINIY, PRUTIY) for

each end-use sector starting with the year preceding the base year, and ending

with the horizon year.

3.6.1 Illustrating local demand curve generation

In what follows, methods for generating and updating local demand

curves are illustrated using a particular kind of demand curves as an example.

To this end, consider local demand curves of the form (Note 20)

3

q " Iref (' ref

51
Figure 3.11: DOE demand regions

These are curves of constant (negative) elasticity

P dq

3 = — • — » constant.

q dp

The remaining two parameters, the local reference volume qj-gf (QTRFV) and the

local reference price Pref (PTRFV) determine the general level of demand at

the particular location (- M-node) by fixing a point, namely (pref » qref )»

through which the demand curve must pass. Indeed, for p = pref *

Pref P 6

q " qref

(

) " qref •! = qref • Pref

52
These local curves can be interpreted as arising from a regional demand curve

of the same form,

p e Q = Qref(- ) , Pref

by proper scaling. Here Qref ^^^ ^ref denote the regional reference volumes

and prices for the given year and end-use sector. The scaling works as follows. For the base year, MARKET determines the consumption volume and the

average burnertip price at each M-node. This volume and this price become

the local reference volume and local reference price for each local demand

curve, respectively. Then the home state of the M-node is determined and its

demand region is deduced from this. The elasticity 3 of the regional demand

curve is then used for the local demand curve, which is completely determined

In this fashion. Note that multiplying the regional demand curve by the

constant factor

<lref Pref &

Qref Pref

will indeed produce the local demand curve in question.

The rationale behind this scheme of generation by scaling is that the

geographic, social, and behavioral factors which determine elasticity or, more

generally, the shape of the demand curve are sufficiently constant for the

purposes of the model throughout each demand region. Thus only the level of

demand is at issue locally.

Demand curves for subsequent years can be generated directly from the

sequence of regional reference volumes and prices together with regional

elasticity information ( Note 21 ).

MARKET specifies local reference volumes and prices because they permit

specification of demand levels not just for the special demand functions

described above, but also in the case of more general demand functions.

3.6.2 The regional demand compatibility condition

The question arises: If the average burnertip price and the total

consumption are calculated for all M-nodes of a given end-use sector in a given region, does this total price-quantity pair determine a point on the

regional supply curve? If the answer is affirmative, then the regional

demand compatibility (RDC) condition is satisfied.

In the base year, the local volumes and prices are known, and the RDC

condition requires only that the observed base year volumes sum to the

regional reference volume and that the average price correspondingly agree

with the regional reference price.

53
In subsequent model years, if equilibration is employed, the actual

prices and volumes as determined by the model at M-nodes will differ from the

corresponding local reference prices and volumes. It can be shown that even

for simple demand curves of constant elasticity, the RDC condition may no longer hold, even if all local reference volumes and prices are compatible

with the regional reference volumes and prices (see Note 22 for an example).

In more recent versions, various demand iteration schemes have been

implemented in which the RDC condition is enforced as much as possible.

Clearly, it cannot be enforced in the case of a regional shortage because in

this case the actual deliveries will fall below the demand as indicated by the

regional demand curve.

Now let

$(P)

be the regional demand curve for source end-use sector in a given year, and

(o)

(j) (p), i=l,...,n ,

a set of corresponding initial local demand curves. Then the equilibration is

carried out, resulting in local price-quantity pairs

(o)

Pi. qi = <l> (p) •

Thus

Q = I qi, p = I Piqi/Q

are the resulting regional quantities and prices. If

Q = *(P) ,

then the RDC condition is satisfied. If not, the local demand curves are rescaled:

(1)^ ^ *(P) (o),

^ ^ (p) » •

<f) (p) , i = l,...,n . i Q i

This scale factor has been chosen so that the rescaled local demand curves satisfy the RDC condition for the local prices p^ which were determined in the

previous demand iteration. Indeed the scaling does not affect the regional

average price as the scale factor cancels:

54
I H (pi)*Pi I H (Pl)*Pi

(1) '

(T)

I <l>i (Pi) I *i (Pi)

= P

Furthermore,

^ (1) *(P) ^ (o) *(P)

I ^i

(Pi) ° *T" ^ *i

(Pi) " V" ' ^

'^ *^^^*

Unfortunately, there is no reason to expect that the scaled demand curves would have equilibrated at the same local prices Pi as the initial ones. To

completely enforce the RDC condition, it is therefore necessary to reequilibrate with the scaled demand curves and, if necessary, to repeat the process

of scaling

.

Note that the result of this iteration process depends on the choice of

the initial local demand curves. Demand iteration will yield different

results when started with different sets of local demand curves, even if the

regional demand curve is the same in both cases, and the local demand curves are sealed replicas of this regional demand curve. Therefore it is important

to select the initial local demand curves with care. The regional references

and prices provide a vehicle for intial demand estimation. Denoting by u and TT the ratios of this year's regional reference volumes and prices to

last year's regional reference volumes and prices, respectively, one might

define initial local demand curves

(o)

\|> (p) = i = l,...,n

with the help of those used in the previous model year:

(o) (o) p

^ (p) = <t) (- ).

1 i TT

In the case of the special demand functions discussed in (3.6.1), this amounts

to simply multiplying the local reference volumes and prices by w and w , respectively. This suggests an alternative way of generating initial local

demand functions: i) multiply the local reference volumes of the previous

year first by the final scaling factors resulting from demand iteration and

then by n to derive new reference volumes; ii) multiply the local reference

pric'es of the previous year by tt to derive new reference prices; iii) for

each M-node, scale the regional demand curve so that it passes through the

point defined by the new local reference volume and price.

55
3.6.3 Cut-off prices

For each supply curve, a cut-off price (PCUTV) is calculated from state

prices for alternative fuels. It indicates the price above which an alternative fuel would be preferred over gas, and demand is assumed zero if

the actual price rises above this cut-off price. Only the cut-off price

derived from the price of residual fuel oil will be low enough to influence

model calculations appreciably; this cut-off price is used for those

industrial and utilities end-use subsectors which can switch to residual fuel

oil (recall Section 3.4.1). For details concerning the handling of cut-off

prices and related issues, consult Note 23.

3.7 Tariff s

Pipeline and distribution companies post tariffs to recover the costs of

purchasing natural gas well as the expenses incurred in handling it. For the

purposes of this report, we use the term tariff for the additional charges

beyond the costs of purchasing gas. The reason for considering such mark-up

or add-on tariffs rather than the posted tariffs is that, during the process

of equilibration, the posted tariffs are assumed to vary in response to

changes in the tentative pipegate purchase prices whereas mark-up tariffs are assumed to remain unchanged during that process. We distinguish transmission

tariffs levied by pipeline companies and distribution tariffs levied by

distribution companies. Storage tariffs will be considered in Section 3.8 . Schematically, we have:

burnertip price = citygate price level + distribution tariff mark-up,

city gate price = pipegate price level + transmission tariff mark-up.

A^ already indicated, tariff mark-ups are determined prior to equilibration,

which then establishes the burnertip (and city gate) prices and therefore, in

a sense, the posted tariffs. For the difference between city gate prices and

city gate price levels see Section 4.1.2.

The model represents tariffs at each system node with the help of two

tariff parameters : a fixed hook-up or demand charge (CFIXV) and a per unit

commodity mark-up (PVARV). For the commercial entity represented by a system

node, the demand charge represents an annual cost of doing business with the

commercial entity represented by the predecessor of this node. The demand

charge must be paid regardless of the volume purchased. If the system node is an M-node, the demand charge is understood to be the total of the annual

hook-up charges for all customers in the particular market that corresponds to

the M-node. For each system node, the commodity mark-up, when added to the

unit price at the predecessor node, will yield the full "commodity charge",

that is, the purchase price per unit of primary supplies at the system node.

56
The above tariff scheme represents a considerable simplification,

especially of distribution tariff schemes, which in reality tend to be more complex and to involve more than two parameters. It amounts to the

approximation, by a rising straight line, of a fairly involved functional

relationship between the volume purchased by a market and the dollar cost of

mark-ups beyond the supply price to the distributor (see Figure 3.12).

Total cost of mark-up above cost of supplies

Fixed cost-^ —(Assumed real) —Approximation

Volume purchased

Figure 3.12. Schematic illustration of a prototype mark-up

relationship and its approximation by a linear

relationship with fixed cost.

The model either derives tariff parameters from direct tariff

specifications made for corresponding arcs in the base network—which is the

procedure currently used for all transmission tariffs—or it estimates them

annually using the distribution tariff module , an NBS-coded subroutine in the

MARKET model. This subroutine is based on general relationships between

consumption and rate bases. These relationships have been developed

empirically for NBS by J.-M. Guldmann [3]. They are outlined in Section

3.7.2. In the case of direct sales D-nodes, tariffs are calculated in the

57
base year as the difference between two node price levels for the D-node

itself and the preceeding P-node , and are assumed zero for the successor M-nodes (see Section 4.2.2). In subsequent years, direct sales tariffs are treated as if they were directly specified. Whether direct tariff

specification or the distribution tariff module is to be used depends on the

value of the tariff indicator which is input via GENNET for each arc of the

base network, (see Section 3.3.3): positive tariff indicators trigger direct

tariff specification, while negative tariff indicators characterize direct

sales distributors.

An escalation option permits the analyst to increase both transmission

and distribution tariffs annually by a fixed specifiable percentage.

3.7.1 Expected flows and peak day volumes

Whether using direct tariff specification or the distribution tariff

module, the derivation of the fixed charges requires the prior estimation of

loadf actors and expected flows (QEXPV). The distribution tariff module

requires, in addition, an expected customer count (ZEXPV). The loadf actors

are derived from Form EIA-50 and are input via GENNET for M-nodes, as explained in Section 3.4.2 . For the remaining nodes they are estimated as weighted averages of loadfactors at succeeding nodes using expected flows as weights. The expected flows and the expected customer counts represent not

model forecasts, but rather the expectations of pipeline and distribution

companies concerning their upcoming sales. The initialization and subsequent

calculation of the expected flows and the expected customer counts are discussed in Sections 4.1 and 4.2.5 . The expected flows and the loadfactors

are combined into an estimate of what a pipeline company might expect as a peak day volume ( Notes 12,13 )

Expected flows and expected customer counts at system nodes associated

with specific States are derived by multiplicatively modifying the annual

flows and customer counts that were obtained for the previous model year. The

model selects the ratio of successive population growth projections as the

modification factor for the State in question. P-nodes are not associated

with specific States; here a growth factor of 1.1 is assumed for expected

flows. Customer counts are not modeled for P-nodes. In the base year, the

actual base year figures are utilized in establishing expected flows and

customer counts whenever the latter are defined.

In the case of direct tariff specification, a tariff scheme consisting of

a demand rate and a commodity mark-up are associated via input with an arc of

the base network (see Section 3.3.3). The demand charge then is again the

product of the demand rate and the expected peak day volume. The commodity

mark-up is transferred directly. For interstate pipeline companies, tariffs

are broken down by zones. They have been extracted by NBS from rate hearing

depositions at the FERC. These transmission tariffs fluctuate considerably

over the course of a year due to new rate hearings, invoking incremental

pricing provisions, and adjustment for previous overcharges. Tariff data thus

represent estimates of annual averages. For intrastate transactions, demand

rates are assumed to be zero and commodity mark-up figures have been estimated

58
using GAS FACTS as follows: In States with substantial intrastate commerce in

natural gas, the difference between statewide averages of citygate and

wellhead prices is assumed to be representative of the commodity mark-up. In

all other States, a volume-weighted average over these particular commodity

mark-ups is used.

The distribution tariff module, on the other hand, derives tariffs via

rate base modeling. It calculates costs of service and then defrays these

costs on the basis of expected flows and expected customer counts by end-use

sector via a commodity mark-up, a customer charge and a—using expected peak

day volume —a peak-demand charge. The latter two charges are then combined

into a single demand charge per end-use sector. Sales to another distributor

are treated as industrial sales, unless the tariff pointer calls for direct

sales specification.

Direct tariff specification is currently used for transmission tariffs,

that is, tariff increments on P-D arcs. Use of the distribution tariff module

is restricted to D-M and D-D arcs ( Note 24 ). Provisions exist in MARKET for

escalating directly specified tariffs (and tariffs in general) by an annual

fixed rate in order to allow for a growth rate of tariffs which exceeds

inflation' ( Note 25 )

3.7.2 Outline of the distribution tariff module

A set of equations relating the total annual sales of a distribution

company to its tariffs, has been developed by J.-M. Guldmann under contract to

NBS and is described in detail in [3]. NBS has selected some of these

equations and modified others for its construction of the distribution tariff

module. We will now outline this procedure.

The module first calculates for the base year the total purchase (not

replacement) values of three categories of plant in service. These categories

are: transmission, distribution and general service. Let

Bx = base year purchase value of transmission plant

Bd = base year purchase value of distribution plant

Bg = base year purchase value of general service plant

Vx = present year purchase value of transmission plant

Vd = present year purchase value of transmission plant

Vq = present year purchase value of general service plant.

With

QbASE ~ Total sales during the base year,

the following equations have been empirically developed:

Br = 4134520 + .4190155'QbasE .

Bd = 7.584965-(Qbase)-^^^^°^ »

Bg = .33520768-(Qbase)*^^^^^^ •

59
(The fact that constraints are expressed using seven or eight digits does not

Indicate that these digits are all significant.) In subsequent model years,

these values of plant are updated by estimated additions and replacements.

Additions are determined as multiples ( addition factors ) of the Increase A In

total sales, provided the latter Is positive. If there Is a drop In sales,

there will be no additions. We denote the addition factors by

For their calculation, we refer to [3].

Replacements are determined as a fraction of the respective plant values.

Their original purchase value Is estimated as follows:

Rt = 0.00176'V^

Rd = 0.00753*Vd

Rg = 0.03624 'Vg .

Replacements add to the purchase value of the plant because the replaced Items

are now more expensive than when they were purchased originally. In other

words, after subtracting the purchase value, the replacement value has to be

added In order to describe the effect of the replacement on plant value. The

replacement value Is estimated using the Handy-Whitman Index [5] for utility

construction under suitable assumptions about the lifetime of the replaced

parts. The resulting replacement value multipliers

PT» PD» PG

vary by State and are directly Input Into MARKET. The new plant values are now calculated from the old ones as follows:

Vx(new) = Vt + a^'A + (p-r-O-RT

VD(new) = Vj) + a£)«A + (pd-I)'Rd

VG(new) = Vq + olq'L + (pg'D'Rg •

A distinction Is made between total plant V^njE and total plant in service,

Vx + Vd + Vg

The following relationship has been determined:

Value = i.04i93-(Vx + vd + vg).

In order to arrive at the rate base, one must now calculate the

accumulated depreciation and then subtract it from V^lue* ^^ the base year,

accumulated depreciation is estimated in terms of plant in service values:

Adep = .36025 'Bx + .30331 'Bj) + .39396'Bg .

60
In subsequent years the accumulated depreciation Is updated by adding

annual depreciation

Dep = 0.03522*Vt + 0.03059»Vj) + 0.03388«Vq ,

and by subtracting the original purchase value of replaced parts,

Rep = Rt + Rd + Rg , from the accumulated depreciation:

Aj)Ep(new) = Aqep + Dep - RfiP •

The module also considers, In the above equation, a term for salvage values

which we have deleted for clarity of exposition.

The rate base RbaS ^^ ^^^ given as follows

Rbas = Value - Adep .

The module goes on to estimate operations and maintenance costs Cqp and to

calculate the revenue requirement Rq excluding gas purchase costs. The latter

are excluded because the purpose of the module Is to estimate add-on tariffs

that are to be added to the model-determined gas purchase price.

Rq = Cop + Dep + wRbas •

Here u) is an input-specified return percentage.

The remainder of the calculation allocates the revenue requirement to the

markets served by the distributor. To this end, the revenue requirement Is

split into three parts: capacity costs , customer costs , and volumetric costs . The procedure then is to prorate the capacity costs over the attached markets

according to their expected peak day volumes, the customer costs according to

their numbers of customers, and to use the volumetric costs as commodity markups.

This method essentially guarantees recouping the revenue requirement.

However equitable, the method is not quite realistic, in particular for

residential end-use. Here the model-generated hook-up charge per customer,

consisting of both the share of the capacity costs and the individual customer

costs, is too large whereas the commodity mark-up is too small. In general,

regulatory agencies tend to require that a major portion of the capacity costs

be recouped via commodity mark-ups, a procedure which favors residential

customers (in the short run). This may result in over- or undercharging

depending on how the actual consunqjtion differs from the expected consumption.

For further developments concerning the distribution tariff module see Note 26.

61
3.8 Storage

Since production of natural gas proceeds at an essentially even pace

while consumption differs according to season, large storage facilities are needed. Smaller storage facilities at the citygate serve to stabilize daily

fluctuations. These smaller facilities are not represented in the model. The

model does, however, provide for the representation of large underground

storage facilities which serve to equalize summer and winter demands (see

Figure 3.13). In fact, each node of the base network is considered as a potential storage location, the capacity of which is input via GENNET together

with an annual storage loss percentage on withdrawal (see Section 3.3.3). The

storage losses are envisioned to consist mainly of the pipeline fuel used for

transportation to and from the storage facility and also for storage operation

( Note 27 ).

For each year following the base year, the model estimates storage needs on the basis of the seasonal differences of the previous year's consumption

pattern. This estimation process is described in detail in Section 4.4 . It

will store — up to the specified storage capacities — these expected needs

during the summer and withdraw them — subject to storage loss -- during the

winter. The underlying assumption is that additions to storage during the summer equal the withdrawals from storage during the winter (compare Figure

3.13).

Shipments to and from storage will be treated as if they were secondary

transactions. This requires the specification of values along with volumes.

The value of a shipment into storage is determined on the basis of the price

level that prevails at the system node in question when the shipment is made.

Upon withdrawal from storage, the model levies a storage tariff in the form of a fixed percentage, say 25%, of the shipment's original value. This tariff is

intended to cover a variety of costs incurred in connection with storage. If

storage is company owned, than the tariff represents investment and operating

costs associated with that facility. If storage is leased, it represents a tariff paid to some other company. In both cases, seasonal differences in

secondary supply costs, which are not accounted for directly, as well as "loss

of opportunity" are considered as storage costs (Note 28).

62
Gas in Storage

10

JMMJSNJMMJSNJ

1980 1981

M J S N

1982

Figure 3.13: Natural Gas in Storage. (Monthly Energy Review, December 82)

3.9 The concept of equilibration

For model years other than the base year ( Note 29 ), the MARKET model uses equilibration of demand and supply curves to determine the volumes produced

and consumed by each pipeline system as well as the respective prices at the

pipegate and the burnertip.

There are two modes of operation. The MARKET model equilibrates either

on an annual or on a semiannual (heating year) basis. A more detailed

discussion of these two options is given in the procedural description of the

equilibration process in Chapter 4.

63
In its sliiq)lest form, the equilibration process balances a single demand

curve against a single supply curve. Our problem is more complex in that it

involves many demand curves (one for each M-node), and several supply curves

(one for each pipeline system). It can be classified as a network

equilibration problem. Fixing secondary volumes and prices simplifies this

problem considerably, because this results in partitioning the set of demand

curves by pipeline systems so that demand curves which are in the same pipeline system are to be balanced against a common supply curve. One might

then consider combining all the demand curves in the pipeline system into a single root demand curve to be balanced against the supply curve at the

pipegate. We will explore this general idea in a brief discussion of

equilibration in general and the structure of the root demand curve in

particular. This discussion will provide a basis for interpreting model

procedures

.

3.9.1 Definition of equilibrium

Consider an arbitrary demand curve

p = D(q) , < q ,

which indicates the maximum unit price p the "buyer" is willing to pay for

quantity q . Thus p-q = q«D(q) would be the cost of the transaction. Note

that this definition of a demand curve is different from the one used in

Section 3.6 , where quantity was expressed as a function of price rather than

the other way around. For a general discussion, we prefer the above

definition of demand curve because the maximum acceptable price is always a unique function of the quantity to be purchased, whereas two different

quantities may well have the same maximum acceptable price. This also means that the function D(q) need not be monotonic in q . (The function q'D(q),

which represents the acceptable dollar cost rather than the acceptable unit

price, is however always monotonic.)

Next we consider an arbitrary supply curve

p = S(q) , < q < q^ax , which states the minimum unit price p at which the "seller" is willing to sell

quantity q . Again p*q = q'S(q) would be the minimum acceptable total return

for quantity q . Note that this definition is compatible with the one used in

Section 3.5 . Again there is always a functional relationship of the above

form. The example of a supply curve in Section 3.5, as illustrated in Figure

3.7, shows that the quantity q may not be expressed uniquely as a function of

the minimum acceptable price p .

Suppose now that all points (q,p) with

P < D(q)

represent deals acceptable to the buyer, and that all points with

P = S(q)

64
represent deals acceptable to the seller. Finally define an equilibrium

point as the point (qo»Po) °^ largest quantity qQ < qniax aox)ng those points

that represent deals with are acceptable to both. Then there are three

possible outcomes (see Figure 3.14).

'^/ ////

Qma:

iP

Qmax

/// / ///A

Qmax

Excess Demand Equilibrium No Equilibrium

Figure 3.14 Schematic illustration of equilibration

In the first case, the buyer would be willing to pay more in order to get more. This can happen only in a price regulated environment. In the second

case, both buyer and seller realize their expectations and an equilibrium

ensues. In the third case, there are no acceptable deals.

The reader notices that this schematic description of equilibration is

asymmetric: on the one hand, we assume that the set of seller-acceptable

price-quantity pairs agrees precisely with the supply curve, whereas on the

other hand, the demand curve bounds an entire area of price quantities

acceptable to the buyer. This asymmetry indeed holds in our application. It

arises because we assume that the producers of natural gas are no longer in a bargaining position. Their bargaining was done in the process of arriving at

longterm contractual agreements with the pipeline company. As a result, the

price of gas in each reserve block is no longer negotiable and the quantity

produced is at the discretion of the pipeline company subject, of course, to

availability limitation and take-or-pay provisions. Depending on the choice

of the withdrawal strategy, the average unit price of supplies at the pipegate

is uniquely determined by the total quantity produced from all dedicated

reserves. This means that only price-quantity pairs which lie on the supply

curve are acceptable.

