Modeling Competition Between Consumers in
Smart Grid by Using Game Theory
Mehdi Khavaninzadeh
Tehran Area Operation Center
Tehran Regional Electric Company
Tehran, Iran
Masoud Rashidinejad
Department of Electrical Engineering
Shahid Bahonar University
Kerman, Iran
Abstract— Network constraints such as an overload of equipments and violations of operational guidelines and problems related to the electricity market, such as facing with high spot prices often occur during off peak times that small customer plays an important role on it. Thus, attention to the consumer and creating necessary conditions for their participation in the electricity market can be an effective tool.
With the development of infrastructures and expansion of advanced metering systems that form the foundation of the smart grid, consumers control and monitoring in real-time, continuous or periodic, and this can help to participation of customer in the power market.
In this regard, demand response programs can have a significant influence and importance. For this purpose the exchange market DR programs for participation of consumers and competition among, have been proposed.
For this purpose, we used game theory framework with a dynamic Nash Equilibrium (NE) and supply function equilibrium (SFE) pricing model to modeling competitions among customers. A non-cooperative game with complete information, and a nine-bus IEEE test system is employed to illustrate the proposed method.
Index Terms-- Bidding strategy; Demand Response Programs; Game Theory;
I. Introduction
Be one of the main goals of the restructuring of the electricity industry was to create a competitive environment. Although initially, the market structure was built to compete between producers, but the always competition between consumers and their participation in the market, considered and investigated [1]. Consumers in the electricity market can play an important role in improving power system reliability and efficiency of the electricity market.
Today, with the use of advanced metering systems and devices that form the basis of smart grid, control and monitoring of the consumers for a moment, continuously or periodically, the behavior of the consumers is possible and also customers be able to receive information about the status of the network and market conditions, and therefore the participation of consumers in electricity markets is provided.
Demand Response Management is one of the main features in smart grid. DR refers to changes in electricity usage by end users from their normal consumption pattern in response to changes to market prices or when network reliability is jeopardized [2].
The demand response capability of the smart grid, essentially, enables the supply and demand sides to interact with each other by exchanging the price and demand information, in order to make wise decisions. When users are provided with sufficient incentives, they are willing to change their energy usage patterns to tradeoff between comfort and electricity bills.
To better understand the importance and benefits of demand response programs should be noted that after restructuring and deregulation of the power industry problems arose as a result of these changes, which can be divided into two general categories. First one associated with network and happens when constrained networks are operating at their limit and TSO or distributors must preserve the security and reliability of their networks. Last one associated with the market when retailers and generators encounter financial risks affected by spot price volatility in the electricity market [3].
Problems that mention above often occur during times of peak demand and customers play an important role in these problems. By using Advanced Metering Infrastructure (AMI), in smart grid, we can monitor consumers' behavior and customers can give information about network and market and with participation in DR programs help to solve those problems.
In [3] all players in power market based on the benefit themselves achieve of Demand Response Programs (DRPs) divided into two groups. Players in the first group include the retailers, distributors, and TSO that they need DR in the form of load curtailment to improve the security and reliability of their own businesses and systems. The second group includes aggregators and large customers that they negotiate DR with the first group.
Aggregators are new independent entities in the electricity market that combining multiple small customers and act as mediators / brokers between DR sellers and the DR buyers. Aggregators possess the technology to perform DR and are responsible for the installation of the communication and control devices (i.e. smart meters) on end-user premises. Since each aggregator represents a significant amount of total demand in the DR market, it can negotiate on behalf of the DR sellers with DR buyer more efficiently.
In recent years, some research has been done on building optimal bidding strategies for competitive market. There are three ways for expanding optimal bidding strategies. The first one relay on estimations of the market clearing price (MCP) in the next trading period, the second utilizes estimations of bidding behavior of the rival participants, and the third is game theory based [4]. The first approach is easy in principle. Based on the approximation of the MCP, it is entirely straightforward for a power supplier to determine its bidding strategy by simply offering a price a little cheaper than the MCP. However, predicting electricity price in a pool market requires analysis that combines demand forecasts with an understanding of transmission congestion and participants’ bidding. Since there are very few historical data available in most electricity markets, it is hard to achieve exact prediction because of the fast moving reform of the electricity industry. Another difficulty with this method is an incidental assumption that the bid from one player will not influence the MCP. Since the electricity market is essentially an oligopoly, this assumption is unseemly to hold for any reasonable length of time. This method has rarely been applied in developing bidding strategies in electricity markets. Most of the techniques published so far are based on estimations of bidding behavior of rival participants in which various methods, such as fuzzy sets and probability analysis, are used for estimation.
The third approach is to apply some techniques or methods from the game theory. There are many publications accessible in the scope of electricity markets, which follow this approach [5]-[6]. There are basically two methods in this catalogue. The former method is the matrix game based [5]-[7]. Where bidding strategies have to be represented as separate quantities. The latter method follows oligopoly games like as the Bertrand model, Cournot model and Supply Function Equilibrium (SFE) model [6]-[7] as shown in “Fig.1”.
Recently, there has been a significant number of works on game theory application to power system problems [8]-[12]. In most papers that have been published, bidding strategy of generators is intended, but in this paper, bidding strategy of customers in a pool based market is considered. During this competition sequence of aggregators has been changed, the effect of this market and limitation on the number of bidding strategy changes for each aggregator in network cost are studied.
F Figure 1. Bidding Strategy Models.
