A quadratic approximation for the optimal power flow in power distribution systems

•This paper introduces a quadratic convex approximation for the OPF in power distribution systems.•It can be used as initial point for other non-linear or heuristic algorithms or as part of another algorithm that requires to call many times an OPF sub-routine.•It is a practical solution in systems in which a close-to-the-optimal solution and a real time fast convergence is desirable.•This formulation is convex even in the three-phase unbalanced case (i.e. the solution is unique and does not depend on the optimization algorithm).

This paper presents a quadratic approximation for the optimal power flow in power distributions systems. The proposed approach is based on a linearized load flow which is valid for power distribution systems including three-phase unbalanced operation. The main feature of the methodology is its simplicity. The accuracy of the proposed approximation is compared to the non-linear/non-convex formulation of the optimal power flow using different optimization solvers. The studies indicate the proposed approximation provides a very accurate solution for systems with a good voltage profile. Results over a set of 1000 randomly generated test power distribution systems demonstrate this solution can be considered for practical purposes in most of the cases. An analytical solution for the unconstrained problem is also developed. This solution can be used as an initialization point for a more precise formulation of the problem.