Optimal substation location and energy distribution network design using a hybrid GA-BFGS algorithm E.G. Carrano, R.H.C. Takahashi, E.P. Cardoso, R.R. Saldanha and O.M. Neto Abstract: A hybrid algorithm combines a quasi-Newton and a genetic algorithm for the optimal expansion of energy distribution systems. The quasi-Newton procedure actuates in the search for optimal substation location co-ordinates, and the genetic algorithm procedure actuates in the design of optimal network topologies. Both searches are performed jointly in the proposed methodology. The costs of facility installation, maintenance and energy losses are considered. The algorithm has been applied in a real energy distribution system expansion problem. 1 Introduction The distribution system is the most extensive part of an electrical system and it is the main loss of electric energy [1] . Therefore the application of optimisation techniques in the design and expansion of such subsystem can lead to significant economic gains, finding networks that minimise immediate costs (facility installation costs) and further costs (related to energy losses and system maintenance). Electrical energy distribution systems are, intrinsically, systems in steady evolution. They are frequently exposed to several changes, such as the appearance of new consumer centres, a change of load pattern in existing centres, a change in geographic distribution of loads in existing centres, and so forth. That situation does not favour the application of efficient design methodologies, since the system would be frequently redesigned in some small part. Traditional approaches only consider this fragment of the system for planning the expansion, disregarding a lot of possible solutions to this combinatorial problem, often resulting in more expensive and lossy networks than would be obtained with global design techniques [2] . In some cases the existing substation facilities are not sufficient to supply a service region with energy. Regions where the cities are growing are a good example of such cases. This phenomenon occurs more often in developing countries, but the economic fluctuations that are intrinsic to globalisation provoke demographic changes even in devel- oped nations. Existing electrical distribution systems which are operating in places where such changes are in progress must follow the eventual increase in the load, keeping some slack capacity to allow future load increments, in a trade-off between the minimisation of the present installation costs and the minimisation of the future needs of facility redesign. In these cases new substations (SS) must be installed and the distribution system must be resized, or completely replaced in some critical cases, to supply the new demand. System expansion in these cases involves two subpro- blems: the SS location and the network topology design. These problems should not be treated separately since they exhibit a strong interaction: when the solution of one of them is changed, the solution of the other also changes. The SS location is an optimisation problem of contin- uous variables (the SS geographical co-ordinates). As the SS location varies, the lengths of the conductors which immediately connect the SS to the network nodes vary continuously too. This influences the problem of optimal network topology design. The distribution network topology optimisation is a combinatorial problem [3, 4] represented by a nonlinear objective function that includes the line installation costs and the energy loss costs. Reference [5] discusses in detail the general class of optimisation problems involving both continuous and discrete variables that arise in combined facility location and network topology design problems. This situation occurs in several contexts, which makes its solution of generic interest. This class of problem constitutes an active research area of optimisation theory [5] . This paper proposes a hybrid algorithm, named GA- BFGS, that combines a genetic algorithm (GA) and a quasi-Newton BFGS algorithm to solve the distribution network expansion problem. The approach considers the two subproblems mentioned and the interaction between them. 2 Description of problem The expansion of distribution systems, including both network topology design and substation location, is the problem addressed here. The algorithm has been developed for general cases, considering both complete and partial reformulation of existing systems. In partial reformulation only conductors with insufficient capacity are replaced. In complete reformulation all conductors are replaced by conductors with greater capacity. The new substation location is to be determined in both cases. Simple cases in which the substation must remain in the original location E.G. Carrano and R.R. Saldanha are with Department of Electrical Engineering, Universidade Federal de Minas Gerais, 6627 Antonio Carlos Av., 30123-970, Belo Horizonte-MG-Brazil R.H.C. Takahashi is with Department of Mathematics, Universidade Federal de Minas Gerais, 6627 Antonio Carlos Av. 30123-970, Belo Horizonte-MG- Brazil E.P. Cardoso is with Electric Energy Utility of Minas Gerais (CEMIG) O.M. Neto is with Department of Electrical Engineering, Universidade Federal de S* ao Jo* ao Del Rei E-mail: taka@cpdee.ufmg.br r IEE, 2005 IEE Proceedings online no. 20050036 doi:10.1049/ip-gtd:20050036 Paper first received 3rd February 2005 and in final revised form 18th June 2005 IEE Proc.-Gener. Transm. Distrib., Vol. 152, No. 6, November 2005 919