The involvement of multiple control strategies in Voltage-Source-Converter-based multi-terminal DC system (VSC-MTDC) makes its power flow formulas highly nonlinear and multivariate quadratic, exacerbating the difficulty of fundamental power flow analysis. This paper presents a generic power flow method and a corresponding convergence analysis theorem. This method possesses the ability to acquire feasible high-voltage solutions without imposing conservative pre-conditions. First, considering various control strategies for VSC-MTDC, an improved fixed-point type method with a compact and simple iterative structure is developed. Second, a post-condition convergence analysis methodology is constructed, which describes the comprehensive convergent properties of the proposed method associated with a complete DC power flow solvability region. Third, a rigorous analytical proof of the post-condition convergence analysis for the proposed method is conducted, validating the reliability and robustness of the proposed method in obtaining feasible power flow solutions. Computational findings in numerical tests further validate the versatility and accuracy of the proposed method.