Transient analysis of heat dissipation due to a HVDC groundelectrode

The temperature of the soil surrounding a high-voltage direct-current (HVDC) ground electrode was computed at various points in time using finite difference methods. The temperature response for various ground electrodes was computed using these same techniques. The results were then compared with results obtained experimentally in a laboratory. It is suggested that peak temperature calculations may be desirable for periodic short-term operation of a HVDC ground electrode. Since the surrounding soil temperatures may not have reached a steady state, a transient analysis may be necessary     

水平分层土壤中矩形混凝土任意形状复合接地网电阻的计算

对水平分层的多层土壤，先使用等效电阻率的方法，将水平多层土等效为二层土壤，然后对矩形混凝土内任意形状的复合接地网的接地电阻，提出2种处理方法，第1种方法是建立分界面上的积分方程，然后用矩量法离散，并用有限面积来代替二层土壤无限大分界面进行求解．第2种方法是用无穷多个镜像代替二层土壤的作用，将二层土壤中的基础接地问题化为均匀土壤中的基础接地问题进行求解．应用静电场和恒定电流场的相似性，论述了第1种方法的实现过程，包括积分方程的建立，矩量法离散，奇点的处理，以及离散后的代数方程式等．编制了能计算矩形混凝土内任意形状复合地网接地电阻的程序，用文献[1，2]的计算结果，检验了方法的正确性．     

Measurements and computations of the performance of groundingsystems buried in multilayer soils

The resistances and earth potentials of two Florida Power Corporation electric substation grounding systems buried in soils with multiple horizontal layers were computed and measured at various phases of their installation, i.e., starting from a one mesh grid to the final design consisting of many regular meshes. Soil resistivity at each site was measured and interpreted to obtain equivalent two-layer and multilayer earth structures. It is shown that good agreement is obtained between the measured and computed values if multilayer earth structure models are used in the computations. Poor agreement results when uniform soil models are considered     

Grounding resistance measurement using fall-of-potential methodwith potential probe located in opposite direction to the current probe

This paper presents errors in grounding resistance measurement using the fall-of-potential method with the potential probe located in the opposite direction to the current probe. Errors are obtained with computer simulation. Such ground electrodes as a counterpoise, a grid, a rod and a combination of them are considered here. The soil is supposed to be extended to two-layer structure. Numerical results are computed by the current source simulation method and the method of images     

Method for calculating the ground resistance of grounding grids using FEM

Taking as given that ground resistance is independent of earth fault current, this paper presents a new way of calculating ground resistance of grounding grids using the finite-element method (FEM). Ground resistance is calculated by means of three consecutive tests, with an acceptable number of elements, and fast resolution. The results of the proposed method are compared with those measured experimentally or determined by other authors. Once ground resistance and earth fault current are known, grid potential and touch-and-step voltages are calculated. The main advantage of the method proposed here is that it permits us to analyze symmetrical and nonsymmetrical grids of any shape in uniform, two-layer, and multilayer soils. The method developed in this paper constitutes a fast-resolution industrial application, with acceptable results, for calculating the ground resistance of grounding grids of any shape.     

特高压直流输电接地极附近的土壤结构对变压器直流偏磁的影响

“十二五”期间,我国将全面推广特高压直流输电线的建设,许多新的科学、技术问题出现.我国幅员广阔,土地结构复杂,因此针对不同的土壤结构对特高压直流接地极地表电位、中性点接地的变压器偏磁进行了研究.首先建立了水平双层土壤模型及其地表电位计算公式,以6种不同的土壤为例,分别流入3000、4500和5000 A直流电流,计算了距离其接地极不同距离的地表电位,根据地表电位计算了偏磁电流的大小,分析了偏磁电流对变压器励磁电流畸变率的影响.结果表明:土壤电阻率越大,流入变压器的直流电流越大,引起的直流偏磁现象越严重,以双层土壤为例,当第2层土壤电阻率从1000?·m增加到3000?·m 时,偏磁电流畸变率从24.2%增加到36.5%.随着接地点距离变压器中性点距离的增大,地电位减小,当距离大于60km 时,地表电位趋近于零.在选择变电站的站址时,需要根据土壤结构计算偏磁电流及其畸变率,确定合理站址     

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.     

