Voltage stability estimation

The proximity of power systems to voltage collapse can be calculated for any of the buses using to the theory of bifurcation and multiple solutions to power flow behavior, in terms of system indicators such as real and reactive power. These indicators can be measured to identify voltage collapse. The application of topology space theory for describing voltage collapse phenomena is effectively demonstrated. The bifurcation points that cause system degradation are detected by evaluating the singularity of power flow Jacobian matrix. The controllability of vulnerable buses is evaluated and network flow limit is calculated to provide early detection warning for planners and operators. The procedure is demonstrated on several power systems. The procedure has been successfully tested on practical power systems, for example, the IEEE-118-bus system. Results obtained, especially with static models, show good correspondence with existing results and indicate some superior features