Power Transmission Scheduling for Generators in a Deregulated Environment Based on a Game-Theoretic Approach

Bingtuan Gao, Tingting Ma, Yi Tang
2015 Energies  
In a deregulated environment of the power market, in order to lower their energy price and guarantee the stability of the power network, appropriate transmission lines have to be considered for electricity generators to sell their energy to the end users. This paper proposes a game-theoretic power transmission scheduling for multiple generators to lower their wheeling cost. Based on the embedded cost method, a wheeling cost model consisting of congestion cost, cost of losses and cost of
more » ... sion capacity is presented. By assuming each generator behaves in a selfish and rational way, the competition among the multiple generators is formulated as a non-cooperative game, where the players are the generators and the strategies are their daily schedules of power transmission. We will prove that there exists at least one pure-strategy Nash equilibrium of the formulated power transmission game. Moreover, a distributed algorithm will be provided to realize the optimization in terms of minimizing the wheeling cost. Finally, simulations were performed and discussed to verify the feasibility and effectiveness of the proposed non-cooperative game approach for the generators in a deregulated environment. of operation, management and staff, in order to maintain good operation and development of the transmission system. Wheeling cost is reasonable and affects not only the survival and development of electric utilities but also the benefit of generators and end users. Various algorithms and methods have been used and proposed to evaluate the cost of transmission services. The current methods can be mainly classified into two categories [2]: embedded cost of wheeling methods [3,5-7] and marginal cost pricing method [8] [9] [10] . Embedded cost of wheeling methods, including the postage stamp method, contract path method, boundary flow methods and so on, recover the embedded capital costs and the average annual operating and maintenance costs of existing facilities from a particular wheeling transaction. The marginal cost pricing method is based on microeconomics. Additionally, Nojeng et al. [11] proposed an improved MW-Mile method by considering not only the changes in MW flows but also the quality of the load, i.e., the power factor. Monsef et al. [12] proposed a reliability-based method for allocating the cost of transmission networks. Moreover, a two-step method based on the perfect coupling of the circuit theory with the Aumann-Shapley method is proposed in [13] . The method can calculate allocation costs for each branch of the transmission system to identify and quantify the individual responsibility of generators and loads. Although the aforementioned papers can calculate wheeling cost under several different conditions, most of them missed studying the effect of congestion cost, which should be covered by wheeling cost. Congestion is defined as the overloading of one or more transmission lines and/or transformers in the power system [14] . In order to solve the problem of congestion, particle swarm optimization (PSO) methods [14, 15] and bacterial foraging algorithms [16,17] were successfully implemented. Kanwardeep Singh et al. [18] presented an effective methodology for congestion management in deregulated power system networks considering optimal placement of a distributed generator based on bus impedance matrix considering contribution factors. Harry Singh et al. [19] proposed a pool model and a bilateral model to deal with the transmission congestion costs in competitive market and evaluated some aspects of the models based on game theory. Erli et al. [20] proposed a cooperative game based scheme for cost allocation of transmission line expansion to tackle with congestion problem in the network. This paper deals with a scenario in a deregulated environment of power market having multiple generators, multiple transmission lines, and one aggregated end user. The generators have to compete with each other to optimize their profit. By considering the game theory-based/double auction-based approaches and control theory-based approaches [21-24], we formulate wheeling pricing including congestion cost for the players in the deregulated environment of power market. To make their electricity more competitive in the end users market, a game-theoretic approach is proposed for generators to schedule their power transmission effectively to lower the wheeling costs. The main contributions of this paper can be summarized as: (1) by assuming generators are selfish and rational, a non-cooperative game approach is proposed for multiple generators to lower their wheeling costs, where strategies of the non-cooperative game are the power transmission scheduling of the generators; (2) a distributed algorithm is presented to realize the optimization in terms of minimizing the wheeling cost, which can be guaranteed at the Nash equilibriums of the formulated non-cooperative games; (3) simulations are performed to verify the effectiveness of the proposed approach, and discussions show that all the generators, electric utilities, and aggregated end users can benefit from the game. The rest of the paper is organized as follows. Section 2 presents the method that this paper adopts for the pricing model of the wheeling cost. In Section 3, the novel proposed method of this paper for optimizing wheeling cost based on the game-theoretic method is presented. Simulation results are presented and discussed in Section 4. Finally, conclusions are provided in Section 5.
doi:10.3390/en81212401 fatcat:i27wjbh5mjhhnfv5abelzpkspi