A multicompartment TLM model for solving first-order rate equations

This paper introduces a simple model for solving a system of first-order rate equations using the TLM numerical method. A general algorithm is developed by setting up a matrix of discrete compartments. The rate constants provide the linkage between each compartment and the neighbouring ones. The method is demonstrated by some examples in which saturation conditions are considered. The TLM solution is compared with analytical solutions and the Rung-Kutta method of solving differential equations.     

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.     

Least squares spectral element method for 2D Maxwell equations in the frequency domain

We propose a high order numerical method for the first order Maxwell equations in the frequency domain, defined in media with arbitrary complex shape. Our approach is based on the combination of the least squares approach with the spectral element method. The former frees the solution from spurious modes, that can be found sometimes in classical finite element simulations. Many examples of such non‐physical solutions exist in literature, and elimination of these spurious effects is a subject of great interest. Spectral elements are a numerical technique for solving partial differential equations which can be regarded as an extension of finite elements: they merge the flexibility of finite elements in dealing with complex geometries, and the better accuracy of spectral methods. Convergence to exact solution is improved by increasing (at run time) the polynomial degree, with no changes on the computational grid: this provides a significant advantage in respect to low order finite element, which necessarily have to resort to grid refinement. In the authors opinion this approach can be successfully used for the treatment of large scale electromagnetic problems or, alternatively, for applications where higher precision is required. We present a few numerical experiments which prove the capability of the method in object. Copyright © 2004 John Wiley & Sons, Ltd.     

阶梯波多电平变换器特定谐波消除的完全解

针对数值算法和智能算法在求解阶梯波多电平变换器特定谐波消除问题时存在初值选取困难且只能求得部分解的问题,依据Groebner基和对称多项式理论的代数算法,将多元高次多项式方程组的求解转化为一元高次多项式方程和线性方程组的求解,给出了无需选取初值且能得出方程组的所有解的求解方法。与目前已有的其他代数算法(例如结式消元法、吴方法)相比,所能求解的开关点数大幅提升。给出了三相13电平阶梯波变换器在全调制比范围内开关角度的所有解,并通过实验对解的正确性进行了验证。     

Quasiperiodic (QP) oscillations in electrical power systems

The occurrence of quasiperiodic (QP) oscillations in power systems, a phenomena hitherto unknown, was first experienced in the French grid when attempting to energize an unloaded transformer at the end of a long transmission line. There are no simple analytical tools available to study conditions for the occurrence of QP oscillations. In this paper, the conditions necessary for the occurrence of quasiperiodicity are shown by solving the system equations using the method of harmonic balance. It is shown that QP oscillations will occur due to the severity of magnetizing nonlinearity of the transformer core. It is also shown that if core losses are high, only frequency locked oscillations can occur. The results are confirmed by numerical solution on the original set of differential equations.     

采用动态多维阶数控制的暂态稳定计算方法

泰勒(Taylor)级数法暂态稳定计算中阶数的选取对提高计算效率有重要意义。在对常微分方程组数值求解方法进行分析的基础上,提出了暂态稳定计算中动态多维阶数控制的概念。在计算暂态稳定轨迹的过程中,根据各个状态变量的不同动态特性和计算精度约束,对时间常数不同的环节采用不同的阶数。基于该概念,实现了采用动态多维阶数控制的高阶Taylor级数暂态稳定计算方法,并对其有效性和计算精度进行了证明。算例分析结果表明,该方法有效提高了高阶Taylor级数法暂态稳定计算的解算效率,具有实用价值。     

A general tool for circuit analysis based on wavelet transform

This paper deals with a generalized method for the time‐domain solution of electrical networks. The aim is to explore a new technique for the numerical simulation of circuits considering linear, time‐varying and non‐linear cases. By using the wavelet transform of the electrical quantities, differentiation and integration in the time domain are replaced by matrix multiplication. Then, the classical circuit differential equations obtained by mesh‐current, node‐voltage or state variables methods are transformed in algebraic equations. The numerical efficiency of wavelets makes the method effective for a fast and reliable numerical circuit simulation. Comparisons with analytical solutions and PSPICE simulations are presented in order to evaluate the numerical characteristics of the proposed method. Copyright © 2000 John Wiley & Sons, Ltd.     

