## 1 Introduction
### Motivation and Main Contributions  
Current strategies promoting green energy adoption remain underexplored within PV-ESS-integrated high-speed railway power systems. This study addresses critical gaps concerning the following: (1) Energy Dispatch Under Carbon Constraints: Existing work often treats emissions statically, neglecting dynamic carbon emission coupling effects. Models inadequately capture carbon price volatility, and dispatch algorithms demonstrate limited responsiveness to market fluctuations, hindering real-time emission control aligned with decarbonization goals. (2) REC-Energy Dispatch Synergy: The absence of coordination between REC pricing dynamics and dispatch decisions limits REC benefit optimization in real-time operations, with REC trading strategies rarely co-optimized with dispatch protocols. (3) Multi-Objective Optimization: Contemporary algorithms face challenges in convergence speed and solution diversity when handling the high-dimensional, strongly constrained problems typical of these systems; fixed or simplistic adaptive-weight strategies are insufficient for dynamic state responses. To bridge these gaps, this paper proposes a high-efficiency optimization algorithm for sizing ESS in high-speed railway hybrid power systems. The methodology strengthens PV-ESS integration while accommodating system complexity, ultimately delivering solutions that synergistically enhance economic efficiency and environmental performance to meet the sophisticated load demands of high-speed railway hybrid power infrastructures. This study proposes a novel methodology for optimizing the capacity and operational power of ESS in high-speed railway hybrid power systems under market trading mechanisms, specifically designed for railway lines with variable weather conditions. To ensure representative weather complexity, the G3176/G3177 high-speed railway route from Shanghai Hongqiao Station to Qinghai Xining Station and its return route G3178 were selected as case studies. Although stations along this route share similar latitudes, significant longitudinal variations induce substantial weather disparities between adjacent stations, resulting in pronounced PV power generation fluctuations. The proposed system reduces grid dependency and operational costs while mitigating carbon emissions through PV panel retrofitting on train roofs and ESS installations above lighting systems, supplement ing conventional grid power. ESS units store surplus energy from PV and Regenerative Braking Energy (RBE). PV integration facilitates renewable energy adoption, enabling REC participation to incentivize solar utilization and generate ancillary economic benefits for high-speed railway power systems. A cradle-to-grave LCA is conducted to quantify total carbon emissions across all life stages of PV and ESS technologies, from raw material extraction to end-of-life disposal. The optimization framework integrates a carbon management model that combines carbon trading, penalty, and incentive mechanisms. Load demand profiles are analyzed for four operational modes, and the proposed Elite Dwarf Mongoose Optimization Algorithm (EDMOA) determines optimal ESS configurations by minimizing system costs and carbon emissions. This algorithm demonstrates enhanced convergence speed and solution diversity, effectively addressing the high-dimensional optimization challenges inherent in high-speed railway hybrid power systems. This study makes three principal contributions to hybrid power systems in high-speed railways: (1) it introduces an integrated framework combining carbon constraints and REC within power system optimization, enabling coordinated management across multiple timescales. (2) It develops a tripartite coupling model that rigorously quantifies dynamic interdependencies among power dispatch, carbon trading, and REC transactions, aligning hourly operational scheduling with daily market participation and annual infrastructure planning.