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The coordination of centralised and distributed generation

Ren\'e A\"id, Matteo Basei and Huy\^en Pham

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Abstract: In this paper, we analyse the interaction between centralised carbon emissive technologies and distributed intermittent non-emissive technologies. A representative consumer can satisfy his 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 laissez-faire market situation represented by a Stackelberg equilibrium where the firm is the leader. We find that, from the social planner's point of view, the high adjustment cost of centralised technology damages the development of distributed generation. The Stackelberg equilibrium leads to significant deviation from the socially desirable ratio of centralised versus distributed generation. In a situation where a power system is to be built from zero, the optimal strategy of the firm is high price/low market-share, but is low price/large market share for existing power systems. Further, from a regulation policy, we find that a carbon tax or a subsidy to distributed technology has the same efficiency in achieving a given level of distributed generation.

Date: 2017-05, Revised 2018-03
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