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Robust market design for power industry deregulation by simulations
Simulation Modelling Practice and Theory 18 (2010) 589–599
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Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat
Robust market design for power industry deregulation by simulations Shenghua Cai a,*, Tetsuo Tezuka b a b
The China Center for Energy Economics Research, Xiamen University, China The Graduate School of Energy Science, Kyoto University, Japan
a r t i c l e
i n f o
Article history: Received 8 June 2009 Received in revised form 4 January 2010 Accepted 7 January 2010 Available online 18 January 2010 Keywords: Robust market design Methodology Simulation System dynamics
a b s t r a c t This paper proposes one concept of robust market design subject to stakeholders’ strategic behavior. The key to robust design is the application of computer simulations, which is used to as a tool to avoid detectable loopholes in the market. An example illustrates the method. Computer simulation not only provides much information about the dynamics of economic agents’ interaction, but also allows modeling of aggregate market outcomes from heterogeneous individual behavior. With this method, the policymakers have a better opportunity to communicate with others and to understand the possible consequences of different decisions under different optional policies and market conditions. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Since the United Kingdom opened a Power Pool in April 1990, the regulatory framework for the electricity industry has been replaced in many countries by introducing market competition in order to generate electricity efficiently and reliably. Although there are various restructured electricity markets operating in the world, there are still continuing debates over various aspects of electric power industry deregulation. For example, the problem of ‘‘deregulation or reregulation” is challenged by some experts [1,2]. Electric power industry deregulation is a complex problem that has engineering, economic, commercial, and legal and policy dimensions and takes place within a broad societal context that itself influences and is influenced by the outcomes. From the national energy-environmental perspective, there is much conflict between electric power industry liberalization and policies of promoting renewable energy development, policies on nuclear power utilization, technological innovation, etc. [3]. On the other side, there are many uncertainties coming from various sources, such as the uncertain Post-Kyoto Regime, uncertain prices of international fuel markets, uncertain future weather conditions, uncertain national macro-economy, uncertain market players’ strategic behavior, etc. All of the aspects above should be taken into account when we design the program of liberalization the electric power industry. Lessons and experience tell us it is impossible to recommend one ‘‘best” solution to solve all problems. However, there is much possibility and necessity for us to intend to look for a ‘‘second-best” solution. This study is meant as a contribution to this inquiry. This paper discusses the conception of ‘‘second-best” from the perspective of systems’ robustness. According to [4], robustness is defined as ‘‘the degree to which a system or component can function correctly in the presence of invalid inputs or stressful environmental conditions.” Robust market design, which is discussed in a narrow sense as a starting point, is
* Corresponding author. Tel.: +86 592 2186 076; fax: +86 592 2186 075. E-mail address: [email protected] (S. Cai). 1569-190X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2010.01.002
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defined as deciding a set of the rules that satisfies the constraints required for realizing desirable or acceptable outcomes of the market no matter of the stakeholders’ strategic behavior [5]. That is, a market is considered robust if the behavior of the market even in the worst cases are still acceptable. Different from this, the literature in mechanism and auction design, a sub-discipline of game theory, analyses how equilibrium behavior in the market game depends on the market rules, and how market rules that implement desired market outcomes look like. Moreover, we mainly concerns the methodological aspect of robust design from a pragmatic viewpoint. The purpose of this paper is to propose a new method for robust market design in decentralized systems with autonomous decision-makers by simulations, such as power markets. And the key to the robust market design is the application of simulation technology. Different from the closed-form deductive analyses, either operations research models in decision science or game-theoretical models in the context of mechanism design [6], in which equilibrial outcomes of the market are their primary concerns, robust design does not differentiate outcomes in equilibrium from those out of equilibrium. All of the outcomes are assessed to be acceptable or not according to the designers’ objectives. Simulation technology is used as a tool to avoid detectable loopholes in the market. The re-design process is intended to remedy the loopholes detected. That is, robust market design includes the process of looking for worse-case strategies that brings unacceptable outcomes and the process of redesigning market rules in order that even in the worst-case situations the outcomes of the market are acceptable. An example illustrates an application of this method. This paper is organized as follows. First, we make a selective literature review on power market analysis and design, and discuss the limitations of each method from a methodological perspective. Then, we describe the mathematical formulation and implementory procedure of robust market design proposed in this study. Next, by taking a capacity payment system for realizing long-term supply–demand balance as an example, we illustrate its design process. Finally, we state the conclusion of this paper and further studies.
2. A selective literature review on power market analysis and design The main methods applied in power market analyses and design include the closed-form deductive analysis, experimental economics and agent-based simulations. Indeed, if the design objectives are clearly defined, some of the recent techniques of simulation and optimization developed by system scientists and computational economists can be used to achieve a better market design directly or indirectly. In the following we selectively introduce several important studies, to the best of our knowledge, on market design in the context of electricity industry restructuring. Green and Newbery (1992) modeled the England and Wales electricity market using the Supply Function Equilibrium (SFE) framework as applied to an empirical characterization of supply and demand, designed to match the attributes of the electricity system in England and Wales. They found that generators were able to drive prices far above competitive levels, depending on the assumed elasticity of demand, while creating a significant deadweight loss and producing supra-competitive profits for the generators. They then examined the impact of restructuring the industry so that there were five equalsized firms. In this case, the equilibrium price was significantly lower and close to competitive levels [7]. Borenstein and Bushnell (1999) modeled the California power industry as a Cournot triopoly with a competitive fringe. They found that the potential for market power was greater when demand was high and the fringe’s capacity was exhausted, making it impossible for the small producers to increase production. During lower demand hours, Cournot producers had less incentive to withhold production because the fringe had excess capacity. In addition they found that the more elastic was the demand, the less was the incentive to exercise market power [8]. Rassenti et al. (2003) tested the effect of demand response and double-sided markets on the extent to which generators could exercise market power by using a laboratory environment with profit-motivated human participants. Their results indicated that demand-side bidding decreased price volatility, the magnitude of price spikes, and the ability of suppliers to exercise market power. Average prices were lower when both demand-side and supply-side bidding existed, as opposed to the one-sided supply-side bidding. This research provides the clear policy implication that active demand plays a valuable role in disciplining the pricing choices of generators in wholesale markets [9]. Thomas et al. (2002) tested auction mechanisms experimentally in a controlled environment to evaluate market designs. Their work described a framework for testing the efficacy of a price-responsive load on a uniform price last accepted offer and soft-cap market. The experimental evidence shows that price responsive load increase efficiency and decrease price volatility in the uniform auction and soft-cap design behaves similarly to the discriminatory auction, such as observed in California in the winter of 2001 [10]. Watanabe et al. (2003) developed a multi-agent simulation model in which power generators and suppliers (customers) are modeled as autonomous adaptive agents which progressively learn the optimal strategy with reinforcement learning mechanism. Their results show that demand increase, market power, price-cap regulation and transmission constraints are important factors of escalating market clearing prices [11]. Backus and Amlin (2005) present how a simulation and gaming approach can be a useful tool in learning about the dynamics of deregulation. UTILITIES 21, an all-fuel, fully integrated energy model, proved itself to be an extremely accurate tool for realistically showing the inevitable evolution of deregulated markets [12]. Wenzler and Mayer (2005) describe why and how different types of simulations can be used to understand and support the challenges of utility deregulation. They present a general classification of seven different types of simulation, including