65
To find the equilibrium for a given pair of supply and demand curves,

one may proceed as follows: Start with the value qmax and check whether

D(qmax) > S(qniax) •

If so, then (qmax* SCqmax)) is the solution. In particular, if D(q,nax) >

S(qiQax)> then the excess demand case prevails* If the above condition fails,

that is, if

•^(^max) < S(qniax) .

then choose some small increment

5 = i • qmax

N

and test successively for k = 1, ..., N whether

D(qmax - k"S) > S(qn,ax " k'^) •

If this condition is satisfied for some integer k, then two values q and q+6

have been found with

D(T) > S(q) , D(q+6) < S(?+6) .

The supply and demand curves must therefore intersect at some argument qo>

q ^ Qo ^ q+^» and thus determine an equilibrium point (qo»Po)* This point

can be found, for instance, by consecutive bipartition. The absence of an equilibrium is expected if

O^^max - k-«) > S(q^x - k-6)

for all k=l, ..., N . Because this test is finite, it does not entirely rule

out the existence of an intersection of the two curves and therefore of an equilibrium. However, it renders it highly unlikely. If an equilibrium

should indeed exist in spite of the above evidence to the contrary, it would

represent a highly unstable situation which would not provide the basis for

safe conclusions. Similarly, if an intersection (qo»Po) ^s found by the

above procedure, then we expect it to be the "rightmost" intersection, that

is, the one that maximizes q^ . That is how the equilibrium is defined.

Again there is no formal assurance that an intersection further to the right

has not fallen "between the cracks". If so, however, we feel again that such an intersection would have provided an unstable equilibrium.

66
3.9.2 Transformation and combination of demand curves

In this section, we will Illustrate the construction of the root demand curve by means of a slnq)le example. Consider two market nodes, 1 and 2, fed

from root node 0. Two fixed charges Ci and C2 are associated with the

deliveries to nodes 1 and 2, respectively. For simplicity, we assume that

there Is no commodity mark-up or transmission loss associated with either

delivery. With each market node 1, 1=1,2, we associate a demand curve D^

(Figure 3.15).

PO = S(qo)

( 1 )Pl <Di(qi) Ci^'V->'

101

^1

\C2 qo

^2%

r2^P2^D2(q2)

Figure 3.15: Example of network equilibration

We want to transform each market demand curve into the corresponding

demand curve at the junction where the delivery arc leaves the root node.

More precisely, we want demand curves expressed in terms of the prices which

hold prior to the addition of the respective fixed charges. The point (qi,Pi)

represents an acceptable deal, if p± < Di(qi). In order to consummate the

deal (qi,Pi), we must have the deal (qj,,Pi) prior to adding fixed charges

where

^1 ~ 11 (^o transmission loss) ,

Pi "^ Pi ~ Ci/qi (fixed charge)

The' deal (qi,Pi) is therefore acceptable if and only if the resulting deal

(<Il»Pi) is acceptable. Thus

67
Pi < Di(qi) <^=?> PI < Di(qi) ,

where Dj denotes the desired transformed demand curve. It follows that Dj

derives from Dj sltiq>ly by substitution for both q± and pi:

Di(?l) = Di(qi) - Ci/ qi ,

or more precisely (see Figure 3.17),

Di(^i) = max {0,Di(qi)-Ci/ qj}

Even If the original demand curves Dj^ are monotonlc, the new demand curves

will in general no longer be monotonlc (see Figure 3.16).

The next step is to combine the demand curves Dj, 1 = 1,2 into a single

demand curve at the root node. That is to say, we ask for a function Dq such

that Po < Do(qo) characterizes all acceptable deals struck upon entering the

root node. A deal (qo»Po) is acceptable if it gives rise to two acceptable

deals leaving the root node at the same price po = p^ , 1 * 1,2. For given

qi and q2» this implies:

Po ^ Do(qo)<^ qo = qi+q2 A Po < Dl(qi) /\ Po < D2(q2).

Do(qo) = max {Di(qi), D2(q2) | qo = ^1 + q2> •

This is clearly not a simple operation, and we will not even try to solve it

for our application. We would like to point out, however, that the solution

can be obtained readily if there are no fixed demand charges, that is, if

Ci = C2 = 0, and if the original demand functions are monotonlc. Then

^1 - Di, inverse functions Df"^ exist, and the reader verifies readily that

D^-1 = Dj-l + D2-I .

This means that the Inverses of the demand functions combine essentially in an additive fashion.

68
— Monotonic burnertip

demand curve

Nonmonotonic citygate

demand curve

Quantity

Figure 3.16: Nonmonotonic citygate demand D curve derived from monotonic

burnertip demand curve D reflecting a demand charge.

In this section, we have described a procedure for constructing a root

demand curve which represents the combination of the burnertip demand curves in the system. From a conceptual point of view, it is important to realize

that a single demand curve at the pipegate can indeed describe the demand

behavior of the entire system. As the above discussion shows, however the

actual construction of the root demand curve does not appear practical. We

therefore approach the system equilibration problem by means of a series of

iterations which are described in Section 4.2. This procedure is conjectured

to yield the same result as employing the actual roof demand curve.

69
CHAPTER 4

Procedural Description of the MARKET Model

Based on the concepts introduced and discussed in Chapter 3, we will now

describe the procedures followed by the MARKETT model. This description will

rely more heavily on detail and stress formal mathematical relationships. We

begin with the procedures used to establish the initial set of conditions for

the base year. Next we describe in detail the equilibration process which is

at the heart of the MARKET model and which has several features that set it

apart from conventional equilibration processes. The rest of the chapter

addresses the updating of secondary transactions, the determination of storage

needs, and the demand projection procedure. We conclude with a summary of

MARKET in the form of a brief step-by-step diagram.

4.1 Modeling the base year

Recall that the MARKET model is essentially a simulation model with

annual (or semiannual) recursion. In order to initialize these recursions, a baseline of model quantities must be established for the base year. In

particular, the base year volumes and price levels are needed to (i) assess

the base year withdrawals from reserve blocks; (ii) set reference volumes and

prices for the demand curves; (iii) initiate volumes and prices for secondary

arcs. Most of these baseline parameters will be direct or only slightly

transformed Inputs. Other model quantities are calculated. Data from

different sources need to be reconciled. At the core of these calculations

are the principles of conservation of matter and of balancing monetary

accounts. For each system node, the conservation equation,

annual inflow = annual outflow + transmission/distribution/storage losses

must hold, and accounts must balance:

cost of delivered supplies + cost of operation = revenues.

We define the cost of operation to include fixed costs due to depreciation,

investment, financing, and dividends, as well as the value of transmission

losses of the company represented by the system node. We assume that the cost

of operation is precisely compensated by add-on tariffs. This assumption will

govern the way sales prices will be calculated from supply prices.

4.1.1 Initial system flows

With each system node of a given pipeline system, we associate in each

year a primary supply quantity or system flow (QANNV). In the base year,

these volumes are calculated from the volumes consumed annually at M-nodes.

As mentioned in Section 3.4.2, these burnertip volumes are a key input

generated by GENNET from Form EIA-50. The idea is to propagate these volumes

backwards towards the roots, balancing inflows and outflows at each system

node and taking into account transmission/distribution losses, secondary

inflows and outflows, as well as storage losses.

70
A data problem, however, arises because distribution losses between the

cltygate and the burnertlp have not been specified. The distinction between

transmission and distribution losses, and the data gap associated with the

latter, have been discussed at the end of Section 3.3.3. We deal with this

data gap by assuming tentatively a fixed distribution loss, say 4%, concerning

M-nodes ( Note 31 )

We will now describe a first round of calculating flows. For the purposes of this description, we will use the term "transmission loss" to cover either transmission loss by a pipeline company or distribution loss by a distribution company. The calculation proceeds from the M-nodes backwards

towards the root, considering each system node after the flows Into Its successor nodes are already known. The following formula expressing flow con- servation Is used for finding the primary Inflow Into such a systen node j :

Qj = ^ieso^i/'^i "^ ^OUT - QlN + (1 - Sj)'QsTOR,

where

Qjj = primary Inflow Into system node h metered at h (h = l»j)

T± = transmission loss factor for system node 1 (RTMLV) (rj < 1.0)

QXN = secondary Inflow metered at system node j (QTPIV)

QOUT ~ secondary outflow metered at system node j (QTPOV)

Sj = storage loss factor for system node j (RSTLV) (sj < 1.0)

QSTOR = amount stored at system node j (QSTOV)

S(j) = set of (direct) successors of system node j .

The transmission loss factor Is the factor by which one has to multiply the

original value so that a reduction by the specified percentage results, e.g.,

.96 for a percentage loss of 4%. (The term "transmission yield" might be more logical, but does not emphasize the Idea of "loss"). The storage loss factor

Is defined analogously. It covers losses due to transportation to the storage

site, and storage operation. The reader Is reminded of the assumption that

during the winter everything Is withdrawn that was stored In the summer (see

Section 3.8). This amount Is QsTOR • The term (1 ~sj)*Qstor represents

storage loss ( Note 27 ). See Section 4.4 for the determination of QsTOR •

The total secondary Inflow Qxn Into a system node, as metered at this

node, can be found by direct summation of the corresponding volume Information

In the base network. The total secondary outflow from a system node, as metered at this node, can be determined similarly, but transmission losses

need to be taken Into account because the volumes In the base network are defined as buyer-received volumes. Thus

71
QlN = I aeB(w)qa ,

QOUT = I aeF(w)qa/ra .

where

w = label in the base network of system node j

B(w) = set of secondary arcs terminating at node w in the base network

F(w) = set of secondary arcs originating at node w in the base network

q^ = base year volume for arc a in the base network

r^ = transmission loss factor for arc a in the base network.

During the above calculation it may happen that the secondary inflow at some system node exceeds or alimsst exceeds the total outflow from this node.

In this case, conservation of flow would force the primary inflow to be

negative or small compared to the secondary inflow or outflows. This may be

due to a data discrepancy, high imports, and so on. The model then

arbitrarily boosts the primary flow at this node to a node-specific minimum

acceptable flow. And we speak of a market adjustment . The MARKET model then

takes the necessary steps to preserve the conservation of flows throughout the

system network ( Note 32 ). These steps may include a boost in the distribution

loss rates (to not more than 10%) and, if this is not sufficient, an actual

increase in consumption at selected market nodes. The majority of

distribution loss factors will not be boosted in this fashion, and will remain

at the level that had been tentatively set before.

The system flows into D-nodes and into some P-nodes correspond to proper

(see Section 3.3.3) primary arcs in the base network, and values for flows on such arcs are input originally along with the base network. These values will

be superseded by the corresponding system flows calculated above.

4.1.2 Initial system price levels

With each system node, the model associates the "at cost" prices with

respect to sales to primary customers averaged over the current model year.

These annual price levels (PANNV) differ from the prices for the primary

supplies in that the former have been adjusted to reflect the costs of

secondary purchases and storage as well as the proceeds from secondary sales.

For system nodes other than the root node, the prices of the primary supplies

are calculated from the price level at the predecessor node using the

specified demand charges and commodity mark-ups. At the root node, the

pipegate price , that is, the average purchase price of dedicated reserves ?©»

plays the role of the price level at the predecessor node in the above

calculation.

72
The price levels will be first calculated without taking Into account

storage, which will be discussed in Section 4.1.3. For nodes i without

storage facilities, the price for primary supplies and the at-cost sales price

can be expressed £is follows:

Ui = Pj + Mi + Ci/Qi ,

Pi = Qi'Ui + CiN - CqUT/Q , Qi + QlN " QOUT

where

j = predecessor of system node i

Pjj = price level at system node h (h=i,j)

ui = unit price of primary supplies for system node i

Mi = commodity mark-up (per unit) on primary supplies

for system node i

Ci = annual demand charge on primary supplies for system node 1

Qi = quantity of primary supply for system node i

QlN ~ secondary supply metered at system node i

QoUT ~ secondary sales metered at system node 1

CiN = sales value of secondary supplies (CTPIV)

Cqut ~ sales value of secondary sales (CTPOV)

8 = secondary price mark-up factor (RSCT)

The parameter 9, say 1.25, represents the effect of add-on tariffs on secondary revenues: The difference between the term Cqut/® *"<^ Cqut ^s the

amount retained by the distributor (or pipeline company) 1 in order to cover expenses. Thus Cqut/® represents the portion of the revenues that is to be

rolled into the calculation of the price level. This is consistent with the

method for pricing the secondary sales (see Section 4.3) at a previous

modeling step.

In the first of the above two price relationships, the two tariff terms are understood to cover the entire cost of operation associated with this

transaction. This includes the value of the transmission/distribution loss.

For this reason, the transmission loss factor does not appear explicitly in

the price formula.

The second price formula is derived by equating two expressions for the

at-cost value of all primary sales from system node i:

73
Pi-(Qi + QiN - Qout) = Qi'^l + CiN - Cout/9 •

Using these price relationships on an annual basis during the base year

permits the propagation of price changes at the pipegate to price changes at

the burnertip in a deterministic fashion, provided system flows have been

specified for the system network. These flows are needed in order to

determine the influence of the (fixed) demand charges and of secondary

transactions on prices levels.

In the base year, the MARKET model determines a complete set of price

levels. There are two sets of data available, each of which can serve as a point of departure from which to calculate price levels. First, there are the

base year citygate sales prices associated with proper (see Section 3.3.3) arcs of the base network. These prices can be utilized to calculate the price

levels at D-nodes preceded by P-nodes. Second, the price of supplies at the

pipegate from dedicated reserves can be determined on the basis of the amount

withdrawn — identified in the model as the primary flow into the root

node - and the prices and take-or-pay ratios of the available reserves.

The first option is more attractive, because the citygate prices are given directly whereas the reserve price is deduced from reserve information

which unavoidably carries with it a large degree of uncertainty. On the other

hand, the price levels will be necessarily calculated from reserve prices in

all model years following the base year. Thus not using the analogous method

in the base year is likely to cause a discontinuity in price levels between

the first two years.

The MARKET first calculates price levels for D-nodes which are preceded

by P-nodes. It then calculates, using tariffs, a putative price level for the

preceding P-node. Because different D-nodes may have the same predecessor,

different price levels may be calculated for the same P-node. This difference

is due to the fact that both tariffs and price levels are annual averages and

coincide only under ideal conditions. In the absence of such conditions, we average over all price levels at the same P-node using the corresponding sales

volumes as weights. In this fashion, we find a particular price level at each

P-node which is succeeded by D-nodes. This procedure is based on inverting

the above price relationships. First the unit price of the primary supplies

for system node i is reconstructed:

"i = Pi«(Qi-QiN-QouT) - Gin + Cqut/Q . Qi

Then tariffs are subtracted from the unit price to yield a price level at the

predecessor node:

Pj = ui - Ml - Ci/Qi.

These candidate price levels are then averaged, using weights proportional to

the volumes, Qi/rj, where r^ = transmission loss factor for system node i, over all (direct) successors of the system node other than direct sales D74
nodes. At this point, the model uses the fact that each P-node has at least

one successor that is not a direct sales D-node (see Section 3.4.1). The

volumes Qi/r^ are primary sales metered at node j, that is, before having

Incurred transmission loss.

The same averaging procedure can now be used to determine price levels

for the remaining P-nodes including the root node. Note that, in this latter

case, we no longer average over numbers that by rights should be equal, but are in effect equalizing the supply prices of different pipeline companies in

the same system. This is necessary because in subsequent model years these

different pipeline companies will incur the same pipegate price.

The resulting pipegate price is now compared with the pipegate price as calculated from the dedicated reserves in order to apprise the analyst of

possible price discrepancies which indicate a need for upgrading his reserve information. The transmission tariffs in the pipeline system are then

adjusted so that calculating the pipegate price from the citygate prices using

the adjusted transmission tariffs would yield the same pipegate price as the one calculated from the reserves. Resulting adjustment factors are retained

and applied in subsequent model years. For details of the adjustment process

consult Note 33 .

The next step is to determine tariffs for direct sales D-nodes. The

predecessor of such a node is, by construction, a P-node, and we choose the

difference between the price level of the direct sales D-node and the price

level of its predecessor as commodity mark-up for the D-node in question. The

demand charge is set to be zero. Here we have used the fact that, by

definition, direct sales D-nodes do not conduct secondary transactions and

that therefore the unit price of primary supplies coincides with the price

level. All successor nodes of direct sales D-nodes are M-nodes. The tariffs

of these M-nodes are all set to zero.

It is now possible to calculate all price levels in the system network,

starting with the reserve price at the pipegate and proceeding to the

burnertip. This sets the stage for the next adjustment procedure. Here the

tariffs at M-nodes, excluding those arising from direct sales distributors are adjusted so that the state averages of the calculated burnertip prices

approximate given state averages by end-use sector. The adjustment factors so determined are kept for the remaining model years. After resetting burnertip

price levels to reflect this adustment, the construction of baseline price

levels is complete ( Note 34 )

.

4.1.3 Adjusting for storage costs .

In the previous section, formulas were derived for the recursive

calculation — both forward and backwards — of price levels at system nodes.

For simplicity of exposition, storage was assumed absent. In this section, we will now discuss a method for adjusting price level formulas in the case that

storage is present.

75
In MARKET, storage costs are represented as arising from storage losses on the one hand and storage tariffs on the other (see Section 3.8). For

semiannual price calculations, which are used in the case of semiannual

equilibration, the adjustment method is clear (see Section 4.2.3.2): in the summer phase, the price level at node i is determined as if there was no storage. Then the quantity QsTOR » which has been determined beforehand (see

Section 4.4), is set aside for storage and priced at the above price level.

In the winter phase, QsTOR is adjusted for storage losses and the storage cost

is increased by storage tariffs. The entire winter transaction is treated as an additional secondary inflow.

In the case of annual equilibration as well as in the base year, which is

modeled on an annual basis, the modeling of storage costs is not as clear-cut.

The method presently in MARKET represents the cost of the retrievable

gas in storage as follows:

'STOR = a Qj.uj + CiN - Cqut/Q

Qi + QlN - QOUT

QSTOR

Note that the fraction in parentheses represents the price level

that would have resulted in the absence of storage. This price le^^el,

however, is an annual average, whereas the gas in storage should be priced on

the basis of the Summer price level. The factor a is intended to adjust for

this price difference. The desired price level can now be calculated:

Pi Qj.ui + Cin - Cqut/Q - q«CsTOR

Qi + QlN - QoUT - (1 - 8i)*QsT0R

Where a denotes the storage tariff, and 8± the storage loss factor.

Altogether, we find:

Ui = Pj + Mi + Ci/Qi ,

RSTOR = QSTOR/(Qi + QlN - QoUT) ,

Pi = Qi.ui + CiN - Cqut/Q

Qi + QiN - Qqut

1 + q.g.RgTQR

1 - (l-Si)'RsTOR

where

j = predecessor of system node 1

Ph TM price level at system node h (h=i,j)

ui = unit price of primary supplies for system node i

Mi = commodity mark-up (per unit) on primary supplies

for system node 1

Ci = annual demand charge on primary supplies for system node 1

76
Qj^ = quantity of primary supply for system node i

QlN ~ secondary supply metered at system node i

QOUT ~ secondary sales metered at system node i

CiN = sales value of secondary supplies (CTPIV)

Cqut = sales value of secondary sales (CTPOV)

QSTOR = amount stored at system node i

^STOR = portion of available supplies stored at systems node i

Si = storage loss factor at system node i

a = storage tariff (percentage to be added on)

a = seasonal price level adjustment factor.

In Section 4.1.2, the converse formula expressing u^ in terms of P-j was needed. It may be left to the reader to do the same for the above

formula.

4.2 Equilibration

In this section, we outline the method for modeling the annual system

flows (QANNV) and price levels (PANNV) during the model years following the

base year. The method consists of equilibrating supply and demand for each

system separately.

The MARKET model gives the analyst a choice between an annual and a semiannual equilibration method. Once the choice is made for a particular run

of GAMS, then the equilibrations will be either all annual or all semiannual,

depending on this choice.

The main difference between annual and semiannual equilibration lies in

the mechanics of propagating prices forward and flows backward. In the case

of annual equilibration, the formulas used for this purpose are the ones described for the base year in Sections 4.1.1 and 4.1.2. In the case, of

semiannual equilibration, the same equilibration procedure is applied twice, once for the nonheating or summer season (April through September) and once for the heating or winter season (October through March). The results of both

equilibrations are then combined into annual figures. The formulas used for

price and flow propagations are similar to the ones described in Sections

4.1.1 and 4.1.2. However, secondary volumes and prices are assumed to be

equal in both seasons and are consequently halved ( Note 35 ). The annual fixed

tariff increments Ci (CFIXV) are also halved. Flows to and from storage are handled as additional secondary outflows and inflows, respectively. The

summer price determines the price of stored gas, which is stored in summer and

withdrawn in the winter. The price propagation formulas developed in Sections

4.1.2 are thus modified as described in Section 4.2.3.2.

77
A new concept, "committed flows", Is needed In the equilibration phase

(see Section 4.2.2). This is because secondary inflows and outflows are treated as fixed side conditions during the equilibration. Care mist

therefore be taken to assure coverage of the fixed demand due to specified

secondary outflows. The handling of committed flows in the annual and

semiannual equilibration modes differs again with respect to the secondary

inflows and outflows. In the case of semiannual equilibration, secondary

volumes and costs are halved with storage treated as a secondary outflow in

the summer and a secondary inflow, reduced by storage losses, in the winter.

In the case of annual equilibration, the secondary outflows are augumented by

the storage losses.

The equilibration is based on a procedure which determines for a given

price-quantity pair (PTST,QTST) whether the pipeline system in question can

absorb, at the pipegate, the quantity QTST at the pipegate price PTST. More

precisely, the question is whether there exists a — not necessarily unique —

pattern of balanced flows and price levels which arise from QTST and PTST at

the root node and terminate at the burnertlp with flows that may be consumed

at resulting prices according to the respective demand curves. If the answer

is "yes", then we call the price-quantity pair feasible .

