Application of coherency and reduced order models to transient stability studies

Study of the transient stability of a large and interconnected power system requires a great deal of computational time. To reduce that time, power system equivalents are employed. A simplified transient stability method, based on the values of the ‘stability measures’, is presented in which generators with small swing are replaced by a new equivalent model, and appropriate simplified models are used for the rest of the generators. Results of this study are used to identify coherent groups of generators. Replacing coherent sets by their equivalent generators will further reduce the size of the system. The validity and accuracy of the method is demonstrated by stimulated tests on a sample power system.     

Dynamic REI equivalents for short circuit and transient stability analyses

This paper proposes a systematic approach for dynamic power system equivalents based on power transfer distribution factors. The proposed method divides the original network into an internal interconnected system and an external one. Static equivalents are computed at frontier buses that separate the retained internal system from the external one. The equivalents are formed using REI (Radial, Equivalent and Independent) networks and generator model aggregation. Generator parameters are computed based on power transfer distribution factors of the generated active power. The equivalent models are able to accurately approximate the behavior of the original system for short circuit and transient stability analyses. Two test systems, namely the Kundur’s 2-area test system and a 1213-bus network that model a real transmission system are used to illustrate and test the proposed technique.     

Method of identifying weak transmission network stabilityboundaries

Methods of determining weak transmission stability boundaries are developed based on the strong controllability and observability properties of power systems. This theory has been previously applied to a dynamical model of the generators and network. It was established previously that the network and generator states associated with a cluster of generator and load buses surrounded by weak transmission boundaries are strongly controllable and observable for a single measurement and control at generators or load buses in that bus cluster. Such a bus cluster is called the control area. Two methods of determining control areas, where strong controllability and observability hold, are developed. Both methods attempt to determine weak transmission stability boundaries that encircle control areas. The groups of generators identified as belonging to each control area is identical to the groups of coherent generators determined using a RMS coherency measure evaluated for the set of all inertial load flow contingencies     

Development of transient stability controller system (TSC) based on on-line stability calculation

A new transient stability controller system (TSC) based on on-line transient stability calculation has been developed. The TSC system prevents the power system from wide-area blackout by shedding generators optimally when a serious fault occurs. This system consists of a central processing unit (TSC-P), and four local units for fault detection (TSC-C), and seventeen units for generator shedding (TSC-T). The TSC-P selects optimal generators to be shed for stabilization based on on-line transient stability calculation for contingencies at 500 kV lines and buses every five minutes. The results are transmitted to the TSC-Cs periodically. Should any fault occur, only one TSC-C will detect the fault occurrence and send control signals to the TSC-Ts which actually generate shedding signals. To realize the TSC system, essential are fast stability evaluation methods for a large number of contingencies and effective selection methods of optimal generators to be shed for stabilization. This paper presents total algorithms applied in the TSC-P, the results of algorithm verification tests using a prototype system combined with a large-scale analog simulator, and the characteristics of the actual system.     

暂态稳定断面功率极限区间和关联度指标计算

针对日益复杂的运行情况和系统对安全经济运行的要求,提出了暂态稳定断面功率极限区间和关联度指标计算方法。基于暂态安全稳定量化分析方法获得的预想故障下安全稳定裕度、模式和元件的参与因子,结合功率对输电断面功率的灵敏度计算发电机和负荷对断面功率极限的影响因子,通过发电机、负荷功率调整计算出功率极限的最大值和最小值。基于安全稳定裕度筛选得到输电断面关键故障,采用裕度为权重的加权平均计算发电机和监视母线的综合参与因子,通过发电机和母线参与因子的相关性分析计算两个输电断面的关联度指标。所提出的方法能够为调度运行人员快速掌握当前运行方式下各个输电断面的暂态安全稳定水平,以及彼此之间的交互影响程度提供技术手段,四川电网的算例分析验证了方法的实用性和有效性。     

Method for identifying coherent generators

A method for identifying coherent generators in a power system is presented. The method is based on the property of equal acceleration for coherent machines and requires only the admittance matrix of the system and the moment of inertia of the generators. An expression is developed for the coherency index between any two generators in a power system, and, based on the value of this index, coherency or otherwise of the generators is established. A method of obtaining the dynamic equivalent of a coherent group is also described. The method of coherency identification and equivalencing is illustrated using a 12-machine sample system. The validity of the method is demonstrated by comparing the transient stability study results of the original system with those obtained for the reduced-order model of the system. The proposed method is computationally simple and fast and requires less memory.     

