Construction of Lyapunov function for power system based on solving linear matrix inequality

This paper presents construction of Lyapunov functions for power systems based on solving the Linear Matrix Inequality (LMI) derived from the Lyapunov stability theorem considering the dynamics of load characteristic and AVR control system. The proposed Lyapunov function is constructed as a quadratic form of state variables and an integral term which satisfies the curl equation and the sector condition. An induction machine and a synchronous machine are considered as load characteristics. One‐machine one‐load infinite bus system is considered taking into account the flux decay effects and AVR with one time constant of the generator. To verify the proposed Lyapunov function, the transient stability assessment is shown. The critical clearing times given by the proposed Lyapunov function are compared with those obtained by the numerical integration method, and they are shown to be practical. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 158(4): 42– 50, 2007; Published online in Wiley InterScience ( www.interscience. wiley.com ). DOI 10.1002/eej.20328     

A BCU method for direct analysis of power system transientstability

A boundary of stability region based controlling unstable equilibrium point method (BCU method) for direct analysis of power system transient stability is presented. Features distinguishing the BCU method from the existing direct methods are that it consistently finds the exact controlling unstable equilibrium point (UEP) relative to a fault-on trajectory and that it has a sound theoretical basis. Moreover, the BCU method appears to be fast. This method is based on the relationship between the boundary of stability region of a power system and that of a reduced system. The BCU method finds the controlling UEP of the original system via a reduced system whose controlling UEP is easier and cheaper to compute. Effective numerical schemes to speed up the presented method are also proposed. This method has been tested on several power systems with very promising results. Simulation results on a 50 generator, 145 bus system are presented along with a comparison between the results obtained using the BCU method and another existing method     

Transient stability evaluation method based on kinetic energy of postfault trajectories

It is very important to maintain supply reliability in the deregulated environment. The transient stability problem is one of the major concerns in studies of planning and operation of power systems. Time domain simulation is currently the best available tool for allowing the use of detailed models and for providing reliable results. The main limitations of this approach involve long computation times. Therefore, this paper proposes a transient stability evaluation method using minimum transient kinetic energy of postfault trajectories. This method can estimate critical clearing times with only two points of the minimum transient kinetic energy, regardless of whether the trajectories after the clearing time are stable or unstable. The validity of the proposed method is shown by simulation studies with the IEEJ EAST 10‐machine 47‐bus system. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 174(3): 18–24, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21018     

Design and Implementation of on-line dynamic security assessment

Despite possible changes in energy sources, the importance of maintaining the stability of interconnected power systems will not change. Technologies for maintaining power system stability must evolve with renewable energy technology. As renewable energy increases, analysis and control methods for transient stability assessment must be reexamined and improved. This paper presents an overview of on-line dynamic security assessment (DSA) systems and related direct methods. The controlling unstable equilibrium point (UEP) method and the boundary of the stability-region-based controlling UEP (BCU) method are briefly described in order to provide a framework of understanding the concept of a transient stability-screening program for DSA systems. The integrated package TEPCO-BCU, a very advanced practical program based on the theory of the controlling UEP method, BCU method, energy function method, and BCU-guided time-domain method, is described from the viewpoint of on-line performance. Finally, the importance of validating the assessment results of the BCU method is discussed. Copyright © 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Transient stability output margin estimation based on the energy function method

In this paper, a new method of estimating the critical generation margin (CGM) in power systems is proposed based on transient stability diagnostics. The proposed method can directly compute the stability limit output for a given fault based on the transient energy function method (TEF). Since CGM can be directly obtained by the limit output using estimated P‐θ curves and is easy to understand, it is more useful than the conventional critical clearing time (CCT) of the energy function method. The proposed method can also estimate CGM as a negative value, which means instability in the present load profile, and so a negative CGM can be directly used as a restriction on generator output. The accuracy and fast solution ability of the proposed method are verified by applying it to a simple 3‐machine model and IEEJ EAST10‐machine standard model. Furthermore, the usefulness of the method for severity ranking of transient stability for various fault cases is discussed by using CGM. 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 173(3): 10–19, 2010; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ eej.21035     

暂态功角稳定不稳定平衡点类型和临界割集数量的对应关系

电力系统暂态功角失稳模式同相关不稳定平衡点密切相关。鉴于电力系统失去暂态功角稳定时总是伴随着电力网络的某个或某些临界割集上支路角度急剧地、过大地增长,人们已经认识到电力网络中存在临界割集与系统模型中存在不稳定平衡点是等价的,并提出了用于电力系统暂态功角稳定分析的割集稳定准则。为了使人们能够放心地、正确地运用与临界割集相关的稳定准则,本文以电力系统结构保留模型为基础,从理论上推导出暂态功角稳定不稳定平衡点为i型的当且仅当事故后电力扩展网络中存在i个临界割集。利用上述结论,可以很容易地将割集稳定准则应用于多群失稳的情况,以消除原准则的保守性。     

