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Вестник СибГАУ. Том 17, № 1
UDC 519.6
Vestnik SibGAU Vol. 17, No. 1, P. 62-66
CAD SYSTEM FOR PERSPECTIVE POWER SUPPLY NETWORK DEVELOPMENT
TASK SOLUTION
I. A. Kuzmina
Moscow State Technical University named after N. E. Bauman 5, building 1, 2-ya Baymanskaya Str., Moscow, 105005, Russian Federation E-mail: kuzminainna@yandex.ru
The process of urban power supply network development is connected with need calculation and accounting a large number ofparameters, possible development ways and complexity of their assessment. These circumstances require the introduction of new technologies for solving specified task.
Declaration of author's developed computer-aided design system (CAD system) ELNET for the task solution automation ofperspective urban power supply network development is presented in article. Description of models, methods and algorithms based in the CAD system are given.
CAD allows to create, correct, calculate parameters, look through and print models of urban power supply networks. ELNET consists of six connected modules: graphic module, control module (dispatcher), input/output module, solutions module, calculations module, reference data base. System possesses the friendly graphical interface allowing ease using.
In CAD ELNET mathematical basis puts designed by author mathematical model of urban power supply network presentation as directed weighted graph and two methods of solving urban power supply network development task: the reduction method to the set of enclosed global minimization tasks and decomposition method. Both methods suggest dividing a given task into three subtasks of smaller dimension: 1. Subtask of definition the number and locations of new substations. 2. Subtask of definition the connection way of new consumers to network. 3. Subtask of definition the optimum connection way of new substations to the existing network.
The optimization algorithms of subtasks solution are realized by the author. For solving subtask 1 three algorithms are designed and realized: algorithm based on the k-averages method; algorithm realizing the method of dividing clustering; heuristic algorithm. For solving subtask 3 three algorithms are also offered: heuristic algorithm of the reduced enumeration; genetic algorithm; algorithm based on constructing Voronoi diagrams. To solve subtask 3 the genetic algorithm is applied.
Technical solutions represented in the article allow reducing time of design and increasing the quality of design decisions.
Keywords: CAD system, modeling, reduction method, decomposition method, urban power distribution network, perspective power supply network development task.
Вестник СибГАУ Том 17, № 1. С. 62-66
СИСТЕМА АВТОМАТИЗАЦИИ ПРОЕКТИРОВАНИЯ ГОРОДСКОЙ РАСПРЕДЕЛИТЕЛЬНОЙ СЕТИ ЭЛЕКТРОСНАБЖЕНИЯ
И. А. Кузьмина
Московский государственный технический университет им. Н. Э. Баумана Российская Федерация,105005, г. Москва, ул. 2-я Бауманская, 5, стр. 1 E-mail: kuzminainna@yandex.ru
Процесс проектирования городских распределительных сетей электроснабжения связан с необходимостью расчета и учета большого числа параметров, возможных вариантов развития и сложностью их оценки. Данные обстоятельства требуют внедрения новых технологий для решения указанной задачи.
Представлено описание разработанной автором системы автоматизированного проектирования (САПР) ELNET, реализующей решение задачи перспективного развития городской распределительной сети электроснабжения. САПР позволяет создавать, корректировать, рассчитывать параметры, просматривать, печатать модели сетей электроснабжения. Структура ELNET состоит из шести взаимосвязанных модулей: графический модуль, модуль управления, модуль расчета, модуль решения, модуль ввода и вывода данных, база данных справочной информации. Система обладает дружественным графическим интерфейсом для легкой работы пользователя.
В основу математического аппарата САПР ЕЬЫЕТ заложены разработанные автором математическая модель представления сети электроснабжения в виде направленного взвешенного графа и два метода решения задачи перспективного развития городской распределительной сети электроснабжения: метод редукции задачи в совокупности задач меньшей размерности и метод декомпозиции. Оба метода предполагают разделение исходной задачи на подзадачи меньшей размерности: подзадача определения числа и места строительства новых подстанций; подзадача определения варианта подключения новых потребителей к сети электроснабжения; подзадача определения оптимального варианта включения подстанций в существующую структуру сети.
