Algorithm for fast calculating the energization overvoltages along a power cable based on modal theory and numerical inverse Laplace transform

Transient overvoltage caused by energization may damage the insulation in a power cable transmission system. Therefore, overvoltage along the cable should be calculated and evaluated carefully. Calculation based on traditional commercial software is time-consuming, therefore, there is a need to develop a new algorithm to improve the computational efficiency. First, coupled cable conductors are transformed into independent modes through phase-mode transformation. Then, the voltage formula of each independent mode in the complex frequency domain is obtained through Laplace transform. Finally, energization overvoltages along the cable are calculated using numerical inverse Laplace transform (NILT) and mode-phase transformation. The proposed algorithm is applied to a 330 kV cable line with a length of 9.6 km to certify the accuracy and computational efficiency. Compared with frequency dependent phase model (FDPM) in PSCAD/EMTDC, relative errors of the obtained results are less than 1%, and the maximum CPU time consumed is only about 8%. The proposed algorithm can improve the computational speed of cable energization overvoltages greatly on the premise of ensuring accuracy and may be contributing to actual applications.