A semi-definite relaxation approach for partial discharge source location in transformers

Current issues on localization algorithms based on the time difference of arrival (TDOA) for the partial discharge (PD) source include its sensitivity to time delay error, easy local convergence or divergence, and the large amount of computational load and time. A semi-definite relaxation method for PD source location to solve the time delay positioning equations is proposed in this paper, which using the semi-definite programming problem has the characteristic that can ensure obtained the global optimal solution. The proposed method converts nonlinear time delay equations into an equivalent semi-definite programming (SDP) problem by equivalent transformation and rank-1 relaxation firstly. Then use the interior point algorithm to solve the SDP problem that to obtain a unique global optimum solution, and extract a rank-1 component from the global optimal solution of relaxed SDP. Finally, to serve as a good approximate of the original problem for the PD location. The method was used to localize a measured PD source signal in the laboratory, and the results were compared with those of positioning by the Newton-iterative method. The comparison showed that the method can reduce sensitivity for the time delay error as well as effectively solve TDOA location equations, thereby ensuring that the result is a unique global optimal solution with high positioning efficiency. The localization algorithm problem is solved with the unavoidable and difficult-to-locate time delay error.