4.2.1 Blpartitlon

The equilibration process now consists of two stages. In the first, the

objective is to find two points on the supply curve such that one is feasible

and the other, with a higher price, is not. To this end, the rightmost point on the supply curve, that is, the point of maximum supply, is examined for

feasibility. If this point is feasible, then it will represent the

equilibrium point. Typically this represents a shortage situation. If the

point of maximum supply is not feasible, then the interval between the

committed amount at the pipegate and the maximum supply is divided into a specified number (NINC) of parts, currently ten, and the resulting grid points

are examined for feasibility. If some of them are feasible, then the

rightmost feasible point, and its Infeaslble neighbor to the right, bracket

the equilibrium point.

During the second stage of the equilibration, the break point between

feasibility and inf easiblllty, that is, between excess of demand and excess of

supply, is determined by consecutive blpartitlon between the above bracketing

points. This breakpoint represents an equilibrium with neither excess nor shortage of demand. The blpartitlon process stops after a fixed, currently

number of steps, say ten, or after quantities agree within a specified

tolerance, whichever happens first. If none of the above grid points is

feasible, then the model declares a failure of the equilibration process.

Failure of equilibration for a single pipeline system stops the execution of

the model ( Note 36 ).

The concept of equilibration by a search for bracketing points to be

followed by a blpartitlon procedure has been discussed in Section 3.9.1. The

difference between the method discussed there and the approach taken here is

that here the feasibility check replaces the comparison of the supply and

demand curve values.

78
4.2.2 Committed flows

As was mentioned before, secondary transactions must be honored first.

So each pipeline system must make sure that It withdraws enough gas to cover

Its secondary outflow commitments. The primary flow will therefore consist of

two components, a free flow (QITRV) and a committed flow (QCFLV), with the

latter determined first and the former subsequently by equilibration. Since

there are no secondary transactions at M-nodes, all flow Into such nodes Is

free.

In computing the committed flow (QCFLV) at each nonmarket system

node, we balance Incoming secondary flows against outgoing ones wherever

possible.

In the case of annual equilibration, we use the formula:

G. = max{0,j; Gi/ri + Qqut " QlN + QsTOR'^^'^i)) •

•^ leS(j) -J In the case, of semiannual equilibration the following two equations are used

according to season:

In the summer:

G. = max{0, I ^ Gi/ri + QOUT - QlN + QstOR) •

•^ leS(j) 2 2

J4 = max{0, y G±/Ti + QOUT - QlN - Si-QcTOR) •

In the winter:

G.

Here

G|j = committed flow Into system node h (h=l,j)

rj^ = transmission loss factor for system node 1

Sj = storage loss factor for system node j

QSTOR ~ amount stored at system node j

QlN " total secondary Inflow metered at system node j

QOUT ~ total secondary outflow metered at system node j

S(j) = set of (direct) successors of system node j.

In the formulas pertaining to semiannual equilibration, Qqut ^^^ QlN ^^®

halved because they represent seasonal Inflow and outflow.

If the total available supply at the plpegate does not suffice to cover

the committed flow, then the execution of the model stops because of

Insufficient supplies .

79
We now introduce the quantity G^^, por annual equilibration, we put

Gin = L ,,.v Gi/ri + QouT + QSTOR'd-Si)

For semiannual equilibration, there are two seasonally different definitions.

In the summer Gin = L^^,. Gi/ri + QoUT + QsTOR .

In the winter:

Gin = I , Gi/n + Qout . ieS(j) 2

This quantity represents the total commitments which have to be covered at

node j. There are now two cases. If annually

Gin < QlN

or semiannually

Gin < M . Gin < M + s.-Qstor

2 2

in the summer and the winter, respectively, then the total secondary inflow

covers all committments at system node j. In this case, none of the primary

flow into this node needs to be set aside for secondary committments and

Gj = 0. However, the portion Gjf,} of total secondary inflow must then be

earmarked as committed, and only the remaining secondary inflow can contribute

to the free flow in the system network. If the total secondary inflow does

not cover the committment Gin, then all of this inflow will be earmarked as committed, and the uncovered portion Gj of the committment has to be passed

back to the predecessor of node j. Similarly to the primary flow, the

secondary flow into node j is thus split into a noncommitted secondary inflow

QlN and the committed secondary inflow (QCOMV).

4.2.3 Feasibility check

The feasibility check would be quite straightforward if fixed charges and

secondary inflows and outflows were absent. In such a case, the unit price at

the burnertip would depend only on the unit price at the pipegate and not on the system flow. All that would have to be done, therefore, is translate the

pipegate price PTST into burnertip prices at the M-nodes by adding commodity

mark-ups, consult the corresponding demand curves on how much gas would be

consumed at each M-node for these burnertip prices and collect the resulting

flows back at the pipegate. If the result exceeded QTST, then the pair (PTST,

QTST) would be feasible.

80
Unfortunately, the feasibility check turns out to be considerably more

complicated in the presence of fixed charges or secondary transactions. In

this case, the system flow must be modeled concurrently with the price levels,

because fixed charges must be spread over, and because secondary transactions

need to be rolled in with, the system flow In order to account for their

effect on unit prices. This calls for an iterative procedure: establish a tentative flow pattern which adds up to QTST at the pipegate; then translate

the given pipegate price PTST into burnertip prices based on the tentative

flow pattern; and repeat these two procedures.

More precisely, we proceed as follows: we initiate all price levels in

the system network at zero. At each M-node, we find the amount consumed at zero prices by evaluating the corresponding demand curve at zero and then

mutiplying the indicated annual demand by either the heating factor or its

complement to 1.0, depending on the season. We propagate the resulting flows

backwards to the pipegate taking into account secondary transactions and

transmission losses.

We then normalize this flow, decreasing or increasing its free portion so that the flow equals QTST at the pipegate and is balanced at intermediate

system nodes. This is achieved by multiplying the free flow at each system

node by a node specific flow normalization factor (RRHOV). These factors are uniquely determined and their calculation is discussed in Section A. 2. 3.1

below. The flow normalization procedure has the following outcomes:

Case I: The generated flow at the pipegate has to be decreased to equal

QTST. This indicates a tentative excess of demand at price PTST. It will be

shown in Section 4.2.3.1 that, in this case, the flow normalization factors at

each system node are less than 1.0. The tentative excess of demand thus

spreads to every D-node in the pipeline system. As the flow into the M-nodes,

we do not choose the normalized values, but rather make the reduced amount of

flow which enters the corresponding D-node available preferentially to

residential customers, then to commercial customers, nonswitching utilities,

nonswitching industrials, switching utilities, and switching industrials in

that order ( Note 37 ). Thus the last end-use subsector in the above order is

the first to be tentatively curtailed. (Here, and in the paragraph below, we use the term "tentative" to indicate that these model results are not final

because the equilibration has not yet been completed.)

Case II: The generated flow at the pipegate has to be increased to equal

QTST. This indicates a tentative excess of supply at price PTST. In this case (see Section 4.2.3.1) the flow normalization factors at each system node

are greater than 1.0. The tentative excess of supply thus spreads to every

D-node in the pipeline system. Again we do not choose the normalized flow as flow into the M-nodes, but rather pick for each distributor the "last" end-use

subsector, that is, the one most likely to be curtailed, to absorb all the

tentative excess flow that enters the distributor node.

Case III: The generated flow has exactly the value QTST at the pipegate.

In this case, all flow normalization factors equal 1.0, and the normalized

flow is identical to the generated flow.

81
Once a balanced flow with strength QTST is available, the price PTST is

carried forward through the system network from the root to the M-nodes,

establishing price levels along the way. Tariffs and secondary transactions

are taken into account essentially as described in Section 4.1.2. At each

M-node, the given demand curve and heating factor yield the consumption

according to the season. These volumes consumed then serve as the starting

point for a repeat of the flow generation and normalization procedures

described above. The price PTST is then carried forward with respect to the

latest normalized flow, and so on. Convergence is declared if the latest

normalized flow differs from the previous one by, say, less than 1000 BBtu at

each system node. It is expected that convergence is bound to occur, but this

has not been formally proved.

After the above iteration has converged, then the price-quantity pair

(PTST, QTST) is considered feasible if and only if the flow normalization

factors have all converged to values less or equal than 1.0 (Cases I and III).

If the price-quantity pair (PTST, QTST) has been shown feasible by the above

process, then a feasible flow has been actually exhibited. If there is a "final" excess of demand, that is, if the feasibility check indicates that the

total available supply and its corresponding average price are a feasible pair

and that more would have been purchased if it were available, then the

indicated curtailment procedure also becomes final. It is conjectured that if

the feasibility check fails, that is, if the above process converges to a flow

whose normalization factors are greater than 1.0, then there does not exist a feasible flow. Again there is no formal proof.

In what follows, we describe the formal relationships which underly the

above operations.

4.2.3.1 Flow generation and normalization

During flow generation, prior to normalization, the free flow satisfies

at each system node j the law of conservation,

where

F^ = free flow into system node h (h=i,j)

r± = transmission loss factor for system node i

QlN ~ seasonal uncommitted secondary inflow at node j

S(j) = set of (direct) successors of system node j .

The volume Qin is found by subtracting the committed portion from the sum of

seasonal secondary inflow and depending on the season withdrawals from storage

(see Section 4.2.2). The above equation is used for generating the free flow

in the system from burnertip consumption.

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The flow normalization factors at system nodes are defined recursively.

Denote by p^ the flow normalization factor needed to normalize the free

portion of the primary flow into the root node. It has to satisfy the

relation.

Po-^l + Gi = QTST

where Fj and Gi are the free and the committed flows, respectively, into the

root node ( = system node number 1). It follows that

Po = QTST - Gi .

Suppose system node k is the predecessor of system node j with the added

convention that is the predecessor of 1. Because flow conservation has to

hold also after normalization, the flow normalization factors pk and pj at

nodes k and j, respectively, must satisfy the relation

Pk -^ -^ ieS(j)

Therefore, and in view of the flow conservation property prior to

normalization,

Pk'Fj + QlN

Pj = •

Fj +

Qjjj

This defines pj recursively for all system nodes j and implies that

Pj < 1.0 if Po < 1.0 ,

pj > 1.0 if Po > 1.0 ,

Pj = 1.0 if Po = 1.0 .

The behavior of the flow normalization factors is thus entirely characterized

by the relation of the initial flow normalization factor Po to 1.0.

The reader is warned, however, that due to the occurence of negative

flows and their subsequent correction, conservation of flow may be violated at some system nodes. We will discuss details concerning negative flows in

Section 4.2.4.

4.2.3.2 Determining price levels

It remains to elaborate the price propagation from the root node to the

M-nodes. We will discuss only the semiannual case, since for annual

equilibration the formulas are the same as in Section 4.1.2 and 4.1.3 In

analogy to these Sections, the following equations are used:

83
u^ = Pj + Mi + I'Ci/Qi . 2

In the summer: Pi = Ql«ui + Cin/2 - CouT/2e

Qi + Qin/2 - Qout/2

In the winter:

Pi = Qi-"i + CIN/2 + (1+J).CST0R - Cout/29 . Qi + QIN/2 + Si-QsTOR - QOUT/2

Here

j = predecessor of system node i

P^ = price level at system node h (h=i,j)

"i = unit price of primary supplies for system node i

Mi = commodity mark-up on primary supplies for system node i

Ci = annual demand charge on primary supplies for system node i

Qi = quantity of primary supply for system node i

Si = storage loss factor at system node i

QlN = secondary supply metered at system node i

QoUT ~ secondary sales metered at system node i

QSTOR ~ amount stored at system node i

CxN = sales value of secondary supplies

CquT ~ sales value of secondary sales

CSTOR ~ value of quantity stored

J = storage tariff (percentage to be added on)

9 = secondary price mark-up factor.

Starting with PTST as the predecessor price level for the root node, the price

levels at all system nodes can be calculated recursively.

4.2.4 Negative flows and negative prices

In the course of generating flows by backward propagation from the

burnertip, enforcing conservation of flow may require that some system flows

turn out negative. This will happen if burnertip demand falls to such a low

level that the pipeline system is unable to absorb some of the predetermined

secondary inflows. In addition to low consumption, the secondary inflow may

have increased suddenly on the basis of pronounced price differences between

pipeline systems during the previous year (see Section 4.3). In such cases, we arbitrarily adjust the flow to a positive level.

84
In a general way, the occurrence of negative flows can be considered an indicator of overly high prices for a particular pipeline system and can serve

as a valid warning signal that the market is out of order. However, certain

system nodes are particularly vulnerable and tend to produce negative flows in

situations where drastic actions are not called for (see Section 6.4). This

difficulty is ameliorated but not fully corrected by the market adjustments

made in the base year. For this reason, the model tolerates —and resets to a small positive quantity—negative flows below a specified tolerance limit. If

the size of the negative flow exceeds this limit, then the price-quantity pair

(PTST,QTST) will fail the feasibility test. Persistent excessive negative

flows may cause failure of the equilibration, and thereby terminate model

execution, by negating feasibility for all test points in the first stage of

the equilibration. The tolerance limit for negative flows is subject to

adjustment from model run to model run depending on the data used and the

requirements of the analysis ( Note 38 )

.

Setting a negative flow arbitrarily to a positive level during flow

generation is to violate the principle of flow conservation. In what follows,

we examine some of the consequences of this violation.

Let D > be the quantity added to the primary flow at system node j in

order to make it positive. Then the conservation of flow equation can be made

valid by including this quantity D into it (compare Section 4.2.3.1):

Fj + QlN = IieS(j)Fi/ri + D,

where

F^^ = free flow into system node h (h=i,j)

ri = transmission loss factor for system node i

QlN ~ seasonal uncommitted secondary inflow at node j

S(j) = set of (direct) successors of system node j .

Because we want to preserve the property that after each iteration step

of the feasibility checking process the flow normalization factors for a pipeline system are either all greater, all less, or all equal to 1.0, we retain the recursion formula for the flow normalization factor p j

,

Pk'Fj + QiN ,

Fj + QlN

even though the assumptions which led to this formula are no longer valid.

As a consequence, the normalized flow will also violate the flow conservation

principle at system node j:

Pk-Fj + QiN = Pj*(Fj + Qin)

= Pj-dF^/ri + D)

= Pj-lFi/n + Pj-D

85
The term p,.D indicates the amount by which the normalized flow violates the

law of conservation. In the case that system node j is a D-node, the excess quantity will be automatically allocated to the succeeding M-node of lowest

service priority (see Case II in Section 4.2.3), thereby restoring the balance

of flows. If the system node j is, however, a P-node then the gap in flow

conservation remains. It is very unlikely that such a gap should be present

in the final solution to the equilibration problem. In model runs with the

current network there were no negative flows into P-nodes, mainly because

imports were the only secondary inflows into P-nodes. However, should a small

gap remain, then it could be explained on the basis of temporary storage, spot

sales, compression equipment failure, etc.

A similar anomaly is the occurrence of negative price levels . Here the

predetermined revenue from secondary outflow may exceed the expenses so that a "profit" is made, which should be passed on to succeeding system nodes. In

this case, however, the model does not take action other than printing a warning message and resetting the price level to a positive default value, say

$1. Negative prices are a symptom of overly cheap system supplies and are likely to occur mainly during the demand projection process described in

Section 4.5.

4.2.5 Post-equilibration wrap-up

In the case of semiannual equilibration, the semiannual volumes and

prices must be combined into annual volumes (QANNV) and prices (PAMMV).

Reporting purposes aside, the latter are needed to estimate secondary

transactions for the subsequent model year, to update customer counts, to

update primary flows in the base network, to withdraw from reserves and so on.

The system flows are, of course, just added up for each individual arc:

annual flow = summer flow + winter flow.

The price levels are averaged using the seasonal primary flows as weights:

annual price = summer price summer flow + winter price winter flow. summer flow + winter flow

This procedure represents an approximation in the presence of secondary

transactions ( Note 39 ). The procedure is, however, correct at M-nodes, for

which the annual prices are to be reported.

The next step is to update the primary flows in the base network. These

flows can be transferred directly from the respective system networks to the

corresponding arcs in the base network. In addition, the unit prices for

these annual flows have to be reconstituted from the annual price levels.

These unit prices will be used for estimating secondary flows (see Section

4.3):

ui = Pj + Mi - Ci/Qi

where

86
j = predecessor of system node 1

\x± = annual unit price of primary flow into system node i

P^ = annual price level at system node j

M^ = commodity mark-up at system node i

C^ = demand charge at system node i

Q^ = annual primary flow into system node i .

This formula works only if system node i is not the root node.

After equilibration, the MARKET model reestimates the customer count

(ZCUSV) at each M-node. Let

Z^ = this year's number of customers at M-node i

W^ = last year's number of customers at M-node i

X = the State associated with M-node i

?jj = the rate of projected population growth for the year

Q^ = this year's consumption at M-node i

L^ = last year's consumption at M-node i .

If there was no increase in consumption at M-node i, that is, if

Qi < Li»

then there will be no change in the number of customers. Also, the model will

not change the number of utilities customers under any circumstances. In all

other cases, let

Ai = W^ • (Qi/Li)

Yi = min {?x*Wi, 1.2*Ai} •

In terms of these quantities, we define

Zi =

(Y^ + Aj)/2 for residential and commercial markets — ^*^i •

^i "^ A^)/3 for industrial markets.

These formulas have been chosen arbitrarily to yield a compromise between

growth expected on the basis of population projections and growth on the basis

of increased consumption volume ( Note 40 ).

87
4.3 Updating secondary prices and volumes

In this section, the modeling of secondary transactions including the

loading and withdrawal from storage will be discussed. While an important

part of the MARKET model, secondary transactions will not affect the results

of the model as strongly as the primary transactions. Secondary transactions

are therefore modeled in a more approximate way than primary transactions.

Contrary to their name, secondary transactions have to be known first, that

is, before the primary transactions can be calculated, and they provide

boundary conditions for these calculations. As soon as the primary

transactions have been modeled, they enter into the estimation of secondary

transactions for the next model year.

Secondary prices and volumes are associated with arcs in the base

network. For the base year, their values have been input and have been taken

into account while constructing a baseline of system flows and price levels

for the base year.

After the construction of the above baseline, the model proceeds to

estimate secondary prices for the next model year. In order to calculate

such a price, it first determines the current average price of supplies at the

origin node of the secondary arc in question. This price differs from the

system price level at this node in that it does not involve the revenues from

secondary sales. It does, however, include the prices of secondary supplies

at their current level.

The supply price is updated according to the formulas,

PSUP = (Qi'^i + CiN)/(Qi + QIN)

Pa = k-(e-Psup/ra + Pa)/2

Where

a = secondary are in question

r^ = transmission loss on are a

Pa = present price on are a

i = system node at which are a originates

Qj^ = primary inflow into system node i

ui = unit price of primary supplies for system node: (from

equilibration)

QlN ~ sales value of secondary supplies

PsUP ~ average price of supplies to system node i

k = secondary price escalation factor

9 = secondary price mark-up factor (RSCT).

88
The quantity Pg^p represents an estimate of the average price of just the supplies. It differs from the price level (PANNV) in that it does not take into

account revenues from secondary sales. The prices of secondary sales should

then be arrived at by adding a mark-up to the supply price PsUP ^^^ taking

transmission losses into account. Of course, a secondary sales price has

already been established prior to the equilibration and, ideally, this price

should be reproduced by the price which is derived from Pgyp*

However, the two prices will in general not coincide. For this reason, the

Market model chooses their average as an upgraded estimate for the secondary

sales price in the current model year. In order to estimate the secondary

sales-price for the upcoming model year, the upgraded estimate for the current

year is multiplied by the secondary price escalation factor k , which so far has always been chosen as l.l ( Note 41 ).

For the year immediately following the base year, the volume on secondary

arcs is left unchanged from that in the base year. After that year, however,

the volume on the secondary arcs is adjusted so as to maintain equal cost

shares . By this we mean that the respective sales values, that is, the the

amount of money spent for each primary or secondary supply should remain at

the same percentage of the total. It is, of course, not possible to maintain

equal cost shares in the strict sense, since the primary flow varies while

secondary flows are kept fixed. With this understanding we proceed as follows. All secondary sales values are multiplied by the ratio of the

primary sales value of the present year to that of the previous year. Since

secondary sales prices are already estimated, secondary volumes can be

determined by a simple division. Various measures are taken to prevent sudden

large changes in the secondary volumes. Such may occur if negative primary

flows below the tolerance level were encountered during the previous model

year ( Note 42 ). Aside from that, the cost shares of secondary suppliers tend

to remain at the same proportions.

Outer arcs, that is, secondary arcs representing imports and Alaskan

supplies , are excluded from the above updating procedure. Their quantities

and prices are specified each year according to exogenous quantity-price

tracks.

In what follows, "present" means "at the end of an annual equilibration"

when primary information for the model year is complete. Also available are the most recent transaction volumes and prices for annual primary flows (see

Section 4.2.3). For updating secondary volumes with equal market shares in

mind, we use the formula

% = Pa . Qb'Pb . Q a . a e A(w),

Pa * ^b*Pb

where

w = node in the base network

A(w) = set of secondary non-outer arcs into w

89
b = predecessor arc of w (= primary arc)

Qa = present flow on arc a

Pa = present price on arc a

Qa = subsequent flow on arc a (to be determined)

Pa = subsequent price on arc a (already known)

Qb = previous year's primary flow on arc b (saved)

Pb = previous year's primary unit price on arc b (saved)

Qb = present year's primary flow on arc b

Pb = present year's primary unit price on arc b .

4.4 Estimation of storage requirements

We now describe the method used in MARKET for determining a storage

requirement at each individual node of a system network. The understanding is

that if this requirement can be satisfied using the storage capacity given for

this node, then the indicated quantity will be stored during the summer equilibration. If the storage requirement cannot be satisfied at this node,

then the satisfied portion will be added to the storage requirement at the

predecessor node, and so on. To initiate this process, the storage

requirements at M-nodes need to be specified. These are the quantities T±

necessary to equalize summer and winter deliveries, and are thus given by

Ti = (Hi - l/2)-Qi

where

H^ = heating factor at M-node i

Qi = previous year's annual flow into M-node i.