Power system dynamic equivalence based on a new model reduction technique

Power system dynamic equivalents play an important role in the effort to reduce the computational burden of the transient stability analysis of power systems. This paper proposes a new efficient practical algorithm for forming linear dynamic equivalents for power systems based on modal analysis. The main feature of the proposed method is that the accuracy of the equivalent model is greatly improved by converting a coordinate system representing the subsystem from the R-J coordinate system of the main system to the reference generator D-Q coordinate system of the subsystem. The order reduction is based on aggregation of similar modes and elimination of the inferior modes without significant effect on the frequency response of the subsystem. Thus the equivalent obtained by the proposed method can be used for both steady-state and transient stability analysis studies. To verify the dynamic equivalent performance stability simulation results for a model power system composed of 16 generators also are shown.     

基于功率传输路径的在线电压稳定性评估新方法

电压失稳本质上是一种局部现象,系统的电压稳定程度可以由最易于电压失稳的功率传输路径的电压稳定性来表征。文中应用局部电压稳定性指标确定薄弱负荷节点,并借助电气距离信息,从无功、有功传输路径两方面确定路径参与节点和关键功率源点,得到系统功率传输的薄弱路径集,通过等值判别最弱功率传输路径,将该路径的电压稳定性指标与关键发电机的无功储备指标相结合,评估整个系统的电压稳定程度。新英格兰10机39节点算例系统的仿真结果表明,该方法速度快、精度高,适合于在线应用。     

高渗透率逆变型分布式发电对 电力系统暂态稳定和电压稳定的影响

为研究大规模逆变型分布式发电对电力系统暂态和电压稳定性的影响,借助PSCAD/EMTDC仿真软件,以一个12母线测试系统为研究对象,建立电力系统和逆变型DG的动态模型。通过暂态仿真和理论分析,重点研究了不同渗透率DG对主同步发电机最大转速偏差和转速偏离频率的影响,分析了不同控制模式的DG在故障前(稳态)、故障期间和故障后对母线电压的影响。研究结果表明:渗透率越高,逆变型DG对系统暂态稳定性的负作用越大,但电压控制的逆变型DG能明显改善系统电压的稳定性。     

基于相似度同调的双馈风电场聚合研究

文章提出了一种基于相似度同调的双馈风电场聚合方法。首先利用Prony算法提取各风电场中双馈风机故障下功率响应曲线的动态特征,基于相似理论确定双馈风机间振荡模式中相似部分,应用相似振荡模式中的频率、阻尼、幅值等信息定义了双馈风机同调判别的相似度量化指标并确定同调机群。然后,根据双馈风机的外特性,提出功率聚合算法,即以双馈风机输出有功功率为权重求取等值机的暂态内电势并确定等值母线及等值机参数。该方法从同调机群识别、同调母线聚合、同调机群参数聚合等方面,系统地解决了不同双馈风电场的同调聚合问题。参数聚合方法不仅解决了聚类分群的复杂性和局限性,而且有效保留原系统中电气与结构特征。最后以实际云南电网中某地区风电场为例进行仿真验证。     

图像化数据驱动的电力系统暂态稳定性在线评估方法

目前电力系统暂态稳定性评估（TSA）大多采用标准算例生成的数据集,然而实际电网的母线、发电机、线路等电力元件的数量巨大,难以实现评估模型的实时监视和在线更新;而现有降维方法常常遗漏重要信息,导致预测精度下降。提出一种图像化数据驱动的电力系统暂态稳定性在线评估方法,将输入时间序列重新排列成二维图像,利用二维主成分分析法（2D-PCA）对原始图像进行特征降维,并建立卷积神经网络（CNN）模型进行系统稳定性预测。在IEEE-39算例中进行验证,结果表明本文所提基于2D-PCA和CNN的TSA模型在保证预测精度的同时能够大幅提高训练效率,有望推进深度学习在电力系统暂态稳定性在线评估的应用。     

Identification of coherent generators considering the electrical proximity for drastic dynamic equivalents

This paper describes an application of the coherency-based dynamic equivalent methodology to determine drastic reductions in the representation of power systems. This condition is necessary for real time power system simulator studies. The paper demonstrates that the exclusion of electrically distant generators from the coherent groups solves the convergence problems that may appear in the power flow algorithm during the calculation of drastic dynamic equivalents. This paper also demonstrates that for each fault neither the strongly coherent generators are always electrically close, nor the approximately coherent generators are always electrically distant. The New England system and two simplified configurations of the Brazilian interconnected power system are considered in the studies.     

