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  8. 38-4

Electronic Modeling

Vol 38, No 4 (2016)

https://doi.org/10.15407/emodel.38.04

CONTENTS

  The 100TH Anniversary of Birth of Georgiy Yevgenievich PUKHOV (1916—2016)
3-8
  SKLYAROV V.F.
Pukhov G.E. — the Man and the Institute
9-12

Mathematical Modeling and Computation Methods

  VASILIEV V.V., SIMAK L.A., VASILIEV A.V.
Signal Processing and Modeling of Fractional Order Dynamical Systems Based on Approximated Type Operational Calculus
13-34
  VERLAN A.F., KLYUCHKA K.N.
Integral Models in the Problems of Analysis of Electrical Circuits
35-48
  SAUKH S.Ye.
Competitive Equilibrium Electricity Market Model with Improved Adequacy of Mathematical Description of Generating Companies, System Operator and Electrical Network
49-64
  VYNNYCHUK S.D.
Determination of Flow Distribution in Networks with a Tree Graph
65-80
  KRAVTSOV H.A.
Measure of Difference Between Classifications
81-98

Computational Processes and Systems

  PETROV V.V., KRYUCHYN A.A., SHANOYLO S.M.
Optical Carriers for Long-Term Data Storage
99-108

Application of Modeling Methods and Facilities

  GURIEIEV V.A., SAMOYLOV V.D., SANGINOVA O.V.
National Staff Training System Concept of Integrated Electric Power System of Ukraine
109-122
  STASIUK O.I., GONCHAROVA L.L.
Mathematical Models and Methods for Computer Control of the Power Supply of Railways on the Basis of Pukhov’s Differential Transformations
123-135

SIGNAL PROCESSING AND MODELING OF FRACTIONAL ORDER DYNAMICAL SYSTEMS BASED ON APPROXIMATED TYPE OPERATIONAL CALCULUS

V.V. Vasiliev, L.A. Simak, A.V. Vasiliev

Èlektron. model. 2018, 38(4):13-34
https://doi.org/10.15407/emodel.38.04.013

ABSTRACT

The application of approximation-operational method based on the local and global versions of the Legendre polynomials for estimating the average signal values, the average values derivatives of the first and second orders, as well as the evaluation of the fractional derivatives of various orders in the Riemann-Liouville and Caputo sense. Illustrative examples of the method application for digital signal processing and simulation of dynamic systems of fractional order in the system software environment «Mathematica®»

KEYWORDS

fractional calculus, approximation and signal processing, operational calculus, dynamical system, Caputo type fractional derivative, Riemann-Liouville type fractional derivative, Matematica® System.

REFERENCES

1. Poularikas, A.D. (2000), The transforms and applications handbook, Ed by A.D. Poularikas, CRC Press & IEEE Press.
2. Pukhov, G.E. (1978), Preobrazovaniya Teilora i ikh primeneniya v elektrotekhnike i elektronike [Taylor transforms and their application in electro engineering and electronics], Naukova Dumka, Kiev, Ukraine.
3. Pukhov, G.E. (1982), “Differential transforms and circuit theory”, Circuit Theory and Applications, Vol. 10, pp. 265-276.
https://doi.org/10.1002/cta.4490100307
4. Simak, L.A. (1986), “Differential transforms based on fractional order derivatives and fractional-power spectra modeling”, Doklady akademii nauk Ukrainy, Seria A: Fiziko-matematicheskie i tekhnicheskie nauki, no. 8, pp. 79-82.
5. Uchaikin, V.V. (2008), Metod drobnyh proizvodnykh [Method of fractional derivatives], Artishok Publ., Ulyanovsk, Russia.
6. Vasiliev, V.V. and Simak, L.A. (2008), Drobnoye ischislenie i approksimatsionnye metody v modelirovanii dinamicheskikh sistem [Fractional calculus and approximated methods in dynamical systems modeling and simulation], Akadem press, Kiev, Ukraine. 
7. Oldham, K.B. and Spanier, J. (1974), The fractional calculus, Academic Press, New York, USA.
8. Podlubny, I. (1999), Fractional differential equations, Academic Press, San Diego, USA.
9. Wolfram, S. (1996), The mathematica book, Wolfram Media / Cambridge University Press, Cambridge, UK.

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INTEGRAL MODELS IN THE PROBLEMS OF ANALYSIS OF ELECTRICAL CIRCUITS

A.F. Verlan, K.N. Klyuchka

Èlektron. model. 2018, 38(4):35-48
https://doi.org/10.15407/emodel.38.04.035

ABSTRACT

The use of integral models in analysis of dynamic processes in electrical circuits has been considered. A possibility of raising efficiency of the methods and means of design of broad class electrical circuits based on the use of integral dynamic models has been substantiated.

KEYWORDS

electrical circuits, dynamic characteristics, Volterra integral equations.

