What Objective Function Should Be Used for Optimal Auctions in the ISO/RTO Electricity Market?

Transcription

1 What Objective Function Should Be Used for Optimal Auctions in the ISO/RTO Electricity Market? Gary A. Stern +, Joseph H. Yan +, Peter B. Luh *, and William E. Blankson * +: Market Monitoring & Analysis, Southern California Edison, Rosemead, CA *: Department of Electrical and Computer Engineering, University of Connecticut, Storrs, CT Abstract In this paper, we provide mathematical formulations for the offer cost and MCP payment cost minimizations for optimal auctions in the ISO/RTO electricity market, and summarize the newly developed solution methodology using augmented Lagrangian relaxation and surrogate optimization for solving the optimal auction with the MCP payment objective function. Data has been used to test the method based on a simplified energy market, and for a given set of offers, the testing result demonstrates significant potential savings for electricity consumers if the MCP payment cost minimization is implemented in the ISO/RTO electricity markets. More importantly, this paper addresses economic implications of the objective function choice, including whether maximizing social welfare should be one of objectives of electricity industry deregulation. We conclude that an objective to maximize social welfare, even if it were determined to be desirable, is not achievable based on current bidding rules after moving from traditional vertically integrated utilities to a market approach, and is certainly not achieved by the offer cost minimization approach in use today. Other implications such as the inconsistency between the actual payment and the cost function minimized, and bidding behaviors are also discussed. Index Terms Deregulated electricity markets, offer cost minimization, payment cost minimization, market clearing price, augmented Lagrangian relaxation, and surrogate optimization. I. INTRODUCTION eregulated wholesale electricity markets (e.g., the day- hour-ahead, and real-time markets in California) Dahead, operated by Independent System Operators (ISOs) generally adopt a market clearing price (MCP) mechanism to pay market participants and charge consumers for energy and ancillary service (capacity) products. The benefit of using this payment scheme has been discussed publicly as summarized in [7]. Under the MCP payment mechanism, market participants submit supply offers and demand bids for energy and ancillary services to an ISO, the ISO runs the auctions for energy and ancillary services and determines the MCPs for each product, and then the MCP is used to pay the market participants for their selected product independent of their offer prices. It is crucial for the ISOs to minimize the appropriate objective function and set the MCPs correctly to capture the true cost (total payment cost) to the markets, since market participants are charged or get paid based on the MCPs. Additionally, inconsistency between total payment cost and the objective function can lead to gaming behavior. Furthermore, the MCPs have financial impacts on forward transactions outside the ISO markets. However, the choice of objective function to be used has not been fully investigated in the literature since the transition from traditional regulation of vertical utility operation to a competitive market structure with a market clearing price mechanism. Currently most ISOs run an auction to minimize the total offer cost 1 [4]. This optimization is treated similarly to the traditional unit commitment problem by incorporating generation offer costs into the objective function instead of generation marginal costs (fuel costs plus variable O&M). The problem is then solved by the Lagrangian relaxation technique, and the system marginal costs derived from this approach are used to establish the MCPs for settlements. In deregulated electricity markets, especially those with market clearing price mechanisms, we question whether the minimization of total offer costs (offer cost minimization) currently in use is appropriate for the determination of MCPs and for the minimization of total procurement costs for consumers. As Yan and Stern [11] identified, the unit commitment and Lagrangian relaxation technique should only be applied to markets in which an offer cost minimization mechanism is adopted for settlements. The market clearing price mechanism dramatically changes the nature of the optimization problem, and adds significant complexities in solving the problem, as the separable structure of the original problem has been lost. Yan and Stern demonstrated with an example that the procurement cost for consumers using offer cost minimization could be significantly higher than under payment cost minimization recognizing market clearing prices explicitly in the problem formulation. They also noted that the total cost of electricity purchased in these systems is in the tens of billions of dollars annually and even a very small change in the efficiency of the solution will results in tens of millions of dollars in annual savings for consumers. In their paper, however, no solution methodology is provided to solve the MCP payment cost minimization problem. Recently, this problem has been solved in Luh and el. [8] and [9], where a method based on the augmented Lagrangian relaxation and surrogate optimization framework has been developed. In this paper, offer cost minimization and payment cost minimization are first formulated mathematically in Section 2. Two simple examples are then used to illustrate the differences between them in Section 3. The methods of [8] and [9] are then summarized in Section 4, together with a testing example in which New England load from May 1999 and cost-based generation offers are used. More importantly, this paper addresses economic implications of the objective function choice, including whether maximizing social welfare 1 Offer cost minimization of the CAISO is the same as the Pay-as-Bid cost minimization or Pay-as-Bid cost minimization. Pay-as-Offer is a new term for Pay-as-Bid. This is consistent with Standard Market Design terminology under which bids are related to demand and offers to supply. 1

