基于分岔理论的电力系统电压稳定性研究
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摘要
随着我国电网“西电东送,南北互供,全国联网”战略的实施和电力市场化改革的进行,电力系统的结构和运行方式日趋复杂,运行条件的不确定性大大增加,系统的运行点比以往更加接近其稳定极限,从而更加容易诱发电压崩溃事故。电压失稳已经被广泛认为是威胁现代大型电力系统安全稳定运行的主要原因之一。因此,电压稳定性研究受到广泛关注。
电力系统是一个大型的、复杂的非线性动态系统,分岔理论是研究非线性动态系统结构稳定性的有力工具。分岔理论在工程中已经得到广泛应用,在许多研究领域已取得了大量的成果,但在电力系统电压稳定性研究方面仍处于初始阶段。本文利用分岔理论对电力系统电压稳定的若干关键问题进行研究,并取得一些具有推广意义的技术成果。
作者研究工作的主要成果概括如下:
1、基于电力系统的微分代数模型、利用奇异诱导分岔的相关理论,提出一种奇异诱导分岔点的追踪和识别算法,它能在已知某一参数下的奇异点和对应非零失配量的前提下,通过只改变发电机节点注入功率,而保持负荷节点注入功率不变,快速、准确地追踪到在另一参数下的奇异诱导分岔点。其中,由于牛顿-拉夫逊法和牛顿-拉夫逊-塞德尔法的结合使用,使得该算法不存在初值困难,同时确保在分岔点附近不出现雅可比矩阵病态现象。
2、提出一种电力系统电压失稳静态分岔自适应分析方法,解决了统一考虑极限诱导分岔点和鞍结分岔点的追踪问题,并能够精确计及设备稳定极限。其中,微分代数模型的建立,克服了以往电压稳定静态分析不考虑元件动态属性的弱点;消除了关于平衡节点、PV节点等与实际电力系统不相符的假设。在充分考虑平衡解流形曲率的情况下,以自适应步长控制指导鞍结分岔点的追踪,以极限点指导极限诱导分岔点的追踪;在不增加计算量的前提下,给出极限诱导分岔的实用判别方法。
3、在考虑发电机无功出力极限的条件下,基于分岔理论和数值计算方法,通过定义最大负荷点、分岔子类型、子类型切换及子曲面等概念,分析电压稳定域的组成,提出一种研究电压稳定传输极限曲面光滑性的方法,并讨论了算法加速收敛策略。研究结果表明:仅考虑单个约束条件,或者考虑两个约束条件且没有并列切换时,传输极限曲面是光滑的;考虑两个约束条件且有并列切换,或者考虑两个以上的约束条件时,传输极限曲面是非光滑的。传输极限曲面的光滑属性,对于与电压稳定相关的预防控制和稳定性指标的计算是非常有用的。
4、基于分岔理论,研究了有载调压变压器对电压稳定性的影响。提出一种利用优化有载调压变压器分接头有效增大系统的负荷裕度,从而提高电压稳定性、预防电压失稳的方法。研究结果表明,该方法的调整效果与负荷所采用的模型密切相关,对电压敏感型负荷,在电压较高的情况下,调整分接头才能改善电压稳定性;通过调整有载调压变压器分接头来增加负荷裕度的程度是有限的,只能适应于较小规模的扰动,对于较严重的扰动,要综合应用各种预防控制措施,比如将发电再调度、电容器投切与有载调压变压器分接头调整结合起来使用。
综上所述,本文以分岔理论为基础,对电力系统电压稳定性中平衡解流形的追踪、分岔失稳点的求取和识别、电压稳定传输极限曲面的光滑性、多级电网有载调压变压器分接头的协调控制等问题进行了较为深入的研究,并取得了一定的成果,在文章的最后还指出了有待于进一步研究的问题。
With the implementation of the stratagem of "power transmission from west China to east China, interchange from North China to South China, Nation-wide interconnection" and power market, the complexity of the power network structure and operation have been enhanced increasingly, the uncertainty of operating conditions is increased greatly, the operation point of power system is pushed closer and closer to its stability limits, the voltage collapse occurs more easily than ever. Voltage instability is widely recognized as one of significant reasons treating the security and stability operation of power system. Therefore, Great concerns over voltage stability have been growing.
Power system is a large, complicated nonlinear dynamic system. It has been proved that bifurcation theory is one of effective tools for studying the structure stability of nonlinear dynamic system. Bifurcation theory has been widely applied in many engineering fields, and a great of results have been obtained, however it has in the initial stage for the application of voltage stability in power system. Based on the bifurcation theory and numerical methods, several critical topics on the voltage stability of power system are studied in the thesis, and some significative results are obtained. Main research works and contributions are summarized as follows.
1、Based on the differential algebraic equations(DAEs) of power system, an effective algorithm is presented for locating and identifying the singularity induced bifurcation (SIB) points by using the SIB theorem, the method indicates that when the singularity point under a given parameter value has been searched and the corresponding mismatch is calculated, in that case the singularity induced bifurcation point under another parameter value can be accurately traced through only changing the input powers at the generator buses but the input powers at load buses keep unchanging. Due to the combination of the Newton-Raphson(NR) method and the Newton-Raphson-Seydel(NRS) method, there is no the initial value problem, and the ill phenomena of the Jacobian matrix in the vicinity of a bifurcation point can be avoided.
