A McKean-Vlasov approach to distributed electricity generation development

René Aïd, Matteo Basei and Huyen Pham
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René Aïd: FiME Lab - Laboratoire de Finance des Marchés d'Energie - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CREST - EDF R&D - EDF R&D - EDF - EDF, LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Matteo Basei: IEOR Dept - Industrial Engineering and Operations Research Department - Columbia University [New York]
Huyen Pham: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité

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Abstract: This paper analyses the interaction between centralised carbon emissive technologies and distributed intermittent non-emissive technologies. In our model, there is a representative consumer who can satisfy her electricity demand by investing in distributed generation (solar panels) and by buying power from a centralised firm at a price the firm sets. Distributed generation is intermittent and induces an externality cost to the consumer. The firm provides non-random electricity generation subject to a carbon tax and to transmission costs. The objective of the consumer is to satisfy her demand while minimising investment costs, payments to the firm and intermittency costs. The objective of the firm is to satisfy the consumer's residual demand while minimising investment costs, demand deviation costs, and maximising the payments from the consumer. We formulate the investment decisions as McKean–Vlasov control problems with stochastic coefficients. We provide explicit, price model-free solutions to the optimal decision problems faced by each player, the solution of the Pareto optimum, and the Stackelberg equilibrium where the firm is the leader. We find that, from the social planner's point of view, the carbon tax or transmission costs are necessary to justify a positive share of distributed capacity in the long-term, whatever the respective investment costs of both technologies are. The Stackelberg equilibrium is far from the Pareto equilibrium and leads to an over-investment in distributed energy and to a much higher price for centralised energy.

Keywords: Decarbonation; Distributed generation; Stochastic game; McKean–Vlasov (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

Published in Mathematical Methods of Operations Research, 2020, 91 (2), pp.269-310. ⟨10.1007/s00186-019-00692-8⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03714163

DOI: 10.1007/s00186-019-00692-8

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