Modeling of competitive equilibrium at the electricity market with regard for energy losses in electric networks

1Saukh S.Ye., Dr. Sci. (Eng.), Professor, 2Borisenko A.V., Dr. Sci. (Eng.), Senior Researcher
1Pukhov Institute for Modelling in Energy Engineering of the National Academy of Sciences of Ukraine, 15 General Naumov St., Kiev, 03164, Ukraine
2Ukrenergokonsalting, OOO, 5 Spasskaia St., Kiev, 04071, Ukraine
Language: Russian
Source: Problemy zahal`noi enerhetyky - The Problems of General Energy, 2016, 3(46):5-11
https://doi.org/10.15407/pge2016.03.005
Section: Development, organization and functioning of energy markets
UDC: 621.311.001.57
Received: 15.09.2016
Published: 28.09.2016
Abstract: We have proposed a mathematical description of a network of power transmission lines, which represents adequately the physical properties of the network in model of the equilibrium state of electricity market. Such a description of the electric network, based on the theory of energy circuits, establishes a relationship between the flows of electricity in power transmission lines and potentials at the nodes of network in strict accordance with Kirchhoff's laws and the Hamilton's principle of least action. Furthermore, this description includes the physical parameters of power transmission lines, which provides its applicability to the practical problems of modeling of the equilibrium states of the electricity market.
Keywords: power transmission line, electric network, market, competition, equilibrium, model.
References:
1. Wei, J.-Y., & Smeers, Y. (1999). Spatial Oligopolistic Electricity Models with Cournot Generators and Regulated Transmission Prices. Operations Research, Vol. 47 (N 1), 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 (N 2), 194-202. https://doi.org/10.1109/59.918286
3. Day, C.J., Hobbs, B.F., & Pang, J.-S. (2002). Oligopolistic Competition in Power Networks: A Conjectured Supply Function Approach. IEEE Transactions on Power Systems, Vol. 17 (N 3), 597-607. https://doi.org/10.1109/TPWRS.2002.800900
4. Murphy, F., & Smeers, Y. (2005). Generation capacity expansion in imperfectly competitive restructured electricity markets. Operations Research, Vol. 53 (N 4), 646–661. https://doi.org/10.1287/opre.1050.0211
5. Borisenko, А.V., & Saukh, S.Ye. (2008). Simulation of equilibrium state of the electric power systems under market conditions. Simulation–2008, Conference Proceedings (pp. 172–177). Kyiv: Pukhov Institute for Modelling in Energy Engineering [in Russian].
6. Hobbs, B.F., Drayton, G., Fisher, E.B., & Lise, W. (2008). Improved Transmission Representations in Oligopolistic Market Models: Quadratic Losses, Phase Shifters, and DC Lines. IEEE Transactions on Power Systems, Vol. 23 (N 3), 1018–1029. https://doi.org/10.1109/TPWRS.2008.926451
7. Schweppe, F.C., Caramanis, M.C., Tabors, R.E., & Bohn, R.E. (1988). Spot Pricing of Electricity. Boston, MA: Kluwer Academic Publishers. https://doi.org/10.1007/978-1-4613-1683-1
8. Saukh, S.Ye. (2011). Mathematical modeling of the energy circuits. Elektronnoe modelirovanie, Vol. 33, no 3, 3-12 [in Russian].
9. Saukh, S.Ye. (2013). Methods of computer simulation of competitive equilibrium in electricity markets. Elektronnoe modelirovanie, Vol. 35, no 5, 11-26 [in Russian].
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, 3-18 [in Russian].