A modal-coherency technique for deriving dynamic equivalents

A technique for deriving dynamic equivalents is developed that combines the advantages of modal and coherency analysis. The electromechanical mode shapes are examined to find all the possible coherent groupings of machines in a given system. The results are displayed as a tree structure in which the whole interconnected power system forms the root of the tree and the various subdivisions of the system constitute the branches. The modal tree can be used to extract coherent machine groups to suit any particular application. A 24-machine test system is presented as an illustration     

Coherency identification and equivalents for transient stability studies

This paper presents techniques for identifying coherent generators without conducting a transient stability study and for developing stability equivalents of a group of coherent generators. Identification is based on the property of equal acceleration for coherent machines and it requires only examination of the elements of the Jacobian matrix of the linearized power system model. After the coherent groups have been identified, the stability equivalents are developed on the basis of the power invariance condition at the tie buses and at the internal buses of the coherent generators. These stability equivalents are used in a transient stability study. The techniques are illustrated with a 12-machine system.These techniques greatly improve the efficiency of calculation of coherency based equivalents. They have potential applications in planning studies of large power systems.     

Eigenvalue estimation of dominant electromechanical modes based on synchronous measurement and generator grouping technique

The authors have been studying a new approach for modal analysis of large power systems that utilizes GPS‐based synchronous measurement technology. The approach is based on the identification of a linearized multi‐input multi‐output model of power system. Since the identified model expresses approximately the electromechanical dynamics of an actual power system, modal frequencies, dampings, and mode shapes corresponding to electromechanical modes can be estimated as eigenvalues and eigenvectors of the identified model. In the paper, in order to advance our approach to a practical technique, it is mainly discussed how to select a small number of machines suitable for measurement locations to estimate eigenvalues associated with dominant slow modes. Such machines can be detected by identifying coherent groups related to the slow modes. The reference generators that behave representatively in each coherent group are the optimal ones to be measured. Therefore, the slow modes can be obtained by observing one generator from each group. The verification of the new modal analysis and coherency‐based machine selection is done through simulation studies using the IEEJ EAST 10‐machine system model. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 164(4): 24–32, 2008; Published online in Wiley InterScience ( www.interscience. wiley.com ). DOI 10.1002/eej.20428     

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.     

电力系统同调机群识别的一种模糊聚类方法

给出了一种能识别电力系统同调机群的模糊聚类方法。首先采用最大－最小方法对线性化后的系统状态矩阵进行标定,得到反映机组间动态相关程度的模糊等价关系矩阵,然后采用模糊聚类方法识别同调机群。最后给出了10机和24机两个试验系统同调机群识别结果,并通过特征根计算证明了此方法的有效性。     

Coherency and model reduction: state space point of view

Analytical connections are determined that relate coherent stability behavior of generators to redundancy in the controllability and observability gramians of the linear model of the power system. This redundancy is removed from the gramians of the reduced-order model generated by aggregating the coherent machines. Model reduction in large power systems is shown to be better if the order estimation information in the controllability and observability gramians is weighted properly by balancing the system. Perfect coherency of generators is related to the parameters of the linear model of the power system. Waveforms for generating the RMS coherency measures are compared. An algorithm for order reduction based on balancing is outlined and justified by testing on a 240-generator, 2500-bus system     

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.     

A generation rescheduling method to increase the dynamic securityof power systems

In this paper, a new method is proposed for dynamic security dispatch. The idea of coherent behavior of generators is used to find a new generation configuration with better transient stability behavior. Rescheduling the generation in the power system improves system security by increasing the critical clearing time or the transient energy margin without changing total generation. The calculation in the proposed method is simple and direct; the generation rescheduling depends only on the original generation and inertia constants of the machines, and their rotor speeds at the fault clearing time. In this work, the transient energy function (TEF) method is used to check the dynamic security of the system by analyzing all credible three phase faults with single line outages. If the worst energy margin is not acceptable, the proposed rescheduling is done, and the security is checked again. The method has been tested on the Ontario Hydro 55-bus 11-generator system, the IEEE 145-bus 50-generator system and the IEEE 162-bus 17-generator system. Results on several loading levels of the 162-bus 17-generator system are also shown     

