2. Home
  3. ARCHIVE
  4. 2018
  5. VOL 40, NO 2 (2018)
  6. Архив номеров
  7. 2017 год
  8. 39-6

Electronic Modeling

Vol 39, No 6 (2017)

https://doi.org/10.15407/emodel.39.06

CONTENTS

Mathematical Modeling and Computation Methods

  SAUKH S.Ye.
Mathematical Model of the Equilibrium State of the New Competitive Electricity Market of Ukraine
3-14
  IVANOV I.L., MARTYNYUK A.A.
Chaos Synchronization in Power System Model Under Impulsive Perturbations Via Controller with Delay
15-32
  MARKOVSKIY O.P., ZACHARIOUDAKIS LEFTHERIOS, MÀKSYMUK V.R.
Galois Fields Algebra Utilization for Implementation of the Conception of Zero-Knowledge Under Identification and Authentication of Remote Users


33-46
  CHUMAKOV A.G.
Preliminary Dependencies Processing by the Projection on the Set of Correct Measurement Data
47-58

Computational Processes and Systems

  HAHANOV V.I., IEMELIANOV I.V., LIUBARSKYI M.M., CHUMACHENKO S.V., LITVINOVA E.I., TAMER BANI AMER
Qubit Method for Deductive Fault Analysis of Logic Circuits

59-92

Application of Modeling Methods and Facilities

  FARHADZADEH E.M., MURADALIYEV A.Z., FARZALIYEV Y.Z., RAFIYEVA T.K., ABDULLAYEVA S.A.
Assessment of Interrelation of Technical and Economic Indicators of EES Objects
93-106
  ARTEMCHUK V.O., KAMENEVA I.P., YATSYSHYN A.V.
Specificity of Application of Cognitive Analysis of Information in the Tasks on Ensuring Environmental Safety
107-124

MATHEMATICAL MODEL OF THE EQUILIBRIUM STATE OF THE NEW COMPETITIVE ELECTRICITY MARKET OF UKRAINE

S.Ye. Saukh

Èlektron. model. 2017, 39(6):03-14
https://doi.org/10.15407/emodel.39.06.003

ABSTRACT

A mathematical model of the equilibrium state of the new liberalized electricity market of Ukraine is proposed. The model is presented in the form of a system of nonlinear optimization problems, which adequately reflects the goals and conditions of activity of key market participants such as generating companies, transmission system operator, distribution system operators, trader, suppliers and end-users. The model establishes interrelations between such prices for electric energy in regional energy units and such volumes of production, transmission, distribution and consumption of electricity, under which the performance of each market participant is most closely related to its own purposes. The model allows you to analyze the market conditions,
achieved with different scenarios of the behavior of its participants.

KEYWORDS

model, market, equilibrium, price, tariff, electric power, network, optimization problems.

REFERENCES

1. The Law of Ukraine dated April 13, 2017 No. 2019-VIII “About the Electricity Market of Ukraine”.
2. 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
3. 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.
https://doi.org/10.1109/59.918286
4. 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
5. 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
6. Saukh, S.Ye. (2016), “Competitive equilibrium electricity market model with improved adequacy of mathematical description of the generating companies, the system operator and the electrical network”, Elektronnoe modelirovanie, Vol. 38, no. 4, pp. 49-64.
7. 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
8. Schweppe, F.C., Caramanis, M.C., Tabors, R.E. and Bohn, R.E. (1988), Spot pricing of electricity, Kluwer Academic Publishers, Boston, USA.
9. Saukh, S.Ye. (2013), “Methods of computer simulation of competitive equilibrium in electricity markets”, Elektronnoe modelirovanie, Vol. 35, no. 5, pp. 11-26.
10. 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.

