Notes

1 The authors would like to acknowledge the contribution of Joseph Mulholland, Office of Energy Efficiency, U.S. Department of Energy, for his engineering and computational analysis of electricity imports.

2 See Federal Energy Regulatory Commission, Docket Nos. RM95-8-000, RM94-7-001, RM95-9-000, and RM96-11-000 (April 24, 1996).

3 The model used is the PowerWorld simulator, jointly developed by several universities led by the University of Illinois.

4 It should be noted that control of natural gas pipelines has become an increasingly challenging task as a result of the restructuring of the natural gas industry.

5 For a description of ancillary services, see Electric Power Research Institute, Transmission Service Costing Framework, Volume 2: Framework Description and Application, EPRI TR-105121-V2 (Palo Alto, CA, April 1995).

6 As noted in the discussion that follows below, the most important characteristic of alternating current is the fact that voltage can vary across the network.

7 For example, a typical transportation problem is as follows: Suppose there are two ways to get commodity Z from point A to point E. One way goes through points B and C and the second goes through point D. The typical problem is to find the least-cost (or quickest) route from A to E. As noted below, the typical transportation algorithm and computer software used to analyze such a transportation problem cannot be used for electricity. Additionally, in a perfectly competitive world, according to the traditional transportation model, the price of good Z at location E cannot exceed the incremental cost of producing good Z plus the cost of transporting it from location A to location E. In electricity networks, however, such relationships may not be true. See W.W. Hogan, “Contract Networks for Electric Power Transmission,” Journal of Regulatory Economics (1992), pp. 211-242.

8 See F.C. Schweppe, M.C. Caramanis, R.D.Tabors, and R.E. Bohn, Spot Pricing of Electricity (Boston, MA: Kluwer Academic Publishers, 1988).

9 Voltage and power are related according to the following equation: P = V × I, where P is power measured in watts, V is voltage measured in volts, and I is current measured in amperes. Voltage is a measure of force, and current is a measure of the rate of flow of the electrons through a wire.

10 See F.C. Schweppe, M.C. Caramanis, R.D.Tabors, and R.E. Bohn, Spot Pricing of Electricity (Boston, MA: Kluwer Academic Publishers, 1988); and S. Herman, Delmar’s Standard Textbook of Electricity (Albany, NY: Delmar Publishing Company, 1995).

11 In general, the amount of reactive power produced by a generator can be altered without affecting fuel costs or operating efficiency. This is done by changing the strength of the magnetic field in the rotor of the generator. See, for example, S. Herman, Delmar’s Standard Textbook of Electricity (Albany, NY: Delmar Publishing Company, 1995), p. 822 and pp. 408-409. In some cases, however, the production of reactive and real power are not independent. In such cases, changing the amount of reactive power would indirectly affect fuel costs, etc.

12 Two products that are jointly produced from the same process are called joint products. Mutton and wool, jointly produced by raising sheep, are a good example of joint products. In the energy area, motor gasoline and jet fuel is another example of a joint product, since both are produced from crude oil.

13 An issue of some importance in many restructuring proposals is the treatment of the units that must operate for reasons such as voltage control. In both the United Kingdom and the United States, plants that are always “must run units” (i.e., nuclear and large hydroelectric power plants) do not participate in competitive bidding schemes. An owner would prefer to have a plant declared “must run” by the regulatory authorities because it eliminates all the uncertainties of the bidding processes. Additionally, there is the issue of the pricing of power from units whose bid is not accepted because the bids are too high, but that must still operate because of voltage control or other factors. In the United Kingdom, the owners of such units receive their bids. If they could correctly guess when a unit must be operated—regardless of the bid price—for the purpose of voltage control, they would bid very high prices.

14 In some cases, the State public utility commissions allocated some of the distribution-related capital costs (e.g., special transformers or capacitors for large industrial customers) to the customers receiving the benefits; however, all the costs associated with long-distance transmission tended to be allocated equally to all consumers.

15 According to conventional wisdom, problems with siting arise because of population growth and environmental/health concerns about long-distance transmission lines. For counter arguments see, for example, J.D. Finney, H.A. Othman, and W.L. Rutz, “Evaluating Transmission Congestion Constraints in System Planning,” IEEE Transactions on Power Systems, Vol. 12, No. 3 (August 1997), pp. 1143-1151; J. Rajaraman and F. Alvarado, “Determination of Location and Amount of Compensation To Increase Power Transfer Capability,” IEEE Transactions on Power Systems, Vol. 13, No. 2 (May 1998), pp. 294-301; and, T.L. Le and M. Negnevitsky, “Network Equivalents and Expert System Application for Voltage and Var Control in Large-Scale Power Systems,” IEEE Transactions on Power Systems, Vol. 12, No. 4 (November 1997), pp. 1440-1455.