A new approach for online coherency identification in power systems based on correlation characteristics of generators rotor oscillations

In this paper, a new approach for identifying coherent groups of generators in power systems based on the correlation coefficients between rotor angle/speed oscillations of generators is presented. The method uses a newly proposed clustering index based on the correlation coefficients of generators oscillations which is able to classify any number of generators into coherent groups. The proposed approach uses real time data of generators oscillations via VAMS/PMUs, so it is able to easily take into account the effect of system detailed modeling, generators and system controllers and type of events. The proposed correlation index evaluated from the real time behavior of generators in time-domain following disturbances are used to evaluate the degree of coherency between any pair of generators. The generators’ rotor angles and speeds can be obtained from synchronized measurements of system quantities using PMUs. Hence, the proposed method could be integrated into a wide-area measurement system enabling fast identification of coherent groups of generators. It is shown that by using COI of the aggregated in-phase coherent groups, the frequency of the inter-area mode can be evaluated. The proposed method is tested on the IEEE 39-bus with 10 generators and realistic power system of Iran with 405 generators.     

基于WAMS和曲线相似的同调机群识别方法*

提出了一种基于曲线相似的电力系统同调机群辨识新方法。首先获取WAMS实时监测得到的功角轨迹曲线作为基础数据,根据离散曲线相似性的定义,将各发电机的轨迹曲线分段,借助遗传算法确定分段轨迹之间的最优相似距离,保存了轨迹段的局部特性。然后整合各段相似距离得到各发电机之间的整体相似度并以此作为聚类指标,再利用层次聚类法实现多机系统同调机组分群。该方法简单可行,不受系统模型参数和故障类型的限制。最后对IEEE39节点系统进行分析计算,该仿真实验佐证了所提算法的有效性。     

故障位置对交直流外送系统暂态功角稳定性的影响分析

分析电源中心交直流外送系统中故障位置对暂态功角稳定性的影响.以三机系统为例建立数学模型,其中2台等值机位于电源中心内部.简化模型后,给出2台相互耦合的等值机转子运动方程.根据转子运动方程中各项的物理意义,分情况讨论了不同位置发生故障后系统的暂态功角稳定性,并结合实际系统运行特点进行概括,得到结论如下:当电源中心内部交流联络线潮流较轻时,电源中心的交流外送通道发生故障,系统更易发生功角失稳;反之,电源中心内部发生故障,系统更易发生功角失稳,并对内部故障位置进行区分.最后,通过基于陕西电网陕北交直流外送系统的算例验证了结论的正确性.     

改进模糊ISODATA法识别电力系统同调机群

引入模糊聚类方法识别电力系统同调机群。首先对原有的基于模糊相关自组织数据分析算法(iterativese lf-organ iz ing data ana lys is techn iques a lgorithm,ISODATA)的同调机群识别法的各个控制参数的选取问题进行了大量仿真实验,给出了优化参数取值的一些经验值。特别在如何确定最优分类数的问题上引入了模糊F统计量的方法,并根据电力系统同调识别的特点改进了模糊相关自组织数据分析算法的同调机群识别算法,使其更能适用于工程应用。最后用EPR I_36节点纯交流系统的仿真计算验证了该方法的有效性。     

Composite system well-being evaluation based on non-sequential Monte Carlo simulation

The reliability evaluation of composite power systems has historically been assessed using deterministic and probabilistic criteria and methods. The well-being approach was recently proposed in order to combine deterministic criteria with probabilistic methods and evaluates the system by healthy, marginal and risky states. This paper presents an efficient method for composite system well-being evaluation based on non-sequential Monte Carlo simulation. It is assumed that the system is coherent, and the frequency and duration indices are calculated by the conditional probability method. The system adequacy is evaluated by a non-linear power flow solved by the Newton–Raphson method and by an optimal power flow solved by the Interior Points method. Results are presented for the IEEE-RTS system with a constant load and with a variable load curve. It is demonstrated that the proposed method, as well as the assumed hypothesis, are valid and provide an efficient alternative for the well-being analysis of large scale power systems.     

