s-Domain analysis of lightning surges in three-phase systems using nonuniform single-phase line model

Surge response of the transmission tower in a three-phase transmission system is computed using s-domain nonuniform single-phase transmission line modelling. First, tower top voltage is obtained considering the tower and the ground wire by excluding the effect of the phase conductors, and then the induced voltages on the phase conductors as a result of the current flowing through the ground wire are computed using the magnetic coupling between the ground wire and the phase conductors. The first step of the analysis is the formulation of the system response in the s-domain, and the second step is the frequency to time domain conversion, which is carried out using fast inverse Laplace transform (FILT). The voltages on the phase conductors and the voltages across the tower insulators are computed, and some of the results obtained using s-domain analysis are compared with those obtaining using electromagnetic transients program (EMTP). The effect of frequency dependence of the line parameters is investigated.     

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.     

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.     

Efficient frequency-domain modelling and simulation of nonuniform coupled transmission lines: application in transient analysis of VLSI circuits

A new method of analysis of the transients in nonuniform lossy multiconductor transmission lines with frequency-dependent parameters is presented. The terminations may be nonlinear, and the interconnections networks are arbitrary. The method of the solution is based on steplines approximation of the nonuniform transmission lines and quasitransverse electromagnetic mode (quasi-TEM) assumptions. Using steplines approximation, the system of coupled nonuniform transmission lines is subdivided into an arbitrarily large number of coupled uniform lines (steplines) with different characteristics. Then, using the modal decomposition method, the system of coupled partial differential equations for each step is decomposed into a number of uncoupled ordinary telegraph equations, which are then solved in the frequency domain. Thereafter each step of the system is modelled as a linear filter with frequency-dependent coefficients. The terminations for linear and nonlinear cases are then modelled as linear or nonlinear systems. Finally, the transfer matrix of the system is obtained. Some examples from the literature are then solved to demonstrate the validity of the method. The method proposed here is very fast and can easily be implemented using general-purpose software packages like MATLAB.     

传输线时域响应格林函数分析法与数值拉普拉斯反变换方法的对比研究

为了更真实地反映传输线终端响应,本文推导了一种通过求解传输线网络节点导纳方程求解终端响应的格林函数法。为验证该方法的正确性与实用性,将其与数值拉普拉斯反变换法(NILT)求解传输线终端响应方法进行了对比,分别用上述两种方法对无损终端匹配及有损终端不匹配传输线瞬态电压响应进行了仿真。经对比看出,格林函数方法仿真结果与实际终端响应的吻合度非常好,误差较小,波形稳定;而数值拉普拉斯反变换的方法,在零点附近有很大的冲击及微弱振荡,在仿真结果后期有明显的衰减,中期的误差近似呈正弦变化,后期误差明显增大,难以反映实际终端响应。所以格林函数法更适用于传输线的时域终端响应分析,比NILT方法更具优势。     

Sensitivity analysis of lossy nonuniform multiconductor transmission lines based on the Lax‐Wendroff technique

This paper applies the Lax‐Wendroff technique, usually used in fluid dynamics, to transmission line sensitivity analysis. A second‐order‐accurate Lax‐Wendroff difference scheme for sensitivity analysis of both uniform and nonuniform transmission lines is derived. Based on this scheme, a new method for analyzing multiconductor transmission line sensitivity, which does not need to be decoupled, is presented by combining with matrix operations. Using numerical experiments, the proposed method is compared with the characteristic method and the fast Fourier transform approach. With the presented method, the sensitivity of a nonlinear circuit including nonuniform multiconductor transmission lines is analyzed and the results are verified by the HSPICE perturbation method. The proposed method can be applied to either linear or nonlinear circuits, which include lossy nonuniform multiconductor transmission lines and is proved to be efficient. Copyright © 2009 John Wiley & Sons, Ltd.     

含二次项型非均匀传输线网络的灵敏度分析

应用科罗达等效方法可将二次项型无损耗非均匀线用无损耗均匀线及集中参数元件组成的等效电路表示。该文利用伴随网络法和基于科罗达等效的等效电路，提出了二次项型无损耗非均匀线的频域灵敏度分析方法，采用类似拉氏反变换的方法获得了无损耗非均匀线的时域灵敏度公式：以无损耗非均匀线的灵敏度公式为基础，通过集中处理非均匀线的损耗，推导出了二次项型有损耗非均匀线的频域和时域灵敏度公式，为解决求解含这类非均匀线网络的灵敏度提供了一种途径。     

Quasi-modes multiphase transmission line model

This article presents a new model to represent transmission lines including the frequency dependence of longitudinal parameters. The model uses the natural modes, for ideally transposed lines, and ‘quasi-modes’ for non-transposed lines, and is applied to lines that have a vertical symmetry plane. The line is represented through π-circuits, with one π-circuit for each mode. The transformation matrix is modeled using ideal transformers. The model is described for three-phase lines, dc lines, double three-phase lines and six phase lines. A 440 kV three-phase transmission line illustrates it and is compared with a frequency dependent EMTP line model, the Semlyen one.     