These storage requirements (QSDFV local) may be negative, if summer consumption exceeds winter consumption, for instance, at some M-nodes in the

utilities sector. The following equations permit these storage requirements

to be passed on to preceding system nodes:

Tj = max{0, I ^,. Ji/ri -

•^ QcaP> ieS(j)

where

j = predecessor of system node i

Tjj = storage requirement at system node h (h=i,j)

r^ = transmission loss factor at system node i

90
Qp.p = storage capacity at system node j

QSTOR ~ volume to be stored at system node j

S(j) = set of (direct) successors of system node j .

If T^ = 0, that is, if all storage requirements can be satisfied at system

node j , then

QSTOR " I ^, . Ji^^i ieS(j)

and there may be unused storage capacity. If Tj > 0, that is, if there is no storage available at system node j or if the storage capacity is insufficient,

then

QsTOR " QCAP •

In networks, storage capacity is input at zero for all system nodes other than

those P-nodes which represent actual pipeline companies. In other words, Mnodes, D-nodes, and those P-nodes which were inserted as root nodes for a rooted cluster of pipeline companies, all have zero storage capacity (see

Section 3.8).

4.5 Demand projection

Consider a given model year, called the present year. Model years after

the present year are referred to as future years or projection years . After

the main modeling task has been completed for the present year, that is, after

the annual flows and prices have been determined, the second kind of

interaction with BID is initiated. This interaction calls for the generation

of a demand projection table with a table grid consisting of pipegate prices

and future years. Each column in this grid is a price track for future years

following the just completed one up to the horizon year or a specied number of

look-ahead years whichever limits the number of years first.

For each of these price tracks, an abbreviated annual modeling procedure

is carried out, where each year's modeling builds on the results of the

previous year. Secondary information including imports is kept unchanged

during this procedure. Tariffs also remain constant except for the optional

escalation discussed in Section 3.7.

Demand projection relies mainly on a seasonal flow maximization method,

which determines the maximum seasonal absorption at specified pipegate prices

^or a particular pipeline system. This method differs from that used for

equilibration mainly in that it skips the flow normalization step. The

tentative flow first generated is again the one resulting from zero burnertip

prices. The pipegate price PTST is then carried forward from the pipegate to

the burnertip on the basis of this tentative flow. The next flow is based on the consumption generated by the new burnertip prices. This flow then

underlies the next price calculation, and so on, until flow and price levels

have converged.

91
In this fashion, flows are generated for the two seasons and are then

combined into an estimate of how much gas from its dedicated reserves the

pipeline system in question will be able to absorb at the specified pipegate

price during the specified year. This value is entered into the demand

projection table.

The demand projection process is speculative and appears to be slightly

biased toward overstating absorption capabilities. In fact, it models the

process of speculation by pipeline companies as to their future sales

potential. Keeping the secondary information unchanged affects the various

pipeline systems differently. Pipeline systems with dominant secondary

outflow will appear to have a captured market and show very little price

elasticity ( Note 43 ). Since secondary inflows will maintain the same price in

constant dollars, and since gas prices tend to rise faster than inflation,

secondary inflows will tend to reduce supply prices for primary customers and

will cause demand to rise in addition to reducing demand elasticity to prices

at the pipegate.

4.6 Diagram of the MARKET model

In what follows, we list the major steps of MARKET to illustrate the

"flow" of its operations. The list cannot be completely specific and the

reader is asked to consult the preceding sections as well as the data chapter

for details. Also the diagram does not document a specific version, but

rather a distillation from all versions which have been used at various times.

"Loops" in the model, that is, sequences of operations which are repeatedly

executed are indented and bracketed by the lines s "FOR EACH..." and "END OF

LOOP".

4.6.1 Input phase

1.1 Enter census projections, price indexes, alternate fuel prices,

transmission rate schemes, distance data.

1.2 Enter number of systems, base network (from GENNET): connectivities,

quantities, prices, transmission losses, storage capacities, storage

losses. States.

1.3 Calculate from distance data those transmission losses which are not

entered.

1.4 Enter import and LNG price-volume tracks for specified outer arcs;

process Alaska data if present.

1.5 Enter demand curve specifications.

1.6 Enter base year burnertip prices averaged by State and end-use sector.

1.7 Enter system networks (from GENNET): connectivities, consumption,

heating factors, loadf actors; transfer certain base network

information to system networks; benchmark burnertip volumes if

necessary.

92
1.8 Fetch calendar parameters from GAMS driver: base year, last year of

modeling, horizon year.

4.6.2 Base year modeling

2.1 Fetch reserve blocks from BID.

2.2 Imports, LNG, Alaska: set outer arc values exogenously.

FOR EACH system:

2.3 Aggregate secondary Inflows and outflows, and their sales costs for

each system node.

END OF LOOP

FOR EACH system:

2.4 Calculate available production for each reserve block; report total

available production and reserves to BID.

2.5 Determine storage need at each system node.

2.6 Establish system flows and estimate distribution losses; make

market adjustments if necessary.

2.7 Allocate pipegate flows to reserve blocks and withdraw indicated

amounts; report to BID; determine pipegate price.

2.8 Collect numbers of customers per distributor; estimate flows for

year prior to base year.

2.9 Estimate expected flows, transmission load factors and demand

charges.

2.10 Model distributor tariffs.

2.11 Calculate pipegate price from citygate prices; reconcile with

previous pipegate price by tariff adjustment.

2.12 Price levels for entire system; set tariffs for direct-sales

distributors; enter this system's contribution to state volumes and

state sales costs by end-use sector into the ledgers of the

respective States.

END OF LOOP

2.13 Total volumes and sales costs by end-use sectors and States;

calculate average unit prices.

93
FOR EACH system:

2.14 Control calculated state average prices against those input;

calibrate distribution tariffs accordingly; reset burnertip

prices.

2.15 Initiate reference volumes and prices for demand curves.

END OF LOOP

FOR EACH system:

2.16 Accumulate state data by end-use sector.

END OF LOOP

2.17 Total state data by end-use sector and calculate average unit

price.

4.6.3 Post base year modeling

3.1 Fetch reserve blocks from BID.

3.2 Imports, LNG, Alaska: set outer arcs exogenously.

FOR EACH system:

3.3 Aggregate secondary inflows and outflows and their sales costs for

each system node.

END OF LOOP

FOR EACH system:

3.4 Calculate available production for each reserve block; report total

available production and reserves to BID.

3.5 Determine storage needs at each system node.

3.6 Estimate expected flows, transmission load factors and demand

changes

3.7 Model distribution tariffs.

3.8 Update reference volumes and prices for demand curves; determine

cut-off prices.

3.9 Equilibrate (annual equilibration option)

3.9.1 Determine committed supply QCFL and committed flows

IF maximal supply QMAX does not cover committed supply QCFL:

94
3.9.2 Terminate: "INSUFFICIENT SUPPLIES TO COVER COMMITMENT"

3.9.3 Determine supply price PMAX from supply curve

IF (QMAX,PMAX) is feasible:

3.9.4 Equilibrium at maximum supply QMAX

ELSE

FOR EACH I=1,...,NINC WHILE (QTST,PTST) not feasible:

3.9.5 QTST = QMAX-I*(QMAX-QCFL)/NINC

3.9.6 Determine supply price PTST from supply curve

IF (QTST, PTST) is feasible:

3.9.7 Bipartition between feasible and infeasible volumes

to find equilibration value QEQU.

IF no feasible (QTST, PTST) is found:

3.9.8 Terminate: "FAILURE OF EQUILIBRATION"

3.10 Reestimate customer counts.

3.11 Allocate pipegate flows to reserve blocks and withdraw indicated

amounts; report to BID; determine pipegate price.

3.12 Transfer primary flows to base network; calculate annual unit

prices for primary transactions from annual price levels; for each

system node, estimate secondary prices for base network arcs originating at this node.

3.13 Enter this system's contribution to state volumes and states sales

costs by end-use sectors into the ledgers of the respective States.

END OF LOOP

3.14 Estimate secondary volumes for all base network arcs.

3.15 Total state volumes and sales costs by end-use sector and States;

calculate average unit price.

95
4.6.4 Set up demand projection table

(requested by BID program)

FOR EACH price track:

FOR EACH look-ahead year:

4.1 Update reference volumes and prices for demand curves; determine

cut-off prices.

4.2 Escalate tariff adjustment factor

4.3 Estimate expected flows, transmissions load factors and demand

charges;

4.4 Maximize flows for specified pipegate price; combine flows.

4.3 Enter value into demand projection table

END OF LOOP

END OF LOOP

END OF LOOP

4.6.5 Project system demand

(query by BID)

3.1 Take row in demand projection table for specified year; interpolate

projected demand at specified price and year from demands at

bracketing grid prices.

96
CHAPTER 5

Network Representation of the Natural Gas Supply System.

This chapter describes GENNET, an automated procedure for generating a network representation of the domestic natural gas transmission and

distribution system. GENNET consists of two distinct phases. The first phase

is concerned with constructing the network, i.e., identifying pipeline and

distribution conq)anies to be represented in the network and determining the

quantities involved in the commercial transactions among the companies. The

second phase processes data on base year prices, storage capacities,

transmission and storage loss rates, and consumption patterns and associates

the processed data values with appropriate entities in the network. The

output from GENNET consists of three data files, two of which are major input

data sources for MARKET. The third output file provides information which can

be used to identify by name the pipelines and distributors represented in the

network.

In the network representation of the natural gas transmission and

distribution system, nodes represent pipeline companies or distribution

companies. Arcs represent commercial relationships, i.e. an arc connects two

nodes if gas can be sold by one node to the other node. The direction of the arc corresponds to the direction of the sale. Note that the arcs do not

necessarily correspond to any physical connection of nodes by actual

transmission/distribution lines (see Section 3.3).

The major source of information used in the first phase of GENNET to

create the gas market network is the Form EIA-50, "Alternative Fuel Demand Due

to Natural Gas Curtailment". The form was designed to collect the data

necessary to support the DOE responsibility for equitable allocation of oil

and petroleum products among all regions of the U.S., all sectors of the

petroleum industry, and all users. The Form EIA-50 is completed by all

interstate and intrastate pipeline companies, municipalities, and other

suppliers of natural gas to end users. Although GENNET does not use the

curtailment data, it does make direct or indirect use of the following Form

EIA-50 information:

• source of gas supplies;

• volume of gas purchased from each source; • nature of supplies (interstate, intrastate, imports, or direct sales

by producers);

• total volume of gas delivered annually to end-use customers and number

of customers by category (residential, commercial, industrial,

electric utility, and other).

5.1 Phase I; Network Generation .

This section describes the procedure used to generate the nodes and arcs

of the network representation of the natural gas transmission and distribution

system. The GENNET user must specify a list of pipeline companies to be

represented explicitly in the model. These pipeline companies are specified

by the 5-digit identification number used in the Form EIA-50 reporting system.

The user also specifies aggregate pipeline companies, which are called

intrastate pipeline companies in this report. They represent supplies to

97
distributors from intrastate sources as well as from pipeline companies, which

are not specifically listed as interstate companies. For the purposes of the

model, such "intrastate" pipeline companies are characterized by groups of

states which are assumed to be "somewhat homogeneous" with respect to the

transmission and distribution of natural gas. (The role of these aggregate

pipeline companies will be further clarified.) One network node, a P-node, is

generated for each specified pipeline company.

After specifying the pipeline companies of the model, the GENNET user identifies groups of the previously defined pipeline companies which act as a single unit with respect to bidding for available reserves. Each such group

forms the basis upon which GENNET constructs pipeline systems . Each pipeline

system consists of one or more pipeline companies, all distributors for which

the pipeline companies are the biggest (in terms of quantity) supplier, and

all end use markets served by those pipeline companies and distributors. (The

construction of pipeline systems will be explained in further detail.) The

concept of pipeline systems was introduced in MARKET to capture some of the

interdependencies among certain pipeline companies, e.g. Florida Gas and

Southern Natural or Texas Eastern and Algonquin, and at the same time to

reduce the computational requirements of MARKET which uses GENNET output. It

is recommended that future analysis examine model sensitivity to pipeline

system specification.

In addition to combining pipeline companies into pipeline systems, GENNET

permits the user to consider several Form EIA-50 respondents as a single

pipeline company, i.e. a single network P-node may represent more then one Form EIA-50 respondent. This feature was originally included in GENNET so that pipeline companies which appear in the Form EIA-50 data with more than

one respondent ID number, either by design or by error, will not be

represented by a separate network P-node for each different ID. Note, however

that the feature can also be used intentionally to combine two different real

pipeline companies and represent them as a single network P-node. Such

combination might be desirable in the case of pipeline companies with

sufficiently small sales volumes that could lead to potential anomolies in

MARKET or elsewhere in GAMS if they are represented as separate P-nodes.

Experience with GENNET and MARKET will provide the best indication of the need

for combination nodes. Analyst judgment will be necessary to determine which

nodes are appropriate for combination. Note that P-nodes of this type are not

the same as the P-nodes representing "aggregate pipeline companies", i.e.

groups of states acting as a pipeline company. Furthermore the user is

reminded that all other data prepared for use by MARKET or the other models in

GAMS should reflect the multiple companies represented by such P-nodes.

For each pipeline system containing more than one pipeline company, a pseudo pipeline node (with no correspondence to any Form EIA-50 respondent) is

created by GENNET to serve as the root node for the system. These root nodes

are also P-nodes and GENNET creates the arcs needed to connect these root

nodes to each of the pipeline company P-nodes in the system. If there is only

one pipeline company in a pipeline system, then the node corresponding to that

pipeline serves as the root node for the system. All of the P-nodes

corresponding to real or pseudo pipelines are designated as "PIPE" nodes.

Table 5.1 lists the pipeline companies now modeled by GENNET and indicates the

grouping of those pipeline companies into pipeline systems. Note that

Midwestern gas and Great Lakes gas are treated as a single pipeline company.

98
Table 5.1 lists the states included in each of the seven aggregate pipelines.

This selection of pipeline companies was approved by DOE/EIA and was input to

GENNET for producing the network to which the October 1982 version of MARKET

was applied. These specifications can be changed by the model user, provided

of course that corresponding changes are made as appropriate in other data

used throughout MARKET and the rest of GAMS.

Given a list of real and aggregate pipeline companies to be included in

the model, GENNET places each of the corresponding P-nodes on a node list and

then begins to read the Form EIA-50 Supply File to identify other nodes to be

added to the network. In the Supply File, every respondent (pipeline or distributor) identifies each source of supply by 5-digit ID number and

quantity in Mcf . For each respondent (not already represented as a P-node), a D-node node is generated and added to the node list if one or more of its

supply sources is on the node list. At present, two complete passes are made

through the Supply File creating and adding D-nodes according to the specified

rule. Thus a respondent whose supplier is in the node list will be recorded

in the node list during one pass, thereby becoming a potential supplier in the

subsequent pass for some other previously unlisted respondent. Note that this

procedure does not pick up every respondent and that inclusion of respondents

on the node list may be dependent upon the order in which they appear in the

Supply File. Some of the omitted respondents would be picked up if additional

passes were made through the Supply File ( Note 44 ) but most are omitted

because they buy from a few small suppliers (perhaps producers) or intrastate

pipelines which were not explicitly included by the user as P-nodes in the

model. Those respondents which are not picked up during the first two passes

through the Form EIA-50 Supply File are not explicitly represented in the

model. Purchases and sales for these respondents are aggregated and

associated with aggregate distributor D-nodes, at most one of which is created

per state as the need is detected by GENNET.

Respondents with relatively small sales volumes (typical of those not

explicitly represented in the network) cause considerable computational

difficulties in MARKET when gas costs rise, sales volumes drop below a theoretical "critical mass", and prices skyrocket toward unreasonable values.

The level of effort required to specify and model the detection of and

response to such phenomena is unwarrented at this stage of the MARKET model

development. In fact, rather than improvising ways to include more respondents in the network, subsequent versions of GENNET (not described

herein) have been implemented and successfully interfaced with MARKET to

produce network representations with even fewer respondents explicitly

modeled, i.e., more of the small companies are included in the aggregate

D-nodes

.

99
Table 5.1. Pipeline Systems Modeled in GENNET

System 1 ; El Paso Natural Gas Company

System 2 ; Columbia Gas Transmission Corporation

System 3 ; Tennessee Gas Pipeline Company

Tennessee Natural Gas Lines Inc.

Alabama Tennessee Natural Gas Company

East Tennessee Natural Gas Company

System 4 ; Texas Eastern Transmission Corporation

Algonquin Gas Transmission Company

Consolidated Gas Supply Corporation

System 5 ; Natural Gas Pipeline Company of America

System 6 ; United Gas Pipeline Company

Mississippi River Transmission Corporation

Texas Gas Transmission Corporation

System 7 ; Transcontinental Gas Pipeline Corporation

System 8 ; Transwestern Pipeline Company

Cities Service Gas Company

Arkansas Louisiana Gas Company

System 9 ; Florida Gas Transmission Company

Southern Natural Gas Company

System 10 ; Michigan Wisconsin Pipeline Company

Midwestern Gas Transmission Inc. /Great Lakes Gas Transmission Company

Intrastate Midwest

System 11 ; Northwest Pipeline Corporation

Colorado Interstate

Mountain Fuel Supply Company

Kansas Nebraska Natural Gas Company

Montana Dakota Utilities

Intrastate Mountain

100
System 12 ; Panhandle Eastern Pipeline Company

Trunkline Gas Company

Northern Natural Gas Company

System 13 ; National Fuel Gas Supply Corporation

Intrastate Appalachla

System 14 ; Pacific Gas Transmission Company

Intrastate Far West

System 15 ; Intrastate Texas -New Mexico

System 16 ; Intrastate Oklahoma-Kansas

System 17 ; Intrastate Louisiana-Arkansas

101
Figure A-2. States Included In "Intrastate" Pipelines

Intrastate Appalachia ; Connecticut

District of Columbia

Delaware

Florida

Georgia

Kentucky

Massachusetts

Maryland

Maine

North Carolina

New Hampshire

New Jersey

New York

Ohio

Pennsylvania

Rhode Island

South Carolina

Tennessee

Virginia

Vermont

West Virginia

Intrastate Far West ; Arizona

California

Idaho

Nevada

Oregon

Washington

Intrastate Texas-New Mexico ; Texas New Mexico

Intrastate Oklahoma-Kansas ; Iowa Missouri

Kansas Nebraska

Oklahoma

Intrastate Louisiana-Arkansas ; Alabama Louisiana

Arkansas

Mississippi

Intrastate Midwest : Illinois

Indiana

Michigan

Minnesota

Wisconsin

Intrastate Mountain ; Colorado

Montana

North Dakota

South Dakota

Utah

Wyoming

102
After making two passes through the Supply File and adding appropriate

D-nodes to the node list, GENNET makes a third pass to create the arcs of the

network. Typically each respondent reports several supply sources. The arc generation procedure depends on whether or not there are nodes corresponding

to the respondent and one or more sources on the node list. If there are nodes corresponding to both the respondent and the source on the node list, an arc Is created with origin at the source node and destination at the

respondent node. If the respondent node is on the list and the source node is

not, than an arc is created with origin labeled zero and destination equal to

the respondent node. When the state location of the respondent's end use

sales is later Identified, the origin of this arc will become the generic

aggregate P-node which serves that state. If the respondent is not on the

list, then all supplies to that respondent are aggregated and associated with

an arc from the appropriate aggregate P-node origin to an aggregate D-node in

the state Indicated by the leading two digits of the 5-diglt ID of the

respondent

.

The only exception to the arc generation rules described above occur in

the case of a respondent represented as a P-node, i.e. a pipeline company

explicitly modeled as such in the network. In the present version of GENNET,

all supplies reported by respondents represented by P-nodes are Ignored, i.e.

No arcs are created to model the situation in which a pipeline company

represented as a P-node buys gas from some other company represented either

explicitly or in the aggregate. To be compatible with the other GAMS modules,

pipeline companies represented by P-nodes are shown in the network as receiving all supplies via reserves available through the Gas Reserve Supply

Table (GRST) or through the purchase of imports and/or Alaskan gas. Gas

purchases by such companies cure Incorporated in GAMS via modifications to the

GRST or appropriate loading of arcs representing Imports or gas from the

Alaskan pipeline.

Two additional types of arcs created during the arc generation process

are outer arcs and Alaskan arcs. Outer arcs are used to represent supplies of

imported or synthetic gas; Alaskan arcs represent gas purchased from the

Alaskan gas pipeline. There is one outer arc for every P-node, but Alaskan

arcs are created only for specific P-nodes designated by GENNET user input.

The origins of both Alaskan arcs and outer arcs are labeled zero. The

destination of these arcs is always a P-node. Neither supply quantities nor prices are associated with these arcs by GENNET. GENNET does however produce

a directory to identify these arcs by arc number so that a GAMS /MARKET user

can specify price and quantity values for these arcs as appropriate for the

scenario being modeled.

After the Supply File is read, GENNET reads the Form EIA-50 End Use Sales

File to establish markets for each D-node in the network. Every Form EIA-50

respondent reports the following information for each state in which there were end use sales: total volume and average number of customers by customer

category, i.e. Residential, Commercial, Industrial, Utility, and Other. The

sales reported as "Utility" refer to electric utilities that burn gas, those

reported as "Other" Include sales to public facilities, e.g. schools and

hospitals. As each End Use Sales record is read, GENNET Immediately makes the

following data transformation:

103
(1) In the states of Maine, Connecticut, New Hampshire, and Vermont,

all utility sales are aggregated with commercial sales and the

utility market is then set to zero. These states have local

legislation to phase out the burning of gas by electric utilities*

Thus utility sales, if any are reported, are assumed to have been

commercial sales which were erroneously labeled.

(ii) All "Other" sales are aggregated with commercial sales and the

"Other" sales are not distinguished subsequently.

(iii) The Industrial and Utility sales reported on the Form EIA-50 are each split into two markets, one of which has the capability of

switching to alternate fuels. The heuristic used to split the

markets evolved from a combination of informal conversations with

representatives of several distribution companies and execution of

MARKET to establish reasonable lower limits on market sizes.

Details of the splitting procedure are presented later; it is a prime target for future study.

The data transformations described above lead to a maximum of six

non-zero markets per state for each respondent: Residential, Commercial,

Utility, Industrial, Utilities with alternate fuel capability, and Industrial

with alternate fuel capability. Subsequent use of GENNET output by MARKET

assumes that the end-use markets have priority in the order listed above, with

residential customers the last to be curtailed during supply shortages.

