Hamilton能量函数方法研究及其在电力系统稳定控制中的应用
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摘要
电力系统是典型的高维非线性动态系统，目前尚不能完全了解其复杂动力学行为的各种特性，特别是电力系统稳定性已成为关系国计民生的重要研究课题之一。随着我国特高压战略的逐步推进，互联电网的规模愈加庞大，发生系统稳定性破坏事故的影响将难以估计。而近十年来北美、巴西、印度等地频频发生的大停电事故时刻为我们敲响警钟。基于能量函数法的暂态稳定性分析是非线性理论在电力系统中较为成功的应用之一，由于能够定量地给出系统的稳定程度并避免了复杂的数值积分，这种方法尤其适用于在线稳定评估，它与时域仿真法相辅相成共同构成了电力系统稳定分析的有效手段。
电力系统稳定分析的最终目的在于系统镇定控制，进而提高电网的稳定性。现有的能量函数法多适用于较为简单的模型，在模型精度、理论深度和系统稳定控制器设计等方面仍需不断完善和发展，而Hamilton系统理论方法为其提供了有力的数学分析工具。本文基于广义受控Hamilton系统理论探讨计及转移电导和发电机励磁及FACTS装置的电力系统稳定控制和各控制器间的协调控制问题；并利用自治Hamilton系统周期解理论分析电力系统低频振荡现象，通过引入交直流互联系统的能量函数研究抑制低频振荡的直流附加阻尼控制器的设计方法，进而研究HVDC与TCSC的协调控制问题。本论文的主要研究内容和结果总结如下。
在广义Hamilton系统理论框架内提出了一种具有更为一般形式的伪广义Hamilton系统结构，在Hamilton能量函数基础上通过构造系统局部Lyapunov函数成功设计了可使系统渐近稳定的控制器，并引入无源性理论，提出一种保证系统具有L2干扰抑制特性的鲁棒控制策略，给出了若干定理、条件和判据。在上述理论基础上，将所提出的系统框架和控制器设计方法应用于含转移电导和发电机励磁的多机系统简化网络模型，基于“能量平衡+阻尼注入”的思想提出一种发电机励磁控制器设计方法，所提出的控制策略理论依据清晰，具有明确的物理含义；进而将含不确定扰动因素的电力系统模型表示成伪广义Hamilton系统形式，给出一种满足L2性能准则的发电机励磁鲁棒控制策略；最后用数值仿真分别验证了所提出的两种控制器设计方法的正确性和有效性。
利用广义Hamilton系统的内在结构特性实现电力系统发电机励磁和TCSC、SVC等FACTS装置的协调控制。首先针对孤立大型发电厂往远方负荷中心送电且输电线加装TCSC的应用场景，通过引入系统等效电纳的虚拟控制输入，在单机无穷大系统基础上完成了系统广义耗散Hamilton实现，以系统暂态能量下降为控制目标给出了保证系统渐近稳定的反馈控策略，利用系统的内在结构特性直接实现了发电机励磁和TCSC间的协调控制，对某典型工程示例进行数值仿真，结果验证了本文所提出控制方法的有效性；进而考虑含SVC和发电机励磁的简化网络模型，将SVC的动态过程包含在时变的系统导纳阵中，给出了多机系统伪广义耗散Hamilton实现，构造系统的局部Lyapunov函数并利用L2增益干扰抑制方法设计了发电机励磁和SVC的鲁棒协调控制器，并将控制策略表示为可量测的形式，最后用3机9节点系统算例仿真验证本文所提出协调控制策略的正确性和有效性。
将Hamilton系统理论应用到电力系统低频振荡分析和抑制这一领域。首先以单机无穷大系统作为研究对象，通过构造系统Hamilton能量函数给出自治Hamilton系统模型，利用Hamilton系统周期解理论分析简单电力系统的低频振荡频率特性，为从非线性系统角度解释低频振荡机理提供了新的思路；进而研究交直流互联电网的低频振荡抑制问题，基于惯性中心等值法建立了区域互联电网的等值系统模型，通过定义具有系统振荡能量概念的Hamilton函数给出了系统的广义Hamilton实现，从降低系统振荡能量角度出发给出HVDC附加阻尼控制器设计方法，利用HVDC的快速功率调制能力快速平息系统振荡；最后研究交直流互联电网在并列交流线路中装设TCSC的情形，给出含TCSC模型的交直流系统Hamilton实现，利用系统的内在结构性质给出HVDC和TCSC的协调控制策略，从而有效提高交直流互联电网抑制区间低频振荡的能力。
Power system is a typical high-dimensional nonlinear dynamic system. The variouscharacteristics of the complex dynamical behavior therein have not been fully grasped.The stability of the power system has been one of the essential research topics for a longtime. With the implementation of the Ultra-High Voltage planning in China, the scale ofthe interconnected grid becomes increasingly large, therefore it is unbearable when theinstability accident occurred in power system. However, the frequent blackouts in NorthAmerica, Brazil, India and other places over the past decade always remind us to pay moreattention on power system stability problems. The transient stability analysis based onenergy function method is a successful application of the nonlinear theory in powersystem, which is able to quantitatively evaluate the stability and is particularly suitable forfast online stability assessment. Along with the time-domain simulation method, these twomethods are powerful tools for power system stability analysis.
