Power system stability and security methods with applications to restorative state operation

This thesis addresses various electric power system stability and security problems. The primary focus is on the dynamic aspects associated with restoring service to a power system that has lost some of its load and/or has separated into electrical islands. An off-line methodology is presented for determining and evaluating restoration decision and control actions. This methodology is an extension of Nadira's hierarchical restoration procedure (1989, 1992). The major additions developed in this thesis are related to the optimizing control problem of the original restoration procedure, and include the following: (i) a dynamic implementation and evaluation of the optimizing control problem solution, and (ii) a method for evaluating and enhancing the security of an island with respect to potential disturbances that may occur during the restoration period.; A detailed power system model is used to simulate the restoration of loads so that various restoration operating strategies can be evaluated. For security evaluation, both probabilistic and statistical stability methods are developed. The statistical method is more computationally efficient and may be applied to large-scale power system problems. This method is based on estimating the mean and variance of the stability margin, and uses a numerical solution algorithm designed to separate the problem into stiff and non-stiff subproblems. Methods are also developed for enhancing stability and security by developing approximate security constraints for either an optimal power flow problem or for the Maximum Load Demand Allocation problem used in the hierarchical restoration methodology. Several examples of power systems operating in the restorative state are presented to illustrate the potential uses of the restoration methodology.; The problem of voltage collapse is also addressed. A new voltage stability methodology is developed for a type of voltage instability that results from a bifurcation of the algebraic load flow equations in a differential-algebraic-equation model. Results from bifurcation theory and dynamical system theory are used to show that some of the stability limiting trajectories are tangent to the boundary of the stability region at a fold bifurcation point. A new energy function stability method is then developed from these theoretical results. The new stability method is used to determine the maximum energy that may be acquired during a disturbance such that the system trajectory still remains within the stability region. In addition, a more general theory is developed for analyzing the stability of constrained systems. For example, in electric power systems the stability region may be restricted such that the bus voltage magnitudes and line power flows remain within pre-defined limits. Based on this new theory, the energy function stability method may be extended to incorporate systems with more general constraints. Several examples are presented to illustrate the results.