Equilibrium Analysis Of Price Competition And Research On Stability Of Electricity Markets

As the worldwide restructuring and deregulation of electric power industry proceeds, a timely topic is how to predict or analyze the performance of a given market design. The reason is that ex post analysis of the market operation can be too expensive. The characteristic of the electric power industry makes the electricity markets more like an oligopoly. So various kinds of oligopolistic game models are used to examine the strategic behaviors of market participants and their impacts on the whole market. This is becoming a mainstream approach. The main contribution of this paper includes Nash equilibrium analysis of the Bertrand static game model under different conditions of the market, and research on stability of the markets in Bertrand dynamic game model. The contributions are summarized as follows:Firstly, the Bertrand price competition game model considering transmission line limits (network constraints) in pool-based electricity markets is presented. The line is divided into two groups according to the difference of the nodes. The characterization of equilibrium with transmission limits is provided combined with the total demand and the power distribution factor. Critical constraint is given to describe the existence of the equilibrium and equilibrium price. The game model is verified by a three-node system. As an application, we derive numerical indices that can be used to provide optimal bidding strategies under certain market conditions.Secondly, a game model considering ramping strategy of the units is presented, for that the capabilities of the units with rapid ramping can be fully applied. The disadvantages of the traditional market model with fixed bidding ramping and the cost of the increased bidding ramping are discussed. The possibility, consequences and restrictive measures of the decrement of bidding ramping of the big GEN-CO are analyzed. The conditions and results of the increased ramping strategy are obtained by replacement method combining graphic analysis with nonlinear marginal cost. The Nash equilibrium shows that, the units with low cost or low operating capacity have strong motivation to increase the bidding ramping. This is beneficial to decrease the clearing price, and to reduce the operation of the units with high cost and unnecessary units commitment, as well as to enhance the stability of the markets.Thirdly, a continuous strategy Bertrand game model for MSNE which is based on probability distribution is presented, according to the situation that there can exist no pure strategy Nash equilibrium in the PAB markets. The focus of the study is the exponential distribution in the standardized interval of bidding strategies. The analytic expression of the MSNE is valuable for strategy making of the GEN-CO. The feasibility of this model is verified by a simple example, the results indicate that, the GEN-CO with large market share wants to bid high price, be price maker and uplift the clearing price. By the way, division can reduce the market share and decrease the clearing price, equal division works more effective.Fourthly, the stability of the markets is analyzed. A qualitative analysis dynamic game model is presented, combined with graphic analysis, the close relationship of the stability and the number of equilibrium is provided. When there is only one pure strategy Nash equilibrium, the equilibrium is globally stable, if there exist multi pure strategy Nash equilibrium, then the equilibrium is locally stable. It means that the market can't operate on the equilibrium all the times, maybe on the oscillation. The stable region is determined by the MRR and initial state.Finally, a Bertrand dynamic game model for MCP electricity markets is presented, for analyzing the dynamic decision-making process of market participants, as well as the stability of electricity markets. According to the constraints of the markets, two market indices are proposed, namely, MRR and RMP. With the electricity price be the decision variable, a difference dynamic game model with self-restriction is established. The global stability and conditional stability of electricity market under different parameters is analyzed, and the stable region of the conditional stability is provided. Simulation results show that, the operation of electricity markets can be effectively reflected by the proposed dynamic game model.