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Contract No. DE-AC36-08GO28308

Capricious Cables: 

Understanding the Key 

Concepts in Transmission 

Expansion Planning and Its 

Models

P. Donohoo and M. Milligan

National Renewable Energy Laboratory

Technical Report

NREL/TP-5D00-61680

June 2014 
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Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

Capricious Cables: 

Understanding the Key 

Concepts in Transmission 

Expansion Planning and Its 

Models

P. Donohoo and M. Milligan

National Renewable Energy Laboratory

Prepared under Task No. SS13.2040

Technical Report

NREL/TP-5D00-61680

June 2014 
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iii

Table of Contents 

List of Figures .......................................................................................................................................... iv

List of Tables............................................................................................................................................ iv

1 Introduction......................................................................................................................................... 1

2 The Basic Formulation....................................................................................................................... 2

3 Temporal Simplifications................................................................................................................... 4

4 Uncertainty Simplifications ............................................................................................................... 9

5 Externalities ...................................................................................................................................... 13

6 Further Technical Simplifications................................................................................................... 17

7 Conclusions...................................................................................................................................... 18

References............................................................................................................................................... 19

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iv

List of Figures 

Figure 1. Test system for the time horizon simplification..................................................................... 5

Figure 2. Test system for hourly demand simplification....................................................................... 6

Figure 3. Test system for generation location uncertainty ................................................................... 9

Figure 4. Test system combining uncertainty and multi-period modeling ........................................ 11

Figure 5. Risk illustration for new generation uncertainty .................................................................. 12

Figure 6. Rerouting externality test system.......................................................................................... 13

Figure 7. Air pollution externality test system ..................................................................................... 15

List of Tables

Table 1. Investment Costs and Capacities for the Time Horizon Simplification ................................. 5

Table 2. Investment Costs and Capacities for Hourly Demand Simplifications.................................. 7

Table 3. Transmission Costs for Generation Uncertainty System ..................................................... 10

Table 4. Generation Uncertainty System Costs Given Different Generation and Transmission

Scenarios .......................................................................................................................................... 10

Table 5. Calculation of Expected Cost for Generation Uncertainty System ...................................... 10

Table 6. Transmission Characteristics for the Uncertainty and Multi-Period Modeling Test System11

Table 7. Minimum Cost of First-Period Transmission Investments.................................................... 11

Table 8. Transmission and Generation Costs with Rerouted Line B-C .............................................. 14

Table 9. Transmission Cost Characteristics Before and After Rerouting Line B-C .......................... 14

Table 10. Transmission Characteristics for Air Pollution Externality Test System .......................... 15

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1 

1 Introduction 

The extra-high-voltage transmission network is the bulk transport network of the electric power 

system. The design of this network determines which generation resources—whether

hydropower, natural gas, wind, solar, coal, or geothermal—can be brought to market. Solving the 

major issues facing the power system—such as continuing drought, climate change, and natural 

gas network coordination—will depend on wide-area coordinated planning of the transmission 

network. However, the complex economic and physical relationships in the power system make 

it difficult to predict how the transmission planning decisions of today will impact the power 

system of the future. To understand how the future power system may react to planning decisions 

today, wide-area transmission models are increasingly used to aid decision makers and 

stakeholders. The goal of this work is to illuminate these models for a broader audience that may 

include policy makers or relative newcomers to the field of transmission planning.

Transmission expansion planning models attempt to simulate trade-offs in the planning process 

in their simplest form. Ideally, a transmission model would be able capture the entire planning 

process; however, even relatively simple models are difficult to solve because of the large 

number of complex computations that are required. As a result of this computational complexity, 

transmission system modelers simplify many aspects of a power system. These simplifications 

can drive the results of an individual model, as will be demonstrated using simple examples 

throughout this paper. 

