СИСТЕМА АВТОМАТИЗАЦИИ ПРОЕКТИРОВАНИЯ ГОРОДСКОЙ РАСПРЕДЕЛИТЕЛЬНОЙ СЕТИ ЭЛЕКТРОСНАБЖЕНИЯ

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Introduction. Urban power distribution network (UPDN) of megalopolis is a difficult system of non-uniform structure. It represents a set of distributive and step-down substations, feeders and distribution lines, current-using equipment. UPDNs cover all city consumers, including industrial enterprises, electric transport etc. Now UPDNs consist of elements which are tens of thousands and which differ in their purpose and characteristics. Considering modern rates of city development, the economic and reliable UPDN building problem is now especially current. Thus, the process of such networks design is connected with need of accounting and calculating a large number of parameters, possible development ways and complexity of their assessment [1; 2]. Thus, the necessity of introducing new technologies for the specified task solution is obvious [3]. The author has developed the computer-aided design system (CAD system) “ELNET” for the task solution automation of perspective power supply network development (PPSND). UPDN model. The mathematical PPSND task formulation is represented in the article [4]. UPDNs contain two types of objects united with cable lines (CL, type L): a transformer substation (TS, type T) and a distributive substation (DS, type D). Upon solving the PPSND task a great number of electric power consumers connected to UPDN is set. The original UPDN with the supplied load (all consumers connected to it) represents the directed graph where D, T, L are the given UPDN set assemblies of D, T and L types respectively. The elements of sets D, T are the graph points, elements of set L correspond to its arcs. Many of all consumers connected to UPDN define the set , where are sets of consumers connected to UPDN at the voltage levels of 10 kV and 0,4 kV respectively. Objects of each type are characterized by a set of parameters. The vector varied parameters structure is expanded. It contains such characteristics of UPDN elements as objects geographical coordinates, CL length and section, required power of consumers, etc. The UPDN fragment model is presented in fig. 1. Fig. 1. The UPDN fragment model: - DS; - TS; - CL; - consumer UPDN design problem. The PPCND task lies in defining such way of UPDN development, where a high level of power supply reliability and transferred electric power quality will be provided with the smallest costs of construction and operation of its elements. Defining a way of the UPDN development means: - to define the number and locations of new electrical power objects (TS, DS); to define the way and parameters of their inclusion into the existing UPDN; - to define the connection way of new consumers to UPDN. The vector of the task varied parameters is presented as where is an unknown number of DS/TS, which a consumer will be connected to; are the numbers of DS/TS, which TS is connected to; are the geographical coordinates of new DS/TS; are the numbers of new DS and TS, construction of which should be for connection of all new consumers (set ) to UPDN. The values of the parameters are elements of a discrete set of unique numbers DS and TS; the coordinates are chosen out of the final value set of possible new DS/TS construction place. The variables are integral valued. Thus, the UPDN task belongs to the discrete programming tasks class. Basic (obligatory) and user (additional) restrictions are imposed upon a number of parameters of UPDN objects of R, T, L types. They are like equalities and inequalities which define basic and user areas of admissible varied parameters vector values. Partial criteria of the UPDN development optimality are defined. Сriteria restrictions are imposed upon the first . They forming an area of admissible varied parameters vector values. Represent the PPCND task in the form , where is optimum values of the varied parameters vector components; is a total set of the vector admissible values. PPCND task solving. The PPCND task belongs to the class of structural and parametrical synthesis problems. The task also differs in big dimension: thus, for calculation UPDN of a megalopolis district the vector dimension X can reach 3000-5000. In case each element of the vector takes one or the other possible value, the number of the task solution versions will be . Thus, the specified task solution with complete enumeration method is not possible and it demands the development of effective approximate methods of its solution [5; 6]. Two methods for solving the PPCND task are developed by author: - the reduction method to the set of enclosed global minimization tasks (the reduction method) [7]; - the decomposition method [8]. The detailed description of the specified methods is provided in the article [9]. Both methods suggest dividing a given task into three subtasks of smaller dimension: Subtask 1. The number and locations of new TS and DS definition. Subtask 2. The connection way of new consumers to UPDN definition. Subtask 3. The optimum connection way of new TS to the existing UPDN definition. In the reduction method it is the consecutive solution of subtasks 1-3. At that, the solution of each subsequent subtask is executed on the dragged area of admissible varied parameters vector values which are received by fixation of solution values of previous subtasks. The second method - a decomposition method - assumes dividing of the PPCND optimization task into the same three subtasks and the coordination task. The coordination task carries out calculating coordination parameters, defining the subtasks solution sequence and the calculating end moment. We carry out the coordination of subtasks by means of vectors of limiting and stimulating parameters. The two-dimensional vector of limiting coordination parameters is considered in the article. Components of this vector make sense of the minimum numbers of TS, DS which have to be constructed. The vector dimension of stimulating parameters is equal to