# Modal analysis of large-scale power systems' voltage stability and voltage collapse

In this research, a theoretical foundation for modeling, analysis, and testing of a system for voltage collapse is developed. The boundary theorem of the load flow feasibility region (FR) is presented. Based on the proposed boundary theorem, a method of voltage stability analysis referred to as the Eigen-Structure Analysis (ESA) method, is developed that does not require complicated nonlinear programming calculations for evaluation of the closest unfeasible or boundary injection corresponding to a given power network operating point with voltage controlled and load buses. Furthermore the steady-state stability margin and the sensitivity of the stability margin to bus voltages and bus injections are defined. An algorithm for determining the stability margin and its sensitivity to bus voltages and bus injections is proposed which is capable of handling large scale power systems by utilizing the sparse matrix techniques for saving computation time and memory space. The unification of the concept of feasibility region and the concept of multiple load flow solution is also presented in this dissertation The Eigen-Structure Analysis method is applied to a number of test system models. The simulation results confirm the theory and show that the proposed stability margin decreases monotonically to zero when the system approaches voltage collapse. The voltage-weak points and key contributing factors affecting the system voltage instability can be identified according to the values of the sensitivity of the stability margin to bus voltages and bus injections