The Irrelevance of Load Dynamics for the Loading Margin to Voltage Collapse and Its Sensitivities

The loading margin to a saddle-node orfold bifurcation is a useful and basic index of proximityto voltage collapse. Sensitivities of the loading margincan be used to select controls to avoid voltage collapse.This paper justifies the use of static power models to com-pute loading margins and their sensitivities. In particular,dynamic load models may be reduced to static equationsand then simplified without affecting loading margins andtheir sensitivities. Alternatively, if dynamic models arenot well known, the computations may be done with staticmodels and conclusions drawn about a general and sensi-ble class of underlying dynamic models. Explicit assump-tions and mathematical underpinnings are presented.