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.

Full text: PDF (in Russian)