Genetic algorithm for optimal sectionalizing in radial distribution systems with alternative supply. Gregory Levitin, Shmuel Mazal-Tov, David Elmakis. Reliabilitv ...
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Electric Power Systems Research 35 (1995) 149 155
Genetic algorithm for optimal sectionalizing in radial distribution systems with alternative supply Gregory Levitin, Shmuel Mazal-Tov, David Elmakis Reliabilitv Department, Research and Development Division, Israel Eleetrie Corporation Ltd., 43 Rachel Street, Hal]a, 34402, Israel Received 5 May 1995
Abstract
A procedure for optimal allocation of sectionalizing switches in radial distribution systems is proposed. This procedure is aimed at minimizing unsupplied energy caused by network failures. Opportunities for alternative source supply made possible by network reconfiguration are considered. Two applications of this procedure are explored: when the allocation of alternative supply tie-lines is given and when the optimal allocation of a specified number of tie-lines, as well as the allocation of sectionalizers, must be determined. The procedure is based upon the genetic algorithm, a search technique motivated by natural evolution. The basic operators of the genetic algorithm are adapted to solve the problems considered. Performance enhancing modifications of the algorithm are suggested when applicable. A medium-scale, practical example is presented to illustrate the validity and effectiveness of the proposed method. Keywords: Distribution network reconfiguration; Sectionalizer allocation; Genetic algorithms
1. Introduction
In an effort to improve customer service, electrical industries have focused upon reliability. New standards have been introduced that guarantee the quality and reliability of electricity supply. In response to the pressure of new requirements, companies have embarked upon an overall strategy to improve system performance. Failure statistics show that medium-voltage distribution systems make the greatest individual contribution to the unavailability of supply to a customer [1,2]. Hence, in order to significantly improve overall system performance, investment emphasis should be on distribution networks. Considerable effort has been devoted to the reduction of unsupplied energy (UE) in these networks, including optimal system reconfiguration and distribution automation [3-5]. A typical radial distribution system consists of a number of single-feeder, tree-like networks interconnected through tie-lines. Tie-lines contain switches that are usually open and are used in supply restoration or line reconfiguration. The single-feeder network consists of a series of lines and cables connecting any load point to the single supply source. These lines and cables are divided into sections by connection nodes and load points. Each section has its individual failure rate which depends on the type of line construction, section length, 0_ 78-7796,, 9> $09.50 ,,~?, 1995 Elsevier Science S.A. All rights reserved S S D I 0378-7796(95)01002-5
and environmental conditions. Usually, failure rates are found to be approximately proportional to section lengths. Short-circuits in each system component cause the main feeder breaker to operate. If there are no points where part of the system can be isolated then all customers who are supplied through the feeder will be in an outage state until the fault is fixed. Sectionalizing switches are used to localize damage caused by the fault. These switches isolate the failed subsystem while the rest of the system is supplied normally. When an interruption occurs, the outage duration for' an individual customer depends on his location relative to the failure and to the sectionalizers. Therefore the allocation of sectionalizers affects the distribution system's reliability. Since economic and technical factors limit the number of sectionalizers, their optimal allocation will lead to the greatest possible improvement in system reliability. An additional application of sectionalizing switches lies in network configuration management. A subsystem that is disconnected from its main source of energy may be alternatively supplied through tie-lines connecting different feeders. The faulted section must be isolated from both sources in order to make alternative supply possible. The number of isolated customers and the unsupplied energy depend on allocation of tie-lines as well as sectionalizers.
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Electric Power ~v,~tems Research 35 (1995) 149 155
Optimal sectionalizer allocation in a single-feeder radial system without alternative supply potential was addressed in Ref. 5. The genetic algorithm based procedure was suggested to minimize the total annual cost of unsupplied energy and capital investment in sectionalizer installation. This paper presents an algorithm that gives optimal sectionalizer allocation taking into account alternative supply possibilities. Sectionalizers are usually installed when the tie-lines already exist. However, to achieve the greatest effect on system reliability, allocation of tie-lines and sectionalizers should be considered simultaneously, as a single combinatorial problem. As the practicalities of protection grading limit the number of sectionalizing switches, it was found expedient to use the algorithm to determine optimal allocation of a user-specified number of sectionalizers. Two types of optimization problem are addressed. Type 1. Optimal allocation of a specified number of sectionalizers in a radial system with a given allocation of tie-lines, The problem is actual when decisions about sectionalizer installation in existing networks are made. Type 2. Optimal allocation of a specified number of tie-lines and sectionalizers in a given radial system. This definition of the problem is relevant during network planning. It may also be used when decisions about network extensions are made. In Section 2 a mathematical model for evaluating reliability indices for radial networks with arbitrary tie-line and sectionalizer allocation is presented. Section 3 contains a brief description of the genetic algorithm and application of its basic procedures to the problem discussed. Modification of the basic algorithm is suggested to improve its performance. A practical mediumscale example is shown in Section 4 to illustrate the validity and effectiveness of the proposed method. In this paper, line capacity limitations are not considered and sectionalizing switches themsleves are assumed to be 100% reliable.
2. Mathematical formulation
The radial distribution system containing K sections may be represented by a tree graph G in which nodes oi (0 ~
