An Equivalent Surface Current Approach for the Computation of the Series Impedance of Power Cables with Inclusion of Skin and Proximity Effects

Abstract

We present an efficient numerical technique for calculating the series impedance matrix of systems with round conductors. The method is based on a surface admittance operator in combination with the method of moments and it accurately predicts both skin and proximity effects. Application to a three-phase armored cable with wire screens demonstrates a speed-up by a factor of about 100 compared to a finite elements computation. The inclusion of proximity effect in combination with the high efficiency makes the new method very attractive for cable modeling within EMTP-type simulation tools. Currently, these tools can only take skin effect into account.

Skin Effect Modeling in Conductors of Arbitrary Shape Through a Surface Admittance Operator and the Contour Integral Method

“…An explicit expression for Y (p) s can be written in terms of the eigenfunctions of the Helmhotz equations (2) and (5), as shown in [26]. However, this approach is viable only for canonical conductor shapes, for which eigenfunctions are known analytically [26][27][28][29]. For arbitrary shapes, eigenfunctions can only be computed numerically.…”

“…where w (p) is a diagonal matrix of size of N p × N p , where entry (n, n) is the width of the n-th segment of γ (p) . As shown in [27], we can manipulate (39) using (34) and (41) to obtain the partial p.u.l. resistance…”

“…This key idea leads to a simple and efficient formulation. However, since eigenfunctions can realistically be obtained only for canonical geometries, this approach has been restricted so far to circular [26,27], tubular [28], rectangular [26], and triangular conductors [29].In this paper, we show how the surface admittance operator for conductors of arbitrary shape can be efficiently obtained from a simple contour integral, through the so-called contour integral method [30]. While the possibility to extract the surface admittance operator from the contour integral is already known [31], it has been applied only to simple scattering problems [31].…”

Cylindrical multipole expansion for periodic sources with applications for three‐phase power cables

“…where a mn and b mn are the cylindrical multipole coefficients for the regular and the outgoing cylindrical vector waves inside the particular region, respectively, and where r E D i! 0 H and the curl of vector waves is given by (2). Note that in (5) Based on the Fourier integral representation (4) and an application of the Poisson summation formula [17], it follows that the periodic electric dyadic Green's function for the free space can be expressed as…”

“…Hence, the purpose of this contribution is to provide the necessary analytical tools in terms of the periodic electric Green's dyadic and its expansion in cylindrical vector waves [8][9][10]. The cylindrical multipole expansion of a helical current distribution is then readily obtained and can be computed efficiently as an input to other numerical methods such as e.g., the method of moments [2,11]. Explicit formulas as well as an in-depth analysis on the quasi-magnetostatic limit of magnetic diffusion [12] are also given.…”