The computational complexity and the difficulty of interpreting model results are driven by two 

characteristics of transmission networks. First, a transmission system is a network driven by the 

laws of physics. Second, new investments in transmission or generation are capitally intensive—

requiring significant financial capital—and “lumpy,” because they can only be built in discrete 

increments. As a result of these two characteristics, planning models may not be intuitive and 

can be very sensitive to input parameters—small variations in model inputs can potentially 

produce very different model outputs. Adding to the complexity of understanding model results, 

modelers rarely have access to data governing specific generator contracts, ad-hoc reliability 

constraints considered by system operators, or other proprietary data. Thus, some of the features 

of the existing transmission system are unknown and cannot be represented in a model at all. 

Given these complexities, the most important outcome of a modeling exercise is an 

understanding of the system’s behavior, the model’s limitations, and the implications of its 

limitations. 

Understanding the implications of modeling assumptions, simplifications, and lack of 

information can be difficult. This paper explains the basic transmission expansion planning 

model formulation and highlights six of the major simplifications made in transmission 

expansion planning models. The six major examples highlight two temporal simplifications, 

future uncertainty in generation development, inclusion of externalities, and technical 

simplifications. The examples presented herein are very simple by design. The intent is to 

highlight the simplifications made by various models and the resulting need to contextualize 

model results using knowledge from other models and knowledge not captured in the modeling 

process. 

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2 

2 The Basic Formulation 

Transmission network expansion planning has been studied using computer algorithms since the 

late 1960s (Garver 1970). Although the algorithmic solving of the transmission expansion 

planning problem has evolved with dramatic increases in computation power, the core of the 

problem has not changed. A planning model is naturally framed as an optimization: minimize the 

cost required for a system to operate subject to physical and institutional constraints. 

Transmission expansion planning models minimize this cost by balancing the cost of new 

transmission investments against decreases in losses, generation costs, and the cost of energy not 

served. (Expected energy not served, EENS, is often the output of a probabilistic algorithm that 

produces a mathematical “expectation” that some load may not be served.) 

Most models are presented in their mathematical forms, not in prose. The set of equations, or 

formulation, describing the model is explained in Box 1, which shows the most common and 

critical elements of most models. 

The core of an optimization model is the objective function. This mathematical equation

expresses the goal, or objective, of the model. In a basic expansion planning model, the objective 

function minimizes the investment of the cost of new lines and operational (generation and nonserved energy) costs on an annualized basis. The quantities that the model can change to achieve 

the lowest cost are called decision variables. In a transmission expansion planning model, the 

key decision variables represent whether a specific transmission line will achieve part of the goal 

of the objective function. This means that in the modeling process some lines will be “built” and 

others will not. 

Following the objective function are constraints. These constraints set the conditions that a 

solution must meet. For example, a generator may not produce more power than its rated size. 

There are two key constraints in the transmission expansion planning problem. The first, 

Constraint 1 in Box 1, is the energy balance at each bus. This constraint requires that the demand 

at each bus is equal to the sum of the energy generated at the bus plus flow into the bus and 

minus flow out of the bus. Throughout an entire electric power system, this constraint implies 

that all demand must be met, and the quantity of generation must be equal to the demand. The 

second key constraint, Constraint 2 in Box 1, is an approximation of the alternating-current load 

flow. It relates the physical properties of the line to the phase of the alternating current at each 

bus. The formulae and terms used in Box 1 are the technical jargon used by modelers when 

describing which aspects of transmission planning their models capture. Understanding this 

terminology is important both for understanding information presented by modelers and being 

able to frame questions to modelers. 

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3 

Box 1. Transmission Expansion Planning Model Formulation 

Objective function—The goal of the model 

Minimize 

transmission_cost+operational_cost

operational_cost=cost_generation+cost_eens

transmission_cost=cost_per_line*x

where x is the variable indicating whether or not a specific investment is selected. 

Decision Variables—The quantities that the model chooses. For transmission planning, 

the primary decision variable of interest is whether or not a transmission line between 

two nodes is constructed. 

Constraints—Restrictions on the values that variables may take or other conditions a 

solution must respect 

Constraint 1) demand(i)=generation(i)+eens(i)+flow_in(i)-flow_out(݅)

The demand at any bus, i, must be equal to the amount of generation at that bus, the nonserved energy, and the flow on any transmission lines into the bus minus any flow out on 

any transmission lines. 

