Published in IET Generation, Transmission & Distribution Received on 23rd April 2007 Revised on 8th October 2007 doi: 10.1049/iet-gtd:20070174 ISSN 1751-8687 Power distribution network expansion scheduling using dynamic programming genetic algorithm E.G. Carrano 5 R.T.N. Cardoso 1 R.H.C. Takahashi 2 C.M. Fonseca 3,4 O.M. Neto 1 1 Department of Electrical Engineering, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil 2 Department of Mathematics, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil 3 Faculty of Science and Engineering, Universidade do Algarve, 8005-139 Faro, Portugal 4 CEG-IST-Centre for Management Studies, Instituto Superior Te ´cnico, Universidade Te ´cnica de Lisboa, 2780-990 Porto Salvo, Portugal 5 Centro Federal de Educac ¸ ~ ao Tecnolo ´ gica de Minas Gerais, 30480-000 Belo Horizonte, MG, Brazil E-mail: taka@mat.ufmg.br Abstract: A genetic algorithm that is dedicated to the expansion planning of electric distribution systems is presented, with incremental expansion scheduling along a time horizon of several years and treated as a dynamic programming problem. Such a genetic algorithm (called dynamic programming genetic algorithm) is endowed with problem-specific crossover and mutation operators, dealing with the problem through a heuristic search in the space of dynamic programming variables. Numerical tests have shown that the proposed algorithm has found good solutions that considerably enhance the solutions found by non-dynamic programming methods. The algorithm has also shown to work for problem sizes that would be computationally infeasible for exact dynamic programming techniques. 1 Introduction The electric distribution system is the most extensive part of the electrical system, and consequently, it is the mainly responsible for energy losses [1]. Therefore the use of optimisation techniques in the design of this subsystem can lead to significant economic gains, obtaining networks, which minimise the immediate costs (those related to installation and reconductoring) and further costs (costs related to energy losses and system maintenance) [2–4]. The fundamental working mechanism of the distribution system is the power flow that is established by the interaction between the power sources, the loads and the branch impedances, for the specific network topology, where the admissible topologies for distribution systems are the planar tree graphs. This means that its design becomes formulated as combinatorial optimisation problems involving non– linear constraints and non-linear objective functions. These characteristics of the problem preclude the employment of most of the traditional (deterministic) optimisation methods, and motivate the employment of the recent evolutionary computation techniques, that are able to deal with problems with such features. Most of the recent works dealing with the problem of power distribution network expansion employ algorithms belonging to this class. See for instance [3–6] and the references therein. It is well known that distribution systems are in constant evolution, subject to load increasing in different places at different times, which leads to the /IET Gener. Transm. Distrib., 2008, Vol. 2, No. 3, pp. 444–455 & The Institution of Engineering and Technology 2008 doi: 10.1049/iet-gtd:20070174 444 www.ietdl.org