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market simulations, policy simulations, dynamic business simulations, capability simulations, day-in-a-life simulations, performance simulations and gaming simulations [13]. All of these approaches have improved our understanding of market behavior and helped to design markets. But more or less, each of them has its limitations. Either SFE or Cournot models have difficulty to deal with complexity that comes from the practical design of electricity markets. And the assumption of perfect rationality and unlimited computational ability on human stakeholders is unrealistic [14]. Experimental economics is criticized for the external validity of the behavior of the human subjects, who might as well shade their decisions in some way since the experiments are of little consequence to them while the real world profits are of enormous consequences. Furthermore, the results of experiments cannot be reproduced. As for agent-based simulations, agents behave in ways that they are programmed to behave; in other words, the model by which agents respond to each other is one that has been foreseen by the researcher and has been programmed into the environment. We argue that the three kinds of approaches are useful in conjunction in testing different market designs, thus achieving better or sub-best designs in different ways. They are complementary to each other. 3. Mathematical formulation and implementory procedure of robust design 3.1. Mathematical formulation of robust design In order for the clearness, the following is the mathematical formulation of the problem of robust market design: Suppose there are n autonomous decision-makers in the market (n e N, n < 1, N is the set of natural numbers), who are electricity sellers, electricity buyers, etc. Let # denotes a certain market design, and H denotes the set of possible designs. Each decision-maker i (i = 1, . . . , n) makes his decision under the constraints of market designed, denoted by ai; all possible decisions for him are denoted by set Ai. Let a = (a1, . . . , an) denotes one combination action of all decision-makers; A = A1 An is the set of all possible combinations. Suppose one scenario sj e S, (j = 1, . . . , m), m e N, m < 1 of supply and demand condition; S denotes all foreseeable scenarios of supply and demand condition. The market behavior is decided by the market rules, supply & demand condition, and the decision-makers’ decisions, denoted with mapping S
f : H A!O
ð1Þ
where O denotes all possible outcomes of the market. Let E(o), o e O denotes the evaluation functions over the market behavior. X denotes the acceptable space (ranges) of design criteria. Therefore, the problem of robust design is to look for a robust decision #* which performs well across the set of autonomous decision-makers’ strategies. That is,
# 2 H;
8i; 8j; 8ai 2 Ai ; 8sj 2 S
EðoÞ ¼ Eðoð# ; sj ; ða1 ; . . . ; an ÞÞÞ 2 X
ð2Þ
From the formulation it is known that robust market design belongs to seeking a satisfactory alternative, that is, a robust decision satisfies all the design criteria and performs well across the set of foreseeable uncertainty. Eq. (2) implies where the robustness comes from. However, due to the complexity of power industry, especially the existence of feedback loop, by analytical methods it is not convenient to get the robust solution. As discussed below, simulations and gaming are one practical way for it. 3.2. The implementory procedure of robust market design Step 1: Identification of the stakeholders in the market considered The stakeholders in an industrial regulation reform are those organizations and individuals who are regarded as having interests affected in the outcome of the reform. As for the case of electricity supply industry restructuring, this could, in theory, include all members of society since they are likely to be affected. In practice, only a limited number of individuals and organizations would be largely affected and take an active interest in this reform. They are electricity generating companies, demand aggregators (retailer) who purchase electricity from generators or market and resell it to the end-users, large-scale consumers, households, industrial and commercial consumers, and the Independent System Operator (ISO) Step 2: Identification of attributes and indicators and their range of feasible values According to the problem of interest, an initial list of several attributes to be pre-specified can be drawn up from an analysis of recent publications, lessons and experience from international electricity markets, and experts’ expertise from various disciplines. Table 1 gives an example for power market design. The designer should rank their importance and select the
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Table 1 Attributes, indicators and their feasible values possibly for power market design. Attribute
Indicator
Acceptable range or values (example)
Competitiveness Sustainability Greenhouse effect Acid rain National security Security of supply Supply adequacy Balance Decentralization etc.
Ratio Japan electricity price to other OECD electricity prices % electricity supply from new energy in 2050 % change in CO2 emitted by 2050 % change in SO2 emitted by 2050 Net imports as % of fuel supply Hours of electricity disruption/person/year % reserve margin % supplied from largest electricity generator in 2050 Number of electricity suppliers in 2050
<1.2 >10% <30% <30% <80% One hour in 10 years 10–30% <20% 30
most important attributes of energy policy, or add new attributes to the list if required. For each of these attributes, the designers should first agree on identifying an appropriate empirical indicator by which performance of the market designed could be measured or assessed, and a range of feasible or acceptable values for the indicator. That is, according to a concrete problem of interest, the consensus of objectives and their indicators of the market to be designed should firstly be achieved. For example, if competitiveness is identified as an important attribute of power market, then a means of measuring competitiveness will be requested, and a range of feasible or acceptable values for that measure identified. Some attributes, especially relating to risks, fair competition and the relative importance of each design objectives, are non-quantifiable and need much negotiation. Step 3: Identification of optional decisions The traditional applications of decision analysis as well as some game-theoretical models have been as the main technique for addressing specific decisions. But in the area of power market design, it is clear that we do not have any single decision (variable), but rather a set of linked decisions, none of which on its own constitutes the policy, which in combination we describe as one market design. When we discuss power market design now, generally we have some preliminary designs or drafts of how to organize the market, which may be learned from international and domestic electricity regulatory reform or may be achieved from the experience of other industries or come from the results of theoretic models. All these contribute the buildup of optional rules. Therefore, when using simulation techniques to design market, we need to represent the options for implementation in a way that enables us to choose between them. Step 4: Development of decision-making algorithms for the players in the market Decision-making algorithm is a computer program with several parameters, which as a whole denotes a strategy as an actual human or organization behaviors. For each parameter, possible values or ranges are either from experts’ opinions or empirical calibration from detailed firm-level data. In the context of electricity industry deregulation, because bidding and investment decisions in power markets are interdependent, it is not possible to know or represent the precise decision processes of each stakeholder in the market. Any decision-making algorithm is necessarily a simplification of reality and many of the parameters of the model cannot be known with certainty, therefore, the decision-making algorithms can be intended to be simple, reasonable, and transparent representations of the fundamental considerations by using simple functional forms with a minimum of parameters only if they facilitate alternative assumptions and improve understanding of the relationship of those assumptions to the results. Because robust design emphasizes the robustness of the market designed, rather than its optimality, the algorithm set includes possible and realistic strategies of the decision-makers which bring unacceptable outcomes, ranging from making decisions simply by rote from a small, fixed repertoire of choices, to making very intelligent decisions, only if the decisionmaking algorithm conforms to the following basic principles [15]: The inputs to any decision-making algorithm must be restricted to information actually available to the real decisionmakers. Every variable and parameters of an algorithm must have a real world counterpart and should be meaningful to the decision-maker in the real market. Physical constraints to the decision-making algorithm should be represented. Equilibrium should not be assumed in any algorithm. Equilibrium may or may not emerge from the interaction of the decision-makers in the market. The set of decision-making algorithms is an open set, that is, it is increasable during the design process. Step 5: Construction of a simulation model Having identified the attributes, the possible decisions and the set of market participants’ strategies, simulation models can be developed using some commercial software. Our model is built in standard C++ programming language on Linux platform [16,17], by which large-scale decentralized decision-making is possible and simulation results are easily provided in text or graphs. Step 6: Interactive design process by simulations
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The interactive design process is based on the general principle that the latter designer should figure out loopholes the former designer never thought of and propose a better design to overcome these loopholes with the demonstration of simulations. If none of the designers can outwit a certain design, then this design is the final decision, thereby growing consensus of market design among the designers. This process includes the following steps: (i) (ii) (iii) (iv)
setting up the objectives that the desirable market satisfies; figuring out a design, a set of rules f the market; looking for strategies that make the current design fails in satisfying the constraints of (i); modifying or re-designing a ‘‘better” set of rules in order that constraints of (i) can be satisfied even in the situation of (iii); (v) repeating (iii) and (iv), until no one can outwit a final design which fails in satisfying constraints of (i).
In short, the whole process is based on the belief that an understanding and appreciation of existing expertise, good theory, good computational modeling and well-designed simulations are critical ingredients to robust market design to market players’ uncertain strategies. From a pragmatic viewpoint, the interactive method is effective for growing/achieving consensus of designing human-made markets with unknown behavior of stakeholders. In the following section one case study is to demonstrate the whole process of this method.
