An Exploration of Network Modeling: The Case of NEPOOL

This paper presents some preliminary results of an ongoing analysis of electricity transmission issues.¹ The overall objective of the project is to examine how the physical, technical, and institutional arrangements for the electric transmission network affect electricity markets. The analysis was undertaken because transmission services are being opened up to competition and, as a result, could alter both the electricity prices that customers will face and the fuels used to generate electricity. Currently the price of transmission services is set by State public utility commissions on the basis of average costs. Consequently, even if the nature of the transmission system (i.e., the number, length, and capacity of the transmission lines) affects costs at the margin, the use of average cost pricing tends to spread the resulting expenditures over all sales. Given this type of pricing, such transmission factors have little effect on the price of electricity. The recent initiative by the Federal Energy Regulatory Commission (FERC) under Orders 888 and 889, mandating that owners of transmission lines (mostly investor-owned electric utilities) make them available to all customers on an equal basis, is expected to bring new providers of electricity generation services into the marketplace and result in new pricing rules that include the costs of bottlenecks on the transmission network.² The FERC action, coupled with legislation by the States to open electricity generation services to competition, is expected to lead to lower electricity prices and a variety of new options for consumers.

In the initial phase of this work, a transmission network model of the New England Power Pool (NEPOOL) was developed to determine what impacts the above changes would have on electricity markets. This network analysis tool³ addresses the approximated flow of power along transmission lines, based on the physical laws of nature, which cause power to flow on paths that are independent of the contract path. That is to say, when power is introduced into the transmission network for delivery to some other point in the network, the actual power flow is different from the path intended by the supplier and consumer (the contract path). In reality, every link in the network is affected to some degree. This complicating factor makes the operation of the network more difficult than operating a pipeline, where the flow can be regulated to a certain extent by adjusting valves.⁴

There is another consideration that further complicates the operation of transmission networks. Electricity has two inherent components, called “real” and “reactive.” Real power is the power consumed in resistive loads, such as a hair dryer or a toaster. Reactive power is associated with magnetic fields, such as those found in the motor of a refrigerator. The amounts of real and reactive power that flow in the transmission network vary with customer needs. It is the job of the operator of the transmission system to assure that the levels of both real and reactive power are balanced. The operator must provide sufficient reactive power to assure that the transmission network remains stable, with the desired frequency and voltage levels staying within prescribed tolerances in order to prevent system failures or blackouts.

Considerations of network stability sometimes force transmission operators to use generators in particular places in the transmission network, even though cheaper sources of power might be available elsewhere in the system. For example, a given generator may be dispatched to meet a need for reactive power, because reactive power by the laws of physics does not travel the same way as real power does. Whereas real power can travel over long distances, reactive power must be provided close to where it is needed.

The issues of actual power flow and stability considerations must be addressed in a network analysis. Simplistic representations of power flow based on contract paths that ignore reactive power have little value. This is especially true when pricing issues are of interest. Because restructuring entails the unbundling of transmission services from other services, transmission costs become more important than they were when all the costs of providing electricity services were lumped together. In order to estimate the price of transmission services, the costs of moving real power from one place to another must be augmented by the cost of “ancillary services,” which include reactive power and voltage control.⁵

The above discussion of network considerations provides a basis for the modeling approach used in this analysis. The analysis uses a complete alternating current model that incorporates both real and reactive power as well as pricing of transmission services. Although this approach is computationally complex and data intensive, it accurately reflects actual transmission operations.

1. If the structure of the transmission network is assumed to be fixed, will the nature of the transmission system have major effects on the operation of generating facilities?

2. Will the existing structure of transmission networks result in substantial differences between marginal and average transmission costs?

3. Can transmission capability issues be analyzed without considering the unique characteristics of alternating electric current?⁶

The National Energy Modeling System (NEMS), used by the Energy Information Administration (EIA) to produce mid-term forecasts (20 to 25 years), is a large integrated model of the energy sector. The model accounts for transmission-related capital and operating expenditures when computing the costs to be recovered from consumers. Additionally, based on data obtained from the North American Electricity Reliability Council (NERC), NEMS specifies limits for power traded between regions. Because of the integrated nature of NEMS, the model endogenously solves for the equilibrium set of energy prices, using iterative solution techniques, such that supply will equal demand.

Even the simplest nationwide electricity network model can consist of more than a thousand nonlinear equations, which must be solved simultaneously to compute power flows. Thus, it is not computationally practical to include a direct representation of the actual electricity transmission system in NEMS. Indeed, the inclusion of a electricity network model in NEMS would increase the computing requirements more than tenfold. Given this consideration, it is necessary to use other means to determine the magnitude of the effects the transmission system could have on the cost of providing generating services. If the effects are small, then the current representation of the transmission network in NEMS is adequate. If not, a methodology will need to be developed to simulate the results of a detailed transmission network in an aggregate regional model such as NEMS. This analysis focuses on gaining insights about the order of magnitude of these effects.

The organization of the remainder of this paper is as follows. The next section discusses the questions in more detail, and how the unique characteristics of electricity affect the results. To determine the potential importance of the questions, a model of the New England Power Pool (NEPOOL) was used. The two following sections describe the model and the necessary data. The final two sections present some initial answers to the three questions posed, summarize the results, and describe future directions for this work.

