Achieving the Dispatchability of Distribution Feeders through Prosumers Data Driven Forecasting and Model Predictive Control of Electrochemical Storage

I. INTRODUCTION

• Renewable generation increases the need for regulating power, while distribution-level flexibility solutions must fit existing grid operations and avoid demanding technical requirements.The paper contrasts its approach with DER aggregation methods requiring extensive ICT, coordination, or changes to operating practices.Source: §I · pp. 1–2
• The proposed strategy schedules heterogeneous prosumers at 5-minute resolution and uses BESS injections under MPC to correct real-time mismatches.Data-driven models support the prosumption forecast and BESS constraint predictions.Source: §I · pp. 1–2
• The control framework is experimentally validated on the EPFL 20 kV feeder with office buildings, rooftop PV, and a 720 kVA/500 kWh lithium titanate BESS.The monitoring infrastructure uses GCP power-flow measurements and information from the battery management system.Source: §I · pp. 1–2

II. PRELIMINARIES AND PROBLEM STATEMENT

• The two-stage operating structure resembles conventional day-ahead planning and intra-day operation, a feature the authors suggest could facilitate grid integration.The framework requires measurements of composite GCP flow and BESS injection.Source: §I · p. 2, Figure 1 · p. 2
• The setup represents feeder demand and generation as composite power flow at the GCP, with BESS real-power flow as the control variable.The paper assumes negligible grid losses and that the feeder has ample capacity to satisfy voltage and line-ampacity constraints.Source: §II · p. 2
• The dispatch plan is set the day before operation, then the operator adjusts BESS power to compensate for deviations during the following day.The plan is a sequence of average feeder power-consumption values at 5-minute resolution.Source: §II · pp. 2–3

III. DAY-AHEAD PROBLEM

• The dispatch plan combines point forecasts of prosumption with an offset profile that restores BESS energy flexibility for the next day.The offset can bias the plan so the BESS charges or discharges when its residual charge is near a limit.Source: §III · p. 3

A. Day-ahead Prosumption Forecasting

• Local prosumption forecasting is challenging because low-population aggregates have volatile demand and generation, and the paper does not claim a forecasting-method contribution.The method is presented as a simple nonparametric strategy for capturing daily and seasonal patterns; a fuller assessment is deferred to future work.Source: A. Day-ahead Prosumption Forecasting · p. 3

1) Training data set:

• The training data comprise historical GCP prosumption measurements organized as daily sequences and averaged to 5-minute resolution.The historical inputs also include daily global horizontal radiation measurements.Source: 1) Training data set · pp. 3–4

2) Forecast computation:

• Forecast profiles are selected from historical days matching the target's working-day status, nearby calendar dates, and forecast irradiance.The procedure narrows the candidates to ten nearby matching days, then selects five with the closest accumulated irradiance; their profiles provide possible prosumption realizations.Source: 2) Forecast computation · p. 4
• The point forecast averages candidate realizations independently at each time interval, without modeling time correlation.Outdoor temperature is excluded because the buildings lack electric space heating, and PV-generation dependence on temperature is neglected.Source: 2) Forecast computation · p. 4

B. Determination of the Offset Profile

• BESS injection is determined to compensate for the mismatch between the dispatch plan and realized prosumption.Because future prosumption is unknown, the method represents it using realizations from an uncertainty set.Source: B. Determination of the Offset Profile · p. 4
• The energy model relates state-of-energy changes to BESS power using charge/discharge efficiency assumed constant with respect to temperature and power magnitude.The efficiency is estimated from measurements at operating rates close to C/5.Source: B. Determination of the Offset Profile · p. 4
• The offset optimization keeps BESS power and state of energy within their allowed bounds under worst-case scenarios.It propagates the energy state from an initial value using the smallest and largest estimated BESS power realizations.Source: B. Determination of the Offset Profile · p. 5
• The experiments use an equivalent convex formulation of the offset problem, while BESS sizing is outside the paper's scope.The initial state-of-charge is unknown at day-ahead planning time and is estimated with a persistent predictor.Source: B. Determination of the Offset Profile · p. 5

C. Implementation of the day-ahead strategy

• The day-ahead strategy forecasts next-day prosumption, computes an offset profile through optimization, and uses it to produce the dispatch plan.The Matlab script is scheduled daily at 23 UTC.Source: C. Implementation of the day-ahead… · p. 5

