S.D. Vynnychuk
Èlektron. model. 2018, 38(4):65-80
https://doi.org/10.15407/emodel.38.04.065
ABSTRACT
An algorithm has been proposed for calculating RPR_D flow distribution in distribution networks with a tree structure graph for the case of linear dependence of the potential change of the current on any arbitrary branch. The algorithm is based on the consecutive replacements of dangles by equivalent branches, where a special variant of the positive direction of current in the branches is formed in order to reduce the number of operations. It is shown that RPR_D algorithm for arbitrary non-zero values of the resistance of branches allows determining with guarantee the unknown currents in the branches and potentials in the nodes regardless of the variants of boundary conditions, and its time complexity is estimated to be about O (V), where V is the number of nodes in the graph.
KEYWORDS
distribution network, load flow, convolution, algorithm, the time complexity.
REFERENCES
1. Akopyan, S.G. “Electrical theory of hydraulic circuits and methodical bases of modes analysis and optimal design of gas transmission systems”, Abstract of Dr. Sci. (Tech.) dissertation, 05.13.12, 05.15.13, State Engineering University of Armenia, Yerevan, Armenia.
2. Saukh, S.Ye. (1991), “Research of power circuits with the help of numerical operator methods”, Abstract of Dr. Sci. (Tech.) dissertation, 05.13.16., Institute for Modeling in Energy Engineering of Academy of Sciences of Ukraine, Kyiv, Ukraine.
3. Merenkov, A.P. and Khasilev, V.Ya. (1985), Teoriya gidravlicheskikh tsepey [Theory of hydraulic circuits], Nauka, Moscow, Russia.
4. Barinov, V.A. and Sovalov, S.A. (1990), Rezhimy energosistem: metody analiza i upravleniya [Power systems modes: methods of analysis and control], Energoatomizdat, Moscow, Russia.
5. Yevdokimov, A.G., Tevyashev, A.D. and Dubrovskiy, V.V. (1990), Modelirovanie i optimizatsiya potokoraspredeleniya v inzhenernykh setyakh, 2-e izd. pererab. i dop. [Modelling and optimization of load flow in engineering networks, 2nd ed., revised. and ext.], Stroyizdat, Moscow, Russia.
6. Vynnychuk, S.D. (2006), “Methods and algorithms for solving problems of analysis, design and management of distribution flows in the hydraulic distribution systems”, Abstract of Dr. Sci. (Tech.) dissertation, 01.05.02., Pukhov Institute for Modeling in Energy Engineering of National Academy of Sciences of Ukraine, Kyiv, Ukraine.
7. Davis, T.A. (2006), Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms), Society for Industrial and Applied Mathematics.
8. Kondraschenko, V.Ya., Vynnychuk, S.D. and Fedorov, M.Yu. (1990), Modelirovanie gazovykh i zhidkostnykh raspredelitelnykh system [Simulation of gas and fluid distribution systems], Naukova dumka, Kiev, Ukraine.
9. Bun, R.A., Vasiliev, E.D. and Semotyuk, V.N. (1991), Modelirovanie elektricheskikh tsepey metodom podskhem, Otv. red. Gritsyk, V.V., AN Ukrainy, Fiziko-mekhanicheskiy in-t. [Simulation of electrical circuits by subcircuits, Ed. Grytsyk, V.V., Academy of Sciences of Ukraine, Physical-Mechanical inst.], Naukova dumka, Kiev, Ukraine.
10. Gritsay, M.A. and Zhuravlev, V.G. (1968), “The calculation of flow distribution in the electric network by the method of determining value”, Elektrichestvo, no. 8, pp. 17-20.
11. Maksimovich, N.G. (1961), Lineinye elektricheskie tsepi i ikh preobrazovaniya [Linear circuits and their conversion], Gosenergoizdat, Moscow-Leningrad, Russia.
12. Pukhov, G.Ye. (1967), Metody analiza i sinteza kvazi analogovykh elektronnykh tsepey [Methods of analysis and synthesis of the quasi analog electronic circuits], Naukova dumka, Kiev, Ukraine.
13. Seshu, S. and Rid, M.B. (1971), Lineinye grafy i elektricheskie tsepi, Per. s angl., pod red. P.A. Ionkina, Uchebnoe posobie dlya vuzov spetsialnostey radiotekhnika, elektronnaya tekhnika, elektropriborostroenie i avtomatika [Line graphs and circuits, Transl. from English., Ed. Ionkin, P.A., Textbook for Universities radio engineering specialties, electronic engineering, electrical instrumentation and automation], Vysshaya shkola, Moscow, Russia.
14. Sigorskiy, V.P. and Petrenko, A.I. (1970), Algoritmy analiza elektronnykh skhem [Algorithms analysis of electronic circuits], Tekhnika, Kiev, Ukraine.