IJCSNS International Journal of Computer Science and Network Security, VOL.7 No.3, March 2007 104 Manuscript received March 5, 2007 Manuscript revised March 25, 2007 The Problem of Restoration of Distribution Networks: a Heuristic Method Eduardo M. Kalinowski 1 ; Maria Teresinha Arns Steiner 2 ; Celso Carnieri 3 ; Nelson H. Mussi 4 ; Cristiane Gulin 1 UFPR – 1,2 Mathematics Department; 2,3,4 Numerical Methods in Engineering Graduate Program CP: 19081; CEP: 81531-990, Curitiba, Paraná, Brazil Summary This paper approaches the problem of restoring a faulted area in an electric power distribution system after locating and isolating the faulted block. Since service restoration is an urgent matter in the operation distribution systems, the proposal is to determine a sequence of operations to restore power supply to as much as possible of the out-of-service area, in the shortest time. For such, it was developed a Heuristic Search Method (Restoration Heuristic Procedure, RHP) that considers the operators' experience. The effectiveness of the proposed heuristic procedure is demonstrated by simulating tests in a real distribution network of COPEL, the utility that serves the city of Curitiba, state of Paraná, Brazil. It was found that the restoration plan(s) can be reached very efficiently, so this method can be considered as a satisfactory alternative to be used in this task. Keywords: Distribution Network Restoration; Restoration Heuristic Procedure; Real Application. 1. Introduction Utilities have been encouraged to improve the services provided to consumers by supervising, controlling and evaluating power supply continuity indices. Thus, the essential objectives are to maintain adequate service and continued power supply to consumers, to the maximum possible extent. When a fault takes place in a certain area of an electrical distribution system, it is essential for the system operators to locate the fault, isolate the faulted block and restore the service to the out-of-service area. This paper is concerned with the problem of service restoration based on the assumption that the fault location has already been identified and the faulted block has already been isolated. The purpose here is to present a Restoration Heuristic Procedure (RHP) to determine some restoration plans (a list of solutions with objective functions values listed in increasing order of quality, i.e., the best solution will be the first one, with the minimum value for the objective function, as will be seen later) for a fault on distribution feeders. The idea is to present the plan list to the system operators to help them make the final decision on how to restore the area that is out of service. The RHP must meet some practical needs of dispatch system that are presented below [4]: • the restoration plan must find the new configuration in the shortest time that is possible in order to avoid inconveniences for the customers and without violating the constraints (block voltages and load sections). Of course, it is expected that the response time will be proportional to the magnitude and complexity of the area under analysis. Results may provide optimal and sub-optimal configurations that reflect an improvement in the operators' decision making; • the plan has to minimize the number of operations involved in each configuration. An increase in the number of operations in large centers increases operating costs and the time to restore the faulted area, and decreases the life of switches; • restore as much load as possible within the out-of- service area; • the plan must not overload any equipment or system component; • the system’s radial structure must be maintained; • the configuration of the restored area should be as close to the original configuration as possible, i.e., only those switches that are in the faulted area’s vicinity may be operated. Typically, the restoration problem is a combinatorial optimization problem, because there is a great number of possible switches to be opened or closed in the distribution system. The magnitude of this kind of problem depends essentially on the quantity of switches involved in the search for an optimal configuration; 2n combinations might be generated, where n is the number of switches involved. In major urban centers there are complex networks and several normally open (NO) and normally closed (NC) switches, thus increasing the magnitude of the problem. That is why the RHP has to narrow down the potential candidates and reach the restoration plan in a short period. This problem is also multi-objective, because it has to satisfy all the practical needs listed above and, finally, is also a non-linear problem considering the operation constraints. This paper is divided into five sections. Section 2 shows a literature review of some papers that also approach the restoration problem. In section 3, we present a description of the real problem and the RHP developed to solve the restoration problem. In section 4, some simulations are made using an academic example and a real example and, finally, in section 5, we present the conclusions and some considerations about this work.