Constraint 2) flow(i,j)=γij൫θi-θj൯

The flow on any transmission line between two buses (i and j) is proportional to the 

physical properties of the line and the difference in voltage angles at each bus. This 

constraint represents Kirchoff’s second law and is an approximation that is called the 

direct-current load flow. 

௞ݓ݋݂݈_ݔ݉ܽ≥௞ݓ݋݂݈ (3 Constraint

The flow on any line, k, between two nodes cannot be greater than the maximum capacity 

rating for that line. 

Constraint 4) gen_min	≤	generation	≤ gen_max

The output of any generator must be between its minimum and maximum output ratings. 

Constraint 5) x∈0,1

Each possible investment, x, must be assigned a binary value of zero or one. The value is 

one if the line is constructed and zero if the line is not selected for construction. 

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4 

3 Temporal Simplifications 

Transmission lines are capitally intensive investments with economic life spans of 40 or more 

years. During the life span of these investments, the power system will continue to evolve. 

Existing generators will retire, and new generators will be added. Loads will increase and 

decrease with economic changes and new development patterns. Fuel prices will fluctuate, as 

will national policies and environmental regulations. None of these potential future values or 

events is known with certainty—and even if they were a transmission expansion model could not 

capture all of these varying future events and do so over all relevant time steps and -scales. 

Instead, modelers simplify the number of time horizons to capture the most important details. 

One of the most common simplifications made in transmission expansion planning models is to 

consider only a single investment decision time period. With this simplification, modelers plan 

for a specific target year. Traditionally, plans have been constructed for short-term horizons (5 to 

10 years) or long-term horizons (20 to 30 years).1 The short-term horizon simplification is 

problematic because economies of scale are not captured in the modeling. As an example of 

these economies of scale on a thermal-capacity basis, a 345-kV double-circuit line (a tower with 

two sets of conductors) costs $1,333/MW-mile, whereas a 765-kV single-circuit line (a tower 

with one set of conductors) costs 70% less, $413/MW-mile2

; however, with a limited time for 

demand to grow, the need for larger lines is never recognized. On the other hand, with a longterm horizon and the assumption of no new transmission for 20 to 30 years, there is pent-up 

demand for new transmission and large lines are almost exclusively selected. 

This concept is illustrated in a simple three-bus model in Figure 1. In this model, a single load 

exists at Bus A with generators at Bus B and Bus C. These generators are already connected to 

Bus A via two 300-MW lines; however; these existing lines cannot meet the new demands in 

years 10 and 20. In this system, there are two investment options to expand capacity: (1) a 750-

MW line from Bus A to Bus B for an annualized cost of $5 million, or (2) a 1,500-MW line in 

the same corridor for $7.25 million annually. In a traditional myopic formulation, only the load 

in year 10 would be considered. In this case, only 400 MW of transmission capacity are required 

to meet the load, and the lowest-cost investment is the smaller 750-MW line. However, if a 

second time horizon, such as 25 years, is considered, the demand has grown to 1,500 MW, and 

now an additional 900 MW of capacity is required to meet the demand at Bus A. The lowest-cost

option is now the more expensive but larger line. 

 

1 The Midcontinent Independent System Operator and Southwest Power Pool have attempted to close these gaps. 

See, for example, the Southwest Power Pools Integrated Transmission Planning Reports: 

http://www.spp.org/publications/20130730_2013_ITP20_Report_clean.pdf. 2 Thermal limits and costs from American Electric Power

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5 

Figure 1. Test system for the time horizon simplification

If the myopic model was used and only the smaller line was constructed, a second 750-MW line 

would need to be added to the system to meet the demand in year 25. This would have a net cost 

of $10 million, $2.75 million more than the single $7.25-million line, which would be sufficient 

to meet demand in both year 10 and year 25. It is important to note that these cost figures, though 

somewhat arbitrary, are scaled to reflect relative costs of transmission lines and generation. 

Given these costs, differentials between transmission options are commonly measured on the 

scale of millions of dollars. 

