基于广域测量系统的电力系统动态稳定分析及控制
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摘要
随着大区电网的互联和现代电力电子设备的介入,电网的规模日益扩大,电网结构日趋复杂,电力系统的动态行为也越来越复杂。离线的仿真分析和实际的电网监测结果均表明,互联后的大系统产生了严重的动态稳定问题。互联电网整体动态稳定性能的恶化使得局部扰动极易引发全网安全稳定事故,从而限制了区间和区内主要断面的送电能力。广域测量系统的出现为广域电力系统的稳定分析和控制提供了新的契机。广域测量系统可以在同一时间参考坐标下捕捉到大规模互联电力系统各地点的实时动态信息,为整个电力系统的优化控制以及紧急控制提供数据平台。
本文首先介绍了广域测量系统的概念,并从开环和闭环两个方面阐述了基于WAMS的电力系统动态稳定分析及控制的研究现状。然后从开环和闭环两个方面展开本文的研究工作。
在基于WAMS的闭环电力系统动态稳定分析及控制方面,本文主要做了如下工作:
在第二章,本文推导出了一种新的线性多时滞系统稳定判据。该判据采用辐角原理来判定线性多时滞系统的特征方程在复平面的右半平面是否有根。该判据不涉及任何符号计算,对系统阶次和时滞空间的维数不敏感,因此可以判定高阶多时滞系统的稳定性。同时,该判据是线性多时滞系统稳定的充分必要条件,可以无保守地判定高阶多时滞线性系统的稳定性。仿真结果表明,该判据可以方便简洁地判定线性多时滞系统的稳定性。
第三章讨论了线性多时滞系统的稳定时滞域的拓扑和具有随机时滞的线性多时滞系统稳定分析的关系。为了分析具有随机时滞的线性多时滞系统的稳定性,本章构建了一个函数,该函数的全局最小值为零,且与稳定时滞域边界上的点对应。该函数在定义域内连续可微,因此可以通过极小化该函数的值来确定稳定时滞域的边界。然后基于上述的拓扑分析,应用遗传算法,LM算法及填充函数法确定合适的反馈增益矩阵,使得控制器对反馈信号中随机变化的时滞不敏感.基于稳定时滞域拓扑分析的控制器设计方法克服了以往方法对系统阶次的敏感性。
第四章分析了闭环时滞电力系统受扰失稳的动态过程和基于线性化模型的控制器的鲁棒性,分析结果表明:反馈信号中的时滞使得控制器的鲁棒性变差,失稳的形式表现为电力系统的电压失稳;闭环时滞电力系统受扰后能否保持稳定取决于受扰后的初始状态是否具有ω极限集。然后在上述分析的基础上,提出了一种控制策略。该策略的本质为非线性系统的切换镇定。仿真结果表明:该控制策略可以有效解决闭环时滞电力系统中控制器的鲁棒性不足问题,且简单可靠,容易在电力系统中实现。
在第五章,基于前三章的理论分析,针对闭环电力系统的非线性、多时滞且变时滞等特点,本文设计了对异步随机变化的时滞不敏感的广域阻尼控制器。时域仿真结果表明:对于2区4机系统,当区内通讯和区间通讯分别具有不同的时滞及其随机性的情况下,所设计的控制器仍能有效阻尼区间联络线上的低频振荡。
在基于WAMS的开环电力系统动态稳定分析及控制方面,本文在第六章提出了一种利用WAMS的信息监测和控制多机电力系统的非线性振荡(Hopf分岔)的方法。该方法采用乘幂法来计算系统雅可比矩阵的最大实部共轭特征根。当前运行(平衡)点与Hopf分岔面之间的距离可以通过计算系统雅可比矩阵的最大实部共轭特征根进行在线动态监控。当系统的当前运行(平衡)点接近Hopf分岔面时,直接计算Hopf分岔面的近似法矢量,并根据该近似法矢量来调节系统的控制参数,从而达到在线控制系统分岔(发生非线性振荡)的目的。本文在IEEE-14节点的系统上通过调节系统的无功功率验证了上述方法的有效性。
Along with the application of modern power electronic equipments and the continual scale extension of the power system,the structure and the dynamic behaves of the interconnected power power system become more and more complicated.Lots of off-line simulation analysis and on-line monitoring results show that there are serious dynamical stability problem in the interconnected power grid. The deterioration of whole dynamical stable performances of the interconnected power grid makes the local disturbances evoke the collapse of the whole grid,so as that the power -transmitting capacities are limited in transmission lines between regions.The emerging of wide area measurement systems(WAMS) offers new opportunities for the monitoring and control of wide area power systems. WAMS can offer the synchronous information of the state and algebraic variables of a wide area power system in real time.Therefore,with the information from WAMS, the synchronous monitoring and the on-line dynamical process analysis and even the on-line urgent or optical control of a wide area power can be done.