基于稳定域边界二次近似的故障临界切除时间估计

基于故障后电力系统稳定域边界的二次近似来估计临界切除时间。在计算中,通过二次项系数矩阵分块来降维计算二次项系数,大大降低了二次项系数的计算量。临界切除时间由持续故障轨迹和主导不稳定平衡点(CUEP)所决定的稳定域边界二次近似的交点确定。在IEEE3机9节点系统和新英格兰10机39节点系统中的仿真表明了该方法的有效性,特别是对非发电机节点故障临界切除时间的估计精度较高,能够满足工程要求。     

Impact of Postfault Active Power Recovery of Photovoltaic Power Generation on Transient Stability

Currently, Japanese grid codes require photovoltaic (PV) power generation systems to continue supplying power to the grid as soon as possible even if the systems temporarily stop their operation. Although the fault ride‐through capability was originally proposed for preventing a cascading frequency drop in the power system, the capability has the impact on other instability phenomena such as transient stability. In this study, we focus on the postfault active power recovery of the PV systems. The impact of the recovery speed on the transient stability is investigated under different load conditions, in particular static/dynamic load condition. Numerical examples are carried out for the one‐machine one‐load infinite‐bus system, and the effects of the recovery speed are evaluated by equal area criterion and critical clearing time. As a result, we have found both desirable and undesirable effects on the transient stability depending on the load condition.     

EEAC与直接法的机理比较

讨论了长期困惑电力系统学术界的暂态稳定性理论和算法;归纳出10个要素,即受扰程度函数、壁垒点、观察点、参考点、积分路径与被积函数、定性判据、轨迹稳定裕度、临界轨迹与参数极限值、迭代求解与初始轨迹、搜索策略与收敛判据.由4篇短文组成的系列文章按照上述各要素,讨论了针对平衡点稳定性的李雅普诺夫法、将平衡点稳定性理论应用于有界稳定性的暂态能量函数(TEF)法以及针对有界稳定性的扩展等面积准则(EEAC)这3种稳定性理论在大扰动稳定性的分析中的应用.作为第3篇,主要讨论参考点、积分路径和被积函数、稳定裕度、极限值搜索等要素的不同处理原则,证明不但对于任何多机系统,并且对于具有非线性负荷或非自治因素的单机系统,稳定分析都离不开包括故障清除后的实际受扰轨迹;指出稳定极限值和临界轨迹之间互相依存,只能通过迭代求解.以单机无穷大系统为例,从理论观点和可计算性观点出发,论证壁垒点和参考点都应该在实际轨迹上,而暂态能量的参考点则必须取故障前的稳定平衡点,而不能取故障后的稳定平衡点.     

基于单机无穷大母线等值和轨迹灵敏度的暂态稳定约束最优潮流

在分析多故障暂态稳定约束最优潮流(transient stability constrained optimal power flow,TSCOPF)轨迹灵敏度法存在问题的基础上,提出基于单机无穷大母线等值和轨迹灵敏度的暂态稳定度约束最优潮流计算方法.根据单机无穷大母线等值,在暂态稳定约束最优潮流模型中引入严格的暂态稳定判据,并应用轨迹灵敏技术提高计算效率.将故障分为稳定故障、极度稳定故障、一般不稳定故障和极度不稳定故障,分别在暂念稳定约束中分别加以处理,可快速地进行放障筛选.同时,对于小稳定故障不需要寻找临界稳定轨迹,可节省大量的仿真时间.在3机、10机和20机系统上的仿真结果验证了所提出算法的有效性.     

基于相平面轨迹凹凸性的暂态稳定性判别方法评述

基于响应的暂态稳定判别与控制技术是目前电力系统暂态稳定分析领域的热点,该技术具有不依赖于系统模型及参数、可以实时判别和计算量小等优点。其中基于角速度-功角相平面轨迹凹凸性的暂态失稳判别是-个活跃的研究分支。本文对这种暂态稳定性判别方法的原理进行了介绍,进而对方法应用于多机系统时存在的问题进行了分析和评述,并对IEEE 39节点系统进行了仿真分析。结果表明:该方法应用于多机系统时,由于分群的不正确及聚合等值后单机系统参数的时变性易造成相平面轨迹的复杂特性,从而容易将稳定案例误判为失稳。     

Antigen energy function: a new energy function for transient stability assessment

Transient stability analysis using direct methods has gained a lot of importance in recent years. Major two approaches i.e. Liapunov's stability criterion and transient energy function (TEF) has attracted most of the researchers. Non-availability of generalized Liapunov's function and the availability of transient energy function only for low loss system has forced the researchers to test the new function, which can suit the conditions of stressed systems of modern age. In this paper, conceptual antigen energy function is proposed and its usefulness is tested over the multi-machine system. The results are quite comparable with potential energy boundary surfaces (PEBS) and controlling UEP (CU) methods. Antigen energy function gives better estimate of the critical clearing time than PEBS and CU methods, without obtaining unstable equilibrium points (UEP). The development and logical detailing of the function is discussed in this paper.     

