Merrill Energy, LLC
Options • Uncertainties • Attributes
Setting Standards or Criteria • Assessment • Generation Planning • Transmission Planning • Least-Cost Planning • Making Choices
Power system planning is the recurring process of studying and determining what facilities and procedures should be provided to satisfy and promote appropriate future demands for electricity. The electric power system as planned should meet or balance societal goals. These include availability of electricity to all potential users at the lowest possible cost, minimum environmental damage, high levels of safety and reliability, etc. Plans should be technically and financially feasible. Plans also should achieve the objectives of the entity doing the planning, including minimizing risk.
The electric power system is a force-at-a-distance energy-conversion system. It consists of three principal elements:
• Current- and voltage-producing, transmitting, and consuming hardware
• Control and protective devices
• Planning, operating, commercial, and regulatory practices and procedures
These definitions are very different from would have appeared on these pages 25 years ago. They no doubt will seem quaint 25 years hence. At this writing, the electric power industry worldwide is experiencing its most dramatic changes in two generations. These changes affect planning, but this section is intended as a practical exposition, not as a history lesson or a prophesy. We therefore will focus on how planning is or should be done today, avoiding flights of fantasy into the past or future (Sullivan, 1977; Kahn, 1988; Ringlee, 1989; Stoll et al., 1989).
Planning considers:
• Options
• Uncertainties
• Attributes
Options are the choices available to the planner. Uncertainties are parameters whose values are not known precisely or cannot be forecast without error. Attributes are measures of “goodness.” Stakeholder objectives are expressed in terms of attributes. Physical, economic, and institutional realities determine how different options and uncertainties affect the attributes.
The planning problem is to identify and choose among options, in the presence of uncertainties, so as to maximize or minimize (as the case may be) the attributes.
Planners generally are trained as engineers, economists, civil servants, businessmen, or mathematicians. They do power system planning for the following entities:
• Vertically integrated utilities owning generation, transmission, and distribution systems.
• Transmission companies, independent system operators (ISO), and regional transmission organizations (RTO). Transmission companies own transmission assets; the latter do not, but may have some responsibility for their planning.
• Pools or combinations of vertically integrated utilities.
Other organizations do planning studies and higher-level power sector planning. A step removed from the operation and management of the power system, their interest is in seeing that it meets society’s goals:
• Various levels of government
• International development banks
Still other organizations do power system planning studies, but without system responsibility. They wish to understand the market for various services and how they might compete in it—its economics and technical requirements for entry.
• Independent power producers (IPP) or nonutility generators (NUG). These include qualifying facilities (QF as defined by the U.S. Public Utilities Regulatory Policy Act of 1978) and exempt wholesale generators (EWG as defined by the U.S. Energy Policy Act of 1992). These are subject to less stringent regulation than are utilities. They neither enjoy monopoly protection nor have an obligation to provide electricity at cost-based tariffs.
• Large industrial users.
• Commercial middlemen who buy and sell electrical energy services.
• Investors.
All of these are supported by independent purveyors of planning information. Consultants with specialized analytic skills also do planning studies.
Planning is done in several arenas, distinguished by the planning horizon and by the types of options under consideration. These arenas include
• Long-term vs. short-term planning. Economists distinguish these by whether capital investment options are considered. For engineers, long-term planning has a distant horizon (perhaps 30 years for generation and half of that for transmission). Short-term planning considers about 5 years. Operations planning is for as short as a few hours and is not treated here.
• Generation vs. transmission vs. least-cost planning. Generation and transmission planning focus on supply options. Least-cost planning includes demand-side options for limiting or shaping load.
• Products and services. Some entities provide power (kW) and energy (kWh). Others plan the transmission system. Others provide for auxiliary services (voltage and power control, electrical reserves, etc.). Still others plan for diversified services like conservation and load management.
Other arenas require engineering and economic skills, but are within the purview of a book on business or policy rather than an engineering handbook.
• Competitive markets. Strategic planning is particularly concerned with financial and business plans in competitive markets.
