هماهنگی رله جهت دار با استفاده از الگوریتم تکاملی و برنامه ریزی خطی

In this article, we present a new method to coordinate the directional overcurrent relay (DOCR) installed in a meshed electricity network. Using evolutionary algorithms and linear programming we solve the problem that allows the calculation of the adjustment intensity (relay setting current, J) and the time multiplier factor, K, such that, in the light of any triphasic or biphasic failure that may occur in the network, the relays may act in the least time possible and in a coordinated manner. We are considering the problem without taking into account the intensity variations that occur when a switch is opened. It may happen that the problem at hand does not have a solution, in that case we determine the constraints that should be removed in order to achieve at least a partial coordination of the relays.

Directional overcurrent relays (DOCR) are often used as primary protection in distribution networks (normally radial) and as secondary protection in Transmission networks (normally meshed). The determination of the DOCR adjustment parameters, in such a way that the primary relay and backup relay coordinate correctly, is relatively easy when it is a radial network. On the other hand, when the network is made up of several meshes, the determination of said parameters is a more complicated task. The methods employed up till now can be classified into the following blocks: □ Topological analysis □ Linear programming □ Non-linear programming □ Genetic algorithms The first ones are heuristic methods that determine the relays that open the highest number of loops. The K parameter of all the DOCR of the network is calculated from those relays, in a sequential and recurrent manner. J is considered constant in those methods [1], [2], [3], [4] and [5]. Methods based on linear programming consider J as constant and suggest a simplified [6] and [7] linear model. Some authors suggest the use of Gauss–Seidel for calculating said K. Methods based on [12] and [13] non-linear programming determine both K and J of each DOCR of the network. And the problem set out in [6] and [7] is solved using non-linear programming techniques. The non-linear problem set out in [6] and [7] is solved with genetic algorithms through a genetic algorithm in which both J and K are codified [8], [9] and [10]. Ref. [11] is an analysis of the different methodologies employed to solve the problem of the coordination of the DOCR of the system, up to the date of publication of the paper. In this paper, Js and Ks of the DOCR of the system are determined through evolutionary algorithms, in which Js become part of the codification of individuals and Ks are obtained through linear programming as an optimal solution for that J group, based on the optimization criterion. An improvement of this method, as against that suggested by other authors, is that should the problem of optimization not have an overall solution, a systematic method of eliminating restrictions is proposed. The elimination of restrictions means that a linear stretch, protected by the relays implicated in the restriction that has been eliminated, would not have backup protection, even though it would have primary protection. Therefore, the solution to the problem must be found eliminating the least possible number of restrictions. The advantage that this method has over the one proposed in [10] is that, for each combination of Js obtained with the evolutionary algorithm, the combination of optimum K is obtained by applying linear programming. Thus the search parameters are reduced by half.

A new method of optimization is presented to determine the time multiplier setting and the current setting of directional overcurrent relays of an electrical network. Due to the fact the operation time of the relays of each (i, j) pair only needs the verification of a small number of restrictions, the main advantages of the method proposed above is that the evolutionary algorithm and that of the linear programming are fast. Besides, unlike the proposals carried out by authors included in the bibliography, it allows the elimination of restrictions so as to seek a solution to achieve the partial coordination of the relays.