Table 1. Investment Costs and Capacities for the Time Horizon Simplification

Cost $M Capacity (MW)

Line A-B Medium 5.0 750

Line A-B Large 7.25 1,500

A possible conclusion from the example above is that larger lines should always be selected. A 

segment of transmission planning community makes this argument, called “right sizing” (Rivers 

2010). This is not the argument we make here. The efficacy of right-sizing a line depends on the 

evolution of the power system over the lifetime of the investment, the size of the lines 

considered, and the difficulty of adding new lines in a specific geographic region. For example, 

right-sizing may not be the most economic solution for an area that has low demand and stagnant 

load growth. Instead, the point of the example above is that models commonly assume a single 

time horizon and different answers can be easily obtained even in small problems when multiple 

time horizons are considered. In large systems with thousands of buses, considering multiple 

time horizons can alter the location of a new transmission investment and its size. 

C

10 year demand: 1,000 MW

25 year demand: 1,500 MW

Capacity: 1,500 MW Capacity: 400 MW

300 MW

A

B

Existing Line

Potential New Line

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6 

A second common temporal simplification in models is to consider few operational hours. 

Production cost modeling programs such as PROMOD, GE MAPS, GridView, and PLEXOS

traditionally include the full 8,760 hours in each year. However, including the full 8,760 hours in 

a year is too computationally demanding for planning models. As a result, a few select hours are 

modeled. In some cases, only a single peak hour is modeled. The logic behind this is intuitive: if 

a primary goal of transmission expansion planning is to meet demand at the lowest possible 

price, why not choose the most demanding hour? Simply put, overemphasizing demand and thus 

generation costs throughout the course of a year biases the system toward over-development. 

For example, consider Figure 2, which depicts the three-bus system now modified to show two 

different demand levels. The system has a peak load of 1,250 MW and an off-peak load of 500 

MW. If only the peak hour is considered, the lowest-cost option is to build the larger 1,500-MW 

line. This configuration and its cost calculations are given in Box 2; the cost of the system with 

different configurations is given in Table 2. This large line allows the full peak load of 1,250 

MW to be met using the lower cost plant at Bus B. However, if peak conditions are assumed to 

exist for 10% of the load hours and the remaining 90% are non-peak, now the lowest-cost option 

becomes building the smaller 750-MW line. The smaller line becomes a lower cost option 

because the demand can be met 90% of the year with the lower cost generator at Bus B. The 

more expensive plant at Bus C is required only during the remaining 10% of peak hours. 

Figure 2. Test system for hourly demand simplification

C

Peak demand: 1,250 MW

Off-peak demand: 500 MW

Capacity: 1,500 MW Capacity: 400 MW

A

B

Cost: $30 MWh Cost: $50 MWh

300 MW

Existing Line

Potential New Line

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7 

Table 2. Investment Costs and Capacities for Hourly Demand Simplifications

Line Cost 

($M)

Capacity 

(MW)

Peak Hour Only System 

Cost ($M)

Peak and Off-Peak System 

Cost ($M)

Line A-B 

Medium 5.0 750 347 157

Line A-B Large 7.25 1,500 336 158

The simple problem shown in Figure 2 also provides insight into one of the fundamental issues 

in transmission expansion planning. The annual generation costs listed in Table 2 are two orders 

of magnitude larger than the annualized transmission costs. This is not an artifact of the example 

selected. In existing power systems, transmission costs are typically less than 10% of the total 

system cost. As a result of this difference in costs, transmission expansion planning models often 

select more transmission lines to access lower cost generation than are constructed in reality

These modeled plans represent the most economic transmission expansion plans but do not 

account for institutional barriers such as siting or cost allocation. These institutional barriers can 

be partially incorporated into transmission expansion planning if an interactive process is used. 

For example, if a line selected by a planning model encounters an area with known siting issues, 

the line can be rerouted and the model rerun with the new capital cost, or it can be removed from 

the set of options that the model can select. 

