PaperlayerView exact revision on arXiv

Source-linked AI summary

User-specified Kelvin-hour budgets within model predictive control for energy-efficient buildings: Simulation and field demonstration

Jicheng Shi, Colin N. Jones

arXiv:2609.06698v1eess.SYcs.SY

TL;DR

Building MPC can violate temperature bounds online, and existing approaches do not let users specify a pre-operation budget for violation severity. This paper introduces Kh-budget MPC, which updates bounds using realized budget surplus or overspend. Prescribed budgets produced running-average responses across simulations and an occupied-home deployment, with energy and violation reductions in the one-zone and coupled two-zone cases.

  • Problem

    Online building MPC can violate temperature bounds, while existing soft-constraint tuning does not let users prescribe the allowed severity before operation.

    Source: §1 · p. 1

  • Method

    Kh-budget MPC uses signed bound adaptation to update softened temperature bounds according to the realized Kh violation relative to the user's running-average budget.

    Source: §2.3.1 · p. 4, §6 · p. 11

  • Results

    Prescribed budgets produced running-average responses across simulation and field evaluations; at α = 0.005 Kh/step, energy use fell 31.9% and Kh violation 36.2% versus the built-in default.

    Source: §6 · pp. 11–12, §5 · p. 11

  • Takeaways & Limitations

    The occupied-home results show that running-average Kh violations respond to prescribed budgets under real sensing, actuation, weather, and occupancy conditions.

    Source: §5 · p. 11, §6 · p. 11

    Field comparator tests used different time windows and weather, preventing weather-matched quantitative energy comparisons; broader validation remains future work.

    Source: §6 · p. 12

Abstract

from arXiv · show

For energy-efficient building control, model predictive control (MPC) has been widely proposed to reduce energy use while maintaining prescribed indoor temperature bounds. In practice, MPC implementations may still produce temperature-bound violations because of model mismatch, weather-forecast errors, and softened constraints introduced to preserve feasibility. Existing soft- constrained MPC usually handles this trade-off through slack-weight tuning, so users cannot prescribe a violation-severity budget before operation. This paper develops a Kelvin-hour (Kh)-budget MPC that allows users to specify a running-average budget for temperature-bound violation severity. During operation, the controller uses the realized Kh budget surplus or overspend to update the temperature bounds, providing step-by-step budget feedback. We evaluate the method in two high-fidelity BOPTEST simulation cases and in an occupied residential deployment. In the first one-zone case, prescribed budgets produce clear running-average Kh violation responses across predictors and disturbance settings. At a prescribed budget of 0.005 Kh/step, the controller reduces energy use by 31.9% and Kh violation by 36.2% relative to the built-in default controller. In the second coupled two-zone case, separate zone budgets produce zone-level responses, with 18.9%-20.5% energy reduction and 9.4%-64.3% zone-level Kh violation reduction. In the occupied residential deployment, the running-average Kh violations remain close to or below their prescribed budgets under real sensing, actuation, weather, and occupancy conditions.

1. Introduction

Building MPC can still violate temperature bounds online, while existing approaches do not let users prescribe a pre-operation budget for violation severity. The paper introduces Kh-budget MPC, which uses realized violations to update temperature bounds and is evaluated in simulations and an occupied home.

1. Introduction

  • Online temperature-bound violations can arise from model mismatch, forecast errors, and actuator limits; existing soft-constraint tuning does not let users specify allowed severity before operation.Source: §1 · p. 1

1.1. Literature review on comfort-violation control

  • Kh captures both the depth and duration of temperature-bound excursions, unlike violation rate, while comfort-model indices require additional environmental and occupant-parameter assumptions.Source: §1.1 · p. 1
  • Prior severity-aware approaches specify violation severity, but deployment gaps include no step-by-step realized-Kh feedback and assumptions of LTI systems with i.i.d. disturbances.Source: §1.1 · p. 2

