Robust Scenario-Based Data-Enabled Predictive Control of a Battery Energy Storage System: An Experimental Study

• Explicit battery models are costly to build because power, state of charge, and terminal voltage interact nonlinearly and cell behavior varies with operating point and health.Source: §I · p. 1
• DeePC avoids an explicit battery model by predicting future behavior from measured input-output trajectories while optimizing constrained reference tracking.Source: §I · p. 1
• Standard DeePC regularization robustifies prediction against noise and mild nonlinearities, but does not explicitly guarantee constraint robustness; Scenario-DeePC targets that gap using sampled scenarios built directly from data.Source: §I · p. 1
• Scenario-DeePC was experimentally validated on a grid-connected battery at the NEST research facility while tracking a cyclic state-of-charge reference.Source: §I · p. 1
• The study compares Scenario-DeePC with standard DeePC on the battery system, quantifying constraint-satisfaction improvement under real operating conditions.Source: §I · p. 2

II. SCENARIO-DEEPC

• DeePC arranges measured input-output trajectories into past and future Hankel blocks, then predicts and optimizes future trajectories directly from data without a parametric model.Source: §II · p. 2
• Scenario-DeePC enforces output constraints over sampled perturbations of DeePC’s predicted output and includes scenario outputs in the tracking cost.Source: §II · p. 2
• Prediction errors are buffered as empirical uncertainty, and retaining only every (M + 1)-th error yields independent samples for the distribution-free probabilistic output-constraint guarantee.Source: §II · p. 2
• Non-negative per-scenario slacks relax output constraints component-wise, restoring feasibility when tightened constraints would otherwise make the problem infeasible.Source: §II · pp. 2–3
• The adaptive variant updates the error buffer online, replacing its oldest entry so constraint tightening reflects recent operating conditions and changes in noise, disturbances, or model mismatch.Source: §II · p. 3

III. APPLICATION

• The NEST BESS aggregates ten lithium-titanate battery modules into a virtual battery exposed to the controller over Modbus/TCP.Its underlying multi-module structure is not directly accessible.Source: §III · p. 3
• The battery’s power and SOC behavior is described through voltage-current power and charging/discharging relationships, with charging and discharging mutually exclusive at each time step.The passage defines SOC, capacity, current, and conversion-efficiency terms for these relationships.Source: §III · p. 3
• The system has a nominal capacity of 96 kWh and is operated within a restricted 20%–80% SOC window.Internal monitoring disconnects the battery if a critical voltage or temperature threshold is exceeded.Source: §III · pp. 3–4
• The controller commands inverter power and receives estimated SOC at the grid interface, with inverter and battery treated jointly as a black-box system.The SOC estimate is aggregated from internal cell estimates whose algorithm is treated as a black box.Source: §III · pp. 3–4, Figure 2 · p. 4
• The estimated SOC has ordinary noise and resolution effects, plus irregular recalibration jumps of several percentage points in either direction.The jumps occur at a priori unknown times and are distinct from ordinary charging and discharging evolution.Source: §III · p. 4

IV. RESULTS

• The results section presents the setup, tuning procedure, selected correlation horizon M, and numerical comparison against standard DeePC.Source: §IV · p. 4

A. Experimental Setup

• At one-minute intervals, the controller commands inverter power from estimated SOC, while the inverter and battery form a joint black-box system.The past-data buffer is prefilled from historical data, allowing operation from the first control step without a warm-up phase.Source: A. Experimental Setup · p. 4
• The repeating reference holds at 50%, ramps down to 35%, then up to 75%, and returns to 50% SOC.The reference uses true, unscaled cell SOC and provides margin against sudden recalibration triggering the internal safety disconnect.Source: A. Experimental Setup · p. 4
• The controllers constrain power to −50–50 kW and SOC to 35%–75%, with the reference deliberately reaching those bounds.Reaching the bounds makes predicted-output uncertainty relevant to actual constraint violations.Source: A. Experimental Setup · pp. 4–5
• Fig. 3 covers all 20 reference cycles and marks irregular abrupt jumps in Scenario-DeePC’s estimated SOC.Its highlighted windows identify the cycles shown in detail in Figs. 4 and 5.Source: Figure 3 · p. 5
• The Hankel-matrix data came from closed-loop operation on 26 March 2026, while the experiment ran from 21 to 27 April 2026.The data window was chosen near the experiment so the battery state of health would align closely.Source: A. Experimental Setup · p. 5

