Behavioral simulation and optimization of generation companies in electricity markets by fuzzy cognitive map

Abstract

Simulation can be used in a wide range of applications in an electricity market. There are many reasons that market players and regulators are very interested in anticipating the behavior of the market. Behavior of a generation company (GENCO) in electricity market is an important factor that affects the market behavior. Several factors affect the behavior of a GENCO directly and indirectly. In this study, a new approach based on fuzzy cognitive map (FCM) is introduced to model and simulate GENCO’s behavior in the electricity market with respect to profit maximization. FCM helps the decision makers to understand the complex dynamics between a certain strategic goal and the related factors. This paper examines how effective factors affect on a GENCO’s profit. To identify key factors relevant to the goal, a FCM is built and then analyzed. To analyze this problem, two cases as simple FCM and weighted FCM are considered. Simple FCM shows how the determined factors affect on goal. A hidden pattern is obtained by this case. Weighted FCM helps sensitivity analysis of the model. In addition, the weighted FCM is used usefully to clearly measure the composite effects resulting from changes of multiple factors. This application is shown by two different case studies. This is the first study that models and simulates the behavior of GENCO in electricity market with respect to profit maximization.

Introduction

Simulation can be used in a wide range of applications in an electricity market. For example, players in the electricity market can use simulation to decide whether or not an investment can be expected to be profitable, and authorities and regulators can by means of simulation find out which consequences a certain market design can be expected to have on electricity prices, environmental impact, etc. As known, in the electricity markets, market structure, market rules, demand levels, market concentration and energy sources to produce electricity have a strong influence on market performances. Modifications on these aspects may considerably affect market outcomes (Bomparda et al., 2008). There are many reasons that market players and regulators are very interested in anticipate the behavior of the market. System monitoring, test the rules before their implementation and detect market deficiencies are some goals of regulators; while the players wish to maximize their own profit (Bomparda et al., 2008).

Behavior of GENCOs in electricity market is an important factor affect on market behavior. Many factors affect of GENCOs behavior directly and indirectly. GENCO’s behavior is a factor that affects market outcomes. Important market outcomes are price and quantity produced by market. In the competitive electricity markets, generation dispatching is based on bid, and each GENCOs are needed to compete with rivals via bidding to the market. Competition creates the opportunities for GENCOs to get more profit (Maa, Wena, Nia, & Liub, 2005).

In this paper, behavior of a GENCO is studied viewpoint of profit maximization. Advanced approaches for modeling are needed for simulating the behavior of participants in electricity markets over time and model how market participants may act and react to changes in the underlying economic, financial, regulatory environments and important output factors. This is particularly useful for developing whole market rules that will allow these markets to function properly.

To simulate the GENCO behavior, it is needed to determine how the GENCO will behave in each probable situation. In any electricity market, conditions are varying more or less randomly. Therefore, there are an infinite number of possible scenarios. All random events in the electricity market are represented by different scenarios. Also, parameter numbers describe the conditions of a particular scenario. All the scenario parameters are collected into the random vector. Furthermore, it is possible that there is some uncertainty in the input data of the simulation. Therefore, sensitivity analysis by varying the assumption of the behavior of the factors may be performed (Amelin, 2004). Sensitivity analysis needs proper simulation tools.

The complex interactions and interdependencies among participants in today’s deregulated and decentralized electricity markets were studied in game theory (Picker, 1997). However, most power market participants use very complex strategies to be conveniently modeled by standard game theory techniques. In particular, the ability of market participants to repeatedly investigate markets and rapidly adjust their strategies adds extra complexity. Computational social science offers appealing extensions to traditional game theory.

The classical method to simulate electricity markets is probabilistic production cost simulation (PPC). This method was first presented in Baleriaux, Jamoulle, and deGuertechin (1967) and Booth (1972), respectively and has later been further developed by several authors; nowadays, PPC is included in most text books on power system planning (e.g. Stoll et al., 1994, Söder and Amelin, 2003, Wang and McDonald, 1994, Wood and Wollenberg, 1996).

In electricity markets, producers interact one with another taking into account that their results are influenced by competitors’ decisions. Game theory is well suited for analyzing these kinds of situations (Ercetin and Tassiulas, 2003, Owen, 1995, The Essence of Game Theory, 2003). It has been successfully applied in many fields: information technology (Michael & Bell, 2000), transportation industry (Yang, 2003), stock market (Garc´ıa-Cort´es, Yagüe, & Moreno, 2000), sociology (Galloway, 2004, Singh, 1999) and electricity markets (de la Torre et al., 2004, Epstein and Axtell, 1996, Ferrero et al., 1997, Martini et al., 2001).