• Sector evolution. Defining the form of the future power sector, including the relationships between competitive forces, regulation, and the broadest social objectives, is a particularly vital planning function.
Power generation, transformer, transmission system, substation, protection, and operation and control options are discussed in other chapters of this handbook. Other options are discussed below.
18.3.1.1 Planning and Operating Standards or Criteria
Planning and operating criteria have a dual nature: they are both attributes and options. Here we will emphasize the fact that they are options, subject to change. Though they have no intrinsic value, standards or criteria are important for several reasons. Their consistent application allows independent systems to interconnect electrically in symmetrical relationships that benefit all. Criteria can also eliminate the need for planners to ask constantly, “How much reliability, controllability, etc. do I need to provide?” Criteria include
• Maximum acceptable loss-of-load probability (LOLP) or expected unserved demand, minimum required reserve margins, and similar generation planning standards
• What constitutes a single contingency (transmission systems are often designed to withstand “any” single contingency) and whether particular single contingencies are excluded because they are unlikely or expensive to forestall
• Permissible operating ranges (voltages, power flows, frequency, etc.) in the normal or preventative state, the emergency state, and the restorative state
• How criteria are to be measured or applied
Most power systems in industrialized nations are designed and operated so that
1. With all elements in service, power flows, voltages, and other parameters are within normal ranges of the equipment
2. The system remains stable after any single contingency
3. Power flows, voltages, and other operating parameters are within emergency ranges following any single contingency
For financial and economic reasons, developing countries choose weaker criteria.
18.3.1.2 Demand Management
Demand-side planning often is tied to generation planning because it affects the power and energy that the power plants will need to provide. There is no perfect classification scheme for demand-side options. Some overlapping classifications are
• Indirect load control vs. direct load control by the bulk system operator
• Power (kW) or energy (kWh) modification or both
• Type of end-use targeted
Table 18.1 shows the type of load under direct utility control in the U.S. early in the 1980s, when enthusiasm for demand-side options was especially high.
One of the most effective examples of load control was reported by a German utility. Typical off-peak winter demand was less than 70% of the peak for the same day. An indirect program promoted storage space heaters that use electricity at night, when demand is low, to heat ceramic bricks. During the day, air forced among the bricks transfers the heat to the living space. Within 5 years the program was so popular that direct control was added to avoid creating nighttime peaks. The winter daily load shape became practically flat.
18.3.1.3 Market and Strategic Options
Market and strategic options are also important. These range from buying a block of power from a neighboring utility to commodity trading in electricity futures to mergers, divestitures, and acquisitions.
TABLE 18.1 Appliances and Sectors under Direct Utility Control, United States—1983
Appliance or Sector |
Number Controlled |
Percent of Total Controlled |
Electric water heaters |
648,437 |
43 |
Air conditioners |
515,252 |
34 |
Irrigation pumps |
14,261 |
1 |
Space heating |
50,238 |
3 |
Swimming pool pumps |
258,993 |
17 |
Other |
13,710 |
1 |
Total |
1,500,891 |
100 |
Residential |
1,456,212 |
97 |
Commercial |
29,830 |
2 |
Industrial |
588 |
– |
Agricultural |
14,261 |
1 |
Source: U.S. Congress, New Electric Power Technologies: Problems and Prospects for the 1990s, OTA-E-246, Office of Technology Assessment, Washington, DC, July 1985.
Uncertainty can seldom be eliminated. Planning and forecasting are linked so that even if the forecasts are wrong, the plans are right (Bjorklund, 1987).
18.3.2.1 Models of Uncertainty (Schweppe, 1973)
Probabilistic models, where different outcomes are associated with different probabilities, are valid if the probability structure is known. The events involved must occur often enough for the law of large numbers to apply, or else the probabilities will have little relationship to the frequencies of the outcomes. Generation planners have excellent probabilistic reliability models. (Generation and transmission reliability evaluation are treated in more detail in a separate section.)
