Abstract: The complex multi-path propagation of local discharge ultrasonic signal in a power transformer may significantly affect the diagnosis and location performance of local discharge sources by the detection devices. To improve the accuracy and anti-interference of the local discharge location of power transformer, a method of PD location of transformer was proposed under the condition of the complex multi-path transmission. Firstly, the local discharge location model was constructed by analyzing the refraction and diffraction propagation path of the local discharge signal in a transformer. Then, the local discharge coordinate of the transformer was obtained by the convex optimization method. The proposed method effectively avoids the requirement of an accurate probability model process considering various forms of errors in the process of solving the spatial location coordinates of the local amplifier positioning sources. The proposed internal local discharge location method was assessed through a set of experiments carried out by MATLAB sound field finite element simulation, the 35kV power transformer testbed, and the 110kV field power transformer test. The numerical results show that the location accuracy can reach about 0.1m.