The investigation of the pole-to-pole (p2p) DC short-circuit fault current in a modular multilevel converter (MMC) based high-voltage direct current (HVDC) grid is of vital importance for protection design and parameter optimization. Existing calculation methods for the p2p fault current primarily rely on differential equations based on the RLC equivalent of the MMC station and the RL model of DC transmission lines. Some of them also take the AC in-feed currents into account. However

these approaches all carry heavy burdens for the complex formation and solving processes of equations

and they can only obtain the numerical solution of the fault current. The analytic solution of explicit physical meaning cannot be acquired at present because of the complex coupling relationship among MMC terminals. To address these issues

this paper builds a simplified and generalized fault equivalence model for the DC grid under a p2p fault. This is due to the fact that the terminals having long electrical distances from the fault point have less impact on the fault current. Next

not only the efficient and accurate fault current calculation is achieved

but also the approximate superposition-based analytical solution of the fault current is derived. The component analysis of the fault current and the sensitivity analysis of the components are provided as well. The calculation method and the analysis are both validated in PSCAD/EMTDC.