Analytical reformulation of security constrained optimal power flow with probabilistic constraints

In this paper, uncertainties from wind power in-feed are taken into account in a DC security-constrained optimal power flow (SCOPF) by formulating probabilistic constraints. The deviations from the wind power forecast are represented as Gaussian random variables and an analytical reformulation of the constraints is proposed, which is exact for the Gaussian distribution. The resulting formulation has the same computational complexity as the deterministic problem. Furthermore, a valuation framework to assess the cost of securing the system against fluctuations in wind power in-feed is proposed. The applicability of the method and the valuation framework is demonstrated on the IEEE RTS96 system. We show that the probabilistic formulation leads to lower probability of thermal overloads, and that it is less costly to secure the system against uncertain in-feed than to secure the system against failures in most cases.