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8 

Box 2. Cost Calculation Example for Temporal Simplification 2, Peak Hour Only

Total Cost Annual

Cost = Transmission cost + Operational cost

Cost = 5,000,000∙xmedium+7,250,000∙xlarge + generation_cost∙hours

Cost = 5,000,000∙xmedium+7,250,000∙xlarge + 8760(30∙genA+50∙genB)

Cost = 0+7,250,000 + 8,760(30∙1250 + 50∙0)

Demand

Demand(i)= generation(i) + non-served energy(i) + flow in(i) - flow out(i)

A: 1,250

= 

0 + 0 + 1,250 - 0

B: 0 = 1,250 + 0 + 0 - 1,250

C: 0 = 0 + 0 + 0 - 0

C

Output: 1,250 MW Output: 0 MW

A

B

Cost: $30 MWh Cost: $50 MWh

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9 

4 Uncertainty Simplifications 

Almost all transmission planning models consider specific scenarios with perfect knowledge. 

That is, the modeler assumes that all future demands, fuel prices, generator locations, and 

reliability issues are known. In reality, of course, there is very imperfect knowledge about the 

future. Natural disasters destroy infrastructure and cause major changes in fuel prices. 

Technological breakthroughs produce new generation types not known to today’s planners. To 

capture some of this uncertainty, planning models can try to produce transmission plans with low 

costs projected to a variety of different futures. 

Consider the three-bus example shown in Figure 3. In this iteration of the model, a new low-cost 

power plant may be constructed at Bus C, and three different investment options are presented by 

the planner (given in Table 3). The total system costs assuming each transmission and generation 

scenario are given in Table 4. If the planner had perfect foresight and knew that the plant would 

not be built, the lowest-cost investment option would be to build Line A-B and Line B-C. Note 

that because the system is networked, the most intuitive solution—building Line A-B only—is 

not the lowest-cost option in any scenario. Instead, building the additional line between Bus B 

and Bus C allows the lower cost power plant at Bus B to meet the entire load at a lower cost by 

sending power across the new lines and the existing line between Bus A and Bus C. On the other 

hand, if the planner had perfect foresight and knew that the new generator would be built, the 

lowest-cost option would be to build only the additional capacity between Bus A and Bus C. If 

the planner assumes that the generation is built and adds only Line A-B, but the generation 

developer pulls out, the system becomes very expensive—by nearly a factor of five more—to 

operate.

Figure 3. Test system for generation location uncertainty

C

Demand: 1,250 MW

A

B

?

Capacity: 1,500 MW Capacity: 400 MW

Cost: $30 MWh Cost: $50 MWh

Capacity: 300 MW

Cost: $5 MWh

300 MW

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10 

Table 3. Transmission Costs for Generation Uncertainty System

Cost ($M) Capacity (MW)

Line A-B 5.0 750

Line A-C 5.0 750

Line B-C 3.0 500

Based on the disparity among potential costs in the example above, it is clear that the objective is 

to find a plan that does well across a variety of possible futures, rather than one that performs 

well for a single scenario. In the example above, if there is a 50% probability that the generation 

will be developed, the transmission build-out with the highest expected value includes Line A-C 

and Line B-C. Expected value is the modeling term for weighted average, and it implicitly 

assumes that the decision maker is neutral. In the example here, if the probability of new 

generation increased to 60%, the expected cost for the Line A-C, B-C build-out would decrease 

from $248 million to $231 million, as shown in Table 5. 

Table 4. Generation Uncertainty System Costs Given Different Generation and Transmission 

Scenarios

System Costs New Generator ($M) No New Generator ($M) Expected Value ($M)

Line A-B 268 369 318

Line A-C 104 500 302

Lines A-B, B-C 161 336 248

Table 5. Calculation of Expected Cost for Generation Uncertainty System

New Generator No New Generator

Scenario Cost 

($M) * Probability of Scenario + Scenario Cost ($M) * Probability of Scenario = Expected Cost ($M)

161 * 0.5 + 336 * 0.5 = 248

161 * 0.6 + 336 * 0.4 = 231

With a risk-neutral decision metric, it does not matter how a transmission plan performs in 

individual scenarios as long as it performs well on average. A selected plan that has a riskneutral decision metric could perform very well under one scenario yet very poorly scenario 

under all other scenarios. Likewise, the plan could perform very well on average but very poorly

in a single scenario. Other decision metrics exist to differentiate between risk-averse and riskseeking plans, but expected value is the most common modeling metric. 