This dissertation introduces the concept of WAMS firstly,and then illustrates the research status of the WAMS-based dynamical stability analysis and control of power systems,classifying into two categories:the open-loop and closed-loop dynamical stability analysis and control of power systems based on WAMS.And then the dissertation unfolds the main work from the two aspects of the open-loop and closed-loop systems,respectively.
In the aspect of WAMS-based dynamical stability analysis and control of closed-loop power systems,the following work is done in this dissertation.
In the second chapter,based on the argument principle,a method is proposed to derive delay-dependent stability criteria without any conservatism for LTI (linear time invariant) systems with multiple time delays.Because the characteristic polynomial of a LTI system with multiple time delays is analytic in the whole complex plane,the argument principle is used to judge whether the characteristic equation has roots in the right-half complex plane.With a straightforward form,the criteria can be considered as a generalized Nyquist criterion.The criteria are sufficient and necessary for the stability of the system. The method involves no symbol calculation so as that can deal easily with the systems of which the orders and time delays are more than 3.The example case study shows that the criteria can judge whether a LTI system is stable exactly,for any given time delays.
In the third chapter,the relation is discussed between the topology of stable time-delay regions and the stability analysis of a linear system with multiple time delays.In order to analyze the topology of stable time-delay regions,this dissertation constructs a function of which the value is equal to zero for the time-delay points on the boundaries of stable time-delay regions.The function is continuous and differentiable in the whole defining field with the global minimum of zero so that can be used to locate the boundaries by minimizing the value of the function.Based the above topology analysis,GA(Genetic Algorithm) and the LM(Levenberg-Marquardt) algorithm together with the Filled Function Method are used to find an appropriate feedback gain matrix that can stabilize the system using feedback signals with randomly varying time delays.As a method without any conservatism,the method based on the topology analysis is simple and reliable so that can deal with a LTI(linear time-invariant) system with high order and multiple time delays(more than 3) easily.The example case study shows that the above method can work reliably.
The fourth chapter analyzes the dynamical process of time-delayed power systems losing stability and the robustness of the controllers based on linearized models.The analyzing results show that the time delays in feedback signals deteriorate the robustness of controllers,and the instability is in the form of the voltage losing stability;and the stability of a closed-loop time delayed power system following a disturbance is determined by whether the initial state following the disturbance has aωlimit set.Based on the above analysis,a control strategy is proposed.The strategy is in essence a kind of switch stabilization of nonlinear systems.Numerical results form a tow-area four-machine power system show that the control strategy can deal with the instability caused by the weak robustness of controllers,and is simple and reliable so that can be easily implemented in power systems.
In the fifth chapter,based on the theory analysis of the 2nd～4th chapters,a controller is designed that is not sensitive to the asynchronous variations of time delays,considering closed-loop power systems as the nonlinear dynamic systems with multiple time delays and varying time delays.Numerical results form a tow-area four-machine power system demonstrate that the controller derived from the above method can damp low-frequency oscillations in the system for the feedback signals with multiple time delays and varying time delays.
In the aspect of WAMS-based dynamical stability analysis and control of closed-loop power systems,this dissertation gives a method in the sixth chapter to monitor and control Hopf bifurcations in multi-machine power systems using the information from wide area measurement systems(WAMS).Power Method (PM) is adopted to compute the pair of conjugate eigenvalues with the algebraically largest real part and the corresponding eigenvectors of the Jacobian matrix of a power system.The distance between the current equilibrium point and the Hopf bifurcation set can be monitored dynamically by computing the pair of conjugate eigenvalues.When the current equilibrium point is close to the Hopf bifurcation set,the approximate normal vector to the Hopf bifurcation set is computed and used as a direction to regulate control parameters to avoid a Hopf bifurcation in the power system described by differential algebraic equations (DAEs).The validity of the proposed method is demonstrated by regulating the reactive power loads in a 14-bus power system.
