寡头垄断电力市场产量博弈模型及其混沌复杂性研究
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摘要
混沌理论是近三十年来新兴起来的一门多学科交叉的科学,目前在许多实际领域尤其是在管理和经济领域中已经得到了非常广泛的应用。众所周知电力经济系统是一个开放的复杂巨系统,电力生产过程是在一定的经济环境中运行的,电力生产者之间的产量决策是一个长期重复的动态博弈过程。本文将混沌动力学理论引入电力市场,建立一系列寡头垄断的动态重复博弈模型,通过本文分析研究,得到如下结果:
1.当前的电力市场改革赋予了电力生产者独自承担经营风险,参与上网电量竞争的权利,这是一个复杂的动态过程,本文将混沌动力学理论引入发电市场的产量博弈中,发现和揭示了这一过程的某些本质特征。建模过程中假设逆需求函数及成本函数均为较复杂的非线性形式,将电力公司收取一定比例的过网费用及生产者的多种策略组合考虑在内,这些方法虽然增加了模型的分析难度,但却使模型更加具有适用性,更加贴近电力市场的实际情况;
2.在分析所建离散非线性博弈模型的混沌特性时,主要通过系统的混沌吸引子、产量随参数演化图、Lyapunov指数及分维数、系统对初值的敏感依赖性、功率谱、密度周期等特性来作为分析研究的切入点,研究了各重要参数如产量调整系数、过网费率及其相互耦合时对于系统进入混沌状态的影响程度;
3.在利用IEEE30节点系统的生产者成本函数数据进行的仿真模拟中发现了系统的混沌吸引子,研究了该系统内的电力生产者在利用本文所建模型进行产量决策时表现出来的复杂动力学特征,重点讨论了生产者的产量调整速度及过网费率等系统参数在一定范围内的微小变化都会引起产量决策系统发生质的变化的特性,这一研究具有重要的实际意义;
4.使用混沌控制方法对所建模型可能出现的混沌性态进行了成功的控制,实现了对离散非线性动力系统的倍周期分岔和混沌吸引子中不稳定周期轨道的有效混沌控制,并以具体的数值模拟结果为例验证了控制方法的有效性和实用性。文中采取的几种控制混沌方法的共同点是要求生产者必须对于混沌控制的目标有一个很明确的预期,即对于在何种状态下生产者能够取得利润最大化的认识非常重要。
本文的研究是建立在高度抽象的理论模型基础上的,所建的模型比经典Cournot模型更复杂也更贴近电力市场运行的实际情况,其结果可以为实际电力系统的政策制定者提供较好的参考作用。下一步工作的研究重点将放在不同扰动作用下高维动力系统及结合电力生产者产量博弈的具体数据,用混沌动力学理论分析电力市场内产量博弈系统的复杂性态与混沌控制的实现上。
Chaos Theory has been an interdisciplinary subject for three decades and applied to many practical fields especially in management and economic area. As is well known, the electric economic system is an open complex giant system, and the production process runs in the given economic environment. The output decision in the electric market is a long-term iterative dynamic procession. In this paper, a series of output game models are proposed by introducing the chaotic dynamic theory into the electricity market. The research results show that:
1. Under the current electric reform, the electric power manufacturers can make outputs decision themselves, so they have to hunt for the most beneficial strategy and maximize their profits. This paper introduces chaos dynamic theory into the output game of electric power market, which shows some natural characteristics in this complex process. To analyze how the producers determine on the optimal outputs for the maximal profits, we suppose the inverse demand function and cost function are all nonlinear, and the wheeling rate is also taken into account. The producers in different model are differentiated with homogeneous or heterogeneous expectations. Although these methods increase the difficulty of the analysis, the models are more applicable and closer to the actual situation of the electric power market.
2. Various numerical results are presented including strange attractors, bifurcation diagrams, Lyapunov exponents and fractal dimension, sensitivity dependence on initial conditions, power spectrum and density cycling. The dynamical behaviors demonstrated in the nonlinear discrete dynamic system and the influences of the parameters on the system are analyzed. These parameters include the adjustment speed of the producers and the wheeling rate.
3. The chaotic attractors are found in the simulations with the data of IEEE30 system, and the dynamical behaviors demonstrated in this system are analyzed. This study has important practical significance.
4. Chaos control methods are successfully applied to the dynamic repeated game models in electric power oligopoly. The stability control of the period-doubling bifurcation and unstable periodic orbits in the nonlinear discrete dynamic systems is realized. The numerical simulation results show that these control methods are effective. The uniform request of these chaos control methods in this paper is the goals for controlling chaos. That is to say, it is extraordinary important for producers to know that when they can get the maximum profit.
