Calculation of transient processes in electrical circuits using Chebyshev polynomials

Transient electromagnetic processes in electrical systems present a significant risk to machines and influence the reliability of relay protection; therefore, the investigation of these processes is important. Transient modeling in transformers is presently done by construction and solution of state equations for magnetoelectrical equivalent schemes that bring together the electric and magnetic circuits of these devices, taking into account the interaction with each other. Modeling of these processes can be quite long when using modern software. An aim of the given work is development of more fast-acting method of calculation of electromagnetic transients, using a polynomial approximation of the solution, and also development of scheme model of method that creates convenience for engineers in modeling. A method of calculation of transients in electric circuits is developed on the basis of expansion of the solution of state equations in series of orthogonal Chebyshev polynomials. A scheme interpretation of the developed method is offered. It is shown that, in the special equivalent scheme, Kirchhoff’s laws apply to images of currents and magnetic fluxes as vectors containing the values of coefficients of decomposition of these values by Chebyshev polynomials. The given method allows replacement of operations with instantaneous values of currents by operations with direct currents in the presented equivalent scheme. Transient calculation via the suggested method in a single-phase transformer processor is twice as fast as with well-known methods. The presented method is especially appropriate for transient calculation in magnetoelectrical circuits, since it allows the use of voltage sources controlled by the current derivative for easy calculation of the integrals of solutions.     

电流互感器的数字实时仿真

电流互感器电磁暂态过程仿真,在电力系统动态仿真系统中是必不可少的,为此提出了一个电流互感器的非线性实时仿真模型。模型中考虑了磁饱和和磁滞的影响,同时给出了相应的数字积分方法。对该电流互感器正常工作电流状态、一次侧大电流故障状态及一次侧开路故障状态的电磁暂态过程进行了仿真。仿真结果表明,提出的实时仿真模型和选用的数字积分方法是正确、有效的。     

Dynamic model of a three-phase power transformer

An adequate mathematical model of a three-phase power transformer is one of the important elements in the programs for the computer analysis of power system transients. Featured in this paper is the simulation model of a three-phase, three-limb core-type power transformer. Nonlinear effects of saturation, hysteresis and eddy currents are considered. Two ways of creating major and minor hysteresis loops are presented. The transformer model, described by a system of time dependent differential equations, is solved by an efficient numerical algorithm. The behaviour of the transformer model during switching-in and fault transients, as well as other types of transients, has been tested. The computed transient waveforms are compared with the measured ones and there exists very close agreement between them     

基于同步开关预判的半桥型VSC快速电磁暂态建模方法

现代电力系统存在大量的半桥型电压源变流器,采用传统电磁暂态仿真程序对其进行大规模仿真分析时,存在耗时高、效率低的问题.以半桥子电路为开关状态判断的基本单元,通过分析其开关状态变化时二极管的续流及关断过程,得出普适于半桥型电压源变流器的同步开关预判方法.该方法可在当前时步通过逻辑判断直接得出稳定的开关状态组合,消除了迭代计算.结合同步开关快速预判方法及内节点收缩方法构建了半桥型电压源变流器的快速仿真模型,通过对比仿真,验证了快速仿真模型具有与全详细化模型相当的仿真精度,且能有效减少仿真耗时,提高仿真效率.与全详细化模型相比,针对80模块固态变压器的快速仿真模型可加速20倍.     

A method for wide frequency range modeling of power transformersand rotating machines

Wide frequency range representation of power system components such as power transformers, reactors and rotating machines is mainly needed for the analysis of electromagnetic transients in power systems. In this paper, a method is presented for state space formulation of machine windings. The described procedure is completely based on external terminal impedance measurements and data related to the internal structure is not required. First, the wide frequency behavior of machine windings is reviewed and the nonlinearity effects of the iron core are discussed. A numerical method is given for calculation of the state equation parameters directly from the measured terminal impedance characteristics. The presented modeling method is applicable to any transformer, reactor or rotating machine in service where sufficient information on the internal design is not available. Besides, the canonical structure of the model offers advantages in terms of computer memory and computation effort in time domain analyses of complex power systems     

