Electromagnetic dispersion modeling and measurements for HVDC power cables

This paper provides a general framework for electromagnetic modeling, computation and measurements regardingthe wave propagation characteristics of High-Voltage Direct Current (HVDC) power cables.The modeling is focused on very long (10 km or more) HVDC power cables andthe relevant frequency range is therefore in the low-frequency regime of about 0-100 kHz.An exact dispersion relation is formulated together with a discussion on practical aspectsregarding the computation of the propagation constant and the related characteristic impedance.Experimental time-domain measurement data from an 80 km long HVDC power cable is used to validate the model.It is concluded that a single-mode transmission line model is not adequate to account for the mismatch between the power cableand the instrumentation.A mismatch calibration procedure is therefore devised to account for the connection between the measurement equipmentand the cable. A dispersion model is thus obtained that is accurate for early times of pulse arrival.To highlight the potential of accurate electromagnetic modeling, an example of high-resolution length-estimation is discussedand analyzed using statistical methods based on the Cram\'{e}r-Rao lower bound.The analysis reveals that the estimation accuracy based on the present model (and its related model error)is in the order of 100 m for an 80 km long power cable, and that the potential accuracy using a ``perfect'' model based on the givenmeasurement data is in the order of centimeters