Abstract: Calculating the critical point of voltage stability quickly and accurately can evaluate the static voltage stability effectively. It is conducive to monitor and control the safe and stable operation of power grid. Referring to the theory of complex analysis and numerical approximation,a static voltage stability analysis method is proposed based on holomorphic embedding method. Firstly,the holomorphic embedding model of power flow is constructed. The voltage function is expanded analytically in the form of series. Then,the rational function of voltage about embedded variable is established with Padé approximation algorithm. A method based on the zero-pole distribution of rational function is proposed to predict the critical point of voltage stability. Finally,the effect of the number of terms of power series and the operating precision of software on the calculation results of voltage stability critical point is studied. Compared with the traditional continuous power flow method,this method adopts the non-iterative idea and does not need to solve the power flow equation for many times. The computational complexity is greatly reduced and the time advantage is more obvious. The effectiveness and accuracy of the proposed method are verified by simulation examples.