Because an electricity transmission network provides the same function as any other transportation system—i.e., it ships the commodity from the source of production to the end user—it is tempting to view the movements of power as a typical transportation problem. The “transportation” of electricity from the generation source to the end user is, however, very different from the movement of other commodities. The unique characteristics of electricity make the examination of the three questions posed above, computationally more involved and conceptually more difficult.⁷

As opposed to many other commodities, the flows of electricity over a given line are influenced by the generation, loads, and flows of power over the entire network, as determined by Kirchhoff’s laws of physics.⁸ Thus, the flows of electricity over all the lines in a network are interdependent and are not “point to point.” The interdependent nature of electricity flows implies that the capacity of the entire network, not just certain subsets of it, must be examined. Additionally, the ability to move power over one part of a network will be influenced by the actions of all the generators and end users that are connected to it. Thus, one party’s access to a network will in part depend upon the actions of others.

Electricity is a multidimensional commodity, and the capability of a transmission network must be evaluated with respect to all its dimensions. That is, the output of a generator or the amount of power used by an electrical device is typically measured in watts of real power—for example, the maximum output of a certain power plant is 500 megawatts, or the amount of power needed to operate a certain motor is 250 watts. Without the needed amount of real power, most electrical devices will simply not operate. Many electrical devices are also designed for a given voltage—110 volts for most household appliances. If the voltage is less than the designed level, the electrical device will not work properly. If the voltage is greater than the designed level, the device will be seriously damaged.⁹ Thus, given that the transmission system is capable of transporting the needed amount of real power, if the voltage, also a function of the entire network, is not sufficient, most electrical devices will not operate.

One way of controlling the voltage level in a network is to alter the amount of reactive power supplied by generators. Reactive power is used by any electrical device that has a coil or motor. It is sometimes called “wattless” power, because in a strict sense of the word, a circuit (an electrical device connected to a source of electricity) that just contains reactive power uses no real power; nevertheless, without it many electrical devices would not operate. More important, at any point in time, both reactive and real power are flowing through power lines. Reactive power is measured in terms of voltage-amperes reactive (VAR).

Because both real and reactive power flow through power lines, the capacity of a power line is measured in terms of voltage-amperes (VA), or what is called “apparent power.” The amount of apparent power flowing through the line is equal to the square root of the sum of the squared amounts of real power (WATT) and reactive power (VAR):

Any evaluation of the capacity of a transmission system that focuses only on real power flows could lead to incorrect conclusions, particularly if the amount of reactive power is relatively large.

The interdependent nature of electricity networks and the fact that voltage variability can be important suggest that a complete alternating current (AC) network model can be computationally complex. A question of interest is whether there are computationally simpler methods of approximating such a network. The simplest approximation would be to ignore all the interdependence issues along with voltage (and reactive power) considerations and treat electricity transmission as a typical transportation problem.

A second approximation is to assume that the current just moves in one direction. The result of this assumption is a “direct current” (DC) model, which accounts for all the interdependence associated with electric power flows but, by assuming that all power moves in one direction, ignores the issues of reactive power and voltage control, which are unique to AC systems. A DC model is somewhat more complex than the traditional transportation model, but it is much simpler than the third alternative—a complete AC model that deals explicitly with voltage and reactive power issues.¹⁰ If voltage control and reactive power are important, then a computationally complex AC model must be used.

Although a generator produces both real and reactive (wattless) power, the day-to-day dispatching of a unit is generally based on the short-run marginal cost of producing real power. That is, almost all utilities use “merit-order” dispatching, with all units ranked according to their short-run marginal costs (per-kilowatthour fuel expenditures and some nonfuel operations and maintenance costs). Then, the units are dispatched on the basis of increasing marginal costs. There are, however, times when units are operated regardless of their per-kilowatthour costs. This is called “out-of-order” dispatching. In some cases, regardless of costs, a specific unit must generate real and reactive power to maintain necessary voltage levels.¹¹ Transmission constraints and very high line losses may also require a unit to be dispatched out of order. Finally, for some generating units the “startup costs” (i.e., the costs of going from zero to some positive level of output) can be substantial. In such cases, it may be more economical to operate the unit at some minimum level than to cease operation and then restart it. In general, the major cost of out-of-order dispatching is the increased variable production costs resulting from the increased operation of higher cost units. In the past, such cost increases would be averaged over all kilowatthours of electricity consumed.

Stated somewhat differently, in some sense, the production of electricity can be considered to be a process whereby a generator produces “joint products”—real power and voltage control.¹² Simple economic theory states that the supply of a joint product will be influenced by the price of both joint products. The marginal kilowatthour cost is essentially the price of real power. In a pure economic dispatch, only the price of real power matters. When out-of-order dispatching occurs, the supply of one of the joint products, real power, is influenced by the “price” of the other, voltage control. In the past, there was no explicit price for voltage control. In the restructured industry, however, voltage control is an ancillary service for which an explicit price will be charged.

Because of computational factors, most large models of the energy sector do not contain any direct representation of electric power networks. Thus, by necessity these models employ pure merit-order dispatching. Additionally, when modeling the competitive pricing of electricity, most analyses assume that prices will equal marginal generation costs (plus some other factors) and that dispatching patterns will also affect marginal generation costs. In a pure economic dispatch, the incremental generation costs for the entire system will equal the marginal cost of the most expensive (in terms of short-run variable costs) plant generating power. If, however, the most expensive unit is operating because of other considerations, such as voltage control, its output will be essentially fixed. In such cases, a lower cost unit will be at the margin, and the system-wide short-run marginal cost will be determined by the variable cost of that unit.