One of simulation tools is agent-based modeling and simulation (ABMS). Computational social science involves the use of ABMS to study complex social systems (Epstein & Axtell, 1996). ABMS consists of a set of agents and a framework for simulating their decisions and interactions. ABMS is related to a variety of other simulation techniques, including discrete event simulation and distributed artificial intelligence or multi-agent systems (Law and Kelton, 2000, Pritsker, 1999). ABMS tools are designed to simulate the interactions of large numbers of individuals so as to study the macro-scale consequences of these interactions (Tesfatsion, 2002). Each entity in the system under investigation is represented by an agent in the model. Thus, an agent is a software representation of a decision-making unit. Agents are self directed objects with specific traits and typically exhibit bounded rationality, that is, they make decisions by using limited internal decision rules that depend only on imperfect local information. In practice, each agent has only partial knowledge of other agents and each agent makes its own decisions based on the partial knowledge about other agents in the system. Several electricity market ABMS tools have been constructed, including those created by Bower and Bunn, 2000, Petrov and Shele., 2000, Lai et al., 2000, Skoulidas et al., 2002, Veselka et al., 2002, North et al., 2002. These models have demonstrated the potential of agent simulations to act as electronic laboratories, or “e-laboratories”, suitable for repeated experimentation under controlled conditions.

Krause et al. (2004) studied the bidding behavior of generating companies in an electricity market based on locational marginal prices (LMPs). Results from an agent-based model with reinforcement learning are compared with those for a computed Nash equilibrium on a five-node test power system. Ernst, Minoia, and Ilic (2004) also used agent-based model to analyze generators’ bidding strategies in an LMP market. In this approach, it is assumed that the generators choose their strategy by maximizing their expected profits, based on available information about current and future market conditions. In a simulation of a two-node system, the influence of line transfer capacity and number and size of generators and GENCOs is analyzed.

Yin, Dong, and Saha (2007) applied generalized autoregressive conditional heteroskedastic methodology to accurately predict electricity prices and estimate the risks involved in electricity prices. They proposed a novel approach of designing the optimal bidding strategies based on generator’s degree of risk taking. Fuzzy logic models recently have also received special attention for prediction purposes in energy context (Azadeh et al., 2010, Azadeh et al., 2009).

Borrie, Isnandar, and Ozveren (2006) developed a simulation platform using Fuzzy Cognitive Agents based upon the encapsulation of FCM generated on the MATLAB Simulink platform within commercially available Intelligent Agent software. Bomparda et al. (2008) presented a medium run electricity market simulator based on game theory that incorporates two different games, one for the unit commitment of thermal units and one for strategic bidding and hourly market clearing. Borrie and Ozveren (2004) proposed that FCM can act as powerful inference engine within an autonomous adaptive agent based architecture to model complex system of electricity market. They examined the generic structure of the FCMs, their construction, and the learning algorithms to allow them to adapt to the dynamic market based environment. They also discussed about the concept of temporal delay within the FCMs to describe the inertia that exists in real time systems.

Trigo, Marques, and Coelho (2009) presented an electricity market multi-agent simulator of an artificial electric power market populated with learning agents. The simulator facilitated the integration of two modeling constructs: (i) the specification of the environmental physical market properties, and (ii) the modeling of the decision-making (deliberative) and reactive agents. Their multi agent based simulation approach to the electricity market, aimed at simulating the interactions of agents and to study the macro-scale effects of those interactions.

Akbari, Kabiri, and Amjady (2009) presented a method for calculating the optimal bidding strategies among GENCOs in electricity markets with assumption of imperfect competition and complete information and with consideration of uncertainty in load forecast. They employed the parameterized supply function equilibrium for modeling the imperfect competition among GENCOs in which they used proportionate parameterization of the sole and the intercept. They utilized fuzzy approach for modeling the uncertainty of load forecast and they compared the result with probabilistic approach. Wang, Audun, Guenter, and Koritrov (2009) applied agent based modeling and simulation to electricity market complex adaptive system to model the market participants in electricity markets as various types of agent with different strategies, risk preferences, and objectives. They expanded simulation capability of the model across several time horizons from day-ahead bidding and scheduling to long-term expansion planning.

