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Two-stage Coordinated Energy Management of Train Operation and Wayside Energy Storage System for Rail Power Supply Systems

Fei Liu, Niklas Biedermann, Stefan Östlund, Qianwen Xu

arXiv:2609.16857v1eess.SYcs.SY

TL;DR

Existing approaches leave gaps in jointly coordinating train operation, wayside storage, and realistic railway-network constraints. The paper proposes day-ahead co-optimization followed by rolling AWC-MPC dispatch updates, and reports reduced peak grid demand and system cost in a Swedish railway case.

  • Problem

    Prior work often treats peak shaving or energy recovery separately from train-operation optimization, and some integrated studies omit wayside storage coordination or realistic network limits.

    Source: §I · pp. 1–2

  • Method

    A two-stage method co-optimizes train trajectories with wayside ESS siting and sizing day-ahead, then updates ESS dispatch through rolling AWC-MPC using refreshed traction-demand and PV forecasts.

    Source: §I · p. 2

  • Results

    35.7% peak reduction and 28.8% total cost reduction are achieved in the real Swedish railway system.

    Source: §V · p. 10

  • Takeaways & Limitations

    The Swedish case demonstrates practical implementation under realistic operating conditions, with rolling dispatch suppressing residual short-term peaks under forecast deviations.

    Source: §V · p. 10

Abstract

from arXiv · show

The increasing electrification of railway power supply system (RPSS) intensify the operational and economic challenges at the railway power system interface. Energy storage systems (ESSs) can provide fast and flexible support to mitigate short term power spikes and to improve the energy management. However, achieving coordinated operation is challenged by the tight coupling among electrical railway operation and ESS dispatch under time-varying traction demand and network limits. This paper proposes a two-stage coordinated energy management method for electrified RPSSs that jointly optimizes railway system operation, train trajectories and ESS dispatch while explicitly accounting for traction power flow constraints. First, a day-ahead operation stage determines the train operating profiles and the ESS setting decisions to establish the baseline operating plan. Then, an intra-day rolling optimization stage based on adaptive weight economic-model predictive control (AWC-MPC) updates ESS dispatch under refreshed forecasts of traction demand and renewable output. A real Swedish railway case is utilized to minimize the energy purchase cost and the ESS cost while reducing peak grid power, demonstrating its practical applicability with 35.7% peak grid power demand and 28.8% total system cost reduction.

I. INTRODUCTION

The introduction motivates coordinated grid–railway energy management because traction systems are increasingly coupled to the grid and existing approaches leave gaps in joint train-operation and wayside-storage planning. It presents a two-stage method and a high-fidelity railway model intended to address those gaps.

I. INTRODUCTION

  • Existing approaches often separate peak shaving or energy recovery from train-operation optimization, while other studies omit wayside storage coordination or realistic network and operating limits.The paper frames these gaps as limiting practical guidance for railway planning and operation.Source: §I · pp. 1–2
  • The proposed two-stage method couples train movement and wayside ESS siting and sizing, with day-ahead references followed by rolling AWC-MPC dispatch updates using refreshed forecasts.The model also incorporates power-flow and timetable constraints, time-varying electricity prices, and peak-demand limits.Source: §I · p. 2
  • A Swedish railway map and timetable are used to capture train, ESS, renewable, power-flow, and grid interactions under realistic operating conditions.The study reports reductions in peak grid power demand and total system cost.Source: §I · p. 2

II. STRUCTURE OF RPSS MODEL

  • The RPSS model represents electrical interactions among substations, section posts, and line segments, with renewable and storage resources treated as nodal power injections.Figure 1 depicts train and ESS integration in the model.Source: §II · p. 2, Figure 1 · p. 2

A. Multi-Train Movement Modeling

2) Trajectory Reference Construction:

A reference trajectory is represented by train speeds at discretized route positions. Operational constraints bound those speeds, and time-space mapping reconstructs the corresponding continuous-time reference.

