Fault location of untransposed double-circuit transmission lines based on an improved Karrenbauer matrix and the QPSO algorithm

Some double-circuit transmission lines are untransposed, which results in complex coupling relations between the parameters of the transmission lines. If the traditional modal transformation matrix is directly used to decouple the parameters, it can lead to large errors in the decoupled modal parameter, errors which will be amplified in the fault location equation. Consequently, it makes the fault location results of the untransposed double-circuit transmission lines less accurate. Therefore, a new modal transformation method is needed to decouple the parameter matrix of untransposed double-circuit transmission lines and realize the fault location according to the decoupled modal parameter. By improving the basis of the Karrenbauer matrix, a modal transformation matrix suitable for decoupling parameters of untransposed double-circuit transmission lines is obtained. To address the difficulties in solving the fault location equation of untransposed double-circuit transmission lines, a new fault location method based on an improved Karrenbauer matrix and the quantum-behaved particle swarm optimization (QPSO) algorithm is proposed. Firstly, the line parameter matrix is decomposed into identical and inverse sequence components using the identical-inverse sequence component transformation. The Karrenbauer matrix is then transformed to obtain the improved Karrenbauer matrix for untransposed double-circuit transmission lines and applied to identical and inverse sequence components to solve the decoupled modal parameter. Secondly, based on the principle that voltage magnitudes at both ends are equal, the fault location equation is expressed using sequence components at each end, and the QPSO algorithm is introduced to solve the equation. Finally, the feasibility and accuracy of the proposed method are verified by PSCAD simulation. The simulation results fully demonstrate that the innovative improvement on the basis of the traditional modal transformation matrix in this paper can realize the modal transformation of the complex coupling parameters of the untransposed double-circuit transmission lines. It causes almost no errors in the decoupling process. The QPSO algorithm can also solve the fault location equation more accurately. The new fault location method can realize the accurate fault location of untransposed double-circuit transmission lines.