In short, as compared with cases in which the marginal generation costs are estimated using pure merit-order dispatching of all units, out-of-order dispatching will tend to cause system-wide marginal generation costs to be overstated. It is, therefore, useful to determine the frequency of out-of-order dispatching and, more importantly, how estimates of fuel use are affected by this type of dispatching. An objective to this paper is to obtain some insights about the size of this overstatement of prices.¹³

The final issue addressed in this paper is the pricing of transmission services. In the past, average cost pricing of transmission was used by all State and Federal regulatory agencies. Thus, the utility recovered all the capital costs associated with transmission and distribution by means of depreciation charges and earned a return on the undepreciated balance. All the operating costs were recovered in the year they were incurred. The costs associated with line congestion and average lines losses were equally spread over all consumers. Because transmission systems were designed to minimize congestion (overloaded power lines) and equalize line losses throughout the system, the equal allocation of these costs across all consumers probably did not result in any major economic distortions.¹⁴

Because the siting new transmission lines is becoming problematic, the redesign of transmission systems to accommodate changes in the geographic distribution of generators and loads may not be possible.¹⁵ As a result, congestion and line losses and their associated costs could increase in the future. Although transmission and distribution will still be regulated, there is some movement toward marginal cost pricing of these services. One pricing scheme that has received considerable attention is to set electricity prices equal to the short-run marginal costs of both generation and transmission.

The short-run marginal cost of generating and transmitting electric power has been derived by Schweppe et al.,¹⁶ who have shown that they include the following three factors:

The first factor will be the same regardless of where the load is located on the grid. The second and third factors are highly dependent on the location of the consumer, resulting in location-specific prices. Because of the interrelated nature of electrical systems, all three factors will be influenced by the actions of all the generators and consumers connected to the grid. This implies that the estimation of location-specific prices can be computationally complex.

By definition, short-run marginal costs do not include any fixed capital or operating costs. Because those costs are very large, short-run marginal cost pricing of transmission services would not recover all the fixed costs. In reality, there would have to be some type of additional charge to make any marginal-cost pricing proposal economically viable. The “prices” used in the present analysis are based solely on short-run marginal costs, without addressing the recovery of fixed costs. Thus, the “prices” computed here are incomplete estimates of actual prices.

Because most energy models do not contain a direct representation of electricity networks, marginal transmission costs cannot be computed directly. Thus, one question of interest is whether marginal line losses and congestion are sufficient to cause major differences between the average and marginal costs of transmission. Moreover, such models operate at a fairly high level of aggregation (i.e., Census or NERC regions), and therefore the intraregional distribution of prices is not relevant. Computational issues aside, it could still be possible to derive an aggregate marginal-cost-based price for each region. That single price could be interpreted as the demand-weighted average of all location-specific intraregional marginal costs. Large intraregional variations in prices could, however, result in an aggregation problem. For this reason, the potential intraregional distribution of marginal costs is of interest.

In addition to these modeling questions, there are some broader public policy issues related to location-specific marginal cost pricing of electricity transmission. Location-specific prices that equal marginal costs will send the “correct” signal to consumers and producers of electricity; however, the estimation of location-specific prices is computationally complex. Moreover, the administrative and billing costs could be substantial. Thus, if there is little variation in location-specific prices, the costs of computing them may exceed the benefits.¹⁸

The PowerWorld network model was used for this analysis. The model consists of an electrical network, an economic component describing costs and demands, and algorithms for calculating power flows and prices. It is also a full AC representation that explicitly includes real and reactive power, line losses, congestion, and generator costs and operating constraints. The model was used to simulate NEPOOL power flows. The next two sections describe PowerWorld, NEPOOL, and the data used for the model analysis.

The power flow with economic dispatch problem is to find the least costly way to meet fixed demands for power at specific locations by assigning attainable operating levels to generators. Generators for which cost estimates are not available are fully committed (assuming that they are run regardless of cost) at the capacity shown on FERC Form 715, “Annual Transmission Planning and Evaluation Report.”²⁰ Generators with minimum operating levels are always dispatched. All other generators can be run at any level up to their capacity. Generator assignments are consistent with the physical laws governing power flow (Kirchhoff’s laws) and account for line losses but not for line limits (congestion). Costs are the sum of the costs of running the generators. When the demands cannot be met, the power flow problem is said to be infeasible. A viable solution would require either lower demands, relocated demands, more generation capacity, or a different transmission line configuration. Economic dispatch and merit-order dispatch are the same when all generators can be dispatched at any level up to capacity and there are no losses.

where a, b, c, and d are constants to be estimated and g is the output from the generator. When there are multiple units at a bus, the bus cost curve is constructed by summing the individual cost curves horizontally.²¹ The average variable cost (AVC) is

The only costs that matter for the computation of efficient prices and generation are the marginal cost curves. The marginal cost, which is the sum of fuel and variable operations and maintenance costs per kilowatthour generated, is approximately b when generators are operating normally. When generation gets near its maximum, the curvature parameters, c and d, become important. The estimates of these parameters are discussed below.

The optimal power flow problem is to find the least costly way to meet fixed demands while satisfying line constraints. A solution to the optimal power flow also satisfies all the constraints in the power flow problem. If the original power flow problem is infeasible, then the optimal power flow is too. If lines are not congested in the optimal power flow, then its solution will be the same as the power flow. Both problems assume that the demand for electricity is fixed and does not respond to costs or prices. That is, given fixed demands, the optimal power flow calculates the competitive prices and quantities. This is a true competitive price in the sense that it includes all relevant operating constraints, network effects, and voltage standards.²²

These optimization problems have real-world counterparts. Power flow with economic dispatch is essentially the approach being followed in the United Kingdom, where some difficulties have occurred because congestion is ignored and because the differences in incremental losses at each location are averaged out. Australia and New Zealand have adopted systems that approximate an optimal power flow, explicitly recognizing network effects. The result in Australia is that competitive prices go up quickly as lines become constrained.