2) Trajectory Reference Construction:

  • A reference trajectory is represented by a speed vector over discretized route nodes from departure to arrival.The route nodes are indexed from s0 to sN.Source: 2) Trajectory Reference Construction · p. 3
  • Trajectory speeds must satisfy boundary and operational constraints, including position-dependent speed limits and allowable acceleration bounds.The passage defines the spatial interval between adjacent nodes as Δs_q = s_q − s_(q−1).Source: 2) Trajectory Reference Construction · p. 3
  • Time-space mapping assigns timestamps to the reference speeds, enabling piecewise-linear reconstruction of continuous-time train position and speed profiles.The mapping links the spatially indexed trajectory to its time-domain reference.Source: 2) Trajectory Reference Construction · p. 3

3) Power Demand Calculation:

Train power demand is derived from traction-force motion and represented alongside multi-train spacing and railway-network injections. This connects train operation and renewable and storage resources to the network constraints used in optimization.

3) Power Demand Calculation:

  • Mechanical power follows traction force and speed, with active demand accounting for traction and regenerative conversion efficiencies and auxiliary power, and reactive demand modeled separately.The cited passages also identify train power factor and auxiliary reactive demand.Source: 3) Power Demand Calculation · p. 3

4) Multi-Train Spatiotemporal Interaction:

  • Neighboring trains traveling in the same direction must maintain a safe spacing constraint at every time step.The spacing margin is speed-dependent and represents signaling and braking safety requirements.Source: 4) Multi-Train Spatiotemporal… · p. 3

B. RPSS Modeling with RESs and ESSs integration

  • The RPSS grid-side model uses equivalent railway supply and demand injections to interface railway operating states with network constraints.The model is intended for use in the subsequent optimization.Source: B. RPSS Modeling with RESs and ESSs… · p. 3

1) Electrified Railway System Modelling:

  • The electrified railway is represented as a graph with railway supply and load buses, including traction substations and section posts, where train, PV, and ESS injections are decomposed.Section posts provide geographical segmentation and load mapping.Source: 1) Electrified Railway System Modelling · p. 3

2) Multi-Train Load Mapping to Grid Buses:

The method maps multi-train traction demand to grid buses, then coordinates day-ahead train and ESS planning with intra-day ESS dispatch updates. The rolling stage tracks day-ahead grid-power and state-of-charge references as forecasts change.

2) Multi-Train Load Mapping to Grid Buses:

  • Train traction power profiles are mapped to grid buses using allocation factors that sum to one across buses.The mapping uses train power profiles from the train movement model.Source: 2) Multi-Train Load Mapping to Grid… · p. 3

III. TWO-STAGE COORDINATED OPTIMIZATION MODEL

  • The coordinated model couples train operation decisions with wayside ESS planning under RPSS operating constraints.Source: §III · p. 3

A. Solution of the two-stage coordinated optimization model for RPSS energy management

  • Stage I selects baseline trajectories and ESS siting and sizing under coupled grid constraints, then establishes day-ahead reference trajectories.Candidate trajectory combinations are evaluated using the day-ahead operation model.Source: A. Solution of the two-stage… · pp. 3–4
  • Stage II uses refreshed forecasts to update ESS charging and discharging commands and mitigate short-term deviations from the day-ahead plan.The adaptive tracking weights use electricity price, current ESS states, and a PV uncertainty indicator.Source: A. Solution of the two-stage… · pp. 3–4

B. Stage I: Day-Ahead Operation With Trajectory Selection and ESS Siting and Sizing

The day-ahead objective combines grid purchase and ESS costs. Grid cost includes a peak penalty, while ESS cost accounts for annualized investment and operating costs.

1) Objective Function:

· CRF

  • ESS cost includes annualized investment cost and operation and maintenance cost allocated to the day-ahead horizon.The investment terms use energy-capacity and power-rating unit costs, with a capital recovery factor.Source: 1) Objective Function · p. 4, · CRF · p. 4

1) Objective Function:

  • Grid purchase cost includes electricity-price-based purchases and a peak penalty on grid exchange.The peak is bounded by an auxiliary variable.Source: 1) Objective Function · p. 4

2) Constraints:

Stage I evaluates feasible train trajectory combinations alongside timetable, ESS, and grid constraints to select a baseline operating plan.