本文首先介绍了广域测量系统的概念,并从开环和闭环两个方面阐述了基于WAMS的电力系统动态稳定分析及控制的研究现状。然后从开环和闭环两个方面展开本文的研究工作。
在基于WAMS的闭环电力系统动态稳定分析及控制方面,本文主要做了如下工作:
在第二章,本文推导出了一种新的线性多时滞系统稳定判据。该判据采用辐角原理来判定线性多时滞系统的特征方程在复平面的右半平面是否有根。该判据不涉及任何符号计算,对系统阶次和时滞空间的维数不敏感,因此可以判定高阶多时滞系统的稳定性。同时,该判据是线性多时滞系统稳定的充分必要条件,可以无保守地判定高阶多时滞线性系统的稳定性。仿真结果表明,该判据可以方便简洁地判定线性多时滞系统的稳定性。
第三章讨论了线性多时滞系统的稳定时滞域的拓扑和具有随机时滞的线性多时滞系统稳定分析的关系。为了分析具有随机时滞的线性多时滞系统的稳定性,本章构建了一个函数,该函数的全局最小值为零,且与稳定时滞域边界上的点对应。该函数在定义域内连续可微,因此可以通过极小化该函数的值来确定稳定时滞域的边界。然后基于上述的拓扑分析,应用遗传算法,LM算法及填充函数法确定合适的反馈增益矩阵,使得控制器对反馈信号中随机变化的时滞不敏感.基于稳定时滞域拓扑分析的控制器设计方法克服了以往方法对系统阶次的敏感性。
第四章分析了闭环时滞电力系统受扰失稳的动态过程和基于线性化模型的控制器的鲁棒性,分析结果表明:反馈信号中的时滞使得控制器的鲁棒性变差,失稳的形式表现为电力系统的电压失稳;闭环时滞电力系统受扰后能否保持稳定取决于受扰后的初始状态是否具有ω极限集。然后在上述分析的基础上,提出了一种控制策略。该策略的本质为非线性系统的切换镇定。仿真结果表明:该控制策略可以有效解决闭环时滞电力系统中控制器的鲁棒性不足问题,且简单可靠,容易在电力系统中实现。
在第五章,基于前三章的理论分析,针对闭环电力系统的非线性、多时滞且变时滞等特点,本文设计了对异步随机变化的时滞不敏感的广域阻尼控制器。时域仿真结果表明:对于2区4机系统,当区内通讯和区间通讯分别具有不同的时滞及其随机性的情况下,所设计的控制器仍能有效阻尼区间联络线上的低频振荡。
在基于WAMS的开环电力系统动态稳定分析及控制方面,本文在第六章提出了一种利用WAMS的信息监测和控制多机电力系统的非线性振荡(Hopf分岔)的方法。该方法采用乘幂法来计算系统雅可比矩阵的最大实部共轭特征根。当前运行(平衡)点与Hopf分岔面之间的距离可以通过计算系统雅可比矩阵的最大实部共轭特征根进行在线动态监控。当系统的当前运行(平衡)点接近Hopf分岔面时,直接计算Hopf分岔面的近似法矢量,并根据该近似法矢量来调节系统的控制参数,从而达到在线控制系统分岔(发生非线性振荡)的目的。本文在IEEE-14节点的系统上通过调节系统的无功功率验证了上述方法的有效性。
Along with the application of modern power electronic equipments and the continual scale extension of the power system,the structure and the dynamic behaves of the interconnected power power system become more and more complicated.Lots of off-line simulation analysis and on-line monitoring results show that there are serious dynamical stability problem in the interconnected power grid. The deterioration of whole dynamical stable performances of the interconnected power grid makes the local disturbances evoke the collapse of the whole grid,so as that the power -transmitting capacities are limited in transmission lines between regions.The emerging of wide area measurement systems(WAMS) offers new opportunities for the monitoring and control of wide area power systems. WAMS can offer the synchronous information of the state and algebraic variables of a wide area power system in real time.Therefore,with the information from WAMS, the synchronous monitoring and the on-line dynamical process analysis and even the on-line urgent or optical control of a wide area power can be done.