The ultimate purpose of stability analysis of power system is stabilization control. Thecurrently available energy function methods are mostly based on simple models. It needsto be further studied on the accuracy of the model, the theoretical depth and the stabilitycontroller design with the Hamilton system theory which can provide as a powerfulmathematical tool. Based on generalized controlled Hamiltonian system theory, thestabilization control and coordinated control of the generator excitation and FACTSdevices in power system considering transfer conductance are investigated in this thesis.Then the periodic solution theory of autonomous Hamilton system is used for theoreticalanalysis of the low frequency oscillation phenomenon in power system. The energyfunction of the AC/DC interconnected power system is used to design the HVDCsupplementary damping controllers that can help to suppress low-frequency oscillation.And then the coordination between HVDC and TCSC damping controllers is studied. Themain research contents and results are summarized as following.
Based on the generalized Hamilton system theory, a new system structure with more general form, named pseudo-generalized Hamiltonian system, is proposed. The localLyapunov function of the newly presented system is constructed based on Hamiltonenergy function and the stabilization controller is proposed for asymptotically stability atthe equilibrium point. Then the passivity theory is introduced for designing the robustcontroller with L2disturbance attenuation characteristics. Some theorem, conditions andcriterion for the new system structure are illustrated. The system framework and thecontroller design method are applied to the simplified network model of multi-machinepower system with transfer conductance and generator excitations. A generator excitationcontroller based on energy balance and damping injection is proposed, which has a clearphysical meaning. Then the actual power system considering uncertainties is expressed asthe pseudo-generalized Hamilton system and a robust excitation controller with L2disturbance attenuation criteria is proposed. Numerical experiments verify the correctnessand validity of the two proposed controller design methods.
The intrinsic structural characteristics of the generalized Hamiltonian system are usedfor coordinated control of power system generator excitation and FACTS devices. Firstly,for the particular scene of long distance power transmission from isolated large powerplants to load center, TCSC can be installed in transmission lines to strength systemstability. By introducing the virtual control input of the equivalent susceptance, the singlemachine infinite bus system is presented into generalized dissipation Hamilton system.The direct feedback control strategy is presented, aiming to reduce the transient energyand make the system asymptotically stable. The coordination between the excitation andTCSC is directly realized with the internal structure. A typical engineering examplesimulation shows the control strategy is effective. Secondly, based on the simplifiednetwork model of multi-machine power system with SVCs, the pseudo generalizeddissipation Hamilton realization is achieved with the dynamics of SVCs being consideredin time-varying system admittance matrix. The Lyapunov function of the system isconstructed and the robust coordinated control of excitation and SVC is designed via L2disturbance attenuation method. The strategy can be approximately expressed as ameasurable form. A numerical example illustrates the correctness and effectiveness of thecontrol design method.
The analysis and control of the low-frequency oscillation in power system are studiedvia Hamilton theory. Firstly, based on the lossless single machine infinite bus powersystem model and a two interconnected power system equivalent model, the autonomousHamiltonian system is realized by constructing Hamiltonian energy function. The periodicsolution theory of autonomous Hamilton system is illustrated and used in analyzing powersystem low frequency oscillation properties. Then, the low-frequency oscillation ofAC-DC interconnected power grid is discussed. Based on the two machine equivalentmodel with inertia center equivalence method, the generalized Hamilton system is realizedby defining the oscillation Hamilton function with the oscillation energy concept. Acontrol strategy aiming to reduce system oscillation energy is proposed which takesadvantage of the HVDC fast power modulation capability to damp low frequencyoscillation. Lastly, the Hamiltonian energy function considering the deviation potentialenergy of TCSC installed in the parallel AC line is constructed. The coordination ofHVDC and TCSC supplementary damping controllers, both for reducing the oscillationenergy of the system, are designed using the internal structure properties to strength theability for damping low-frequency oscillations.
