Stochastic optimal power flow problem with stability constraints

Summary form only given. Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only limits on line flows have been used as stability constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. In this article we aim to extend the stochastic optimal power flow problem to include constraints for voltage stability as well as small-signal stability. This is done by approximating the voltage stability and small-signal stability constraint boundaries with second order approximations in parameter space. Then we refine methods from mathematical finance to be able to estimate the probability of violating the constraints. In the first part of the article, we derive second-order approximations of stability boundaries in parameter space. In the second part of the article, we look at how Cornish-Fisher expansion combined with a method of excluding sets that are counted twice, can be used to estimate the probability of violating the stability constraints. We then show in a numerical example how this leads to an efficient solution method for the stochastic optimal power flow problem.