电力市场稳定性研究
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摘要
世界范围内的电力工业市场化改革,在电力系统规划、运行、管理、安全稳定分析与控制等领域催生了大量新课题,亟需新的理论和方法指导。电力市场稳定性不仅包括功角稳定、电压稳定以及频率稳定等物理系统的稳定,还需要考虑与电力市场相关的经济系统的稳定性。电力市场的经济稳定性与电力系统的物理稳定性,既相互影响又相互制约,致使电力市场稳定性的研究成为富有挑战性的课题之一。
论文旨在结合电力市场的特点,利用稳定性理论、控制理论和经济学中的研究思想和方法,对电力市场稳定性及其相关问题展开深入研究,主要包括以下工作:
电力市场是电力的卖方和买方相互作用以决定其电价和需求量的过程,以电价和需求量等时间序列作为研究对象,提出了一般分组分离建模方法和改进的Lyapu -nov指数预测方法,并在理论上证明了时间序列分离融合的合理性,提高了预测精度,并用实例验证了二者的有效性。
应用经济学原理对电力市场进行动态均衡分析,建立了若干描述电力市场行为的微分和差分模型。在假设市场需求是价格预测的变系数线性函数(或非线性函数),市场供给是现货价格的变系数线性函数(或非线性函数)的条件下,对电价和需求量等时间序列进行了分析,建立了自治、非自治的连续或离散线性周期的数学模型描述电力市场行为。
结合已建立的描述电力市场行为的模型,借助于构造合适的Lyapunov函数、比较方法、微积分不等式、矩阵测度等工具,系统研究了一般的自治、非自治连续或离散线性周期系统的Lyapunov稳定性和实用稳定性,针对变系数周期系统第一次得到了用模型系数来描述其实用稳定性的一系列稳定性判定条件和最终收敛边界的估计公式。给出了离散系统连续化的条件及连续和离散系统系数之间的关系。
首次将实用稳定性理论和方法应用于电力市场稳定性的研究中,借助于构造合适的Lyapunov函数、柯西矩阵、矩阵测度、常数变易法等工具,系统研究了所建电力市场模型的实用稳定性,得到了用模型的系数来描述其实用稳定性的一系列判定条件和最终收敛边界的估计公式;同时对电力市场的Lyapunov稳定性进行了研究,得到了电力市场稳定性的若干判据,部分结论改进了Alvarado等人的结果;随后将Lyapunov稳定的结果与实用稳定进行了比较。最后利用MATLAB、MAPLE等数学软件,对这些模型及稳定条件的有效性用加州电力市场等数据进行了仿真分析,分析了其供应量、供应价格、用户需求量和需求价格对形成稳定、合理的电力市场经济机制的影响。
The worldwide reform of power industry market-oriented makes the birth of a large number of new issues in various fields, such as the power system planning, operation, dispatching, management, security stability analysis and control. So electri- city market needs new theories and methods to guide it. The stability of electricity market does not only embody physical stability such as the power angle stability, voltage stability and frequency stability of the system, but it also needs to consider the stability of economic system related with the electricity market. Because the economic stability of electricity market and the physical stability of the power system are lined and affect each other, the study on the stability of electricity market has become a very challenging task.
Combining the characteristics of the electricity market, this paper deeply studies some issues related to electricity market stability by the stability theory, control theory and economics research ideas and methods.This paper includes the following content.
The electricity market is the process that the seller and the buyer affect each other to determine power prices and demand. This paper studies time series, including the power prices and the power demand and so on. Based on this, the separated modeling method of Gompertz model is put forward, and Lyapunov index forecasting method is improved. The reasonableness of separation of mergence for the time series is proved and the forecast accuracy is improved. Paper also gives examples to verify the validity of these in theory.
The paper uses the principle of economic to analysis the dynamic balance of the electricity, establishes a number of actions described and differential-difference model in electricity market. In the assumption that market demand is the linear equation (or non-linear equation) with variable coefficient of forecast price and market supply is the linear equation (or non-linear equation) with varied coefficient of spot price, paper analysis time series of the power price and the power demand. And paper establishes autonomous and non-autonomous continuous or discrete linear periodic mathematic models to describe actions of electricity market.
Combining models have been established to describe the behavior of the electri- city market; the paper studies the Lyapunov stability and practical stability of the autonomous and non-autonomous continuous or discrete linear periodic system by tools, for example, the appropriate structure Lyapunov functions, comparison, the calculus inequality, the matrix measures. The paper obtains series of stable critical conditions and estimated formula of ultimate convergence boundary .At last it gives continuation of discrete system conditions and the relations between coefficients of continuous and discrete systems.
Theories and methods of the practical stability are first time used for the studying of the electricity market stability. Paper studies the practical stability of electricity market models by tools, for example, the appropriate structure Lyapunov functions, Cauchy matrix, the matrix measure, constant variation. Judging practical stability sufficient conditions and estimating formula of ultimate convergence boundary are provided. Conditions are descriptive by coefficients of models. At the same time, paper studies the Lyapunov stability of the electricity market. As well as the sufficient conditions of judging electricity market Lyapunov stability are provided. Some of conclusions improved the results of Alvarado and others. The conclusion of Lyapunov stability has made a comparative with practical results. Finally, in order to prove the effectiveness of conditions of the models stability, paper uses Matlab and Maple mathematical softwares to analysis the date of California power market. And paper analysis the affection of power supply, supply prices, user demand and demand price make stability and reasonable electricity market economy mechanism.