Unknown-but-bounded (set theoretic) models are used when one or both of the conditions above are not met. For instance, transmission planners design to withstand any of a set of single contingencies, usually without measuring them probabilistically.
18.3.2.2 Demand Growth
Planners forecast the use of energy (MWh) for a period (e.g., a year) first. They divide this by the hours in the period to calculate average demand, and divide again by the projected load factor (average MW demand/peak MW demand) to forecast peak demand. Three techniques are used most often to forecast energy.
Extrapolation—Exponential growth (e.g., 4% per year) appears as a straight line on semi-log paper. Planners plot past loads on semi-log paper and use a straight edge to extrapolate to the future.
Econometric models—Econometric models quantify relationships between such parameters as economic activity and population and use of electricity. The simplest models are linear or log-linear:
(18.1) |
where
Di is the demand or log(demand) in period i
Pi is the population or log(population) in period i
GDPi is the gross domestic product or log(gross domestic product) or some measure of local economic activity
k1, k2, k3, etc. are coefficients
Econometric models are developed in a trial-and-error process. Variants of Equation 18.1 are hypoth-esized and least squares (regression) analysis is used to find values of coefficients that make Equation 18.1 fit historical data. Econometric models are used by first forecasting population, economic activity, etc. and from them calculating future energy demand using Equation 18.1.
End-use models—First, the number of households is forecast. Then the per-household penetration of various appliances is projected. The average kWh used by each appliance is estimated and is multiplied by the two previous numbers. The results are summed over all types of appliances.
Performance—Extrapolation became suspect after U.S. load forecasts in the 1970s were consistently too high. Econometric modeling is more work but is more satisfying. End-use modeling requires considerable effort but gives the most accurate forecasts of residential load.
Real drivers—One fundamental driver for per-capita load growth is the replacement by electricity of other forms of energy use. The second is the creation of new uses of energy that are uniquely satisfied by electricity.
During the decades when U.S. electric demand grew at over 7% per year, the demand for all forms of energy (of which electricity is a part) grew at about 2% per year. This obviously could not continue: the two cannot cross. The growth of electricity demand began to drop off about 1955, declining noticeably in the 1970s and thereafter. The drop in load growth was attributed to the oil crises of the 1970s. Post-1973 conservation played a part, but by then electricity had captured about all the market share it was going to get by replacement and creation of new demands for energy.
In developing countries, both fundamental drivers are limited by the ability of the electric companies to finance the necessary generation and distribution infrastructure, which is very expensive. Demand is also limited by their ability to generate. In industrialized countries, availability of capital and power plant performance are not constraining. In all countries, elasticity reduces demand if electricity is costly. This effect is much stronger in countries with low per-capita income and for energy-intensive industrial load.
18.3.2.3 Fuel and Water
In the near term, strikes, weather, and natural disasters can interrupt production or delivery. Fuel inventories and the ability to redispatch provide good hedges. In the intermediate term, government action can make fuel available or unavailable. For instance, in 1978, the U.S. Congress forbade burning natural gas by utilities, perceiving that there was a shortage. The shortage became a glut once the U.S. natural gas market was deregulated. In the long term, any single source of fuel is finite and will run out. British coal, which had fueled the industrial revolution, was shut down in the 1990s because it had been worked out.
The more important fuel uncertainties, however, are in price. For instance, Figure 18.1 shows that the price of crude oil doubled in 1974 and again in 1979. Recognizing the high variability, in 1983 the U.S. Department of Energy forecast a fuzzy band instead of a single trajectory (U.S. Dept of Energy, 1983a).
FIGURE 18.1 World oil price projections, 1983.
It is interesting that within a year of the publication of this projection, the price of oil had dropped below the low limit of the band, and it has remained there until this writing. Planners must consider extreme possibilities for all uncertainties.
Brazil, Norway, the Pacific Northwest, Quebec, and a number of developing countries are highly dependent on hydropower. Systems usually are planned and operated so that there will not be a shortfall unless one of the worst hydrological years in recorded history recurs.
