A Long-Term Voltage Stability Margin Index Based on Multiple Real Power Flow Solutions

In this paper, we demonstrate the distribution of real-valued power flow solutions and its application to the long-term voltage stability. It is the first time in power engineering we realize that even a small-scale IEEE standard power system can admit a humongous number of real-valued solutions for a single load and generation profile. For example, the IEEE 30-bus system can achieve 25686 many different real-valued solutions at a light loading condition. Furthermore, a mysterious class of false power flow solutions is reported and analyzed rigorously as legitimate numerical solutions. All solution sets investigated in this paper are posted online associated with this paper to support potential future applications [1]. Based on these extensive solved power flow solutions, we exhibit their occurrence patterns and distributions at different loading levels, and propose a long-term voltage stability margin index to quantify the long-term voltage stability of a given power flow condition. Numerical studies on a 5-bus system and a 57-bus system show the feasibility and effectiveness of the proposed index in assessing power system long-term voltage stability margin.