SAUKH S.E., BORISENKO A.V., PODKOVALNIKOV S.V., KHAMISOV O.V.

ABSTRACT

Conceptual approaches to construction of mathematical models of oligopolistic power markets of the Russian Federation and Ukraine are considered. The power market modeling problems are formulated as a nonlinear programming problem and nonlinear mixed complementarity problem. The results of modeling of current market equilibrium and long-term planning of introduction of generating capacities are represented.

KEYWORDS

energy market, oligopoly, the mathematical model of the market, the mixed complementarity problem, nonlinear programming.

REFERENCES

1. Borisenko, A.V. and Saukh, S.E. (2008), “Modeling equilibrium state of electric power systems in market conditions”, Sb. tr. konf. «Modelirovaniye-2008». Kiev : In-t problem modelirovaniya v energetike im. G.Ye. Pukhova [Proc. tr. Conf. "Modeling 2008"], [Pukhov Institute for Modeling  in  Energy Engineering NAS of Ukraine], Kiev,  pp. 172-177.
2. Borisenko, A.V. (2009),  “Simulation of power plants under imperfect competition”,  Elektronnoe modelirovanie, Vol.  31, no.  5, pp. 3-27.
3. Podkovalnikov, S.V. and  Khamisov, O.V. (2011),  “Development of generating capacity under oligopolistic electricity market”, Ibid.,  Vol. 33, no. 4,  pp. 1-16.
4. Podkovalnikov, S.V. and  Khamisov, O.V. (2011), “Simulation study of organizational structures and electricity markets”, Upravleniye razvitiyem krupnomasshtabnykh sistem (MLSD'2011): Materialy Pyatoy mezhdunarodnoy konferentsii  [Managing the development of large-scale systems (MLSD'2011): Proceedings of the Fifth International Conference in 2 v. Vol. 1.], Moscow, V.A. Trapeznikov Institute of Management Problems RAS, October 3-5, 2011, pp. 378-380.
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7. Saukh, S.E. and Borisenko, A.V. (2010),  “Equilibrium models of the functioning and development of generating capacities of Ukraine in market conditions”,  Energetika Rossii v XXI veke: strategiya razvitiya — vostochnyy vektor. Energeticheskaya kooperatsiya v Azii: chto posle krizisa? Sb. dokl. ob"yedinennogo simpoziuma  [Energy of Russia in XXI Century: Development Strategy - Eastern vector. Asian Energy Cooperation: after the crisis? Coll. rep. Joint Symposium], Irkutsk, ISEM SO RAN, August 30-September 3, 2010,  pp. 413-419.
8. Saukh,  S.E. and  Semagina, E.P. (2011),  “Determination of the equilibrium state of the electricity market in Ukraine methods of mathematical modeling”, Elektronnoe modelirovanie,  Vol.  33, no. 4,  pp. 3-14.
9. Hobbs, В.F. (2001), “LCP models of Nash-Cournot competition in bilateral and POOLCO-based power markets”, IEEE Transactions on Power System, Vol. 16, pp. 194-202.
10. Murphy, F. and  Smeers, Y. (2005), “Generation capacity expansion in imperfectly competitive restruc­tured electricity markets”, Operations Research, Vol. 53,  no. 4, pp. 646-661.
11. Wang, L. and Mazumdar, M. (2006), “Contingency Selection in Security Constrained Optimal Power Flow Problem: A Multi-Objective Approach”, Department of Industrial Engineering University of Pitts­burgh, available at: www.ece.cmu.edu/~electricityconference/2006/Wang_Mazumdar_paper.pdf.
12. Facchinei,  F. and  Pang,  J.-S. (2003), Finite-dimensional Variational Inequalities and Complementarity Problems, Vol. I, Springer, NY.
13. Facchinei, F. and  Pang, J.-S. (2003), Finite-dimensional Variational Inequalities and Complementarity Problems Vol. II, Springer, NY.
14. Cottle, R.W., Pang, J.-S. and Stone, R.E. (2009), The Linear Complementarity Problem, SIAM.
15. Billups, S.C., Dirkse, S.P. and  Ferris, M.C.  (1997), “A comparison of large scale mixed complemen­tarity problem solvers”, Computational Optimization and Applications,  no. 7,  pp. 3-25.
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VYNNYCHUK S.D.

ABSTRACT

It is proposed to consider power of the three-phase current as the power of the generator (source) placed in a certain point of the three-phase system. The complete power components have been determined for the symmetric and asymmetric periodic operations.

KEYWORDS

active and reactive power, distortion power, power asymmetry.