2 should be one of objectives of electricity industry deregulation in Sections 5-9. We conclude that such an objective which is to maximize social welfare, even if it were determined to be desirable, is not achievable based on current bidding rules after moving from traditional vertically integrated utilities to a market approach, and is certainly not achieved by the offer cost minimization approach in use today. Other implications such as the inconsistency between the actual payment and cost function minimized, and bidding behaviors are also discussed. II. OFFER COST MINIMIZATION AND PAYMENT COST MINIMIZATION FOR THE INTEGRATED FORWARD MARKET A. Offer Cost Minimization In its MD02 market design proposal filed on July 22, 2003, the California Independent System Operator (CAISO) stated the objective function of the CAISO s optimization of energy and ancillary services is offer cost minimization, and this is consistent with the optimization software package utilized by the other independent system operators. In order to provide a clear and simple mathematical description of the CAISO s objective function and solution methodology, consider an energy only market with I supply offers, i = 1, 2,, I. For simplicity of presentation, the following simplifying assumptions are made: system demand over the auction horizon {P d (t)} are given, system reserve constraints and transmission congestion are not considered, startup costs are fully compensated, and participants submit single block constant price offers with maximum/minimum power levels. For supply offer i, the offer curve (or price) for supplying power p i (t) at time t (1 t T) is denoted by o i (p i (t),t) ($/MW), and the cost curve, which is the integral of the offer curve, is denoted by C i (p i (t),t). The startup or capacity related cost is denoted by S i (t), and is incurred if and only if a participant supplies power from an off state. The CAISO objective function for the integrated forward market is to select supply offers and their associated power levels so that the system demand and other individual offer constraints (such as minimum up/down, and minimum and maximum generations) are satisfied at the minimum offer cost. Mathematically, the problem is follows: T I min J, with J { C i ( pi ( t ),t ) + Si ( t )}. (2.1) { p i ( t )} t= 1i= 1 System demand constraints require that the total power from all selected offers should equal the system demand P d (t) at time t, i.e., I i= 1 p () t = P () t, t 1,2,...,T. i d = (2.2) It should be noted that the optimization problem in (2.1) and (2.2) is similar to the traditional unit commitment problem, the only difference being that the unit cost functions of the unit commitment (fuel cost plus variable O&M) has been replaced by the offer cost curve of the supply resources. The objective function (2.1) is additive and individual offers are only coupled through the system demand constraints. This is an ideal separable structure for the Lagrangian relaxation technique, which has been well developed and applied to this type of problems with a complex set of system constraints and individual offer constraints as reported in the literature. An important result deserving elaboration is that the Lagrange multipliers relaxing the system demand constraints are actually the marginal costs to provide one unit of energy. Based on this, the CAISO has adopted the MCP mechanism, and the Lagrange multipliers will be used to pay suppliers who are selected to provide energy. It can also be seen that there is inconsistency between the objective function minimized, which is the total offer cost, and total energy payment, which is based on the MCPs. B. Payment Cost Minimization Payment cost minimization for a market-clearing price settlement mechanism is to minimize the total payment cost for energy, and mathematically can be simplified for illustration and comparison purposes as follows: T I i t= 1 i= 1 { min J, with J MCP( t) pi ( t) + Si ( t), (2.3) { MCP( t) }{, p ( t) } where MCP (t) is the market clearing price at time t, and MCP( p 1 ( t),..., p ( t)) max{ O ( p ( t)), i s. t. pi ( t) > 0}, (2.4) I subject to system demand requirements (2.2), and individual offer constraints as described above. Comparing the two objective functions in (2.1) and (2.3), the difference is that the individual cost curves O i ( p i ( t ),t ) in (2.1) has be replaced by selected offer level p i (t) times market clearing price MCP (t), which is a function of selected offers. It is important to note that the objective function (2.3) is no longer additive on offers, and the ideal separable structure of (2.1) does not exist so that Lagrangian relaxation may not be effective for the problem in (2.3). For mathematical convenience, the supply offer curves or prices are re-defined to be zero if no power is selected, i.e., O ( p ( t), t), p ( t) > 0, r i i i Oi ( pi ( t), t) (2.5) 0, pi ( t) = 0. Therefore MCP(t) becomes dependent on all offers as opposed to only selected offers, and (2.4) can be re-written as r MCP( t) Oi ( pi ( t), t), i and t, or equivalently, r gi ( t) Oi ( pi ( t), t) MCP( t) 0, i and t. (2.6) III. TWO SIMPLE EXAMPLES As can be seen from the previous section, the problem formulation of payment cost minimization is different from that of offer cost minimization. Is it equivalent, or as an approximation, or reasonable to solve the offer cost minimization based on the Lagrangian relaxation technique as described in Section 2, and then pay all selected offers by the system marginal cost (Lagrangian multiplier) derived from the method? Two simple examples as follows are designed to answer the above question from two different angles. The first example considers only one energy product for auction i i } 2

3 with the capacity related costs such as start-up and no-load costs, while the second is a two product auction. Example 1. Assume for simplicity a one-hour auction with four offers from four units, and system demand of 100 MWh with no reserve requirement. The supply offer prices and characteristics of the four units are summarized in Table 3.1: Capacity (MW) Table 3.1 Offer Price ($/MWh) Capacity Cost Unit A Unit B Unit C Unit D The optimal solutions for offer cost minimization of (2.1) and payment cost minimization of (2.3) are provided, respectively, in Tables 3.2 and 3.3. It is clear that the two minimizations produce different energy schedules, as expected. In offer cost minimization, Unit C with a higher offer price is selected to provide the last 10 MWh of energy since only the costs of the units are considered. The latter problem considers the impact of the incremental energy market clearing price since once this unit is selected and this price is set for MCP, then every MWh of energy is paid at this higher price. That is why Unit D, with a lower energy offer price but a higher unit capacity cost, is selected for payment cost minimization, despite its large capacity cost. Table 3.2 Offer Cost Minimization Capacity Total (MWh) Cost Cost Unit A Unit B Unit C Unit D Total Pay the Market Clearing Price = $100/MWh (MWh) Cost Capacity Cost Total Unit A Unit B Unit C Unit D Total However, if the payment scheme is to pay the units the market-clearing price (pay-at-mcp), $100/MWh in the case of the offer cost minimization, then the total payment cost increases dramatically to $10,200 as shown on the right side of Table 3.2 as compared to $5,000 from payment cost minimization in Table 3.3, and this results in an uneconomic decision by using offer cost minimization. As this simple example clearly demonstrates, the two minimizations produce different auction results and the payment cost minimization can potentially reduce the total payment significantly. Table 3.3 Payment Cost Minimization (MWh) Cost Capacity Cost Total Unit A Unit B Unit C Unit D Total Example 2. When more than one product is considered in the auction at the same time, the auction is referred to as a simultaneous optimal auction. Although the formulations of offer cost minimization and payment cost minimization given above were for energy, a single product, we give a simple example of a simultaneous optimal auction for a two-product auction involving energy and ancillary service, and show that the cost savings observed under the single product case still holds. Assume a one-hour auction with two generation units and system demand of 100 MWh and ancillary service requirement of 5 MW. The supply offer prices and characteristics of the two units are summarized in Table 3.4. Capacity (MW) Table 3.4 Ancillary Service (MW) Offer Price ($/MWh) AS Offer Price ($/MW) Unit A Unit B The two optimal solutions for the offer cost minimization and payment cost minimization are summarized in Tables 3.5 and 3.6. It is again clear that the two minimizations produce different selected energy and ancillary service, as expected. For offer cost minimization, Unit A with a total of 100 MW capacity and lower energy and ancillary service prices is selected to provide the 5 MW ancillary service instead of providing the last 5 MWh of energy since it compares only the cost of 5 MW ancillary service and the cost of 5 MWh energy. However, payment cost minimization considers the impacts of the incremental market clearing prices for both energy and ancillary services. In this case, the last 5 MW capacity from Unit A is selected for energy but not ancillary service so that the MCP for energy is $20/MWh which applies to a total of 100 MWh even through the market clearing price for ancillary service is $8/MW which only applies to 5 MW. As presented above, the two examples clearly demonstrate that the two optimizations produce different solutions, and they are not equivalent. Payment cost minimization provides a significant savings potential for consumers. A summary of the solution methodology developed to solve the payment cost minimization problem for energy, a single product auction, is provided in the next section 2. 2 The formulation and solution methodology for a simultaneous optimal auction with multiple products is currently being developed. 3

4 (MWh) Table 3.5 Offer Cost Minimization Cost AS Cost AS (MW) Total Unit A , ,910 Unit B Total , ,035 Pay the Market Clearing Prices MCP for = $25/MWh MCP for AS = $7/MW (MWh) Cost AS Cost AS (MW) Total Unit A , ,410 Unit B Total , ,535 (MWh) Table 3.6 Payment Cost Minimization MCP for = $20/MWh MCP for AS = $8/MW 3 AS (MW) Cost AS Cost Total Unit A ,000-2,000 Unit B Total , ,040 IV. SUMMARY OF AUGMENTED LAGRANGIAN RELAXATION AND SURROGATE OPTIMIZATION 4 As reported in [8] and [9], major difficulties that must be overcome to effectively solve the payment cost minimization problem include inseparability of the objective function, the maximum term in defining MCPs, and solution oscillation caused by linear subproblem objective functions. The difficulty of solution oscillation is overcome by using the augmented Lagrangian, which is formed by adding quadratic penalty terms of coupling constraints to the standard Lagrangian, leading to a quadratic relaxed problem with improved convergence. Although this leads to additional inseparability, the surrogate optimization framework used to handle the inseparability difficulties and the maximum term in defining MCPs is able to efficiently handle this. The key idea of surrogate optimization is that it is not necessary to accurately minimize the relaxed problem. Rather, approximate optimization is sufficient if the surrogate optimization conditions are satisfied. Since the relaxed problem cannot be decomposed ([9]), it is optimized as a whole with respect to the decision variables of a particular offer or a particular MCP (an offer subproblem or an MCP subproblem) by using dynamic programming. In solving an 3 The MCP is derived from the system marginal cost of the Lagrangian Relaxation methodology, and may not equal to the marginal bid cost which is $2/MW in this example. This inconsistency or over-pricing problem will not be addressed in this paper. 4 The solution methodology for the MCP payment cost minimization problem using Augmented Lagrangian Relaxation and Surrogate Optimization is US patent pending. offer subproblem, the decision variables of other offers may have to be adjusted to overcome the difficulties caused by the structural change of the augmented Lagrangian as MCP varies when the selection status of the offer under consideration is changed. Once the surrogate optimization conditions are satisfied, multipliers are updated by using the surrogate subgradient obtained. The solution methodology is used to solve a medium sized 24-hour problem ([9]). Using historical values of the average New England Load over five days in May 1999, the system demand was randomly generated using a Gaussian distribution. Twenty-five participants bid to supply the load with offers randomly generated using a Gaussian distribution, and the total supply capacity is 30% above the maximum mean system demand. The payment cost minimization and the offer cost minimization algorithms were then applied to this problem. Hourly MCPs for offer cost minimization and payment cost minimization are plotted in Figure 4.1, and various costs are summarized in Table 4.1. It can be seen from the table that a savings of 4.7% corresponding to $354,326 is realized by payment cost minimization over offer cost minimization. MCP ($/MW ) Hour M CP - Paym ent M inim ization System Dem and (GW ) MCP - Bid C o st M inim ization Figure 4.1 Hourly MCPs for the offer cost minimization and the payment cost minimization formulations Table 4.1 Summary of Purchase Costs for This Example METHOD TOTAL OFFER COSTS MCP PAYMENT COSTS OFFER COST MINIMIZATION $5,640,736 $7,570,446 MCP PAYMENT COST MINIMIZATION $5,679,169 $7,216,120 SAVINGS $354,326 The above result shows that the payment cost minimization algorithm is applicable to medium sized problems and results in lower payment costs as compared to the offer cost minimization algorithm for the same set of offers. V. ECONOMIC IMPLICATIONS OF THE OBJECTION FUNCTION CHOICE As mentioned in the Introduction, the appropriate choice of the objective function to be used for optimal auctions has not been fully and publicly discussed. Surely, one ought to System D em and (G W ) 4