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.     

电力系统动态等值参数聚合的实用方法

在大规模电力系统暂态稳定分析中，为减少数值仿真的计算量，可采取动态等值的方法对系统进行简化。电力系统动态等值包括相关机群动态识别、网络化简和相关机群参数聚合3部分。针对第三部分提出了一种基于加权法的相关机群详细模型参数聚合的方法，该方法可用于获得等值发电机组及其调节系统的详细模型参数和负荷等值异步电动机的详细模型参数。这种方法既达到了参数聚合的目的，又减少了计算时间。对IEEE10机39节点系统和简单配电系统进行仿真，并与频域法相比较，结果表明了该等值方法的有效性。     

多绕组电机模型的Matlab／SimPowerSystem实现

为满足重量、体积、谐波等方面的特殊要求,独立电力系统常采用交直流多绕组发电机、多相电动机等特种电机。这使得系统的仿真分析与陆用广域电力系统相比差异较大。基于MATLAB/SimPowerSystem,本文提出了一种多绕组发电机的三相发电机等值模型。通过在普通三相发电机基础上增加磁耦合,该模型能够实现多绕组发电机的模拟。与其他实现方法相比,所提出的方法能够充分利用现有仿真算法,可方便地实现独立电力系统的时域仿真。     

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     

Novel system for generating constant mechanical power from solar energy

In order to make use of solar energy instead of oil and coal, the authors have proposed a new driving system which is composed of two coupled induction machines with a photovoltaic array. One induction machine is driven by electric power of the photovoltaic array through a general‐purpose inverter, and the other induction machine is interconnected to the utility line. This system can generate the required mechanical power even in fluctuating insolation and supply the surplus electric power of the photovoltaic array to the utility line. In this paper, it is shown that the proposed method can be realized by using not only an induction–induction machine system but also an induction–synchronous one. The latter system can drive a mechanical load with a strictly constant speed and high efficiency. Such parallel running using two rotary machines has the advantage of decreasing the total loss compared to a single motor system when the no‐load loss is less than a certain ratio of the load loss. Furthermore, this paper presents a practical method to measure the solar power, track the maximum power point, and control the connection–disconnection of the photovoltaic array to the general‐purpose inverter. © 1999 Scripta Technica, Electr Eng Jpn, 130(2): 32–39, 2000     

基于无功功率捕捉失步解列断面的理论研究

就等值双机系统在失步振荡过程中失步断面联络线的电气量进行了研究分析。当多机电力系统失步成2组同调机群,失步断面通常是由考虑到解列后子系统的同步运行并可以将系统解列成2个同调子系统的一组联络线组成。这组联络线的电气量的共同特征主要是:失步断面联络线上有功功率周期性过零振荡;失步断面联络线上有一点(失步中心),其电压幅值的变化幅度明显大于联络线的其他地方,且距离失步中心越远,幅值变化越小,即在失步振荡过程中,失步断面联络线存在明显的电压梯度;失步过程中,无功功率由失步断面两侧流向失步断面中。利用有功过零判断振荡周期并在该周期内对无功功率进行积分,该积分值能够反映出失步断面的这些特征。基于此,提出了基于无功功率寻找失步解列断面的方法。     

采用受扰轨迹和独立分量分析技术识别同调机群的方法

针对大区电网互联运行中出现振荡失步时,需要正确划分同调机群以解列电网的问题,提出采用独立分量分析技术(independent component analysis,ICA)对故障后的发电机受扰轨迹进行特征提取,来识别系统中同调机群的方法。与现有方法相比,这种方法不需要获得系统元件模型和参数,而是直接球化广域测量系统(wide area measurement systems,WAMS)提供的发电机电角速度信号,再利用最大负熵准则进行独立分量分析得到特征矩阵,将高维数的多机受扰轨迹数据变换到低维空间,通过模式识别得到分群结果。8机36节点系统和西北750 kV电网规划系统算例表明,该方法能有效消除噪音和坏数据的影响,准确识别出同调机群。