Numerical calculations of three-phase transformer transients

A three-phase, two-winding transformer model is presented in this paper. Nonlinear magnetizing curves are piecewise linearized, while the input winding capacitances are lumped onto the transformer terminals. A stiff system of differential equations in a state space, describing the transformer transient behavior, is solved using the L-stable backward differentiation formulas (BDFs) numerical rule. It has been shown that using the BDF numerical rule has resulted in better stability properties than using the trapezoidal rule. A computer program has been developed for generation of variable-state waveforms. The developed program is suitable for simulations of low-frequency three-phase transformer transients such as inrush currents and ferroresonance. This computer program has proved to be numerically stable for the problems investigated in this paper. The results acquired in this way are compared to results obtained using MATLAB/Power System Blockset, as well as to results of laboratory measurements.     

Transients during 138-kV SF6 breaker switching of low inductivecurrents

The authors discusses the effects of switching low inductive currents with 138 kV SF₆ breakers in a petrochemical plant. Switching transients are believed to have contributed to the failure of a 13.8 kV PT and a 13.8 kV air magnetic circuit breaker. The high-frequency transient surge can transfer across a transformer due to transformer capacitances between the high- and low-voltage windings. The electromagnetic transient program system (ETPS) model and different case studies are discussed with the effect of different transformer winding capacitances. The interruption mechanism of low inductive currents is also described. This analysis demonstrates the need to conduct switching transient studies and the need for surge arresters on transformer secondary terminals under certain system conditions     

Coupling capacitor voltage transformer: A model for electromagnetic transient studies

In this work, an accurate coupling capacitor voltage transformer (CCVT) model for electromagnetic transient studies is presented. The model takes into account linear and nonlinear elements. A support routine was developed to compute the linear 230 kV CCVT parameters (resistances, inductances and capacitances) from frequency response data. The magnetic core and surge arrester nonlinear characteristics were estimated from laboratory measurements as well. The model is used in connection with the electromagnetic transients program (EMTP) to predict the CCVT performance when it is submitted to transient overvoltages, as are the cases of voltages due to the ferroresonance phenomenon and circuit breaker switching. The difference between simulated and measured results is fairly small. Simulations had shown that transient overvoltages produced inside the CCVT, when a short circuit is cleared at the CCVT secondary side, are effectively damped out by the ferroresonance suppression circuit and the protection circuit.     

利用数值仿真方法确定三相变压器深度饱和等效电路模型参数

精确的变压器深度饱和模型是分析电网过电压暂态过程的基础。而目前端口试验的方法只能得到额定运行时等效电路模型的参数,却无法得到过电压下深度饱和区的参数。该文提出利用数值仿真的方法确定三相变压器深度饱和等效电路模型参数,数值仿真的方法分为两种,包括基于端口数值试验的方法和基于电磁场分布计算磁阻方法。前者通过磁场和电路耦合的方法在变压器的端口设置开路或短路状态以确定等效电路参数,后者利用变压器各部分的磁通和能量的积分结果计算磁阻,再转换得到等效电路参数。计算磁阻的方法更适用于分析拓扑复杂、深度饱和的变压器等效电路模型参数。     

基于离散状态事件驱动的电力电子瞬态过程仿真方法

为分析计算电力电子系统的电磁瞬态过程,需采用非理想开关器件模型,并计及电路中的杂散参数和控制回路中的时间延迟等,此时描述电力电子系统的数学模型呈现出高阶非线性特性,且往往具有较强的刚性。采用常规微分方程的数值解算方法对于这种非线性的电力电子系统瞬态过程进行仿真求解,存在仿真时间超长和数值稳定性很差的问题。为解决这一问题,基于离散状态事件驱动(DSED)思想提出一类电力电子瞬态过程数值仿真方法,摒弃对时间离散的常规数值解算,而直接以状态量的变化值作为仿真计算依据。理论推证和仿真解算比较结果表明:该方法能有效缩短解算时间,同时解决了常微分方程组的刚性问题,使得解算具有很好的数值稳定性。     

