  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.
