Conic relaxation method for optimal power flow

Abstract

This paper describes a relaxation method for the multi-period Optimal Power Flow problem solved for a typical meshed transmission network. The need for relaxation of the OPF problem arises due to the inherent non-linearity and non-convexity the problem possesses. Relaxation of the problem means linearizing the non-linear and the polynomial constraints to have convexifiable constraints, which can thus be easily solved with the help of linear or quadratic solvers, and a global solution is guaranteed with this approach. This paper demonstrates a relaxation approach based on McCormick’s relaxation on various IEEE transmission and distribution test cases. The solution obtained was compared with the non-linear unscaled solution obtained using the interior point (IpOpt) method. It is seen that the former is in very good agreement with the latter, however, it was noticed that the direct solution for the rectangular formulation of the AC-OPF may lose the bound tightness, and can settle for a local optimum, based on the branch and bound technique.