Simulation of transformer PD pulse propagation and monitoring for a500 kV substation

This paper discusses the development of a simulation model to study the propagation of partial discharge (PD) pulses of transformers in a 500 kV substation. The results will be used to design an on-line PD monitoring system for transformers. The impedance matrix of a 500 kV, single-phase transformer is computed based on geometry data and its external coupling network (often referred to as coupling impedance) is calculated with electromagnetic transients program (EMTP). It was found that the frequency characteristic of the coupling network is complex and that the traditional lumped coupling capacitance representation is only feasible at <60 kHz. The entire substation network was included to calculate the PD propagation of the transformer. PD responses are obtained at the tank grounding and 500 kV bushing tap grounding with a simulated PD pulse injected at the 500 kV terminal and 220 kV terminal of the transformer, respectively. Simulation shows that, using the resonant frequency of the substation network as monitoring frequency, one effectively can increase the monitoring sensitivity. The off-line and on-line PD calibration can also be made based on the developed simulation model     

工频电磁场对智能电能表干扰仿真分析研究

文中根据工频电磁场对智能电表关键部分的干扰原理,以工频电磁场作为干扰源,运用有限元软件ANSYS的电磁场分析功能对工频磁场干扰智能电能表电源变压器、电压互感器和电流互感器进行了分析和研究。根据有限元分析思想,建立了有限元分析模型,并对模型进行了计算、比较和分析,根据有限元的计算结果和分析结果提出了一些智能电表防电磁干扰的措施。     

A novel probabilistic neural network‐based algorithm for classifying internal fault in transformer windings

The major function of protective devices in a power system is to detect the occurrence of faults and to isolate the faulty sections from the rest of the system. Much progress has been made in the development algorithms for detecting faults in power transformers, which depend on transients‐based techniques. This paper presents an algorithm based on a combination of discrete wavelet transforms and probabilistic neural networks (PNNs) for classifying internal faults in a two‐winding three‐phase transformer. Fault conditions of the transformer are simulated using alternative transients program/electromagnetic transients program (ATP/EMTP) in order to obtain current signals. The mother wavelet Daubechies4 is employed to decompose the high‐frequency components from these signals. All three phases of the differential current signals are used in the fault detection decision algorithm. The variations of first‐scale high‐frequency component that detects fault are used as an input for the training pattern. The training process for the neural network and fault diagnosis decision is implemented using toolboxes on MATLAB/Simulink. Various cases and fault types based on the Thailand electricity transmission and distribution systems are studied to verify the validity of the algorithm. Backpropagation neural network is also compared with the PNN in this paper. It is found that the proposed method gives satisfactory accuracy with less training time, and will be particularly useful in the development of a modern differential relay for a transformer protection scheme. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

应用VB语言开发单相电磁式电压互感器的计算软件

介绍了如何应用ＶＢ（Ｖｉｓｕａｌ Ｂａｓｉｃ）语言开发高效的单相电磁式电压互感器计算软件，阐述了计算软件应用的原理与数学模型，论述了其功能。     

考虑集肤效应和邻近效应的变压器绕组谐波损耗计算及实验研究

基于国内外现有变压器谐波模型发展情况及其适用范围的局限性,以进一步精确量化变压器绕组谐波损耗为目的,建立了绕组谐波损耗模型。该模型综合考虑谐波情况下集肤效应、邻近效应对绕组的影响,基于电磁场原理分析绕组电阻参数畸变特性。进行了各次谐波电流下的绕组电阻测量实验,将实验测量值、传统模型计算值与该模型计算值进行对比,结果证明该模型提高了计算精度,使得变压器绕组损耗计算更加精确。最后基于实验测量值,建立了变压器绕组谐波电阻工程实用模型,对工程计算具有一定的指导价值。     