Для решения подзадач автором разработаны оптимизационные алгоритмы. Для решения подзадачи 1 разработаны и реализованы три алгоритма: алгоритм, основанный на методе кластеризации; алгоритм, основанный на методе разделительной кластеризации; эвристический алгоритм. Для подзадачи 2 также предложены три алгоритма: эвристический алгоритм ограниченного перебора; генетический алгоритм; алгоритм, основанный на построении диаграмм Вороного. Для решения подзадачи 3 применяется генетический алгоритм.
Представленные в работе технические решения позволяют снизить время проектирования и повысить качество принимаемых проектных решений.
Ключевые слова: САПР, моделирование, метод редукции, метод декомпозиции, городская распределительная сеть электроснабжения, задача перспективного развития электросети.
Introduction. Urban power distribution network (UPDN) of megalopolis is a difficult system of nonuniform 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 G = (R,T, L),
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 N = Nhigh u N/ow, where Nhigh, N/ow 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:
Q-DS;0-TS; y _ 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
X = (xi , X1j, X2j, (xk,yk), Xf5ä, XT5ä),
where Xi is an unknown number of DS/TS, which a consumer Ni will be connected to; x 1 j, X2j are the numbers of DS/TS, which TS Tj is connected to; (xk, yk) are the geographical coordinates of new DS/TS;
BecmrniK Cu6rAY. Tom 17, № 1
XRja, Xfja are the numbers of new DS and TS, construction of which should be for connection of all new consumers (set N ) to UPDN.
The values of the parameters Xi, X1 j, X2j are elements of a discrete set of unique numbers DS and TS; the coordinates (xk, yk) are chosen out of the final value set of possible new DS/TS construction place. The variables Xm, X/ja 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 D ^ and user Dp areas of admissible
varied parameters vector values.
Partial criteria of the UPDN development optimality
Z(X) = (Z1(X), Z2(X), ..., Z|Z|(X) are defined. Criteria
restrictions are imposed upon the first |z| . They forming an area of admissible varied parameters D Z vector values.
Represent the PPCND task in the form Z(X*) = min Z(X) ,
XeD
where X* is optimum values of the varied parameters vector components; D = DX n D^ n DZ 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 23000 - 25000. 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 parame-
ters, 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 a 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).
USER
Graphic module
Control module (dispatcher)
Solutions module
Calculations module
-
Reference data base
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. 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
Calculation results display area
Fig. 3. ELNET main screen form
Conclusion. 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.
References
1. Ananicheva S. S., Kalinkina M. A. Prakticheskie zadachi elektricheskikh setey [Electric network practical tasks]. Ekaterinburg, UrFU Publ., 2012, 112 p.
2. Kozlov V. A. Gorodskie raspredelitel'nye elek-tricheskie seti [Urban power electric network]. Leningrad, Energoizdat Publ., 1982, 224 p.
3. Chow J. H., Wu F. F., Momoh J. A. et al. Applied mathematics for restructured electric power systems. Optimization, control, and computational intelligence. Springer Science. 2005. 342 p.
4. Karpenko A. P., Kuz'mina I. A. [A mathematical model of urban distribution electro-network considering its future development]. Nauka i obrazovanie. 2014, No. 05 (In Russ.). Available at: http://technomag.bmstu.ru/ doc/709781.html (accessed 14.02.2016). DOI: 10.7463/ 0514.0709781.
5. Gorbatov V. A. Fundamental'nye osnovy diskret-noy matematiki. Informatsionnaya matematika [Fundamental of discrete mathematic. information mathematics]. Moscow, Nauka - Fizmatlit Publ., 2000, 544 p.
6. Berkul'tsev M. V. Metody evristicheskogo poiska v zadachakh planirovaniya i upravleniya. [Electric search
Вестник СибГАУ. Том 17, № 1
methods in planning and control tasks]. Moscow, MAI Publ., 2000, 43 p.
7. Feofanova V. A., Vorotnikov V. I. Diskretnaya matematika: uchebno-metodicheskoe posobie [Discrete mathematic. Teaching tutorial]. Nizhniy Tagil, NTI (filial) UrFU Publ., 2013, 256 p.
8. Borodachev S. M. Teoriya prinyatiya resheniy [Decision theory]. Ekaterinburg, Izdatel'stvo Ural'skogo universiteta Publ., 2014, 124 p.