Each end use market is explicitly associated with the one D-node from

which the gas is purchased. Direct sales by a pipeline company to end users

are treated in the model by creation of a pseudo D-node and an arc connecting

it to the P-node corresponding to the pipeline company. The end use markets

are then associated with the pseudo D-node and the quantity associated with

the arc from the P-node to the pseudo D-node is set equal to the total end use

sales by the pipeline company to end users.

When a Form EIA-50 respondent reports end use sales in more than one state, additional D-nodes are created so that the respondent is represented by

a different D-node for each state in which the sales are reported. Since

supplies purchased by the respondent are not reported by state, the

respondent's total supplies are allocated proportionally to the end use sales

by state.

If end use sales are reported by a respondent for whom there is not a corresponding node on the node list, those markets are associated with the

generic D-node in the state in which they occur. This might be one of the

generic D-nodes created to accommodate supplies reported by a respondent not on the node list. Or, if no generic D-node exists for that state, one is

created at this point and it is connected to the network by an arc from the

appropriate aggregate P-node.

The Form EIA-50 End Use Sales File is also used to establish the state

location of each D-node in accordance with the states in which the companies

report end use sales. These state designations help determine appropriate

tariff and distance data by contributing to the specification of pipeline

104
"utility". GENNET assigns a utility number to each network arc with a P-node

origin and a D-node destination. This utility assignment depends on the

company represented by the P-node and the state associated with the D-node.

Because MARKET uses the utility number to determine which transmission

distance and tariff data apply to each arc originating at a P-node, the

utility definitions must be consistent with the data discussed in section

5.1.6 of this report. Recall from that earlier discussion that the first 56

utilities correspond to the 56 jurisdictions described in section 5.1.1. Thus an arc originating at a P-node representing an aggregate pipeline company will

be assigned a utility number between 1 and 56 inclusive corresponding to the

state associated with the destination node. The other utility numbers, 57 and

higher, are defined by the GENNET user. There should be one such utility for

each rate zone of every pipeline company selected by the user to be

represented explicitly in the network. The GENNET user supplies for each

selected pipeline company the utility numbers and lists of states covered by

the utilities. Then, for each arc originating at a P-node representing a real

pipeline company (as opposed to a root node or a P-node representing an aggregate pipeline company), GENNET assigns the utility number corresponding

to that pipeline company selling gas in the state associated with the

destination node. Although the numbers defined for the utilities by the

GENNET user are somewhat arbitrary, they must be integers greater than 56. It

is recommended that they run consecutively beginning at 57 and that all

utilities for a particular P-node be numbered consecutively.

The network associated with the natural gas market is quite complex;

cycles are common, e.g. company A may sell to company B who sells to company C

who sells to company A. To simplify the situation and render the model more computationally tractable, the concept of primary arcs is introduced. The

primary arc associated with D-node j is that arc, of all arcs with destination

j, with the largest 1980 supply. For a P-node in a multi-pipeline system, the

single arc connecting the P-node to the system root node is the primary arc. Except in the case of ties (where an aribtrary choice could, if necessary, be

made from among the candidate arcs), there is thus a unique primary arc for

every non root node. Furthermore the primary arcs can then be used to

decompose the network into the systems specified by the user. For each

pipeline system, starting at the root node and working in the forward

direction through the network, any node beyond the root node can be associated

with the same system as that of the origin of its primary arc. All arcs in

the network which are not primary arcs are then referred to as secondary arcs. Note that the outer arcs and Alaskan arcs are defined to be secondary arcs at

the P-nodes. Subsequent use of GENNET output assumes that secondary arcs are representative of "take-or-pay" market relationships between the origin node

(seller) and destination node (buyer).

At this point it is convenient to tighten the definitions of "network"

and "pipeline system". Specifically the term "Base Network" will refer to all

P-nodes and D-nodes and all primary and secondary arcs representing

transactions among these nodes. Each "pipeline system" is an augmented subset

of the Base Network consisting of the P-nodes corresponding to the userspecified grouping of pipeline companies for the system, a root P-node for

multi-pipeline company systems, any D-node such that the origin node of its

primary supply arc is in the system, and all primary arcs connecting these

nodes. To complete the definition of a pipeline system, these nodes and arcs

105
are augmented by all market nodes associated with the D-nodes in the system.

Secondary arcs are in the Base Network, but no secondary arcs are in any

pipeline system. Every node and every primary arc in the Base Network is in

exactly one pipeline system.

The Network generation procedure is illustrated in Figures 5.3 through

5.7 and the various steps are described below.

Step 1 ; Initialize the node list. The user specifies the pipeline

companies of the network model and the grouping of these companies into

pipeline systems. Interstate pipeline companies are specified by a 5-digit ID

number used in the Form EIA-50. Aggregate pipeline companies are described by

the two-letter state abbreviations for the states to be served. Note that

every state should be served by exactly one of these aggregate pipeline

companies. A P-node is created for every interstate and aggregate pipeline

company specified. For every multi-pipeline company system a root P-node is

generated and primary arcs are created to connect such nodes to the other

P-nodes in the system. These P-nodes are the initial nodes on the node list.

Figure 5.3 illustrates this step with five pipeline companies and three

systems. The letter "P" designates interstate pipeline companies, "A"

designates aggregate or generic intrastate pipeline companies, and "R"

designates root nodes.

Step 2 ; Augment the node list. The Form EIA-50 Supply File is scanned

(presently twice) and a D-node is created and added to the node list for every

respondent who purchases supplies from a source represented by another node

already on the node list. This step is illustrated in Figure 5.4 where the

letter "D" represent the D-nodes added in this step.

Step 3 : Create arcs and generic state distributors. In this step the

Form EIA-50 Supply File is again scanned. This time if there is a D-node on the node list corresponding to a respondent, arcs are created to connect that

D-node with the nodes corresponding to the supply sources. If there is a supply source not on the node list, an arc is created to the D-node from the

P-node serving the state in which the respondent conducts business. If the

respondent is not on the list then supplies to that respondent are associated

with an arc from an appropriate P-node to a D-node representing a generic

state distributor in the state where the respondent conducts business. In

Figure 5.5 which illustrates this step, the generic state distributors are D-nodes represented by the letter G.

Step 4 : Identify Primary Arcs. Consider all arcs with destination at a particular node. Except for ties which can be resolved arbitrarily, one of

those arcs corresponds to the biggest supplies purchased by the company

represented by the node. That arc becomes the primary arc of the node. All

of the other arcs are secondary arcs. If cycles occur in the arcs of the

network they are effectively eliminated by flow reduction techniques which

might alter the identification of primary arcs. The resulting primary arcs then decompose the network into the systems specified by the user. This is

accomplished by associating a node with the same system as the origin node of

its primary arc. In Figure 5.6, the heavy lines represent primary arcs.

106
"PIPE" Nodes

P. = interstate pipeline

3

A. = aggregate pipeline

R. = dummy root node for

*' multi-pipeline systems

Figure 5.3. Step 1: Initialize the Node List

107
'D 'D

'D

'D 6i

"DIST" Nodes

D = node corresponding to a

^ Form EIA-50 respondent

vho purchases supplies from

a PIPE node or another DIST

node.

Figure 5.4. Step 2: Augument the Node List

108
©-

y^ -©

^^^^q\ more "pi ST" Nodes

G. = generic state ^—w ^—^ distributors; at most one ^A2^~~~~ ~^\G2) P^^ state created to

v->^^ V--^ represent aggregation of all

**»^ Form EIA-50 respondent not

"^^^/^^^ explicitly modeled.

Figure 5.5 Step 3: Create Arcs and Generic State Distributors

109
Primary Arcs

Arcs associated with largest

supplies purchased by a DIST

node plus arcs from system root

nodes to PIPE nodes in that

system.

Figure 5.6. Step 4: Designate Primary Arcs

110
More "PI ST" Nodes

D^ is D. with end-use sales

in another state. Dg is P^

v;ith end-use sales.

Figure 5.7. Step 5: Create Markets and Outer Arcs

111
Step 5 ; Create Markets and Outer Arcs. The Form EIA-50 End Use Sales

file is processed to determine the markets associated with each D-node . The

transformations for converting from Form EIA-50 customer categories to GENNET

markets is described later in this appendix. Since markets require different

data from the other network nodes, market nodes and arcs leading to them are

not treated by GENNET as a part of the Base Network. Their inclusion in the

network shown in Figure 5.7 is, however, conceptually accurate. Note that Dy

and Dg are new D-nodes created in this step. Dy is created because the Form

EIA-50 End Use Sales file indicates that the respondent associated with node

Dl has end use sales in more then one state. There will be one D-node for

each state in which a respondent has end use sales. D-node Dg is created

because the respondent associated with P-node P3 has end use sales. Because

MARKET does not permit end use sales by P-nodes, a psuedo D-node (Dg in the

example), is created to accommodate these sales. Finally, note the secondary

arcs coming into each P-node. These are "Outer Arcs" designed to represent

imports, synthetic fuel, etc. There is one "outer arc" for each P-node. In

addition, the GENNET user specifies which, if any, P-nodes have access to

Alaskan gas. These P-nodes have an extra secondary arc coming into them. One

of the GENNET outputs is a directory which gives the arc numbers of the outer

arcs and Alaskan arcs for the P-nodes. MARKET users refer to this directory

when "loading" these arcs with projected price and quantity estimates.

Before describing the second phase of GENNET, this section of the

appendix concludes with a discussion of the heuristic used to establish the

sizes of the Industrial and Utility Markets with alternate fuel capabilities,

i.e., gas consumers capable of switching to another fuel source. As described

earlier, GENNET transforms the Industrial and Utility markets reported on the

Form EIA-50 into two markets each, one of which has the capability of

switching to alternate fuels. Conversations with several pipeline company

representatives indicated that as a general rule -of -thumb, approximately 15

percent of the industrial sales and 50 percent of the utility sales are subject to immediate loss if consumers with dual-fuel capability find an alternate fuel more desirable.

Early versions of GENNET used the rule-of -thumb verbatim, i.e. if Vj and

Vu are the volumes reported on Form EIA-50 for Industrial and Utility markets

respectively, then .15 Vj and .50 Vu were base year quantities for the

corresponding switching markets for GENNET. The remaining volumes, .85 Vi and

.50 Vu, became the base year quantities for the non-switching counterparts.

The same transformations were used with the number of customers. Subsequent

use of GENNET output encountered difficulties as a result of very small

switching markets which occurred in some instances. Accordingly the following

procedure was devised to eliminate very small markets and to insure reasonable

average consumption levels.

Let Vmin equal some minimum volume level which is

acceptable for a switching market. (Presently Vmin = 10000 Mcf .)

Then if Vj < Vniin> the entire industrial volume Vj is added to the

commercial market and no industrial market is created for that

respondent. If, .15Vi < Vmin, then no industrial switching market

is created; all of the industrial market is assumed to lack dualfuel capability. Otherwise, the transformation was as before for

volume, but the number of customers in the switching market was calculated differently.

112
If Cj is the number of industrial customers reported by a Form

EIA-50, the number of industrial customers with dual fuel capability

is calculated as the minimum of .15Cx and •ISVi/Vmin* This

calculation ensures an average consumption of at least V^^n for each

customer in the switching market. Note that the number of customers

is always rounded to the closest integer and there must be at least one customer if the volume is positive.

The calculations for the utility market are identical to those for

the industrial market except that the switching factor is .5 instead

of .15.

The switching factors (.15 and .50) and the minimum acceptable volume

(10000 Mcf.) are all parameters of the GENNET model. Their values can be

changed by the user. In fact, it is highly recommended that they be carefully

considered for reasonability, and that the sensitivity of model results to

these parameters be thoroughly investigated. After the network was "finalized" for a first run of the base case, switching factors for the

industrial markets became available on a DOE demand region bases. Because

these factors would generate a new network, it was decided to postpone their

Inclusion in GENNET until after a reasonable base case had been modeled

successfully.

5.2 Phase II: Processing Additional Data .

This section describes the operation in GENNET associated with processing

data on prices, storage capacities, transmission and storage losses, and

consumption patterns.

There are several types of price data processed by GENNET. For sales by a P-node representing an interstate pipeline company to another company

represented by a D-node, prices are taken directly from the average annual

prices reported in the Form FERC-2 by the pipelines for each recipient of

"Sales for Resale". In those instances where Form EIA-50 reports a transaction which is not reported in Form 2, the weighted average price of

sales by the pipeline is used.

For sales by a P-node representing an interstate pipeline company to a pseudo D-node created to accommodate direct sales by that pipeline, the base

year price is taken from the Form 2 as the average annual price reported by

state for "Field and Main Line Industrial Sales." The appropriateness of the use of this price depends entirely on subsequent use of GENNET output. It is

noted here that Form 2 also includes prices for "Distribution Type Sales" by

the reporting pipeline. These prices are further subdivided by "Residential",

"Commercial", and "Industrial". At present, GENNET and MARKET do not use these prices from Distribution Type Sales. Although their use would require

keypunching and analysis, future versions of the model should consider the

Impact of this more detailed information on direct sale prices.

Prices on sales from P-nodes representing aggregate pipeline companies to

D-nodes are the "Resale Prices" reported in the 1980 Gas Facts [1]. According

to a Gas Facts footnote, these state average prices are representative of

113
city-gate prices. The reported prices are used directly for D-nodes in any of

the following states: Alabama, Arkansas, California, Kansas, Louisiana,

Mississippi, New Mexico, Ohio, Oklahoma, Texas, West Virginia, and Wyoming.

These twelve states all have substantial intrastate gas sales which would be

reflected in the reported prices and would account for many of the

transactions represented in the network by sales from P-nodes representing

aggregate pipelines. For all other states, the average of these twelve prices

is used for sales from P-nodes representing aggregate pipelines to D-nodes in

those states.

The only remaining resale prices are those for sales from one D-node to

another D-node. No source for price data on these transactions has yet been

identified. The following procedure is used in GENNET to calculate prices for

these sales. The network nodes are first ordered in such a way that if node A

precedes node B, then the longest path (i.e. most number of arcs) from a root

node to node A is less than the longest path from a root node to node B.

Proceeding through the network ordered in this way, the prices on all sales by

D-node A can be calculated as the weighted average of the prices paid for

supplies by D-node A increased by some markup. The markup currently used in

GENNET is 10 percent.

Another important data item provided through GENNET is storage capacity.

GENNET was designed to accept input specifying non-zero storage capacities

available at P-nodes or D-nodes identified by their 5-digit Form EIA-50 ID

number. GENNET then determines the network node corresponding to each 5-digit

ID and associates the storage capacities with those nodes.

Initial attempts to obtain storage capacity data were complicated by

unsubstantiated data sources with incomplete and often conflicting values. As

a result of these complications, the following procedure was used to obtain

usable values for storage capacities. A complete run of GENNET and a base-year-only run of MARKET was made with all storage capacities set equal to zero. MARKET calculates the storage requirement at each market as one half of

the difference between summer and winter consumption. These needs are then

aggregated back (from destination to origin) along the primary arcs of the

Base Network to determine total storage needs at each P-node (excluding

P-nodes which are pseudo root nodes). GENNET is then rerun using these

calculated storage needs as the capacities available at the P-nodes and zero

storage capacities at all other nodes. If this procedure for obtaining

storage values had been anticipated at model Inception, all storage

calculations would have been handled in MARKET without the need for

intervention via GENNET.

Data describing consumption patterns are input to GENNET for each Form

EIA-50 respondent with end-use sales. For each respondent, identified by its

5-digit Form EIA-50 identification number, this data set includes a "heating

factor" and a "monthly load factor" for each Form EIA-50 customer category

(Residential, Commercial and and other. Industrial and Utility) in each state

in which the respondent reports end-use sales. GENNET simply identifies the

network D-node corresponding to the respondent in the appropriate state and

then associates the factors with the corresponding market nodes.

114
The consumption pattern data which are input to GENNET were generated by

Science Management Corporation (SMC) under contract to EIA/DOE. Using the

Form EIA-50 monthly end-use sales data for the period April 1980 through March

1981, SMC calculated a heating factor and a monthly load factor for each of

the four Form EIA-50 customer categories in each state served by every Form

EIA-50 respondent. At the present time, Industrial and Utility markets with

alternate fuel capabilities are assigned the same heating and load factors as their non-switching counter parts. Thus the four categories processed by SMC are used to establish values for six categories in GENNET. Roughly speaking,

the heating factor is the ratio of winter consumption to total annual

consumption. The heating factor is defined as end use sales to a customer

category from October through March divided by total annual end use sales

(April through March) to that customer category. MARKET uses the heating

factors to differentiate between summer and winter demand. The monthly load

factor is defined as the peak monthly sales to a customer category divided by

the average monthly sales to the customer category. MARKET uses daily load

factors. The transformation from monthly load factors to daily load factors

in performed in MARKET

.

There are two remaining data items which GENNET prepares for use by

MARKET. These are storage loss factors for each node with non-zero storage

capacity, and transmission loss factors for each arc between two nodes,

neither of which is a market node or a pseudo node, i.e. a pseudo P-node or a pseudo d-node. Sources of information regarding precise values for these data

items have not been identified. At present GENNET parameters set the value of

storage loss factors to .02 and transmission loss factors to .04. MARKET uses the storage loss factor in such a way that all quantities of gas stored

experience a one-time 2 percent storage loss. This corresponds to the loss

incurred during the process of retrieving gas from storage. Each time that a quantity of gas "flows" from an origin node to a destination node, the

quantity leaving the origin node is reduced by 4 percent before it it received

at the destination node. MARKET has the capability of ignoring some of these

factors and substituting calculated loss factors based on transmission

distance.

5.3 GENNET Output .

The output from GENNET consists of three data files, two of which are major input files for MARKET. The GENNET output file which is not used by

MARKET is a dictionary relating Form EIA-50 identification numbers and network

nodes. There is a DOE Form EIA-50 data file which contains names, addresses,

telephone numbers, a personal contact, and the 5-digit identification number

for each Form EIA-50 respondent. The dictionary can be used in conjunction

with this Form EIA-50 name and address file to identify the individual

pipeline and distribution companies represented by each node in the network.

The ability to determine the respondent represented by particular network

nodes has proven useful when unusual data values are observed and it becomes

desirable to determine the source and possible explanation for the values.

The network nodes are not otherwise identified by company in any of the GAMS

or MARKET output in an attempt to preserve anonymity.

115
The two GENNET output files used by MARKET contain data describing the

Base Network and each of the individual pipeline systems. Much of the data in

these files is concerned with a computationally convenient method for

describing the nodes and arcs of the network. The GENNET/MARKET user is

unlikely to be concerned with these data; further details will be presented in

the computer program documentation. For the sake of completeness, all output

data items are listed below, but only those marked with an asterisk (*) are

likely to be of interest to readers of this document.

The Base Network data file hereafter referred to as NETWORK, contains

information about all of the PIPE and DIST nodes and all of the primary and

secondary arcs connecting PIPE and DIST nodes. This file does not contain any

data relating to market nodes or arcs connecting market nodes to DIST

nodes. The following data are contained in the NETWORK file for each PIPE and

DIST node in the Base Network:

• a number corresponding to the state in which the company represented

by the node does business;

• the type of node, i.e. "PIPE" or "DIST" for P-nodes ^nd D-nodes

respectively;

• the arc number of the first arc in the forward star' of the node;

• the arc number of the first arc in the backward star^^ of the node;

• the number of arcs in the backward star of the node;

• the arc number of the primary arc supplying the node;

• the storage capacity available at the node;

• the storage loss rate at the node, zero if storage capacity is zero

for the node.

The following conventions were used in developing the structural

description of the Base Network: (i) the ordering or numbering of arcs is

arbitrary provided that all arcs with the same destination are numbered

sequentially; and (ii) since arcs with the same origin are not sequentially

numbered, each arc should indicate the next arc with the same origin. With

these conventions in mind, the reader is advised that the following data are contained in the NETWORK file for each arc joining two nodes in the

^The forward star of a node is the set of all arcs with origin at the node.

There is no special significance to the ordering of arcs within the forward

star so that the designation of first arc is arbitrary.

^^the backward star of a node is the set of all arcs with destination at the

node.

116
Base Network:

• the node number of the origin of the arc;

9 the node number of the destination of the arc;

• the next arc in the forward star of the origin of this arc;

• the quantity of gas sold by the company represented by the origin node

to the company represented by the destination node; units are Mcf

;

• the average price of the gas sold by the company represented by the

origin node to the company represented by the destination node; units

are hundredths of a cent per Mcf.;

• a "utility" number indicating the pipeline rate zone under which

tariffs are determined for arcs from P-nodes to D-nodes; for arcs from

P-nodes to pseudo D-nodes this value is -1; for all other arcs the

value of this number is zero.

• the transmission loss rate for the arc.

At the end of the NETWORK file there is some additional information which

is not used directly by MARKET. It is furnished for reference by the MARKET

user who may wish to prepare input data files for MARKET to represent

transactions involving imports or Alaskan gas. Recall that one Outer Arc,

with origin labeled zero, is created for each P-node in the Base Network.

Such arcs can be used in MARKET to represent imports or synthetic gas

supplies. An Alaskan arc, also with origin zero is created only for those

P-nodes specified by the GENNET user as having access to Alaskan gas. The

following information is available at the end of the NETWORK file for each

P-node

:

• node number;

• pipeline system of the node,

• the arc number of the Outer Arc for the node;

• the arc number of the Alaskan arc for the node; zero indicates there

is no Alaskan arc for the node.

The second output file created by GENNET for use by MARKET contains data

describing the pipeline systems. This file, referred to as the THREAD file,

contains the following information for each pipeline system:

o pipeline system number;

• number of nodes (including all P-nodes, D-nodes, and market

nodes) in the system.

117
For each node In the system, the following information Is provided:

118
• network node number, e.g. the first node in the system might be

network node number 9; this Is blank for market nodes.

