Multi-stage portfolio optimization for GenCo considering multi-correlation between electricity and carbon markets

Under the electricity and carbon (E&C) markets, generation companies (Gencos) need to trade among multiple options including forward contract markets and spot markets for electricity and carbon emission allowance (CEA), a process known as portfolio optimization. However, there exists a complicated multi-correlation between E&C markets, i.e., quantity and temporal correlation, which is seldom considered in the previous studies. This paper for the first time proposes a multi-stage portfolio optimization framework that determines the optimal composition of electricity and CEA in contract and spot markets to maximize revenue. The multi-stage framework is formulated as yearly, monthly, and spot stages: The yearly stage decides on the forward contract signing and allocation strategies to various monthly stages; The monthly stage adjusts contract signing and allocation strategies to spot stages; The spot stage considers the bidding strategies of electricity and CEA in two respective spot markets while integrating with the clearing processes. Then, the multi-stage portfolio optimization model is formulated as a multi-stage nonlinear stochastic programming with bilevel problems in the substage. To improve the solution efficiency, the alternating stochastic dual dynamic programming (A-SDDP) algorithm is innovatively proposed to cope with it. Finally, the case study demonstrates the importance of modeling the multi-correlation between E&C markets in Genco's portfolio optimization. Compared to the models that either only consider the carbon tax in the objective functions or models that ignore the temporal correlation, the proposed framework significantly improves profit for Genco.