REFERENCES

1. Tonkal, V.E., Novoseltsev, A.V., Denisyuk, S.P. and et al.  (1992),   Balans energiy v elektricheskikh tsepyakh  [Balance    energy in electrical circuits],  Naukova Dumka, Kiev, Ukraine.   
2. Krogeris, A.F., Reshevits, K.K., Treymanis, E.P. and  Shinka, Ya.K. (1993),   Moshchnost peremennogo toka  [AC power],  Fiz.-energ. in-t  Latv. AN,Riga,   Latvia.    
3. Chizhenko, A.I. (2003),  Obmennyye energeticheskiye protsessy v tsepyakh ventil’nikh poluprovodnikovykh preobrazovateley  [Exchange energetic processes in the valve circuits semiconductor converters],  Naukova Dumka, Kiev, Ukraine.     
4. Czamecki, L.S. (2003),  “Power Properties of Electrical Circuits and their Misinterpretations by the Instantaneous   Reactive Power p-q Theory”, Proc. of XII International Simposium of Theoretical Electrical Engineering ISTET '03,  Vol. II, Warsaw, pp. 261- 267.
5. Vynnychuk, S.D. (2006),  “AC power. A new look”,  Modelirovanie — 2006.    Sbornik trudov konferentsii «Modelirovanie- 2006»  [Modelling-2006. Proceedings of the Conference "Modelling-2006"],    Kiev, IPME NASU, pp.  161-164.       
6. Rodkin, D.I. and  Korenkova, T.V. (2010),  “The instantaneous power arbitrary waveform”,  Elektromekhanichni i enerhozberihayuchi systemy,  Vol.  4, pp. 10-21.  
7. Kizilov, V.U. and  Svetelik, A.D.  (2005), “On the concept of "reactive power"”,  Enerhetyka ta elektryfikatsiya,  no.  2, pp.  35-38.  
8. Zhdanov, P.S. (1979),   Voprosy ustoychivosti elektricheskikh sistem, Pod red. L. A. Zhukova   [Questions Stability electric systems, Ed. Zhukov, L.A.],  Energiya,  Moscow, Russia.   
9. Akagi, Н. and Nabae, A. (1993), “The p-q theory in three-phase systems under nonsinusoidal conditions”,  Eurp. Trans. on Electric Power (ETEP), Vol. 3, no. 1, pp. 27-31.
10. Agunov, M.V. (1997), Energeticheskiye protsessy v elektricheskikh tsepyakh s nesinusoidalnymi rezhimami i ikh effektivnost  [Power in electric circuits with non-sinusoidal modes and their effectiveness],  MoldNIITEI, Chisinau-Tolyatti, Moldova-Russia.
11. Pukhov, G.Ye.  (1953), ”The theory of the power system of periodic multiphase currents”, Elektrichestvo, no. 2, pp. 56-61.

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LISTROVOY S.V., PARKHOMENKO A.A.

ABSTRACT

The subexponential algorithm for decision of the SAT problem is offered.

KEYWORDS

SAT-task subexponential complexity.

REFERENCES

1. Geri, M. and Dzhonson, D. (1982),  Vychislitelnye mashiny i trudnoreshaemye zadachi [Computers and intractable problems], Mir, Moscow, Russia.
2. Skatov, A.V.  and  Borisevich, A.V. (2008), “Hardware acceleration for solving the feasibility of constructing test digital circuits”,  Informatika, elektronika, svyaz. Sbornik nauchnykh trudov,  Sevastopol, izd-vo Sev. NTU, pp. 9-15.
3. Cheremisinova, L. and Novikov, D. (2008), “SAT-Based Approach to Verification of Logical Descriptions with Functional Indeterminacy”, 8 Intern. Workshop on Boolean Problems, Freiberg, Sep­tember 18-19, 2008,  pp. 59-66.
4. Devis, M. and  Putnam, H. (1960), “A computing procedure for quantification theory, J. of ACM, no. 7, pp. 201-215.
5. Davis, M., Longemann, G. and  Loveland, D. (1962), “A machine program for theorem proving”, Communication of the ACM,  no.  5, pp. 394-397.
6. Regular Logic Bricks (2007), Proc. of the 44th Conference on Design Automation, pp. 344-349.
7. Dulkeyt, V.I., Fayzullin, R.T. and  Khnykin, I.G. (2009), “Continuous approximation of the solution of the problem "feasibility" in relation to cryptographic analysis of asymmetric ciphers”,  Computer Optics, Vol. 33, no. 1, pp. 86-90.
8. Papadimitriu, X. and  Stayglits, K. (1985), Kombinatornaya optimizatsiya. Algoritmy i slozhnost. Perevod s angl. [Combinatorial Optimization. Algorithms and Complexity], Translated from English, Mir, Moscow, Russia.
9. Listrovoy, S.V.  (2011),  “On the class of NP and NP-complete problems”,   Elektronnoe modelirovanie, Vol. 33, no.  1, pp. 31-45.

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BOMBA A.YA., SAFONIK A.P.