5 wonder if the economic theories established for a regulated, vertically integrated market structure are still applicable in today s world of market clearing price auctions. For instance, under vertical integration, maximizing producer surplus was consistent with minimizing total production cost; can this apply to the new deregulated electricity markets? The CAISO has expressed skepticism regarding the potential for application of a MCP payment cost minimization objective function in its market design. We agree that the payment cost minimization as we proposed is not well understood in practice because it has not been implemented in any of the currently operational markets, and there is no empirical evidence to gauge its impact on bidding behavior and resulting price [4]. However, our initial results show promise and provide a basis for completing our research, testing our results, and if these results show that costs can be saved, implementing a solution to the changed objective function in the currently operational markets. We certainly hope that the CAISO did not intend to argue that a new method should not be considered for implementation because most systems use another method, but rather that we should study the alternative prior to considering its implementation, an approach which we support. VI. CONSUMER AND PRODUCER SURPLUS In discussions regarding what is the proper objective function to use in the California ISO (CAISO), some have suggested that the proper objective should be to maximize total social welfare defined as the sum of producer and consumer surplus. We will briefly discuss whether social welfare maximization is appropriate for an ISO, then we will demonstrate that such an objective, even if it were determined to be desirable, is not achievable based on current bidding rules, and is certainly not achieved by using the offer cost minimization approach in use today. Consider traditional unit commitment and economic dispatch prior to restructuring electricity markets. A utility would minimize the cost of serving its native load using the set of resources it had available, possibly also considering access to energy markets as an alternative to the use of its own resources. These costs would include fuel costs, start-up costs, costs of regulating the system and maintaining operating reserves, and the costs of meeting any other system operating constraints so as to provide reliable electric service to customers. The previously described alternative optimization problems, i.e., maximizing social welfare and minimizing the cost of serving the load, degenerate into a unique objective function. Minimizing the cost of production is equivalent to minimizing the consumer s cost, as fuel cost were directly passed on to consumers through fuel adjustment clauses in utility ratemaking. Social welfare maximization, i.e., maximizing the sum of producer and consumer surplus, was also equivalent to minimizing production costs, as consumer surplus would depend only on the price which was established based on utility cost recovery, and would not depend on the marginal cost of dispatch, whereas producer surplus would automatically be maximized by minimizing the cost of production necessary to serve the load. This convergence of objective functions ceased to exist when the introduction of competitive electricity markets operated by ISOs replaced traditional unit commitment and economic dispatch. Many years of work and a wealth of literature had been dedicated to improving the solutions and simulating the solutions to the unit commitment and economic dispatch problem with a myriad of operating constraints. A plethora of optimization algorithms and simulation software were available in the market. When the operation of electric systems was undergoing a transition to independent system operators, some new problems were introduced leading to much new research. The new efforts focused primarily on resolving transmission congestion when the transmission system was to be opened up to equal access by various market participants. The desire to efficiently resolve the allocation of scarce transmission paths in complicated electricity networks led to investigations into zonal congestion management versus locational marginal pricing debates, and to flowgate models to efficiently reflect the physics of electron flow. Transmission rights allocations physical or financial, were considered as market participants wanted to be able to efficiently hedge their scheduled transactions in the presence of uncertain congestion prices. As we moved from the traditional utility operating environment to the ISO environment, one debate which is absent in the literature is the discussion over the objective function to be minimized in the restructured electricity system dispatch. A seamless transition occurred with the continuation of the cost minimization algorithms based on traditional production cost objective functions. There are no papers in which there is an examination of alternative objective functions for dispatch and operation of electric systems in a restructured environment. Most references to the objective function simply refer to it as production cost minimization, cost minimization, and in some limited circumstances, characterize the problem, incorrectly as we will demonstrate, as social welfare maximization. Should the objective function in independent system operator dispatch be the maximization of social welfare? We will not engage in the debate here regarding the merits of such an objective function. We note however that FERC has stated in its Standard Market Design (SMD) [5] that the objective of the Regional Transmission Operator in effectuating its implementation of SMD should be the minimization of costs to consumers. Thus the only official word on the subject is unequivocal. ISOs should be operating their systems to provide reliable electric service in a manner than minimizes electricity costs to consumers. Perhaps more important than FERC s stated objective or the lack of academic debate on the subject of the objective function are the practical facts. In order to maximize social welfare one would have to be able to establish a reasonable measure of social welfare. Social welfare is the sum of producer and consumer surplus. Setting aside the lack of 5

