A Contribution to the Frequency Analysis and Transient Response of Power Transformer Windings

Abstract—This article proposes a new approach to study the frequency response and the transient analysis of power transformer windings. For improved accuracy, the suggested model includes, among other equivalent circuit elements, the mutual magnetic couplings between any winding turn and all others. This implies that the equivalent inductance of any considered turn will be a location-dependent parameter. Accordingly, the winding will be analyzed as a non-uniform transmission line. Through the application of a recursive circuit reduction technique, a closed-form Laplace s-domain analytical expression for the winding's input impedance can be obtained for any neutral treatment. The resulting expression can be used to determine the winding's series and parallel resonance frequencies. The s-domain expression for the input impedance, in connection with the numerical inverse Laplace transform, will be utilized for determination of the winding's time-domain transient response for any input voltage or current time waveform. Accuracy increases with the assumed number of winding sections, which can be even increased to the actual number of turns, limited only by the available computation resources. The results of case studies are in good agreement with those available in the literature using the time-domain solution of the simultaneous differential equations in the state variables.     

汽轮发电机暂态分析中计及励磁电流集肤效应的时步有限元模型

在利用场路耦合时步有限元方法对汽轮发电机暂态过程进行仿真计算时,对励磁绕组模型的考虑,往往通过列写整个回路的电路方程表示;该方法无法准确描述励磁绕组中涡流的分布及其对损耗的影响等问题;为了准确的反映电机暂态过程下励磁绕组中涡流的影响,该文先对励磁绕组中各导体单独列写方程,再利用整个回路的电压方程将其联系起来,同时施加串联约束条件;最终得出考虑串联约束条件下计及涡流分布的励磁绕组新模型及基于该模型下的场路耦合时步有限元方程。以一台300 MW汽轮发电机定子三相突然短路情况为例,采用不同的励磁绕组模型进行时步有限元计算,通过对比分析励磁绕组中的电流分布与瞬时损耗等,说明该方法的合理性。     

Modeling of the Saturated Leakage Reactance of Induction Motors as a Time Varying Parameter for Transient Computations

ABSTRACT

A procedure has been developed for incorporating the saturated leakage reactance of induction motors into starting transient performance evaluation. An empirical formula has been provided for simulating the envelope of the transient current in terms of time. This faciliated to express the transient rmg stator winding current in terms of time. Then saturated leakage reactance is expressed in terms of the transient rms stator winding current, which in turn, made it possible to express the leakage reactance as a time varying parameter. All types of slot openings, i.e., closed slots, semi closed slots and open slots are considered separately. Transient performance of a machine having closed slots on the rotor and semi closed slots on the stator is evaluated using the approach described in this article and the effect of leakage path saturation is demonstrated.     

Transient analysis of an advanced static var compensator using quad-series voltage-source PAM inverters

This paper deals with an advanced static Var compensator (ASVC) using quad-series voltage-source PAM inverters. The ASVC consists of four three-phase voltage-source inverters with a common dc capacitor and four three-phase transformers, each primary winding of which is connected in series with each other. Each inverter outputs a square-wave voltage, while the synthesized output voltage of the ASVC has a 24-step wave shape. This results not only in a great reduction of harmonic currents and dc voltage ripples but also in fewer switching and snubbing losses. In this paper, transient analysis is performed with the focus on the response of reactive power and the resonance between the dc capacitor and ac reactors. Experimental results obtained from a small-rated laboratory model of 10 kVA are also shown to verify analytical results based on the p-q transformation. The analytical results help in the design of system parameters such as the capacity of the dc capacitor and feedback gains.     

Hybrid modelling of inhomogeneous transformer winding for very fasttransient overvoltage studies

This paper presents a novel approach for the modelling of transformer windings, which is valid in the frequency range of 10 kHz to a few MHz. It is a hybrid model; coil-by-coil detailed plus inter-coil black box model. The parameter estimation of the detailed model and the synthesis of the black box model is based on frequency domain measurements. The technique is applied to a high-voltage transformer winding. The comparison of the measurements and the frequency domain simulation of the model with EMTP confirms the validity and accuracy of the model for the intended frequency range. Experiments in the frequency range of several MHz reveal that remarkable overvoltages appear at the connecting point of the inverted and interleaved part of this winding. It is shown that the reason of the VFTO (very fast transient overvoltage) in the MHz range is the inhomogeneity of the winding parts     

VSC-HVDC输电系统的电磁暂态建模与仿真

基于电压源换流器(VSC)的新型直流输电(VSC-HVDC)系统技术优点很多,建立能够准确描述VSC-HVDC动态特性的详细模型及仿真算法对该项输电技术的深入研究具有重要意义,还可为含有VSC-HVDC的电力系统机电、电磁混合仿真奠定基础。为此首先分析了VSC-HVDC的工作原理;利用隐式梯形积分法建立了双端VSC-HVDC的详细电磁暂态仿真模型,并利用一阶惯性环节模拟锁相环测量了VSC交流母线电压相位的动态特性;鉴于对应VSC-HVDC电磁暂态模型的差分方程为右端项含有待求变量的隐式方程,提出了相应的迭代求解数值计算算法。在VSC交流母线电压幅值和相位突变的条件下,通过与PSCAD/EMTDC中所建VSC-HVDC仿真电路电磁暂态响应的对比,验证了VSC-HVDC电磁暂态模型及其数值计算算法的正确性。     