2、Based on the bifurcation theory, a systematic and adaptive method for tracing the static bifurcation points of the DAEs is presented in the analysis of power system voltage stability. The two main types of static bifurcations, a common saddle node bifurcation(SNB) and a new type of bifurcation --limit induced bifurcation(LIB), are studied simultaneously and all kinds of device limits are considered. Compared with the existing static analysis methods of voltage stability, the proposed method takes account into the dynamics of devices by using the DAEs model in voltage stability, and overcomes the unreasonable assumptions for practical power system such as equilibrium bus, pv bus and so on. The step size control considers the curvature of equilibrium manifold, the SNB point is traced in terms of the adaptive stratagem of the step size control. The LIB point is traced in terms of the location of device limit points, an additional calculation is unnecessary. The recognition criterion of LIB in the practical engineering application is given.
3、The reactive power limit of a generator is thought as constrain, based on the bifurcation theory and numerical methods, by the definitions of a series of correlative concepts such as maximum loading point, bifurcation subtype, transition of bifurcation subtype, and subsurface and so on, the voltage stability region of power system is analyzed, a new methodology for investigating the smoothness of the transfer limit surface of voltage stability is presented by characterizing the state of a generator using a maximum loading point, and the accelerate stratagem of algorithm convergence is also discussed. The transfer limit surface is smooth without constraint, with single constraint and two constrains without a duplicate-switching. The transfer limit surface is nonsmooth when two constraints with a duplicate-switching or more constrains are considered. The smoothness of the transfer limit surface is very useful for calculations of preventive controls and stability indices related to voltage stability.
4、Based on the bifurcation theory, on the bases of the analysis of On-load tap changer on the effect of voltage stability, a new method for improving voltage stability and preventing voltage instability is presented by optimizing the modification of the On-load tap changers, the proposed method increase also the loadability. The study has shown that the modification effect of the proposed method is closely related to the model of load. In high voltage circumstances, the voltage stability can be improved by adjusting taps for the voltage-sensitive load. The loadability increase obtained using tap optimization is relatively small in this case. Thus, it appears that tap modification by itself should be used only for minor security limit violations. For more serious security problem, tap adjustment could be combined with other preventive control measurements such as capacitor Switching, generation rescheduling, and so on.
To sum up, based on the bifurcation theory, a series of topics on the voltage stability of power system such as tracing of the equilibrium manifold, locating and identifying of bifurcation points, smoothness of transfer limit surface of voltage stability, optimizing modification of On-load tap changers, and so on are studied thoroughly, and many results are obtained.
At the end of this dissertation, a systematical summary and future study are given
电力系统是一个大型的、复杂的非线性动态系统,分岔理论是研究非线性动态系统结构稳定性的有力工具。分岔理论在工程中已经得到广泛应用,在许多研究领域已取得了大量的成果,但在电力系统电压稳定性研究方面仍处于初始阶段。本文利用分岔理论对电力系统电压稳定的若干关键问题进行研究,并取得一些具有推广意义的技术成果。
作者研究工作的主要成果概括如下:
1、基于电力系统的微分代数模型、利用奇异诱导分岔的相关理论,提出一种奇异诱导分岔点的追踪和识别算法,它能在已知某一参数下的奇异点和对应非零失配量的前提下,通过只改变发电机节点注入功率,而保持负荷节点注入功率不变,快速、准确地追踪到在另一参数下的奇异诱导分岔点。其中,由于牛顿-拉夫逊法和牛顿-拉夫逊-塞德尔法的结合使用,使得该算法不存在初值困难,同时确保在分岔点附近不出现雅可比矩阵病态现象。
2、提出一种电力系统电压失稳静态分岔自适应分析方法,解决了统一考虑极限诱导分岔点和鞍结分岔点的追踪问题,并能够精确计及设备稳定极限。其中,微分代数模型的建立,克服了以往电压稳定静态分析不考虑元件动态属性的弱点;消除了关于平衡节点、PV节点等与实际电力系统不相符的假设。在充分考虑平衡解流形曲率的情况下,以自适应步长控制指导鞍结分岔点的追踪,以极限点指导极限诱导分岔点的追踪;在不增加计算量的前提下,给出极限诱导分岔的实用判别方法。
3、在考虑发电机无功出力极限的条件下,基于分岔理论和数值计算方法,通过定义最大负荷点、分岔子类型、子类型切换及子曲面等概念,分析电压稳定域的组成,提出一种研究电压稳定传输极限曲面光滑性的方法,并讨论了算法加速收敛策略。研究结果表明:仅考虑单个约束条件,或者考虑两个约束条件且没有并列切换时,传输极限曲面是光滑的;考虑两个约束条件且有并列切换,或者考虑两个以上的约束条件时,传输极限曲面是非光滑的。传输极限曲面的光滑属性,对于与电压稳定相关的预防控制和稳定性指标的计算是非常有用的。
4、基于分岔理论,研究了有载调压变压器对电压稳定性的影响。提出一种利用优化有载调压变压器分接头有效增大系统的负荷裕度,从而提高电压稳定性、预防电压失稳的方法。研究结果表明,该方法的调整效果与负荷所采用的模型密切相关,对电压敏感型负荷,在电压较高的情况下,调整分接头才能改善电压稳定性;通过调整有载调压变压器分接头来增加负荷裕度的程度是有限的,只能适应于较小规模的扰动,对于较严重的扰动,要综合应用各种预防控制措施,比如将发电再调度、电容器投切与有载调压变压器分接头调整结合起来使用。
综上所述,本文以分岔理论为基础,对电力系统电压稳定性中平衡解流形的追踪、分岔失稳点的求取和识别、电压稳定传输极限曲面的光滑性、多级电网有载调压变压器分接头的协调控制等问题进行了较为深入的研究,并取得了一定的成果,在文章的最后还指出了有待于进一步研究的问题。
With the implementation of the stratagem of "power transmission from west China to east China, interchange from North China to South China, Nation-wide interconnection" and power market, the complexity of the power network structure and operation have been enhanced increasingly, the uncertainty of operating conditions is increased greatly, the operation point of power system is pushed closer and closer to its stability limits, the voltage collapse occurs more easily than ever. Voltage instability is widely recognized as one of significant reasons treating the security and stability operation of power system. Therefore, Great concerns over voltage stability have been growing.