B. Hyperparameter Tuning

• The prediction model is calibrated offline on historical power and SOC data, tuning λg and λy for prediction accuracy before deployment.This fixes those weights relative to one another and leaves their ratio to Q and R for deployment tuning.Source: B. Hyperparameter Tuning · p. 5
• Nscen and Nbuffer are fixed a priori, while the scenario buffer is updated online during operation.Source: B. Hyperparameter Tuning · p. 5

C. M-Dependence in Practice

• 0.5% SOC resolution makes prediction errors persist across hold intervals, so restoring independence by subsampling would require a large M.At one-minute intervals and a 500-error buffer, only a few errors per hour would be added, taking several days to fill the buffer.Source: C. M-Dependence in Practice · p. 5
• M = 0 retains every prediction error, filling the buffer quickly and preserving disturbances relevant to current operating conditions.The choice prioritizes practical robustification over the theoretical guarantee, which does not formally apply under correlated errors.Source: C. M-Dependence in Practice · pp. 5–6
• Fig. 4 superimposes Scenario-DeePC and standard DeePC traces for reference-trajectory cycles without a recalibration event.Source: Figure 4 · p. 6

D. Experimental Results

• 20 reference cycles were completed by Scenario-DeePC despite recalibration jumps; standard DeePC left the admissible SOC range after 7 cycles.Source: D. Experimental Results · p. 6
• Controllers were compared on event-free reference cycles recorded at different times because they could not run simultaneously on the physical system.Source: D. Experimental Results · p. 6
• Standard DeePC had 158 constraint violations versus none for Scenario-DeePC; both achieved 0.78% RMSE over compared windows of 810 samples each.All standard DeePC violations occurred where the reference lay exactly on a constraint bound, and most exceeded it by one 0.5% quantization step. Scenario-DeePC robustifies constraints against prediction error.Source: D. Experimental Results · p. 6
• Opposite recalibrations of approximately +3% and −10% entered the scenario buffer as prediction errors, tightening constraint handling until the entries were discarded.Each entry remained available for sampling for 500 control steps.Source: D. Experimental Results · p. 6, Figure 5 · p. 7
• Recalibration errors do not generally meet the scenario approach’s independence assumptions, although practical robustification was observed.Source: D. Experimental Results · p. 6
• After a recalibration enters the buffer, tighter constraints reduce tracking accuracy temporarily; tracking improves as the entry is discarded.Source: D. Experimental Results · pp. 6–7
• Buffer size and scenario count govern the likelihood and duration of recalibration sampling, but were not fine-tuned for the observed events.The recalibration mechanism remained a black box.Source: D. Experimental Results · p. 7
• A further same-sign recalibration of comparable or smaller magnitude within the buffer window would be covered by the already-tightened handling on that bound.Source: D. Experimental Results · p. 7

V. CONCLUSION

• Scenario-DeePC matched standard DeePC’s tracking performance while incurring substantially fewer constraint violations on a real, aged, multi-cell system.The system used an undisclosed SOC estimator and faced uncertainty departing from the method’s theoretical assumptions.Source: §V · p. 7
• After SOC recalibration events, Scenario-DeePC automatically tightened constraint handling for a limited number of subsequent control steps.This robustified the system against renewed violations until the corresponding buffer entry was discarded.Source: §V · p. 7
• The approach supports operation within the admissible SOC range, reducing risks of overcharge, deep discharge, and accelerated battery degradation without explicit models of the battery, inverter, or estimation process.Source: §V · p. 7
• Future work is needed to characterize recalibration and choose buffer size and scenario number, and to address M-dependence or obtain i.i.d. scenarios to restore scenario-approach guarantees.Source: §V · p. 7