The researches in this paper are based on the abstract theoretic models which are more accordant with the reality of the electric power system than the classical Cournot model. The results will provide references for electric power producers to make optimal output decision. The emphasis of future work will concentrate on high dimensional dynamical system modeling, considering perturbation, analyzing and controlling the chaotic characters with data in the real output decision-making system.
1.当前的电力市场改革赋予了电力生产者独自承担经营风险,参与上网电量竞争的权利,这是一个复杂的动态过程,本文将混沌动力学理论引入发电市场的产量博弈中,发现和揭示了这一过程的某些本质特征。建模过程中假设逆需求函数及成本函数均为较复杂的非线性形式,将电力公司收取一定比例的过网费用及生产者的多种策略组合考虑在内,这些方法虽然增加了模型的分析难度,但却使模型更加具有适用性,更加贴近电力市场的实际情况;
2.在分析所建离散非线性博弈模型的混沌特性时,主要通过系统的混沌吸引子、产量随参数演化图、Lyapunov指数及分维数、系统对初值的敏感依赖性、功率谱、密度周期等特性来作为分析研究的切入点,研究了各重要参数如产量调整系数、过网费率及其相互耦合时对于系统进入混沌状态的影响程度;
3.在利用IEEE30节点系统的生产者成本函数数据进行的仿真模拟中发现了系统的混沌吸引子,研究了该系统内的电力生产者在利用本文所建模型进行产量决策时表现出来的复杂动力学特征,重点讨论了生产者的产量调整速度及过网费率等系统参数在一定范围内的微小变化都会引起产量决策系统发生质的变化的特性,这一研究具有重要的实际意义;
4.使用混沌控制方法对所建模型可能出现的混沌性态进行了成功的控制,实现了对离散非线性动力系统的倍周期分岔和混沌吸引子中不稳定周期轨道的有效混沌控制,并以具体的数值模拟结果为例验证了控制方法的有效性和实用性。文中采取的几种控制混沌方法的共同点是要求生产者必须对于混沌控制的目标有一个很明确的预期,即对于在何种状态下生产者能够取得利润最大化的认识非常重要。
本文的研究是建立在高度抽象的理论模型基础上的,所建的模型比经典Cournot模型更复杂也更贴近电力市场运行的实际情况,其结果可以为实际电力系统的政策制定者提供较好的参考作用。下一步工作的研究重点将放在不同扰动作用下高维动力系统及结合电力生产者产量博弈的具体数据,用混沌动力学理论分析电力市场内产量博弈系统的复杂性态与混沌控制的实现上。
Chaos Theory has been an interdisciplinary subject for three decades and applied to many practical fields especially in management and economic area. As is well known, the electric economic system is an open complex giant system, and the production process runs in the given economic environment. The output decision in the electric market is a long-term iterative dynamic procession. In this paper, a series of output game models are proposed by introducing the chaotic dynamic theory into the electricity market. The research results show that:
1. Under the current electric reform, the electric power manufacturers can make outputs decision themselves, so they have to hunt for the most beneficial strategy and maximize their profits. This paper introduces chaos dynamic theory into the output game of electric power market, which shows some natural characteristics in this complex process. To analyze how the producers determine on the optimal outputs for the maximal profits, we suppose the inverse demand function and cost function are all nonlinear, and the wheeling rate is also taken into account. The producers in different model are differentiated with homogeneous or heterogeneous expectations. Although these methods increase the difficulty of the analysis, the models are more applicable and closer to the actual situation of the electric power market.
2. Various numerical results are presented including strange attractors, bifurcation diagrams, Lyapunov exponents and fractal dimension, sensitivity dependence on initial conditions, power spectrum and density cycling. The dynamical behaviors demonstrated in the nonlinear discrete dynamic system and the influences of the parameters on the system are analyzed. These parameters include the adjustment speed of the producers and the wheeling rate.
3. The chaotic attractors are found in the simulations with the data of IEEE30 system, and the dynamical behaviors demonstrated in this system are analyzed. This study has important practical significance.
4. Chaos control methods are successfully applied to the dynamic repeated game models in electric power oligopoly. The stability control of the period-doubling bifurcation and unstable periodic orbits in the nonlinear discrete dynamic systems is realized. The numerical simulation results show that these control methods are effective. The uniform request of these chaos control methods in this paper is the goals for controlling chaos. That is to say, it is extraordinary important for producers to know that when they can get the maximum profit.
The researches in this paper are based on the abstract theoretic models which are more accordant with the reality of the electric power system than the classical Cournot model. The results will provide references for electric power producers to make optimal output decision. The emphasis of future work will concentrate on high dimensional dynamical system modeling, considering perturbation, analyzing and controlling the chaotic characters with data in the real output decision-making system.
引文
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