电流源型逆变器SHE-PWM开关角度的计算方法研究

该文以电流源型逆变器（CSI）为研究对象,对特定消谐技术（SHE）的应用进行了分析和研究;针对用数值方法求解SHE-PWM开关角度时,非线性超越方程组计算初值选择困难的问题,提出了以梯形调制法（TPWM）生成方程组初值的方法,使求解速度明显加快;根据非线性方程组的数值解进行了仿真和实验,其结果证明了计算结果的正确性.     

A frequency‐domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential‐algebraic equations

A general numerical technique is proposed for the assessment of the stability of periodic solutions and the determination of bifurcations for limit cycles in autonomous nonlinear systems represented by ordinary differential equations in the differential‐algebraic form. The method is based on the harmonic balance (HB) technique, and exploits the same Jacobian matrix of the nonlinear system used in the Newton iterative numerical solution of the HB equations for the determination of the periodic steady state. To demonstrate the approach, it is applied to the determination of the bifurcation curves in the parameters' space of Chua's circuit with cubic nonlinearity, and to the study of the dynamics of the limit cycle of a Colpitts oscillator. Copyright © 2007 John Wiley & Sons, Ltd.     

汽轮机组的数学机械化建模与算法分析

对于大型汽轮发电机组,描述系统运行状态的微分方程相对复杂且维数很高,为对其进行解析分析,首先应用模态综合法建模得到降阶后的微分方程组,经代数变换后应用数学机械化方法进行解析建模分析。由于参加消元的节点位移变量均是线性变量,故消元时可保留油膜力表达式的非线性成分不变,这样就得到了维数相对较低且等式右端含有非线性油膜力表达式的代数方程组。为实现具有上述特点的代数方程组的求解,提出了既不同于解析法又与经典数值算法不完全相同的微分控制算法思想,据此实现对复杂汽轮发电机组转子系统的建模及对节点位移响应的分析与预测。     

Semi-implicit Runge—Kutta methods for power system transient stability studies

Some semi-implicit numerical integration algorithms for solving a set of differential equations are developed and applied for power system transient stability studies. These methods possess the desirable properties of explicit methods (no iteration) as well as those of implicit methods (numerically A-stable). Much larger time steps can be used without encountering any numerical instability problems, even for systems characterized by stiff differential equations. The algorithms have been tested on a number of sample systems.     

An Optimal Load Dispatch Program Using a Fast Power Flow Technique

ABSTRACT

This paper presents a new technique of Economic Dispatch for allocating generation in a power system. Penalty factors associated with generating units are calculated from a particular eigenvector of the transposed Jacobian matrix which is obtained while solving the load flow problem using a modified version of the fast power flow method developed earlier. The evaluation of the required eigenvector is simple and straightforward as the order of the Jacobian matrix is equal to the number of voltage controlled busbars in the system. The optimal allocation of each generating unit for the given demand on the system is obtained by solving the co-ordination equations along with load flow problem. The technique is found to be fast, reliable and suitable for on-line implementation.     

多电平逆变器特定谐波消除脉宽调制方法的初值问题研究

特定谐波消除脉宽调制(SHEPWM)方法，通过开关时刻的优化选择，消除选定的低频次谐波，具有波形质量、效率、直流电压利用率都高、直流侧滤波器尺寸小等一系列优点，所以受到人们的普遍关注。该文提出一种基于面积相等和注入零序谐波相结合的非线性方程组的初值求取的方法，简化了多电平逆变器SHEPWM非线性方程组初值的求取方法，显著提高了初值的有效性，根据一个调制度数值和谐波消除目标确定的初值，往往适用于同样谐波消除目标下、调制度在该值附近的一个范围内的所有SHEPWM非线性方程组，并且较大加快了求解非线性方程组的迭代过程的收敛速度；以五电平电压源逆变器为例，采用电力电子专用仿真软件POWERSIM6，对非线性方程组的数值解进行了仿真研究，结果证实了所提初值求取方法的有效性和实用性。 关键词：；特定谐波消除脉宽调制；非线性方程组；初值     

电力系统稳定计算隐式积分交替求解

本文介绍一种基于微分方程隐式积分梯形公式的电力系统稳定计算隐式积分交替求解算法。该算法具有数值稳定性好、可采用较大积分步长、能够适应较长过程动态稳定模拟计算的特点，并具有显式积分编程简单可靠、便于扩展的优点。     