NEPOOL is one of three tight power pools in the Northeast region of the United States. It was established in September 1971 to serve the New England region (Maine, Vermont, New Hampshire, Connecticut, Rhode Island, and Massachusetts). Currently there are more than 130 participants in NEPOOL, including a variety of nontraditional utilities such as power marketers, exempt wholesale generators, and independent power producers. The power travels over about 8,000 miles of transmission lines, belonging to about 29 transmission owners. The original cost of the transmission facilities was about $3.3 billion.

The pool has operated as a single entity dispatching generators within the pool to meet regional demands. In September 1996, NEPOOL’s Executive Committee announced plans to replace its dispatching operations with an independent system operator (ISO) to satisfy FERC’s Order 888 requirement to reform access to power pools. On June 25, 1997, the FERC conditionally approved creation of the ISO. The ISO now has operating control of NEPOOL’s transmission and generation facilities.

The representation of NEPOOL used here consists of 148 buses, comprising 85 generators, one DC line that is represented as a generator equivalent (Sandy Point, bus #17896), 82 load buses, the high-voltage AC lines connecting them, and two DC lines from Canada.²³ The smallest generation bus is 10 megawatts, the smallest load is 3 megawatts, and the AC lines are mostly 345 kilovolts. The input data for the NEPOOL model are aggregated from the data appearing on FERC Form 715, summer peak 1995. PowerWorld was used to aggregate the data to represent only high-voltage lines. The representation of NEPOOL contains 136 high-voltage bus-to-bus line segments. The input data for the PowerWorld model for generators, loads, lines, transformers, and the network are available on computer disk from EIA.²⁴

This representation of NEPOOL accounts for 85 percent of FERC’s reported load (20,178 megawatts) and 87 percent of its generation (18,696 megawatts). The model totals are less than on the FERC file because some of the demand and generation are netted out against each other in the aggregation process. Each bus connected to a high-voltage power line generates its own “tree” of lower voltage lines connecting smaller buses. When one of these trees contains both load and generation, they are combined. The remaining input data that need to be specified include the electricity the generators put onto the high-voltage lines and the electricity withdrawn from them.

As noted above, the economic portion of the model consists of marginal costs for each generator. The fuel cost part of the marginal cost curve, the b parameter, was estimated by multiplying each generator’s heat rate (British thermal units per kilowatt) by its fuel cost (dollars per British thermal unit).²⁵ Each generator’s heat rate and fuel cost were derived from FERC Form 1 filings for 1995, resulting in estimates for 53 of the 85 generators, representing about 74 percent of the generation capacity. Excluding a biomass plant and small oil-fired plants, the estimated fuel costs range between 4 and 33 mills per kilowatthour. Appendix Table A1 lists the estimated marginal costs of the generators. The curvature parameters in the model are based on analyst judgement.

PowerWorld also requires maximum and minimum limits for each generator’s output. The capacity listed on FERC Form 715 was taken as the maximum operating level. Appendix Table A1 lists the operating limit data. If a lower limit was listed on FERC Form 715, it was taken to be the minimum operating limit. Otherwise, the minimum operating limit was taken as zero. Of the 53 generators on automatic generation control, 36 had operating limits strictly greater than zero. The sum of their minimal operating levels (5,243 megawatts) accounts for 26 percent of the total capacity (20,063 megawatts) listed on FERC Form 715.

As suggested earlier, PowerWorld dispatches only those generators for which estimated cost curves are available. It was assumed that the output of generators for which cost data are not available (3,015 megawatts) is committed regardless of price. The sum of the minimal operating levels plus the fixed output of those generators for which cost data are not available amounts to about 41 percent of NEPOOL’s total capacity and is committed prior to the start of dispatch.

The current NEPOOL model consists of the high-voltage network, generator capacities, estimates of the marginal costs of about 74 percent of generator capacity, and two solution algorithms (power flow and optimal power flow). The marginal-cost estimates represent fuel costs. The optimal economic equilibrium has not been implemented because estimates of vocational demand curves are not available.

The NEPOOL model described in this paper was built using FERC data on network characteristics (FERC Form 715) and generator costs (FERC Form 1, “Annual Report of Major Electric Utilities, Licensees and Others”). The coverage and quality of the data diminish as the level of aggregation decreases. It is also expected that, as more unregulated generators enter electricity markets, the coverage of the FERC cost data will decrease.

FERC Form 715 exhaustively lists the physical attributes of the network, and system maps developed by NEPOOL are usually adequate for locating generators. However, because of the general mismatch between the names in FERC Form 715 and the names on maps, there is ambiguity about the location of demand buses. One cannot determine the location of some of the larger buses with certainty. FERC Form 715 does not report flows experienced at a point in time. Instead, the demand and generation reported on the form are estimates of summer peak. As a result, the power flows are calculated rather than measured values.

Data on heat rates and average annual costs of fuel are available on FERC Form 1 for investor-owned utility generators. The annual averages are estimates of the marginal fuel costs to generators at any particular time. Variable operations and maintenance costs can also be estimated from FERC Form 1, but these are not currently included in the model. Searches of secondary sources and an attempt to estimate the curvature parameters of the cost curves failed to improve the resolution of the cost estimates. The capacity of utility-owned generators is also available on FERC Form 715 and on Form EIA-860, “Electric Utility Generator Report,” although the values are not always the same.

There are no comparable cost data for generators owned by municipalities, cooperatives, cogenerators, or independent power producers, which amount to 26 percent of the NEPOOL generation capacity. It is assumed that these suppliers put all their generation reported on FERC Form 715 on the grid regardless of price. The impact of these generators on competitive prices could be out of proportion to their relatively small share of NEPOOL generation capacity. If they are the incremental sources of supply, then their marginal costs would determine the competitive price. The accuracy of the estimates of their marginal costs would determine how accurately competitive market prices could be forecast.