• node type, I.e. "PIPE", "DIST" or "MART"

f the system node number of the origin of the primary arc Into the node;

• the number of primary arcs for which the node Is an origin; this is zero for all market nodes;

• the system node number of the first node connected to this node by a primary arc originating at this node; this is zero for all market

nodes

;

• the type of market node, i.e."RSDL", "CMCL", "UTIL", "INDL", "UTSW", or "INSW" to designate residential, commercial, utility, Industrial,

utility with alternate fuel capability, or industrial with alternate

fuel capability respectively; this is blank for all P-nodes and Dnodes;

• the quantity of gas consumed at a market node; units are Mcf .; this is

blank or all P-nodes and D-nodes;

• the number of customers at each market node; this is blank for all

P-nodes and D-nodes;

• the heating factor at each market node; this is blank for all P-nodes

D-nodes;

• the monthly load factor for each market; this is blank for all P-nodes

and D-nodes.

119
NOTES

Not e 1 ^ Model years (p. 30)

A recent modi J 1 cat ion and extension of its input data has enabled GAMS to

handle model years 1980-1995 with year 2000 as horizon.

Note 2 Absence of absorbable quantity (p. 32)

The model may determine that there is no absorbable quantity at all at a given price in a price track. This happens whenever secondary supplies cannot

be accomodated, leading to persistent negative flows (see Section 4.2.4).

Otherwise, there will always be a positive absorbable quantity because the

model maintains a very small positive flow in excess of 1.0 BBtu.

If zero absorbable quantity is found for one of the track prices, then zero absorbable quantity is immediately assigned to all subsequent prices in

the same track. Absence of an absorbable quantity for the first year in the

cheapest price track is considered a model error and terminates the model

run.

Note_ 3 Demand projection table look-up (p. 32)

Currently the interpolation is linear, and default conventions are as follows: for query prices that are smaller than the smallest grid price for

the future year in question, the absorbable quantity is considered equal to

that of the smallest grid price; for query prices that are bigger than the

biggest grid price, the absorbable quantity is considered zero. Exponential

interpolation and using a declining exponential default for large prices would

be preferable. By exponential interpolation, we mean linear interpolation

between logarithms of the table quantities to find the logarithm of the

absorbable quantity.

No te 4_ Different configurations for pipeline systems (p. 35)

The MARKET model has the flexibility to accept representations of

pipeline systems that differ from the rooted pipeline clusters described in

Section 3.3.1. For instance, several P-nodes connected "in series" may be

used to represent the various rate zones of a pipeline company and also to

mimic its physical layout to some extent.

Note 5 GENNET and Form EIA-50 (p. 36)

Form EIA-50 provides volume data for input into GENNET. Although GENNET

is essentially a generic network generator, a considerable amount of its

structure is specifically geared towards Form EIA-50, so that a change-over to

another form of volume input, say, to Form EIA-176, would require some reprogramming. Because it is based on calendar years rather than heating

years, the Form EIA-176 would be more consistent with other inputs to GENNET,

although it is by no means clear whether it can fully replace Form EIA-50 for

the purposes of MARKET. A benchmarking capability has been included into

MARKET to provide compatibility with Form EIA-176 data ( Note 11 ).

120
Note 6 Alaskan gas (p. 37)

For the handling of Alaskan gas, MARKET provides the option of specifying

general cost and volume figures and of identifying participating pipeline

companies on a percentage basis. The price and volume tracks for corresponding outer arcs will then be created automatically.

Note 7 Estimation of pipeline fuel (pp. 37, 38)

The input of transmission losses due to fueling pipeline compressors

between pipe-gate and city-gate is in conjunction with the input of the base

network. The input is arc specfic and is in terms of the relative loss, e.g.,

•04 means a loss of 4%. A loss specification of 1.0 or more is considered as

a flag which triggers calculation of the transmission loss for a particular

arc from a mileage estimate on the basis of .0008% per mile.

In all networks used so far, a uniform loss of 4% per arc has been

specified (transmission loss factor = .96). No transmission losses have been

calculated from mileage.

Note 8 Secondary transactions (p. 39)

Although the MARKET model will accept secondary arcs between P-nodes in

the base network, the networks that have been created using GENNEJT do not

include such secondary arcs. The reason is that Form EIA-50 contains

information on supplies from one pipeline company to another only if the

latter sells to end-users. Because of this incomplete reporting requirement,

it was decided, for the first production versions of MARKET, to leave P-P arcs

out of the network altogether (with the exception of the improper arcs which

connect pipelines to their roots within a rooted cluster (see Section 3.3.1))

rather than "manually" supplementing the network. An estimate of deliveries

between pipeline companies for the base year 1980 was found in Form FERC-15.

This information was used to shift corresponding shares of reserves from one pipeline system to another by adjusting the GRST-table (see Note 15 ). In

later versions, the Form FERC-15 data were used to introduce P-P secondary

arcs. However, these arcs were not introduced explicitly into the base

network, but rather a coding change in MARKET was made by EIA in order to

accomodate them as virtual arcs. Currently, the volumes and prices on these

secondary transactions are kept fixed for all model years.

One reason for using virtual P-P arcs, as opposed to including actual

arcs in the base network, was the fact that GENNBI searches for and eliminates

feed-back cycles in the base-network (see Chapter 5). These feed-back cycles

represent supplies which are passed on in a circular fashion until they are returned to one of the original suppliers. The pattern of P-P arcs as derived

from Form FERC-15 contains such feed-back cycles, the removal of which was considered undesirable by EIA.

The 15% estimate of secondary flow includes only secondary flows between

different pipeline systems. However, secondary arcs between nodes of the same pipeline system are accepted by MARKET and do occur in networks generated by

GENNET. The 15% estimate of secondary flow also does not include arcs of the

P-P variety.

121
Note 9 Subdivision of end-use sectors (p. 39)

The actual determination of base year volumes at M-nodes which belong to

subdivisions of the industrial or utilities sectors, respectively, is part of

the network generation process. For the pertinent assumptions in GENNET , the

reader is referred to Chapter 5.

New kinds of demand curves, such as recently introduced ones for

utilities, tend to obliterate the distinction between switching and

nonswitching subsectors. On the other hand, important specific uses of gas,

such as refinery fuel, are suggesting different additional subdivisions. It

should be understood, that MARKET is not conceptually tied to any particular

pattern of subdivisions.

Note 10 Use of back-up storage (p. 40)

A vast amount of information is associated with each pipeline system. To

keep all this information simultaneously in memory would increase the memory

space occupied by the program and thereby slow down model execution. For this

reason, pipeline system information is kept in back-up memory and only the

information pertaining to a single pipeline system is kept in core memory at

any given time.

Note II Benchmarking (p. 40, Notes 5, 29)

The definition of end-use categories in EIA data collection efforts is

not uniform. Commercial and industrial use, for instance, are defined

differently for Forms EIA-50 and EIA-176. Furthermore, the time frames

differ: Form EIA-50 reports on a heating year (April-March) basis, whereas

Form EIA-176 reports on a calendar basis. The reporting basis of EIA-176 is

preferable since it also forms the basis of NGA compilations. In addition,

the price data, which are extracted from the Forms FERC-2 filed by the

individual interstate pipelines, are for calendar years. For these reasons,

the burnertip volumes in the network data are "benchmarked", that is, scaled

by state and end-use specific factors, so that burnertip volumes by state and

end-use sector match the ones reported by the NGA in the base year. As was mentioned before, the NGA data derive from Form EIA-176.

The benchmarking code has been included in the MARKET model, rather than

in GENNET for the following reasons: (i) More recent developments extend

benchmarking to years after the base year. In the latter use, the network to

be benchmarked is no longer the one generated by GENNET. Thus a benchmarking

capability is needed in MARKET anyway, (ii) The NGA data would have

represented a new input item for GENNETT , whereas they are already an input item into MARKET because they are needed for burnertip price

calibrations (see Note 34 ). (iii) The benchmarking capability reduces

the need for network generators like GENNET to account for all burner-tip

volumes

Besides the state-level benchmarking refered to above, MARKET also has

the optional capability to benchmark at the regional level using regional

reference volumes (QRRSIY, ORCMIY, QRINIY, QRUTIY) (see Section 3.6).

Starting from benchmarked local burner-tip volumes in the base-year, which in

each region are supposed to add up for respective end-use sectors to the

122
regional base year reference volumes, the local reference volumes are multiplied by the ratio of the next year's over the present year's regional

reference volume. These updated local reference volumes are then chosen as volumes at the corresponding M-nodes. Summed by region for each end-use

sector, the local volumes will reproduce the regional volumes. In particular,

if the regional volumes agree with available NGA data, the above procedure

benchmarks at the region level. The procedure does not guarantee agreement at

the state level, although the divergence should be minimal. Nevertheless, EIA

felt it necessary to benchmark to state levels rather than regional levels for

those years for which NGA state level data are available.

Note 12 Monthly and daily loadfactors (p. 42,58)

(Oral communication by P . Cur ley of AGA to R.E. Schofer of NBS on November 17,

1981).

Peaking factors are defined as the ratio of the peak day sendout to the

average day sendout in the peak month. The peak day may or may not lie

within the peak month. 1980 input data was used and included all reporting

companies which qualified in each region. Qualification is defined as follows:

1 - Company must report all data required for determining peak ratio.

2 - Company service territory cannot extend beyond regional boundaries.

3 - The reporting company cannot be a transmission company.

The results for the nine 1980 census regions are as follows:

Census Region

New England

Mid Atlantic

South Atlantic

East North Central

East South Central

West North Central

West South Central

Mountain

Pacific

All Lower 48

Ratio, Peak Day to Average Day

in Peak Month

1.47

1.45

1.36

1.28

1.36

1.14

1.58

1.44

1.40

1.37

Sample Size

59%

53%

42%

62%

34%

10%

19%

26%

53%

123
Sample Size is the ratio of gas sales by companies used in this sample to

total gas sales for regions from 1980 editions of Gas Facts .

Note 13 Loadfactors for interruptible customers (p. 42,58)

In the MARKET model, loadfactors on arcs leading to M-nodes are used for

two purposes: (i) to estimate peak-day loads at the burnertip to which demand

rates may be applied in order to establish fixed distribution tariff

increments; (ii) to estimate peak-day usage at the city-gate in order to

establish transportation tariffs in a similar fashion.

Industrial customers and utilities with dual firing capability involving

residual oil (switching subsectors in Section 3.4.1) can be considered

interruptible customers. As such they are not likely to contribute to peak

loads or be billed on the basis of peak loads. These customers rather act as peak-sharers. As a consequence, loadfactors of 1.0 or less are recommended

for M-nodes in switching subsectors or, more generally, for all industrial

customers and utilities. Most recently loadfactors of .1 have been used for

all utilities. Of course, the name "loadfactors" is then a misnomer. The

practice of introducing loadfactors which are smaller than 1.0 makes even more

sense, when the loadfactors of all end-use sales of a particular distributor

are combined to estimate the loadf actor pertaining to the primary supply of

the distributor. The weighted sum of all loadfactors of sales yields an unrealistic worst-case estimate of peak usage, because it is based on the

assumption that all end-use consumption peaks at the same day. Load factors

that are smaller than 1.0 will contribute to a more realistic combined

loadf actor.

Note 14 Root loss rate (p. 42)

The MARKET model contains a provision for a single root-loss rate to be

entered into the model as a loss quantity for all root nodes. This number

might be interpreted as representing losses between the wellhead and the

pipe-gate. Since current reserve data have been adjusted for processing

losses and lease-and-plant fuel ( Note 15 ), the root loss has been entered as zero in all production runs so far.

Note 15 The GRST table (p. 64, Notes 8, 30, 37)

The data structure which contains reserve information is called the "GRST

table". It is input and maintained by the GAMS driver rather than by MARKET,

although MARKET does update the quantities of reserves by subtracting the

amounts withdrawn from each of the reserve blocks. MARKET does not access the

complete GRST information, such as production regions and production

categories.

In addition to reserve blocks of the various NGPA categories and flavors,

th GRST table contains reserve blocks of socalled "888 gas". These are highly

priced pseudo-reserves which may be interpreted as supplemental gas sources

such as butane or coal gas and which are only utilized in the case of extreme

gas shortage. In a very recent development, pseudo-reserves representing

import committments have been introduced.

124
Note also that all versions of the GRST table used so far contained

reserve data and prices which were adjusted to account for removal of

lease-and-plant fuel, typically 5%-7.5% of gross production at the wellhead.

Note 16 Mathematical discussion of minimum cost take supply curves (p. 45)

Consider K reserve blocks dedicated to a given pipeline system, and let

qk = available annual production

ujt = unit price at the wellhead

tk = take-or-pay portion (o < tk < 1)

for the k^^ reserve block, 1 < k < K. The reserve blocks are numbered by

increasing price:

uj < u2 < ••• < u^.

The supply curve which results from the minimum cost-take strategy

described in Section 3.5.1 has a constant unit price for all quantitites

between zero and the total take-or-pay quantity

Qo = Il<i<K'l"!.

This constant price is given by

y tiqiUi y tiqiUi

l<i<K l<i<K

Po =

y tiqi

l<i<K

which is the average price paid if the take-or-pay obligations were satisfied

but no purchases were made beyond these minimum limits.

Withdrawal proceeds in several stages. Each corresponds to a smooth

portion of the supply curve. Withdrawal up to the total take-or-pay limit Q^

corresponds to the constant portion of the beginning of the supply curve. In

each of the stages which follow the initial constant stage, the supply curve takes the form of a hyperbola,

P(Qk-l+q) = (Qk-iPk-H-quk)/(Qk-l+q), < q < (l-tk)qk,

where

Qk = I ^i + I ^i*li . l<i<k k<i<K

l<i<k k<i<K

125
Qk-1 > ^k-l ^^^ Qk> Pk> respectively, are the coordinates of the two endpoints

of the k-th hyperbolic curve segment. The values

Qk = I qi

l<i<K

pk = I Piqi/QK

l<i<K

are the coordinates of right most or "last" point of the supply curve. The

asymptotic value of the k^^^ hyperbolic segment as q

-> ~ is pj^. It follows

that if Pic-1 > Pk t'^s segment is convex and decreasing; if Pfc-i < pi^ the

segment is concave and increasing, and if Pk-i = pk the segment is a horizontal line at value pj^. The supply curve will always assume its minimum

at a breakpoint between two curve segments. In particular, the curve point

with the coordinates Q]^, Pk, l<k<K, is minimum if P^-l ^ Pk ^^'^ either pk < Pk or k = K. In the latter case, the minimum is assumed at the last point. In

the absence of take-or-pay provisions, minima are at Qq = 0, Pq = ui as well

as at Qi = qi. Pi = ui, and the curve points in between. In these extreme

cases, the supply curves exhibit either economy or diseconomy of scale,

respectively. In the general case, a regime of economy of scale is followed

by a regime of diseconomy of scale. According to current data, economy of

scale dominates for most pipelines systems.

Note^ ^17 Handling supplemental gas under rateable take (p. 46)

Reserve blocks of supplemental gas ( Note 15 ) must clearly be excluded

from the across-the-board withdrawal assignment specified by the rateable take

option. This is achieved by assigning a zero take-or-pay ratio to

supplemental reserve-blocks. During the second phase of the rateable take

withdrawal process, zero take-or-pay is treated as a flag causing supplemental

reserve blocks to be removed from consideration. Supplemental reserves are tapped only after all others are exhausted, and then they are withdrawn on a minimum cost-take basis.

Note 18 Rectangular production profiles (p. 50)

A rectangular profile requires Ti=T2, and q(T)=0 for T>T3. The latter

condition can be met only approximately by choosing Ti=T2, T3, and Qres such

that

Te-qmax = Qres " (T3-T2)-qmax = l.l'BBtu >

Note 19 Average versus marginal prices in equilibration (p. 51)

S. Wade of BNL pointed out that the quantity of gas purchased in the

presence of fixed charges depends both on the fixed charge and the marginal

price. More precisely, a price-quantity relationship should be of the form

Q = d'^a^^gi'^alCPM.Cf),

where P^ denotes the marginal price and CF the fixed cost of doing business.

Q then stands for the maximum quantity of gas absorbable by a particular

126
purchasing entity under the indicated pricing assumptions. In the particular

case of the MARKET model, the marginal price is assumed to be constant, that

is, independent of the quantity purchased. It thus coincides with the full

commodity tariff, that is, the average price of gas at the city gate plus the

commodity mark-up. Let P^ denote the corresponding average price of gas at

the burnertip. Then

pA = pM + cF/Q

and

A = dniarginal(pA + cF/Q, CF).

The latter relation defines implicitly a price-quantity relationship of the

form

Q = daverage(pA^cF).

S. Wade further provided the following interesting argument which derives a price-quantity relationship from a utility maximization principle. His basic

assumption is that a given "income" may be spent either on gas or on "other

goods". If Q^ denotes the purchased quantity of gas and QO the purchased

quantity of other goods, then the "utility function"

U = (QG)a(QO)e, a,B > o,

determines the "utility" of having amounts qG and (p at one's disposal. The

combined cost of this purchase equals the given income I:

CF + pMqG + pOqO = I ,

where pO is the average price of other goods, and cF and pM are as above.

With I, cF, pM, pO as well as a and B being given, the question is what is

the most advantageous purchase pattern? In other words.

Maximize U = (Q^)" (qO)3 for qG, qO > o

subject to pMqG + pOqO = i - cF .

This maximization problem is equivalent to the following one:

Maximize V = a»log Qp + 3 'log (f for qG, qO > o

subject to pMqG + pOqO = i - cF.

The objective function of the second problem is simply the natural logarithm

of the first, and since the logarithm is a monotonically increasing function,

the second objective function is maximized for the same values of qG and Q^.

In addition, one may assume that

a + 3 = 1 , a, 3 > o ,

since this relation can always be achieved by multiplying the objective

function in the second problem by a suitable positive normalization factor.

127
With the Lagrange multiplier X, the (necessary) conditions

3Q^ 3Q^ 3qO 3qO

yield

g = xp'^ , 3_ = XP .

From that and from the constraint equation follows

a F^qO - P^qG =

pOqC „ pMqG =, j_ qF^

Solving this linear system gives:

(f = a(I-cP)/pM = d"»^'^gi"^l(pM.cF),

or in terms of the average price P^:

QG = (aI+0cF)/pA = d^^^'^^g^CpA.cF).

For most users, particularly residential ones, one would expect that the fixed

cost C represents a very small portion of the disposable income I,

I » C^ ,

so that the price-quantity relationship takes the form

qG =i 9/p^

in which the quantity depends only on the marginal price P . In contrast, the

corresponding formula featuring the average price, arrived at by substituting

pM^pA_cF/QG ij^tQ the above formula, is

Q^ = (6 + C^)/P^ , and definitely depends on C^. (The reader notices that the fixed cost C^

enters with a seemingly wrong sign: increase of the fixed cost seems to

increase the amount purchased. This conclusion, however, is erroneous because

an increase of the fixed cost entails an increase in average price.)

One might be tempted to interpret the preceding observations as implying

that demand curves should be in terms of marginal rather than average prices.

We do not agree with this interpretation. One reason is that, for industrial

users, fixed costs C'' may not be neglible when compared to a suitable

interpretation of disposable income I. Furthermore, the utility function on which the analysis is based is clearly oversimplified. For instance, the

second form of the utility function indicates that the amount of other goods

purchased does not affect the utility of gas. This is certainly not the case

if the other goods include alternative fuels. In reality, the amount of the

payment required up-front influences the willingness to accept particular

128
marginal prices. There is a definite need for further research. Until a better understanding has been reached, the assumption that the price-quantity

relationship depend on the average price P^ alone appears to be justifiable.

The argument by S. Wade, however, is illuminating and points the way towards

improving the foundations of demand models.

Not_e 2 EIA supplied demand curves (p. 51, Note 40)

Demand for natural gas has two kinds of elastic responses to price

increases. There may be an immediate restriction of consumption such as residential customers turning down their thermostats or industrial boilers

switching to another fuel in the presence of a dual firing capability. There

may be other actions, however, whose effects will not be immediately apparent

such as boosting insulation, installing equipment for burning alternative

fuels, and so on. The terms "shortterm" and "longterm" elasticity are used

for these two kinds of responses to price changes, respectively.

EIA provided demand curves for use in GAMS which are of constant

elasticity but make the demand also responsive to the consumption observed

during the previous year. The intent of the latter scheme is to represent

longterm elasticity effects.

The demand curves provided by EIA are of the following form:

3 , .Y > v6

Q = ^ref

Uref] ""^^ (.Lrefi V ^ref J Here Q is the dependent variable representing the quantity of gas expected to

be consumed, price P is the independent variable, and the following are parameters:

Qpgf = reference volume (QTRFV)

Pj.gf = reference prices (PTRFV)

L = previous year's volume (QLYRV)

^ref ~ previous year's reference volume (QLRFV)

Q £ = lag-adjusted reference volume

e = price elasticity (RBET) (negative)

Y = lag exponent (RGAM)

Price elasticities and lag exponents are given for end-use sectors rather

than end-use subsectors. Therefore some supplementary decisions had to be

made regarding these values for subsectors. For nonswitching end-use

subsectors, the lag exponents of the respective sectors are used. The

switching end-use subsectors are equipped to exploit opportunities for cheap

fuel. Their short term elasticity is consequently high. Their long term

elasticity as individual customers, on the other hand, is very small: if the

previous year yielded fewer opportunities for purchasing cheap gas, then this

129
would not deter these customers from exploiting this year's opportunities. A

nonzero lag exponent, however, would predict —• incorrectly ~ a diminishing

effect on demand. Therefore, zero lag exponents were assumed for the demand curves of switching end-use subsectors. The same price elasticities are assumed to apply for both the switching and nonswitching subsectors of

Individual end-use sectors.

In order to avoid for computational purposes unacceptably large demand

values in the neighborhood of zero prices, the demand curves are defined to be

level in the price range from zero to half of the reference price. Also the

quantity L, which represents consumption during the previous year, is bounded

below and above by '^'L^^f and 1.5*Li-ef» respectively, to avoid an excessively

large influence by the lag factor.

For early versions of the model it became apparent that the above supply

curves were not robust enough to achieve "normal" model termination in the case of steep price increases. Minimum demand levels were therefore

introduced to prevent demand from falling in a given year below a specified

percentage of the corresponding reference volume no matter what the price.

Such demand floors have been lowered or removed in later versions of the

model.