一类垂直双层土壤中地网接地电阻的简易计算公式

针对特高压输电系统变电站地网常跨越垂直分层土壤,研究垂直双层土壤中地网接地电阻的工程计算方法。用待求接地电阻与参考电阻的比值以及双层土壤两侧电阻率比值减少参数数量,并通过数据拟合得到这两个比值的函数关系,分析自变量等于1和趋向无穷大对应的地网接地电阻和土壤结构获得函数系数的表达式,将表达式代入函数之后进行化简,得到垂直双层土壤中地网接地电阻的计算式。计算式中包含的参考电阻和辅助电阻都是均匀土壤中地网接地电阻,这两个接地电阻可用IEEE标准或中国电力行业标准的推荐公式代替。与仿真软件相比,所得式不需建立土壤和地网模型,不需要仿真计算电流分布,能简单快捷地计算出接地电阻。通过几个算例分析可知,所得计算式的精度受推荐公式的影响,其精度能满足工程设计的需要。     

Two-layer soil model for power station grounding system calculation considering multilayer soil stratification

Two-layer soil models are commonly used for the design of power station grounding systems. Calculations based on such models usually give correct values for the gound resistance of grounding electrodes and for the step and touch potentials on the surface of the ground. However, the two-layer model of the actual soil can give absurd results if incorrect values of the layer resistivities and the first layer thickness are used. Conventional methods of fitting the apparent resistivity curve in order to obtain those parameters do not give good results in all cases. This may happen when the soil has a multilayer structure and certain combinations of different layer resistivities exist. In this paper, an analysis of critical cases was carried out, and a novel calculation method for the parameters of the two-layer soil model is presented. The proposed method is valid for an arbitrary number of soil layers with arbitrary values of resistivity, and it is applicable to simple as well as complex grounding systems. The numerical results of this method were compared with electromagnetic field calculations carried out with a computer program based on the finite-element method. The proposed model permits the use of computer programs based on the method of images and a two-layer soil model for the design of station grounding systems buried in horizontal multilayer soil stratifications. Thus, the risk of serious calculation errors that may appear by application of the apparent resistivity fitting method can be avoided.     

计算双层土壤参数的一种新方法

针对接地系统电气参数计算需要建立准确的大地模型和土壤参数问题,分析了水平分层土壤结构的地表电位,定义了土壤的视在电阻率,建立了土壤模型目标函数,并对建立的函数模型进行了最优化计算.计算分析结果表明,采用改进的Levenberg - Marguardt最优化方法计算所得的双层土壤模型可以反映实际地下土壤分层状况,可快速求出双层土壤参数.     

Magnetic field distribution around a current-carrying conductor above a two-layer ground

The present work is aimed at calculating the magnetic field around a current-carrying conductor positioned in air at a given height above a two-layer ground. The method is based on the successive imaging technique. A three-phase transmission model was constructed to simulate three-phase transmission line above a two-layer ground. The measured magnetic fields agreed reasonably with those calculated for one- and two-layer ground models. The proposed method of calculation is extended for magnetic field assessment in AC substations. The effect of magnetic ores in the top-layer of the ground on substation magnetic field values is discussed.     

Analysis of apparent resistivity in a multi-layer earth structure

An expression for the apparent resistivity in an earth structure with an arbitrary number of layers is derived for the Wenner four-electrode method. The expression is arrived at by performing an analysis of apparent resistivity in a multilayer structure as an extension of studies that have concentrated on the two-layer model. Applying a series of parameter data to this expression enabled the preparation of ρ-a curves for such a multilayer structure, and these curves were compared with actual ρ-a curves obtained from two case studies. The results showed good agreement, indicating that the proposed expression and parameter estimation technique could be practically applied to ground design problems. In particular, earth parameters for a multilayer structure obtained through the proposed method can be used for calculating the ground resistance required by deep-driven rods in a particular geologic formation     

Interpretation of resistivity sounding measurements in N-layer soilusing electrostatic images

Geophysical inversion involves the estimation of soil parameters from a set of observations. Multilayer soils are modeled by N horizontal layers with distinct resistivities and depths. For known soil parameters, the apparent resistivity distribution can be computed efficiently from electrostatic images. Since the model responses are generally nonlinear functions of the model parameters, least-squared minimization techniques prove to be useful for evaluating layer resistivities and depths to agree with measurements. This paper demonstrates how electrostatic images can be combined for increasing efficiency in the computation of apparent resistivities and sensitivity factors such as the first and second gradient of the distance with respect to the model parameters. The factors are then used to solve the more demanding task of resistivity interpretation of measurements from Wenner, Schlumberger, Dipole or alternate electrode configurations. Results are presented for two-layer soil and for actual cases with three layer soil     

