【作者】 王洁；

【导师】 童小娇； 杨洪明；

【作者基本信息】 长沙理工大学 ， 计算数学， 2008， 硕士

【摘要】 非线性互补函数因其能有效转化互补条件为半光滑方程组而被广泛应用于求解非线性规划、变分不等式等问题。本文根据电力市场的运作机制,运用非线性互补函数建立电力市场的一类动态投标模型并分析模型的特点和计算方法。其主要内容如下:第一章绪论部分介绍了电力市场的投标模型和均衡理论、数学基础,以及本文的主要工作概括。第二章基于双层优化理论,系统分析了计及输电网约束的一类静态投标模型的均衡点,通过求解市场参与者的最优响应曲线,来确定市场均衡点的状态,以三节点的电力市场为例,分析了不同输电网状态(阻塞和不阻塞)下的均衡点,计算结果与分析结论一致。第三章基于供应函数和非线性互补函数理论,提出了计及输电网约束和投标变量界约束的电力市场动态投标模型。新模型由差分动态系统和非线性互补函数(NCP)转换的半光滑方程系统构成。以三节点和五节点组成的电力市场为例,分析了在不同的市场参数和不同的输电网运行状态(阻塞和不阻塞)下,市场的Nash均衡状况和均衡点的局部稳定性;通过数值仿真探讨了不同市场参数对市场的动态行为及局部稳定性的影响。仿真结果显示了新模型的有效性。第四章为了准确模拟电力市场参与者的投标过程,在第三章建立的模型基础之上,引入集团投标模型,提出了一类新的电力市场动态集团投标模型。以三节点的电力市场为例,数值仿真分析了集团投标在不同的市场参数下,系统将出现不同的输电网运行状态(阻塞和无阻塞)和市场的Nash均衡。更多还原

【Abstract】 Nonlinear complementarity function method could transfer the complementarity programming to a system of semismooth equations, it has been widely raised in solving nonlinear programming and variational inequality etc. Considering the principle of power market, we present a new dynamic bidding model with Nonlinear complementarity function. Furthermore, the characteristic and calculation method of this new model is investigated. The primary contents are as follows:In the first section, we mainly introduce the bidding models, equilibrium theory and math knowledge. In addition, our research works of this paper are also briefly introduced.In the second section, we analysis bidding equilibrium involving transmission constraints based on bilevel programming. The property of equilibrium points is studied through the intersection of optimal response curves in different region. As an example with three lines and three buses, the Nash equilibrium is analyzed in different market parameters and different operational conditions of transmission network, i.e. congestion and non-congestion; By using the numerical simulation approach, the result of numerical simulations is identical to the analysis.In the third section, we present a dynamic bidding model of power markets based on the supply function and the nonlinear complementarity theory in which the transmission constraints of the network and bounded constraints of bidding variables are involved. The new model is composed of difference dynamic system and semi-smooth equations reformulated by NCP. As two examples, three buses and five buses of a power market are as numerical examples to test the dynamic models, the Nash equilibrium and its stability are analyzed with different market parameters and different operational conditions of transmission network, i.e. congestion and non-congestion; By using the numerical simulations, the effect of different market parameters to the dynamic behaviors and stability of markets is studied. The simulating results show that the new model is valid.In the fourth section, to accurately simulate the bidding of market participants, introducing the multi-team model based on the model in the third section, propose a dynamic multi-team model of electricity market. As examples with three buses, numerical simulations analyze that under the different parameters of the market, the system will appear different operation states of transmission (i.e., congestion and non-congestion) and different Nash equilibriums.更多还原