4. An example of robust market design 4.1. Overview In this section, one case study intends to demonstrate the application of this method of robust market design by taking a capacity payment system for realizing long-term supply–demand balance as an example. The fundamental idea of capacity payment systems is that construction of generation capacity in a restructured electricity market represents a dynamic process with lags due to construction lead times, short-sightedness (investment decisions are made based on looking-back behavior, that is, on recent energy and ancillary service market behavior, rather than perfect looking-forward), and uncertain demand growth. Investors may make construction decisions based on forecast profits, but since forecasts are generally based on past experience, investment decisions can therefore be represented as ultimately depending on the recent history of profits. Investments based on recent profit histories can result in an unstable system exhibiting overshoot-type behavior according to the theory of systems. This behavior could result from an overreaction of merchant generation to high profit opportunities, resulting in a glut of capacity that then depresses prices, which then throttles capacity construction, leading subsequently to a shortage of capacity, and so forth. Instabilities can be exacerbated by demand uncertainties due to the variable economic growth and uncertain weather conditions. The unstable profits lessen generators’ willingness to invest because investors are likely to be risk averse according to the results of field studies of behavioral economics. Capacity payment systems are designed to dampen the boom–bust cycles, improve the stability and predictability of system adequacy, and minimize costs to consumers at the same time. It is reasonable to expect that different payment systems will affect the stability of the capacity margin and, ultimately, prices and reliability in different ways. A good capacity payment system will create some predictability and stability of market prices and capacity reserve margin, which is desirable to facilitate continued generating capacity investments. The case study focuses on these objectives. We describe the design process consistent with the procedures as given in Section 3. 4.2. Stakeholders in this hypothetic market For the sake of simplicity, the power market considered is pool-based with uniform pricing. And there are 32 coal-fired power generation units and 8 gas-fired power generation units, which belongs to three power generation companies. One demand aggregator is considered in this case study on account that there are still many market in real world in which there are no open retail market and after all we focus only on the design methodology. For each generating company, its marginal costs curve is aggregated from its generation units’ marginal cost curve, which is a linear function calculated from its Incremental Heat Rate, fuel prices, its Rated Output, and its availability. As for the demand aggregator, the hourly load profile of the base year and yearly growth rates for extending years are exogenous to this model. Each yearly demand growth rate over prior year is subjective estimation. Random numbers with normal distribution simulates hourly demand estimation errors. All data simulated are available on request. The demands develop as the following equation:
Dyþ1;t ¼ ð1:0 þ K yþ1 Þ Dy;t þ et T ¼ 0; 1; . . . ; T 1 Y ¼ 0; 1; . . . ; Y 1
ð3Þ
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where the low subscript y denotes simulation year and Y is the simulation period; the low subscript t denotes the time in hour of the year and T is the total hours in a year. Ky+1 is subjective estimation of yearly demand growth rate over the prior year; e is estimator error modeled by pseudo-random numbers with a normal distribution; Dy,t means demand at time t of year y. Because the model randomly samples demand growth rate and estimation error, in ‘‘Monte Carlo” simulations, it is typical to repeat the random draws many thousands or more times. That is, one particular simulation does not represent a prediction of the market’s development over the next years; rather it is one sample path which, when repeated a number of times, allows for a statistically precise estimate of the average long-run performance of a particular payment system and set of assumptions. However, it is not necessary in this study to repeat the simulations because any particular simulation is of the same importance to the robust design proposed. 4.3. Identification of attributes and indicators and their acceptable ranges As discussed in Section 3, for a real market design, there are many attributes to be considered during the design process. In this example, it is supposed that only the supply adequacy and prices are concerned, as shown in Table 2. Here price is the weighted average price (i.e. WAP) of each year, which is computed by dividing total payments for a given year of all consumers by the total number of MWh consumed in that year as shown in Eq. (4), where MP is the market price; GAC is the gross available capacity; RM is the reserve margin, as a percentage of total generation capacity. DPEAK is the peak demand of the year:
Pt¼T1 WAPy ¼ RMy ¼
MP y;t Dy;t Pt¼T1 t¼0 Dy;t
t¼0
ð4Þ
GAC y DPEAK y GAC y
4.4. Optional capacity payment systems There are many capacity adequacy mechanisms implemented in real markets and proposed in the literature [18,19]. Here we only discuss a robust capacity payment system. Capacity payments encourage generation investment by subsidizing firms directly for their newly invested capacity regardless of its dispatch status. A firm’s capacity subsidy is equal to the product of its new capacity and the per-MW capacity payment. How to decide the payment rates is of interest in this case study. 4.5. Decision-making algorithms for the stakeholders Before discussing concrete decision-making algorithms developed for this case study, it is necessary to make a necessary simplification first. The simplification is the separation of investment decision-making and bidding supply decision-making. In actual electricity market, each company makes two kinds of decisions: investment decision and supply bidding decisions simultaneously or sequentially. The two kinds of decisions are interdependent. In this model, we have simplified the decision process. We artificially separate the investment and bidding decision-making. By doing so, this model is composed of two distinct elements: a short-term or ‘‘spot market” competition in electricity generation and a long-term model in investment decisions competition. As for the bidding decision-making, we model it as ‘‘hockey stick bidding” strategies which are found in real markets [20]. That is, below its desired minimal market share, bidding based on its marginal costs; otherwise, asking extremely high prices for more profits as shown in the following equation:
PBi ¼
8 h i > < MC i ðqÞ; q 2 AC MIN ; qi i
> : ð1:0 þ ai ðqÞÞ MC i ðqÞ; q 2 qi ; AC MAX i h i qBi ¼ q 2 AC MIN ; AC MAX i i q q ai ðqÞ ¼ Li MAX i AC i qast i
ð5Þ
Table 2 Attributes and indicators considered. Attribute
Indicator
Acceptable values
Supply adequacy Price volatility
Reserve margin in % Ratio of maximum WAP to minimum WAP
5–35% Less than 3
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In this equation, the low subscript i denotes any one of the decision-makers; the high subscript B denotes bidding decisions; is maximum available generating capacity; MC( ) is marginal cost function; p is bidding price; q is supply quantity; AC MAX i is minimum generating capacity; qi is desired minimal operation capacity. In this strategy, decision variables are qi AC MIN i and markup rate Li. The qi is a parameter that is set at the beginning of the simulation. Each Li is a positive variable, less than 1.0 assumed in this case study, which is calculated from the following equation:
Li;dþ1 ¼ Li;d þ adi;dþ1 AQ i;d qi adi;dþ1 ¼ AT i d ¼ 0; 1; . . . ; ð365 1Þ
ð6Þ
where ATi, an equivalent adjustment-time factor, and Li,0 are set at the beginning of simulation; AQi,d is the generation quantity accepted at the prior day. As for the adjustment of markup factor L, which can be changed daily or monthly flexibly. As for the decisions on investments, in the standard model of investment, a firm invests in a new plant as long as the expected net present value (i.e. NPV) of additional profits earned from the investment exceeds the investment cost. In the decision-making algorithm, it is assumed that new capacity will be constructed when the discounted cost of new capacity is less than net revenue from the short markets. Therefore, investment decisions are a function of near past market prices, the capacity payments in the system and costs of new generation capacity. The theory of investment under uncertainty says that a higher return is required to compensate for the uncertain nature of the operating cost rents [21]. We consider these uncertainties or risks in asking for high return rate. The condition for new investment is
ðMPy OCÞ cfi;y 8760 þ CPy FC FC ¼ CC r
ð1 þ rÞN
ð7Þ
ð1 þ rÞN 1
where MPy is the market average price of year y; OC is unit operation cost of the generation industry; cfi,y is capacity factor of company i of year y; CPy is the capacity payment of year y; FC is the levelized fixed cost; CC is initial capital construction cost per-MW of generating capacity. In order to differentiate decision-makers, they can ask for different rate-of-return required. Two cases are considered in the case study. ‘‘High rate-of-return required”, rH = 13%; ‘‘low rate-of-return required”, rL = 10%. Other assumption includes, (a) one generating technology is available for investment; (b) its capital cost CC is 526$/kW, its lifetime N equals to 20 years; (c) the size of newly invested power plant is 600 MW; (d) its lead time for construction of gas turbine is 2 years; (e) the fuel prices do not change. 4.6. Construction of a dynamic simulation model As shown in Fig. 1, the simulation model being developed is a simplified structural model based on system dynamics [15]. The long-term dynamic performance of the power market is determined by modeling the variables have direct influence on
Weather condition Macro-economy conditions
(+) Generation Capacity (+) Delay Investment Decision (+) Delay
Reserve Margin
Electricity Demand
(-)
(-) Regulatory Policies: 1. Price Cap 2. Reserve Margin 3. Capacity Payment
Short-term Market Prices/Revenue (+) Expectations on future prices/Profitability (-)
Human Decision Making
Uncertainty of Fuel Prices & Environmental Tax/Subsidy
System boundary
Fig. 1. A simplified causal-loop diagram of the power market.
