Review of distribution system planning models: a model for optimal multistage planning

A representative set of electric power distribution system planning models published in the literature has been reviewed. The models have been classified according to their characteristics, from the point of view of stages of the plan and overall time span; the methods of treating distribution feeders and/or substations in terms of cost representation, location and sizing problems; radiality and voltage drop considerations; and the mathematical programming techniques used to solve them. Some of the particular features of models have been discussed in detail. The paper also presents a model to solve the optimal sizing, location and timing of the distribution substations and feeder expansion simultaneously. The model is based on mixed-integer programming and its objective function represents the present value of costs of investment, energy and demand losses of the system which take place throughout the duration of the plan. The objective function is minimised subject to Kirchhoff's current law, power capacity limits, and logical constraints. The model developed allows explicit constraints of radiality and voltage drops to be included in its formulation.