电力系统混沌动力学行为分析与控制研究
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摘要
混沌理论是目前非线性科学中的重要研究方面,已经渗透到诸多学科和工程领域。随着电力系统规模越来越大,其非线性特点越来越明显,在一定条件下会发生混沌运行行为,表现为无规则的机电振荡,对系统的安全稳定运行构成威胁。论文主要研究混沌理论在电力系统中的应用,具体研究目的:探索电力系统的混沌动力学行为特点、混沌诱发机理、电力系统混沌现象检测方法和消除电力系统中混沌振荡的有效措施。
论文内容主要包括以下几个部分:
(1)分析电力系统的非线性动力学行为和它的混沌运行特征。电力系统是典型的非线性动力系统,混沌是非线性动力系统中特有又特殊的一种运行状态。对非线性电力系统的混沌动力学行为分析,属于非线性动力系统分析范畴。论文在分析中,主要应用非线性动力系统相关理论和方法,具体采用了庞加莱相图法、庞加莱截面法、分岔理论、李亚普诺夫指数法和关联维数法等方法和理论,通过绘制相图、计算系统状态特征参数,来判断系统的运行行为(包括混沌现象)。在分析中,采用非线性电力系统模型作为研究对象,利用龙格-库塔积分法,进行数值计算,绘制出系统运行状态仿真图,并计算出一些反应系统状态特点的参量值。分析和仿真结果表明,非线性电力系统具有复杂的动力学行为特征,在一定条件下会产生混沌振荡。
(2)检测电力系统中的混沌现象。通过对非线性电力系统模型进行数值分析,观察其相图、时序图、相邻轨迹发散或收敛情况,定量计算系统的最大李亚普诺夫指数、关联维数和测度熵等,判断和检测系统混沌现象。在实际电力系统中,精确模型往往无法获得,只能测得某一个或某些状态量的时间序列。论文在上述分析的基础上,采用非线性时间序列分析方法,进行电力系统混沌现象检测。在此过程中,主要采用了非线性时间序列分析中的相空间重构法,其中,嵌入维和时间延迟,用以Taken定理为基础的G-P法和自相关函数法求取,试验用的数据,通过MATLAB仿真获得。仿真显示,重构的相图具有混沌的特性。分析结果表明,采用非线性时间序列分析方法,利用系统某一状态变量的测量值(即时间序列),能够检测电力系统中的混沌现象。
(3)采取控制措施消除非线性电力系统中的混沌振荡。电力系统中的混沌振荡是有害的,应该采取措施抑制和消除。控制混沌的方法有多种,优、缺点和适用条件各不相同。论文在第四章,采用微分几何方法,设计电力系统的镇定控制器和输出渐近跟踪控制器,达到消除系统混沌振荡的目的。该方法基本路线为:对系统非线性模型通过微分同胚进行坐标变换,再采用状态反馈,完成对电力系统非线性模型的精确线性化处理,之后,采用最优控制方法,设计控制器。论文在此基础上,又通过调整控制方法,设计了电力系统的输出渐近跟踪控制器。分析和仿真结果显示,基于微分几何方法设计的控制器,不仅能够消除混沌振荡,而且能够把系统控制到任意给定轨道上,控制效果明显优于传统近似线性化方法。
论文在第五章,采用滑模变结构控制方法,设计了混沌电力系统的输出渐近跟踪控制器。滑模变结构控制的主要缺点是,在滑动模态中会出现高频抖振,论文为此进行了方法上的改进,改进一:采用动态切换函数和准滑动模态相结合的控制方法设计控制器,消除抖振;改进二:在滑模变结构控制器设计中,加入模糊控制规则,并以指数趋进率代替等速趋进率,消除抖振。理论分析和数值仿真结果证明,基于以上两种方法设计的滑模变结构控制器,能够消除电力系统中的混沌振荡,使系统输出渐近跟踪预期给定信号,并且能够有效地消除滑动模态中的高频抖振,提高跟踪速度,控制效果明显优于常规滑模变结构控制器。
Chaos theory is an important aspect of non-linear research, and has infiltrated a number of disciplines and engineering fields. With the increasing scale of power systems, the nonlinear characteristics are more and more obvious, under certain conditions there will even be chaotic behavior, appears as irregular electromechanical oscillations, constituting a threat to the system. The thesis concentrates on chaos theory in power system applications. The specific purpose of the study: To explore behavior characteristics of the chaotic dynamics in the power system, to study inception mechanism of chaos, chaotic detection in power system and effective measures to elimination of chaotic oscillation in power system. The Thesis includes following sections:
(1) The thesis analyzes nonlinear dynamic behavior of power system and its operation characteristics of chaos. Power system is a typical nonlinear dynamic system; chaos is a unique and special operation in nonlinear dynamic system. Analysis of chaotic behavior for Power system is the scope of nonlinear dynamic analysis. Nonlinear dynamical systems theory and methods are used in the thesis, especially with the use of the phase diagram and the poincar section method, bifurcation theory, lyapunov exponent method and correlation dimension method. Through drawing phase diagram and calculating state characteristic parameters of the system, the running behavior (including the phenomenon of chaos) of the operating system is determined. With the use of non-linear power system model and numerical calculation based on the Runge-Kutta method, simulation figure is drawled and eigen value is calculated. Analysis and simulation results show that the power system under nonlinear model with different control parameters, shows complex dynamic behavior, even will produce chaotic oscillations under certain conditions.
