In this paper, the pole-mode transformation method is used to address the problem of inter-pole coupling under asymmetrical operating conditions of a bipolar DC system with dedicated metallic return. The study begins by examining the equivalent model of the modular multilevel converter (MMC) during the DC system faults. Next, considering four different configurations of the converter station connected to the bipolar DC system, the fault equivalent model in the modulus component coordinate space is derived using the pole-mode transformation matrix. Subsequently, integrating the modulus domain decoupling model and the boundary conditions of the fault point, the paper establishes the composite modulus equivalent network for different fault types and analyzes the modulus characteristics of the fault currents. A two-terminal bipolar DC system with dedicated metallic return was constructed in PSCAD/EMTDC for simulation verification. The simulation results demonstrate the effectiveness and accuracy of the proposed derivation method and analytical conclusions.