IV. REAL-TIME OPERATION

• Real-time operation adjusts BESS real-power injection so average consumption at each 5-minute period's end matches the dispatch-plan setpoint.The control action is a piecewise-constant converter power setpoint.Source: §IV · p. 5
• The control strategy updates every 10 seconds, using measured feeder, BESS, and prosumption power from the preceding interval.The 10-second sample time was chosen to capture early BESS dynamics and support control performance.Source: §IV · p. 5
• Each 5-minute dispatch-plan value supplies the target for its 30 constituent 10-second intervals.At the start of interval k=2, the first two BESS setpoints have been applied, and the next uses the latest prosumption measurements.Source: §IV · pp. 5–6

A. Formulation of the Control Objective

• Within a 5-minute slot, the average composite consumption uses information available so far, and short-term predictions extend the expected average across the slot.At a slot's opening instant, the stated average composite consumption is zero because no information is yet available.Source: A. Formulation of the Control Objective · p. 6
• The current implementation uses a persistent predictor for future realizations; more advanced short-term prediction models are left for future work.The persistent predictor sets future prosumption values to the previous realization.Source: A. Formulation of the Control Objective · p. 6

B. Formulation of Model Predictive Control

• Unlike PID control based on current and past values, MPC schedules a trajectory over the target horizon and can react preemptively to forecast mismatch.The formulation explicitly enforces BESS operational constraints during this scheduling.Source: B. Formulation of Model Predictive… · p. 6
• The optimization uses DC current rather than AC real-power injection because current admits a convex equivalent formulation.The stated rationale is that convex optimization can be solved efficiently and reliably.Source: B. Formulation of Model Predictive… · pp. 6, 8
• MPC targets zero dispatch-plan error by the end of each 5-minute slot while respecting BESS state-of-charge, DC-voltage, and current limits.The control objective is expressed as an energy-tracking problem.Source: B. Formulation of Model Predictive… · pp. 6–7
• The convex formulation maximizes BESS DC current subject to predicted energy throughput not exceeding the target, bringing throughput to that target.The energy-throughput function is convex when its quadratic term is positive semidefinite, a condition verified numerically for the identified voltage models.Source: B. Formulation of Model Predictive… · p. 7
• The MPC includes current magnitude and rate limits plus predicted voltage and state-of-charge constraints; voltage models are selected according to measured SOC.Five linear voltage models cover different SOC ranges, and SOC is assumed not to vary significantly during an actuation period.Source: B. Formulation of Model Predictive… · pp. 7–8
• At each time step, MPC solves over the shrinking remainder of the current 5-minute slot and applies only the first control action.The control is reevaluated with updated information.Source: B. Formulation of Model Predictive… · p. 8

1) BESS Voltage:

• Grey-box identification augments the two-time-constant equivalent-circuit model by increasing model complexity until prediction errors are satisfactory.The target is zero-mean, independent, identically distributed residuals, indicating that the model captures the experimental BESS dynamics.Source: 1) BESS Voltage · p. 8
• Parameters were identified using random ±200 kW PRBS power sessions across five SOC ranges, while C-rate and temperature dependencies were left unmodeled.The batteries were maintained at 20 °C, where temperature effects were expected to play a minor role.Source: 1) BESS Voltage · p. 8
• A three-time-constant model (n = 3) performed best for the experimental BESS, with uncorrelated residuals observed across the tested SOC ranges.At 50% SOC, the residual autocorrelation was within the 95% confidence interval for white noise; the same behavior was observed for the other SOC ranges.Source: 1) BESS Voltage · pp. 8–9
• The estimated voltage-model parameters are reported by SOC range, and the three capacitor voltages form the model state vector.The equivalent circuit relates BESS terminal voltage and DC current to state components vC1, vC2, and vC3.Source: Figure 4 · p. 8, 1) BESS Voltage · p. 9, Table I · p. 9
• The continuous-time stochastic state-space model is discretized at 10-second resolution for MPC, dropping the quickest time constant in favor of an algebraic state to avoid numerical instability.The reduced model is used to form the predictive voltage constraints.Source: 1) BESS Voltage · p. 9
• Kalman filtering estimates the unmeasured model state from DC-voltage measurements through repeated prediction and measurement-update steps.Full system observability is enforced by construction because the model is estimated from measurements.Source: 1) BESS Voltage · pp. 9–10

2) BESS SOC:

• The section introduces the BESS SOC model as an input to the MPC constraint formulation.The model’s predictive constraints are formed from the discretized state-space matrices.Source: 2) BESS SOC · p. 10
• The SOC model uses a nominal BESS capacity of 810 A h and neglects capacity dependence on C-rate and cell temperature.The capacity value comes from datasheet information.Source: 2) BESS SOC · p. 10
• The discretized SOC state-space matrices are A = 1, B = 10/3600/Cnom, C = 1, and D = 0.These matrices generate the transition matrices used for SOC predictive constraints.Source: 2) BESS SOC · p. 10