(2) The thesis detects chaos in power system. Through numerical analysis of nonlinear power system model, and observing of the phase diagram, timing diagram, divergence and convergence of adjacent tracks, as well as the quantitative calculation of the maximum Lyapunov exponent, correlation dimension and the measure of entropy, the Thesis judges and detects chaotic in system. However, the actual power system, are often unable to obtain accurate models can only obtain one or some of the time series of state variables. The thesis in the above analysis, detects chaotic phenomena of power system based on nonlinear time series analysis method. In this process, mainly the non-linear time series phase space reconstruction method is deployed. Embedding dimension and delay time are determined by G-P method based on Taken theorem and auto-correlation function method. MATLAB simulation tools are used for validation and experimentation, to map out the phase diagram based on a specific state of the power system time-series. The simulation results show that reconstruction of the phase diagram is with the characteristics of chaos, and can to detect the phenomenon of chaos using non-linear time series analysis method, and measured value of state variables (i.e. time series) of power system.
(3) The thesis takes effective control measures to curb or eliminate the chaotic oscillations in the non-linear power system. Chaos oscillation in the power system is harmful and should take measures to suppress and eliminate. There have been a lot of chaos control methods, and each has its own advantages and disadvantages and different application conditions. ChapterⅣin the thesis using differential geometry method, designs nonlinear power system controllers and systems asymptotic tracking output controller to eliminate the chaotic oscillations. The basic idea of the method is: take a diffeomorphism mapping and coordinate transformation to the nonlinear model, to get exact linearization model of the power system, with the state feedback. At last, optimal control method is adopted to design the chaos controller of the power system. Asymptotic tracking output controller is designed on this basis, by adjusting the control rate. The theoretical analysis and simulation results show that, based on the differential geometry of the chaotic controller not only can eliminate the chaotic oscillation, but also be able to control the system to any given orbit, the effect was better than the traditional method of linear approximation.
ChapterⅤin the thesis designs asymptotic tracking output controller of the chaos power systems using sliding mode control method. The main drawback of sliding mode variable structure is that there will be high-frequency chattering. The thesis improved the algorithm, improvement 1: Dynamic switching function and the quasi-sliding mode control method of combining are designed to eliminate the high-frequency chattering ; improvement 2: Fuzzy control rules are introduced in the sliding mode variable structure controller design and isokinetic convergence rate is replaced by exponential convergence rate to eliminate the high-frequency chattering. The theoretical analysis and numerical simulation results show that two methods based on the above sliding mode controllers can eliminate the chaotic oscillation, make the system track with a given signal, effectively eliminate the high-frequency chattering appearing in the sliding mode, and can improve the tracking speed, control effect is better than conventional sliding mode controller.