Transient characteristics of a tapped‐winding capacitor motor

Tapped‐winding capacitor motors are widely used for fans in air conditioners as speed adjusting motors. In tapped‐winding capacitor motors, the burnout accidents of phase‐shifting capacitors have been seen on occasion. The cause of such accidents is considered to be the transient capacitor current. In this paper, equations for calculating transient characteristics are derived for three types of tapped‐winding capacitor motors. Based on these equations, transient characteristics are clarified in high‐ and low‐speed winding connections. Further, from the design viewpoint, the effects of the turn ratio and capacitance of the capacitor on the transient characteristics are examined and a procedure for choosing the winding ratio and capacitance of the capacitor is suggested. Using this method, the transient current is shown to decrease by about 40%. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 141(4): 69–77, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10063     

Power Factor Control of Photovoltaic Generation Output for Improving Transient Stability

Because of significant change in environmental policies and electric power deregulation in the last decades, a lot of photovoltaic (PV) generations have so far been installed to the power system in Japan. When a huge amount of PVs generation is installed into the power system, we are very much concerned that the disconnection of the PVs due to a system fault has a big impact on the power system stability and transient voltage stability. So it is important to equip the PV with Fault Ride Through (FRT) function in order to maintain power supply–demand balance. In addition, Dynamic Voltage Support (DVS) function of the PV is effective to recover the voltage after the system fault. However, it is unclear how the PVs which are equipped with the FRT and DVS functions affect transient stability and voltage stability. In this paper, how the power factor of the PV power output affects the power system after a system fault is analyzed using P–δ curve. Then, a new PV power factor control method for improving the transient stability is proposed and its effectiveness is shown by digital simulations on a simple power system model.     

Transient performance improvement of model reference adaptive control: LMI‐based resetting

In this paper, a resetting mechanism is proposed to enhance the transient performance of model reference adaptive control. While the suggested method has a simple structure, it is capable of taking into account both the desired steady‐state behavior and the transient response, simultaneously. Whenever the transient specification is not satisfying, there is a jump in the controller parameters. This jump is determined by designing an optimal reset law. At the reset times, the after‐reset values of parameters are calculated based on a minimization problem. The considered cost function is a mixed H₂/H_∞ criterion, which minimizes the tracking error. The optimization problem is converted to an LMI formulation, and the reset law is designed by solving this LMI at certain reset times. To verify the effectiveness of the proposed approach, simulation results are presented.     

Transient magnetic fields in the superconducting alternator

Contents The Fourier Transform method is used to compute transient magnetic fields in a 1.3 GVA superconducting alternator. The necessary frequency-response functions are measured in a scale-model and are used to show the spatial variation of the transient field. The study brings out the points on the field winding at which magnetic transients will be most severe.

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Transiente Magnetfelder beim Generator mit supraleitender Erregerwicklung

Übersicht Zur Berechnung transienter Magnetfelder bei einem 1,3 GVA Generator mit supraleitender Erregerwicklung wird die Fourier-Transformation verwendet. Die erforderlichen Frequenzgänge werden an einem maßstabgerechten Modell gemessen und daran die räumliche Änderung des transienten Feldes dargestellt. Die Untersuchung zeigt die Punkte stärkster Flußänderung auf der Erregerwicklung.

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List of Symbols B Flux density,T - f Frequency, Hz - f Frequency sampling interval, Hz - F/2 Folding frequency, Hz - i _o (t), I _o (f) Driving-current and its Fourier Transform - i _d (t), I _d (f),i _q (t), I _q (f) d- andq-axis transient stator currents and their Fourier Transforms - N Number of samples in Fourier Transform - S Screening-ratio frequency-response function - T Duration of transient calculated by Fourier Transform, sec - t Time sampling interval, sec - Permeability, H/m - Resistivity, Ohm-m     

Transient model for induction machines with stator winding turnfaults

A transient model for an induction machine with stator winding turn faults is derived using reference frame transformation theory. A state-space representation of the dynamic equations, suitable for digital simulation is provided. Steady-state equivalent circuits are derived, from which the sequence components of the line currents can be estimated as a function of fault severity. Experimental results are provided to validate the derived model     

雷电波侵入XLPE电缆绕组的暂态特性

利用雷电波侵入XLPE电缆绕组的外端口特性得出其暂态等值电路,并进行分析求解.发现避雷器的放电电压和残压越高,电缆绕组上的电压越高;但是侵入波越陡、入口电容越大,反而可能使得电缆绕组上不会出现高于避雷器残压的过电压,有利于电缆绕组的保护.这与传统变压器绕组出现具有余弦振荡性质的过电压有很大不同.对绕组输入模拟雷电波进行实验并使用EMTDC仿真,对比表明电缆绕组在雷电冲击电压作用时外端口特性可用R、C串联支路来近似等效.为这种新型变压器的设计、保护技术提供了参考依据.     