The simplifications thus far have been presented individually. In reality, however, the effects are 

not easily separable. The test system presented in Figure 4 considers two time periods and 

uncertainty regarding the construction of a new generator. The test system shown includes two 

existing generators, at costs of $30 MWh and $45 MWh, as well as two existing 400-MW 

capacity transmission lines. Three possible lines may be constructed: (1) a large line from Bus A 

to Bus B, (2) a medium line from Bus A to Bus B, or (3) a medium line from Bus A to Bus C. 

This example combines the effects of uncertainty and multi-period modeling. 

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11 

Figure 4. Test system combining uncertainty and multi-period modeling

A myopic view of the test system that considers only the first period would always select only 

the medium-size Line A-B. The medium-size line allows the demand at Bus A to be met at the 

lowest possible cost in the near term. However, this solution is blind to both the development of 

new generation and the growth in demand. If both time periods are considered and the planner 

knows that the new generation will not be built, the lowest-cost investment option is the largesize Line A-B. The large line allows the full demand at Bus A to be met with the cheaper 

generation available at Bus B across both horizons. However, if the planner considers both time 

periods and knows that the generation plant will be built, the lowest-cost transmission decision is 

to build the medium-size Line A-B during the first period and add Line B-C during the second 

period. 

Table 6. Transmission Characteristics for the Uncertainty and Multi-Period Modeling Test System

Cost ($M) Capacity (MW)

Line A-B Medium 5.0 750

Line A-C Large 7.5 1,500

Line B-C 5.0 750

Table 7. Minimum Cost of First-Period Transmission Investments

First-Period Transmission 

Investment

New Generation ($M) No New Generation ($M)

Line A-B Medium 363 411

Line B-C Large 366 400

In this example, the lowest-cost decision depends on whether or not the new generation will be 

built. Each point shown in Figure 5 represents the expected total cost for the test system shown 

in Figure 4 for different transmission investments when the probability of new generation varies 

from 0% to 100%. For example, when the probability of new generation is 10%, the expected 

C

10 year demand: 1,000 MW

25 year demand: 1,500 MW

A

B

?

Capacity: 1,500 MW Capacity: 1,500 MW

Cost: $30 MWh Cost: $45 MWh

Capacity: 500 MW

Cost: $5 MWh

400 MW

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12 

system cost with the medium line is $396 million, and the expected cost with the large line is 

$406 million. When the probability of new generation is 90%, the large line—which has an 

expected cost of $367 million—becomes a less-expensive option than the medium line, which 

has an expected cost of $369 million. As shown in Figure 5, building the medium line from Bus 

A to Bus B is the lowest-cost decision as long as the probability of developing new generation is 

less than 80%. Although not shown in this small example, using an expected value across 

scenarios may identify line combinations with average values in individual scenarios but with 

high expected values when considering multiple scenarios. Lines with average values may not be 

identified if only high value lines from scenario analyses are considered. From a planning 

perspective, there is some certainty about whether an existing generator will retire or a new 

generator will come online if construction has begun. This timescale, however, is mismatched to 

the transmission planning timescale—a new transmission line takes 5 to 10 years to plan and 

build, whereas a new wind plant may be permitted and constructed in less than 3 years. Thinking 

further into the future and considering the 40-year life span of a transmission investment, it is 

impossible for a planner to know how the future will evolve. As a result, the planning discussion 

returns to one of risk. In the example here, the risk of no new generation and constructing the 

wrong size line must be weighed against the potential economic benefits of developing new 

generation. 

Figure 5. Risk illustration for new generation uncertainty

350

360

370

380

390

400

410

420

Expected 

Cost $M

Probability of New Generation Construction

Large Line Medium Line

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13 

5 Externalities 

Thus far, the costs included in the transmission expansion planning process have not included the 

external costs imposed by the power system. External costs, such as land use impact and air 

pollution, are those that are not directly priced and may be imposed on unwilling or unknowing 

participants. These costs can greatly influence the lowest-cost transmission plan by accessing 

different generation resources and rerouting lines. 