Recently, different demand curves have been specified for the utilities

sector. These demand curves have been developed by EIA in connection with the

IFFS model. They are specified on a regional and yearly basis, and do not

take into account the amount consumed during the previous year.

It is important, that the lag exponent be considerably smaller than 1.0

in order to avoid unstable behavior. Indeed, once the consumption falls below

the reference volume, then the demand in the next year is biased also towards

falling below the reference volume in that year, and so on, resulting in a cumulative demand depression unless either the lag effects are small or prices

drop sufficiently below the reference prices to push demand back towards the

reference volume. Analogously, once the consumption exceeds the reference

volume, demand in the following year is biased also towards further exceeding

the reference volume, and again this effect feeds upon itself. As a result,

a very small difference in consumption in an initial year may lead to a big

difference in later years, depending on which side of the reference volume the

initial consumption happened to fall. This situation amounts to a "switch" as described in Section 2.7.

Although the above effect of "correcting away" from the reference will

not necessarily hurt the model and may capture some features of the real world

provided the lag exponents are sufficiently small, it is clear that a fully

satisfactory representation of both shortterm and longterm elasticities has

yet to be developed.

Another issue concerning demand estimation is the role of the numbers of

customers. Because of the close relationship between customers to be served

and the particular distribution company with which it is connected physcially

as well as commercially, the number of customers of a distribution company is

important to the latter 's expectation of demand. Changes in the number of

130
customers in response to price provide a natural measure for longterm

elasticity, whereas changes in the average usage indicate shortterm

elasticity.

Note 21 Utility demand curves (p. 53)

By the Summer of 1982, the original EIA-supplied utility demand curves were replaced by a set of regional demand curves of quite different character.

Instead of having log-linear demands curves scaled by an input track of annual

regional prices and demands, a different set of demand curves are input for

each year and region. These demand curves are "step-linear" functions, that

is, they drop off discontinuously at each of a finite set of breakpoints and

are linearly nonincreasing between adjacent breakpoints.

The curves are generated by the utility submodel of the EIA-developed

IFFS model. For stand-alone runs of GAMS, the output of some particular IFFS run may be chosen to provide a suitable set of utility demand curves. IF Gams

operates in conjunction with IFFS, then various sets of utility demand curves are generated by IFFS in real time and transmitted to GAMS.

Note 2 2 Example of a violation of the RDC condition (p. 54)

Suppose the regional demand curve for some end-use sector has the form

Q = Qr(Pr/P)

(elasticity = -1), with regional reference quantity Q^ stipulated at some regional reference price P^. Suppose further that there are only two markets

of that particular end-use sector in the region, and that the demand curves of

these markets are characterized by stipulated local reference quantities qoi,

*^R2 ^^^ prices Prj , Pr2» respectively. The corresponding individual demand curves then take the form

q = qRl^PRl/p) ' ^ = qR2(PR2/P)*

Suppose, finally, that the local reference parameters are compatible with the

regional reference parameters, that is, they satisfy

(RDC) qRi + qR2 = Qr , PriQri + PR2qR2 = ^rQr*

The purpose of this note is to show that the above compatibility

relations do not imply the RDC condition. The latter requires

qi + q2 = Qr » Pl^l + P2q2 " ^rQr

for every set of local prices pj, P2 and the corresponding quantities qj, q2 as determined from the local demand curves:

qi = ^RI^Pri/Pi) » ^2 = qR2(PR2/P2)-

131
The second of the RDC conditions is satisfied for the special case (elasticity

= -1) under consideration. However, the first of the RDC conditions is

violated for the following reference values

Qr = 1000 Pr = 1.10

qRl = 300 pRl =1.50

qR2 = 700 PR2 = 0.80

and the local prices

Pi = 1.80 p2 = 0.70.

For those prices,

qi = 450/1.80 = 250, q2 = 560/0.70 = 800

and

qi + q2 = 1050 * 1000 = Qr

Note 23 Cut-off prices (p. 56)

For each supply curve, a cut-off price (PCUTV) is calculated from state

prices for alternative fuels. It indicates the price above which an alternative fuel would be preferred over gas. Only the cut-off price derived

from the price of residual fuel oil will be low enough to influence model

calculations appreciably; this cut-off price is used for those industrial and

utilities end-use subsectors which can switch to residual fuel oil (Section

3.4.1). The other cut-off prices are included for consistency. Residential

cut-off is currently set at twice the price for distillate fuel oil ("Number

2"), commercial cut-off at 1.5 times the price of distillate fuel oil, and for

non-switching industrial users and utilities, the minimum of the commercial

cut-off and seven times the price for coal is used as a cut-off price.

If in the base year the cut-off price lies below the reference price,

then the cut-off price should be increased to 1.1 times the reference price to ensure that the consumption observed at an M-node agrees with its reference

volume and that, in subsequent model years the reference price and volume

define a point on the demand curve. While this procedure was followed for all

years, not just the base year, in the first versions of MARKET, it has been

discarded altogether in recent versions.

Cut-off prices are not invoked for recent directly specified demand

curves for the utilities sector, because switching effects are already built

into these demand curves.

Note 24 The transmission tariff module (p. 59)

J.^. Guldmann, who developed the regressions upon which the distribution

tariff module is based, also developed regressions for determining transmission tariffs from rate base and distance information. A corresponding

transmission module was coded in 1982 by R.E. Chapman and R.E. Schofer, but

has not been included into the MARKET model.

132
Note 25 Implementation of tariff escalation procedures (p. 59)

A single tariff escalation factor may be specified, which Increases all

mark-up tariffs, for transmission as well as for distribution, by a fixed

percentage model year after model year. The factor works indirectly by

Increasing the tariff adjustment factors (RTAFV) (See Note 33 ). If the latter

are found to be negative, then they are reduced rather than increased.

Note 26 Recent developments concerning the distribution tariff module (p. 61)

S. Wade of BNL has upgraded several aspects of the distribution tariff

module. He has reintroduced a tax component into the rate calculation. NBS

had removed tax terms from the original equations developed by J.-M. Guldmann.

He has also removed an instance of double counting. Finally a scheme was

atteiiq}ted for reducing tariff mark-ups to customers with residual oil burning

capability whenever the burnertlp price with the original mark-ups would

exceed the residual oil price. The latter feature, however, does not affect

the distribution tariff module as such, but is rather a part of the

equilibration process, since the burnertlp price is calculated by

equilibration and not by application of the distribution tariff module.

A. Davles of NBS has Investigated the variables in an earlier version of

the distribution tariff module as to their significance, using T-statistics

provided by J.-^. Guldmann. His major finding was that values for the annual

general costs (GENA) of the distributor were exceeded by their error bounds.

In other words, they were not significantly different from zero. This

indicates that present data do not support a further refinement of the

distribution tariff module along the lines of its present design.

Note 27 Storage losses (pp. 62,71)

Storage losses are assumed to be 2% of gas put into storage. This

assumption is made for all network nodes uniformly.

Note 28 Storage tariffs (p. 62)

In the semiannual equilibration mode, the constant o = .25 has been

chosen arbitrarily. For annual equilibration, the combined constant a.a has

been set to .15. It would be desirable to calibrate the constants a and a

by conducting experiments in the base year and following it.

Note 29 Options other than equilibration (p. 63)

The MARKET model contains options for "benchmarking" ( Note 11 ) rather

than equilibration for years following the base-year. For 1981 and 1982 state

level data are available for benchmarking at the state level. Benchmarking at

the regional level is available for any number of years after the base year.

Once the model enters the equilibration mode, however, it stays in this mode

for all subsequent model years.

133
Note 30 Determining initial reserve profiles (p. 33)

The GRST-table of dedicated reserves ( Note 15 ) is initiated with a base

year estimate of the dedicated reserves available to the respective pipeline

syteras. The GRST-table provides both content and deliverabllity Information.

Content information, namely the total amount of gas contained in each

particular reserve block, is given directly as an entry in the GRST-table.

The deliverabllity, namely the amount that can be actually produced during the

base year, is calculated in MARKET from profile information contained in the

GRST-table. This profile information is representative of the "maturity" of

the reserve block in question: reserve-production ratios are large before

production reaches its optimum plateau, and decrease subsequently to a value

which remains constant during the decline phase.

So far in GAMS, initial reserves have been assumed to be in the decline

phase, with pre-base year production equated with the profile parameter qmax*

and the calculation of the dellverabllltles for the base year as well as the

following model years are based on these assumptions. A more exact approach

would be to derive maturity information from observed reserve-production

ratios.

The first step in such a scheme, is to estimate the (constant) reserveproduction ratio for the decline phase. To this end, the reserve -product ion

ratios of suitable populations of reserves (grouped, say, by NGPA category and

production region) are plotted, and an accumulation point will be observed,

which indicates the expected decline-phase reserve-production ratio for the

class of reserve blocks. The existence of an accumulation point is due to the

fact, that reserve-production ratios approach the decline-phase ratio

assymptotlcally as reserves are exploited. If a population of reserve blocks

exhibits several different accumulation points, then one either splits the

population accordingly or choses a suitably weighted mean of the corresponding

ratios.

In the second step, assumptions need to be made about the typical

durations of the start-up and maximum production periods. These assumptions,

together with the above determined reserve-production ratios during the

decline phase (=Te), determine both the profile and the maturity of a reserve

block. This determination can be based on the following formulas (C.

Wltzgall, April 1982).

13A
(0) Given: a) TELI = 1/2 (TLCON-TLIN) = half-length of linear phase

b) TECO = TDCL-TCON = length of constant phase

c) TEXP = exponential decline factors

QRTE*TELI = production during linear phase

QRTW*TECO = production during constant phase

QRrE*TEXP = production during decline phase

k- 2 TELI-4--

t f

TLIN ICON TDCL

Given also : d) available reserves at start of 1979 = R

e) 79/80 production = P

Task ; determine profile and start of production from a),,

particular:

=> QKTE = maximum production rate

=> TLIN = start of production

., e), in

Assumption :

TELI > 1 ; TECO > 2 ;

135
(1) Regime #1 ;

2 TELI

T = time at end of production period (actual production start = 0)

< T < 1 :

P = 1/2 HT = QRTE*

H QBCTE

T 2*TELI

2

T

; H = QRTR • 2*TELI

4*TELI

R = QKrE*(TELl+TECO+TEXP)

n

IT

QRTE =

i^

4*TELI*(TELI + TECO + TEX?)

1 ; IT = 1

' 1 4*TELI*(TELI + TECO

R

+ TECP) '

TELI + TECO + TEX?

136
(2) Regime #2 :

QRTE

p = 1/2 (Hq + Hi) ; H = QRTE* "^ ^ ; H = QRTE* ^

o 2*TELI 1 2*TELI

P = QBO-E* r 2T - 1 1

L 4*TELI J

R = QRrE*(TELI + TECO + TEXP - 1/2»(T-1)*Hq)

2 = QRTE*(TELI + TECO + TEXP - (T-1)

4*TELI

n = 2T-1

4*TELI*(TELI + TECO + TEXP) - (T-1)^ R

T7 = 2*TELI ; n = ^*TELI " ^ ^ 4*TELI*(TELI + TECO + TEXP) - (2-TELI-l)

n ^ 4*TELI - 1 ^ 4*TELI(TEC0 + TEXP + $*TELI - 1

QRTF. = R

TELI + TECO + TEXP - (T-1)^

4*TELI

137
(3) Regime //3 :

remaining reserves as before:

R = QRTE*(Th:LI + TECO + TEXP - Illl^. y H =

"^"^

• QRTE

4*TELI o 2*TELI

P =

Q^'^^ '*' ^o * (2*TELI + 1 - T) + QRTE * (T - 2*TELI)

1 +

(T-1)

= QRTE * ^^^^^ (2*TELI * 1-T) + T - 2 * TELI

2

= QRTE * _^*^^^^' - ^^-^?'

^- T -2 * TELI

= QRTE *

= QRTE *

4*TELI

-(T-1)^ - 4*TELI^ + 4*TELI * (T-1) + 4*TELI

5*TELI

4*TELI - (2*TELI + 1-T)

4*TELI

^3 = 4*TELI - (2*TELI + 1 - T)"^

4*TELI*(TELI + TECO + TEXP) - (T-1)^

4*TELI

4*TELI*(TELI+TEC0+TEXP) - 4.TELI^

T^ = 2*TELI + 1 ; n^ =

1 TECO + TEXP

QRTE = TELI + TECO + TEXP _ (T-l)2

4*TELI

138
(4) Regime #4 ;

i^^^^^

R = (TECP + TEX] - (T-2*TELI) + 1) QKTE

P = QKTE

n =

1 2*TELI + TECO + TEX? - T + 1

T, = 2*TELI + TECO .; n, = - 4 4 TEXP + 1

QKTE = t

2*TELI + TECO + TEXP - T + 1

139
(5) Regime it5

R = as before = QRTE * (2*TELI + TECO + TEXP - T + 1)

P = QKTE * (2*TELI + TECO - T + 1) + E * QRTE

T-2*TELI-TEC0 T-2*TELI-TEC0

/

exp (___) ds

TEXP

= - TEXP* exp ( ) ds

TEXP

= -TEXP* -1 + exp (- T-2*TELI-TEC0 , ^qrte

TEXP

P = QRTE* (2*TELI*TEC0-T+1) + TEXP*(1 - exp (_ T-2*TELI-TEC0^^

TEXP

n =

, T-2*TELI - TECO ^^ 2*TELI + TECO - T + 1 + TEXP *(1 - ^^^ ^~ TEXP '''' 2*TEL1 + TECO + TEXP - T + 1

T5 = 2*TELI + TECO + 1

TEXP * (1 - exp(ZL_.))

n = ^^^^ = (1 - exp ("^ ))

^ TEXP TEXP

ORTE = R

2*TELI*TEC0 + TEXP - T + 1

140
(6) Regime »b

T-l-2*TELI-TEC0x

exp (- ) R = TEXP*H ; H = QRTE* TEXP

T-2*TELI-TEC0

P = QRTE*

exp ill—) ds

TEXP

T-2*TELI-TEC0-1

= QRTE* TEXP* T-2*TELI-TEC0v

exp ( ) TEXP

exp ( T~2*TELI-TEC0-l v TEXP

'

= QRrE*TEXP* exp ^_ T-2*TELI-TEC0-1

^ ^ (1 - exp (lL_))

TEXP TEXP

QRTE*TEXP* exp ^_ T-2*TELI-TEC0-1

^ ^j _ ^^p (-1_ ^

II = TEXP * TEXP

TEXP * QRTE* exp ( T-2*TELI-TEC0-1)

TECP

(I = 1 - exp ill ) TEXP

QRTE = TEXP * exp (_ T-2*TELI-TEC0-1)

TEXP

141
(7) Sunmary ;

a) P/R - ratio break points:

n = 1

1 4*TELI*(TELI + TECO + TEXP) Regime #1 / Regime #2

IT « 4*TELI - 1 Regime #2 / Regime #3

^ 4*TELI*(TEC0 + TEXP) + 4*TELI - 1

IT - 1 Regime #3 / Regime #4

^ TECO + TEXP

IT - 1 Regime #4 / Regime #5

^ TEXP + 1

n - 1 - exp ("^ ) 5 TEXP

Regime #5 / Regime #6

(constant form Regime #6)

142
b) II,QRTE formulas:

<n<ni: QRTE = ^ TELI+TECO+TEXP

2

T

4*T EL I* (T EL I+T ECO+T EXP )

n <n<n2: qkte = 4*teli*r

i AT EL I* (TEL I+T ECO+T EXP) - (T-l)2

^ ^ 2*T-1

4T EL I* (TEL I+T ECO+T EXP) - (T-l)2

4*TELI*R

n„<n<n^: qkte = -. 2 3 4T EL I* (TEL I+T ECO+T EXP) - (T-l)2

4*TELI-(2*TELI+1-T)^

4T EL I* (TEL I+T ECO+T EXP) - (T-l)2

n-<n<Il, : QRTE = ^

3 4' ^ 2*TELI + TECO + TEXP + 1

n = 2*TELI + TECO + TEXP + 1

n, <n<n : qrte = 5^ ^ J 2*TELI + TECO + TEXP + 1

2*TELI + TECO - T + 1 + TEXP* (1 - exp (- T-2*TELI-TEC0

)

)

jj = TEXP

2*TELI + TECO + TEXP + 1

n <n: QRTE = _L * exp r T-2*TELI-TEC0-l^

5 TEXP TEXP

n = 1 - exp (_lL_)

TEXP

143
c) Continuity checks ;

1 T, = 1 : n

1 1 4*TELI*(TELI + TECO + TEXP)

lit' '

1 4*TELI*(TELI + TECO + TEXP)

T = 2*TELI : iC - ^*TELl'l

2 2 4*TELI*(TELI + TECO +YEXP) - (2tECI-1)2

JJ+ ^ 4*TELI-1

2 4*TELI*(TELI + TECO + TEXP) - (2«TELI-1)^

4*TELI 1 T^= 2*TELI+1 : n, - ,^ , - 1 3 3 4*TELI*(TEC0 + TEXP) TECO + TEXP

,+ 1 n

3 TECO = TEXP

T, = 2*TELI+TEC0 : n~

^ 4 4 TEXP + 1

+ 1 + TEXP*(1-1) 1 n^ TEXP + 1 TEXP + 1

T^ = 2*TELI+TEC0+1 : nl -

^^ TEXP* TTEXF ^ i - exp (Z! ) 5 5 TEXP TEXP

n^ - 1 - exp (lL_)

5 TEXP

144
Note 31 Calibration of tentative distribution loss rates (p. 71)

These 4% have nothing to do with the 4% loss assumed for transmission

losses, that is, pipeline fuel. The setting of a tentative distribution loss

rate can be calibrated by comparing the actual total national production with

the total national production as calculated by MARKETT . In April 1982, a set

of such calibration experiments was performed by BNL and NBS, and a tentative

distribution loss rate of 4% was found to lead to a reasonable agreement

between observed and calculated production.

The tentative distribution loss rate is a parameter of the MARKET model.

It is called "tentative", because it may be boosted by the model during the

base year at selected nodes in the case of so called "market adjustments" (See

Note 32 ).

Note 32 Market adjustments (p. 72, Note 31)

The minimum acceptable flow of each node should be adjusted as needed for

different networks and data. The purpose of the adjustment is not just to

exhibit a positive flow in the base year, but to provide a cushion to keep

flows positive during the following model years. A typical rule for defining

flow is that the total secondary Inflow into a node should not exceeds its

primary inflow. Currently it is also required that the primary inflow is not

exceeded by 1.5 times the excess of secondary outflow over secondary Inflow.

This rule guarantees that the primary outflow is more than one half of this

excess, and is designed to limit the dependency of burnertip prices on the

costs of secondary sales. This rule is responsible for the majority of the

current market adjustments, which are typically below 1% of the total

consumption.

Note 33 Transmission tariff adjustment (p. 75, Note 25)

Mechanically, the tariff adjustments are handled by associating a tariff

adjustment factor (RTAFV) with each node in a system network. A

multiplicative correction factor for transmission tariffs, that is, an RTAFV

value associated with P-nodes, is calculated as follows.

Note that the price Pq of primary supplies at the root node, as calculated from the cltygate prices by the backwards averaging procedure

described above, is a linear function

Po = a + Imi-Mi + 5;ni-Ci

of the tariff parameters Mi and Ci for all those system nodes that

participated in the procedure. The coefficients a, mi, ni, depend only on primary and secondary flows, secondary costs, and cltygate price levels. If

the tariffs in the above expression are multiplied by a single variable x,

then a linear function in x results:

Po(x) = a + (Imi'Mj^ + Jni*Ci)'X = a + b'x

145
with

Pod) = Po .

Instead of calculating a and b directly, which would be too complicated, the

model repeats the backward averaging procedure with all parameters halved.

This then provides the value

Po(l/2) = a + b-1/2 .

The question is: what value x will yield

PqCx) = Po ,

where Pq is the target price at the root? All one has to do to answer this

question is write Pq as weighted mean

Po = A-Po(l) + ij-Po(l/2), X + M = 1,

which amounts to solving a linear system of two unknowns, and then combine the

adjustment factor x from the values 1 and 1/2 with the weights so calculated:

X = X-1 + yl/2.

For several systems, it was found that a full reconciliation between

citygate prices and reserve prices was not possible without adjusting negative

add-on tariffs. This conflicts to some extent with the concept of

multiplicative adjustments. S. Wade of BNL has therefore modified the

transmission tariff adjustment scheme by including additive adjustments and by

assigning an artifical compensatory add-on tariff at the root -node.

Note 34 Distribution tariff adjustment (p. 75, Note 11)

The modeling effort was particularly hampered by the absence of

sufficiently detailed burnertip price information for the base year. The

MARKET model was therefore forced to estimate burnertip prices from known

citygate prices using estimates of tariff mark-ups. The latter were obtained

by applying the Guldmann distribution tariff module. The strength of this

procedure is that it displays the correct "dynamics", but it is not well

suited to the actual reproduction of base line data, because it is based on national averages and does not capture local behavior. The baseline of

burnertip prices for the base year as calculated by the above procedures is

therefore not a fully satisfactory substitute for actual data, necessitating

an adjustment of the distribution tariffs associated with M-nodes . Adjustment

factors for these tariffs are desired so as to approximate given averages of

burnertip prices by state and end-use sector in the base year. The end-use

sectors considered here are the main sectors: residential, commercial,

industrial, electric utilities. In order to calculate these adjustment

factors, burnertip prices are first determined on the basis of nonadjusted

distribution tariffs. These tentative burnertip prices are averaged, with

volume weights, by State and end-use sector. Each such average is compared

146
with the corresponding target value and a correction factor is derived. By

multiplying the burnertip price at each M-node with the correction factor that

is associated with the State and the end-use sector of the M-node, we determine at each M-node a desired burnertip price.

At each M-node, except those serviced by direct sales distributors, the

difference between the desired and the tentative burnertip price is to be

absorbed by multiplicatively adjusting the tariff parameters of the M-node.

This requires that these parameters are not both zero, which is why direct

sales customers have been excluded. For all other M-nodes i, let

j = predecessor of M-node i (j is a D-node)

Pi = tentative price level at M-node i

Pi = desired price level at M-node i

Qi = primary supply at M-node i

Pj = tentative price level at D-node j.