9. Karpenko A. P., Kuz'mina I. A. [Problem-Solving Methods for the Prospective Development of Urban Power Distribution Network]. Nauka i obrazovanie. 2014, No. 10 (In Russ.). Available at: http://technomag. bmstu.ru/doc/727891.html (accessed 14.02.2016). DOI: 10.7463/1014.0727891.
10. Pisaruk N. N. Issledovanie operatsiy [Operations research]. Minsk, BGU Publ., 2015, 300 p.
11. Lotov A. V., Pospelova I. I. Mnogokriterial'nye zadachi prinyatiya resheniy [Multicriteria decisionmaking tasks]. Moscow, MAKS Press Publ., 2008, 197 p.
12. Kureychik V. M. Geneticheskie algoritmy i ikh primenenie [Genetic algorithms and their application]. Taganrog, Taganrogskiy RTU Publ., 2002, 244 p.
13. Kogan D. I. Dinamicheskoe programmirovanie i diskretnaya mnogokriterial'naya optimizatsiya [Discrete programming and discrete multicriteria optimization]. Nizhniy Novgorod, Izdatel'stvo Nizhegorodskogo universiteta Publ., 2004, 150 p.
14. Karpov F. F. Raschet gorodskikh rasprede-litel'nykh elektricheskikh system [Urban distribution electric systems calculation]. Moscow, Energiya Publ., 1968, 223 p.
15. Karapetyan I. G., Faybisovich D. L., Shapiro I. M. Spravochnik po proektirovaniyu elektricheskikh setey [Directiry of electric network design]. Ed. D. L. Faybiso-vicha. Moscow, Izdatel'stvo NTsENAO Publ., 2006, 349 p.
Библиографические ссылки
1. Ананичева С. С., Калинкина М. А. Практические задачи электрических сетей : учеб. пособие. Екатеринбург : УрФУ, 2012. 112 с.
2. Козлов В. А. Городские распределительные электрические сети. Л. : Энергоиздат, 1982. 224 с.
3. Applied mathematics for restructured electric power systems. Optimization, control, and computational
intelligence / J. H. Chow, F. F. Wu, J. A. Momoh (eds). Springer Science, 2005. 342 p.
4. Карпенко А. П., Кузьмина И. А. Математическая модель распределительной городской сети электроснабжения с учетом ее перспективного развития // Наука и образование : электронное научное издание. 2014. № 05. URL. http://technomag.bmstu.ru/doc/ 709781.html. (дата обращения: 14.02.2016). DOI: 10.7463/0514. 0709781.
5. Горбатов В. А. Фундаментальные основы дискретной математики. Информационная математика. М. : Наука : Физматлит, 2000. 544 с.
6. Беркульцев М. В. Методы эвристического поиска в задачах планирования и управления : учеб. пособие. М. : МАИ, 2000. 43 с.
7. Феофанова В. А., Воротников В. И. Дискретная математика : учеб.-метод. пособие. Нижний Тагил : НТИ (филиал) УрФУ, 2013. 256 с.
8. Бородачев С. М. Теория принятия решений : учеб. пособие. Екатеринбург : Изд-во Урал. ун-та, 2014. 124 c.
9. Карпенко А. П., Кузьмина И. А. Методы решения задачи перспективного развития распределительной городской сети энергоснабжения // Наука и образование : электронное научное издание. 2014. № 10. URL: http://technomag.bmstu.ru/doc/727891.html (дата обращения: 14.02.2016). DOI: 10.7463/1014.0727891.
10. Писарук Н. Н. Исследование операций. Минск : БГУ, 2015. 300 с.
11. Лотов А. В., Поспелова И. И. Многокритериальные задачи принятия решений : учеб. пособие. М. : МАКС-Пресс, 2008. 197 с.
12. Курейчик В. М. Генетические алгоритмы и их применение. Таганрог : Таганрогский РТУ, 2002. 244 с.
13. Коган Д. И. Динамическое программирование и дискретная многокритериальная оптимизация. Нижний Новгород : Изд-во Нижегород. ун-та, 2004. 150 с.
14. Карпов Ф. Ф. Расчет городских распределительных электрических систем. М. : Энергия, 1968. 223 с.
15. Карапетян И. Г., Файбисович Д. Л., Шапиро И. М. Справочник по проектированию электрических сетей / под ред. Д. Л. Файбисовича. 3-е изд., перераб. и доп. М. : Изд-во НЦЭНАО, 2006. 349 с.
© Kuzmina I. А., 2016