the number of possible TS, DS construction sites. The vector components of stimulating parameters make sense of “usefulness” of constructing new TS, DS in the specified places. For the solution of subtasks 1-3 various optimization algorithms and various iteration end conditions can be used. The following solution algorithms of subtasks 1-3 are realized by author. Subtask 1. The given data for a subtask is the great number of consumers for whom there are no connection options to UPDN. The result solution of a subtask is many TS and DS, which construction needs to be for connection of all consumers to UPDN. Algorithm based on the k-averages method. It realizes the clustered k-averages method the main idea of which is a task of some given dividing of new consumers into clusters with the subsequent change of cluster centers (supposed DS/TS construction sites) and redistribution of new consumers [10]. Algorithm realizing the method of dividing clustering. The algorithm basis is the hierarchical clustering method which advantage, in comparison with the k-averages method, is no need of defining the number of clusters. The main algorithm idea is that at the first solution task stage all new consumers are located in one cluster which consistently divides into subclusters before fulfillment of the dividing end conditions. Heuristic algorithm. The idea of the approach applied in it is consecutive singling groups out of many new consumers connected to UPDN including the greatest possible number of consumers for whom DS/TS can be constructed [11]. Subtask 2. The given data for a subtask are data on initial UPDN topology and connected consumers, and many TS and DS defined in the course of the solution of subtask 1. Heuristic algorithm of the reduced enumeration. The basic algorithm principle is to add the first possible connection way of a consumer with sorting in accordance with the decreasing order of connection costs. This algorithm can be referred to the so-called “greedy” algorithms class of solving optimizing tasks. Genetic Algorithm (GA). We associate one chromosome gene with each connected consumer. The gene value (allele) is the number of DS/TS, which a consumer will be connected to. The chromosome length is equal to the number of connected consumers [12]. Algorithm based on constructing Voronoi diagrams. The algorithm is reduced to consecutive constructing Voronoi diagrams for all TS of UPDN with subsequent connection attempts of all consumers who are in the TS area. At the next stages of constructing Voronoi diagrams TS is excluded, the connection of consumers to them is not possible [13]. Subtask 3. The given data for a subtask is the TS set, constructed in the course of solution of subtask 1. To find a connection way of new TS to UPDN is required. To solve subtask 3 the genetic algorithm is applied. In it each new TS corresponds to two chromosome genes which define the numbers of TS/DS to which it is necessary to connect a new TS. Beforehand a set of such possible ways is given for each new TS. CAD system ELNET. ELNET allows to create, correct, look through and print UPDN models. The system also allows to make calculation of parameters of UPDN elements, to find optimum UPDN development ways taking into account the city development prospects. ELNET has а friendly interface for a user and the system interaction and the UPDN models visualization system. Electrotechnical calculations in ELNET are made by techniques offered in [14; 15] and meet requirements of Rules for electric equipment. Decomposition end reduction methods are the basis for mathematical ELNET apparatus. Optimizing algorithms (algorithm of limited enumeration, genetic algorithm, parallel threshold clustering algorithm, k-averages clustering algorithm) are developed to solve each subtask. The analysis of their efficiency is carried out. ELNET consists of six following modules (fig. 2). Fig. 2. ELNET modules The graphic module realizes the window interaction “user and system” interface. This module is also responsible for visualization of the UPDN models. The control module (dispatcher) is intended for interaction of all system modules among themselves. It processes received orders/requests of modules and coordinates the task solution process by means of producing operating signals. The module is also responsible for maintaining the register of operations and error messages. The input/output module carries out functions of reading and temporary storage of the UPDN data. Besides, after ending the task solution the module forms the final text file. The solutions module is the main computing ELNET module which realizes methods and algorithms of the task solution. The calculations module is intended for calculating the UPDN parameters, checking fulfillment of restriction conditions, calculating the objective function value, etc. In this module all calculations which are general for the solution methods and algorithms of subtasks are included. The reference data base contains reference data which are necessary for calculating UPDN modes, and parameters of the task solution methods and algorithms. ELNET possesses the graphic interface allowing to exercise control and setting of necessary values of calculation parameters, and to display results of calculations. The ELNET screen form consists of three main areas: the control field consisting of a toolbar and setup panel of calculation parameters; the network model display area and the calculations results display area (fig. 3). Fig. 3. ELNET main screen form Сonclusion. The ELNET application for the PPCND task solution will allow to reduce time of receiving and comparison of network development ways significantly and, therefore, gives a chance of obtaining the optimum solution in the course of an acceptable time limit.

Об авторах

И. А. Кузьмина

Московский государственный технический университет им. Н. Э. Баумана

Email: kuzminainna@yandex.ru
Российская Федерация,105005, г. Москва, ул. 2-я Бауманская, 5, стр. 1

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