Transient stability assessment for network topology changes:application of energy margin analytical sensitivity

Developments in direct transient stability assessment using the Transient Energy function (TEF) method have included the exit point technique to determine the controlling unstable equilibrium point (u.e.p.). In this paper, analytical sensitivity of the energy margin is coupled with the exit point based TEF method to assess system stability when there is a change in system parameters: plant generation or network configuration. The principal features of this paper include: introduction of a very fast sensitivity technique to account for network configuration changes; elimination of the assumption that the mode of disturbance of the controlling u.e.p. does not change; and correlation of the sensitivity results with time simulation through swing curves. The technique is tested on the 50-generator IEEE test system and the 161-generator Northern States Power (NSP) system     

网络结构保持下的能量裕度灵敏度分析

阐述了电力系统结构保持模型了基于灵敏度的ＢＣＵ方法,其显著特征是当运行参量变化时不依赖于主导不稳定平衡点不变的假设,用该方法可以快速有效地提供运行人员感兴趣的安全信息,运行参量变化时系统稳定裕度的灵敏度以及受一定故障支配的临界机极限输出动率等,６机２２节点系统的试验结果表明用这种方法是行之有效的。     

Critical Generation Evaluation Using Hybrid Energy Function Method

It is well known that the transient energy function (TEF) method is useful for an efficient transient stability assessment as represented by the estimation of the critical clearing time (CCT). However, there still remains an issue for practical use: most of the TEF methods adopt the classical model of a synchronous machine in which the internally generated voltage is assumed to be constant. Moreover, critical generated output can be a more practical stability index instead of the CCT used in the conventional TEF methods. In this paper, a conventional hybrid TEF method is developed in order to estimate the transient stable critical generated power by using an improved hybrid simulation. The proposed method can handle the detailed model for a synchronous machine and can estimate the critical generated power with higher accuracy. Experimental results for a large network model are given in order to verify the practicability of the proposed method.     

基于改进信号能量法估计暂态稳定极限

信号能量法是一种基于时域仿真数据来快速求取电力系统暂态稳定极限的方法。它的基础是认为在给定故障条件下，暂态电压响应的信号能量将随着功率增加而渐近增长，其渐近线对应于暂态稳定极限，从而建立信号能量与传输功率和稳定极限的解析函数关系。另外，对于不同功率水平的暂态仿真数据可以得到该水平下的暂态电压数值信号能量。应用这些数值信号能量和解析信号能量表达式即可对稳定极限做出估计。文中提出了两种新的解析信号能量表达式，即1阶近似法和3阶近似法。在新英格兰系统和四川重庆系统中的应用证实了所提出方法的正确性，并且与原方法比较，所提出的方法适应性更强，更有效。特别是1阶近似法能够保持以较高精度确定系统的暂态稳定极限。     

EEAC与直接法的机理比较(四)回顾与瞻望

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) 等3种稳定性理论在大扰动稳定性分析中的应用。作为最后一篇,综合比较了这些理论和方法,并归纳了李雅普诺夫法和暂态能量函数 (TEF) 法不适合电力系统暂态稳定性分析的本质原因。指出：严格的李雅普诺夫法可以给出偏保守的近似结果;TEF法给出的近似结果则既可能保守也可能冒进;扩展等面积准则 (EEAC) 在受扰轨迹精度的含义上保证了结果的严格性。进一步完善了EEAC的描述,为其严格的证明提出了更规范的思路,并瞻望了有关的发展。     

归一化能量函数在河南电网暂态稳定性评估中的应用

介绍了归一化暂态能量函数在河南电网暂态稳定分析中的应用，通过归一化发电机转子运动方程，将故障后电力系统的动态过程比拟为在n维欧几里得角度空间势能谷中滚动的单位质量小球，研究故障后系统归一化暂态动能极小值与故障切除时间的关系，并在此基础上提出通过能量平移评估暂态稳定能量裕度的思想，基于能量平移及故障后系统归一化暂态能量函数的守恒性，还提出了计算故障后系统吸收归一化动能能力的新方法，最后通过该归一化能量函数在河南省网暂态稳定评估中的应用，说明了该方法的有效性。     

