摘要
随着电力产业市场化改革的深入,电力市场的逐步建立与完善,发电商通过竞争获取上网电量。对发电商而言,报价策略在一定程度内决定其收益的多寡;而对整个电力市场而言,均衡的电力报价在很大程度内维持着市场供需的平衡,相对稳定的电力市场是保证稳定电力供给的前提,由于电力产业的基础性,电力短缺将带来巨大的经济损失和社会损失。因此,研究报价策略及其均衡对发电商与电力产业的健康发展以至对整个社会都是十分重要的。
基于微分博弈原理,本文首先构建了贴现率相同情况下发电商报价动态模型,运用Hamilton-Jacobi-Bellman方法对其进行求解基础上,针对三家发电商的情况进行了数值仿真分析;在此基础上,考虑在贴现率不同情况下基于微分博弈原理,构建了完全状态下发电商报价动态微分博弈模型,针对贴现率以及学习速度两个影响因素,分析其取值的不同,将解得的完全状态下的发电商报价策略函数分别退回到部分状态以及静止状态下的发电商报价策略函数,并对其进行数值仿真,考虑了贴现因子这个影响因素对三种状态下发电商的贴现收益的影响,并对其进行了分析与比较;由于在实际的电力市场环境下,电力市场需求是不确定的,假设其是一随机过程,最后,构建了发电商报价随机微分博弈模型,对该模型进行求解分析,并对其进行数值仿真,通过求解偏微分方程,可以得到关于市场清除价的随机过程表达式,将得到的关于市场清除价的表达式代入优化方程,不难得到在考虑市场需求随机情况下发电商的最优报价策略,但在实际求解过程中这是相当困难的,不过当一些参数为特定值时,随机微分方程可以退回为常微分方程的形式,即为前面两章探讨的内容,因此,本章可以看做是前两章探讨内容的一个延伸。
分析表明:高边际成本的发电商报价策略的动态均衡会大于其Cournot-Nash均衡,而边际成本较低的发电商报价策略动态均衡略低于Cournot-Nash均衡;随贴现率的增大,发电商的均衡报价策略会经历由递增到递减的变化过程,而学习速度对发电商报价策略的影响则是相反的;当贴现率与学习速度同时变化时,对市场清除价的局部影响较为复杂,但当两者同时逐渐增大时,发电商报价策略的动态均衡会逐渐稳定在较高水平。
As the power industry market-oriented reforming, and the power market gradually establishing and perfect, the power generations to obtain the Internet electricity competitively. For the power generators, the bidding strategy in a certain extent decide the amount of its revenue; while for the entire electricity market, the equilibrium pricing in a large extent to maintain the balance of market supply and demand, and the relative stable power market is the premise to ensure the stability of the power supply, and the power shortages will lead to huge economic losses and social losses due to the basic of power industry. Therefore, it is important for the power generator and the healthy development of electricity industry as well as on the whole society to study the bidding and their equilibrium.
Firstly, Based on Differential game, with the same discount rate the dynamic bidding model is presented and solved by using the Hamilton-Jacobi-Bellman method, and the situations of three electric power producers are analyzed by numerical simulations; on the basis of this, Based on Differential game, with the different discount rate the dynamic bidding model in the complete situation is presented, and for the two factors of discount rate as well as the learning speed, their different values are analyzed , and bidding strategy function in the completely state solved were separately returned to the part state as well as the static state, and taking into account the discount factor influenced on the discount earnings of power generators in the three kinds of state, and its analysis and comparison is conducted by numerical simulations; finally, because the power demand is uncertain in the actual electricity market and assumed to be a random process, Based on Stochastic Differential game, the dynamic bidding model is presented and solved and analyzed by numerical simulations. The stochastic process expression about market clear price can be got by solving the partial differential equations, and let the expression into the optimization equation, it is not difficult to obtain optimal bidding strategy of power generators in considering the case of market demand that is stochastic. But it is difficult to solve in the actual situation, and when some parameters is a specific value, the stochastic differential equation can be returned to the form of ordinary differential equations, that is the contents of the two previous chapters, therefore, this chapter can be seen as an extension to the contents of the two previous chapters.
It can be indicated that, the bidding strategy’s dynamic Nash equilibrium will be greater than Cournot-Nash equilibrium of the electric power producer with higher marginal cost ,but the bidding strategy’s dynamic Nash equilibrium will be slightly lower than Cournot-Nash equilibrium of the generator with lower marginal cost; with the discount rate increasing, the equilibrium bidding will experience the process from increasing to decreasing, whereas the influence of learning speed on the equilibrium bidding has opposite process; And when the discount rate and learning speed change at the same time, the partial impact of market clear price is more complex , but when both of them gradually increase, the bidding strategy’s dynamic Nash equilibrium will gradually stabilize at a high level.
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