High-frequency propagation on nonuniform multiconductor transmission lines in uniform media

The asymptotic form, for high frequencies, of the equations of propagation on a nonuniform N-conductor transmission line is considered. Under the assumption of perfect conditions in uniform, isotropic media, all N propagation velocities are the same, but the characteristic impedance matrix is allowed to vary with position along the line. Closed-form solutions are obtained for some cases of interest.     

高铁穿越风引起的输电线路振颤研究

跨高速铁路输电线路的断线事故是影响电力系统安全的重要因素之一。通过建立跨高铁区段输电线路有限元模型,分析了高铁穿越线路过程中的流场扰动,计算了线路风载荷与导(地)线的动力特性。采用数值模拟方法,建立了不同高度、档距的工况组合,研究时域内输电线路的振动响应特征,同时考虑了列车时速与车身长度的影响,并进行了现场测量验证。结果表明,高铁穿越引起的流场扰动将引起十余秒的线路振颤,且振动频率接近线路模态自振频率,易引发线路共振。升高线路高度、减小档距可减轻线路振颤现象。本文结果对跨高铁输电线路结构设计的理论研究有重要意义。     

不受波速影响的特高压直流输电线路单端故障测距方法

现行特高压直流输电线路故障测距大多采用行波法,但单端/双端行波测距受行波波速影响较大,加上输电线路弧垂效应,测距精度较差。利用对端行波到达本端测距装置的时刻,通过公式推导消除行波波速的影响,推导出一种不受波速影响的特高压直流输电线路单端故障行波测距方法,将无需准确计算线路沿线波速也能实现直流输电线路故障测距。在PSCAD/EMTDC中搭建哈郑±800 kV特高压直流输电系统模型,在不同故障位置和不同过渡电阻下进行仿真。大量仿真结果表明,该改进单端测距方法不受输电线路沿线波速和故障位置影响且耐受过渡电阻能力强。     

确定非均匀传输线网络时域灵敏度的伴随网络法

基于模量分析、特征值灵敏度和数值逆拉普拉斯变换技术,提出采用伴随网络法计算含有耦合均匀与非均匀传输线网络的时域灵敏度。通过求解原网络方程和伴随方程,可一次计算出任意输出对网络元件以及传输线电气参数的灵敏度,与扰动法相比效率更高。通过仿真实例与采用扰动法的计算结果进行比较,验证了所提方法和公式的正确性。     

A practical method for evaluation of ground fault currentdistribution on double circuit parallel lines

The paper presents an original analytical procedure for quick and, for practical purposes sufficiently accurate evaluation of the principal components of the ground fault current. The procedure is valid for faults at any of the towers of a double 3-phase circuit line with an arbitrary number of spans. The method is obtained by application of relatively simple and exact equations for uniform ladder circuits of any size (for any number of pis, from one to infinity) and for any terminal conditions. The method can be applied to solve several practical problems: the evaluation of the maximum substation grounding system fault current, the selection of a ground wire capable of withstanding the fault currents and the prediction of step and touch voltages near the transmission towers. In the case of a double circuit 3-phase line, the solution of these problems is additionally complicated by the mutual inductive coupling between the two parallel lines     

利用双端不同步数据的高压输电线路故障测距实用算法及其实现

利用单侧电压电流工频分量的输电线路故障测距算法,进行双原系统的线路故障定位时,远端系统等值阻抗变化对测距精度的影响时我法克服的。中提出一种双电源系统的高压输电线路故障定位的实用算法,其特点为：（１）两端数据不必同占;（２）用于短、中等长度线路时,不需要迭代求解,即定位方程为一个算式;（３）不需要区分故障类型;（４）该方法适用于换位线路、不换位线路以及双回线路。     

PMU-based Fault Location Technique for Three-terminal Parallel Transmission Lines with Series Compensation

Abstract

This study introduces a fault location technique for three-terminal series-compensated untransposed parallel transmission lines utilizing the three terminals’ synchronized data. The proposed technique is applicable for short or long lines as distributed parameter line model is employed and the potential couplings are considered. The fault location for both uncompensated line sections is obtained adopting previously introduced fault location technique. The faulty phases are required initially to be recognized for series-compensated transmission line. The adopted fault location technique for series-compensated line section is derived based on the resistive nature of the fault impedance. The obtained fault locations for each line section are compared with each other to distinguish the faulty branch and obtain the fault location. DIgSILENT Power Factory and MATLAB programs are utilized for simulation studies and required calculations. The obtained results prove the efficacy of the introduced technique.     