18.3.2.4 Construction
Three major construction uncertainties are: How long will it take to build? How much will it cost? Will the project be completed?
A World Bank study of 41 hydro projects revealed that 37% experienced a schedule slip of 30% or more, including 17% with schedule slips of 60%–100% (Crousillat, 1989).
Figure 18.2 shows the range of actual vs. budgeted cost for a number of World Bank-financed projects. The distribution is not symmetrical—overruns are much more frequent than under-budget projects. Some of the worst cases in Figure 18.2 data occurred during periods of unexpected high inflation (Crousillat, 1989). A 1983 report projected that the cost of some 40 U.S. nuclear plants scheduled for completion by 1990 would be close to normally distributed, with the least expensive costing a bit under $2000/kW and the most expensive three times higher, at $6000/kW (U.S. Dept of Energy, 1983b).
Possibly the most expensive nuclear plant ever built, the Shoreham Plant on Long Island, was completed at a cost of some U.S. $16 billion. It was shut down by the state before producing a single kWh of commercial energy.
18.3.2.5 Technology
New technologies are generally less certain than mature technologies in their cost, construction time, and performance.
Even mature technologies may have important uncertainties. For example, transmission transfer capability is an important measure of transmission system capability. It is usually expressed as a single number, but it is actually a time-varying random variable.
18.3.2.6 Demand Management
Demand management programs are risky, in part because of uncertainty in the public’s response to them. The two major uncertainties are
• What fraction of eligible customers will respond to a particular program?
• How much will the average customer change his use of electricity?
FIGURE 18.2 Budget vs. actual costs, power projects in developing countries.
These uncertainties are affected strongly by the design of the program, the incentives offered, how it is marketed, etc. Carrying out a carefully designed pilot program can reduce the uncertainty. The pilot program should be done in the region of the future commercial program.
18.3.2.7 Markets and Capital Recovery
For many years, vertically integrated utilities were guaranteed the recovery of all costs, including capital invested, plus a modest but sure profit. The customer paid this and absorbed the market uncertainties. At this writing, the regulated monopoly, cost-recovery market is being replaced in many states and countries by a more competitive market. Some market risks are being transferred from customers to utilities, power marketers, generating companies, speculators, and others.
This creates new uncertainties. For example, in competitive generation markets it is not known which potential generating units will be built. This affects both transmission and generation planning.
18.3.2.8 Regulation
For the foreseeable future, government will play a key role. The uncertainty in what governments will do propagates into uncertainties in profitability of various players, in market entry, in prices, etc.
For example, in the 1980s, U.S. state and federal governments encouraged utilities to implement demand-side programs. Program costs, and in some cases costs of foregone sales, were recovered through tariffs. The government interest later switched to competitive markets. These markets do not have such a convenient mechanism for encouraging demand-side management. As a result, demand-side programs became less attractive.
18.3.2.9 Severe Events
High-risk, low-probability events usually are not considered by standard planning practices. For example, transmission planners design so that the system will withstand any single contingency. Planning procedures, criteria, and methods generally ignore several simultaneous or near-simultaneous contingencies. The power system is not designed to withstand them—whether or not it does is happenstance.
In January 1998 an ice storm of unprecedented magnitude struck the northeastern United States and Quebec. Ice on transmission lines greatly exceeded design standards. Many towers collapsed. All lines feeding Montreal, and all lines south and east of the city, were on the ground. The government later announced a high-risk, low-probability standard: the system should be designed and operated to prevent loss of more than half of the Montreal load should such an event recur.
Attributes measure “goodness” in different ways, from different perspectives. Each stakeholder has objectives; they are expressed in terms of attributes.
Customers of various kinds (residential, commercial, industrial, etc.):
• Cost of electricity
• Other costs absorbed by the customer
• Quality of service (reliability, voltage control, etc.)
Investors in various providers of energy and services
• New capital required
• Net income, earnings per share, and other measures of income
• Cash flow, coverage ratios, and other measures of cash use and replacement
FIGURE 18.3 Options, uncertainties, and attributes.
