Abstract: Power system static voltage stability boundary(SVSB) plays an important indication role in monitoring voltage stability and evaluating the voltage stability margin, so the rapid and accurate calculation of SVSB is of great significance for the safety and stability of power grid. As an ultra-high-dimensional multivariate nonlinear system, the SVSB of a power system is essentially a nonlinear high-dimensional boundary composed of the voltages which can maintain the balance of supply and load under a certain topology. This paper considers the SVSB as a voltage stability hypersurface and proposes a new method to calculate the SVSB. First, multidimensional holomorphic embedding method(MDHEM) is used to find the multivariate power series(MPS) expressions for the bus voltages. Then, based on the Cauchy-Hadamard theorem, the analytical relationship between the SVSB and the coefficients of the voltage MPS front and back terms is derived and proved, and through theoretical proofs the proposed method is extended from single-dimensional to high-dimensional scenarios. Then, based on the derived SVSB analytical expression, the high-dimensional SVSB calculation and voltage stability evaluation methods are proposed. Finally, the validity of the proposed method is verified in the IEEE 14-bus, New England 39-bus and IEEE 118-bus systems.