6 recognition of consumer surplus in the offer cost minimization mechanism currently in use in ISOs, we will focus on the producer surplus component of the social welfare function. Producer surplus is defined as the difference in the price received by producers for their products and the cost to producers to supply the product. This is often depicted graphically in economics texts as the area between the market clearing price and the supply curve. As long as the supply curve represents the marginal cost of production, this graphical depiction is appropriate. If the supply curve is based on offers that are not related to the cost of production, then this representation does not reflect a component of social welfare. Clearly, from a social welfare perspective, if a unit can generate at a cost lower than the price at which it can be sold in the market, then that unit should generate. The facts associated with electricity market optimization are clear. Suppliers submit to the ISO generation offers which are incorporated into the optimization and dispatch algorithm. Unlike the traditional utility problem, in which cost curves were input to the dispatch function, we now have offers that may bear no resemblance to costs of production. As evidence of the lack of relationship between offers and cost of production, consider the examination that has taken place regarding the California electricity market. Studies by Borenstein, Bushnell, and Wolak [3] and by Joskow and Khan [6] have examined the differences between offer-based market clearing prices and marginal costs of production. Sheffrin [10] has analyzed supplier bidding behavior in California, and the testimony put forth by Berry [1] in FERC Docket EL-095 also demonstrates that bidding behavior was not related to costs of production. If offers bear no systematic relationship to costs of production then they provide no useful information to the calculation of producer surplus, and thus no value in maximizing social welfare. The conclusion is simple. We cannot measure producer surplus with offer information, therefore we cannot maximize social welfare. The question of whether we should be using social welfare maximization as an objective is moot. The FERC SMD establishment of consumer cost minimization remains the only reasonable objective to pursue. We submit it is also the proper objective to pursue. Why should we prefer a solution that minimizes costs to consumers over one that minimizes offer costs? In order to consider this issue we should consider a simple example that may be illustrative of the difference between these solutions. Assume a simple system with 100 MW of demand. There are three units available to serve demand in a particular hour. One, call it unit A, is an online, low marginal cost of production, base-load generating station whose offer cost is $20/MWh with a capacity of 90 MW. Unit B is an intermediate unit, not online, with a $2,000 start-up cost whose offer is $30/MWh. Finally, Unit C is a quick start unit, not online, but with only a $20 start-up cost, whose offer cost is $100/MWh. Units B and C can generate as little as 10 MWs. The dispatch only considers energy cost and start-up costs. Under offer cost minimization units A and C would be selected with an offer cost equal to $2,820 ($20/MWh x 90MW from A + $100/MWh x 10 MW plus $20 start-up from C) compared to using A and B, which would have resulted in $4,100. The costs to consumers would be $10,020 (MCP of $100/MWh x 100 MW + $20 start-up). Under a MCP payment cost minimization system units A and B would be selected with a cost to consumers of $5,000 (MCP of $30/MWh x 100 MW + $2,000 start-up). This example, essentially the same as used in Section 2, is shown in the table below. Table 6.1 Capacity (MW) Offer Price ($/MWh) Capacity Cost Unit A Unit B ,000 Unit C Ultimately, the question we face, even in this simple example, is whether the better solution includes the dispatch of unit B, whose start-up cost makes it look costly under offer cost minimization, or unit C, whose dispatch significantly raises the MCP used to pay suppliers. If you believe the correct answer to this question is to dispatch unit C, then consider the following scenarios 5 : (1) Unit A and C are owned by the same company Unit A has marginal cost of production of $20/MWh Unit C has marginal cost of production of $25/MWh (2) Unit C has marginal cost of production of $25/MWh Unit C has actual start-up costs of $3,000 Units A and B have production and start-up costs equal to their offer costs. If the facts were consistent with scenario (1), then the owner of Units A and C is exercising market power by offering Unit C at a much higher cost than its cost of production, knowing that it is in competition against a unit with large start-up costs, thus raising the market price to be paid to unit A s output. Such an outcome hardly seems consistent with maximization of social welfare. If the facts were consistent with scenario (2), then the actual costs of dispatching Unit C would be $3,250, compared to $2,300 for Unit B, though under offer cost minimization Unit C would be dispatched, and would earn a profit. In this case, clearly society s cost of producing power is reduced by dispatching B. Note that in this case start-up costs are provided as offers rather than cost justified. Some market rules might not allow this flexibility. If, as noted above, cost justification were required for energy offers, the issue of maximizing social welfare would be germane as it would be feasible to measure social welfare. These two scenarios illustrate, for this simple example, why it is not possible to determine the impact on social welfare from the dispatch of resources based on offers rather than costs. Absent the alternative of maximizing social 5 Note that the demand and offers are not changed in these scenarios, though assumptions regarding ownership and actual production costs are added, in no way contradictory to the example as presented above. 6

