Analysis of ill-conditioned power-flow problems using voltage stability methodology

Ill-conditioned power-flow problems have been widely investigated and repor ted in the literature. A typical approach develops enhanced solution algori thms when a power-flow case is found divergent with the conventional Newton method. It is known that a genuine ill-conditioned problem is caused by th e presence of a large condition number in the power-flow Jacobian matrix. S ince a large condition number is associated with small singular values or e igenvalues of a matrix and the voltage collapse is also related to small ei genvalues, it is therefore postulated that an ill-conditioned power-flow pr oblem is actually a voltage collapse problem. The objective of this paper i s to investigate the relationship between power-flow ill-conditioning and v oltage instability. The findings confirm that power-flow ill-conditioning o nly occurs at the voltage collapse point. As a result, developing improved algorithms to solve the problem is an unprofitable strategy. The well-known voltage stability assessment techniques such as the PV curve method are su fficient for the problem. This conclusion is supported with case studies on five widely known ill-conditioned power-flow problems and rigorous mathema tical analysis.