TCSC系统暂态稳定控制的动态模拟实验研究

基暂态能量函数（TEF）方法,讨论了可控串联补偿（TCSC）装置对电力系统暂态稳定的作用,设计了相应的稳定控制策略。针对不同的故障类型,应用数值仿真和动态模拟实验进行了验证,结果均证明了该控制策略的有效性。     

基于能量函数的FCL的可控串联补偿稳定控制策略

本文将暂态能量函数(TEF)值作为系统稳定的指标,并用TEF对时间的导数来决定具有串联补偿功能的故障限流器(FCL)在暂态稳定过程中的控制策略,可有效地改善系统暂态稳定性并迅速平息后续振荡。同时,针对三相短路故障,用数字仿真对控制策略进行了验证,结果表明该控制策略是有效可靠的。     

基于能量函数的可控串联补偿稳定控制策略

将暂态能量函数（TEF）值作为系统稳定的指标，并用TEF对时间的导数来决定可控串联补偿（TCSC）装置在暂态稳定过程中的控制策略，可以有效地改善系统暂稳特性并迅速平息后续振荡。文中还了多机系统下TEF对时间的导数的一般公式，并以单机无穷大系统为例，图示说明了所设计的TCSC稳定控制策略的效果，针对三相短路故障，用数字仿真和动态模拟实验对控制策略进行了验证，结果表明该控制策略是有效可靠的。     

基于典型故障集的暂态功角稳定近似判别方法

为适应特高压电网安全风险的新特征,需要研究考虑系统暂态功角稳定的风险评估评价方法。现有电力系统暂态功角稳定性判断方法计算量很大,无法满足特高压电网风险评估的计算要求。研究了影响系统故障后暂态功角稳定的因素,基于EEAC法推导了这些因素对于系统临界稳定性的灵敏度,进而设计了在已知典型故障临界稳定信息条件下近似判断边界条件变化后近似场景下暂态功角稳定性的方法。最后设计了考虑电力系统暂态功角稳定的风险评估流程,为特高压电网风险评估提供了新的思路。     

Integration of HVDC control dynamics into transient energy functions

A common approximation used in the formulation of transient energy functions (TEFs) for ac/dc power systems involves the omission of dc control dynamics. The differential equations representing the dc system dynamics are used to track the fault-on trajectory, but not to derive the TEF. This approach leads to an error in TEF-based stability prediction. In this paper, a method is presented to derive the TEF with dc system dynamics explicitly integrated. By using this comprehensive transient energy function, the accuracy of the stability prediction in ac/dc systems is improved. In addition, because differential equations representing dc dynamics are included directly in the TEF, the calculation of the post-fault equilibrium point is done only once. This leads to a considerable reduction in CPU time. The method is validated by comparing results from 12-bus and 30-bus ac/dc test systems with those obtained from time simulation.     

电力系统暂态稳定域近似边界可信域及其扩展

电力系统稳定域边界的逼近一直是应用直接法进行电力系统暂态稳定分析的难点。该文给出一种基于可信域和暂态能量函数的边界近似方法,该方法利用特征不变流形(characteristic invariant manifolds,CIMs)确定的可信域和其边界上故障轨迹相关方向处暂态能量函数常值能量面的并集确定近似边界。采用该方法对WSCC4机11节点标准测试系统稳定域边界进行逼近,并依据近似稳定域边界估计临界清除时间。通过对采用纯多项式近似的边界及与采用纯能量函数近似边界的比较,表明该方法即排除了多项式近似边界收敛域外的不确定性,又在很大程度上克服了传统能量函数近似边界的保守性,提高了直接法分析电力系统暂态稳定的精度。     

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。     

The transient energy function method

The status of the transient energy function (TEF) method of direct analysis of transient stability of power systems is reviewed. The mathematical model is presented; an elementary theoretical basis of the method is introduced; the procedure for using the method in assessing power system transient stability is outlined; and the present condition of the technique and the available computer program is given. The outstanding issues, current development work and new applications are then summarized.     