Power system is a large, complicated nonlinear dynamic system. It has been proved that bifurcation theory is one of effective tools for studying the structure stability of nonlinear dynamic system. Bifurcation theory has been widely applied in many engineering fields, and a great of results have been obtained, however it has in the initial stage for the application of voltage stability in power system. Based on the bifurcation theory and numerical methods, several critical topics on the voltage stability of power system are studied in the thesis, and some significative results are obtained. Main research works and contributions are summarized as follows.
1、Based on the differential algebraic equations(DAEs) of power system, an effective algorithm is presented for locating and identifying the singularity induced bifurcation (SIB) points by using the SIB theorem, the method indicates that when the singularity point under a given parameter value has been searched and the corresponding mismatch is calculated, in that case the singularity induced bifurcation point under another parameter value can be accurately traced through only changing the input powers at the generator buses but the input powers at load buses keep unchanging. Due to the combination of the Newton-Raphson(NR) method and the Newton-Raphson-Seydel(NRS) method, there is no the initial value problem, and the ill phenomena of the Jacobian matrix in the vicinity of a bifurcation point can be avoided.
2、Based on the bifurcation theory, a systematic and adaptive method for tracing the static bifurcation points of the DAEs is presented in the analysis of power system voltage stability. The two main types of static bifurcations, a common saddle node bifurcation(SNB) and a new type of bifurcation --limit induced bifurcation(LIB), are studied simultaneously and all kinds of device limits are considered. Compared with the existing static analysis methods of voltage stability, the proposed method takes account into the dynamics of devices by using the DAEs model in voltage stability, and overcomes the unreasonable assumptions for practical power system such as equilibrium bus, pv bus and so on. The step size control considers the curvature of equilibrium manifold, the SNB point is traced in terms of the adaptive stratagem of the step size control. The LIB point is traced in terms of the location of device limit points, an additional calculation is unnecessary. The recognition criterion of LIB in the practical engineering application is given.
3、The reactive power limit of a generator is thought as constrain, based on the bifurcation theory and numerical methods, by the definitions of a series of correlative concepts such as maximum loading point, bifurcation subtype, transition of bifurcation subtype, and subsurface and so on, the voltage stability region of power system is analyzed, a new methodology for investigating the smoothness of the transfer limit surface of voltage stability is presented by characterizing the state of a generator using a maximum loading point, and the accelerate stratagem of algorithm convergence is also discussed. The transfer limit surface is smooth without constraint, with single constraint and two constrains without a duplicate-switching. The transfer limit surface is nonsmooth when two constraints with a duplicate-switching or more constrains are considered. The smoothness of the transfer limit surface is very useful for calculations of preventive controls and stability indices related to voltage stability.
4、Based on the bifurcation theory, on the bases of the analysis of On-load tap changer on the effect of voltage stability, a new method for improving voltage stability and preventing voltage instability is presented by optimizing the modification of the On-load tap changers, the proposed method increase also the loadability. The study has shown that the modification effect of the proposed method is closely related to the model of load. In high voltage circumstances, the voltage stability can be improved by adjusting taps for the voltage-sensitive load. The loadability increase obtained using tap optimization is relatively small in this case. Thus, it appears that tap modification by itself should be used only for minor security limit violations. For more serious security problem, tap adjustment could be combined with other preventive control measurements such as capacitor Switching, generation rescheduling, and so on.
To sum up, based on the bifurcation theory, a series of topics on the voltage stability of power system such as tracing of the equilibrium manifold, locating and identifying of bifurcation points, smoothness of transfer limit surface of voltage stability, optimizing modification of On-load tap changers, and so on are studied thoroughly, and many results are obtained.
At the end of this dissertation, a systematical summary and future study are given
引文
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