用于特快速暂态仿真的大型电力变压器线圈频域分段建模

针对超高压和特高压电力变压器特快速暂态仿真的需要以及以线匝为单元的多传输线模型难以用于完整绕组的建模、在单一模型中难以在近10MHz频率范围内确定频率依赖参数的问题,提出了一种频域分段建模的方法。在低于4MHz频率范围内采用新型的集总参数RLC电路模型,在高于4MHz频率范围内采用无损多传输线(multitransmission line,MTL)电路模型进行建模,在保证求解准确度的基础上,比单纯采用MTL模型有效降低了求解的复杂度,因而可用于具有大量线匝的绕组的建模。在分段模型中,频率依赖的损耗参数和电感参数可以分别考虑,避免了在单一模型中确定这些参数的困难;同时,在所关心的10MHz以下频率范围内以100kHz,4MHz为2个分界点,从低频到高频分别采用1,10和50kHz3种分辨率求解频域方程,既提高了低频段求解精度,又减少了高频段计算时间。理论分析和实例仿真表明该方法适用于大型电力变压器特快速暂态仿真。     

瞬态不对称负荷下水轮发电机阻尼绕组的温升计算

本文对大型水轮发电机不对称运行时阻尼条的损耗及温升计算进行了研究.文中将阻尼绕组等效为阻抗网络,推导了网络参数的计算公式.采用快速富立叶变换方法进行了阻尼条损耗及温升的计算,给出了空载情况下线间短路和单相对地短路时阻尼条瞬态温升随时间的变化规律.     

Transient simulation technique for studies of self-excited generator systems

This paper presents a digital simulation technique which may be used to study the operations of self-excited generator systems with arbitrary external switching network configurations and to analyze the system transient responses under various system conditions. Using this technique, a mathematical model of the self-excited generator system can be formulated in a generalized, detailed, and compact form. Results from the numerical verifications presented in the paper also illustrate the convenience of this simulation technique.     

特高压自耦变压器的建模和电磁暂态仿真

为了在特高压环境下正确应用变压器差动保护,需要对特高压变压器进行合理建模,并进行相应的电磁暂态仿真。根据三绕组自耦变压器星型等值电路的原理,用电磁暂态仿真软件EMTDC中的统一电磁等效电路(unified magnetic equivalent circuit,UMEC)普通三绕组变压器模型来模拟1000MVA/1050kV三绕组自耦变压器,将特高压变压器参数折算成UMEC模型参数,形成特高压变压器模型。在特高压环境下,分别进行励磁涌流和故障电流仿真,并用于考察应用得最为广泛的2次谐波闭锁的变压器差动保护的动作可靠性。分析表明:当合闸角和剩磁满足一定条件时,特高压变压器三相励磁涌流的2次谐波含量都会在10%以下,即使采用一相制动三相的2次谐波闭锁策略,如果2次谐波门槛值维持在15%～20%,也不能避免差动保护误动;另外,在某些轻微故障的情况下,故障初期故障电流的2次谐波含量成分较高,会使保护动作短暂延迟。     

暂态过电压检测电力变压器绕组匝间短路故障

变压器在运行过程中,其内部初始故障最终有可能发展成灾难性事故,导致设备停运和电网停电,绕组变形被认为是变压器内部的最主要的故障之一。利用变压器运行时遭受过电压信号冲击的特性,提出利用暂态过电压可实现绕组变形故障的在线检测。首先,介绍了该方法的基本原理,在此基础上搭建了验证性试验平台,进行了匝间短路故障模拟试验。试验结果表明,该方法在一定程度上可实现绕组匝间短路故障的检测,具有一定的参考价值。     

有载分接开关工作顺序／过渡时间微机测量装置的研究

介绍有载分接开关工作顺序／过渡时间微机测量装置的研制及应用情况。该装置可带绕组进行测量，能屏幕显示和直接打印测试结果。     

The Similarities of Electrical Machines under Transient Conditions

This paper draws attention to the considerable similarity that exists in electrical machines when operating in the transient mode. An analysis is made of a salient pole synchronous machine, which has a damper winding. Using these equations it is possible to deduce the equations of other types of machines. In this way the similarities are highlighted.     

Three winding transformer s-domain model for modal analysis of electrical networks

This paper describes an s-domain sequence model for three winding transformers to be used in modal analysis of ac networks. The model takes into account off-nominal tap positions and the phase shifts among the windings. The main contribution of this proposed model is to complete the set of s-domain models of electrical system components already developed (loads, transmission lines, generators, harmonic filters, shunt elements) suitable for modal analysis of complex electrical networks. Modal analysis provides an important set of system information that is hard to be obtained using the conventional time simulation and frequency response methods. This information may be effectively used to improve the harmonic performance of electrical networks, to build linear equivalents for harmonic and electromagnetic transient studies and to perform linear dynamic performance analysis.