应用模态级数3阶解析解分析大干扰低频振荡机理

在动态电力系统3阶解析解的基础上,分析了遭受大干扰的电力系统所表现出来的复杂的非线性动态特性.提出由于3阶解析解中非线性高阶项被大干扰激发,使系统模态间的高阶非线性相关作用加剧,才导致了系统出现增幅低频振荡这一新观点,从理论上有效地解释了大干扰下增幅低频振荡出现的原因.对一个电力系统算例的分析验证了上述观点的正确性,也证明了3阶解析解与2阶解析解相比在分析大干扰下系统动态特性的有效性.     

三阶非线性对主导低频振荡模式的影响

在电力系统动态方程3阶解基础上,分析了3阶非线性对基本模式作用的影响,提出了2阶和3阶非线性对基本模式影响的评价指标,并进一步应用3阶解,提出了识别大干扰主导低频振荡模式的指标,应用Prony算法验证了该指标的有效性。研究结果显示,最靠近虚轴的小干扰主导低频振荡模式,在大干扰情况下可能不被激励或激励较弱,因而大、小干扰主导低频振荡模式可能不同,考虑3阶非线性对大干扰主导低频振荡的影响是必要的。     

互联电力系统的Adomian分解法求解及其混沌特性分析

利用Adomian分解法研究了一个互联电力系统,给出了其近似解析解。根据近似解析解,通过MATLAB仿真分析了互联电力系统的混沌特性,给出了不同周期负荷扰动下的分岔图和相平面图。仿真结果表明,在受到较大的周期负荷扰动时,系统将会出现混沌振荡。最后,在不同的时间步长下,对比了Adomian分解法和四阶Runge-Kutta法的数值解。对比结果表明Adomian分解法不仅精确度更高、计算时间更少,而且收敛速度更快。     

计及发电机内电抗的链式电力系统机电扰动传播研究

机电扰动在系统中传播可能危害电力系统安全。基于计及发电机内电抗的一维链式电力系统连续体模型,研究了机电扰动传播机理。给出描述一维链式电力系统连续体模型的色散波动方程;在此基础上,利用拉普拉斯变换和留数法求得系统受阶跃功率扰动后母线电压相角增量及有功功率增量的解析解,仿真证明该解析解的正确性;在典型参数下,分析了母线电压相角增量解析解中每一项对扰动传播的影响。该解析解能够描述扰动后功率变化的整个过程,从而进一步揭示了机电扰动在电网中的传播机制。     

计及不对称故障影响的感应电动机负荷模型解析算法

针对三相对称正序电压的仿真计算模型无法准确模拟感应电动机负荷动态特性的问题，提出一种计及不对称故障影响的感应电动机负荷模型解析算法。首先，基于转子一阶机械暂态方程获取感应电动机的转差率，再开展各项运算分析以获取扰动后感应电动机的电流变化和功率响应；然后，从电压稳定性和参数可辨识性角度，比较三阶机电暂态模型和一阶机械暂态模型的精度；最后，基于PSCAD/EMTDC平台搭建模型，对不同故障电压跌落场景下感应电动机的动态响应进行仿真分析。仿真结果表明，所提的解析算法能够获得不对称故障影响下感应电动机的动态响应且具有计算准确性和快速性的优势。     

应用模态级数方法分析电力系统模态谐振

本文推出了一种分析电力系统模态谐振的方法———模态级数(modalseries)方法。用该方法求取2阶解析解不用解高维非线性代数方程,而且把谐振情况和非谐振情况的公式融为一体,推导容易,计算简单。在2阶解析解的基础上推导出了系统谐振时非线性相关因子的表达式。用该方法分析了简单电力系统中出现的模态谐振情况,获得了良好的效果,由此验证了本文所提出方法及谐振时2阶非线性相关因子的正确性。     

