An efficient covexified SDP model for multi-objective optimal power flow

This paper proposes a convexified multi-objective model for optimal power flow (OPF) that simultaneously minimizes the operational cost and total emission. The proposed multi-objective OPF (MO-OPF) is modeled based on semidefinite programming (SDP) and ε-constraint method and employed to generate Pareto optimal solutions. This work extends the existing OPF based on SDP by presenting a general model that contains all security constraints along with operational constraints, extending the convex OPF framework to a multi-objective form, and implementing ε-constraint method in the context of SDP. To corroborate the performance of the proposed model, simulations are conducted on the standard IEEE 30, 57, and 118-bus test systems and the obtained results are compared with those of a well-known multi-objective optimization algorithm, namely Non-dominated Sorting Genetic Algorithm II (NSGA-II). The numerical results show that (i) the required zero duality gap and rank condition of all Pareto solutions are satisfied, (ii) SDP is capable of effectively producing a more accurate Pareto-optimal solutions and better distribution of non-dominated solutions, and (iii) better convergence characteristics, especially in dealing with the OPF problem of large scale systems with multiple objective functions.