Employees
• Security
• Promotion opportunities
• Salaries
• Healthiness and safety of working conditions
Taxpayers
• Tax revenues
• Expenditures from public funds
Neighbors (environmentalists, visitors, local inhabitants, competitors, etc.)
• Emissions or thermal discharges
• Community disruption
• Employment opportunities
• Rights-of-way and other intrusions
• Flooding
• Measures of market power
The list of attributes given above is not complete, and different attributes are important for different studies. Deciding on the planning objectives and the attributes for a given study is an important initial step in power system planning.
Some attributes are measured using complex computer models. For others, approximate or ad hoc models may be adequate or may be the best that is available. The planner calculates how the options and the uncertainties (Figure 18.3) affect the attributes.
Standards or criteria are surrogates for some attributes that are difficult or impossible to compute.
18.4.1 Setting Standards or Criteria
Planning objectives often conflict. For example, maximizing reliability and minimizing environmental impacts generally conflict with minimizing costs.
Since all attributes cannot be measured in dollars, achieving the right trade-off can be a difficult socio-technico-economic-institutional problem. Doing this every day would burden the planning process. Having standards avoids having to revisit such judgments continually. For instance, once it is decided that (say) 20% generation reserve provides adequate reliability at an acceptable cost, the planner accepts 20% as a standard and designs to meet it. Testing whether a particular plan meets the reserve criterion is easy; the planner can concentrate on other issues.
Standards should be examined from time to time. If society becomes poorer or richer, its pocketbook may speak for lower or higher standards of service. Changes in technology may justify a change in standards—for instance, development of better scrubbers may make it reasonable to insist on reduced SO2 or NOx emissions. Increased reliance on electricity may require more reliability: a proposal to shut off the power throughout the United States for 1 min to salute Edison’s death was quashed. Had he died in 1900 instead of 1931, it might have been practical.
18.4.2.1 Forecasts and Projections
Not all uncertainties create risk for every planning study. Those that do for a particular study are identified. Forecasts and projections are developed for these uncertainties.
18.4.2.2 System State
The state assessment begins with an evaluation of the technical and economic attributes of the present and future power system. Does it and will it satisfy established technical standards? Is it economical? Does it meet other objectives?
Chapter 8 of this handbook, “Power System Analysis and Simulation,” describes the analytical tools available to planners. It also describes how these tools are used. The phenomena analyzed are described in Chapters 10 through 12.
Chapter 2 of this handbook, “Electric Power Generation: Conventional Methods,” describes generation planning options and their characteristics. The generation planner does a preliminary selection from among them, recognizing any special features of his planning problem.
Planners measure how the various options would alleviate deficiencies discovered in the assessment step. The effects of various options or combinations of options and the effects of uncertainties on other attributes are also measured.
In particular, planners compute reserve margin or other measures of reliability. They simulate the operation of the system to measure operating cost and to determine if the operation is within acceptable ranges of other parameters.
Traditional transmission options and new technologies are described in Chapters 3, 4, 11, 15, and 16 of this handbook. Like the generation planner, the transmission planner makes a preliminary selection based on the needs and development pattern of his system.
For instance, for technical and commercial reasons, a given system will use only a few distinct voltage classes. So a system whose existing transmission consists of 138, 345, and 765 kV equipment will rarely add new circuits at 230 or 400 kV, even though these may be popular elsewhere.
Transmission planners then identify a set of specific options and measure how these options in various combinations, along with the important uncertainties, affect the attributes. Load flow, short circuit, and stability analyses are performed to determine if voltages and currents are within acceptable bounds under various system states, and if the system will remain stable for all contingencies. How often and how much the operation of the generation system will be constrained by transmission limitations is an important consideration.
Least-cost planning is also known as integrated resource planning or integrated demand/supply planning. It considers supply-side options (generally generation options) on a level playing field with demand-side options (generally conservation, indirect load shifting, or direct load control). These options include incentives to encourage utilities and consumers to change energy consumption patterns.