电力系统非线性振荡模态分析

利用Carleman线性化原理研究电力系统非线性振荡稳定性问题,通过分析得到了二阶及二阶以上电力系统动态方程解析解的表达式。通过Carleman线性化分析方法得到了系统的非线性高阶模态,可以用于研究电力系统的非线性动态特性及大干扰下系统的稳定性,揭示了非线性模态相关性对系统动态特性的影响。同时将线性模态参与因子的概念扩展到非线性模态中,定量地衡量各振荡模式之间的非线性相关作用。通过36节点系统的仿真计算与Prony分析结果进行了对比。通过Carleman线性化方法分析电力系统非线性模式之间的相互作用,可以在小干扰稳定和传统的线性化分析基础上更加深入地理解非线性系统的动态特性, 为分析大干扰和强非线性情况下系统的稳定性和动态特性提供了一种新的手段。     

正规形方法在互联电网低频振荡分析中的应用

该文介绍了正规形方法在互联电力系统低频振荡研究中的应用,详细讨论了其数学模型和处理过程.正规形方法揭示了非线性模式相关性对系统动态特性的影响.通过非线性向量场的正规形变换得到了电力系统状态方程的2阶解析解,扩展了线性相关因子的概念.正规形方法、特征值计算和Prony分析的综合应用将小信号稳定和时域仿真有效地结合起来.仿真分析的结果证明了该方法是低频振荡分析的有效工具.     

电力系统非线性振荡模态分析

利用Carleman线性化原理研究电力系统非线性振荡稳定性问题,通过分析得到了二阶及二阶以上电力系统动态方程解析解的表达式.通过Carleman线性化分析方法得到了系统的非线性高阶模态,可以用于研究电力系统的非线性动态特性及大干扰下系统的稳定性,揭示了非线性模态相关性对系统动态特性的影响.同时将线性模态参与因子的概念扩展到非线性模态中,定量地衡量各振荡模式之间的非线性相关作用.通过36节点系统的仿真计算与Prony分析结果进行了对比.通过Carleman线性化方法分析电力系统非线性模式之间的相互作用,可以在小干扰稳定和传统的线性化分析基础上更加深入地理解非线性系统的动态特性, 为分析大干扰和强非线性情况下系统的稳定性和动态特性提供了一种新的手段.     

基于机电波连续体模型的机电扰动传播研究

连续体模型是一种将离散电力系统连续化处理以研究电力系统动态特性的一种新方法。针对一维均匀无损耗链式系统建立基于机电波连续体模型的偏微分方程,在给定初始条件下得到方程解析解,比较了不同惯性密度情况下,母线电压相角增量幅值和有功功率增量幅值的差异。精确解下的算例仿真曲线比较结果也吻合了以波的反射、透射特性为基础的机电扰动传播控制。     

Perturbation analysis of power systems: effects of second- and third-order nonlinear terms on system dynamic behavior

The study of nonlinear behavior near an equilibrium point is of considerable importance in power system stability analysis. In this paper, a systematic analytical procedure based on normal form (NF) theory is proposed for studying the influence of high order terms arising from the Taylor series expansion of the system model on power system dynamic behavior. Using this method, a third-order model of the power system is proposed in which weak system nonlinearities are explicitly represented. Analytical expressions are then developed that provide approximate solutions to system performance near a singularity and techniques for interpreting these solutions in terms of modal functions are given. The application of these procedures is illustrated on a single-machine infinite-bus system using a classical representation, but the results can be extended to accommodate more complex systems.     

Efficient starting point of load-flow equations

Load flow is the solution of the static operating state of an electric power transmission system and is the most frequently computer-performed power system calculation.

In this paper, an initial linear solution of the load-flow equations is developed taking into consideration the decoupling principles, i.e. the active power depends on the voltage angle and the reactive power on the voltage magnitude.

This initial decoupled linear solution is utilized as the starting point for the solution of the load-flow equations using such numerical methods as the fast linear method, Newton's decoupled method and the Gauss—Seidel method. Its performance is compared with that of the flat starting point (V = 1.0 p.u., D = 0.0 radians). The test power systems used to test its performance are these of the standard 14, 30, 57 nodes IEEE test power systems.     