Then the adjustment factor x must satisfy:

Mi'x + Cj.x ^ (p^ _ p"j).x = P^ - Pj .

Hence

Pi - Pj

X =

Pi -Pj

Because of limiting the adjusted tariffs mark-ups to nonegative values

and because the burnertip prices of direct sales customers will not be changed — their burnertip tariff mark-up is zero and therefore not affected by

multiplicative adjustments — , the average adjusted burnertip prices will

only approximate their target values. Again, the step of admitting negative

tariff mark-ups has been taken by EIA. The corresponding change from a multiplicative to an additive adjustment scheme has been developed by S. Wade

of BNL, but as of the time of this report has yet to be incorporated into

production versions.

Note 35 Seasonality of supply at the citygate (p. 77)

Spreading secondary supplies equally over both seasons is a controversial

judgemental assumption concerning the semiannual mode of operating the MARKET

model. An analysis of this assumption ties in with questions concerning the use of storage. Indeed, if a secondary flow from one pipeline system to

another occurs predominantly during the heating season, then the first system

storage requirements are increased whereas those of the second system are

147
decreased. Finetuning the seasonal variations in secondary transactions

should therefore go hand in hand with a detailed exploration of storage

availability and use.

The storage capacities owned by the various pipeline and distribution

companies are available data. There is a major difficulty, however, in that

storage ownership and storage usage do not coincide. So far NBS has not been

able to determine a pattern of storage using indicating whether a company is

able to satisfy its storage needs by using its own facilities or whether it

leases storage and, if so, from whom.

Note 36 On failure of equilibration (p. 78)

The issues surrounding "failure of equilibration" have been the topic of

extensive discussions and controversies during the development of the MARKET

model. These issues are summarized in a 6/11/83 memorandum to EIA

from C. Witzgall. This memorandum is quoted verbatim below:

I have become increasingly aware of a need for clarifying issues

concerning "failure of equilibration "

( FOE ) . Please do read and react to the

following ideas and concerns because they affect the planning and mode of

operation of GAMS development.

1) Why are there FOEs

Basically, a FOE indicates that the supplies of a pipeline system are priced too high at the wellhead, resulting in burnertip prices which are to

high for consumers to accept. Whether consumers in a given market will or will not accept a given price, depends on the demand curve specified at that

market. A FOE is thus caused by a mismatch between supply and demand as modeled by GAMS.

While a FOE may indicate a true market failure, it is more likely caused

by glitches in nodel procedures. A discussion of potential remedies is one of

the purposes of this memo.

2) Friend or FOE ? Should FOE's be avoided at all reasonable costs? The answer depends on the part of GAMS you are talking about. MARKET, for one, is the messenger of

bad tydings. We thus ask more specifically, should Market refrain from

producing FOEs?

This question is still ambiguous. It may be ionterpreted in two ways:

a) Should MARKET abend GAMS because of a FOE?

b) Should MARKET be made "robust" so that FOEs don't happen in the first

place?

The second question is of greater concern to me, and I would like to discuss

it first.

148
3) BID/AWARD has responsibility to avoid FOEs ! This statement will be qualified below. However, it basically stands:

The purpose of the BID/AWARD routine is to make sure that each pipeline system

acquires sufficiently many new reserves at prices that will be acceptable with

respect to specified demand curves. This may not be possible for a given set

of market parameters, because these parameters would not support the gas

market in real life. In this case, FOE is for real and constitutes a legitimate model result.

In most cases, however, the FOE will be the result of the way the bidding

procedure is modeled: if the bidding goes too high compared to available

demands, then there will be a FOE. The FOE is simply a signal to the

BID/AWARD routine that it needs adjustment. In this function, FOE is a friend . Under certain circumstances, it may well be desirable to "bail out" a pipeline system which experiences a FOE, rather than to abend the entire GAMS

run. However, to completely avoid the occurrence of FOEs by means fair and

foul would not be in the best interests of the developers of BID/AWARD.

4) Concern with present mode of operation

Presently, new MARKET versions are run with an antiquated version of

BID/AWARD, and the criterion of success is avoidance of FOE. Some of that is

quite justified. The danger to guard against is to make model adjustments in

MARKET simply so as to make it perform without FOE for a specific BID/AWARD

pattern. If this pattern then changes, the MARKET! adjustments may turn out to

be unneccessary or even counter-productive, once a new BID/AWARD routine is

installed.

5) Not all is the fault of BID/AWARD

In order to be successful, BID/AWARD needs

a) anticipation of supply price developments.

b) anticipation of demand.

It is clear that without reasonably correct anticipation in the supply and

demand areas, BID/AWARD will not be able to prevent shortages or FOEs.

In addition, BID/AWARD may be done in by spurious FOEs , resulting from

design inadequacies in MARKET

.

6) Anticipating supply and demand

The need for BID/AWARD to anticipate prospective regulatory/deregulatory

price movements is well recognized, and no elaboration on this point is

needed.

Demand anticipation is a different story. The main source for this

information is provided by MARKET during its demand projection phase . The

demand projections currently suffer from the fact that secondary volumes and

prices are kept constant in overly optimistic assessments, especially for

later years. Discounting would help as well as making secondary volumes

price-sensitive. The latter feature has been coded and tested, but still

awaits inclusion into the production package.

149
7) Demand anticipation on the demand file

The basic source for estimating demands is the specification via input of

annual reference volumes and prices for each demand region and end-use sector.

These numbers are used as indexes for the reference volumes and prices at the

individual markets. Under the old log-linear demand procedure, these

reference volumes and prices are the primary determinants of demand. Under

the new procedures, their influence is drastically reduced. In both cases,

however, the understanding is that the reference volumes and prices represent

a point on the regional demand curve for the year in question.

Should the demand file be altered to reflect an anticipated price hike?

The answer is _no, unless a corresponding drop in volumes is also included.

Increasing just the price would in effect signal increased tolerance to price

increases. While this would make it less likely that a price increase would

result in FOE, it appears to be not justifiable on any factual basis.

8) Minimum demand levels . A more justifiable means of demand stabilization is to impose minimum

demand levels regardless of price.

The demand/supply equilibration in MARKET is formulated in terms of unit

prices rather than marginal prices. This feature, together with fixed charges

resulting from demand rates and predetermined secondary transactions, is

responsible for the fact that prices occasionally grow very large . Indeed zero consumption in the presence of a fixed charge will lead to an infinitely

high unit price. It may well reach a level at which demand curves, say

log-linear ones, become very small if not zero. Demand will then be choked

off and FOE results.

Dramatic drop-off in demand, say below one half of the reference volume

is not realistic, and it is therefore recommended to maintain minimum demand

levels at least for residential and commercial end-use-sectors. This would

make demand more robust and thereby prevent unnecessary FOEs.

Tariff calculations may also be thrown out of whack if consumption

becomes unrealistically small. The next section will provide a procedural

reason for minimum demand levels.

9) Two types of FOE . There are two different situations in the computer program, in which a FOE is declared. The first is simply a failure of pipegate supply and demand

curves to overlap. The second situation is the persistent occurence of a negative flow beyond tolerable limits. This is a local phenomenon. It will

be discussed later in more detail.

For now it suffices to note that in the presence of some minimum demand

levels, demand and supply curves will always intersect , and the only FOE that can therefore occur is of the local kind involving negative flows. This

knowledge is useful since fewer possibilities need be considered in diagnosing

the reasons for a FOE.

150
10) FOE during demand iteration . During the first iteration, parameters may assume unrealistic values and

thereby cause a FOE. This FOE does not occur once the iteration parameters

have settled down. Thus the model will run successfully once it gets past the

first iteration.

Remedies are: good initial values plus anything improving robustness as,

for instance, minimum demand levels.

11) FOEs due to secondary quantitites . Secondary quantities currently stay either fixed (P-P arcs), are predetermined (imports), or are estimated on the basis of last year's results.

In all these cases there is lack of anticipation of major supply price

movements. In the model, the pipeline systems are thus likely to be caught

undercharging or overde live ring on secondary sales.

The effect of undercharging is serious for systems with predominantly

secondary sales (#13, #14, #8). This is because in the model, pipeline

systems must recoup losses from secondary sales by increasing the price for

primary ones. The resulting price increase at primary markets may stifle

demand to the point of a FOE.

Overde live ring on secondary sales — and this includes imports — will cause negative flows , as incoming secondary volume exceeds demand. This also can cause FOE.

There is an almost sure-fire curve for both these problems: use equilibration with the secondary quantities as estimated currently in order to

get a fairly correct estimate of the supply prices from the reserve prices of

the actual model year, and to reduce observed overdeliveries. Then

equilibrate again. This additional equilibration doubles equilibration time

(but not the larger time required for NXTSYS). If one is unwilling to invest

this time, then various stop-gap measures can be taken, which are discussed

below.

For IFFS/GAMS integration, the information from a previous iteration

could be used to improve the modeling of secondary quantities.

12) Improving secondary price estimation . M. Minasi has proposed to input yearly escalation factors which would

reflect anticipated supply price increases. These escalation factors would be

used to improve secondary price estimates by providing missing anticipation.

This simple device may go a long way towards improved secondary prices, but

does not address the problem of overdeliveries.

13) Adjusting the network . Experience has shown that certain "trouble spots" exist in the network:

these are downstream nodes with a high incidence of negative flows, although

the demand involved is very small (typically less than 10,000 BBTU).

Furthermore, this reduction in secondary supply does not affect the quantity

of supplies available overall: it just reroutes supply from one pipeline

system to another. The elimination of such trouble spots can be regarded as a legitimate part of the network generation process.

151
The model has a build in "market adjustment" procedure, which boosts

demands if necessary to ensure that, in the base year, primary flows exceed a fractin of the total adjacent secondary inflow. This fraction is currently

set at .5. The resulting market adjustment is very small, and would remain

negligible even if the fraction was increased to, say, .6. This would also

increase robustness of the model.

14) Imports

Since imports are hardwired, they may cause FOE. Some limited

rearrangement of imports within a pipeline system is possible. To gear import

prices automatically to world oil prices would help. Even more beneficial

would be the capability to treat some imports as production from a pseudoreserve in the GRST table.

15)

" Bail outs" Sometimes it is undesirable to stop GAMS because of a FOE. To "bail out"

the affected pipeline system, either demand must be boosted, or supply prices

reduced, prior to a subsequent new try at equilibration.

Boosting demand can be achieved by increasing reference prices at the

markets: this will increase the tolerance of consumers to price rises. Of

course, reference volume may be increased also, effecting an even more direct

increase in demand. Such demand increases may be restricted to occur down

stream from arcs with negative flow problems, and therefore be small enough

not to affect overall model results.

Reducing supply prices is problematical, because it is difficult to assess how this would influence the bidding procedure — bid prices being then

not really binding — and because this may interfere with supply price

scenarios.

Neither the implementation (logically a new level of loops) nor the

understanding of the effects of a "bail out" is easy.

A possibility is a "silent bail out ", by ignoring negative flows

entirely. Suitable warning messages would have to be posted, since the

conservation of flow principle may now be seriously jeopardized.

Note 37 Distribution in the case of excess demand (p. 81)

In the case of excess demand, the question arises how to distribute the

available resources. If some market represented by an M-node in a pipeline

system receives less than it would be willing to consume at the specified

price, then we say that this market has been "curtailed". Curtailment in the

model is not of a short term nature: it represents a shortage extending over

an entire season. It would be especially serious if it extended to

residential or commercial markets. In the case of the industrial and

utilities end-use subsectors with residual fuel oil capability, a curtailment

of the above kind would not necessarily be serious. In this case, it would

rather highlight the opportunistic (no value judgement!) market behavior that

is characteristic for these end-use subsectors.

152
For these reasons, an order of service priority has been established, and

each distributor serves residential customers before commercial customers, and

so on (see Section 4.2.3). The problem with the current version lies in the

way delivery is made to the distributors themselves: their supply is

curtailed by the same fraction for all D-nodes in the pipeline system. If a distributor has only residential customers, then he must curtail them, whereas

if the distributor has industrial customers, the latter may be able to absorb

the curtailment so that the commercial and residential end-use customers are fully served. Whether a residential market will be curtailed thus depends, in

the MARKET model, on the sector profile of the distributor serving the market.

This obvious inequity has not had a major effect on model results so far,

because the incidence of excess demands in final model results was minor, and

also because of the inclusion of so called "888 gas" reserves (see Note 15 ).

This "888 gas" from pseudo-reserve blocks representing synthetic and expensive

alternatie gas sources. The price of this gas is set sufficiently high to

enter the picture only in case of a shortage. The "888" artifice effects the

residential sectors mor than the other sectors because of the low elasticity

of the former.

The amount of curtailment in the result of an equilibration is of

considerable interest to the analyst and should therefore be compiled by the

MARKET model by State and end-use sector. In the presence of "888" gas, this

cannot be done because, the amount of "888 gas" at the pipegate can be readily

determined at the burnertip.

Note 38 Tolerance limit for negative flows (p. 85)

At the time of this report, the negative flow tolerance is set at 25% of

the total secondary inflow or 2000 BBtu, whichever is bigger.

Note 39 Averaging of seasonal prices (p. 86)

The fact that the price averaging method is only approximate for prices

at the root node, if secondary inflow or outflow are present, does have

undesirable effects during the demand projection phase, where it leads to a slight inconsistency between the stipulated pipegate price and the one calculated by averaging. To correct this shortcoming, and also to permit a certain consistency check, the correct formula for calculating annual prices

has been included by NBS in a developmental version of semiannual

equilibration, but is not yet included in production versions.

Note 40 Estimation of the number of customers (p. 87)

The estimation of the number of customers, in particular, residential

customers, is a recognized weakness of the GAMS system. The roots for this

shortcoming lie in the demand modeling portion of the system, for which NBS

did not have responsibility (see Note 20 ). We contend that a proper

representation of "shortterm" and "longterm" elasticity requires a two-tier

modeling approach in which the effect of price on average usage per customer

and changes in the number of customers depending on price are estimated

separately.

153
Note 41 General remarks about updating secondary transactions * (p. 89)

It Is clear that the estimation of next year's prices for secondary

outflows is very rough. Moreover, this estimation is based entirely on results for the current year. Should there be any major changes in supply

prices caused, say, by deregulation, the price estimates will not reflect this

development. Since the prices determine the quantities vis the equal cost

shares assumption, the estimate of secondary volumes is also problematic.

For the purposes of a general discussion of this problem we recapitulate

briefly the role of secondary transactions. They are distinguished from

primary transactions, on the basis of a 1980 snapshot of supply relationships

compiled from Form EIA-50, by designating dominant suppliers as primary. Each

node in the base network is connected via a unique string of several primary

arcs to a root node. All nodes connected to the same root node define a pipeline system (see Section 3.4.1).

The volumes and prices of secondary transactions are specified prior to

equilibration, for which they serve as a boundary condition (See section

4.2.2). The equilibration can then be carried out in an efficient and

straight-forward manner, because each demand curve is connected to a single

supply curve. As a consequence of the latter observation all demand curves in a pipeline system can be thought of as combining into a single root demand

curve, which then can be matched against the supply curve in classical fashion

(see Section 3.9). After two seasonal equilibrations the secondary flows and

prices are reestimated on the basis of retaining expected (financial) market

shares among suppliers of the same node (Section 4.3). These estimates then serve as boundary conditions for next year's equilibration. In Operations

Research parlance: we set up a decomposition method and abort it after the

initial iteration step.

The different treatment for primary and secondary arcs is not entirely

without parallel in reality. In many instances, a distribution company will

have a major and a minor supplier, with strong contractual obligations to buy

from the minor supplier. Indeed, the minor supplier will be needed in times

of high demand, and will insist on contractual protection in return for his

availability. Also a shift away from expected demand may hit the minor

supplier relatively harder. (In view of these considerations, one would

expect deliveries by minor suppliers to occur predominantly in the heating

season. This clashes with another assumption of the model, namely that all

secondary supplies are divided equally between seasons.

By halting the equilibration process early, we hope to preserve some of

the qualitative take-or-pay aspects of secondary transactions. In addition,

we avoid the extensive computational effort of additional iterations.

However, the effect of secondary arcs on the functioning of the model may be more pronounced than anticipated. Although their total influence on model

results is minor, secondary transactions do cause trouble spots in the base

network and consequently led to unnecessary failures of equilibration.

Two typical problem situations occur. In the first such situation, a secondary inflow occurs at a system node with a comparatively small sales

potential. A price increase in the system may well reduce the demand at this

154
system node below the fixed inflows from the secondary arc. Thus a "negative

flow" would be required to balance the in-and outflows of gas for this system

node (see Section 4.2.4). In the second situation, a small "intrastate"

pipeline system has a secondary outflow which exceeds the primary demand

considerably. Systems 13 and 14 are prime examples. In these cases, a sudden

price increase at the wellhead may cause a price imbalance because the

secondary revenues are based on the price expectation of the previous year and

may therefore be priced too low. In the current version, the ensuing losses

are recouped by price increases to primary customers which may be

unrealistically high.

A somewhat academic problem is the occasional overpricing of secondary

outflows, the revenues from which may exceed the total cost of supplies (see

"negative prices" in Section 4.2.4)

All these problems are caused by the reliance on past year's results in

order to estimate the prices and from these, via the equal market shares

assumption, the volumes of secondary transactions. If the results of the

ensuing equilibration, or a modification thereof, would be used to reestimate

secondary transactions for the current year, thus permitting current pipegate

supply prices to affect the estimation of secondary transactions, then the

aforementioned problems may well disappear. This amounts, of course, to

executing the second step of an iterative decomposition procedure, and the

question arises, whether the iteration should be continued, if possible to

convergence. We surmise at this time, that two iterations will be sufficient

for the purpose of making the equilibration procedure more robust and of

improving the quality of secondary estimates, while preserving some of the

desirable qualitative effects of fixed boundary conditions. We are also

hesitant to recommend more iterations because of the difficulties involved in

monitoring the performance of such iterations for large systems, in

particular, since each of these iterations already contains several nested

levels of iterations.

Notfi 42 Effect on secondary transactions of sudden loss in primary volume

(p. 89)

Suppose that the primary supply of a node dropped suddenly to QEPS = iBBtu (the smallest permissible quantity) from, say, 50,000 BBtu. Typically

this happens in the presence of secondary supplies of say 40,000 BBtu, if a negative flow within tolerance limits was encurred. In order to enforce the

equal cost shaver assumption, the secondary volumes are — provided there are no major price changes — multiplied by a factor of roughly reduced to zero for the next year. In that year's equilibration, the primary supplier is

therefore without competition and will consequently bounce back to a healthy

level, say, 35,000, which causes the secondary supplier to be blown yp

accordingly. In this oscillatory process, the danger of negative flows beyond

the tolerance level is ever present.

It is to guard against this and similar drains of events, that measures

are taken to prevent large changes in secondary volumes. In particular,

secondary volumes may not be decreased by more than 50% or increased by more than 25% in a single year.

155
Note 43 Elasticity of demand projections (p. 92)

During the demand projection process, secondary quantities and prices are kept constant (see Section 4.5) throughout the entire projection period. This

leads to certain distortions of the system demand elasticity, in particular,

for prices which deviate strongly from the last pipegate price calculated by

the model. What is needed to improve the elasticity of demand projection are simple plausibility assumptions about how secondary transactions would be

affected by primary price changes. A very straightforward modification rule

would be to keep, for the first projection year only, the secondary

transactions at the same volumes as during the last year for which modeling

has been completed; to determine prices of secondary sales from the prices of

primary and secondary supplies and to employ equal market share rules to

update secondary volumes for all subsequent projection years.

iipte 44 Experiments with passes through Form EIA-50 (p. 99)

In an experiment conducted with the pipelines listed in Table 5.1, 1202

nodes were on the node list after 2 passes and no additional nodes were added

beyond the fifth pass at which time there were 1242 nodes on the list and 224

nodes which would never be included by additional passes.

156
References

[1] Gas Facts , American Gas Association, Arlington, VA, 1979, 1980, and 1981

[2] Natural Gas Rate Design Study ; Vol. I, IGF, Inc. Washington, DC.

[3] "Rate Design for Natural Gas Pipeline Companies and Distributors and

Storage Cost Estimates for Distributors: Six Reports by Jean-Michel

Guldmann", Letter reports to the National Bureau of Standards,

Washington, DC, 1981.

[4 J Rate Schedules of Natural Gas Pipeline Companies , H. F. Zlnder and

Associates, Washington, DC, March and September 1980, March 1981.

[51 The Hardy-Whitman Index of Public Utility Construction Costs , Bulletin

No. 110, Whitman, Requard and Associates, Baltimore, MD.

[6] B. Commoner, A Nearly Perfect Fuel , A Reporter at Large, The New Yorker,

May 2, 1983.

157

<»U..S. GOVERNMENT PRINTING OFFICEt > 9 8 5-4 6 I • I 5 / 2 008 2
NBS-114A iREv. 2-8C1 U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS/TN-1209

2. Performing Organ. Report No, 3. Publication Date April 1985

4. TITLE AND SUBTITLE

MARKET: A Model for Analyzing the Production, Transmission, and Distribution

of Natural Gas

5. AUTHOR(S)

C. Witzgall and P.B. Saunders

6. PERFORMING ORGANIZATION (tf joint or other than NBS, see instructions)

National Bureau of Standards

U.S. Department of Commerce

Gai thersburg , MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

Analysis and Forecasting Branch

Reserves and Natural Gas Division

U.S. Department of Energy

1000 Independence Ave. Washington, D.C. 20461

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

This report describes the MARKET submodel, one of three that combine to form the

Gas Analysis Modeling System (GAMS) . GAMS was developed for use by the Energy

Information Administration of the U.S. Department of Energy. It provides a tool

for analyzing the regional effects on the domestic natural gas market of various

policies for regulating the price of natural gas at the wellhead. MARKET is

concerned with the production of gas reserves and the transmission and distribution

of gas to consumers. It solves a network equilibration problem to arrive at

estimates of production quantities and prices.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Demand; deregulation; energy model; equilibration; gas distribution; gas production;

gas transmission; natural gas; network; pipeline; policy modeling; simulation; supply

13. AVAILABILITY

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reorder From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

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PRINTED PAGES

164

15. Price

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