论文内容主要包括以下几个部分:
(1)分析电力系统的非线性动力学行为和它的混沌运行特征。电力系统是典型的非线性动力系统,混沌是非线性动力系统中特有又特殊的一种运行状态。对非线性电力系统的混沌动力学行为分析,属于非线性动力系统分析范畴。论文在分析中,主要应用非线性动力系统相关理论和方法,具体采用了庞加莱相图法、庞加莱截面法、分岔理论、李亚普诺夫指数法和关联维数法等方法和理论,通过绘制相图、计算系统状态特征参数,来判断系统的运行行为(包括混沌现象)。在分析中,采用非线性电力系统模型作为研究对象,利用龙格-库塔积分法,进行数值计算,绘制出系统运行状态仿真图,并计算出一些反应系统状态特点的参量值。分析和仿真结果表明,非线性电力系统具有复杂的动力学行为特征,在一定条件下会产生混沌振荡。
(2)检测电力系统中的混沌现象。通过对非线性电力系统模型进行数值分析,观察其相图、时序图、相邻轨迹发散或收敛情况,定量计算系统的最大李亚普诺夫指数、关联维数和测度熵等,判断和检测系统混沌现象。在实际电力系统中,精确模型往往无法获得,只能测得某一个或某些状态量的时间序列。论文在上述分析的基础上,采用非线性时间序列分析方法,进行电力系统混沌现象检测。在此过程中,主要采用了非线性时间序列分析中的相空间重构法,其中,嵌入维和时间延迟,用以Taken定理为基础的G-P法和自相关函数法求取,试验用的数据,通过MATLAB仿真获得。仿真显示,重构的相图具有混沌的特性。分析结果表明,采用非线性时间序列分析方法,利用系统某一状态变量的测量值(即时间序列),能够检测电力系统中的混沌现象。
(3)采取控制措施消除非线性电力系统中的混沌振荡。电力系统中的混沌振荡是有害的,应该采取措施抑制和消除。控制混沌的方法有多种,优、缺点和适用条件各不相同。论文在第四章,采用微分几何方法,设计电力系统的镇定控制器和输出渐近跟踪控制器,达到消除系统混沌振荡的目的。该方法基本路线为:对系统非线性模型通过微分同胚进行坐标变换,再采用状态反馈,完成对电力系统非线性模型的精确线性化处理,之后,采用最优控制方法,设计控制器。论文在此基础上,又通过调整控制方法,设计了电力系统的输出渐近跟踪控制器。分析和仿真结果显示,基于微分几何方法设计的控制器,不仅能够消除混沌振荡,而且能够把系统控制到任意给定轨道上,控制效果明显优于传统近似线性化方法。
论文在第五章,采用滑模变结构控制方法,设计了混沌电力系统的输出渐近跟踪控制器。滑模变结构控制的主要缺点是,在滑动模态中会出现高频抖振,论文为此进行了方法上的改进,改进一:采用动态切换函数和准滑动模态相结合的控制方法设计控制器,消除抖振;改进二:在滑模变结构控制器设计中,加入模糊控制规则,并以指数趋进率代替等速趋进率,消除抖振。理论分析和数值仿真结果证明,基于以上两种方法设计的滑模变结构控制器,能够消除电力系统中的混沌振荡,使系统输出渐近跟踪预期给定信号,并且能够有效地消除滑动模态中的高频抖振,提高跟踪速度,控制效果明显优于常规滑模变结构控制器。
Chaos theory is an important aspect of non-linear research, and has infiltrated a number of disciplines and engineering fields. With the increasing scale of power systems, the nonlinear characteristics are more and more obvious, under certain conditions there will even be chaotic behavior, appears as irregular electromechanical oscillations, constituting a threat to the system. The thesis concentrates on chaos theory in power system applications. The specific purpose of the study: To explore behavior characteristics of the chaotic dynamics in the power system, to study inception mechanism of chaos, chaotic detection in power system and effective measures to elimination of chaotic oscillation in power system. The Thesis includes following sections:
(1) The thesis analyzes nonlinear dynamic behavior of power system and its operation characteristics of chaos. Power system is a typical nonlinear dynamic system; chaos is a unique and special operation in nonlinear dynamic system. Analysis of chaotic behavior for Power system is the scope of nonlinear dynamic analysis. Nonlinear dynamical systems theory and methods are used in the thesis, especially with the use of the phase diagram and the poincar section method, bifurcation theory, lyapunov exponent method and correlation dimension method. Through drawing phase diagram and calculating state characteristic parameters of the system, the running behavior (including the phenomenon of chaos) of the operating system is determined. With the use of non-linear power system model and numerical calculation based on the Runge-Kutta method, simulation figure is drawled and eigen value is calculated. Analysis and simulation results show that the power system under nonlinear model with different control parameters, shows complex dynamic behavior, even will produce chaotic oscillations under certain conditions.