Liu and Wu (2006) proposed a sequential optimization approach to electric energy allocation between spot and contract markets, taking into consideration the risks of electricity price, congestion charge, and fuel price based on the mean-variance portfolio theory. They analyzed and simulated the impact of the fuel market on electric energy allocation with historical data in respect of the electricity market and other fuel markets in the US. Chen, Tsay, and Gow (2009) presented a methodology for bidding strategies of electricity participants in a congestion environment. They modeled the problem as a two steps optimization problem. At first steps they maximized expected profit with a bidding strategy and at the second step they performed a curtailment strategy to maximize the participant’s profit when the system occurs the transmission congestion.

Yin, Zhao, Saha, and Dong (2007) proposed a novel approach of designing the optimal bidding strategies based on incomplete market information that predict the expected bidding productions of each rival generator in the market based on publicly available bidding data. They used support vector machine to estimate the nonlinear relationship between generators’ bidding productions and the market clearing price from historical bidding and price data. Finally they transformed the optimal bidding problem into a stochastic optimization problem and solved it with differential evolution and Monte Carlo simulation based on the predicted rivals’ behavior and market clearing price. Botterud, Thimmapuram, and Yamakado (2005) used an agent-based simulation model to analyze market power in electricity markets focused on the effect of congestion management on the ability of GENCOs to raise prices beyond competitive levels. They compared a market design based on locational marginal pricing with a market design that uses system marginal pricing and congestion management. They also illustrated that agent-based modeling can contribute important insights into the complex interactions between the participants in transmission-constrained electricity markets.

Wang (2009) presented a novel conjectural variation-based bidding strategy combined with a Q-learning algorithm. They modeled GENCOs as adaptive agents in the electricity markets. They used Q-learning to model the bidding behavior of GENCOs that can learn and adjust their strategies over time. They applied SA-Q-learning algorithm with Metropolis criterion to balance exploitation and exploration in the reinforcement learning process. Saleh, Tsuji, and Oyama (2009) proposed a method to build optimal bidding strategies in a day-ahead electricity market with incomplete information considering both risk management and unit commitment. The proposed methodology employs the Monte Carlo simulation for modeling a risk management and a strategic behavior of rival. A probability density function, value at risk and Monte Carlo simulation used to build optimal bidding strategies for a GENCO.

Da-Wei and Xue-Shan (2009) presented a risk evaluation method considering fuzzy uncertainty of GENCOs’ competitive bidding behaviors, the creditability of the real profit less than the fuzzy expected profit is taken as risk index and On this basis, the chance-constrained programming model of the GENCOs’ optimal bidding strategy presented. They used a hybrid intelligent algorithm of fuzzy simulation and neural network combined with GA to solve the problem. Since in the chance-constrained programming model the object function and the chance-constrained formulas are uncertain functions, they used fuzzy simulation technique to obtain the function value and neural network to approach the uncertain function.

Hong and Hong (2005) proposed a bidding strategy using the fuzzy Markov decision process and fuzzy-c-means. They used fuzzy Markov decision process to transform the crisp transition probabilities into fuzzy transition probabilities. They used a 30-bus system to illustrate the applicability of the proposed method. Bajpai and Singh (2008) developed an optimal bidding strategy for a GENCO in the network constrained electricity markets and to analyze the impact of network constraints and opponents bidding behavior on it. A bi-level programming technique is formulated in which upper level problem represents an individual GENCO payoff maximization and the lower level represents the independent system operator’s market clearing problem for minimizing customers’ payments. The objective function of bi-level programming problem used for bidding strategy by economic withholding is highly nonlinear. Fuzzy adaptive particle swarm optimization applied to obtain the global solution of the proposed bi-level programming problem for single hourly and multi-hourly market clearings.

Badri, Jadid, Moghaddam, and Rashidinejad (2009) investigated the problem of developing optimal bidding strategies of GENCOs considering participants’ market power as well as transmission constraints. The problem was modeled as a bi-level optimization that at the first level each GENCO maximizes its payoff through strategic bidding, while at the second level, an independent system operator dispatches power, solving an optimal power flow problem. The objective of proposed optimization model is generating optimal bidding strategies for GENCOs, while satisfying transmission constraints. Jain and Srivastava (2009) used equal incremental cost criteria for developing the optimal bidding strategy. They formulated the rival’s bidding behavior using a stochastic optimization model. They used genetic algorithm to decide the optimal bidding strategy including congestion management to maximize the profit of the suppliers, considering single sided as well as double sided bidding. Both pure as well as probabilistic strategies have been simulated in their paper. Value at risk calculated as a measure of financial risk.

