Utkarsh R. Patel

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

We present a fast 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 speedup 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 EMTPtype simulation tools. Currently, these tools can only take skin effect into account.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 skin and proximity effects. The application to a three-phase armored cable with wire screens demonstrates a speedup 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 Electromagnetic Transients Program-type simulation tools. Currently, these tools can only take skin effect into account.

Proximity-Aware Calculation of Cable Series Impedance for Systems of Solid and Hollow Conductors

Wideband cable models for the prediction of electromagnetic transients in power systems require an accurate calculation of the cable series impedance as a function of frequency. A surface current approach was recently proposed for systems of round solid conductors, with the inclusion of skin and proximity effects. In this paper, we extend the approach to include tubular conductors, allowing to model realistic cables with tubular sheaths, armors, and pipes. We also include the effect of a lossy ground. A noteworthy feature of the proposed technique is the accurate prediction of proximity effects, which can be of major importance in three-phase, pipe-type, and closely packed single-core cables. The new approach is highly efficient compared to finite elements. In the case of a cross-bonded cable system featuring three-phase conductors and three screens, the proposed technique computes the required 120 frequency samples in only six seconds of CPU time.

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

An accurate modeling of skin effect inside conductors is of capital importance to solve transmission line and scattering problems. This paper presents a surface-based formulation to model skin effect in conductors of arbitrary cross section, and compute the per-unit-length impedance of a multiconductor transmission line. The proposed formulation is based on the Dirichlet-Neumann operator that relates the longitudinal electric field to the tangential magnetic field on the boundary of a conductor. We demonstrate how the surface operator can be obtained through the contour integral method for the conductors of arbitrary shape. The proposed algorithm is simple to implement, efficient, and can handle arbitrary cross sections, which is the main advantage over the existing approach based on eigenfunctions, which is available only for canonical conductors shapes. The versatility of the method is illustrated through a diverse set of examples, which includes transmission lines with trapezoidal, curved, and V-shaped conductors. Numerical results demonstrate the accuracy, versatility, and efficiency of the proposed technique.

MoM-SO: A Complete Method for Computing the Impedance of Cable Systems Including Skin, Proximity, and Ground Return Effects

The availability of accurate and broadband models for underground and submarine cable systems is of paramount importance for the correct prediction of electromagnetic transients in power grids. Recently, we proposed the MoM-SO method for extracting the series impedance of power cables while accounting for the skin and proximity effects in the conductors. In this paper, we extend the method to include ground return effects and to handle cables placed inside a tunnel. Numerical tests show that the proposed method is more accurate than widely used analytic formulas, and is much faster than existing proximity-aware approaches, such as finite elements. For a three-phase cable system in a tunnel, the proposed method requires only 0.3 s of CPU time per frequency point, against the 8.3 min taken by finite elements, for a speed up beyond 1000 X.

Accurate Impedance Calculation for Underground and Submarine Power Cables Using MoM-SO and a Multilayer Ground Model

Accurate knowledge of the per-unit length impedance of power cables is necessary to correctly predict electromagnetic transients in power systems. In particular, skin, proximity and ground return effects must be properly estimated. In many applications, the medium that surrounds the cable is not uniform and can consist of multiple layers of different conductivity, such as dry and wet soil, water, or air. We introduce a multilayer ground model for the recently proposed MoM-SO method, suitable to accurately predict ground return effects in such scenarios. The proposed technique precisely accounts for skin, proximity, ground, and tunnel effects, and is applicable to a variety of cable configurations, including underground and submarine cables. Numerical results show that the proposed method is more accurate than analytic formulas typically employed for transient analyses, and delivers an accuracy comparable to the finite-element method (FEM). With respect to FEM, however, MoM-SO is over 1000 times faster, and can calculate the impedance of a submarine cable inside a three-layer medium in 0.10 s per frequency point.

A single-source surface integral equation formulation for composite dielectric objects

This paper presents a single-source equivalence formulation to solve for the scattering from composite dielectric objects. In the proposed formulation, all regions of the composite dielectric object are replaced by the surrounding free space medium and an equivalent electric current density on their boundary. Since the formulation only uses a single equivalent current source, it requires 4 times less memory storage than the PMCHWT formulation, and could result in up to 8 times faster solution time.

A Novel Single-Source Surface Integral Method to Compute Scattering From Dielectric Objects

Using the traditional surface integral methods, the computation of scattering from a dielectric object requires two equivalent current densities on the boundary of the dielectric. In this letter, we present an approach that requires only a single current density. Our method is based on a differential surface admittance operator and is applicable to dielectric bodies of arbitrary shape. The formulation results in four times lower memory consumption and up to eight times lower time to solve the linear system than the traditional Poggio–Miller–Chang– Harrington–Wu–Tsai (PMCHWT) formulation. Numerical results demonstrate that the proposed technique is as accurate as the PMCHWT formulation.

Inclusion of Wire Twisting Effects in Cable Impedance Calculations

Cable-series impedance modeling is widely applied in electromagnetic transients simulations and power-loss calculations. The calculations are usually performed in a 2-D frame using the finite-element method or alternative approaches, such as MoM-SO, thereby losing the 3-D effects imposed by twisting wire screens and armors. One of the implications of using 2-D modeling for three-core and closely packed single-core cables is that currents will always circulate among the individual wires of each wire screen or armor. However, in the case of twisted screens/armors where the wires are insulated from each other, such current circulation will in reality not exist. As a result, the calculated impedances become incorrect as well as the induced currents and losses on individual conductors. A procedure is introduced for preventing such false current circulations in a 2-D calculation frame by simple manipulation of the system impedance matrix. The approach is demonstrated for the modeling of single-core and three-core cables, with and without external armor. It is shown that the representation of the wire screen/armor armor with respect to current circulations can substantially influence the calculated result, both for the 50/60 Hz impedance and the cable transient behavior. The use of tubular screen representations is also investigated.

Analysis of radiating microstrip structures using the contour integral method

In this paper, we discuss the possibility of numerically solving electromagnetic radiation problems from microstrip structures with only contour discretization of the radiating elements. We demonstrate that such a numerical method can be realized by exploiting the underlying physics of microstrip surfaces, and combining the so-called contour integral method with the equivalence principle. Such a numerical technique requires fewer unknowns and can potentially lead to significant computational savings in the simulation of large microstrip structures such as arrays, reflectarrays, metasurfaces, etc. Preliminary results show that the technique can accurately predict the input impedance and radiation pattern of a patch antenna in an array environment.

Fast parameter extraction for transmission lines with arbitrarily-shaped conductors and dielectrics using the contour integral method

This paper presents an accurate surface formulation based on the contour integral method and the Dirichlet-to-Neumann operator to calculate the impedance and admittance parameters of transmission lines of arbitrary shape. The formulation only requires a discretization of the boundaries of the conductors and dielectrics, as opposed to the entire cross-section, which results in fast computations.