电力系统稳定分析的最终目的在于系统镇定控制，进而提高电网的稳定性。现有的能量函数法多适用于较为简单的模型，在模型精度、理论深度和系统稳定控制器设计等方面仍需不断完善和发展，而Hamilton系统理论方法为其提供了有力的数学分析工具。本文基于广义受控Hamilton系统理论探讨计及转移电导和发电机励磁及FACTS装置的电力系统稳定控制和各控制器间的协调控制问题；并利用自治Hamilton系统周期解理论分析电力系统低频振荡现象，通过引入交直流互联系统的能量函数研究抑制低频振荡的直流附加阻尼控制器的设计方法，进而研究HVDC与TCSC的协调控制问题。本论文的主要研究内容和结果总结如下。
在广义Hamilton系统理论框架内提出了一种具有更为一般形式的伪广义Hamilton系统结构，在Hamilton能量函数基础上通过构造系统局部Lyapunov函数成功设计了可使系统渐近稳定的控制器，并引入无源性理论，提出一种保证系统具有L2干扰抑制特性的鲁棒控制策略，给出了若干定理、条件和判据。在上述理论基础上，将所提出的系统框架和控制器设计方法应用于含转移电导和发电机励磁的多机系统简化网络模型，基于“能量平衡+阻尼注入”的思想提出一种发电机励磁控制器设计方法，所提出的控制策略理论依据清晰，具有明确的物理含义；进而将含不确定扰动因素的电力系统模型表示成伪广义Hamilton系统形式，给出一种满足L2性能准则的发电机励磁鲁棒控制策略；最后用数值仿真分别验证了所提出的两种控制器设计方法的正确性和有效性。
利用广义Hamilton系统的内在结构特性实现电力系统发电机励磁和TCSC、SVC等FACTS装置的协调控制。首先针对孤立大型发电厂往远方负荷中心送电且输电线加装TCSC的应用场景，通过引入系统等效电纳的虚拟控制输入，在单机无穷大系统基础上完成了系统广义耗散Hamilton实现，以系统暂态能量下降为控制目标给出了保证系统渐近稳定的反馈控策略，利用系统的内在结构特性直接实现了发电机励磁和TCSC间的协调控制，对某典型工程示例进行数值仿真，结果验证了本文所提出控制方法的有效性；进而考虑含SVC和发电机励磁的简化网络模型，将SVC的动态过程包含在时变的系统导纳阵中，给出了多机系统伪广义耗散Hamilton实现，构造系统的局部Lyapunov函数并利用L2增益干扰抑制方法设计了发电机励磁和SVC的鲁棒协调控制器，并将控制策略表示为可量测的形式，最后用3机9节点系统算例仿真验证本文所提出协调控制策略的正确性和有效性。
将Hamilton系统理论应用到电力系统低频振荡分析和抑制这一领域。首先以单机无穷大系统作为研究对象，通过构造系统Hamilton能量函数给出自治Hamilton系统模型，利用Hamilton系统周期解理论分析简单电力系统的低频振荡频率特性，为从非线性系统角度解释低频振荡机理提供了新的思路；进而研究交直流互联电网的低频振荡抑制问题，基于惯性中心等值法建立了区域互联电网的等值系统模型，通过定义具有系统振荡能量概念的Hamilton函数给出了系统的广义Hamilton实现，从降低系统振荡能量角度出发给出HVDC附加阻尼控制器设计方法，利用HVDC的快速功率调制能力快速平息系统振荡；最后研究交直流互联电网在并列交流线路中装设TCSC的情形，给出含TCSC模型的交直流系统Hamilton实现，利用系统的内在结构性质给出HVDC和TCSC的协调控制策略，从而有效提高交直流互联电网抑制区间低频振荡的能力。
Power system is a typical high-dimensional nonlinear dynamic system. The variouscharacteristics of the complex dynamical behavior therein have not been fully grasped.The stability of the power system has been one of the essential research topics for a longtime. With the implementation of the Ultra-High Voltage planning in China, the scale ofthe interconnected grid becomes increasingly large, therefore it is unbearable when theinstability accident occurred in power system. However, the frequent blackouts in NorthAmerica, Brazil, India and other places over the past decade always remind us to pay moreattention on power system stability problems. The transient stability analysis based onenergy function method is a successful application of the nonlinear theory in powersystem, which is able to quantitatively evaluate the stability and is particularly suitable forfast online stability assessment. Along with the time-domain simulation method, these twomethods are powerful tools for power system stability analysis.
