## 2 Optimized Hybrid Energy System for High-Speed Rail Integrating Carbon-REC Trading  
### Problem Description  
This study focuses on optimizing the capacity and operational power of ESS in high-speed railway hybrid power systems under low-carbon constraints while exploring synergistic benefits of renewable energy through carbon trading mechanisms and REC transactions. The Fuxing CR400 BF high-speed railway Electric Multiple Unit (EMU) was selected as the research platform, featuring an eight-car configuration with four powered cars ( cars 2, 4, 5, 7) and four trailer cars ( cars 1, 3, 6, 8). Key technical parameters include a total length of 209.06 m, width of 3360 mm, height of 4050 mm, and a horizontally mounted PV array covering 2000 m\({}^{2}\) on the train roof (as shown in Figure 1). ESS units are installed above lighting systems with negligible aerodynamic resistance. The EMU has an unladen mass of 461.8 tons and a maximum operational mass of 506.3 tons, with a passenger capacity of 576 seats. Under full occupancy conditions (70 kg average mass per passenger including luggage), the total mass reaches 502.12 tons, leaving 4.18 tons of mass allowance for PV and ESS installation. ESS operational parameters are constrained to 1500 kWh maximum capacity and 1500 kW power output. The integrated optimization framework systematically addresses carbon-REC coordination while maintaining mass-energy equilibrium for safe high-speed railway operations. This study analyzes the hybrid power system for high-speed railways illustrated in Figure 1, comprising three core components: PV arrays, grid power as the primary energy supply, and ESS for renewable energy integration and system reliability enhancement. The output of PV system varies significantly under different irradiance and temperature conditions, necessitating advanced control strategies to maintain optimal performance. To address this, the PV system employs MPPT control within its power conversion units, which continuously adjusts operating points to maximize solar energy utilization across diverse conditions. Given the inherent limitations of high-speed railway trains in generating sufficient onboard power, the capability of grid to reliably energize all loads under any operational scenario proves critical for maintaining system stability and safety. The trading architecture of system comprises carbon trading and REC mechanisms. The cap-and-trade mechanism tackles decarbonization bottlenecks via market-driven price signaling, transforming carbon allowances into tradable commodities within a cap-and-trade framework. Governments allocate emission quotas based on corporate power generation while enforcing aggregate emission controls. Enterprises with actual emissions below allocated quotas may monetize surplus allowances through carbon markets. All participants incur baseline costs proportional to carbon prices, while non-compliant entities must purchase deficit allowances to fulfill obligations. This mechanism economically incentivizes optimized carbon management strategies through dual market pressures. Concurrently, the REC trading system mandates market participants with renewable energy consumption below quota thresholds to procure RECs for compliance, while surplus REC holders may trade certificates through dedicated platforms. To incentivize renewable adoption in high-speed railway systems, this study sets the renewable quota at zero for railway operators, enabling full REC monetization through market transactions. The revenue model exclusively considers net REC trading income, a methodology that enhances interregional renewable energy allocation efficiency while directly improving market dynamics. The operational route from Shanghai Hongqiao Station to Qinghai Xining Station is illustrated in Figure 2. The entire journey takes 12 h and 20 min. This high-speed train service operates only once daily in one direction, departing from Shanghai Hongqiao Station at 06:32 and arriving in Xining Station at 18:52.