Nash Equilibrium Estimation and Analysis in Joint Peer-to-Peer Electricity and Carbon Emission Auction Market With Microgrid Prosumers

The joint Peer-to-Peer (P2P) electricity market (EM) and carbon emission auction market (CEAM) among prosumer microgrids (MGs) in the distribution network is a promising paradigm to facilitate the participation of distributed energy resources (DERs) and incentivize the decarbonization. In this market, MGs will modify their bidding strategies to be adaptive to other rival MGs' for profit maximization. Such modification will converge to the Nash Equilibrium Point (NEP), where each MG cannot obtain more profits by modifying its strategy subject to the fixed strategy of other rival MGs. In this paper, the NEP under such a joint market paradigm is investigated, in which MGs will trade electricity in the EM and purchase carbon emission quotas (CEQs) in the CEAM. In addition, MGs must adjust their bidding strategies considering penalties due to deviations between day-ahead (DA) scheduling and real-time (RT) procurement caused by uncertainties of net load, as well as the price fluctuation in the CEAM. The NEP is estimated by a novel Multi-agent Deep Deterministic Policy Gradient (MADDPG) algorithm, and the risk mitigation is achieved by incorporating the conditional value-at-risk (CVaR) constraint. The computational performance and effectiveness of risk mitigation of this proposed algorithm, and the obtained NEP in the joint EM and CEAM, are analyzed in the case studies.