Gao and Sheble (2010) first identified a proper supply function equilibrium model, which can be applied to a multiple-period situation then developed the equilibrium condition using discrete time optimal control considering fuel resource constraints and finally they discusses the issues of multiple equilibria caused by transmission network and shows that a transmission constrained equilibrium may exist. Vahidinasab and Jadid (2009) described a method for developing optimal bidding strategy based on a bi-level optimization, considering suppliers’ emission of pollutants. They employed supply function equilibrium model to represent the strategic behavior of each supplier. In their paper, locational marginal pricing mechanism assumed for settling the market and calculating the supplier profit. It modeled as a bi-level optimization problem in which the upper-level subproblem maximizes individual supplier payoff and the lower-level subproblem solves the independent system operator’s market clearing problem.

Sadeh, Rajabi Mashhadi, and Latifi (2009) focusing on Iran’s electricity market structure modeled the bidding problem from the viewpoint of a GENCO in a pay-as-bid auction. Their goal was to present a tool for determining the optimal bidding strategy of a price-taker producer in an electricity pay-as-bid auction taking into account the relevant risks. Due to uncertainties in power market, the market-clearing price of each hour is assumed to be known as a probability density function. The optimal solution of bidding problem obtained analytically based on the classical optimization theory. Also, the analytical solution for a multi-step bid protocol generalized and the properties of the generalized solution discussed. They developed a model to consider concept of risk using two different methods. The two proposed methods were then compared and the results interpreted using numerical examples.

Soleymani, Ranjbar, and Shirani (2007) considered the combined energy and reserve markets, and determined the Nash equilibrium points then presented the bidding strategies for each GENCO at these points. The bids for the energy and 10 min spinning reserve markets are separated in the second stage, and again, demonstrated the bidding strategies for each GENCO for the two separated markets. Comparison of the results showed that the separated bidding strategies, while being simplified with the algebraic optimization model and reducing the time consumed, give the same results as the combined ones. They employed the Western system coordinating council (WSCC) nine bus test system to illustrate and verify the results of the proposed method.

Ma, Wen, Nia, and Liu (2005) developed an approach for building optimal bidding strategies with risks taken into account for GENCO participating in a pool-based single-buyer electricity market. They assumed that each GENCO bids a linear supply function and that the system is dispatched to minimize the total purchasing cost of the single-buyer. In their model each GENCO chooses the coefficients in the linear supply function for making tradeoff between two conflicting objectives: profit maximization and risk minimization. They established a stochastic optimization model for the purpose and presented a novel method for solving this problem. Jia et al. (2009) presented a maintenance scheduling of generating units game in competitive electricity markets to analyze strategic behaviors of GENCOs. A simplified offer price methodology and a stochastic programming one are adopted to determine player’s optimal bidding strategies for the day-ahead market, whose trends of game result are similar. The maximal payoff of each GENCO is obtained by tabu search algorithm. The solutions of non-equilibrium, unique equilibrium, and multiple equilibria are coordinated.

In this study, a new approach based on FCM is introduced to model and simulate GENCO behavior in the electricity market viewpoint of profit maximization where FCM helps the decision makers to understand the complex dynamics between a certain strategic goal and the related factors. Moreover, it is studied how determined factors by an expert affect on GENCO profit. An expert defines important factors that affect on strategic behavior performed by a GENCO. To identify key factors relevant to the goal, a FCM should be built and then analyzed. We consider two cases for analysis and illustration. In the case 1, expert determines simple values as {−1, 0, 1} for connections. By this approach, decision maker can study how determined factors affect on goal. A hidden pattern is obtained by this case. In case 2, expert determines weighted values for connections. By this case, decision maker can analyze model sensitivity by changing factor values. In addition, the FCM matrix can be used usefully for clearly measuring the composite effects resulting from changes of multiple factors. To the best of our knowledge this is the first paper that studies how determined factors by an expert affect on GENCO profit using FCM. Also, it analyzes model sensitivity by changing weighted factor values to help understand the complex dynamics between a certain strategic goal and the related factors.

This article is organized as follows: Section 1 gives an introduction to FCM. Section 2 presents FCM procedure used for this study consisting of concepts and definitions and algorithm. Modeling of defined problem is given by Section 3. Simulation and sensitivity analysis are presented in Section 4. Concluding remarks are drawn in Section 5.