Full text: PDF (in Russian)

CHAOS SYNCHRONIZATION IN POWER SYSTEM MODEL UNDER IMPULSIVE PERTURBATIONS VIA CONTROLLER WITH DELAY

I.L. Ivanov, A.A. Martynyuk

Èlektron. model. 2017, 39(6):15-32
https://doi.org/10.15407/emodel.39.06.015

ABSTRACT

The paper deals with the global chaos synchronization in two identical single-machine-infinitebus (SMIB) power systems under impulsive perturbations. Sufficient conditions of exponential synchronization via controller with delay are established by the Lyapunov-Razumikhin stability analysis of impulsive differential equations with delay. Obtained results are confirmed by numerical methods. Chaotic behavior of the SMIB power system under impulsive perturbations has also been studied.

KEYWORDS

power system, SMIB, Lyapunov-Razumikhin method, impulsive systems with delay, chaos synchronization.

REFERENCES

1. Bainov, D.D., Lakshmikanthan, V. and Simenov, P.S. (1989), Theory of impulsive differential equations, World Scientific, Singapore.
2. Samoilenko, A.M. and Perestyuk, N.A. (1987), Differentsialnye uravneniya s impulsnym vozdeistviem [Impulse differential equations], Vyshcha shkola, Kiev, Ukraine.
3. Halanai, A. and Wexler, D. (1971), Kachestvennaya teoriya impulsnykh system [Qualitative theory of impulse systems], Mir, Moscow, Russia.
4. Tsypkin, Ya.Z. (1958), Teoriya impulsnykh system [Theory of impulse systems], Fizmatgiz, Moscow, Russia.
5. Ivanov, I.L. (2014), “Delayed control of power system under pulse perturbations”, Elektronnoe modelirovanie , Vol. 36, no. 5, pp. 17-26.
6. Ivanov, I.L. and Martynyuk, A.A. (2015), “Stability results for delay power system under impulse perturbations”, Communications in applied analysis, Vol. 15, no. 2, pp. 275-286.
7. Ivanov, I.L. (2016), “Regulation of power systems under impulsive perturbations”, Elektronnoe modelirovanie, Vol. 38, no. 6, pp. 3-14.
8. Wang, L., Sun, Y., Li, L. and Liu, Y.N. (2014), “Impulsive control of stochastic interconnected power systems based on TS fuzzy model”, Transactions IEEE 33rd Chinese Control Conference (CCC), pp. 4500-4505.
9. Burtsev, A.V., Nevretdinov, Yu.M. and Smirnov, A.A. (2014), “Laboratory experimental studies of impulse characteristics of a power transformer”, Trudy Kolskogo nauchnogo tsentra RAN, Energetika, Iss. 7(26), pp. 35-40.
10. Berger, K., Anderson, R.Â. and Kroninger, H. (1975), “Parameters of lightning flashes”, Electra, no. 41, pp. 23-37.
11. Chiang, H.D., Liu, C.W., Varaiya,P.P., Wu, F. F. and Lauby, M. G. (1993), “Chaos in a simple power system”, IEEE Transactions on Power Systems, Vol. 8, no. 4, pp. 1407-1417.
https://doi.org/10.1109/59.260940
