Based on the sensitivities of the voltage stability index to node injections， a heuristic method for estimating the shortest radius of power system voltage security region in node injection space is proposed. In the proposed method， the closest boundary of voltage security region in node injection space is approached step by step. The proposed approach can consider all kinds of operating constraints， and has no numerical convergence problems. Moreover， the basic principle of this method can also be extended to estimate the shortest radius of transient security region and small signal security region， which provides a uniform numerical approach to estimate all kinds of power system security regions. Numerical results demonstrate that the proposed method is valid and effective.