This dissertation introduces the concept of WAMS firstly,and then illustrates the research status of the WAMS-based dynamical stability analysis and control of power systems,classifying into two categories:the open-loop and closed-loop dynamical stability analysis and control of power systems based on WAMS.And then the dissertation unfolds the main work from the two aspects of the open-loop and closed-loop systems,respectively.
In the aspect of WAMS-based dynamical stability analysis and control of closed-loop power systems,the following work is done in this dissertation.
In the second chapter,based on the argument principle,a method is proposed to derive delay-dependent stability criteria without any conservatism for LTI (linear time invariant) systems with multiple time delays.Because the characteristic polynomial of a LTI system with multiple time delays is analytic in the whole complex plane,the argument principle is used to judge whether the characteristic equation has roots in the right-half complex plane.With a straightforward form,the criteria can be considered as a generalized Nyquist criterion.The criteria are sufficient and necessary for the stability of the system. The method involves no symbol calculation so as that can deal easily with the systems of which the orders and time delays are more than 3.The example case study shows that the criteria can judge whether a LTI system is stable exactly,for any given time delays.
In the third chapter,the relation is discussed between the topology of stable time-delay regions and the stability analysis of a linear system with multiple time delays.In order to analyze the topology of stable time-delay regions,this dissertation constructs a function of which the value is equal to zero for the time-delay points on the boundaries of stable time-delay regions.The function is continuous and differentiable in the whole defining field with the global minimum of zero so that can be used to locate the boundaries by minimizing the value of the function.Based the above topology analysis,GA(Genetic Algorithm) and the LM(Levenberg-Marquardt) algorithm together with the Filled Function Method are used to find an appropriate feedback gain matrix that can stabilize the system using feedback signals with randomly varying time delays.As a method without any conservatism,the method based on the topology analysis is simple and reliable so that can deal with a LTI(linear time-invariant) system with high order and multiple time delays(more than 3) easily.The example case study shows that the above method can work reliably.
The fourth chapter analyzes the dynamical process of time-delayed power systems losing stability and the robustness of the controllers based on linearized models.The analyzing results show that the time delays in feedback signals deteriorate the robustness of controllers,and the instability is in the form of the voltage losing stability;and the stability of a closed-loop time delayed power system following a disturbance is determined by whether the initial state following the disturbance has aωlimit set.Based on the above analysis,a control strategy is proposed.The strategy is in essence a kind of switch stabilization of nonlinear systems.Numerical results form a tow-area four-machine power system show that the control strategy can deal with the instability caused by the weak robustness of controllers,and is simple and reliable so that can be easily implemented in power systems.
In the fifth chapter,based on the theory analysis of the 2nd～4th chapters,a controller is designed that is not sensitive to the asynchronous variations of time delays,considering closed-loop power systems as the nonlinear dynamic systems with multiple time delays and varying time delays.Numerical results form a tow-area four-machine power system demonstrate that the controller derived from the above method can damp low-frequency oscillations in the system for the feedback signals with multiple time delays and varying time delays.
In the aspect of WAMS-based dynamical stability analysis and control of closed-loop power systems,this dissertation gives a method in the sixth chapter to monitor and control Hopf bifurcations in multi-machine power systems using the information from wide area measurement systems(WAMS).Power Method (PM) is adopted to compute the pair of conjugate eigenvalues with the algebraically largest real part and the corresponding eigenvectors of the Jacobian matrix of a power system.The distance between the current equilibrium point and the Hopf bifurcation set can be monitored dynamically by computing the pair of conjugate eigenvalues.When the current equilibrium point is close to the Hopf bifurcation set,the approximate normal vector to the Hopf bifurcation set is computed and used as a direction to regulate control parameters to avoid a Hopf bifurcation in the power system described by differential algebraic equations (DAEs).The validity of the proposed method is demonstrated by regulating the reactive power loads in a 14-bus power system.
引文
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