Sensitivity of the loading margin to voltage collapse with respect, to arbitrary parameters

Loading margin is a fundamental measure of proximity to voltage collapse. Linear and quadratic estimates to the variation of the loading margin with respect to any system parameter or control are derived. Tests with a 118 bus system indicate that the estimates accurately predict the quantitative effect an the loading margin of altering the system loading, reactive power support, wheeling, load model parameters, line susceptance, and generator dispatch. The accuracy of the estimates over a useful range and the ease of obtaining the linear estimate suggest that this method will be of practical value in avoiding voltage collapse.