基于相关发电机识别的动态等值法的算例仿真

对具有庞大规模的现代电力系统进行暂态稳定计算时,计算存储量大,计算时间长。因而采用基于相关发电机识别的动态等值法对电力系统进行化简以克服上述问题。该方法利用相关的充要条件对相关发电机进行判定,从而达到简化网络的目的。算例中等值网络的节点数目、支路数目、发电机数目和负荷数目大约只有原始网络的50%,用等值网络进行暂态稳定计算大约可以节省一半的计算时间,且计算结果的精确度完全满足工程的需要。     

A stability measure for use in power system transient stability studies

Large system transient stability calculations may be carried out using network equivalents, and generator grouping, and by reducing the order and complexity of the system representation. Engineering judgement and, in most cases, prior knowledge of transient system performance is required to implement the models.In this paper a new parameter called ‘stability measure’ is introduced. The stability measure can easily be calculated on the basis of load flow and short-circuit results. Upon calculation of the stability measure set for a given fault condition, an estimate of the likely response of the respective generators to the fault is obtained.The validity and generality of the stability measure has been demonstrated by simulated tests on a sample power system.Application of the method with respect to grouping of generators in transient stability studies is also discussed.     

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     

Power system model reduction using identification techniques

Identification techniques are applied to the construction of lower order nonlinear power system equivalents which can be used in stability calculations, and simulation of dynamic and transient conditions of a multimachine power system. Development of an equivalent machine for a group of dissimilar machines operating at a generating station is considered. An efficient algorithm based on the minimum principle to determine the parameters of the equivalent model which is lower in order than the actual system is also presented.     

启发式电力系统暂态稳定裕度在线评估方法研究

本文定义了一个能综合反映电力系统特定结构和运行方式下整体暂态稳定水平的连续指标：综合临界切除时间。结合知识库,模糊逻辑推理和综合技术,本文提出了一种能以较高精度在线估计ＧＣＣＴ值的暂态稳定估计方法。     

A new intelligent algorithm for online voltage stability assessment and monitoring

This paper presents a new approach for assessing power system voltage stability based on artificial feed forward neural network (FFNN). The approach uses real and reactive power, as well as voltage vectors for generators and load buses to train the neural net (NN). The input properties of the NN are generated from offline training data with various simulated loading conditions using a conventional voltage stability algorithm based on the L-index. The performance of the trained NN is investigated on two systems under various voltage stability assessment conditions. Main advantage is that the proposed approach is fast, robust, accurate and can be used online for predicting the L-indices of all the power system buses simultaneously. The method can also be effectively used to determining local and global stability margin for further improvement measures.     

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。     

基于PMU和改进支持向量机算法的同调机群在线识别

鉴于现代电力系统中发生暂态稳定问题时,为了给后续的主动解列措施提供依据,需要快速准确地辨识出系统中的同调机群,基于同步相量测量单元（phasor measurement unit,PMU）实时采集的发电机动态轨迹信息具有高维度和非线性等特点,提出了一种在线识别同调机群的新方法：由PMU得到故障后发电机组的动态功角轨迹量测信息;对PMU量测信息进行标准化处理,生成标准化高维数据;利用留一交叉验证法确定Gauss径向基核函数参数g和惩罚系数C的最优取值,得到准确的分类器;使用此分类器对未知分类的样本进行分类,并得到最终的同调分群结果。仿真结果表明：该方法能有效克服传统方法识别准确率低和速度慢的缺点,能在线识别系统中的同调机群,且兼具识别的快速性和准确性,可满足现代电力系统暂态稳定的在线分析和实时计算等要求。