ABSTRACT

The article deals with the methods of accounting for reverse influence of the process characteristics (the pollution concentration of liquid and sediment) on the medium characteristics (the coefficients of porosity, filtration, diffusion, mass-transfer and others) on the example of the liquid treatment for multicomponent pollution in magnetic and sorption filters. The algorithm is proposed for numerical-asymptotic approximation of solution of the relevant model problem which is described by the system of nonlinear singularly perturbed differential equations of the «convection-diffusion-mass-transfer» type. Results of the computer experiment are presented.

KEYWORDS

filtration, reverse influence, multicomponent concentration, asymptotic solution, nonlinear problems.

REFERENCES

1. Elimelech, M. (1992), “Predicting collision efficiencies of colloidal particles in porous media”, Water Research, Vol. 26, no.  1, pp. 1-8.
2. Elimelech, M. (1994), “Particle deposition on ideal collectors from dilute flowing suspensions: Mathe­matical formulation, numerical solution and simulations”, Separations Technology, no. 4, pp. 186-212.
3. Jegatheesan, V. (1999), Effect of surface chemistry in the transient stages of deep bed filtration, Ph Dissertation, University of Technology Sydney.
4. Johnson, P.R. and Elimelech, M. (1995), “Dynamics of colloid deposition in porous media: Blocking based on random sequential adsorption”,  Langmuir, Vol. 11, no.  3, pp. 801-812.
5. Ison, C.R. and  Ives, K.J. (1969), “Removal mechanisms in deep bed filtration”, Che. Engng. Sci., no. 24, pp. 717-729.
6. Ives, K.J. (1969), “Theory of filtration”, Int. Water Supply Congress. Special subject. Vienna, no. 7, pp. 23-37.
7. Ives, K.J. (1970), “Rapid filtration”,  Water Research, Vol. 4, no.  3, pp. 201-223.
8. Petosa, A.R., Jaisi, D.P., Quevedo, I.R. and et al. (2010), “Aggregation and Deposition of Engineered Nanomaterials in Aquatic Environments: Role of Physicochemical Interactions”, Environ­mental Science & Technology, Vol. 44, pp. 6532-6549.
9. Bomba, A.Ya., Baranovskyy, S.V. and  Prysyazhnyuk, I.M.  (2008), Neliniyni synhulyarno-zbureni zadachy typu «konvektsiya — dyfuziya»  [Nonlinear singularly perturbed problem-type "convection - diffusion"], NUVGP,Rivne, Ukraine.
10. Burak, Ya.Y.,  Chaplya, Ye.Ya. and  Chernukha, O.Yu. (2006),  Kontynualno-termodynamichni modeli mekhaniky tverdykh rozchyniv [Continual-thermodynamic models of mechanics of solid solutions], Naukkova dumka, Kyyiv, Ukraine. 
11. Chaplya, Ye.Ya. and Chernukha, O.Yu. (2009), Matematychne modelyuvannya dyfuziynykh protsesiv u vypadkovykh i rehulyarnykh strukturakh [Mathematical modeling diffusion processes in random and regular structures], Naukova dumka, Kyiv, Ukraine.
12. Mints, D.M. (1964), Teoreticheskiye osnovy tekhnologii ochistki vody [Theoretical foundations of water treatment technology], Stroyizdat, Moscow, Russia.
13. Bomba, A.Ya., Prysyazhnyuk, I.M. and  Safonyk, A P. (2007),  “Modeling of wastewater treatment in modular sediment filters based on reverse effect”, Fizyko-matematychne modelyuvannya ta informatsiyni tekhnolohiyi, no. 6, pp. 101-108.
14. Bomba, A.Ya., Garashchenko, V.I., Safonyk, A.P.  and et al. (2009), “Nonlinear Mathematical modeling of magnetic impurity deposition”,  Visnyk Ternopilskoho derzhavnoho tekhnichnoho universytetu im. I. Pulyuya,  no.  3, pp. 118-123.
15. Bomba, A.Ya., Gavrilyuk, V.I., Safonik, A.P.  and et al. (2011), Nelineynyye zadachi tipa filtratsiya-konvektsiya-diffuziya-massoobmen pri usloviyakh nepolnykh dannykh [Nonlinear problems of the type of filtration-convection-diffusion and mass transfer under conditions of incomplete data]  NUVGP,  Rovno, Ukraine.
16. Bomba, A.Ya., Safonyk, A.P. and  Sivak, V.M.  (2009), “Mathematical modeling of nonlinear filtering based reverse effect”, Visnyk Natsionalnoho un-tu vodnoho hospodarstva ta pryrodokorystuvannya, Zbirnyk naukovykh prats,  Vol. 3, no. 47, Part 2,  pp. 150-157.
17. Sandulyak, A.V. (1984), Ochistka zhidkostey v magnitnom pole [Cleaning liquid in a magnetic field], Izd-vo Lvov, un-ta «Vysshaya shkola» , Lvov, Ukraine.
18. Orlov, V.O. (2005), Vodoochysni filtry iz zernystoyu zasypkoyu  [Water treatment filters with soft filling], NUVGP,Rivne, Ukraine.

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