7 welfare even as an option for consideration, are there other reasons why it might be preferable to dispatch using offer cost minimization, even while paying based on MCP? Other reasons listed by the California ISO (CAISO) are provided below. offer cost minimization optimization while using a pay-at- MCP mechanism to compensate winning participants is exactly analogous to California BRPU debacle, and can be anticipated to produce similar types of inefficiencies and gamed offers. VII. INCONSISTENCY BETWEEN THE ACTUAL PAYMENT AND OBJECTIVE FUNCTION MINIMIZED California, in addition to being the victim of an immensely costly electricity crisis in , also fell victim to a manipulated auction process associated with the addition of new resources in the time period. The California Public Utilities Commission instituted a process called the Biennial Resource Plan Update (BRPU) in order to identify and add least cost new resources to California investor-owned utilities portfolios. The process was designed as an auction in which new resource options competing to fill an identified utility need at a cost lower than a regulatorily determined utility cost to fill that need, submitted offers. The rules for evaluating the winners of this auction differed from the rules establishing payments to the winners of the auction. One key element of the difference between evaluation rules and payment rules is that for evaluation purposes an assumed level of production from generating units was included in the comparison of resource alternatives. For example, wind resources were assumed to operate at some capacity factor, say 30%, in order to compare the cost of production from these resources with higher capacity factor resources such as a combined cycle facility that might operate at an 85% capacity factor. The capacity and energy offers of resources were converted to a total cents per kilowatt hour of expected production cost, and lower cost offers were selected as winners. Payment was based on the offer parameters of the winning offers, but it was also based on actual, not assumed production levels. A clever wind power producer submitted an offer with an extremely large capacity component on the order of $5,000/MW with a large negative energy offer. The result at an assumed 30% capacity factor was an operating cost for offer evaluation purposes of about $15/MWh. Operating restrictions associated with contracts allowed for outages such that the offer was only required to operate at a 25% capacity factor. If the winning offer in fact operated at a 25% capacity factor instead of the 30% assumed for offer evaluation, its actual payment costs would be about $150/MWh, making it more costly than any other offer in the auction. While FERC eventually rejected the results of this process as a violation of PURPA (due to the restriction in the auction to offers from Qualifying Facilities under the 1978 PURPA statute, not due to the flawed design of the auction evaluation/payment process), the lesson is on point here. When evaluating between the choice of alternatives in an auction, if the payment structure differs from the offer evaluation rules than there is an incentive for participants to seek offers that will minimize their perceived cost in offer evaluation while maximizing their payment if they are selected in the auction. Establishing a mechanism such as an VIII. IMPACTS ON BIDDING BEHAVIOR The transition of markets from a vertically integrated structure to a competitive wholesale market using auctions to set market clearing prices has occurred in numerous locations nationally, and around the world. As noted previously, the discussion of objective function has apparently been absent in these transitions, such that it is unlikely that many market participants are even aware of the objective functions used by the ISOs in which they operate. The authors experience in discussing objective functions with market participants has been uniform: no evidence of knowledge of ISO objective functions let alone incorporation of that objective function into the behavior of the participant has been observed. While we suspect that behavior to date of market participants has not incorporated the objective functions in use to evaluate offers and determine winning offers and market prices, it is certainly possible that bidding behavior of some may have been affected by the objective function. This could occur either through more in depth knowledge of ISO practices by market participants than the authors have observed, or, without any knowledge of the inner workings of ISOs, by learning through the use of successful bidding strategies over time. Since it is possible that bidding behavior could be a function of the ISO objective function used in the optimal auction, we must consider the impacts of such behavioral changes. 6 If, in fact, participants, either through learning, or through complex strategy development, are capable of modifying their bidding behavior based on the ISO s choice of objective functions in their optimal auction procedures, then the conclusion of lower cost for one objective function compared to another cannot be guaranteed. The use of MCP payment maximization as an objective function will produce the lowest system cost for a given set of offers by market participants. However, if it is assumed that a different set of offers would occur under MCP payment cost minimization compared to offer cost minimization then no final conclusion on the total cost to consumers can be drawn without examination of bidding behavior. The authors intend to continue their research into the question of changed bidding behavior under different objective functions to determine whether in practice, bidding behavior differences would occur, and if so, if the conclusions regarding the impact of the objective function on costs to customers described in this paper continue to hold. As in the California BRPU case described above, the incentives associated with inconsistency between auction evaluation mechanisms and payments to winning offers will 6 Concern regarding market participant behavior was raised as an issue by the researchers of the University of California Institute (UCEI) during discussions relating to changing the objective function. 7