基于临界能量灵敏度法研究FACTS的暂态稳定控制

介绍用临界能量对电力网络参数的灵敏度法研究FACTS的暂态稳 定控制。通过对灵敏度较大的线路或母线上FACTS设备参数进行控制,以提高FACTS的暂态稳 定性。对10机39母线系统的仿真结果表明,临界能量灵敏度法是提高FACTS暂态稳定性的有 效控制措施。     

基于轨迹信息的发电机暂态稳定指标分析方法

在已知各发电机相角及角速度的条件下，构造了一种δ-Ek扩展相平面。基于各相δ-Ek扩相平面的轨迹信息提出了一种发电机暂态稳定指标，并给出了相应的分析方法。特点是采用曲线拟合的方式。根据上述轨迹的曲线形状，可以快速算得发电机在故障后的暂态稳定指标。经过算例的验证，该稳定指标能够定量地描述发电机承受故障的能力，从而用来衡量故障后系统中各发电机的稳定程度。     

求解暂态稳定约束最优潮流的混合算法

借助单机无穷大母线等值建立严格稳定判据,将轨迹灵敏度和微分进化技术结合起来求解暂态稳定约束最优潮流问题。以临界稳定功角作为暂态稳定约束功角阈值,并用预测失稳时刻修正功角阈值,提高了功角阈值的准确性和优化精度。按照单机无穷大母线等值,将故障分为稳定故障、极度稳定故障、一般不稳定故障和极度不稳定故障,将极度稳定故障从暂态稳定约束中剔除,省略相应灵敏度计算。为充分发挥改进轨迹灵敏度法的快速收敛特性和微分进化算法较强的全局搜索能力,提出将两者适当结合构造求解多故障暂态稳定约束最优潮流问题的混合算法。所提微分进化种群规模和计算量大大减小;含不稳定故障规格化稳定度的评价函数值更能综合反映种子的安全经济指标。在3机和10机试验系统上验证了所提算法的高效性和实用性。     

Unified Analysis of Single Machine Equivalent and Trajectory Sensitivity to Formulate a Novel Transient Stability-constrained Optimal Power Flow Approach

Abstract—This article proposes a new transient stability constraint that permits quantifying the degree of instability of a power system from the active power dispatched by generators. Based on this constraint, which is derived from both single machine equivalent and trajectory sensitivity methods, a new transient stability-constrained optimal power flow is formulated in the Euclidian space to preventively control the transient stability in realistic power systems. The validity and the effectiveness of the proposed method are numerically demonstrated in the WSCC 3-machine, 9-bus and Mexican 46-machine, 190-bus systems.     

基于轨迹灵敏度的暂态稳定约束最优潮流计算

为将暂态稳定约束最优潮流问题转化为最优潮流和暂态稳定两个子问题,根据暂态稳定计算结果求出发电机转角及转速相对于机械输入功率的轨迹灵敏度。基于轨迹灵敏度,计算出在最领先发电机和最落后发电机之间转移的有功功率,据此修改其在最优潮流模型中的有功功率上下限,从而实现两个子问题的交替求解。并且推导出准确的轨迹灵敏度及初值计算公式,利用上述公式,得更小的转移功率值,从而使功率转移后系统的优化程度更高。同时在惯性中心坐标下采用最大转角判据找出最领先机和最落后机,并以3机9节点和10机39节点系统为例,验证了该方法的可行性。     

电力系统暂态稳定切机控制策略表的快速整定方法

提出了一种基于轨迹凹凸性理论的暂态稳定切机控制策略表整定方法,该方法能够有效提高策略表整定过程的效率,避免了大量的重复性仿真工作。针对会给系统带来重大冲击的预想故障,基于时域仿真结果,可以得到系统的暂态功角稳定性;当系统发生暂态失稳时,根据不稳定事故的仿真信息,得到控制时刻和不稳定平衡点处的功角以及控制时刻的角速度,可以计算出较准确的控制量。实际电网系统的仿真结果验证了所提整定方法的快速性。     

融合轨迹预测技术的输电线路新型自适应重合闸

输电线路故障的重合闸时刻对系统的暂态稳定有很重要的影响.针对目前最佳重合时刻难以在线确定的问题,提出融合轨迹预测技术的重合时刻在线捕捉方法.核心是利用机组功角的轨迹预测信息,确定系统振荡机组的主导模式,并按主导模式对机组进行分群,将多机系统复杂的暂态稳定性问题转化为对应的单机无穷大系统的功角稳定性分析,选其单机无穷大系...     

Transient stability simulation of wind generator expressed by two‐mass model

Recently, wind power generation is increasing worldwide. In wind power stations, induction machines are mostly used as generators. Since induction generators have a stability problem similar to the transient stability of synchronous machines, it is important to analyze the transient stability of power systems including wind generators. Although there have been some reports analyzing the transient stability problem, wind turbine and wind generator are, in most cases, modeled as a one‐mass shaft system having total inertia constant. This paper presents simulation analyses of transient stability of power system including induction generator which is expressed by a two‐mass shaft model and analyzes an effect of shaft system modeling on the transient stability characteristics. Simulations are performed by PSCAD/EMTDC in this study. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 162(3): 27–37, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20394