Integral planning of primary-secondary distribution systems using mixed integer linear programming

Important research effort has been devoted to the topic of optimal planning of distribution systems. However, in general it has been mostly referred to the design of the primary network, with very modest considerations to the effect of the secondary network in the planning and future operation of the complete grid. Relatively little attention has been paid to the optimization of the secondary grid and to its effect on the optimality of the design of the complete electrical system, although the investment and operation costs of the secondary grid represent an important portion of the total costs. Appropriate design procedures have been proposed separately for both the primary and the secondary grid; however, in general, both planning problems have been presented and treated as different-almost isolated-problems, setting aside with this approximation some important factors that couple both problems, such as the fact that they may share the right of way, use the same poles, etc., among other factors that strongly affect the calculation of the investment costs. The main purpose of this work is the development and initial testing of a model for the optimal planning of a distribution system that includes both the primary and the secondary grids, so that a single optimization problem is stated for the design of the integral primary-secondary distribution system that overcomes these simplifications. The mathematical model incorporates the variables that define both the primary as well as the secondary planning problems and consists of a mixed integer-linear programming problem that may be solved by means of any suitable algorithm. Results are presented of the application of the proposed integral design procedure using conventional mixed integer-linear programming techniques to a real case of a residential primary-secondary distribution system consisting of 75 electrical nodes.