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long-term movement of supply and demand. Causal relationships between two variables, say x and y, are identified by arrows. The positive (negative) sign at the end of each arrow can be understood as a small positive change in variable x that provokes a positive (negative) variation on variable y. The diagram shows the basic balancing feedback governs the long-run development of power market. Two delays are considered, one is waiting for enough information for certainty; the other is for building new investments. A year-to-year simulation, extending over 20 years, is to be done on this long-term simulation model. Each year, each electricity generator (hereafter market player) submits its production & bidding supply to the market at the spot market. Short-term electricity prices are derived from the intersection of supply curve and demands without elasticity under uniform-pricing mechanism. Investment decisions are made at the end of each year simultaneously. One negative feedback loop is included in the simulation model. Supposing other factors affecting reserve margin are unchanged, reserve margin increases when generation capacity is increased. When the reserve margin rises, prices/revenues from short-term market are likely down. Low spot market prices decrease the likelihood of expectation future prices & profitability, which gives less incentive for capacity investment. In return, decreased generation capacity increases the likelihood of short-term prices of electricity. Therefore, this is a negative feedback loop, which limits too much or too little investments in new generation. 4.7. Interactive design process by simulations The design process begins with the first design. The designer proposes the fixed capacity payment system on the ground that the capital costs of the investment and fuel costs are constants over the simulation period as assumed. 1st Design: The fixed payment level is $20/kW year, about 30% of the amortized fixed cost of the new investment. Worst-case: When the companies are competitive to each other, bidding at a relatively low prices (Li,0 less than 0.5) and asking high return rate, as shown in Fig. 2, there are several years when the gross available supply is less than the peak demand, that is, short of generating capacity occurred. This kind of results is out of the acceptable range. 2nd Design: In order to provide more incentives for new investment even when the stakeholders are competitive, one way is to increase the payment level to $35/kW year, nearly half of the levelized fixed cost. Merit: The performances are getting better, that is, high payment level has attracted investments, power curtailments did not happen during the simulation period when the market players bid at low prices and ask high investment return. Worst-case: When the players begin bidding at high prices (Li,0 larger than 0.5) and require low investment return, the market keeps at high level of capacity reserve margin as shown in Fig. 3. Moreover, when the biggest company bid in high prices and others keep bidding based on marginal costs, even under high capacity subsidies, the spike of annually weighted average price (WAP) still happened because of the construction delay as shown in Fig. 4. 3rd Design: The 3rd Design is a variable payment system. At the beginning of each year, the regulatory decides the payment level according to current reserve margin. Lower the reserve margin, higher payments. We use an Inverse Sigmoid function. Its mathematical form is
1 ! ðRMy RM Þ CPyþ1 ¼ f ðRM y Þ ¼ k1 1 1 þ exp k2 RM
ð8Þ
where RM* is the best acceptable reserve margin; k1, k2 are factors. In this case, k1 = 50.0, k2 = 0.2, RM* = 0.16 are simulated. Merit: Compared to fixed payment systems, the downward sloping curve of the payment function signal a higher value for capacity if reserve margin is in short, and a lower value if reserves are enough. We have simulated many times for various situations, and the overall performances are becoming better than fixed payment systems. As shown in Fig. 5, Case I shows the statistically average results of cases when at least one takes different strategy from others; Case II shows the average results when each stakeholders require a high discount rate. Case III demonstrates the results of an extreme case that each
Competitively Bidding at Lower Prices ( Payment=$20/kW-yr )
Reserve Margin
0.25 0.2
Short of capacity
0.15
Short of capacity
0.1 0.05
Unacceptable
Unacceptable
0 1
3
5
7
9
11 Year
13
15
17
19
Fig. 2. Competitive bidding at lower prices leads to be short of capacity.
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Higher Capacity Subsidies, Higher Capacity Levels ( Payment=$35/kW-yr ) 0.6
Unacceptable
Reserve Margin
0.5 0.4 0.3 0.2 0.1 19
17
15
13
11
9
7
5
3
1
0 Year Fig. 3. Bidding at higher prices under higher subsidies led to over-investment.
90 80 70 60 50 40 30 20 10 0
19
17
15
13
11
9
7
5
3
Unacceptable
1
Weighted Average Price ( $/MWh)
High Price Spike ( Payment=$35/kW-yr )
Year Fig. 4. High weighted average price spike occurred.
Performance Getting Better (Variable Payment System)
0.4 0.3 0.2
19
17
15
13
11
9
7
5
0
3
0.1 1
Reserve Margin
0.5
Year Case I
Case II
Case III
Fig. 5. Variable payment system.
stakeholder takes the same strategy. One invests capacity, the others also do investments. In all, whole outcomes of the market are acceptable according to our objectives. Discuss: Although higher capacity payments produce higher capacity levels, there is a fundamental problem with fixed payment systems. That is, fixed payment systems does not signal a higher value for capacity if reserves are short, and a lower value if reserves are ample. In addition, no matter what the payment level is, the market long-term performance demonstrates boom-and-bust character. It is nearly impossible to determine the optimal level of the payments. Variable payment systems are designed to dampen the boom-and-bust cycles. As concluded in Table 3, there is trade-off between fixed payment systems and variable payment systems for capacity. One disadvantage of variable payment systems is that it brings
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Table 3 Trade-off between different systems. Capacity payment system
Merit
Demerit
Fixed payment systems Variable payment systems
Provide a foreseeable and stable subsidies
Low payment leads to under-investment; high payment leads to over-investment Unstable subsidies bring risks to the investors
Higher value for capacity when reserve margins are in short; lower values if reserves are ample
unstable subsidies to investors. Unstable payments mean risks to investors. If the investors are risk averse, shortage of capacity would happen, thereby resulting in higher costs and risks to consumers. On the contrary, fixed payment systems provide foreseeable and stable capacity subsidies to attract investments. In real markets, Chile and Argentina operate a fixed capacity payment, while the former England and Wales Pool adopted variable capacity payment system. Furthermore, designing the implementation mechanisms required to achieve the correct capacity payment is more complicated and involves harmonizing engineering reliability criteria with the developments of capacity markets to determine the appropriate capacity prices (see Joskow (2008) for a more detailed discussion [22]).
5. Conclusions In this paper, a new concept of robust market design subject to market players’ strategic behavior is presented. Its workability is demonstrated by simple simulation studies. By means of this method, the policymaker has a better opportunity to communicate with each other, thereby achieving consensus of market design, and to understand the possible consequences of different decisions that they may make under different market conditions. Better than the alternatives, computer simulations provide much information about the dynamics of economic agents’ interaction, which are often more significant to robust market design than the equilibria of the underlying behavioral processes. Policymakers are not only interested in equilibrium selection or convergence properties in the long-term, but also the dynamics of the industrial transition from regulation regime to deregulation era. Moreover, from the example study, it is proved that computer simulation allows modeling of aggregate market outcomes from heterogeneous individual behavior. While in economics, aggregate behavior is merely the outcome of the summation of the behaviors of homogeneous representative agents. The relaxation of the assumption of the representative agent, which is possible only in computer simulation, has potentially far reaching consequences in social science. The further studies include the development of more practical decision-making algorithms and robust design against large set of uncertainties. Acknowledgements Special thanks to Kyoto University 21st Century COE Program (Establishment of Center of Excellence on Sustainable Energy System) for financial support. Thanks also go to the anonymous referees of this Journal for their valuable comments. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
Lester B. Lave, Jay Apt, Seth Blumsack, Rethinking electricity deregulation, The Electricity Journal 17 (2004) 11–26. Peter V. Doren, Jerry Taylor, Rethinking Electricity Restructuring, Policy Analysis, CATO Institute, No. 530, 2004. Inoue Masaharu, Electric power liberalization: the door of 2007, Energy Forum (2004) (in Japanese). Institute of Electrical and Electronics Engineers, IEEE Standard Computer Dictionary: A Compilation of IEEE Standard Computer Glossaries, New York, 1990. Shenghua Cai, Tetsuo Tezuka, Robust framework design for electric power market by simulation-based experiment, in: Proceedings of the 11th International Energy Conference and Exhibition, Stavanger, Norway, 2006. L. Hurwicz, S. Reiter, Designing Economic Mechanisms, Cambridge University Press, 2006. Richard Green, David Newbery, Competition in the British electricity spot market, Journal of Political Economy 100 (5) (1992) 929–953. Severin Borenstein, James Bushnell, An empirical analysis of the potential for market power in California’s electricity industry, Journal of Industrial Economics 47 (3) (1999) 285–323. Stephen J. Rassenti, Vernon L. Smith, Bart J. Wilson, Controlling market power and price spikes in electricity markets: demand-side bidding, Proceedings of National Academic Science 100 (2003) 2998–3003. R.J. Thomas et al., Testing the effects of price responsive demand on uniform price and soft-cap electricity auctions, in: Proceeding of 35th Hawaii International Conference on System Sciences, 2002. I. Watanabe et al., Simulation of Electricity Market: Electricity Market Simulator Development and Analysis of Agent Model, Central Research Institute of Electric Power Industry, Research Report R02022, 2003 (in Japanese). Backus George, Amlin Jeff, Using gaming simulation to understand deregulation dynamics, Simulation & Gaming 36 (1) (2005). Wenzler Ivo et al, Deregulation of utility industries and roles of simulation, Simulation & Gaming 36 (1) (2005). H.A. Simon, Models of Bounded Rationality: Behavioral Economics and Business Organization, MIT Press, Cambridge, MA, 1982. John D. Sterman, Business Dynamics-System Thinking and Modeling for a Complex World, McGraw-Hill, 2000. Harvey M. Deitel, Paul J. Deitel, C++ How to Program, fourth ed., Pearson Education Inc., 2003. Michael K. Johnson, Erik W. Troan, Linux Application Development, Addison-Wesley, 1998.
