Multi-Time Scale Distributed Stochastic Economic Dispatch for Flexible Traction Power Supply System

Flexible traction power supply system (FTPSS), integrated with renewable energy, energy storage, and power flow controllers (PFC), offers great potential for safe and economical railway operation. However, the uncertainty in traction load and photovoltaic (PV) output poses significant challenges to cost-effective dispatch. Therefore, a multi-time scale distributed stochastic economic dispatch method for FTPSS is proposed. The prediction module uses LSTM to produce point forecasts, while KDE models the forecast errors to construct predictive intervals and generate scenarios for PV output and traction load. A stochastic programming model is then formulated, where uncertainties in traction load and PV are represented by chance constraints and scenarios. In the first stage, the day-ahead forecast is used to solve the stochastic optimization model to minimize daily operational cost. In the second stage, the scheduler uses the day-ahead plan as a soft reference and reoptimizes at each rolling step with updated probabilistic forecasts, implementing only the first control move to maintain real-time responsiveness and economic efficiency. The optimization model is solved using an ADMM-based distributed algorithm, which accounts for limited inter-subsystem communication and reduces computational complexity. A case study based on a real electrified railway demonstrates that the proposed method improves economic performance by reducing operating costs by approximately 9% under uncertainty.