An analysis of Seydel's test function methods for nonlinear power flow equations

One of the important planning and operations problems in electrical power systems is to determine the distance of a loading parameter from the voltage collapse point the so-called performance index. Such an index indicates the severity of a power network with regard to voltage collapse. This paper investigates a class of test function methods due to Seydel (1979) that may be adapted to produce a performance index. Experiments have shown that an arbitrary choice of the parameters in the method leads to unreliable indexes. We first present a result that gives an equivalent formula, involving determinants, for the Seydel test function. We then analyse the behaviour of such determinants in order to determine what parameters are suitable to produce reliable indexes. For typical power systems with reactive power changes, it turns out that only a restricted set of parameters can ensure a reliable index by the Seydel method; for other cases, a general modification is proposed. Promising numerical results using several standard IEEE test examples are presented.