快速计算电力系统暂态稳定极限

能量函数法是分析电力系统暂态稳定问题的一个非常有效的方法。本文首次推导了严格的单 机能量函数灵敏度分析的全套解析公式。然后,利用能量函数法中已有的假设条件,提出了一 套快速算法,使在运行能量函数法的同时,只需增加极少的计算量,便可进行灵敏度分析和快 速计算系统暂态稳定极限。     

Rescheduling of power systems constrained with transient stability limits in restructured power systems

This paper investigates various approaches to relieve the transient stability constraint in restructured power systems. The approaches adopted fall into two broad categories: those based on eliminating the constraint in the least-cost way and those based on eliminating with the least possible rescheduling. The latter group can, on the other hand, emerge in the form of a pool-protected policy in which the bilateral contracts are rescheduled to maintain the stability or in the form of a contract-protected policy in which the realizable bilateral contracts are maximized while minimizing the rescheduling in pool market. Transient energy function (TEF) method is used as a tool to calculate the sensitivity of energy margin to the variations in the magnitude of generation and load. The effectiveness of the method is illustrated by case studies on Western System Coordinating Council (WSCC) 3-machine 9-bus power system and on the 10-machine 39-bus New England test system and the results are compared. The results are also verified by time domain simulations.     

基于投影能量函数和Pin-SVM的电力系统暂态稳定评估

提出一种基于Pin-SVM的电力系统暂态稳定评估方法。首先,采用系统指标(如平均机械功率、初始加速度和系统冲击等)和投影能量函数指标(如投影角速度、投影角加速度和投影动能PKE)构建暂态稳定指标的原始特征集,通过最大相关最小冗余特征选择方法对暂态指标集进行特征压缩,寻找对电网暂态变化敏感度高的特征子集;然后,基于Pin-SVM思想将特征子集映射到高维空间,实现非线性暂态稳定评估问题的线性转换,进而引入分位数改变系统稳定类与不稳定类之间的最近点位置,将暂态稳定分类问题转换为在Pin-SVM中寻找最优分位数距离问题,以减小边界干扰样本的影响,提高电力系统暂态评估方法的评估准确率和稳定性。最后,以IEEE-39节点系统、IEEE-145节点系统和某实际算例进行仿真计算,计算结果验证了该方法的有效性和准确性。     

基于一维卷积神经网络的电力系统暂态稳定在线评估

传统电力系统暂态稳定评估基于时域仿真计算,计算复杂度高,难以在线应用。提出一种基于一维卷积神经网络的电力系统暂态稳定在线评估,可极大提升暂态稳定在线评估速度。通过马尔可夫链蒙特卡洛抽样算法进行电力系统运行状态模拟,生成大规模运行数据。通过电力系统时域仿真计算确定发电机最大功角差。将电力系统运行数据作为一维卷积神经网络的输入,发电机最大功角差作为输出,训练一维卷积神经网络。在线应用场景下,一维卷积神经网络可基于当前运行数据快速计算发电机最大功角差,实现暂态稳定性在线评估。新英格兰39节点系统验证了所提在线评估算法的可行性。     

A sensitivity-based BCU method for fast derivation of stabilitylimits in electric power systems

For a given power system with a given contingency, called the base case, if parameters (such as real power generation) in the power system change (due to some emergency, perhaps), to form what is referred to as the new case, one would like to know how these changes will affect the system stability as quickly as possible. Also, there is a growing need of a fast approach to determine the transient stability loading limits of a system and to decide how to make generation rescheduling and load shedding in order to improve the system's transient stability. In this paper, a sensitivity-based BCU method is proposed to resolve these problems. One feature that distinguishes the proposed method from the existing methods is that it does not rely on the invalid assumption that the mode of the controlling u.e.p. does not change for any new case. A counter-example to this assumption is also provided. The proposed method has been tested on a 50-generator system. A good, fast assessment of the system stability and the stability loading limits has been obtained     

含暂态能量裕度约束多故障最优潮流计算

借助暂态能量裕度对发电机有功和无功出力的解析灵敏度，将暂态能量裕度约束直接加入最优潮流模型中，建立含暂态能量裕度约束多故障最优潮流逐次线性规划模型，采用单纯形法求解，取得了较好的效果。此外，还提出了根据大步长单故障最优潮流近似计算获得的暂态能量裕度进行故障扫描方法，并寻找到同一失稳模式下影响系统稳定的关键故障，验证了满足关键故障稳定性要求的最优潮流解可以同时满足同失稳模式下的其它故障的稳定约束。新英格兰10机39节点系统的最优潮流及暂态稳定计算验证了所提方法的有效性。所有优化结果均用一个在电力系统中广泛使用的暂态稳定仿真程序进行了验证。