The goal of an optimization-based transmission planning model is to plan the lowest-cost system. 

Given the large number of transmission lines under consideration, often transmission line costs 

are modeled using straight lines between buses. Modelers do not have sufficient geographic or 

political knowledge to route lines, and it can be untenable to try to route them individually when 

thousands of lines are being considered. As a result, plans from transmission expansion models 

underestimate transmission costs and may produce transmission routes going over mountain

peaks or through protected habitat. Correcting these may change the optimal decision set. 

In the test system shown in Figure 6, it has been discovered that a straight-line route must be 

modified to avoid using sensitive land. This test system contains two existing generators; two

existing 400-MW capacity lines; and two new investment options, one between Bus A and Bus C 

and one between Bus B and Bus C. Without rerouting, the lowest-cost solution was to build Line 

A-B and Line B-C. The solution assumed that a straight line could be drawn between all buses. 

However, in the example below, it has been discovered that the proposed line between Bus B and 

Bus C passes through a protected forest. To avoid using the sensitive area, the line must be 

rerouted. The additional cable, right-of-way, and installation required with the new route

increases the cost such that the lowest-cost solution becomes building only Line A-B, as shown 

in Table 8 and Table 9.

Figure 6. Rerouting externality test system

C

Demand: 1,250 MW

A

B

Capacity: 1,500 MW Capacity: 400 MW

Cost: $30 MWh Cost: $50 MWh

400 MW

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14 

Table 8. Transmission and Generation Costs with Rerouted Line B-C 

Rerouting Line B-C ($M)

Line A-B 377

Line A-C 337

Line A-B, B-C 378

Table 9. Transmission Cost Characteristics Before and After Rerouting Line B-C 

Cost ($M) Capacity (MW)

Line A-B 5.0 600

Line A-C 5.0 600

Line B-C (Straight Line) 3.0 300

Line B-C (Rerouted) 9.0 50

Another set of externalities that may affect the results of a transmission expansion planning 

model is that of generator pollutant emissions. These include local air pollutants such as NOX

and SOX as well as greenhouse gas emissions such as CO2. Although it should be reiterated that 

these pollutants are unlikely to be included in a model unless explicitly stated, there are two 

common ways to include them. The first method is to develop a cost for each type of pollutant. 

These costs may be set to mirror market costs for the specific pollutant or may be set to the 

“social cost” of the emissions. Social costs are intended to quantify all external impacts of the 

pollution on current and future generations. For example, CO2 could be priced at $50/ton; this 

type of pricing is often referred to as a carbon tax. In the second method, a cap is set for each 

pollutant type. For example, a system could be limited to emitting 1 million tons of CO2 per 

annum. Both the cap and pricing methods can be calibrated to produce the same generator 

dispatches and transmission plan results; however, it is difficult to compare the stringency of 

imposed cap and cost policies across models. Our goal here is not to debate which method—cap 

or price—is preferred, but to demonstrate the effect of emission externalities on transmission 

expansion planning. 

In the example below, there are two existing generators and two 300-MW capacity transmission 

lines. The two generators have been assigned generation costs and emissions rates. In the base 

case, in which no pollutant-externalities are considered, the most economic option is to build 

Line A-B; this line accesses cheaper generation from the plant at Bus B. However, if a $45 

emissions price is added, the effective price of the plant at Bus B raises from $30/MWh to 

$97.50/MWh. In this case, the plant at Bus C is now more economic because it has an effective 

price of $72.50/MWh. The most economic solution to meet demand with a $45/ton emissions 

price is to build Line A-C. As shown in this small example, the inclusion or exclusion of 

emissions prices has the ability to change the optimal transmission plan.

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
15 

Figure 7. Air pollution externality test system

Table 10. Transmission Characteristics for Air Pollution Externality Test System

Transmission 

Characteristics

Cost ($M) Capacity (MW)

Line A-B 5.0 750

Line B-C 5.0 750

A closer look at the example shows that there is a pollutant price at which both generators will 

have the same effective price. At $40/ton, both generators have an effective price of $70/MWh. 

