Fuzzy credibility chance-constrained multi-objective optimization for multiple transactions of electricity–gas–carbon under uncertainty

This paper proposes a fuzzy credibility chance-constrained multi-objective optimization model to optimize market transactions in the electricity–gas–carbon sectors under uncertainty. The model aims to maximize the profit of an integrated energy service provider by incorporating a ladder-type carbon trading mechanism, which adjusts carbon prices based on emission levels, and detailed multi-energy flow constraints. To effectively manage uncertainties in electricity, gas, and carbon markets, we derive credibility distributions for uncertain variables and introduce fuzzy credibility chance constraints—tools that assess the likelihood of meeting multiple transactions under uncertainty. The proposed model hedges the risks associated with multiple uncertainties while maximizing the credibility of expected costs, effectively balancing risk and cost. Through simulation analysis on an IEEE 33-node power network and a 32-node heat network, the proposed model achieved a 9.8% reduction in total system cost and an 8.5% reduction in total carbon emissions. Additionally, the model effectively determined credibility levels under different risk preferences, demonstrating its robustness in enhancing electricity–gas–carbon trading and promoting a low-carbon economy. This research provides a novel planning method for formulating trading strategies in multi-energy markets, with significant real-world implications for energy management and environmental sustainability.