8 be problematic. One form of bidding behavior observed during the California electricity crisis of was what has been denoted by FERC and others as hockey stick offering. This moniker is due to the graphical image of such offers as shown in Figure 8.1 below. The supply offer in such circumstance includes a small segment of offer at a very large price. In an offer cost minimization evaluation system such an offer will only be selected if the offer cost of this small additional supply segment is lower than the offer cost of alternative supply options. But the offer cost in the evaluation will be limited to the product of the offer price and the quantity offer. The offer price in hockey stick offering is large, but the offer quantity is small, thus the resulting total cost impact from adding this offer segment may not be large. If the alternative options to the optimization algorithm include larger total offer costs (for example, as has been shown in section 4, if these alternatives include substantial capacity cost components), then the hockey stick offer segment may indeed be selected. The theory behind the hockey stick offer is that if market conditions are such that a segment on the steep section of the supply curve is needed, then the market clearing price that will be paid to the entire portfolio will be set at a level at least as high as that costly segment. In other words, the hockey stick offer is premised on the fact that actual payment is based on a pay-at-mcp system. During the California energy crisis the use of hockey stick offering was successful because it was combined with other factors such as a tight demand/supply balance, physical and economic withholding of generation by many market participants, and other market manipulations to create a false scarcity of supply. In that system the success of hockey stick offering did not require an offer cost minimization optimization to be successful 7, it merely required the necessity of high priced offer segments to clear the market. The strategy was in wide use however, and this same strategy appears to be an effective means of manipulating market clearing prices in an auction with an offer cost minimization optimization but a pay-at-mcp settlement structure. Price ($/MW) Hockey Stick Bid IX. OTHER ISSUES In the discussion of California electricity market redesign, some misunderstood the difference between the aforementioned two auction approaches and expressed their concerns that generators would not necessarily be receiving the marginal value of their outputs under a MCP payment cost minimization approach; consequently, in the short run, the MCP payment cost minimization approach could lead to a different offering strategy targeting higher profit margins. As demonstrated in the Sections 2 and 3, in either offer cost minimization or payment cost minimization, the energy payment is based on the offer cost of the highest offer necessary to clear the market, i.e. the MCP. One possible concern is whether the MCP is determined to be the system marginal cost (lambda) derived from the Lagrangian relaxation technique. At this point, we see no basis for the conclusion that using MCP payment cost minimization provides incentives for offering strategies leading to higher profit margins for some firms. To the contrary, as demonstrated in the prior example, the disconnect between the algorithm used for dispatch and the algorithm used for payment can create opportunities to offer such that the evaluation of the offer has a smaller perceived cost than the outcome from payment, thus creating gaming incentives. In addition, the MCPs derived in the payment cost minimization are not guaranteed to be lower than those of offer cost minimization as one can see in Figure 4.1 of Section 4, but the total payment cost is always lower than that of the offer cost minimization, for a given set of offers. One might wonder whether minimizing payment cost could discourage economic maintenance, upgrading, and other decisions that impact the amount of capacity available to provide energy and ancillary services. The only rational interpretation of this question is that it is somehow better to pay generators more, because they will use this increased revenue to improve the performance of their units. The conclusion that more payment is desirable, disconnected from either the cost of operation or the cost to the system, lacks any foundation or merit. If this question is predicated on the assumption that producer surplus would be lost under the MCP payment cost minimization algorithm, that flawed critique has previously been addressed. The fact remains that if a unit offers its marginal cost of production and it is selected in the auction process, it will receive revenue at least as great as that marginal cost of production. Quantity (MW) Figure Though the optimization method was Bid cost minimization, since it was not a simultaneous auction but a single product energy auction, the choice of algorithm would have made no difference in the outcome this system essentially stacks energy bids and determines how much supply is needed to meet demand to choose the equilibrium P and Q and associated winning bidders. X. CONCLUSION In this paper, we have provided the mathematical formulations for offer cost and MCP payment cost minimizations, and summarized the solution methodology for solving the MCP payment cost minimization problem by using augmented Lagrangian relaxation and surrogate optimization. Data has been used to test the method based on a simplified energy market, and the testing result demonstrates significantly potential savings for electricity consumers in the 8

9 ISO/RTO electricity markets. More importantly, this paper addresses economic implications of the objective function choice, including whether maximizing social welfare should be one of objectives of electricity industry deregulation. To answer this question, we conclude that such an objective, even if it were determined to be desirable, is not achievable based on current offering rules after moving from traditional vertical integrated utilities into the market approach, and is certainly not achieved by the offer cost minimization approach in use today. Other implications such as the inconsistency between the actual payment and cost function minimized, and bidding behavior are also discussed in the paper. Generally speaking, the research is still at the early stages before actual implementation. We are going to pursue this research from two main perspectives: first, economic implications should be explored further; and more testing should be performed for different power systems; and bidding strategies should be evaluated for both offer cost and MCP payment cost minimizations. Second, real market structures and products in the ISO/RTO markets should be incorporated into augmented Lagrangian relaxation and surrogate optimization, including ancillary service products and compensations of no-load cost or minimum generation cost and start-up costs, and more physical power system constraints, such as AC or DC power flow constraints in order to produce locational marginal prices (LMP). ACKNOWLEDGMENT This work was supported in part by the Southern California Edison Company under purchase order number Q and in part by the National Science Foundation under Grant ECS The authors would like to thank Dr. Severin Borenstein, Dr. Frank