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[18] Shenghua Cai, Tetsuo Tezuka, Evaluation of power market designs on investment incentives and capacity adequacy, Engineering Sciences 6 (2) (2008) 61–68. [19] Shmuel S. Oren, Ensuring Generation Adequacy in Competitive Electricity Markets, Electricity Deregulation: Choices and Challenges, University of Chicago Press, Chicago, 2005. [20] Peter Cramton, Competitive bidding behavior in uniform-price auction market, in: Proceedings of the Hawaii International Conference on System Sciences, 2004. [21] Dixit, Pindyck, Investment under Uncertainty, Princeton University Press, 1994. [22] Joskow Paul, Capacity payments in imperfect electricity markets: need and design, Utility Policy 16 (2008).
Contents lists available at ScienceDirect
Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat
Robust market design for power industry deregulation by simulations Shenghua Cai a,*, Tetsuo Tezuka b a b
The China Center for Energy Economics Research, Xiamen University, China The Graduate School of Energy Science, Kyoto University, Japan
a r t i c l e
i n f o
Article history: Received 8 June 2009 Received in revised form 4 January 2010 Accepted 7 January 2010 Available online 18 January 2010 Keywords: Robust market design Methodology Simulation System dynamics
a b s t r a c t This paper proposes one concept of robust market design subject to stakeholders’ strategic behavior. The key to robust design is the application of computer simulations, which is used to as a tool to avoid detectable loopholes in the market. An example illustrates the method. Computer simulation not only provides much information about the dynamics of economic agents’ interaction, but also allows modeling of aggregate market outcomes from heterogeneous individual behavior. With this method, the policymakers have a better opportunity to communicate with others and to understand the possible consequences of different decisions under different optional policies and market conditions. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Since the United Kingdom opened a Power Pool in April 1990, the regulatory framework for the electricity industry has been replaced in many countries by introducing market competition in order to generate electricity efficiently and reliably. Although there are various restructured electricity markets operating in the world, there are still continuing debates over various aspects of electric power industry deregulation. For example, the problem of ‘‘deregulation or reregulation” is challenged by some experts [1,2]. Electric power industry deregulation is a complex problem that has engineering, economic, commercial, and legal and policy dimensions and takes place within a broad societal context that itself influences and is influenced by the outcomes. From the national energy-environmental perspective, there is much conflict between electric power industry liberalization and policies of promoting renewable energy development, policies on nuclear power utilization, technological innovation, etc. [3]. On the other side, there are many uncertainties coming from various sources, such as the uncertain Post-Kyoto Regime, uncertain prices of international fuel markets, uncertain future weather conditions, uncertain national macro-economy, uncertain market players’ strategic behavior, etc. All of the aspects above should be taken into account when we design the program of liberalization the electric power industry. Lessons and experience tell us it is impossible to recommend one ‘‘best” solution to solve all problems. However, there is much possibility and necessity for us to intend to look for a ‘‘second-best” solution. This study is meant as a contribution to this inquiry. This paper discusses the conception of ‘‘second-best” from the perspective of systems’ robustness. According to [4], robustness is defined as ‘‘the degree to which a system or component can function correctly in the presence of invalid inputs or stressful environmental conditions.” Robust market design, which is discussed in a narrow sense as a starting point, is
* Corresponding author. Tel.: +86 592 2186 076; fax: +86 592 2186 075. E-mail address: [email protected] (S. Cai). 1569-190X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2010.01.002
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defined as deciding a set of the rules that satisfies the constraints required for realizing desirable or acceptable outcomes of the market no matter of the stakeholders’ strategic behavior [5]. That is, a market is considered robust if the behavior of the market even in the worst cases are still acceptable. Different from this, the literature in mechanism and auction design, a sub-discipline of game theory, analyses how equilibrium behavior in the market game depends on the market rules, and how market rules that implement desired market outcomes look like. Moreover, we mainly concerns the methodological aspect of robust design from a pragmatic viewpoint. The purpose of this paper is to propose a new method for robust market design in decentralized systems with autonomous decision-makers by simulations, such as power markets. And the key to the robust market design is the application of simulation technology. Different from the closed-form deductive analyses, either operations research models in decision science or game-theoretical models in the context of mechanism design [6], in which equilibrial outcomes of the market are their primary concerns, robust design does not differentiate outcomes in equilibrium from those out of equilibrium. All of the outcomes are assessed to be acceptable or not according to the designers’ objectives. Simulation technology is used as a tool to avoid detectable loopholes in the market. The re-design process is intended to remedy the loopholes detected. That is, robust market design includes the process of looking for worse-case strategies that brings unacceptable outcomes and the process of redesigning market rules in order that even in the worst-case situations the outcomes of the market are acceptable. An example illustrates an application of this method. This paper is organized as follows. First, we make a selective literature review on power market analysis and design, and discuss the limitations of each method from a methodological perspective. Then, we describe the mathematical formulation and implementory procedure of robust market design proposed in this study. Next, by taking a capacity payment system for realizing long-term supply–demand balance as an example, we illustrate its design process. Finally, we state the conclusion of this paper and further studies.
