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.

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McKean-Vlasov的分布式发电开发方法

本文分析了集中式碳排放技术与分布式间歇性非排放技术之间的相互作用。在我们的模型中，有一个有代表性的消费者，可以通过投资分布式发电（太阳能电池板）并以公司设定的价格从集中式公司购买电力来满足其用电需求。分布式发电是间歇性的，并给消费者带来了外部性成本。该公司提供非随机性发电，需缴纳碳税和传输成本。消费者的目标是在满足其需求的同时，将投资成本，对企业的付款和间歇成本降至最低。公司的目标是满足消费者的剩余需求，同时最大程度地减少投资成本，需求偏离成本并最大程度地增加消费者的支付。我们将投资决策表述为具有随机系数的McKean-Vlasov控制问题。我们为每个参与者所面临的最优决策问题，帕累托最优解以及公司作为领导者的Stackelberg均衡提供明确的，无价格模型的解决方案。我们发现，从社会计划者的角度来看，碳税或传输成本对于长期分配容量的正份额是必要的，而无论这两种技术各自的投资成本是多少。Stackelberg均衡远离帕累托均衡，并导致对分布式能源的过度投资以及集中式能源的更高价格。无需价格模型即可解决每个参与者所面临的最优决策问题的解决方案，帕累托最优解决方案以及公司在其中处于领先地位的Stackelberg均衡问题。我们发现，从社会计划者的角度来看，碳税或传输成本对于长期分配容量的正份额是必要的，而无论这两种技术各自的投资成本是多少。Stackelberg均衡远离帕累托均衡，并导致对分布式能源的过度投资以及集中式能源的更高价格。无需价格模型即可解决每个参与者所面临的最优决策问题的解决方案，帕累托最优的解决方案以及公司在其中处于领先地位的Stackelberg均衡。我们发现，从社会计划者的角度来看，碳税或传输成本对于长期分配容量的正份额是必要的，而无论这两种技术各自的投资成本是多少。Stackelberg均衡远离帕累托均衡，并导致对分布式能源的过度投资以及集中式能源的更高价格。碳税或输电成本对于长期分配容量的正份额是必要的，无论这两种技术各自的投资成本是多少。Stackelberg均衡远离帕累托均衡，并导致对分布式能源的过度投资以及集中式能源的更高价格。碳税或输电成本对于长期分配容量的正份额是必要的，无论这两种技术各自的投资成本是多少。Stackelberg均衡远离帕累托均衡，并导致对分布式能源的过度投资以及集中式能源的高价。