In engineering, the main method used to analyze the stability of a system is to solve a set of differential-algebraic equations by alternating iterative methods, but the low degree of analysis is its inherent disadvantage. In order to make up for this shortcoming, an analytical method for solving the network voltage closed solution is proposed for different load models using the Dommel-Sato iteration. This method can decouple the differential equation and the algebraic equation in the mathematical model, and then the mathematical model of transient stability analysis is transformed from the differential-algebraic equations to total differential equations, avoiding the alternating iteration of the solution process. Based on the closed solution of the network voltage, a method for quickly calculating the short-term voltage after a system fault is proposed. Comparison with the PSD-BPA simulation results shows that the method can quickly and accurately calculate the short-term voltage after a system fault. This work is supported by the National Key Research and Development Program of China (No. 2016YFB0900600).