The ultimate purpose of stability analysis of power system is stabilization control. Thecurrently available energy function methods are mostly based on simple models. It needsto be further studied on the accuracy of the model, the theoretical depth and the stabilitycontroller design with the Hamilton system theory which can provide as a powerfulmathematical tool. Based on generalized controlled Hamiltonian system theory, thestabilization control and coordinated control of the generator excitation and FACTSdevices in power system considering transfer conductance are investigated in this thesis.Then the periodic solution theory of autonomous Hamilton system is used for theoreticalanalysis of the low frequency oscillation phenomenon in power system. The energyfunction of the AC/DC interconnected power system is used to design the HVDCsupplementary damping controllers that can help to suppress low-frequency oscillation.And then the coordination between HVDC and TCSC damping controllers is studied. Themain research contents and results are summarized as following.
Based on the generalized Hamilton system theory, a new system structure with more general form, named pseudo-generalized Hamiltonian system, is proposed. The localLyapunov function of the newly presented system is constructed based on Hamiltonenergy function and the stabilization controller is proposed for asymptotically stability atthe equilibrium point. Then the passivity theory is introduced for designing the robustcontroller with L2disturbance attenuation characteristics. Some theorem, conditions andcriterion for the new system structure are illustrated. The system framework and thecontroller design method are applied to the simplified network model of multi-machinepower system with transfer conductance and generator excitations. A generator excitationcontroller based on energy balance and damping injection is proposed, which has a clearphysical meaning. Then the actual power system considering uncertainties is expressed asthe pseudo-generalized Hamilton system and a robust excitation controller with L2disturbance attenuation criteria is proposed. Numerical experiments verify the correctnessand validity of the two proposed controller design methods.
The intrinsic structural characteristics of the generalized Hamiltonian system are usedfor coordinated control of power system generator excitation and FACTS devices. Firstly,for the particular scene of long distance power transmission from isolated large powerplants to load center, TCSC can be installed in transmission lines to strength systemstability. By introducing the virtual control input of the equivalent susceptance, the singlemachine infinite bus system is presented into generalized dissipation Hamilton system.The direct feedback control strategy is presented, aiming to reduce the transient energyand make the system asymptotically stable. The coordination between the excitation andTCSC is directly realized with the internal structure. A typical engineering examplesimulation shows the control strategy is effective. Secondly, based on the simplifiednetwork model of multi-machine power system with SVCs, the pseudo generalizeddissipation Hamilton realization is achieved with the dynamics of SVCs being consideredin time-varying system admittance matrix. The Lyapunov function of the system isconstructed and the robust coordinated control of excitation and SVC is designed via L2disturbance attenuation method. The strategy can be approximately expressed as ameasurable form. A numerical example illustrates the correctness and effectiveness of thecontrol design method.
The analysis and control of the low-frequency oscillation in power system are studiedvia Hamilton theory. Firstly, based on the lossless single machine infinite bus powersystem model and a two interconnected power system equivalent model, the autonomousHamiltonian system is realized by constructing Hamiltonian energy function. The periodicsolution theory of autonomous Hamilton system is illustrated and used in analyzing powersystem low frequency oscillation properties. Then, the low-frequency oscillation ofAC-DC interconnected power grid is discussed. Based on the two machine equivalentmodel with inertia center equivalence method, the generalized Hamilton system is realizedby defining the oscillation Hamilton function with the oscillation energy concept. Acontrol strategy aiming to reduce system oscillation energy is proposed which takesadvantage of the HVDC fast power modulation capability to damp low frequencyoscillation. Lastly, the Hamiltonian energy function considering the deviation potentialenergy of TCSC installed in the parallel AC line is constructed. The coordination ofHVDC and TCSC supplementary damping controllers, both for reducing the oscillationenergy of the system, are designed using the internal structure properties to strength theability for damping low-frequency oscillations.
引文
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