Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Allocation of shunt capacitor banks on radial electric power distribution networks allow reduction of energy losses and aggregated benefits. Four decades ago Duran proposed the use of dynamic programming to find optimal capacitor placement on these networks; however, with the restricting assumption of single-ended networks, which precluded its application to real capacitor allocation problems. Subsequently heuristic methods prevailed in the capacitor allocation literature. Here the Extended Dynamic Programming Approach (EDP) lifts Duran's restricting assumption; a richer definition of state and the projection of multidimensional informations into equivalent one-dimensional representations are the supporting concepts. In addition to allow consideration of multi-ended networks, EDP deals with other requirements of capacitor allocation studies, including the use of both fixed and switched capacitors and representation of voltage drops along the networks. When switched capacitors are considered the optimization procedure also solves the capacitor control problem, obtaining the best tap adjustments for them. Case studies with real scale distribution networks put into perspective the benefits of the methodology; EDP has the appeal of providing global optimal solutions with pseudo-polynomial computational complexity in the worst-case, and with linear complexity for practical applications. (C) 2012 Elsevier B.V. All rights reserved.2221149156Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)