Trajectory simulation and optimization for interactive electricity-carbon system evolution

Many countries have set power system emissions reduction goals. However, in developing the electricity‑carbon system, regulators may prioritize final targets while overlooking the planning of pathways. The paper aims to develop a simulation framework for the long-term interactive evolution of electricity‑carbon systems and optimize a developing trajectory. To begin, the electricity system is modeled as a daily spot market over 365 days, and simulated by fast unit commitment (FUC) method. Then, considering the internal multi-player gaming, the multi-class mean field game (MMFG) theory is introduced to simulate the carbon market. Subsequently, a state transition equation for the electricity‑carbon evolution is formulated based on the concept of trajectory optimization from optimal control theory. Here, the regulator can steer the evolution by adjusting the carbon emission intensity benchmark (CEIB) in the carbon market. Finally, employing the Twin Delayed Deep Deterministic Policy Gradients (TD3) technique, the problem characterized by high-dimensional state space and continuous action space is efficiently solved. The effectiveness of the proposed method is examined by case studies on a provincial-scale grid with over 200 units, where the optimal CEIB can be achieved within a second and the control precision of trajectory evolution can be limited to 2%.