Nonuniformity correction factors for maximum mesh- andstep-voltages of ground grids and combined ground electrodes

Correction factors for calculating maximum mesh and step voltages associated with grid and combined grid-multiple rod ground electrodes are defined and calculated for a wide set of ground electrodes and various two-layer soil structures. The results obtained are presented as graphs appropriate for a straightforward practical application. Empirical expressions for correction factors matching well with the calculated data are also proposed providing an insight in the most effective ground electrode parameters which might be important in the design process     

双层Halbach永磁电机解析建模与优化

提出双层Halbach永磁电机的二维解析模型,模型中转子永磁包括内外两层,每层每极均由两块永磁构成,且每层中间磁块均为径向磁化。通过分区域求解标量磁位的微分方程,解析得到双层Halbach无槽电机的气隙磁场。利用卡特系数考虑齿槽作用,解析获得双层Halbach有槽电机的气隙磁场。接着,为优化气隙磁场波形,分别解析获得外层径向磁化磁块的最优极弧比和内层径向磁化磁块的最优极弧比,从而获得双层Halbach电机气隙磁场的优化解。计算结果表明,双层Halbach电机不仅气隙磁场和反电势的波形正弦度都优于单层Halbach电机,而且电磁转矩的波动更小,因此具有更好的电磁性能。二维有限元法与二维解析法计算结果一致性较好,验证了二维解析模型的正确性。     

接地装置地表铺设复合高阻层对保护人身安全的影响

在接地工程中通过在地表铺设防护层来提高人体的耐受能力是一种经济有效的方法。在传统铺设单一高阻层的方法基础上,提出了高阻层和低阻层的复合层防护方法。基于地电位对人身安全的作用机理、人体耐受电流的影响因素等全面分析了复合高阻层的特点和有效性,并分析了复合层参数对地表电位、接触电位差、跨步电位差、大地等效电阻、人体耐受限值等影响。研究表明:在高阻层的下面增设低阻层对接地电阻、接触电势的影响很小,但可以显著降低跨步电位差,原始土壤电阻率越高,低阻层的效果越好。低阻层的厚度取0.1~0.2 m时,即使其电阻率达50 Ω·m也具有良好的降低跨步电势的效果,布置位置比较灵活。     

Heat dissipation computations of a HDVC ground electrode using asupercomputer

The temperature of soil surrounding a high-voltage direct current (HVDC) toroidal ground electrode of practical dimensions in both homogeneous and nonhomogeneous soils was computed at incremental points in time using finite-difference methods on a supercomputer. The results obtained validated the expected result, that the time constant of the system is large, requiring long-term and short-term simulation curves, as shown. It is concluded that by being able to compute the thermal response and by calculating the thermal time constant, the option for possible improved design is available     

基于云遗传算法的接地网优化设计

在双层土壤结构和不等电位模型的基础上,研究了按指数规律布置接地导体的可行性,建立了最大接触电压值达到最小的目标函数,并利用云遗传算法求取最优解。该方法采用自适应算法和云模型建立交叉和变异概率,得到地网横向和纵向最佳压缩比,从而获得接地网拓扑结构。变电站接地网计算实例表明,该方法具有快速寻优能力,优化布置后的接地网消除了等间距布置出现的边缘效应和邻近效应,能有效地均匀地表电位分布,降低最大接触电位差。     

Resistance to earth of earthing grids buried in multi-layer soil

Expressions for the resistance to earth of earthing grids buried in uniform, two- and three-layer soils are proposed based upon the examination of a large set of grids and soil structures using the finite-element approach. Simple empirical correction factors are introduced to modify the earth resistance formulae for uniform soil to account for the multi-layer soil structure. A comparative analysis of available expressions for uniform and two-layer soils is performed in order to check their applicability in various cases.     

A Two-Layer Soil Model for the Calculation of Electrical Parameters of Grounding Systems under Lightning Strikes

This article aims to overcome the drawback of the consideration a uniform soil model in approaches based on the transmission line model by considering a two-layer soil structure. In this regard, the electrical parameters equations for the two-layer soil model based on the method of images in the literature which are suitable for power frequency waves are developed to be applicable to the lightning studies. Also, the developed equations are then used in the multiconductor transmission line approach to study the lightning behaviors of grounding systems. Furthermore, in order to check the validity of the procedure, the results of the multiconductor transmission line approach are compared with those obtained by the electromagnetic field approach through the simulation of horizontal, vertical and mesh grounding grids. The results show the accuracy of the two-layer soil model for the lightning analysis of grounding systems.