一种病态电网潮流的数值解法

针对病态电网的潮流计算问题,提出对潮流延拓方程的龙格–库塔数值计算方法。其核心在于:在延拓法的基础上,将潮流方程解的问题转变为微分方程的初值问题,通过龙格–库塔法进行求解。在求解过程中,沿用多延拓多启动技术,以扩大解的收敛范围;将计算格式转变为常规牛顿潮流法形式,与成熟(如稀疏)技术有机衔接,使该算法符合工程实际。总之,该算法是一种大范围收敛的潮流算法,对病态潮流及电压静态稳定等问题分析有良好的适应性,修改后的IEEE 5和IEEE 118系统算例,验证了该算法的有效性。     

DYNAMIC MODEL OF CHOPPER FED DC SEPARATELY EXCITED MOTOR

ABSTRACT

This paper describes the transient response of a chopper fed dc separately excited motor using time ratio control. An approximate second order model for predicting the transient behaviour of the motor is developed using perturbation technique. The transient response for small and sudden variations of duty interval and load torque is deduced during discontinuous and continuous current mode operations. The effect of external inductance on the performance of motor in the armature circuit has also been investigated. The results are compared with those obtained from a digital computer by numerically solving the simultaneous differential equations valid for different intervals of chopper cycle and also with the first order model. It is shown that the second order model is more accurate than the first order model and much simpler and efficient than the numerical approach. The theoretical results obtained are also verified with an experimental set up. Experimental results closely agree with theoretical predictions.     

Model order reduction of coupled circuit‐device systems

We consider model order reduction of integrated circuits with semiconductor devices. Such circuits are modeled using modified nodal analysis by differential‐algebraic equations coupled with the nonlinear drift‐diffusion equations. A spatial discretization of these equations with a mixed finite element method yields a high dimensional nonlinear system of differential‐algebraic equations. Balancing‐related model reduction is used to reduce the dimension of the decoupled linear network equations, whereas the semidiscretized semiconductor model is reduced using proper orthogonal decomposition. Because the computational complexity of the reduced‐order model through the nonlinearity of the drift‐diffusion equations still depends on the number of variables of the full model, we apply the discrete empirical interpolation method to further reduce the computational complexity. We provide numerical comparisons that demonstrate the performance of the presented model reduction approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Exact solutions of cyclically symmetric oscillator equations with non-linear coupling

Kaplan and Yardeni have found very simple exact limit cycle solutions in cyclically symmetric systems of N oscillator equations with linear coupling in zero order of a perturbation parameter and non-linear coupling in first order. In contrast with such solutions in other non-linear systems, each of these limit cycles is a normal mode of the unperturbed equations, with no change in frequency. the sources of this simple behaviour are studied here with the equations expressed in terms of the normal mode co-ordinates of the unperturbed system rather than in the original co-ordinates. It is found that the simplicity of the Kaplan-Yardeni solutions arises partly from an additional symmetry of the perturbation terms beyond the cyclic symmetry and partly from the specific choices of the perturbations. Extension of their systems to arbitrary N leads to the result that all such sets of equations have similar simple limit cycles. More general cyclically symmetric sets of equations are also discussed, with limit cycle solutions whose frequencies are shifted from the zero-order values by easily calculated amounts or with solutions which are linear combinations of zero-order normal modes.     

特定消谐技术中非线性方程组数值等效及求解方法的改进

针对非线性方程组求解过程中大量的三角函数计算影响求解速度、增大计算误差以及非线性方程组求解过程中初值选取困难、影响求解收敛性等问题,提出三角函数数值等效转化的方法,即将高倍角三角函数转化成单倍角三角函数,使得非线性方程组中不含三角函数,因此,在计算中避免大量三角函数的计算,减小误差,提高了计算精度.同时,在方程求解时引入同伦算法,利用该算法的大范围收敛特性,降低初值给定难度,加快求解速度.此外,基于提出的方法,给出了两组初值给定方法,并通过实际算例计算,验证了该方法的有效性.     

电力系统动态仿真的一种改进迭代算法

基于电力系统动态仿真计算中微分方程与代数方程的交替迭代算法,提出了一种新的混合式迭代解法。该方法的基本原理是在延续了电力系统模块化建模及迭代算法特点前提下,将微分方程的求解方法多样化。仿真结果证明,混合式迭代解法应用在电力系统动态仿真计算中,计算结果正确,突破了传统的电力系统各模块计算时使用单一的数值解法的局限。