II. Demand Response
Due to environmental and economic constraints, power systems are currently being operated closer to their limits [13]. Different techniques have been proposed to manage this situation. Demand response program (DRP), also called a demand relief program by some utilities, can play an important role in meeting the challenges involved [14]. DR refers to changes in electricity usage by end-users from their normal consumption pattern in response to changes in market prices or when network reliability is jeopardized [3]. By this definition, DR supports both the market efficiency and the network reliability in a power system. Another important and significant benefits of DR include: cost reduction, risk management, environmental, market power mitigation, system efficiency and energy efficiency.
Demand response programs are divided into two main groups namely; time-based rate programs (TBRPs), and incentive based programs (IBPs) [15]. Each of these groups is composed of various programs. In time-based rate programs, i.e. Real Time Pricing (RTP), Time of Use (TOU), and Critical Peak Pricing (CPP) programs, the electricity price varies for different periods according to the electricity supply cost. RTP rates change continuously during the day reflecting the wholesale price of electricity. TOU rates establish two or, more daily periods that reflect hours when the system load is peak or off peak, and vary a higher rate during peak hours.
Figure 2. Categories of Demand Response Programs [16].
CPP is a cover on either TOU, or flat pricing. CPP uses real-time prices at times of extreme system peak. Incentive based programs include; Direct Load Control (DLC), Emergency Demand Response Program (EDRP), Interruptible/Curtailable (I/C) service, Capacity Market Program (CAP), Demand Bidding (DB), and Ancillary Service (A/S) program. The above programs can be categorized into three main subgroups namely; voluntary, mandatory and market clearing programs [16].
In [3] all DR players categorized into two groups based on the benefit they achieve of Demand Response Programs (DRPs). Players in the first group include the retailers, distributors, and TSO. They need DR in the form of load curtailment to improve the reliability of their own businesses and systems. The second group includes aggregators and customers. They negotiate DR with the first group.
Under this classification, DR can be acted as a virtual resource to be acted between the first group, buyers and the second group, sellers. A Demand Response Exchange (DRX) could be set up to comfort this trade by creating a separate DR market, creating a DRX means that DR as a virtual resource is conceptually separated from an electricity resource. Such a separation has already been demonstrated to be feasible [3]-[17]. While electricity is the main resource to be managed within the electricity markets and physical networks, DR is an auxiliary resource, which is integrated to improve reliability of both networks and markets [3]. In “Fig. 3,” two market domain systems are shown.
Investigated a particular type of business model for DRX, namely the pool-based model is shown in “Fig. 4” As be shown in “Fig. 4,” aggregators are competing with each other and try to maximize own benefit in a pool of DR market (DRX). In this paper, we used game theory to a modeling competition between this agent. The problem is formulated as a two-level optimization in which first level maximizes each aggregator’ payoff and second level minimizes network cost.
Figure 3. Power system structure with a pool-based DRX model.
Figure 4. Pool-based DRX model.
III. GAME THEORY
Game theory is a study of strategic decision making. More formally, it is the study of mathematical models of cooperation and conflict between intelligent, rational decision- makers [18]. An another term suggested as a more anatomic name for the discipline is an interactive decision theory [19], and is now finding application in the study of strategic behavior in a deregulated power market. In particular, the concept of Nash Equilibrium (NE) determines strategies by which competing companies aim at maximizing their profits on a non-cooperative basic, can be applied to understand the likely behavior of rational companies in deregulated yet oligopolistic markets.
The Nash Equilibrium conditions specify that each player is satisfied with its choice of strategy. This means that, even knowing the exact strategies of other players, every player is unable to find a more profitable strategy than her equilibrium strategy. In other words, the NE is simply a set of strategies, one for each player, such that no player can do better by changing its strategy, given that the other player stick to their equilibrium strategies.
In this paper, we used game theory framework with a dynamic Nash Equilibrium (NE) and supply function equilibrium model to modeling competition between DR sellers.
Figure 5. Pool-based DRX model.
IV. Supply Function Equilibrium
In 1989 a publication by Klemperer and Meyer [20] has proposed a new oligopolistic market model, called Supply Function Equilibrium (SFE). The basic model was set as an oligopolistic framework in which the market players are facing variable demand. Each company in this non-cooperative game selects a strategy based on a supply function that explains the quantity it is willing to sell for its price. This supply-curve bidding allows a company to adjust better to changing conditions, such as an uncertain environment, than either bidding fixed quantities or in a commitment to fix prices as in the Cournot and Bertrand settings. The decision variables for the strategic company are the parameters of their supply functions that are usually related to production costs, demand elasticity to price and capacity constraints. Qualitative examples in general, linear and step-wise supply function bids are shown in “Fig. 5”, (a), (b) and (c) respectively.
At the equilibrium point of the supply function game each player specified its optimum supply-curve bid that maximizes its profit based on how the other players will adapt their output to changes in market prices, anticipating their strategies. This kind of competition leads to a less profitable outcome for all players compared with Cournot competition. In [20] have shown that quantity and price in any SFE are bounded by the Bertrand and Cournot outcomes. Bertrand equilibrium corresponds a horizontal supply curve, and Cournot equilibrium resembles a vertical supply function, being a worst-case scenario.
Therefore, they proposed that a Cournot competition could be a better approximation in markets with steep marginal cost curves relative to demand, while markets with flat marginal costs may be approximated by Bertrand model. However, if the supply-curve bidding is let, a fixed price or a fixed quantity cannot be an equilibrium strategy if marginal costs are upward sloping, as in the case of the electricity market.
V. Problem Formulation
In competitive electricity markets, the suppliers are required to submit MW outputs, along with associated prices. The general rule that applies is that the price at which the power is offered is a non-decreasing function of the amount of power. Two bidding schemes have been implemented, the block bidding and the continuous bid curve. In this paper, a continuous bid curve model for consumers is assumed where a consumer is requested to submit its marginal cost function.
Figure 6. Examples of supply function bids.