Constraint at a Saddle Node Bifurcation

Many power engineering systems have dynamic state variables which can encounter constraints or limits affecting system stability. Voltage collapse is an instability associated with the occurrence of a saddle node bifurcation in the equations which model the electric power system. We investigate the effect of constraints on voltage collapse by studying the effect of constraining state variables on systems of nonlinear differential equations which exhibit saddle node bifurcations. When a dynamic state variable is constrained it becomes a constant and the system stability margin can change. We quantify the change in stability margin resulting from the constraint of one or several state variables. More precisely, we approximate the new distance to bifurcation in parameter space for a system which encounters a limit at a saddle node bifurcation. The emphasis of this thesis is on the derivation and interpretation of this calculation. Future work will test the applications of this calculation to various power system limits, the placement of voltage support, and model reduction for the study of voltage collapse.