REFERENCES

1. Pukhov, G.E. (1966), “Integral methods for calculating electric circuits”, Teoreticheskaya elektrotekhnika, no. 2, pp. 5-14.
2. Ginzburg, M.Ì. (1960), “Production of integral equations for nonlinear circuits using the operator method”, Elektrichestvo, no. 5, pp. 17-22.
3. Verlan, A.F. (1983), “The method of integral equations in the problem description and calculation of electrical circuits”, Elektronnoe modelirovanie, Vol. 5, no. 5, pp. 8-12.
4. Verlan, A.F. and Klyuchka, K.N. (2011), “The method of integral equations in the problem of identification of parameters of electric circuits”, Visnyk Cherkaskogo derzhavnogo tekhnologichnogo universytetu, no. 1, pp. 55-58.
5. Verlan, A.F., Sitnik, O.O. and Klyuchka, K.M. (2009), “Integral equation analysis of non-stationary electrical systems”, Visnyk Natsionalnogo universytetu «Lvivska politekhnika”, no. 637, pp. 12-18.
6. Klyuchka, K.M. (2013), “Modeling of circuits based on nonparametric integrated models”, Visnyk Cherkaskogo derzhavnogo tekhnologichnogo universytetu, no. 2, pp. 96-101.

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COMPETITIVE EQUILIBRIUM ELECTRICITY MARKET MODEL WITH IMPROVED ADEQUACY OF MATHEMATICAL DESCRIPTION OF GENERATING COMPANIES, SYSTEM OPERATOR AND ELECTRICAL NETWORK

S.Ye. Saukh

Èlektron. model. 2018, 38(4):49-64
https://doi.org/10.15407/emodel.38.04.049

ABSTRACT

The model of competitive equilibrium of the electricity market is presented, in which a set of objective functions of profits of the system operator and generating companies contains all components of the balance of commodity-money relations between them. In particular, the total cost of electricity losses in transmission lines is included in the objective function of profit of the system operator. Separate components of this cost of losses are accounted in the objective functions of profits of the generating companies in the form of cost of transmission services of electrical power belonging to these companies. The cost of these services for each generating company is based on the principle of superposition of flows of electricity in transmission lines, acting in terms of amodel representing the electrical grid as a linear circuit of DC. To simulate the flows of electricity and losses in transmission lines the representation of the power grid in a form of a non-linear DC circuit is used.

KEYWORDS

electrical network, model, electricity market, equilibrium state.

REFERENCES

1. Wei, J.-Y. and Smeers, Y. (1999), “Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices”, Operations Research, Vol. 47, no. 1, pp. 102-112.
https://doi.org/10.1287/opre.47.1.102
2. Hobbs, B.F. (2001), “Linear complementarity models of Nash–Cournot competition in bilateral and POOLCO power markets”, IEEE Transactions on Power Systems, Vol. 16, no. 2, pp. 194-202.
3. Day, C.J., Hobbs, B.F. and Pang, J.-S. (2002), “Oligopolistic competition in power networks: a conjectured supply function approach”, IEEE Transactions on Power Systems, Vol. 17, no. 3, pp. 597-607.
https://doi.org/10.1109/TPWRS.2002.800900
4. Murphy, F. and Smeers, Y. (2005), “Generation capacity expansion in imperfectly competitive restructured electricity markets”, Operations Research, Vol. 53, no. 4, pp. 646-661.
https://doi.org/10.1287/opre.1050.0211
5. Borisenko, A.V. and Saukh, S.Ye. (2008), “Simulation of equilibrium state of the electric power systems under market conditions”, Sbornik trudov konferentsii “Modelirovanie-2008” [Simulation-2008, Conference Proceedings], Pukhov Institute for Modelling in Energy Engineering, Kyiv, Ukraine, pp. 172-177.
6. Hobbs, B.F., Drayton, G., Fisher, E.B. and Lise, W. (2008), “Improved transmission representations in oligopolistic market models: quadratic losses, phase shifters, and DC lines”, IEEE Transactions on Power Systems, Vol. 23, no. 3, pp. 1018-1029.
https://doi.org/10.1109/TPWRS.2008.926451
7. Schweppe, F.C., Caramanis, M.C., Tabors, R.E. and Bohn, R.E. (1988), Spot pricing of electricity, Kluwer Academic Publishers, Boston, USA.
8. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (1972), Abramowitz, M. and Stegun, I., National Bureau of Standards, USA.
9. Saukh, S.Ye. (2011), “Mathematical modeling of the energy circuits”, Elektronnoe modelirovanie, Vol. 33, no 3, pp. 3-12.
10. Saukh, S.Ye. (2013), “Methods of computer simulation of competitive equilibrium in electricity markets”, Elektronnoe modelirovanie, Vol. 35, no 5, pp. 11-26.
11. Saukh, S.Ye. (2015), “Method of shearing matrix elements of the Clarke’s generalized Jacobian for providing numerical stability of the quasi-Newton methods of solving of the variational inequalities problems”, Elektronnoe modelirovanie, Vol. 37, no 4, pp. 3-18.

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DETERMINATION OF FLOW DISTRIBUTION IN NETWORKS WITH A TREE GRAPH

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.

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