Practical boundary expression of static voltage stability region in injection space of power systems

Static voltage stability region (SVSR) in power injection space is a promising framework for voltage security assessment and control. An accurate expression of the SVSR boundary and the fast determination of coefficients of the expression are important issues for its application in bulk power systems. In this paper, we derive the analytical expression of SVSR boundary in a single-generator-single-load system, which brings new insight into characteristics of SVSR boundary's expression. By using Taylor series expansion of the critical condition of static voltage stability, a quadratic analytical formulation is then proposed as the approximation of SVSR boundary in injection space. Furthermore, we also provide a method for critical nodes selection based on modal analysis, which aims at reducing the huge dimension of injection space. The effectiveness of the proposed method is demonstrated through IEEE 14-bus, 57-bus systems and EPRI 1000-bus system. The estimation errors of the proposed boundary description in injection space are not more than 3% for various operating conditions when generators and loads change over a wide range.