(2) The thesis detects chaos in power system. Through numerical analysis of nonlinear power system model, and observing of the phase diagram, timing diagram, divergence and convergence of adjacent tracks, as well as the quantitative calculation of the maximum Lyapunov exponent, correlation dimension and the measure of entropy, the Thesis judges and detects chaotic in system. However, the actual power system, are often unable to obtain accurate models can only obtain one or some of the time series of state variables. The thesis in the above analysis, detects chaotic phenomena of power system based on nonlinear time series analysis method. In this process, mainly the non-linear time series phase space reconstruction method is deployed. Embedding dimension and delay time are determined by G-P method based on Taken theorem and auto-correlation function method. MATLAB simulation tools are used for validation and experimentation, to map out the phase diagram based on a specific state of the power system time-series. The simulation results show that reconstruction of the phase diagram is with the characteristics of chaos, and can to detect the phenomenon of chaos using non-linear time series analysis method, and measured value of state variables (i.e. time series) of power system.
(3) The thesis takes effective control measures to curb or eliminate the chaotic oscillations in the non-linear power system. Chaos oscillation in the power system is harmful and should take measures to suppress and eliminate. There have been a lot of chaos control methods, and each has its own advantages and disadvantages and different application conditions. ChapterⅣin the thesis using differential geometry method, designs nonlinear power system controllers and systems asymptotic tracking output controller to eliminate the chaotic oscillations. The basic idea of the method is: take a diffeomorphism mapping and coordinate transformation to the nonlinear model, to get exact linearization model of the power system, with the state feedback. At last, optimal control method is adopted to design the chaos controller of the power system. Asymptotic tracking output controller is designed on this basis, by adjusting the control rate. The theoretical analysis and simulation results show that, based on the differential geometry of the chaotic controller not only can eliminate the chaotic oscillation, but also be able to control the system to any given orbit, the effect was better than the traditional method of linear approximation.
ChapterⅤin the thesis designs asymptotic tracking output controller of the chaos power systems using sliding mode control method. The main drawback of sliding mode variable structure is that there will be high-frequency chattering. The thesis improved the algorithm, improvement 1: Dynamic switching function and the quasi-sliding mode control method of combining are designed to eliminate the high-frequency chattering ; improvement 2: Fuzzy control rules are introduced in the sliding mode variable structure controller design and isokinetic convergence rate is replaced by exponential convergence rate to eliminate the high-frequency chattering. The theoretical analysis and numerical simulation results show that two methods based on the above sliding mode controllers can eliminate the chaotic oscillation, make the system track with a given signal, effectively eliminate the high-frequency chattering appearing in the sliding mode, and can improve the tracking speed, control effect is better than conventional sliding mode controller.
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