Wolak, Dr. Jim Bushnell, Dr. Shmuel Oren, and other researchers of the University of California Institute (UCEI) in the University of California at Berkeley for their valuable suggestions and comments. The authors also take any and all responsibility for any errors. This paper represents the views of the authors and only the authors. Specifically the views expressed herein do not represent the views of the authors employer, Southern California Edison Company. REFERENCES [1] Berry, Carolyn, Prepared Testimony of Dr. Carolyn A. Berry on Behalf of the California Parties, March 3, Docket No: EL00-95 and EL [2] Bertsekas D. P., Nonlinear Programming, Second Edition, 1999, Athena Scientific, Belmont, Massachusetts. [3] Borenstein, S., J. Bushnell and F. Wolak, Measuring Market Inefficiencies in California s Restructured Wholesale Electricity Market, American Economic Review, Vol. 92, No. 5, pp , December 2002 [4] California Independent System Operator (CAISO), Amendment to Comprehensive Market Design Proposal, July 22, 2003, [5] Federal Regulatory Commission (FERC) Working Paper on Standardized Transmission Service and Wholesale Electric Market Design, March 15, [6] Joskow, P.L. and E. Kahn, A Quantitative Analysis of Pricing Behavior in California s Wholesale Electricity Market during Summer 2000: The Final Word, Revised February Available at [7] Kahn, A.E., P.C. Cramton, R.H. Porter, and R.D. Tabors, Pricing in the California Power Exchange Electricity Market: Should California Switch from Uniform Pricing to Pay-as-Bid Pricing? Blue Ribbon Panel Report, January [8] Luh, P. B., W. E. Blankson, Y. Chen, J. H. Yan, G. A. Stern, S. C. Chang, and F. Zhao, Optimal Auction for the Deregulated Electricity Market Using Augmented Lagrangian and Surrogate Optimization, 2004 IEEE PES Power Systems Conference & Exposition, October 10 13, 2004, New York, USA. [9] Luh, P. B., W. E. Blankson, Y. Chen, J. H. Yan, G. A. Stern, S. C. Chang, and F. Zhao, Payment Cost Minimization Auction for Deregulated Electricity Markets Using Surrogate Optimization, has been submitted to the IEEE Transactions on Power Systems, and is available at [10] Sheffrin, A., Empirical Evidence of Strategic Bidding in California ISO Real Time Market, March 21, [11] Yan, J. H. and G. A. Stern, Simultaneous Optimal Auction and Unit Commitment for Deregulated Electricity Markets, the Electricity Journal, November [12] Zhao X., P. B. Luh, J. Wang, Surrogate Gradient Algorithm for Lagrangian Relaxation, Journal of Optimization Theory and Applications, Vol. 100, No. 3, March 1999, pp Gary Stern is the Director of Market Monitoring and Analysis for Southern California Edison Company (SCE). He reports to the Senior Vice President of the Power Production Business Unit, and manages a division responsible for monitoring the wholesale electricity market in California. Gary leads SCE s efforts, working with the California Independent System Operator (CAISO) and the Federal Regulatory Commission (FERC), to ensure that the wholesale electricity market design being implemented by the CAISO results in a reliable and efficient outcome for SCE as a large buyer and seller of electricity on behalf of its customers. Gary s recent endeavors have included managing SCE s efforts to obtain several billion dollars in refunds for market manipulation and market power abuse during the electricity crisis in California. Gary s participation in the refund settlements negotiations has resulted in several FERC Decisions that have refunded over $2 billion to California Utilities. He is also managing the design of a new resource adequacy requirement partnering with the California Public Utilities Commission (CPUC), the California Commission (CEC) and other stakeholders. Gary Stern holds a Ph.D. in Economics from the University of California at San Diego. Joseph Yan is a project manager in the Market Monitoring and Analysis Division of Southern California Edison. For the last ten years, he has worked in areas of the electricity system operations, wholesale energy market analysis for both regulated and non-regulated affiliates, market monitoring and market design in California, and California Electricity Refund case of the crisis. His research interest includes operation research, optimization, unit commitment/scheduling and transaction evaluation, and optimal simultaneous auction in deregulated ISO/RTO markets. Joseph Yan holds a Ph.D. in Electrical and Systems Engineering of the University of Connecticut. Peter B. Luh (M 80-SM 91-F 95) received his B.S. degree in Electrical Engineering from National Taiwan University, Taipei, Taiwan, in 1973; M.S. degree in Aeronautics and Astronautics Engineering from M.I.T., Cambridge, MA in 1977; and Ph.D. degree in Applied Mathematics from Harvard University in Since then he has been with the University of Connecticut, and currently is the SNET Professor of Communications & Information Technologies in the Department of Electrical and Computer Engineering. He is a Visiting Professor at the Center for Intelligent and Networked Systems, 9

10 Department of Automation, Tsinghua University, Beijing, China. He is interested in planning, scheduling, and coordination of design, manufacturing, supply chain; configuration and operation of building elevator and HVAC systems; schedule, auction, portfolio optimization, and load/price forecasting for power systems and decision-making under uncertain or distributed environments. He is a Fellow of IEEE, the founding Editor-in-Chief of the new IEEE Transactions on Automation Science and Engineering, an Associate Editor of IIE Transactions on Design and Manufacturing, an Associate Editor of Discrete Event Dynamic Systems, and was the Editor-in- Chief of IEEE Transactions on Robotics and Automation ( ). William E. Blankson (S 04) received his B.S. degree in Electrical Engineering from the Kwame Nkrumah University of Science and Technology, Kumasi, Ghana in 1997; M.S degree in Electrical Engineering from the University of Connecticut, Storrs, CT in 2003, and is currently a Ph.D. student in the Electrical Engineering program at the University of Connecticut, Storrs, CT. From 1998 to 2001 he was a Controls and Instrumentation Engineer at the Takoradi Thermal Power Plant in Ghana. He was an intern in the Resource Planning & Strategy department of Southern California Edison Company during the summer of 2004, and a Market Support Intern with the Electric Reliability Council of Texas (ERCOT) during the summer of His research interests include optimization theory and algorithms, neural networks, power systems, and their application to the restructured electricity markets. 10