D. On the use of BESS models in the day-ahead and real-time stages

• Day-ahead BESS models represent long-term flexibility, whereas more accurate real-time models capture short-term constraints for reliable control actions within operational limits.The day-ahead stage can use back-off terms on SOC and power-flow constraints to produce a more conservative usage plan.Source: D. On the use of BESS models in the… · p. 10

E. Implementation of the real-time strategy

• Real-time operation runs daily in Matlab and records GCP power flow and BESS voltage, current, SOC, and AC power measurements; the experimental BESS is a 720 kVA/500 kWh lithium-titanate system.The BESS includes nine parallel racks and a four-quadrant converter in a temperature-controlled container.Source: E. Implementation of the real-time… · p. 10, Figure 7 · p. 10

V. EXPERIMENTAL RESULTS AND DISCUSSION

• On day 0, the offset plan slowly charges a low-SOC BESS while the grid-point power flow follows the dispatch plan and BESS constraints are generally respected.The offset plan is intended to restore energy capacity for absorbing forecast errors.Source: §V · p. 11
• After day 0 ended above 50% SOC, a slightly negative day-1 offset restored a lower SOC, and the BESS SOC varied less than on day 0.The authors interpret the smaller variation as indicating a smaller accumulated forecasting error.Source: §V · p. 11
• On day 2, the controller tracked the dispatch plan while SOC drifted from 50%; average PV production was overestimated.Source: §V · pp. 11–12
• Less than 0.5 kW RMS tracking error (about 0.2% of 200 kW average feeder consumption) accompanies better dispatched-operation figures than no dispatch.The reported tracking performance summarizes experiments on days 0–2.Source: §V · p. 12, Table II · p. 13
• With Pmax set to 210 kW, the day-3 dispatch plan limited feeder power despite prosumption peaks of 250 kW, achieving peak shaving while maintaining dispatch.Source: §V · pp. 12–13
• Real-time computation took less than half a second, below the 10-second control interval, on the reported Matlab and Debian Linux setup.The reported computation-time statistics exclude communication time.Source: §V · p. 13, Table IV · p. 13

• The framework sets a 5-minute dispatch plan by combining forecast prosumption with an offset profile that restores BESS flexibility, then uses MPC to correct realization-plan mismatch.Source: §VI · pp. 13–14
• Data-driven prosumption and BESS voltage models feed convex optimization; the real-time MPC represents energy throughput while retaining linear SOC, voltage, and current constraints.Source: §VI · p. 14
• The EPFL feeder experiments report 0.5 kW RMS tracking error and mean error below 0.01 kW against 200 kW average prosumption across multiple operating days.Source: §VI · p. 14
• The strategy uses BESS and grid-connection power-flow measurements with minimal upper-layer coordination; future work includes contingency management, storage sizing, and economic assessment.Source: §VI · p. 14

APPENDIX A CONVEX FORMULATION OF DAY-AHEAD PROBLEM

• The original day-ahead problem is nonconvex because relationship (10) is nonlinear in a decision variable; the authors apply an augmented formulation proposed in to obtain a convex equivalent.Source: Appendix A · p. 14
• The formulation decomposes quantities into positive and strictly negative parts, then couples the resulting decision variables through equalities that require the offset profile to match across the two parts.Source: Appendix A · p. 14
• The offset profile is obtained from a linear convex program, and the dispatch plan is then determined from the resulting quantities.Source: Appendix A · p. 14
• The linear relationship can also impose additional offset-plan constraints, including for peak shaving.Source: Appendix A · p. 14

APPENDIX B DERIVATION OF THE TRANSITION MATRICES FOR MPC

• The discrete state-space model represents BESS state-of-charge and voltage dynamics for MPC.The derivation begins with a linear dynamic model and its state-space representation.Source: Appendix B · p. 14
• Starting from a known x0, the state at interval N is expressed as ANx0 plus accumulated input contributions propagated through powers of A.The derivation iterates the single-input state equation through interval N.Source: Appendix B · pp. 14–15
• Applying the output equation to the state evolution produces a matrix mapping the input sequence to system outputs.The displayed matrix contains feed-forward gain D and terms such as CA^iB.Source: Appendix B · p. 15
• For multiple inputs, the model adds an input r and applies transformation ψr to r for the system output.The passage refers to the multiple-input state-space model in equations (83)–(86).Source: Appendix B · p. 15