As with generation planning and transmission planning, a preliminary selection weeds out options that are clearly not of interest in a particular area.
The least-cost planning process includes computing values of key attributes for various options and uncertainties.
A key question in generation, transmission, and least-cost planning is: How is one plan selected over another? A few distinctive approaches will be described.
18.4.6.1 Minimize Revenue Requirements
The planner selects the best option from the ratepayer’s perspective. He selects the plan that will minimize the ratepayer’s cost of electricity while satisfying reliability, environmental, and other criteria.
The ratepayer’s cost—an attribute—is the revenue that the utility will have to collect to recover all operating and capital costs and to earn a commission-approved return on unrecovered investor capital:
(18.2) |
where
RRi(O, U) is the revenue requirements in period i
FCi(O, U) is the fixed costs in period i
VCi(O, U) is the variable costs in period i
O is the selection of the various options
U is the realizations or values of the various uncertainties
Fixed costs are independent of how much or how little a piece of equipment is used. Depreciation (recovery of investors’ capital), interest on debt, and profit (return on unrecovered capital) are typical fixed costs.
Variable costs—fuel cost—for example, are related to how much a piece of equipment is used. These costs include all system costs, not just the cost of the individual option. For instance, old plants may run less when a new plant is built. The variable cost includes fuel cost for all plants.
To apply this traditional method, the planner must know his company’s return rate, which is set by the regulator. In a closely related method, the market defines the cost of electricity and Equation 18.2 is solved for the internal rate of return (IRR). The option selected is the one that maximizes the IRR, the investor’s profit.
18.4.6.2 Cost-Benefit Analysis
If the benefits exceed the costs, a project is worth doing.
Typically, costs are incurred first, and benefits come later. A dollar of benefit later is not worth the same as a dollar of cost today. Present worth analysis is a way to compare dollars at different times. The basic equation is
(18.3) |
In Equation 18.3, P is the present worth or equivalent value today of an amount S, n years in the future, with i the discount rate or annual cost of capital.
Cost-benefit analysis is also used to rank mutually exclusive projects—the one with the highest benefit/cost ratio wins.
18.4.6.3 Multi-Objective Decision analysis
18.4.6.3.1 Utility Function Methods
Table 18.2 compares two options for a new power plant in Utah (Keeney et al., 1981). Which choice is better? The attributes are combined in a utility function of the form:
(18.4) |
TABLE 18.2 Attributes: Nuclear Plant vs. Coal Plant
Wellington Coal Plant |
Green River Nuclear Plant |
|
Economics ($/MWh) |
60.7 |
47.4 |
Environment (corridor-miles) |
532.6 |
500.8 |
Public disbenefits ($ × 000,000) |
15.0 |
22.6 |
Tax revenues ($ × 000,000/year) |
3.5 |
1.0 |
Health lost (equivalent years) |
446.7 |
6.3 |
Public attitudes |
0.33 |
−1.0 |
Feasibility |
60.0 |
37.0 |
Source: Keeney, R.L. et al., Decision Framework for Technology Choice, Report EA-2153, Electric Power Research Institute, Palo Alto, CA, 1981. With permission.
In Equation 18.4, x takes on one of two values, “coal” or “nuclear.” (The actual functional form for a particular study may be more complicated than Equation 18.4.) The coefficients ki reflect the relative importance of each attribute. These coefficients convert the different attributes to a common measure. The choice that minimizes the utility function wins. In this study, for the values of coefficients selected U(coal) was $131.4/MWh; U(nuclear) was $162.9/MWh.
This approach has many variants. Uncertainties can be included, making U(x) a random variable. Work has been done to develop methods for determining the decision-maker’s values (the coefficients) and risk tolerance.
18.4.6.3.2 Trade-Off Analysis
Trade-off analysis measures each attribute in its natural units, without reducing them all to a common measure, and seeks reasonable compromises at points of saturation or diminishing return. A good compromise will not necessarily optimize any of the attributes, but will come close to optimizing all of them.
