A stochastic SOCP optimal power flow with wind power uncertainty

Recent research shows that non-convex AC OPF problem can be recast as a convex Semidefinite (SD) problem or Second Order Cone Programming (SOCP) problem. This paper presents a stochastic SOCP OPF (SSOCP-OPF) model for power systems connected to the wind farms. This is performed by reformulating the original non-convex OPF problem using more practical parameters of the power system. Finally, we obtain a convex optimization problem through some well-known approximations and an exact relaxation incorporating the stochastic nature of wind power. One of the advantage of convex SOCP problems, which are a general form of linear problems, is that they can be efficiently solved through Interior Point Methods (IPMs). The proposed OPF model takes advantage of both DC-OPF models (solution efficiency) and full AC-OPF models (solution accuracy). As an application of SSOCP-OPF model, we study the impact of wind power uncertainty on the transmission loss in the power systems. To evaluate the proposed stochastic model modified IEEE 30-bus test system is used. The optimization problem is coded in GAMS platform and solved using its embedded interior point optimizer MOSEK.