Abstract
A game with a finite (more than three) number of players on a polyhedron of connected player strategies is studied. This game describes the interaction among (a) the base load power plant (the generator), (b) all the large customers of a regional electrical grid that receive electric energy from the generator, as well as from the available renewable sources of energy, both directly and via electricity storing facilities, and (c) the transmission company. An auxiliary three-person game on polyhedra of disjoint player strategies that is associated with the initial game is also considered. It is shown that an equilibrium point in the auxiliary game is an equilibrium point in the above game with connected player strategies. Verifiable necessary and sufficient conditions of an equilibrium in the auxiliary three-person game are proposed, and these conditions allow one to find equilibria in (the auxiliary) solvable game by solving three linear programming problems two of which form a dual pair.
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Belenky, A.: A game-theoretic approach to optimizing the scale of incorporating renewable sources of energy and electricity storing systems in a regional electrical grid. Energy Syst. (2015). doi:10.1007/s12667-015-0145-9
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Acknowledgments
The idea of using a game-theoretic approach to optimizing the scale of incorporating renewable sources of energy and electricity storing systems in regional electrical girds was first presented at the Conference “Network Models in Economics and Finance,” at the National Technical University of Athens, June 13–15, 2013, organized and held under the leadership of Prof. Panos Pardalos, a world-leading scientist in the field of optimization of energy systems, whose support of this idea and the encouragement in developing it the author highly appreciates. The author expresses his gratitude to Prof. Fuad Aleskerov, a world-leading scientist in the field of developing decision-making systems, with whom the author has had fruitful discussions on developing tools for quantitatively analyzing electrical grids as large-scale systems. The author appreciates support rendered to his research works by the MIT Center for Engineering Systems Fundamentals, headed by Prof. Richard C. Larson, a world-leading scientist in the field of modeling service systems, who has drawn the author’s attention to modeling the use of electricity storing systems in electrical grids. Finally, the author would like to thank two anonymous referees whose critical reviews of the paper have been very useful. The paper was prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE) and supported within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program.
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Belenky, A.S. Finding an optimal strategy of incorporating renewable sources of energy and electricity storing systems in a regional electrical grid. Energy Syst 6, 291–308 (2015). https://doi.org/10.1007/s12667-015-0144-x
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DOI: https://doi.org/10.1007/s12667-015-0144-x