A McKean-Vlasov approach to distributed electricity generation development
Aïd, René; Basei, M.; Pham, H. (2019), A McKean-Vlasov approach to distributed electricity generation development, Mathematical Methods of Operations Research, p. 1-42. 10.1007/s00186-019-00692-8
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1705.01302v3
Journal nameMathematical Methods of Operations Research
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Abstract (EN)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.
Subjects / KeywordsDecarbonation; Distributed generation; Stochastic game; McKean–Vlasov; L94; C73; C61; O33; Q41; Q42
JELL94 - Electric Utilities
C61 - Optimization Techniques; Programming Models; Dynamic Analysis
C73 - Stochastic and Dynamic Games; Evolutionary Games; Repeated Games
O33 - Technological Change: Choices and Consequences; Diffusion Processes
Q41 - Demand and Supply; Prices
Q42 - Alternative Energy Sources
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