There are no adequate publicly available data for making realistic estimates of price-sensitive demand curves at major NEPOOL demand locations. To make such estimates would require information on the demand (loads) at the location and the concurrent price. As mentioned above, the FERC does not require measures of actual load at demand centers. Data are available for annual sales within regions and real-time price elasticities of demand. They are, however, based on limited information. This analysis assumes that demand (load) is fixed at the levels in NEPOOL’s FERC Form 715 filing.

The emergence of the ISO and competitive spot markets at major trading points may substantially improve the availability of data for estimating demand. The ISO will need to know the real-time deliveries of power at major nodes throughout the system. Spot markets at these locations would provide the corresponding prices. In the event that spot markets do not emerge, the ISO in some designs could calculate “pseudo” competitive prices corresponding to the loads.²⁶

To check that the model approximates the actual network, it was solved with the configuration of generation and loads reported in the FERC Form 715 file. The historical configuration was a feasible solution for the network. The line flows were also close to those reported to the FERC. Except for two outliers, the distribution of percentage errors ranged from -2 percent to 13 percent. The average absolute percentage error across all lines was 1.3 percent. The outliers of 37 and 60 percent occurred on two small lines, the discrepancies amounting to less than 1.8 megawatts each.

The starting point for the analysis of the three questions posed above is the “base case” that uses the 1995 summer peak loads, power plant, and transmission network data as reported on FERC Form 715. NEPOOL is heavily dependent on nuclear power, and in 1995 all seven of its nuclear units were in operation. In 1996, however, two of the older units—Connecticut Yankee and Maine Yankee—were permanently retired, and the three Millstone units were taken out of service because of safety concerns. Connecticut Yankee and the Millstone units, located in southern New England, provide 70 percent of the generation in that part of NEPOOL.

To gain some insights about the importance of reactive power and voltage control in assessing capacity, a “nuclear shutdown” case was run. In that case, the two Yankee and three Millstone units were taken out of service and replaced with equivalent amounts of capacity located in the northern part of NEPOOL.²⁷ The question is whether the transmission system has the capability to handle the flows of power from the northern to the southern part of NEPOOL. Because this case entails substantial changes in the regional distribution of generating capacity, the results provide an indication of the sensitivity of marginal-cost-based prices to changes in the spatial distribution of generation relative to loads. To examine the question of how network (and other) factors affect dispatching and marginal generation costs, a series of cases were run in which the 1995 peak loads were reduced. The details of those cases are described below.

Table 1 shows summary results for the base case. As noted above, because both real and “wattless” power actually flow through power lines, the correct measure of the capacity of a transmission line is apparent power (i.e., MVA), which includes both real and reactive power. As Table 1 indicates, in the aggregate, the ratio of real to apparent power is 0.88 (18,125/20,629).²⁸ A DC model that ignores reactive power would, therefore, on average, understate the actual flows of power over the lines by about 15 percent. The ratio of real to apparent power is also called the “power factor.” Utilities will typically not directly charge a customer for reactive power unless its power factor falls below 0.85. It is, therefore, not surprising to see an average power factor of 0.88.

Parameter	Real Power (Megawatts)	Reactive Power (Million Voltage-Amperes Reactive)	Apparent Power (Million Voltage-Amperes)
Load	17,093.1	2,174	22,913
Generation	17,732.9	2,546	18,290
Losses	240.7	1,544	NA
NA = not applicable. Notes: Shunts are not included. Thus, loads plus losses do not equal generation. The outflows of power to other regions are depicted as negative loads. If the negative loads were excluded, the total amount of real power and apparent power would be 18,125 and 20,629 megawatts, respectively. The power factor would be about 0.88 (18,125/20,629). Source: Energy Information Administration, Office of Integrated Analysis and Forecasting.

The results of the nuclear shutdown case illustrate the importance of correctly accounting for voltage control and reactive power in assessing capability issues. In this case a few power lines were overloaded, and their capacity was consequently increased to handle the power flows. Even after removing the line constraints on the movements of power, however, it was still impossible to obtain a solution. The problem was with voltage control and reactive power. In particular, the voltage was not sufficient to meet the needs of about 70 percent of the loads, generators, and transformers in southern New England (21 of the 34 buses in Connecticut are part of the Northeast Utilities and United Illuminating service areas).

One way to control voltage is to alter the generation of reactive power. Because of line losses, reactive power must be produced relatively close to the loads. (As Table 1 shows, in the base case, the line losses for reactive power are over 50 percent.) All four nuclear units are located within 100 miles of the Hartford-New Haven area. Without these units, there were not sufficient supplies of reactive power in that area. As a result, the voltage collapsed in this simulation. This conclusion was confirmed by allowing the Millstone 1 unit to operate, which raised the marginal cost from 0.6 to 6 cents per kilowatthour. Because of the high assumed marginal cost, Millstone 1 did not produce any real power, although it did generate about 1,000 megaVAR of reactive power. This increase was sufficient to meet the needs for voltage support in that part of NEPOOL.

To summarize, if only real power were considered, it would appear that there was sufficient capacity to handle increased flows of power from the northern to the southern part of NEPOOL This conclusion would, however, be incorrect, because there was insufficient capacity in this case for reactive power used to control voltage.²⁹ This result suggests that the use of anything less than a full AC model could produce incorrect conclusions about transmission capability when major portions of generating capacity are removed from the system.