12. Chen, H.-K., Lin, T.-N. and Chen, J.-H. (2005), “Dynamic analysis, controlling chaos and chaotification of a SMIB power system”, Chaos, Solitons & Fractals, Vol. 24, no. 5, pp. 1307-1315.
https://doi.org/10.1016/j.chaos.2004.09.081
13. Lin, J.-S., Yang, Y.-S., Hung, M.-L., Liao, T.-L. and Yan, J.-J. (2010), “Observer design for chaos synchronization of time-delayed power systems”, Proceedings of the World Academy of Science, Engineering and Technology, Vol. 4, no. 5, pp. 498-501.
14. Harb, A.M. and Abdel-Jabbar, N. (2003), “Controlling Hopf bifurcation and chaos in a small power system”, Chaos, Solitons & Fractals, Vol. 18, no. 5, pp. 1055-1063.
https://doi.org/10.1016/S0960-0779(03)00073-0
15. Shahverdiev, E.M., Hashimova, L.H. and Hashimova, N.T. (2008), “Chaos synchronization in some power systems”, Chaos, Solitons Fractals, Vol. 37, no. 3, pp. 829-834.
https://doi.org/10.1016/j.chaos.2006.09.071
16. Lin, Q. and Wu, X. (2011), “The sufficient criteria for global synchronization of chaotic power systems under linear state-error feedback control”, Nonlinear Analysis: Real World Applications, Vol. 12, no. 3, pp. 1500-1509.
https://doi.org/10.1016/j.nonrwa.2010.10.009
17. Jiang, G. and Lu, Q. (2007), “Impulsive state feedback control of a predator–prey model”, Journal of Computational and Applied Mathematics, Vol. 200, no. 1, pp. 193-207.
https://doi.org/10.1016/j.cam.2005.12.013
18. Jiang, J., Lu, Q. and Qian, L. (2007), “Chaos and its control in an impulsive differential system”, Chaos, Solitons and Fractals, Vol. 34, no. 4, pp. 1135-1147.
https://doi.org/10.1016/j.chaos.2006.04.024
19. Lakmeche, A. and Arino, O. (2000), “Bifurcation of nontrival periodic solutions of impulsive differential equations arising chemotherapeutic treatment”, Dynamics of Continuous, Discrete and Impulsive System, Vol. 7, pp. 265-287.
20. Tang, S.Y. and Chen, L.S. (2002), “Density-dependent birth rate, birth pulses and their population dynamic consequences”, J. Math. Biol., Vol. 44, pp. 185-199.
https://doi.org/10.1007/s002850100121
21. Ivanov, I.L. (2015), “An approach for stability analysis of impulsive systems with delay”, Matematychni problemy mekhaniky ta compyuternoi tekhniky: Zbirnyk prats Institutu Matematyky NAN Ukrainy, Vol. 12, no. 5, pp. 30-38.
22. Slynko, V. (2005), “On stability conditions for linear impulsive systems with delay”, Prikladnaya mekhanika, Vol. 41, no. 6, pp. 697-703.
https://doi.org/10.1007/s10778-005-0138-9
23. Gantmakher, F.R. (1966), Teoriya matrits [The theory of matrices], Nauka, Moscow, USSR.
24. Jordan, D.W. and Smith, P. (2007), Nonlinear ordinary differential equations: Introduction for scientists and engineers (4th Edition), Oxford, Oxford University Press, UK.