A novel fast distance relay for long transmission lines

The measuring accuracy and the measurement stability of conventional distance relay will be influenced by complex and remarkable harmonic components due to the large capacitance of the line when it is used for a long line. Correspondingly, the tripping speed will be delayed to some extent. To solve this problem, a fast distance relay for long transmission lines is presented, which is on the basis of the differential equation algorithm using π transmission line model and the theory of Equal Transfer Process of Transmission Lines (ETPTL). The shortcomings of π model differential equation algorithm due to the impact of high frequency components can be overcome by using a low-pass filter. The problem resulting from the difference between the transfer feature of the voltages used by the distance protection and that of the currents due to the transient characteristic of coupling capacitor voltage transformers (CCVT) can be solved by using virtual digital CCVT. Then, the new distance relay can trip quickly by re-structuring the voltage at the fault point and iterative calculations. A variety of ATP simulation tests show that the new relay has fast tripping speed and high reliability when applied to the long transmission lines.     

Statistical variation of currents in overhead transmission lines

Knowledge of the statistical variation of the current in an overhead transmission line is required in order to calculate the probabilistic heating and the cumulative loss of tensile strength of the conductors. However, although some utilities may record the statistical variation of the currents in their transmission lines, there is very little published information on this subject. This paper presents cumulative frequency distributions of line currents recorded over a period of 1 year for eight lines on three continents. The distributions are then normalized in terms of the ratio of the current to a reference current. Reference currents used are: the maximum current, the median current, the mean current, the modal current, and the current that is exceeded for 50% of the total time. The modal currents are found from the probability density functions of current. The normalized distributions are compared with one another, and it is found that the distributions of I/I_mean and I/I₅₀ have the lowest dispersion. Algorithms are derived to calculate the distributions for various degrees of loading of lines. The distributions are also compared with those obtained with constant temperature of the conductors.     

Practical method for evaluating ground fault current distributionin station, towers and ground wire

The paper presents an original analytical procedure which enables a quick and, for practical purposes sufficiently accurate evaluation of the significant parts of the ground fault current, for a fault at any of the towers of a transmission line of an arbitrary number of spans. The advantages of the method are the simplicity and accuracy of the formulae for solving uniform ladder circuits of any size (from one up to an infinite number of pis) and any terminal conditions. The formulae are obtained by applying the “general equations of the line represented by discrete parameters” on a specific electrical circuit formed by a transmission line ground wire during ground faults. The presented method is suitable for analyses aimed at evaluating the maximum substation grounding system fault current, at selecting the ground wire capable of withstanding the fault currents and at the prediction of step and touch voltages near transmission towers     

风电场并网输电线路单相接地故障单端测距方法

采用故障后及单相跳闸后2个时间断面的信息构建方程描述输电线路两侧断路器之间的网络拓扑,能够实现输电线路故障单端精确测距。但该方法假设2个时间断面下量测点对端系统阻抗保持不变且故障支路恒定,使得现有立足风电场并网输电线路系统侧开展测距的常规做法失效。针对该问题,提出了立足风电场侧面向于系统侧开展测距研究的思路,克服了量测点对端系统阻抗在2个时间断面下变化的问题;针对测距算法中使用迭代搜索解法带来的风电场侧电流量测值偏小导致的高阻故障测距精度显著下降的问题,提出了不受故障类型影响的直接求解方程测距新算法,能够直接计算得到故障距离和过渡电阻值,不仅实现了精确测距且对于后续的自适应重合闸研究提供了新思路。     

Evaluation of voltage and current profiles and Joule losses for a half-wavelength power transmission line

Half-wavelength lines (HWLLs) have been studied as an option to be applied to power transmission regarding line lengths around 2500 km for a 60 Hz frequency. The main advantage of this type of transmission line, which has not yet been put in commercial operation in any country, is the elimination of reactive compensation, which contributes to cost reduction if compared to a conventional ac transmission. This paper presents a demonstration of voltage and current magnitude profiles along the line, using phasors and graphic calculations. In addition, an algebraic expression for Joule losses is proposed, to be used in economical evaluation of a HWLL solution.