Abstract: Static voltage stability analysis is an important part of the power system stability analysis. According to the singularity of power flow Jacobian matrix at the critical point of static voltage stability, the characteristic was described by making the power flow Jacobian determinant equal to zero, and the static voltage stability analysis was carried out based on it. The equation which can directly solve the critical point of static voltage stability was constructed, and a unified solution method was proposed. In order to solve the problem that the Jacobian determinant of power flow needs to be calculated many times in the unified solution method, a decoupled solution method was proposed by combining the Newton-Raphson method, secant method and bisection method. Then, by using the Jacobian determinant of power flow and combining the line load rate and line failure rate, a static voltage stability index was proposed, which could be used for the identification of the vulnerable lines. In simulation results the proposed static voltage stability critical point calculation methods were compared with the existing methods through different scale power systems, and the characteristics and applicable scenarios of different methods were summarized. The vulnerable lines of the IEEE 39 bus system were analyzed by the proposed static voltage stability index, and the rationality of the index was verified.