2. A selective literature review on power market analysis and design The main methods applied in power market analyses and design include the closed-form deductive analysis, experimental economics and agent-based simulations. Indeed, if the design objectives are clearly defined, some of the recent techniques of simulation and optimization developed by system scientists and computational economists can be used to achieve a better market design directly or indirectly. In the following we selectively introduce several important studies, to the best of our knowledge, on market design in the context of electricity industry restructuring. Green and Newbery (1992) modeled the England and Wales electricity market using the Supply Function Equilibrium (SFE) framework as applied to an empirical characterization of supply and demand, designed to match the attributes of the electricity system in England and Wales. They found that generators were able to drive prices far above competitive levels, depending on the assumed elasticity of demand, while creating a significant deadweight loss and producing supra-competitive profits for the generators. They then examined the impact of restructuring the industry so that there were five equalsized firms. In this case, the equilibrium price was significantly lower and close to competitive levels [7]. Borenstein and Bushnell (1999) modeled the California power industry as a Cournot triopoly with a competitive fringe. They found that the potential for market power was greater when demand was high and the fringe’s capacity was exhausted, making it impossible for the small producers to increase production. During lower demand hours, Cournot producers had less incentive to withhold production because the fringe had excess capacity. In addition they found that the more elastic was the demand, the less was the incentive to exercise market power [8]. Rassenti et al. (2003) tested the effect of demand response and double-sided markets on the extent to which generators could exercise market power by using a laboratory environment with profit-motivated human participants. Their results indicated that demand-side bidding decreased price volatility, the magnitude of price spikes, and the ability of suppliers to exercise market power. Average prices were lower when both demand-side and supply-side bidding existed, as opposed to the one-sided supply-side bidding. This research provides the clear policy implication that active demand plays a valuable role in disciplining the pricing choices of generators in wholesale markets [9]. Thomas et al. (2002) tested auction mechanisms experimentally in a controlled environment to evaluate market designs. Their work described a framework for testing the efficacy of a price-responsive load on a uniform price last accepted offer and soft-cap market. The experimental evidence shows that price responsive load increase efficiency and decrease price volatility in the uniform auction and soft-cap design behaves similarly to the discriminatory auction, such as observed in California in the winter of 2001 [10]. Watanabe et al. (2003) developed a multi-agent simulation model in which power generators and suppliers (customers) are modeled as autonomous adaptive agents which progressively learn the optimal strategy with reinforcement learning mechanism. Their results show that demand increase, market power, price-cap regulation and transmission constraints are important factors of escalating market clearing prices [11]. Backus and Amlin (2005) present how a simulation and gaming approach can be a useful tool in learning about the dynamics of deregulation. UTILITIES 21, an all-fuel, fully integrated energy model, proved itself to be an extremely accurate tool for realistically showing the inevitable evolution of deregulated markets [12]. Wenzler and Mayer (2005) describe why and how different types of simulations can be used to understand and support the challenges of utility deregulation. They present a general classification of seven different types of simulation, including
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market simulations, policy simulations, dynamic business simulations, capability simulations, day-in-a-life simulations, performance simulations and gaming simulations [13]. All of these approaches have improved our understanding of market behavior and helped to design markets. But more or less, each of them has its limitations. Either SFE or Cournot models have difficulty to deal with complexity that comes from the practical design of electricity markets. And the assumption of perfect rationality and unlimited computational ability on human stakeholders is unrealistic [14]. Experimental economics is criticized for the external validity of the behavior of the human subjects, who might as well shade their decisions in some way since the experiments are of little consequence to them while the real world profits are of enormous consequences. Furthermore, the results of experiments cannot be reproduced. As for agent-based simulations, agents behave in ways that they are programmed to behave; in other words, the model by which agents respond to each other is one that has been foreseen by the researcher and has been programmed into the environment. We argue that the three kinds of approaches are useful in conjunction in testing different market designs, thus achieving better or sub-best designs in different ways. They are complementary to each other. 3. Mathematical formulation and implementory procedure of robust design 3.1. Mathematical formulation of robust design In order for the clearness, the following is the mathematical formulation of the problem of robust market design: Suppose there are n autonomous decision-makers in the market (n e N, n < 1, N is the set of natural numbers), who are electricity sellers, electricity buyers, etc. Let # denotes a certain market design, and H denotes the set of possible designs. Each decision-maker i (i = 1, . . . , n) makes his decision under the constraints of market designed, denoted by ai; all possible decisions for him are denoted by set Ai. Let a = (a1, . . . , an) denotes one combination action of all decision-makers; A = A1 An is the set of all possible combinations. Suppose one scenario sj e S, (j = 1, . . . , m), m e N, m < 1 of supply and demand condition; S denotes all foreseeable scenarios of supply and demand condition. The market behavior is decided by the market rules, supply & demand condition, and the decision-makers’ decisions, denoted with mapping S
f : H A!O
ð1Þ
where O denotes all possible outcomes of the market. Let E(o), o e O denotes the evaluation functions over the market behavior. X denotes the acceptable space (ranges) of design criteria. Therefore, the problem of robust design is to look for a robust decision #* which performs well across the set of autonomous decision-makers’ strategies. That is,
# 2 H;
8i; 8j; 8ai 2 Ai ; 8sj 2 S
EðoÞ ¼ Eðoð# ; sj ; ða1 ; . . . ; an ÞÞÞ 2 X
ð2Þ
From the formulation it is known that robust market design belongs to seeking a satisfactory alternative, that is, a robust decision satisfies all the design criteria and performs well across the set of foreseeable uncertainty. Eq. (2) implies where the robustness comes from. However, due to the complexity of power industry, especially the existence of feedback loop, by analytical methods it is not convenient to get the robust solution. As discussed below, simulations and gaming are one practical way for it. 3.2. The implementory procedure of robust market design Step 1: Identification of the stakeholders in the market considered The stakeholders in an industrial regulation reform are those organizations and individuals who are regarded as having interests affected in the outcome of the reform. As for the case of electricity supply industry restructuring, this could, in theory, include all members of society since they are likely to be affected. In practice, only a limited number of individuals and organizations would be largely affected and take an active interest in this reform. They are electricity generating companies, demand aggregators (retailer) who purchase electricity from generators or market and resell it to the end-users, large-scale consumers, households, industrial and commercial consumers, and the Independent System Operator (ISO) Step 2: Identification of attributes and indicators and their range of feasible values According to the problem of interest, an initial list of several attributes to be pre-specified can be drawn up from an analysis of recent publications, lessons and experience from international electricity markets, and experts’ expertise from various disciplines. Table 1 gives an example for power market design. The designer should rank their importance and select the
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Table 1 Attributes, indicators and their feasible values possibly for power market design. Attribute
Indicator
Acceptable range or values (example)
Competitiveness Sustainability Greenhouse effect Acid rain National security Security of supply Supply adequacy Balance Decentralization etc.
Ratio Japan electricity price to other OECD electricity prices % electricity supply from new energy in 2050 % change in CO2 emitted by 2050 % change in SO2 emitted by 2050 Net imports as % of fuel supply Hours of electricity disruption/person/year % reserve margin % supplied from largest electricity generator in 2050 Number of electricity suppliers in 2050
<1.2 >10% <30% <30% <80% One hour in 10 years 10–30% <20% 30
most important attributes of energy policy, or add new attributes to the list if required. For each of these attributes, the designers should first agree on identifying an appropriate empirical indicator by which performance of the market designed could be measured or assessed, and a range of feasible or acceptable values for the indicator. That is, according to a concrete problem of interest, the consensus of objectives and their indicators of the market to be designed should firstly be achieved. For example, if competitiveness is identified as an important attribute of power market, then a means of measuring competitiveness will be requested, and a range of feasible or acceptable values for that measure identified. Some attributes, especially relating to risks, fair competition and the relative importance of each design objectives, are non-quantifiable and need much negotiation. Step 3: Identification of optional decisions The traditional applications of decision analysis as well as some game-theoretical models have been as the main technique for addressing specific decisions. But in the area of power market design, it is clear that we do not have any single decision (variable), but rather a set of linked decisions, none of which on its own constitutes the policy, which in combination we describe as one market design. When we discuss power market design now, generally we have some preliminary designs or drafts of how to organize the market, which may be learned from international and domestic electricity regulatory reform or may be achieved from the experience of other industries or come from the results of theoretic models. All these contribute the buildup of optional rules. Therefore, when using simulation techniques to design market, we need to represent the options for implementation in a way that enables us to choose between them. Step 4: Development of decision-making algorithms for the players in the market Decision-making algorithm is a computer program with several parameters, which as a whole denotes a strategy as an actual human or organization behaviors. For each parameter, possible values or ranges are either from experts’ opinions or empirical calibration from detailed firm-level data. In the context of electricity industry deregulation, because bidding and investment decisions in power markets are interdependent, it is not possible to know or represent the precise decision processes of each stakeholder in the market. Any decision-making algorithm is necessarily a simplification of reality and many of the parameters of the model cannot be known with certainty, therefore, the decision-making algorithms can be intended to be simple, reasonable, and transparent representations of the fundamental considerations by using simple functional forms with a minimum of parameters only if they facilitate alternative assumptions and improve understanding of the relationship of those assumptions to the results. Because robust design emphasizes the robustness of the market designed, rather than its optimality, the algorithm set includes possible and realistic strategies of the decision-makers which bring unacceptable outcomes, ranging from making decisions simply by rote from a small, fixed repertoire of choices, to making very intelligent decisions, only if the decisionmaking algorithm conforms to the following basic principles [15]: The inputs to any decision-making algorithm must be restricted to information actually available to the real decisionmakers. Every variable and parameters of an algorithm must have a real world counterpart and should be meaningful to the decision-maker in the real market. Physical constraints to the decision-making algorithm should be represented. Equilibrium should not be assumed in any algorithm. Equilibrium may or may not emerge from the interaction of the decision-makers in the market. The set of decision-making algorithms is an open set, that is, it is increasable during the design process. Step 5: Construction of a simulation model Having identified the attributes, the possible decisions and the set of market participants’ strategies, simulation models can be developed using some commercial software. Our model is built in standard C++ programming language on Linux platform [16,17], by which large-scale decentralized decision-making is possible and simulation results are easily provided in text or graphs. Step 6: Interactive design process by simulations
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The interactive design process is based on the general principle that the latter designer should figure out loopholes the former designer never thought of and propose a better design to overcome these loopholes with the demonstration of simulations. If none of the designers can outwit a certain design, then this design is the final decision, thereby growing consensus of market design among the designers. This process includes the following steps: (i) (ii) (iii) (iv)
setting up the objectives that the desirable market satisfies; figuring out a design, a set of rules f the market; looking for strategies that make the current design fails in satisfying the constraints of (i); modifying or re-designing a ‘‘better” set of rules in order that constraints of (i) can be satisfied even in the situation of (iii); (v) repeating (iii) and (iv), until no one can outwit a final design which fails in satisfying constraints of (i).
