Loss minimization of distribution feeders: optimality and algorithms

Determining open switch positions for the minimum-loss configuration of a radial distribution system is a discrete optimization problem. The authors present a global optimality condition of the problem and two algorithms: one is based on the uniformly distributed load model and the other on the concentrated current (or power) demand model. The derivation of the optimality condition relies on a concept of `basic´ current profiles of feeder sections and a transformation of the optimization problem. In the first algorithm, a closed form of the minimum-loss open point of a feeder pair can be found since the loss function is piecewise-parabolic. The algorithm obtains the optimal solution when the minimum is obtained for every feeder pair. In the second algorithm, a similar procedure is performed by moving open points, one at a time, from an actual switch position to another until no further loss reduction can be achieved. The proposed algorithm can be utilized as an online aid to distribution system operators