Frequency-Adaptive Power System Modeling for Multiscale Simulation of Transients

A multiscale power system modeling methodology for the integrative simulation of electromagnetic and electromechanical transients is introduced, implemented and validated. It makes use of frequency-adaptive simulation of transients (FAST) in which the shift frequency appears as a new parameter in addition to the time step size. For fast electromagnetic transients, tracking of instantaneous waveforms as in the Electromagnetic Transients Program (EMTP) is performed. When slower electromechanical transients involving power oscillations prevail, the Fourier spectra of the waveforms are shifted by typically either 50 or 60 Hz to eliminate the ac carrier and enable envelope following as in phasor-based simulation. An algorithm for the automatic setting of both shift frequency and time step size is proposed. Multiscale models of transformers, synchronous machinery, and transmission lines based on FAST are developed. The line model is distinguished in that it bridges both lumped and distributed parameters to efficiently emulate scale-bridging phenomena from steady state to traveling waves. The overall methodology is thoroughly validated: first against a staged field test involving transients of line energization and recovery on the network of the Bonneville power administration (BPA); then through comparison with an EMTP-type simulator in modeling diverse transients on a four-machine two-area power system.     

Effect of CCVT Gap Protection Circuit on Voltage Distortion

Long-term voltage records of coupling capacitor voltage transformers (CCVTs) indicate that CCVT voltage is occasionally distorted under normal operating conditions. Serious voltage distortion in CCVTs can cause the protection relay to trigger a circuit breaker (CB). This work analyzes the reasons accounting for voltage distortion of CCVTs and the impact of voltage distortion due to deterioration of gap insulation in CCVTs. In this work, the CCVT parameters are measured by using an LCR meter in a power laboratory. The electromagnetic transients program/alternative transients program software is used to establish a CCVT model. Finally, the simulating results are compared with the test records to confirm that voltage distortion is caused by an instantaneous short-circuit fault in the CCVT gap. Additionally, simulation analysis confirms that a permanent short-circuit fault at the gap burns the damping resistor in the CCVT, and the protection relay warns of a burden voltage drop at the secondary side of the potential transformer.     

Test System for Detailed Model of Transformers for Transient Analysis Using the Electromagnetic Transient Program (EMTP)

This paper describes a detailed model of a transformer designed to evaluate the ability of winding insulation to withstand transients. The time domain electromagnetic transient program (EMTP) was used to develop a model of the transient characteristics of the winding. It is difficult for students to use EMTP and understand simulation results. This paper contains all the data needed to develop a detailed model for transient analysis and presents basic case studies and alternative design/operating configurations.     

Y/Δ接线电力变压器内部异常励磁电流辨识

本文针对Y/Δ接线电力变压器,基于时域场路耦合模型提出一种励磁电流参数辨识方法。建立磁场-电路耦合模型,基于能量扰动原理计算动态电感与时域电流两个状态变量,在此基础上利用端口电气信息研究变压器励磁电流参数的辨识方法。通过研究交直流混杂、匝间短路情况下的变压器电磁特性,结合变压器励磁饱和状态,总结励磁电流在不同异常状态下的变化规律。搭建220V三相组式变压器动模实验平台,在不同直流扰动、不同电压等级匝间短路条件下,利用励磁参数辨识模块辨识励磁电流,并将仿真结果与实验数据进行对比,验证仿真模型的正确性。     

变压器直流扰动下励磁谐波与铁心饱和失稳研究

变压器遭受直流入侵时铁心励磁饱和程度加深,励磁电流发生畸变,谐波含量显著升高。针对该问题研究变压器励磁谐波与铁心饱和特性,并提出一种变压器直流扰动下铁心饱和失稳判据。基于电磁耦合原理构建交直流混杂模式下的变压器状态方程,利用端口电气信息研究励磁电流辨识方法,对励磁电流进行谐波分析并总结其变化规律,通过分析变压器直流扰动铁心饱和机理,研究铁心饱和失稳判别方法。通过仿真计算与动模实验深入分析变压器的电磁特性,并验证该方法的有效性。该研究为变压器直流扰动下铁心饱和失稳判别提供可行方法。