In short, the whole process is based on the belief that an understanding and appreciation of existing expertise, good theory, good computational modeling and well-designed simulations are critical ingredients to robust market design to market players’ uncertain strategies. From a pragmatic viewpoint, the interactive method is effective for growing/achieving consensus of designing human-made markets with unknown behavior of stakeholders. In the following section one case study is to demonstrate the whole process of this method.
4. An example of robust market design 4.1. Overview In this section, one case study intends to demonstrate the application of this method of robust market design by taking a capacity payment system for realizing long-term supply–demand balance as an example. The fundamental idea of capacity payment systems is that construction of generation capacity in a restructured electricity market represents a dynamic process with lags due to construction lead times, short-sightedness (investment decisions are made based on looking-back behavior, that is, on recent energy and ancillary service market behavior, rather than perfect looking-forward), and uncertain demand growth. Investors may make construction decisions based on forecast profits, but since forecasts are generally based on past experience, investment decisions can therefore be represented as ultimately depending on the recent history of profits. Investments based on recent profit histories can result in an unstable system exhibiting overshoot-type behavior according to the theory of systems. This behavior could result from an overreaction of merchant generation to high profit opportunities, resulting in a glut of capacity that then depresses prices, which then throttles capacity construction, leading subsequently to a shortage of capacity, and so forth. Instabilities can be exacerbated by demand uncertainties due to the variable economic growth and uncertain weather conditions. The unstable profits lessen generators’ willingness to invest because investors are likely to be risk averse according to the results of field studies of behavioral economics. Capacity payment systems are designed to dampen the boom–bust cycles, improve the stability and predictability of system adequacy, and minimize costs to consumers at the same time. It is reasonable to expect that different payment systems will affect the stability of the capacity margin and, ultimately, prices and reliability in different ways. A good capacity payment system will create some predictability and stability of market prices and capacity reserve margin, which is desirable to facilitate continued generating capacity investments. The case study focuses on these objectives. We describe the design process consistent with the procedures as given in Section 3. 4.2. Stakeholders in this hypothetic market For the sake of simplicity, the power market considered is pool-based with uniform pricing. And there are 32 coal-fired power generation units and 8 gas-fired power generation units, which belongs to three power generation companies. One demand aggregator is considered in this case study on account that there are still many market in real world in which there are no open retail market and after all we focus only on the design methodology. For each generating company, its marginal costs curve is aggregated from its generation units’ marginal cost curve, which is a linear function calculated from its Incremental Heat Rate, fuel prices, its Rated Output, and its availability. As for the demand aggregator, the hourly load profile of the base year and yearly growth rates for extending years are exogenous to this model. Each yearly demand growth rate over prior year is subjective estimation. Random numbers with normal distribution simulates hourly demand estimation errors. All data simulated are available on request. The demands develop as the following equation:
Dyþ1;t ¼ ð1:0 þ K yþ1 Þ Dy;t þ et T ¼ 0; 1; . . . ; T 1 Y ¼ 0; 1; . . . ; Y 1
ð3Þ
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where the low subscript y denotes simulation year and Y is the simulation period; the low subscript t denotes the time in hour of the year and T is the total hours in a year. Ky+1 is subjective estimation of yearly demand growth rate over the prior year; e is estimator error modeled by pseudo-random numbers with a normal distribution; Dy,t means demand at time t of year y. Because the model randomly samples demand growth rate and estimation error, in ‘‘Monte Carlo” simulations, it is typical to repeat the random draws many thousands or more times. That is, one particular simulation does not represent a prediction of the market’s development over the next years; rather it is one sample path which, when repeated a number of times, allows for a statistically precise estimate of the average long-run performance of a particular payment system and set of assumptions. However, it is not necessary in this study to repeat the simulations because any particular simulation is of the same importance to the robust design proposed. 4.3. Identification of attributes and indicators and their acceptable ranges As discussed in Section 3, for a real market design, there are many attributes to be considered during the design process. In this example, it is supposed that only the supply adequacy and prices are concerned, as shown in Table 2. Here price is the weighted average price (i.e. WAP) of each year, which is computed by dividing total payments for a given year of all consumers by the total number of MWh consumed in that year as shown in Eq. (4), where MP is the market price; GAC is the gross available capacity; RM is the reserve margin, as a percentage of total generation capacity. DPEAK is the peak demand of the year:
Pt¼T1 WAPy ¼ RMy ¼
MP y;t Dy;t Pt¼T1 t¼0 Dy;t
t¼0
ð4Þ
GAC y DPEAK y GAC y
4.4. Optional capacity payment systems There are many capacity adequacy mechanisms implemented in real markets and proposed in the literature [18,19]. Here we only discuss a robust capacity payment system. Capacity payments encourage generation investment by subsidizing firms directly for their newly invested capacity regardless of its dispatch status. A firm’s capacity subsidy is equal to the product of its new capacity and the per-MW capacity payment. How to decide the payment rates is of interest in this case study. 4.5. Decision-making algorithms for the stakeholders Before discussing concrete decision-making algorithms developed for this case study, it is necessary to make a necessary simplification first. The simplification is the separation of investment decision-making and bidding supply decision-making. In actual electricity market, each company makes two kinds of decisions: investment decision and supply bidding decisions simultaneously or sequentially. The two kinds of decisions are interdependent. In this model, we have simplified the decision process. We artificially separate the investment and bidding decision-making. By doing so, this model is composed of two distinct elements: a short-term or ‘‘spot market” competition in electricity generation and a long-term model in investment decisions competition. As for the bidding decision-making, we model it as ‘‘hockey stick bidding” strategies which are found in real markets [20]. That is, below its desired minimal market share, bidding based on its marginal costs; otherwise, asking extremely high prices for more profits as shown in the following equation:
PBi ¼
8 h i > < MC i ðqÞ; q 2 AC MIN ; qi i
> : ð1:0 þ ai ðqÞÞ MC i ðqÞ; q 2 qi ; AC MAX i h i qBi ¼ q 2 AC MIN ; AC MAX i i q q ai ðqÞ ¼ Li MAX i AC i qast i
ð5Þ
Table 2 Attributes and indicators considered. Attribute
Indicator
Acceptable values
Supply adequacy Price volatility
Reserve margin in % Ratio of maximum WAP to minimum WAP
5–35% Less than 3
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In this equation, the low subscript i denotes any one of the decision-makers; the high subscript B denotes bidding decisions; is maximum available generating capacity; MC( ) is marginal cost function; p is bidding price; q is supply quantity; AC MAX i is minimum generating capacity; qi is desired minimal operation capacity. In this strategy, decision variables are qi AC MIN i and markup rate Li. The qi is a parameter that is set at the beginning of the simulation. Each Li is a positive variable, less than 1.0 assumed in this case study, which is calculated from the following equation:
Li;dþ1 ¼ Li;d þ adi;dþ1 AQ i;d qi adi;dþ1 ¼ AT i d ¼ 0; 1; . . . ; ð365 1Þ
ð6Þ
where ATi, an equivalent adjustment-time factor, and Li,0 are set at the beginning of simulation; AQi,d is the generation quantity accepted at the prior day. As for the adjustment of markup factor L, which can be changed daily or monthly flexibly. As for the decisions on investments, in the standard model of investment, a firm invests in a new plant as long as the expected net present value (i.e. NPV) of additional profits earned from the investment exceeds the investment cost. In the decision-making algorithm, it is assumed that new capacity will be constructed when the discounted cost of new capacity is less than net revenue from the short markets. Therefore, investment decisions are a function of near past market prices, the capacity payments in the system and costs of new generation capacity. The theory of investment under uncertainty says that a higher return is required to compensate for the uncertain nature of the operating cost rents [21]. We consider these uncertainties or risks in asking for high return rate. The condition for new investment is
ðMPy OCÞ cfi;y 8760 þ CPy FC FC ¼ CC r
ð1 þ rÞN
ð7Þ
ð1 þ rÞN 1
where MPy is the market average price of year y; OC is unit operation cost of the generation industry; cfi,y is capacity factor of company i of year y; CPy is the capacity payment of year y; FC is the levelized fixed cost; CC is initial capital construction cost per-MW of generating capacity. In order to differentiate decision-makers, they can ask for different rate-of-return required. Two cases are considered in the case study. ‘‘High rate-of-return required”, rH = 13%; ‘‘low rate-of-return required”, rL = 10%. Other assumption includes, (a) one generating technology is available for investment; (b) its capital cost CC is 526$/kW, its lifetime N equals to 20 years; (c) the size of newly invested power plant is 600 MW; (d) its lead time for construction of gas turbine is 2 years; (e) the fuel prices do not change. 4.6. Construction of a dynamic simulation model As shown in Fig. 1, the simulation model being developed is a simplified structural model based on system dynamics [15]. The long-term dynamic performance of the power market is determined by modeling the variables have direct influence on
Weather condition Macro-economy conditions
(+) Generation Capacity (+) Delay Investment Decision (+) Delay
Reserve Margin
Electricity Demand
(-)
(-) Regulatory Policies: 1. Price Cap 2. Reserve Margin 3. Capacity Payment
Short-term Market Prices/Revenue (+) Expectations on future prices/Profitability (-)
Human Decision Making
Uncertainty of Fuel Prices & Environmental Tax/Subsidy
System boundary
Fig. 1. A simplified causal-loop diagram of the power market.