Figure 1 shows the distribution of short-run marginal costs of generating and transmitting electricity. This figure shows the number of load buses with marginal costs equal to or less than the amount shown on the y-axis. Costs for a selected number of cities in NEPOOL are shown in Table 2. All the costs were derived from the base case as described above. As noted above, actual market prices would be expected to be higher than these costs, because they do not include charges to recover fixed transmission costs. Such charges would be needed to ensure that the transmission system would be economically viable.³⁰

At least at the level of aggregation used in this analysis, the results shown in Figure 1 suggest that the short-run marginal cost pricing of generation and transmission would result in relatively small locational variations in electricity prices. That is, excluding two outliers, the maximum difference in locational costs is about 3 to 4 mills per kilowatthour. Moreover, marginal generation costs for NEPOOL were about 2.6 cents per kilowatthour, and most of the costs shown in Figure 1 are within 2 to 3 mills per kilowatthour of that amount, suggesting that short-run marginal transmission costs are relatively small.³¹

Short-run marginal transmission costs are influenced by the amount of congestion (i.e., line overloads) and the value of the marginal line losses. In the base case, at the level of aggregation used, there were no line overloads and, therefore, no congestion. Additionally, in most cases, marginal line losses were about 4 to 5 percent. That is, at most buses, about 1.04 kilowatthours of electricity is generated to satisfy the last kilowatthour of electricity demand.³² It was, therefore, not surprising that the regional variations in costs were small and short-run marginal transmission costs were small.

The high-voltage transmission system in NEPOOL was, in part, designed to minimize congestion and equalize line losses across the system. The design of the transmission system also assumed, however, that substantial amounts of baseload generating capacity would be located in southern New England. (As of 1995, Connecticut Yankee and the three Millstone units provided that capacity.) The nuclear shutdown case offers an interesting “case study” on what would happen if the bulk of the generating capacity in the southern part of NEPOOL were shifted to the northern part of the region.³³ That is, this case provides insights about how substantial changes in the regional distribution of generating capacity affect costs when the distribution of loads is held constant.

Figure 1. Cumulative Distribution of Short-Run Marginal
Generating and Transmission Costs in the Base Case

Notes: The figure shows the number of load buses with marginal costs less than or equal
to the amounts shown on the y-axis. the data do not include changes to recover fixed
transmission and distribution costs, which would be needed to ensure the financial
viability of the transmission and distrubution systems.
Source: Energy Information Administration, Office of Integrated Analysis and Forecasting.

Table 2. Short-run Marginal Generation and Transmission Costs for Selected Cities in Two Cases
(Mills per Kilowatthour)

City	Base Case	Nuclear Shutdown Case
Portland, ME	25.4	26.5
Boston, MA	25.6	26.2
Providence, RI	26.4	27.5
New Haven, CT	27.5	33.6
Hartford, CT	26.9	32.8
Springfield, MA	26.3	26.7
Note: These data do not include any charge to recover the fixed transmission and distribution costs. Such a charge would be needed to ensure the financial viability of the transmission and distribution sectors. Source: Energy Information Administration, Office of Integrated Analysis and Forecasting.

The distributions of short-run marginal generation and transmission costs in the nuclear shutdown case for NEPOOL as a whole and for selected cities are shown in Figure 2 and Table 2, respectively. These results suggest that a substantial shift in the regional distribution of generation, holding the distribution of loads and the structure of the transmission system constant, would have a modest impact on the distribution of prices based on short-run marginal generating and transmission costs. In the nuclear shutdown case, the maximum difference is about 7 to 8 mills per kilowatthour. In the New Haven and Hartford areas (i.e., southern New England), costs are only about 6 mills per kilowatthour (about 20 percent) higher than those in the base case. Although there still are no line overloads in the nuclear shutdown case, there are substantial increases of power flows from the north to the south. As a result, marginal line losses in the south increase to about 20 percent. Marginal generation costs in that area are about 30 mills per kilowatthour, and the value of the 20-percent increase in lost power is therefore about 6 mills per kilowatthour.

Figure 2. Cumulative Distributionof Short-Run Marginal
Generating and Transmission Costs in the Nuclear Shutdown Case

Notes: The figure shows the number of load buses with marginal costs less than or equal
to the amounts shown on the y-axis. The data do not include changes to recover fixed
transmission and distribution costs, which would be needed to ensure the financial
viability of the transmission and distrubution systems.
Source: Energy Information Administration, Office of Integrated Analysis and Forecasting.

To summarize, at the level of aggregation used in this analysis, it would take extreme changes in the regional distribution of generation to produce modest variations in location-specific prices. It is unclear whether the changes in behavior caused by such modest changes in costs would be sufficient to outweigh the ISO’s administrative and computation costs. Moreover, prices would actually be higher than those estimated here, because some charge would be required to recover fixed transmission costs, which could vary by location.

The PowerWorld model chooses the dispatching pattern that minimizes variable generation costs, subject to a series of voltage, transmission, and unit-specific operational constraints. It is, therefore, possible to compare this dispatching pattern with one that ignores the constraints and simply dispatches plants on the basis of marginal costs. Such comparisons yield some insights about the frequency of out-of-order dispatching and its effects on fuel consumption and marginal generation costs.

In the base case, given the lack of excess capacity, the overall constraint stating that generation must equal demand should override network and operational constraints.³⁴ That is, to supply enough power to meet peak load, almost all units must operate at full capacity regardless of cost. However, the network and other constraints should become more important in the off-peak periods when there are relatively large amounts of excess capacity. To study how these constraints affect dispatching of power plants in off-peak periods, two reduced demand cases were run, with the peak demand at each load bus reduced by 15 and 30 percent, respectively. In the absence of any network or operational constraints, the 15 and 30 percent of the capacity with the highest marginal costs would not operate in the 15 and 30 percent demand reduction cases, respectively. If, however, binding constraints arose, some relatively high-cost units would operate. That is, such units would be operated “out of order.”

