Modeling and optimization of an electric power distribution network planning system using mixed binary integer programming

Abstract

In this paper, the electric distribution network expansion planning problem (EDNEPP) was solved by a mixed binary integer programming (MBIP) formulation of the network, where the steady-state operation of the network was modelled with non-linear mathematical expressions. The non-linear terms are linearized, using piecewise linearization of the non-linear expressions, so as to ensure the model computational compatibility with existing commercial optimization solvers. The linearized formulation is verified to ensure its solution optimality and degree of error deviation. The proposed network model formulation considers the alternatives of installation of new transformers of various capacities to reinforce already existing ones at substations of the network, choosing and construction of new substations given feasible locations, re-conductoring of existing feeders in the network, construction of new feeders given various conductor types alternatives, cost lost as a result of power interruption, and changes in the overall network topology. The cost of interruption would contain a cost term called ‘cost of goodwill’, which was brought into the model formulation, to measure the loss in confidence of consumers to distributors of power as a result of interrupted power supply, which is prevalent in developing nations. Two test systems of 23 and 54 nodes was used in showing the efficiency of the proposed network model formulation.

Keywords: Distribution network, mixed binary integer programming, linearization, re-conducting, optimization.