Full text: PDF (in Russian)

GALOIS FIELDS ALGEBRA UTILIZATION FOR IMPLEMENTATION OF THE CONCEPTION OF ZERO-KNOWLEDGE UNDER IDENTIFICATION AND AUTHENTICATION OF REMOTE USERS

O.P. Markovskiy, Zacharioudakis Leftherios, V.R. Maksymuk

Èlektron. model. 2017, 39(6):33-46
https://doi.org/10.15407/emodel.39.06.033

ABSTRACT

The new approach is proposed to implementation of theoretically strict identification and authentication of remote users in accordance with zero-knowledge conception. The proposed approach consists in the use of irreversible transformations of the Galois field algebra. This allows us to speed up the process of user identification process both under software and hardware implementation. The cyclic properties of special class Galois field exponentiation have been investigated. Based on those properties the procedures of user registration and user identification procedures have been developed. A numerical example for designed procedures is given. It is shown, both theoretically and experimentally that the proposed approach provides for acceleration of user authentication process by 1-2 orders of magnitude, via a hardware implementation.

KEYWORDS

zero-knowledge conception, remote users identification, authentication of users, irreversible transformation on Galois fields.

REFERENCES

1. Schneier, B. (1996), Applied cryptography. Protocols. Algorithms and source codes in C., Ed. John Wiley, NY, USA.
2. Stavroulakis, P. (2011), “Efficient zero-knowledge identification based on one way Boolean transformations”, IEEE of GLOBECOM Workshops, Houston, Texas, USA, December 5-9, 2011, pð. 275-280.
3. Feige, U., Fiat, A. and Shamir, A. (1988), “Zero knowledge proofs of identity”, Journal of Cryptology, Vol. 1, no. 2, pp. 77-94.
https://doi.org/10.1007/BF02351717
4. Mukhin, V.E., Zacharioudakis Leftherios, Gerasimenko, O.Yu. and Kozeratskiy, M.S. (2017), “Method of zero-knowledge identification of remote users based on the conception of “zero knowledge”, Telecommunikatsiyni ta informatsiyni tekhnologii, Vol. 54, no. 1, pp. 37-45.
5. Nikolaychuk, Ya.M. (2012), Kody polya Galua: teoriya ta zastosuvannya [Galois field codes: theory and applications], TzOV Ternograf, Ternopil, Ukraine.
6. Markovskyy, O., Bardis, N. and Doukas, N. (2010), “Fast subscriber identification based on the zero knowledge principle for multimedia content distribution”, International Journal of Multimedia Intelligence and Security, no. 1, pp. 78-82.

Full text: PDF (in Russian)

PRELIMINARY DEPENDENCIES PROCESSING BY THE PROJECTION ON THE SET OF CORRECT MEASUREMENT DATA

A.G. Chumakov

Èlektron. model. 2017, 39(6):47-58
https://doi.org/10.15407/emodel.39.06.047

ABSTRACT

The article deals with the procedure of preliminary processing of measurement data, which is an addition to the standard linear methods of regularization. It is a projection on a set of dependencies with bounded values of the derivatives. Analytical accounting of a priori physical information about the processed dependency is used to suppress random errors, including blunders. In the course of adaptive smoothing, an estimate of the random error is minimized when the value of systematic error is restricted. The operation of the algorithm is illustrated by a typical problem of structural analysis. The algorithm combines the high efficiency of machine implementation, the availability of control parameters with minimal, and controlled, distortions of the smoothed dependency.

KEYWORDS

dependencies smoothing, correct measurement data.

REFERENCES

1. Tukey, J.W. (1981), Analiz rezultatov nablyudeniy [Analysis of the results of observations], translation from English, Mir, Moscow, Russia.
2. Tikhonov, A.N. and Arsenin, V.Ya. (1974), Metody resheniya nekorrektnykh zadach [Methods for solving ill-posed problems], Nauka, Moscow, Russia.
3. Fomin, A.F., Novosyolov, O.N. and Plyushchev, A.V. (1985), Otbrakovka anomalnykh rezultatov izmereniy [Culling of abnormal measurement results], Energoatomizdat, Moscow, Russia.
4. Loner, R.L., and Uilson, G.N., eds. (1985), Ustoychivye statisticheskie metody otsenki dannykh [Robust statistical methods of data evaluation], (translation from English), Mashinostroenie, Moscow, Russia.
5. Gimelfarb, G.L. (1985), “Hardware and features of interactive digital image processing software”, Zarubezhnaya radioelektronika, no. 10, pp. 87-105.
6. Yaroslavskiy, L.P. (1979), Vvedenie v tsifrovuyu obrabotku izobrazhenii [Introduction to digital image processing], Sovetskoe radio, Moscow, Russia.
7. Vonk, C.G. (1975), “A gåneral computer program for the processing of small-angle X-ray scattering data”, J. Applied Crystallografica, Vol. 8, no. 2, pp. 340-341.
https://doi.org/10.1107/S0021889875010618
8. Walter, G. (1975), “Ein FORTRAN-Programmsystem zur Auswertung von Licht- und Rontgenkleinwinkelstreukurven von Glasern mit Phasentrennungen”, Wiss. Z. Univ. Rostok, Math.-naturwiss., Rostok, Vol. 24, no. 5, pp. 599-604.
9. Ayvazyan, S.A., ed. (1989), Prikladnaya statistika [Applied Statistics], Vol. 2, Nauka, Moscow, Russia.
10. Barchuk, O.I., Kurashov, V.N. and Chumakov, A.G. (1989), “Determination of the correlation functions of the of phase diffusers amplitude transmission by solving the inverse problem of coherent light scattering”, Kvantovaya elektronika, no. 38, pp. 82-88.
11. Chumakov, A.G. (1993), “The robust smoothing program UTIR, version 03.06”, Software of Ukraine, SJ TEKNA, Kiev, pp. 28-29.

Full text: PDF (in Russian)