电力市场价格竞争均衡分析及稳定性研究
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摘要
全球性的电力工业结构重组和解除管制的市场化改革,使得预测和分析一个给定市场设计的性能成为一个日益重要的课题。一方面是因为对市场实施事后的分析代价非常昂贵,另一方面也是因为研究电力市场的方法越来越丰富。电力工业的特性使得电力市场具有明显的寡头竞争特征,因而采用基于博弈论的各种寡头博弈模型来研究市场参与者的各种博弈行为及其对市场产生的影响成为了一种主流方法。本论文主要涉及各种市场条件下Bertrand静态博弈模型的均衡分析,以及动态博弈模型下市场的稳定性研究。具体而言,本文主要做了如下工作：
(1)建立了一个在统一出清(market clearing price, MCP)机制下考虑线路传输容量约束的Bertrand价格竞争博弈模型。按照连接节点的不同将线路分为两种类型,结合功率分布因子和系统总负荷分别描述了这两种线路存在传输容量约束时市场均衡的性质。给出了临界约束区间和临界约束值的概念,用来判断博弈模型均衡点的存在性与均衡价格的高低,并用简单系统验证了博弈模型的正确性与高效性。基于本模型得出的数值参数,在一定市场条件下可以为发电商的最优报价策略提供参考,同时可以作为电网规划、负荷管理及市场行为监控的指标。
(2)为了充分发挥具有快速爬坡能力的机组的性能,建立了一个考虑机组自主申报爬坡率的电力市场博弈模型。讨论了传统市场模型中固定爬坡率申报值的弊端和机组提高爬坡率的成本等问题；分析了大发电商降低爬坡率申报值的可能性、带来的后果及限制措施；利用置换法结合图形分析,重点研究了在符合市场运行实际情况的非线性边际成本环境下,发电商提高爬坡率申报值的条件和结果。其Nash均衡结果表明：市场中发电成本和运行容量越低的机组,提高爬坡率申报值的动机越强。这有利于降低市场出清价格和系统购电费用,减少高成本机组的运行与不必要的开停机,促进市场稳定。
(3)针对按报价支付(pay as bid, PAB)机制下市场中不存在纯策略Nash均衡的情形,建立了基于概率分布的连续策略Bertrand博弈模型以求解其混合策略Nash均衡(mixed strategy Nash equilibrium, MSNE)。将报价策略区间标准化之后,求出了MSNE的通解。随后针对一类指数形式的报价策略分布函数进行了研究,得到了MSNE的解析表达式,对发电商制定报价策略具有一定的参考价值。通过一个简单算例验证了该模型的可行性与有效性,结果表明：市场份额越大的发电商越倾向于申报高价,成为价格制造者(price maker),抬高市场出清价格；通过拆分可以减少大发电商在市场中所占的份额,从而达到降低市场出清价格的目的,其中等额拆分的效果更好。
(4)从均衡价格的角度出发,分析了市场的稳定性。建立了一个用于定性分析的动态博弈模型,结合图形分析,证明了市场的稳定性与均衡点的个数关系密切：当市场仅有一个纯策略Nash均衡点时,均衡是全局稳定的；当市场中存在多个纯策略Nash均衡点时,均衡是局部稳定的,即市场运行并不一定能达到均衡点,很有可能处于振荡中,局部稳定区域由市场成员的发电容量必须运行率(must run ratio, MRR)、初始报价状态等共同决定。
(5)建立了MCP机制下的Bertrand动态博弈模型,用于分析电力市场各博弈方的动态决策过程,以及市场在各种运行条件下的稳定性。将市场约束条件所确定的优化问题解的可行集区间转换成为两个便于研究应用的市场参数：MRR和最小理性利润(rational minimum profit, RMP),在此基础上以价格为决策变量建立了具有自我约束能力的差分动态博弈模型。对各种参数条件下的市场稳定性进行了研究。用一个考虑线路传输容量约束的系统验证了该模型的有效性,结果表明用本模型分析比静态博弈分析所得到的结果更深入,能有效的反映市场实际运行的情况,为市场成员的实时竞价策略提供参考意见。
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.
(1)建立了一个在统一出清(market clearing price, MCP)机制下考虑线路传输容量约束的Bertrand价格竞争博弈模型。按照连接节点的不同将线路分为两种类型,结合功率分布因子和系统总负荷分别描述了这两种线路存在传输容量约束时市场均衡的性质。给出了临界约束区间和临界约束值的概念,用来判断博弈模型均衡点的存在性与均衡价格的高低,并用简单系统验证了博弈模型的正确性与高效性。基于本模型得出的数值参数,在一定市场条件下可以为发电商的最优报价策略提供参考,同时可以作为电网规划、负荷管理及市场行为监控的指标。
(2)为了充分发挥具有快速爬坡能力的机组的性能,建立了一个考虑机组自主申报爬坡率的电力市场博弈模型。讨论了传统市场模型中固定爬坡率申报值的弊端和机组提高爬坡率的成本等问题；分析了大发电商降低爬坡率申报值的可能性、带来的后果及限制措施；利用置换法结合图形分析,重点研究了在符合市场运行实际情况的非线性边际成本环境下,发电商提高爬坡率申报值的条件和结果。其Nash均衡结果表明：市场中发电成本和运行容量越低的机组,提高爬坡率申报值的动机越强。这有利于降低市场出清价格和系统购电费用,减少高成本机组的运行与不必要的开停机,促进市场稳定。
(3)针对按报价支付(pay as bid, PAB)机制下市场中不存在纯策略Nash均衡的情形,建立了基于概率分布的连续策略Bertrand博弈模型以求解其混合策略Nash均衡(mixed strategy Nash equilibrium, MSNE)。将报价策略区间标准化之后,求出了MSNE的通解。随后针对一类指数形式的报价策略分布函数进行了研究,得到了MSNE的解析表达式,对发电商制定报价策略具有一定的参考价值。通过一个简单算例验证了该模型的可行性与有效性,结果表明：市场份额越大的发电商越倾向于申报高价,成为价格制造者(price maker),抬高市场出清价格；通过拆分可以减少大发电商在市场中所占的份额,从而达到降低市场出清价格的目的,其中等额拆分的效果更好。
(4)从均衡价格的角度出发,分析了市场的稳定性。建立了一个用于定性分析的动态博弈模型,结合图形分析,证明了市场的稳定性与均衡点的个数关系密切：当市场仅有一个纯策略Nash均衡点时,均衡是全局稳定的；当市场中存在多个纯策略Nash均衡点时,均衡是局部稳定的,即市场运行并不一定能达到均衡点,很有可能处于振荡中,局部稳定区域由市场成员的发电容量必须运行率(must run ratio, MRR)、初始报价状态等共同决定。
(5)建立了MCP机制下的Bertrand动态博弈模型,用于分析电力市场各博弈方的动态决策过程,以及市场在各种运行条件下的稳定性。将市场约束条件所确定的优化问题解的可行集区间转换成为两个便于研究应用的市场参数：MRR和最小理性利润(rational minimum profit, RMP),在此基础上以价格为决策变量建立了具有自我约束能力的差分动态博弈模型。对各种参数条件下的市场稳定性进行了研究。用一个考虑线路传输容量约束的系统验证了该模型的有效性,结果表明用本模型分析比静态博弈分析所得到的结果更深入,能有效的反映市场实际运行的情况,为市场成员的实时竞价策略提供参考意见。
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.
引文
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