Electromagnetic Dispersion Modeling and Analysis for Power Cables

Abstract: This thesis addresses electromagnetic wave propagation in power cables. It consists of five papers, where the three first papers are based on one and the same model, and the last two papers are based on a similar but slightly different model. The first model considers electromagnetic modeling in connection with basic transmission line theory with a mismatch calibration of the scattering parameters, while the second model is based on a magnetic frill generator with calibration on the input current.The two models describe the dispersion characteristics of an 82 km long High Voltage Direct Current (HVDC) power cable, and the results are validated with Time Domain Reflectometry (TDR) measurements. In both models the relevant bandwidth is 100 kHz, with the result that the fields inside the metallic layers must be calculated due to a large skin-depth. The present study is concerned with Transversal Magnetic (TM) modes of order zero. Higher order TM modes, including the Transversal Electric (TE) modes, will essentially be cut-off in this low-frequency regime.An asymptotic analysis regarding the low-frequency dispersion characteristics is provided in Paper I. Comparing the result with a numerical solution shows that the low-frequency characteristics of the power cable is complicated, and an asymptotic solution is only valid at frequencies below 1 Hz.Paper II presents a sensitivity analysis of the propagation constant. It is concluded that some of the electrical parameters of the metallic layers, and of the insulating layer, have a large impact on the model, while other parameters do not perturb the model in any substantial way.In Paper III a general framework for the electromagnetic modeling is provided. The paper addresses sensitivity analysis, computation, and measurements regarding wave propagation characteristics in power cables.The asymptotic behavior of the non-discrete radiating mode, the branch-cut, is presented in Paper IV. The result is compared with the first and second propagating Transversal Magnetic (TM) mode.Finally, Paper V addresses the numerical problems associated with large arguments in the Bessel functions, which are due to the large conductivity parameters of the metallic layers. The introduction of a perfect electric conductor (PEC) and a short illustration of an inverse problem are also discussed in the paper. At the end an analysis is presented regarding uncertainties in the model parameters, which shows that temperature is an important parameter to consider.