Tables 3, 4, and 5 show the units that are dispatched out of order, in the base and the two reduced demand cases. Using pure economic dispatch results in no generation for the units. The column, “constrained economic dispatch” shows the level of generation based on cost minimization subject to all the constraints in the PowerWorld model. As expected, at the peak period, virtually all units must operate to meet demand; therefore, only a few units are operated out of order (Table 3). In the two reduced demand cases, however, the number of plants operated out of order increases substantially (Tables 4 and 5). These results suggest that out-of-order dispatching in off-peak periods can be substantial.

Also shown in Tables 3, 4, and 5 are the minimum generation levels reported on FERC Form 715. These values were used as the minimum generation constraints in PowerWorld. A comparison of the level of generation from the units dispatched out of order with the minimum generation levels gives some indication of whether network constraints or operational constraints (i.e., minimum generation level) are binding. If a unit that otherwise would not be dispatched is operating at its minimum level, then it would appear that the minimum operating constraint, as opposed to the network constraint is binding. This is important because the minimum operating constraints are in some sense exogenous data inputs, whereas the other constraints are more in the nature of endogenous model outputs.

Plant Name	Marginal Cost (Mills per Kilowatthour)	Pure Economic Dispatch (Megawatts)	Constrained Economic Dispatch (Megawatts)	Fuel	Minimum Generation (Megawatts)	Capacity (Megawatts)
West Springfield	26.0	0	107.05	NG	20	107
Canal 2	26.1	0	143.63	Oil	0	576
Norwalk Harbor 1	28.6	0	39.97	Oil	40	162
Norwalk Harbor 2	28.6	0	39.97	Oil	40	168
Middletown 3	30.7	0	94.84	Oil	95	233
Cleary Flood	32.5	0	34.73	Oil	35	85
Montville 5	32.6	0	20.70	Oil	21	81
NG = natural gas. Note: The cost data reported on FERC Form 1 are at the plant level, and the FERC Form 715 data are at the unit level. Whenever the Form 1 data indicated the use of oil and natural gas, it was assumed that all units used natural gas. Source: Energy Information Administration, Office of Integrated Analysis and Forecasting.

Table 4. Units Dispatched Out of Order in the 15 Percent Demand Reduction Case

Plant Name	Marginal Cost (Mills per Kilowatthour)	Pure Economic Dispatch (Megawatts)	Constrained Economic Dispatch (Megawatts)	Fuel	Minimum Generation (Megawatts)	Capacity (Megawatts)
New Boston 1	24.2	0	99.67	NG	100	205
New Boston 1	24.2	0	85.07	NG	85	175
New Boston 3	24.2	0	184.86	NG	185	380
Salem Harbor 1	25.9	0	34.78	Coal	35	79
Salem Harbor 2	25.9	0	34.78	Coal	35	78
Salem Harbor 3	25.9	0	59.77	Coal	60	143
Salem Harbor 4	25.9	0	99.77	Coal	100	400
West Springfield	26.0	0	19.79	NG	20	107
Norwalk Harbor 1	28.6	0	39.67	Oil	40	162
Norwalk Harbor 2	28.6	0	39.67	Oil	40	168
Middletown 3	30.7	0	94.55	Oil	95	233
Cleary Flood	32.5	0	34.47	Oil	35	85
Montville 5	32.6	0	20.42	Oil	21	81
NG = natural gas. Note: The cost data reported on FERC Form 1 are at the plant level, and the FERC Form 715 data are at the unit level. Whenever the Form 1 data indicated the use of oil and natural gas, it was assumed that all units used natural gas. Source: Energy Information Administration, Office of Integrated Analysis and Forecasting.

For example, in the base case, in the absence of any constraints, the Canal G2 oil-fired power plant should not operate because its marginal costs are too high. When all the constraints are considered, however, the cost-minimizing solution is to generate about 104 megawatts of real power from that unit. Because the optimal level of generation for Canal G2 is far above its minimal level, it would appear that the network constraints are binding. (Such a plant is often called a “must run” unit, because its operation is based on transmission or voltage factors.) The Middletown 3 unit is also dispatched out of order. Because the optimal level of generation of that unit is at the minimum level, it would appear that the minimum output constraint is binding.

In the base case, only two units are dispatched out of order as a result of binding network constraints, In the two reduced demand cases, all the out-of-order dispatching appears to be the result of the minimum output level, as opposed to network constraints. This result is noteworthy because these minimum output levels, reported on FERC Form 715, are data inputs and, at this point, are subject to two interpretations.

In particular, for some units it is prohibitively expense to cease operation and then restart the power plant. (A good example of this is a nuclear power plant.) In such cases, the minimum generation levels are dictated by engineering considerations. For other units, however, the startup costs are substantial but not prohibitively expensive. In these cases, the minimum generation levels reported by the utility could be the result of an implicit (or explicit) cost-benefit analysis. Stated somewhat differently, it is possible that the minimum generation levels could be based more on economics than on engineering considerations. In the present analysis, the minimum generation levels are used as fixed constraints, an approach that is valid only if they are dictated largely by engineering, as opposed to economic, considerations.

