Conic Programming-Based Lagrangian Relaxation Method for DCOPF With Transmission Losses and its Zero-Gap Sufficient Condition

This paper presents a fast optimization approach framework for the DC optimal power flow (DCOPF) with the consideration of transmission losses, which is confronted with nonconvex quadratically constrained quadratic programming. Specifically, a second-order cone programming-based Lagrangian relaxation method is employed to obtain the lower bound of the original DCOPF. Furthermore, a sufficient condition for the zero-gap relaxation is derived, which is easy to be satisfied in practice. Finally, the comparison with existing DCOPF solvers shows that the proposed method could achieve the global optimal solution and jump out of the local optimality. Also, the comparison with the widely used semidefinite programming relaxation approach indicates that the proposed relaxation method needs less dummy variables, and thus can be more efficiently solved and more applicable for large-scale power systems.