The algorithm of the static voltage stability region's tangent plane through the characteristic vector method or the implicit function derivative method is presented in the total parameter space， which can provide quantitatively the influence degree of all kinds of parameters on the voltage stability region. The implicit function derivative method can calculate the partial derivative of state variables to independent parameter variables. Hyper-plane approximation in the cut-set space can be derived analytically based on the partial derivative through the mapping from power injection space to cut-set space， which can bypass the data fitting algorithm and improve the calculating speed. The practical voltage stability region's tangent plane， which is formed by constraints of the power system， is also presented. Three kinds of voltage stability indices based on the tangent plane analysis method are presented to assess the voltage stability level comprehensively. Simulations of the IEEE 9-bus and IEEE 39-bus system show that the research on the static voltage stability region's tangent plane can assess the voltage stability level objectively and lay the foundation for correct decision-making for secure and stable operation of power systems.