Assessment of maximum loadability in a probabilistic framework

The calculation of power system maximum loadability consists in determining, from a point for which the power flow has a solution, the maximum increase of system load until the system reaches the point of collapse. Therefore, it is a measurement of the margin or distance to the voltage collapse. This problem is related to the computation of margins with respect to bifurcations. Under certain conditions, saddle-node bifurcations occur when the Jacobian matrix associated with the power flow balance equations becomes singular. These points belong to the surface which defines the frontier of the power flow solvability region. Outside this region, the power flow is unsolvable, i.e. the power flow balance equations have no real solutions. In turn, power flow solvability problems can be handled by a special purpose AC optimal power flow (OPF) which is solved by an interior point (IP) algorithm. In this paper, this special IP OPF is introduced into a probabilistic simulator, allowing the calculation of probabilistic indicators of system margins or maximum loadability, taking into account random forced outages of generators, lines and transformers. Mathematical formulation and numerical examples are presented and discussed