2) Constraints:

  • For each candidate trajectory combination, the day-ahead operation model evaluates mapped railway injections under grid and ESS constraints to select the lowest-cost baseline.Source: 2) Constraints · p. 4
  • Train arrival and departure times at each station must satisfy the specified dwell-time limits.Source: 2) Constraints · p. 4
  • ESS installation is represented by a binary decision, with energy capacity and power rating bounded for candidate installations.Charging and discharging powers are also introduced as decision variables.Source: 2) Constraints · p. 5

P ESS

The ESS constraints model storage operation and interface capability alongside AC power-flow constraints for the RPSS grid.

P ESS

  • ESS operation includes charging and discharging powers, state-of-charge dynamics, and charging and discharging efficiencies.Source: P ESS · p. 5
  • The ESS converter constraints account for reactive-power injection and the apparent-power rating.Source: P ESS · p. 5
  • AC power-flow constraints express bus current injections using complex bus voltages and branch impedances.The nodal active and reactive power injections include railway-related injections.Source: P ESS · p. 5

C. Stage II: Intra-Day Rolling Optimization Based on AWC-MPC

The intra-day AWC-MPC tracks day-ahead references while smoothing ESS control changes. Its adaptive weights shift with price, SOC, and PV uncertainty, and the constraints define ESS controls and grid exchange.

1) AWC-MPC Objective Function: 

  • The AWC-MPC objective penalizes deviations from day-ahead references and ESS control increments over a prediction horizon.The output vector includes grid exchange and ESS state-of-charge references.Source: 1) AWC-MPC Objective Function:  · p. 5
  • High electricity prices increase grid-reference tracking weight, while SOC limits or rising PV uncertainty increase SOC tracking weight to preserve operating margins.These adaptive weights balance economic tracking and operational robustness.Source: 1) AWC-MPC Objective Function:  · p. 5

2) Constraints:

  • The constraints define ESS charging and discharging sequences, their control increments, and grid exchange through active-power balance.The charging and discharging sequences are stacked into the control vector.Source: 2) Constraints · pp. 5–6

P RES

The case study models shared-substation interactions between two Swedish train services and evaluates power balance, operating assumptions, and staged optimization cases.

P ESS

  • Grid exchange is defined through active-power balance involving net grid supply, train demand, PV injection, and ESS injection.The balance terms are identified at the grid, train, PV, and candidate ESS buses.Source: P ESS · p. 6

IV. CASE STUDY

  • The Swedish study considers intersecting Train 245 and Train 965 services whose routes overlap in Stockholm’s SE3 region and share substations.Timetables and service information come from Trafikverket.Source: §IV · p. 6, Figure 3 · p. 6
  • The railway case uses regional electric multiple units, with movement-model parameters accounting for passenger load, rotary allowance, and regenerative-braking efficiency.The study also uses a 15 kV AC supply at 16.7 Hz.Source: §IV · p. 6, Table II · p. 6
  • Monthly procurement prices and normalized hourly SE3 price fluctuations form the time-varying prices used in both optimization stages.The adopted December base price is 61.07 öre/kWh.Source: §IV · p. 6, Figure 4 · p. 7
  • Four cases separate baseline operation, ESS integration with fixed trajectories, joint ESS and trajectory optimization, and intra-day adjustment for PV and load forecast errors.ESS investment parameters are drawn from IRENA reference data.Source: §IV · pp. 6–7, Table III · p. 7

A. Base case: Initial train trajectory, without ESS

The baseline exhibits acceleration-driven grid peaks and only partial use of regenerative braking. ESS integration reduces peak demand, while trajectory optimization further smooths demand and coordinates storage dispatch.

A. Base case: Initial train trajectory, without ESS

B. Case 1: Initial Trajectories With ESS Integration

C. Case 2: Optimized Trajectories With ESS Integration

D. Case 3: Optimized Trajectories and ESS With Uncertainty Consideration

Case 3 retains the optimized day-ahead trajectories and ESS deployment while rolling updates adjust ESS dispatch under refreshed traction-demand and PV forecasts. The paper reports reductions in peak demand and total cost for the real Swedish railway system.

D. Case 3: Optimized Trajectories and ESS With Uncertainty Consideration

V. CONCLUSION

  • 35.7% peak reduction and 28.8% total cost reduction are reported for the real Swedish railway system.Source: §V · p. 10
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