Stochastic optimal power flow by multi-variate Edgeworth expansions

• A method for solving stochastic optimal power flow is suggested.
• The method is based on approximating the stability boundary.
• The method can be applied both in planning and in operation.

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 steady-state variable limits have been used as security constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation.Recently an extension of the stochastic optimal power flow formulation that included constraints for voltage stability as well as small-signal stability was proposed. This was done by approximating the voltage stability and small-signal stability constraint boundaries with second order approximations in parameter space. In this article an alternative solution method to this problem will be proposed. The new improved solution method, which is based on Edgeworth series expansions, is both more efficient and accurate.We also give details on convexity of the problem and discuss some computational issues.