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This paper presents a quadratic approximation for the optimal power flow inpower distributions systems. The proposed approach is based on a linearizedload flow which is valid for power distribution systems including three-phaseunbalanced operation. The main feature of the methodology is its simplicity.The accuracy of the proposed approximation is compared to thenon-linear/non-convex formulation of the optimal power flow using differentoptimization solvers. The studies indicate the proposed approximation providesa very accurate solution for systems with a good voltage profile. Results overa set of 1000 randomly generated test power distribution systems demonstratethis solution can be considered for practical purposes in most of the cases. Ananalytical solution for the unconstrained problem is also developed. Thissolution can be used as an initialization point for a more precise formulationof the problem.

A Quadratic Approximation for the Optimal Power Flow in Power Distribution Systems