16 See F.C. Schweppe, M.C. Caramanis, R.D.Tabors, and R.E. Bohn, Spot Pricing of Electricity (Boston, MA: Kluwer Academic Publishers, 1988).

17 Congestion occurs when a line is overloaded. When this occurs, there will be a different flow of power that increases line losses that in turn changes the dispatching of all the generating units. The congestion costs are the resulting increases in production costs.

18 This paper does not examine the pricing of reactive power and voltage control, which generally are regarded as ancillary services. It must be noted that there has been very little discussion of exactly how ancillary services will be priced and how (or if) their capital costs will be recovered.

19 An accessible reference to PowerWorld is PowerWorld Simulator Version 4.1 (Urbana, IL: PowerWorld Corporation, October 1997).

20 Because these units are not economically dispatched, costs are not relevant; therefore, an arbitrary cost of 1 cent per kilowatthour was used.

21 A bus is any node or connection point in a transmission network where electrical devices come together.

22 The optimal economic equilibrium is to assign generation and demands that maximize net social benefit consistent with a feasible power flow. Net social benefit is benefit less cost. Benefit is taken as the area under the demand curve (consumers’ surplus), and cost is usually just the sum of generation costs. Because of the lack of location-specific price and quantity data, the requisite demand curve estimates do not exist. It is not possible to calculate this solution for NEPOOL. See J. Weber, T. Overbye, and C. DeMarco, “Inclusion of Price Dependent Load Models in the Optimal Power Flow,” accepted for presentation at the 1998 Hawaii International Conference on System Sciences (1998).

23 The two DC lines are represented as a single generator located at their junction with the NEPOOL grid. The imports were generally set to 1,500 megawatts, corresponding to the imports reported on FERC Form 715.

24 The data can be obtained from James Hewlett (202-586-9536 or e-mail at jhewlett@eia.doe.gov).

25 Variable operations and maintenance (O&M) costs may be added to the model at a later date.

26 See, for example, W. Hogan, “Contract Networks for Electric Power Transmission,” Journal of Regulatory Economics, Vol. 4 (1992), pp. 211-242.

27 It was assumed that all the power was replaced with imports from Canada. The interconnection between Canada and the NEPOOL is located in northern New England. Similar results were obtained when the capacity of various fossil fuel units in northern New England was increased.

28 The data shown in Table 1 include loads with negative amounts of real power. Using these data, the power factor would be about 0.75. The power factor cited here (0.88) excludes the negative loads. When the loads with negative amounts of real power are excluded, the total amount of real power increases from 17,093 to 18,125 megawatts. Apparent power equals the square root of the squared amount of real and reactive power. Thus, when all the loads with negative amounts of real power are excluded, the total amount of apparent power decreases from 22,913 to 20,629 megawatts.

29 Some initial analysis of the 1997 FERC Form 715 data suggests that the short-term replacement capacity was obtained from old “mothballed” units and cogeneration facilities located in southern New England. Voltage control was probably one reason why that was done. Additionally, Commonwealth Edison recently announced the retirement of Zion (two 1,100-megawatt nuclear power units in Illinois). There is some discussion about using one of the “retired” units to produce reactive power for voltage control.

30 Additionally, since these are short-run marginal costs, they do not include some generating costs that are fixed in the very short run but are variable over longer periods of time. Examples of such costs include variable nonfuel operating and maintenance costs and some overhead expenses. See Energy Information Administration, Electricity Prices in a Competitive Environment, DOE/EIA-0614 (Washington, DC, August 1977), Chapter 3.

31 The two outliers appear to be the result of errors in the FERC Form 715 data. PowerWorld computes the marginal generation costs by “backing out” the line losses. The marginal line losses can be negative when a small increase in demand at one bus causes network-wide changes in generation and line flows that in turn result in fewer line losses. See F.C. Schweppe et al., op. cit., for more details.

32 Note that the estimated marginal line losses are only slightly greater (in absolute terms) than the average line losses of about 1.5 percent (see Table 1).

33 Connecticut Yankee was permanently retired in 1996.

34 Actually, in PowerWorld, there is no overall constraint stating that generation must equal demand. Instead, there are a series of constraints stating that at every bus the sum of inflows of power and generation must equal the sum of the outflows plus consumption.

35 The cost data reported on FERC Form 1 are generally available only at the plant level. In a number of cases, units at the same site use different fuels. When the FERC Form 1 data showed the use of oil and natural gas, it was assumed that all units used natural gas.

36 In reality, nuclear units generally are not cycled. They are, however, taken out of service for refueling during off-peak periods.

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An Exploration of Network Modeling: The Case of NEPOOL