A bi-objective DC-optimal power flow model using linear relaxation-based second order cone programming and its Pareto Frontier

The DC optimal power flow (DC-OPF) plays an important role in the operation and planning of modern power systems. In this paper, a bi-objective DC-OPF model minimizing both network losses and generation costs is introduced, which can further be converted into a single objective model via the weighted sum method. Furthermore, the Pareto Frontier is employed to solve this problem. In the mathematical view, the model is a special non-convex quadratic constraints quadratic programming problem. In order to obtain a continuous Pareto Frontier, the original non-convex feasible region is relaxed to its convex hull using a linear relaxation-based second order cone programming method. Compared with the semi-definite relaxation method, the proposed method can greatly reduce the number of dummy variables and the complexity of solutions. Finally, simulations on eight small systems and four practical, large systems are performed, in addition to the comparison of a Monte Carlo simulation. The results verify the effectiveness of the proposed algorithm.