If the pollutant price were set to $39.99/ton, the model would select Line A-B; however, if the 

pollutant price were set to $40.01, the model would select Line A-C. This type of “knife-edge” 

behavior, in which a minor change in input produces a dramatic change in output, is not unique 

to pollutant prices. Small changes in fuel prices, line costs, and other inputs can produce widely 

varying transmission plans. These abrupt changes are a result of the optimization algorithms 

underlying planning models. If the optimization algorithm finds a solution with a lower cost 

solution because of a small change in input, no matter how small, it will adopt the new solution.

This type of sensitivity is not revealed by a single model run, and without a sensitivity analysis

there can be a false sense of confidence in the answer provided by the model. A sensitivity 

analysis is the process of changing the model inputs, rerunning the model, and comparing the 

C

Demand: 1,000 MW

A

B

Capacity: 1,500 MW Capacity: 1,500 MW

Cost: $30 MWh

Emissions: 1.5 ton/MWh

Cost: $50 MWh

Emissions: 0.5 ton/MWh

300 MW

Existing Line

Potential New Line

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16 

change in outputs. If a model shows little sensitivity to varying input parameters, the solution 

found may be considered more robust. In our example problem above, if the generator at Bus B 

cost $75/MWh, building line A-C would be the lowest-cost solution regardless of the emission 

price or cap. A sensitive model is not a poorly formulated model and can provide stakeholders 

and decision makers with additional insight into the planning problem. On the other hand, 

depending on the results of the sensitivity analysis, a sensitive model may indicate that there are 

many good solutions, each with costs very near one another. A sensitivity analysis may also 

reveal the drivers of model behavior. One or two inputs, such as the cost of natural gas or the 

financial discount rate, may drive the results of planning models. Changing more than a single 

variable—for example, natural gas price and the financial discount rate—at a time reduces the 

number of model runs to be completed, but this type of sensitivity analysis does not provide 

insight into which variable is driving the change in results. Understanding these key drivers can 

help direct future studies and elucidate the major issues for stakeholders and decision makers. 

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17 

6 Further Technical Simplifications 

The test systems presented here vastly simplify the physics of the real transmission expansion 

planning problem. In each of the test systems, we assumed that flow was directable rather than 

using the direct-current approximation of the alternating-current load flow presented in Box 1. 

We also ignored reactive power, transformer costs, and reliability issues, such as N-1 

contingencies and stability issues. The type of modeling presented here provides very valuable 

insight into the value of future transmission investments; however, it is fundamentally ill-suited 

to identify near-term reliability and power quality issues. 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
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7 Conclusions 

Wide-area transmission investments need to be planned today to prepare for an uncertain future. 

Future natural gas prices will almost certainly fluctuate as a result of demand and supply 

variations, potential future liquefied natural gas terminals, and/or governmental regulation on 

shale gas. National carbon-emission policies may result in high penetrations of renewable 

energy. Potential transmission line routings may change with the discovery of cultural heritage 

sites. Given these uncertainties and the complexity of transmission expansion planning, models 

are needed to help inform and guide decision-making processes. Temporal, technical, 

uncertainty, and externality simplifications and assumptions are made in planning models to 

reduce an otherwise computationally intractable problem; however, as we have shown in the 

examples presented, the simplifications made in transmission expansion planning models can 

greatly affect the results. 

Because of modeling simplifications and because of the uncertainty in future power system 

development, no single model can capture or explore all aspects of the transmission expansion 

planning problem. The benefits of using transmission planning models do not result from 

considering a single solution, but rather by comparing sensitivities and trends across a variety of 

planning models and combining these results with broader contextual information.

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
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References

Garver, L.L. (1970). “Transmission Network Estimation Using Linear Programming.” IEEE 

Transactions on Power Apparatus and Systems PAS-89 (7) Sept.; pp. 1,688, 1,697. 

Stoel Rivers, LLC. (2010). “The Way Forward: Why Transmission Right Sizing and Federal 

Bridge Financing Hold the Key to Western Renewable Resource Development.” Portland, OR: 

September. Accessed April 2014: 

http://commerce.mt.gov/content/Energy/docs/TransmissionRightSizing.pdf. 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.