For example, Figure 18.4 shows 22 plans examined in an energy strategy study. The plans in region A minimize SO2 emissions, but are very costly. The plans in region B are cheap but have high emissions. The plans at the knee of the trade-off curve are at the point of diminishing returns for one attribute against the other. Significant reductions in emissions can be had at little cost by moving from B to the knee. Going beyond the knee toward A will not reduce SO2 much more but will increase the cost significantly. The plans at the knee come close to minimizing both cost and emissions.
Trade-off analysis can be done graphically for two-attribute problems. More than two attributes cannot be graphed easily but can be analyzed mathematically (Crousillat et al., 1993).
FIGURE 18.4 Trade-off: cost vs. SO2 emissions.
18.4.6.4 Risk
Risk is the hazard due to uncertainty. Risk is also associated with decisions. Without uncertainties and alternatives, there is no risk.
System planning, engineering, and operating procedures have evolved to reduce the risks of widespread or local service interruptions. Another section of this handbook describes methods for modeling and enhancing reliability.
Not all risks are included in reliability analysis, however. Much talk about risk is directed to financial risks. Other important risks are not quantified in dollars.
One measure of risk is robustness, the likelihood that a particular decision will not be regretted. Exposure is the possible loss (in terms of an attribute) under adverse realizations of uncertainties. Regret is the difference between the value of an attribute for a particular set of decisions and realizations of uncertainties, and the value of the attribute for optimized decisions with perfect foreknowledge of the uncertainties.
Planners develop hedges, options that increase robustness or decrease exposure or regret. Building small generating units instead of large ones is an example; an insurance policy is another (De la Torre et al., 1999).
Bjorklund, G.J., Planning for uncertainty at an electric utility, Public Utilities Fortnightly, Oct. 15, 1987.
Crousillat, E., Incorporating Risk and Uncertainty in Power System Planning, I&ED Energy Series paper # 17, The World Bank, Washington, DC, 1989.
Crousillat, E.O., Dörfner, P., Alvarado, P., Merrill, H.M., Conflicting objectives and risk in power system planning, IEEE Trans. Power Syst., 8(3), 887–893, Aug. 1993.
De la Torre, T., Feltes, J.W., Gómez, T., and Merrill, H.M., Deregulation, privatization, and competition: Transmission planning under uncertainty, IEEE Trans. Power Syst., 14(2), 460–465, May 1999.
Kahn, E., Electric Utility Planning & Regulation, American Council for an Energy-Efficient Economy, Washington, D.C., 1988.
Keeney, R.L., Beley, J.R., Fleischauer, P., Kirkwood, C.W., Sicherman, A., Decision Framework for Technology Choice, Report EA-2153, Electric Power Research Institute, Palo Alto, CA, 1981.
Ringlee, R.J., Ed., Special section on electric utility systems planning, Proc. IEEE, 77(6), June 1989.
Schweppe, F.C., Uncertain Dynamic Systems, Prentice-Hall, Englewood Cliffs, NJ, 1973, chap. 3.
Stoll, H.G., Garver, L.J. (sic), Jordan, G.A., Price, W.H., Sigley, R.F., Jr., Szczepanski, R.S., Tice, J.B., Least-Cost Electric Utility Planning, John Wiley & Sons, New York, 1989.
Sullivan, R.L., Power System Planning, McGraw-Hill, New York, 1977.
U.S. Dept of Energy, Energy Projections to the Year 2010, Report DOE/PE-0029/2, Office of Policy, Planning and Analysis, Washington, DC, Oct. 1983a.
U.S. Dept of Energy, The Future of Electric Power in America: Economic Supply for Economic Growth, Report DOE/PE-0045, Office of Policy, Planning and Analysis, Washington, DC, June 1983b.
U.S. Congress, New Electric Power Technologies: Problems and Prospects for the 1990s, OTA-E-246, Office of Technology Assessment, Washington, DC, July 1985.