Multiobjective Optimization of Distribution Networks Using Genetic Algorithms Fatemeh Afsari Department of Computer Engineering, School of Engineering Shahid Bahonar University of Kerman, Kerman, Iran afsari@mail.uk.ac.ir Abstract-This paper presents the application of multiobjective optimization, for finding out the optimal power distribution network. A multiobjective optimization model simultaneously minimizing the system expansion costs while achieving the best reliability (optimal sizing and location of future feeders and substations). Furthermore, the problem has some constraints. The proposed methodology has been tested for real distribution systems with dimensions that are significantly larger than the ones frequently found in the literature. We have used the Pareto-optimum model to find the suitable curve of non dominated solutions, composed of a high number of solutions. I. INTRODUCTION The optimal design of a power distribution system has been usually approached as the minimization of a single objective (mono-objective) function which represents the economic costs of the global system expansion. However, minimizing costs and getting the best reliability state cannot be solved by previous methods. Therefore, a multiobjective model is used. Genetic algorithms are global methods, which aim at complex objective functions (e.g., non differentiable or discontinuous). In addition, some constrains should be satisfied (e.g. radial structure, voltage and current limits). The multiobjective optimal design has been dealt with by few authors showing examples of application to distribution systems. In previous works [1, 2] several optimal multiobjective planning models were tested and validated intensively by computer experiments, optimizing simultaneously various objectives. However, only classic multiobjective optimization techniques were used [3, 4] to obtain a subset of satisfactory optimal non dominated solutions. This paper presents a new application of genetic algorithm to the multiobjective optimal design of distribution systems that allows optimizing n objectives simultaneously (based on Pareto optimality [3, 4]), using a new toolbox in MATLAB environment. The distribution systems used here present significantly larger dimensions and optimization complexity than most of the networks frequently found in the specialized papers. Also this paper uses a real alphabet that is more flexible than binary alphabet. However, this paper with genetic algorithm method obtains the optimal configuration of the distribution network with the best reliability and the lowest economic costs. II. POWER DISTRIBUTION PROBLEM The problem that we want to solve is a simplified form which shows a series of sources (substations) and a series of drains or demand nodes. Each source has a maximum limit of the power supply. Moreover, the possible routes for the construction of electric line to transport the powers from the sources to the demand nodes are known. Each line possesses a cost that depends principally on its length (fixed costs) and the power value that transports (variable costs). The model contains an objective function that represents the costs corresponding to the lines and substations of the electric distribution system. Multiobjective optimization (also called multi criteria optimization, multi performance or vector optimization) can be defined as the problem of finding [6]; A vector of decision variables which satisfies constraints and optimizes a vector function whose elements represent the objective functions. These functions form a mathematical description of performance criteria which are usually in conflict with each other. Hence, the term “optimizes” means finding such a solution which would give the values of all the objective functions acceptable to the designer. Formally, we can state it as follows: Find the vector [ ] T n x x x x ∗ ∗ ∗ = ,..., , 2 1 which will satisfy the m inequality constraints: ( ) m i x g i ,..., 2 , 1 0 = ≥ (1) and the p equality constraints ( ) p i x h i ,..., 2 , 1 0 = = (2) and optimize the vector function ( ) ( ) ( ) ( ) [ ] T k x f x f x f x f ,..., , 2 1 = (3) where, [ ] T n x x x x ,..., , 2 1 = is the vector decision variable. The constraints given by (1) and (2) define the feasible region X and any point x in X defines a feasible solution. The vector function ( ) x f is a function which maps the set X in the set F which represents all possible values of the objective functions. The k components of the vector ( ) x f represent the non commensurable criteria which must be considered. The constraints () x g i and () x h i represent the restriction imposed on the decision variables. The vector will be reserved to denote the optimal solutions (normally there will be more than one).