论文旨在结合电力市场的特点,利用稳定性理论、控制理论和经济学中的研究思想和方法,对电力市场稳定性及其相关问题展开深入研究,主要包括以下工作:
电力市场是电力的卖方和买方相互作用以决定其电价和需求量的过程,以电价和需求量等时间序列作为研究对象,提出了一般分组分离建模方法和改进的Lyapu -nov指数预测方法,并在理论上证明了时间序列分离融合的合理性,提高了预测精度,并用实例验证了二者的有效性。
应用经济学原理对电力市场进行动态均衡分析,建立了若干描述电力市场行为的微分和差分模型。在假设市场需求是价格预测的变系数线性函数(或非线性函数),市场供给是现货价格的变系数线性函数(或非线性函数)的条件下,对电价和需求量等时间序列进行了分析,建立了自治、非自治的连续或离散线性周期的数学模型描述电力市场行为。
结合已建立的描述电力市场行为的模型,借助于构造合适的Lyapunov函数、比较方法、微积分不等式、矩阵测度等工具,系统研究了一般的自治、非自治连续或离散线性周期系统的Lyapunov稳定性和实用稳定性,针对变系数周期系统第一次得到了用模型系数来描述其实用稳定性的一系列稳定性判定条件和最终收敛边界的估计公式。给出了离散系统连续化的条件及连续和离散系统系数之间的关系。
首次将实用稳定性理论和方法应用于电力市场稳定性的研究中,借助于构造合适的Lyapunov函数、柯西矩阵、矩阵测度、常数变易法等工具,系统研究了所建电力市场模型的实用稳定性,得到了用模型的系数来描述其实用稳定性的一系列判定条件和最终收敛边界的估计公式;同时对电力市场的Lyapunov稳定性进行了研究,得到了电力市场稳定性的若干判据,部分结论改进了Alvarado等人的结果;随后将Lyapunov稳定的结果与实用稳定进行了比较。最后利用MATLAB、MAPLE等数学软件,对这些模型及稳定条件的有效性用加州电力市场等数据进行了仿真分析,分析了其供应量、供应价格、用户需求量和需求价格对形成稳定、合理的电力市场经济机制的影响。
The worldwide reform of power industry market-oriented makes the birth of a large number of new issues in various fields, such as the power system planning, operation, dispatching, management, security stability analysis and control. So electri- city market needs new theories and methods to guide it. The stability of electricity market does not only embody physical stability such as the power angle stability, voltage stability and frequency stability of the system, but it also needs to consider the stability of economic system related with the electricity market. Because the economic stability of electricity market and the physical stability of the power system are lined and affect each other, the study on the stability of electricity market has become a very challenging task.
Combining the characteristics of the electricity market, this paper deeply studies some issues related to electricity market stability by the stability theory, control theory and economics research ideas and methods.This paper includes the following content.
The electricity market is the process that the seller and the buyer affect each other to determine power prices and demand. This paper studies time series, including the power prices and the power demand and so on. Based on this, the separated modeling method of Gompertz model is put forward, and Lyapunov index forecasting method is improved. The reasonableness of separation of mergence for the time series is proved and the forecast accuracy is improved. Paper also gives examples to verify the validity of these in theory.
The paper uses the principle of economic to analysis the dynamic balance of the electricity, establishes a number of actions described and differential-difference model in electricity market. In the assumption that market demand is the linear equation (or non-linear equation) with variable coefficient of forecast price and market supply is the linear equation (or non-linear equation) with varied coefficient of spot price, paper analysis time series of the power price and the power demand. And paper establishes autonomous and non-autonomous continuous or discrete linear periodic mathematic models to describe actions of electricity market.
Combining models have been established to describe the behavior of the electri- city market; the paper studies the Lyapunov stability and practical stability of the autonomous and non-autonomous continuous or discrete linear periodic system by tools, for example, the appropriate structure Lyapunov functions, comparison, the calculus inequality, the matrix measures. The paper obtains series of stable critical conditions and estimated formula of ultimate convergence boundary .At last it gives continuation of discrete system conditions and the relations between coefficients of continuous and discrete systems.
Theories and methods of the practical stability are first time used for the studying of the electricity market stability. Paper studies the practical stability of electricity market models by tools, for example, the appropriate structure Lyapunov functions, Cauchy matrix, the matrix measure, constant variation. Judging practical stability sufficient conditions and estimating formula of ultimate convergence boundary are provided. Conditions are descriptive by coefficients of models. At the same time, paper studies the Lyapunov stability of the electricity market. As well as the sufficient conditions of judging electricity market Lyapunov stability are provided. Some of conclusions improved the results of Alvarado and others. The conclusion of Lyapunov stability has made a comparative with practical results. Finally, in order to prove the effectiveness of conditions of the models stability, paper uses Matlab and Maple mathematical softwares to analysis the date of California power market. And paper analysis the affection of power supply, supply prices, user demand and demand price make stability and reasonable electricity market economy mechanism.
引文
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