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long-term movement of supply and demand. Causal relationships between two variables, say x and y, are identified by arrows. The positive (negative) sign at the end of each arrow can be understood as a small positive change in variable x that provokes a positive (negative) variation on variable y. The diagram shows the basic balancing feedback governs the long-run development of power market. Two delays are considered, one is waiting for enough information for certainty; the other is for building new investments. A year-to-year simulation, extending over 20 years, is to be done on this long-term simulation model. Each year, each electricity generator (hereafter market player) submits its production & bidding supply to the market at the spot market. Short-term electricity prices are derived from the intersection of supply curve and demands without elasticity under uniform-pricing mechanism. Investment decisions are made at the end of each year simultaneously. One negative feedback loop is included in the simulation model. Supposing other factors affecting reserve margin are unchanged, reserve margin increases when generation capacity is increased. When the reserve margin rises, prices/revenues from short-term market are likely down. Low spot market prices decrease the likelihood of expectation future prices & profitability, which gives less incentive for capacity investment. In return, decreased generation capacity increases the likelihood of short-term prices of electricity. Therefore, this is a negative feedback loop, which limits too much or too little investments in new generation. 4.7. Interactive design process by simulations The design process begins with the first design. The designer proposes the fixed capacity payment system on the ground that the capital costs of the investment and fuel costs are constants over the simulation period as assumed. 1st Design: The fixed payment level is $20/kW year, about 30% of the amortized fixed cost of the new investment. Worst-case: When the companies are competitive to each other, bidding at a relatively low prices (Li,0 less than 0.5) and asking high return rate, as shown in Fig. 2, there are several years when the gross available supply is less than the peak demand, that is, short of generating capacity occurred. This kind of results is out of the acceptable range. 2nd Design: In order to provide more incentives for new investment even when the stakeholders are competitive, one way is to increase the payment level to $35/kW year, nearly half of the levelized fixed cost. Merit: The performances are getting better, that is, high payment level has attracted investments, power curtailments did not happen during the simulation period when the market players bid at low prices and ask high investment return. Worst-case: When the players begin bidding at high prices (Li,0 larger than 0.5) and require low investment return, the market keeps at high level of capacity reserve margin as shown in Fig. 3. Moreover, when the biggest company bid in high prices and others keep bidding based on marginal costs, even under high capacity subsidies, the spike of annually weighted average price (WAP) still happened because of the construction delay as shown in Fig. 4. 3rd Design: The 3rd Design is a variable payment system. At the beginning of each year, the regulatory decides the payment level according to current reserve margin. Lower the reserve margin, higher payments. We use an Inverse Sigmoid function. Its mathematical form is
1 ! ðRMy RM Þ CPyþ1 ¼ f ðRM y Þ ¼ k1 1 1 þ exp k2 RM
ð8Þ
where RM* is the best acceptable reserve margin; k1, k2 are factors. In this case, k1 = 50.0, k2 = 0.2, RM* = 0.16 are simulated. Merit: Compared to fixed payment systems, the downward sloping curve of the payment function signal a higher value for capacity if reserve margin is in short, and a lower value if reserves are enough. We have simulated many times for various situations, and the overall performances are becoming better than fixed payment systems. As shown in Fig. 5, Case I shows the statistically average results of cases when at least one takes different strategy from others; Case II shows the average results when each stakeholders require a high discount rate. Case III demonstrates the results of an extreme case that each
Competitively Bidding at Lower Prices ( Payment=$20/kW-yr )
Reserve Margin
0.25 0.2
Short of capacity
0.15
Short of capacity
0.1 0.05
Unacceptable
Unacceptable
0 1
3
5
7
9
11 Year
13
15
17
19
Fig. 2. Competitive bidding at lower prices leads to be short of capacity.
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Higher Capacity Subsidies, Higher Capacity Levels ( Payment=$35/kW-yr ) 0.6
Unacceptable
Reserve Margin
0.5 0.4 0.3 0.2 0.1 19
17
15
13
11
9
7
5
3
1
0 Year Fig. 3. Bidding at higher prices under higher subsidies led to over-investment.
90 80 70 60 50 40 30 20 10 0
19
17
15
13
11
9
7
5
3
Unacceptable
1
Weighted Average Price ( $/MWh)
High Price Spike ( Payment=$35/kW-yr )
Year Fig. 4. High weighted average price spike occurred.
Performance Getting Better (Variable Payment System)
0.4 0.3 0.2
19
17
15
13
11
9
7
5
0
3
0.1 1
Reserve Margin
0.5
Year Case I
Case II
Case III
Fig. 5. Variable payment system.
stakeholder takes the same strategy. One invests capacity, the others also do investments. In all, whole outcomes of the market are acceptable according to our objectives. Discuss: Although higher capacity payments produce higher capacity levels, there is a fundamental problem with fixed payment systems. That is, fixed payment systems does not signal a higher value for capacity if reserves are short, and a lower value if reserves are ample. In addition, no matter what the payment level is, the market long-term performance demonstrates boom-and-bust character. It is nearly impossible to determine the optimal level of the payments. Variable payment systems are designed to dampen the boom-and-bust cycles. As concluded in Table 3, there is trade-off between fixed payment systems and variable payment systems for capacity. One disadvantage of variable payment systems is that it brings
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Table 3 Trade-off between different systems. Capacity payment system
Merit
Demerit
Fixed payment systems Variable payment systems
Provide a foreseeable and stable subsidies
Low payment leads to under-investment; high payment leads to over-investment Unstable subsidies bring risks to the investors
Higher value for capacity when reserve margins are in short; lower values if reserves are ample
unstable subsidies to investors. Unstable payments mean risks to investors. If the investors are risk averse, shortage of capacity would happen, thereby resulting in higher costs and risks to consumers. On the contrary, fixed payment systems provide foreseeable and stable capacity subsidies to attract investments. In real markets, Chile and Argentina operate a fixed capacity payment, while the former England and Wales Pool adopted variable capacity payment system. Furthermore, designing the implementation mechanisms required to achieve the correct capacity payment is more complicated and involves harmonizing engineering reliability criteria with the developments of capacity markets to determine the appropriate capacity prices (see Joskow (2008) for a more detailed discussion [22]).
5. Conclusions In this paper, a new concept of robust market design subject to market players’ strategic behavior is presented. Its workability is demonstrated by simple simulation studies. By means of this method, the policymaker has a better opportunity to communicate with each other, thereby achieving consensus of market design, and to understand the possible consequences of different decisions that they may make under different market conditions. Better than the alternatives, computer simulations provide much information about the dynamics of economic agents’ interaction, which are often more significant to robust market design than the equilibria of the underlying behavioral processes. Policymakers are not only interested in equilibrium selection or convergence properties in the long-term, but also the dynamics of the industrial transition from regulation regime to deregulation era. Moreover, from the example study, it is proved that computer simulation allows modeling of aggregate market outcomes from heterogeneous individual behavior. While in economics, aggregate behavior is merely the outcome of the summation of the behaviors of homogeneous representative agents. The relaxation of the assumption of the representative agent, which is possible only in computer simulation, has potentially far reaching consequences in social science. The further studies include the development of more practical decision-making algorithms and robust design against large set of uncertainties. Acknowledgements Special thanks to Kyoto University 21st Century COE Program (Establishment of Center of Excellence on Sustainable Energy System) for financial support. Thanks also go to the anonymous referees of this Journal for their valuable comments. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
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