Although the network and operational constraints do affect off-peak dispatching patterns substantially, there is some evidence that, in the aggregate, the effects on fuel usage may be relatively minor. Table 6 shows capacity dispatched by fuel type based on pure and constrained merit-order dispatching in the base case and the two reduced demand cases. When the network and operational constraints are binding, the effect is to increase generation from relatively high-cost units. Since demand would not be affected by these constraints, the increased generation must be offset by reduced generation from lower cost units.³⁵ As Table 6 shows, the effect of binding network and operational constraints is to increase generation from oil-fired units. In the 15 percent reduction case, such increases are offset by decreases from gas-fired units. Since many of these gas-fired units are not dispatched in the 30 percent reduction case (Table 5), the increases are offset by decreased generation from nuclear power plants.³⁶ In all cases, the effects are relatively small—generally, less than 1 gigawatt.

Table 6. Estimated Capacity Use by Fuel Type, Based on Pure and Constrained Economic Dispatch, in Three Cases
(Gigawatts)

Fuel	Base Case		15 Percent Demand Reduction		30 Percent Demand Reduction
Fuel	Pure Economic Dispatch	Constrained Economic Dispatch	Pure Economic Dispatch	Constrained Economic Dispatch	Pure Economic Dispatch	Constrained Economic Dispatch
Nuclear	6.45	6.46	6.45	6.46	6.45	5.72
Coal	1.49	1.40	0.84	1.07	0.84	0.70
NG	5.08	5.03	4.24	3.29	1.65	1.80
Oil	1.14	1.22	0.06	0.68	0.06	0.67
Other/Unknown	2.07	2.12	2.07	2.17	2.07	2.17
Total^a	16.23	16.23	13.66	13.67	11.07	11.06
^aImports not included. NG = natural gas. Note: The cost data reported on FERC Form 1 are at the plant level, and the FERC Form 715 data are at the unit level. Whenever the Form 1 data indicated the use of oil and natural gas, it was assumed that all units used natural gas. Source: Energy Information Administration, Office of Integrated Analysis and Forecasting.

The effects of the network and operational constraints on marginal generation costs are much more pronounced (see Table 7). When these constraints become binding, they tend to constrain the operation of relatively high-cost units. Since the operation of such units is “fixed,” the last or marginal kilowatthour of real power must be obtained from units lower in the merit order. When these constraints become binding, the effect is to cause system-wide marginal generation costs to be lower than otherwise would be the case. In the base case, the effects are small; however, in the two reduced demand cases, the effects become larger. It must be stressed that in the two reduced demand cases, the minimum generation level constraint is always binding. As noted above, it is valid to use these minimum generation levels as exogenous constraints only if they are largely based on engineering as opposed to economic considerations.

Table 7. Estimated Marginal Generation Costs, Based on Pure and Constrained Economic Dispatch, in Three Cases
(Mills per Kilowatthour)

This paper presents some initial results of an ongoing project. Although the model of NEPOOL used here is highly aggregated and a few data problems remain, a number of points are worth making. First, it appears that transmission capacity issues can be examined adequately only with a full AC model of the transmission network. The nuclear shutdown case was designed so that the line capacity was sufficient to avoid any line overloads. Nevertheless, in this hypothetical scenario, the system was not capable of meeting demand because the voltage was not sufficient. This, in turn, was caused by a lack of capacity for reactive power. A DC model would consider only the flow of real power, ignoring reactive power. Thus, a voltage collapse caused by a lack of reactive power can only be detected with a full AC model. Moreover, the FERC Form 715 data suggest that the flows of reactive power are substantial and, therefore, can not be ignored. For example, if reactive power is ignored, the FERC data suggest that, on average, the actual flows over power lines would be understated by about 15 percent.

Second, at least at the level of aggregation used in this analysis, the issue of the locational pricing of real power appears to be of secondary importance. Even in an extreme case, the maximum variation in marginal costs was only about one-half of a cent. This analysis did not, however, examine issues dealing with the pricing of ancillary services such as voltage control and reactive power. The results of the nuclear shutdown case suggest that these factors can be important, and that attention should be paid to how these services will be priced.

Third, the reduced demand cases suggest that out-of-order dispatching could have substantial effects on estimates of marginal generation costs. At least according to the conventional wisdom, much of the out-of-order dispatching occurs because of very localized network factors (e.g., localized transmission constraints or voltage control problems over a fairly small area). Many of these factors were probably “lost” in the process of aggregating a 2,000-bus system to a 150-bus representation. At this level of aggregation, the minimum generation level, as opposed to network constraints, was binding. This point is noteworthy because it is not clear how the minimum generation levels reported on FERC Form 715 should be interpreted.

These results suggest that a more disaggregated version of NEPOOL should be used to determine whether network constraints actually cause most of the out-of-order dispatching. If this is the case, then the electricity dispatching algorithm in NEMS should be enhanced to include this feature. If the minimum generation constraints are still binding, then the FERC Form 715 data should be more closely examined. One way of doing this would be to compare the data with EIA’s monthly generation information. If the minimum operating level data from FERC Form 715 are “real,” then the cost data used in the NEMS electricity generation algorithm should be modified.

In addition, to study whether the transmission network can handle large flows of power from one NERC region to another (e.g., flows of power generated by inexpensive coal-fired power plants in eastern Ohio to Boston), two or three NERC regions could be linked, so that the effects of hypothetical trades across NERC regions could be simulated. With existing PC-based software able to handle 10,000 to 15,000 bus networks, the amount of aggregation required for the analysis of linked NERC regions should be minimal.

Case	Pure Economic Dispatch	Constrained Economic Dispatch
Base	26.1	25.8
15 Percent Demand Reduction	24.2	20.7
30 Percent Demand Reduction	20.6	7.9
Source: Energy Information Administration, Office of Integrated Analysis and Forecasting.