Polynomial Approximation of Transient Voltage Stability Region Boundary in the Parameter Space Based on Collocation Method

Transient voltage stability region boundary (TVSRB) in the parameter space corresponds to a set of system variable parameters, under which the transient voltage trajectory of a key bus marginally meets the criterion of transient voltage stability. This paper proposes a method for polynomial approximating TVSRB in the parameter space based on collocation method. Firstly, an improved transient voltage stability index (TVSI) is proposed based on a practical criterion for transient voltage stability, which varies smoothly rather binarily as system parameters crossing TVSRB and hence can be better approximated by polynomials. Secondly, the relationship between TVSI and system variable parameters is approximated by polynomials using collocation method, and then adopted to derive approximated TVSRB by equaling it to be critical value of TVSI. The feasibility and accuracy of the proposed method is verified by the case studies of IEEE 9-bus test system. The obtained approximated TVSRB can be used to monitor system transient voltage stability or serve as the stability constraints of system operation and control.