发电机单机无穷大系统动力学模型的理论研究

将动力学方法用于发电机及电力系统分析和控制时,能量函数的物理意义不明确。根据分析动力学原理,分析单机无穷大系统的能量关系,分别给出了各子系统的拉格朗日函数、耗散函数和广义外力形式,进而导出了整个系统的拉格朗日-麦克斯韦方程组,用统一的动力学观点描述系统的运动。导出了系统的哈密顿函数,并将系统转化为广义哈密顿控制系统。最后,给出了相应于传统3阶发电机模型的哈密顿函数和控制模型,并进行了仿真对比。仿真结果表明,这种方法获得的哈密顿模型能提供更多的信息。     

Command governor‐based adaptive control for dynamical systems with matched and unmatched uncertainties

In this paper, we propose a command governor‐based adaptive control architecture for stabilizing uncertain dynamical systems with not only matched but also unmatched uncertainties and achieving the desired command following performance of a user‐defined subset of the accessible states. In our proposed solution, online least‐squares solutions for the matched and unmatched parameters are obtained through integration method and they are employed in the adaptive control framework. Specifically, the matched uncertainty is identified and its effect upon the system behavior is entirely attenuated. Moreover, using the unmatched uncertainty approximation obtained through radial basis function neural networks, the command governor signal is designed to achieve the desired command following performance of the user‐defined subset of the accessible states. With this command governor‐based model reference adaptive control architecture, the tracking error of the selected states can be made arbitrarily small by judiciously tuning the design parameters. In addition to the analysis of the closed‐loop system stability using methods from the Lyapunov theory, our findings are also illustrated through numerical examples.     

A fast numerical algorithm for transient stability studies of power systems

A fast numerical solution of a technique for improving the speed of the transient stability solution of power systems is presented in this paper. The system is described by a set of first-order differential equations which consist of both linear and nonlinear parts. The linear set of equations is considered separately and is solved by modal analysis using closed-form solutions. The nonlinear part of the equations is solved by a numerical method. As explicit solutions are available for the linear part of the equations, the solution time is considerably reduced. The proposed technique is employed for computing the transient stability of a sample power system represented in detail. A comparison is made with a conventional solution procedure.     

计及运行方式变换条件的多SVC布点方法

针对多静止同步补偿器(static var compensator,SVC)对系统共同影响的问题,提出计及运行方式变化的多SVC布点方法。利用规范形分析,基于摄动方程2阶解析解信息建立拓展静态电压稳定边界的多SVC布点分析方法。首先根据静态电压稳定分析方法,确定系统危险运行方式(即距离系统电压崩溃最近的运行方式);然后在该运行方式下,利用规范形方法对系统进行小扰动电压稳定分析,求出所有负荷节点的电压振荡曲线解析解;最后利用2阶解析解所给出的小扰动1阶振荡幅值和2阶振荡幅值信息,以多SVC布点多种方案对系统降低小扰动幅值的贡献为指标,给出多SVC布点结果。所提方法应用于IEEE 30节点系统,试验结果表明,该方法相对于不考虑多点共同影响的多SVC布点方式,其静态电压稳定边界的拓展效果更好。     

SECOND ORDER DECOUPLED LOAD FLOW

ABSTRACT

This paper presents a second order decoupled load flow method. The salient features are consideration of all terms in the Taylor series expansion, use of constant decoupled Jacobians and extremely simple computations involved in evaluating the active and reactive power mis-match vectors. Load flow solutions for several test systems have been obtained using the proposed and Fast Decoupled Load Flow (FDLF) methods. The test cases include systems with large R/X ratio transmission lines and series compensated lines.Limited investigations reveal that the proposed method has an edge over the FDLF method in terms of reliability of convergence and solution time.     

Experimental Determination of Numerical–Analytical Model Coefficients of Electrophysical Processes in Silicon Power Devices

A method has been presented of experimental determination of numerical–analytical model coefficients describing electrophysical processes in silicon power devices that does not use “transistance” (the effect of on-again modes) to decrease loss of power in a device. It has been demonstrated that experimental determination of the coefficients allows one to dispense with numerical solutions of the fundamental systems of equations of semiconductors and use a low-level model for solution of practical problems related to the maximum permissible current loads of silicon power devices in regimes specified by a customer.