1.2. Contributions and paper structure

  • Kh-budget MPC converts budget surplus or overspend into step-by-step signed temperature-bound adaptation, and is evaluated across predictors, disturbances, coupled zones, and an occupied home.Source: §1.2 · p. 2, §1.1 · p. 2
  • At α = 0.005 Kh/step, one-zone MPC reduced energy use by 31.9% and Kh violation by 36.2% versus the built-in default; two-zone cases reduced energy 18.9%–20.5% and zone-level Kh violation 9.4%–64.3%.Source: §1.2 · pp. 2–3
  • Across three six-day field tests, running-average Kh responses were close to or below prescribed budgets under real sensing, actuation, weather, and occupancy conditions.Source: §1.2 · p. 3

2. Methodology

The Kh-budget MPC lets users prescribe a running-average temperature-violation severity budget and adapts softened temperature bounds using realized violations. Its framework retains the nominal MPC objective while adding budget feedback, with extensions for different predictors and multiple zones.

2.1. Preliminaries

  • The building model maps states to a comfort-relevant output and represents comfort with temperature bounds that may change with occupancy schedules.The framework writes the dynamics abstractly and allows different predictive model types.Source: §2.1 · p. 3

2.2. Nominal MPC with soft constraints for energy-efficient building control

  • Nominal soft-constrained MPC minimizes predicted energy cost while slack variables preserve feasibility when predicted temperatures cannot satisfy bounds.A penalty on slack discourages bound relaxation.Source: §2.2 · p. 3
  • Slack-weight tuning affects Kh violation only indirectly, with a generally nonlinear relationship and different outcomes across weather, buildings, and HVAC systems.Thus, a slack weight does not directly specify the allowed violation severity.Source: §2.2 · p. 3

2.3. Kh-budget MPC

  • Users prescribe a running-average Kh budget α in Kh/step, corresponding to an average temperature-bound violation magnitude of α dT.The same average can arise from violations with different magnitudes and durations.Source: §2.3 · pp. 3–4

2.3.1. Bound adaptation and step-by-step budget feedback

  • After each realized violation, the controller updates its budget-feedback state: surplus increases relaxation, while overspend reduces relaxation and can make the MPC more conservative.The per-step budget balance is α − v(t); bound adaptation tightens or relaxes the softened temperature bounds according to the feedback state.Source: §2.3.1 · p. 4, §2.3 · p. 4

2.3.2. Implementation settings and multi-zone extension

  • Prediction margins shape the bounds and may be selected using engineering judgment or uncertainty calibration; a user-set maximum caps relaxation.For multiple zones, each zone can have its own budget and feedback while coupling is handled within the MPC model, constraints, and objective.Source: §2.3.2 · p. 5

3. Case studies and validation configurations

The validation uses one-zone and coupled two-zone BOPTEST simulations plus an occupied-home deployment, organized into five configurations. The simulations examine budget response, predictor portability, disturbance sensitivity, and separate zone budgets.

3. Case studies and validation configurations

  • Three complementary cases support five configurations: a one-zone BOPTEST benchmark, a two-zone BOPTEST benchmark, and an occupied residential deployment.The configurations cover simulation budget response, predictor portability, disturbance sensitivity, coupled-zone operation, and field evaluation.Source: §3.1 · p. 5, §3 · p. 5

3.1. Validation logic and building cases

  • The cases span a Brussels single-zone dwelling, a Milan two-zone apartment, and an occupied Swiss home with a Mitsubishi Ecodan heat pump.The Swiss deployment monitored and controlled one living-area floor, treated as occupied throughout; its Kh violation counts only lower-bound violations.Source: §3.1 · p. 5

3.2. Simulation validation configurations

  • The simulation evaluation comprises four configurations, V1–V4, using a shared protocol and case-specific controller implementations.The configurations vary the tested question while retaining the simulation setup described for each case.Source: §3.2 · p. 5

3.2.1. Simulation protocol and controller implementation

  • Simulation runs use 15-minute sampling and a 12-hour horizon, with a two-week peak-heating-day scenario and fixed Kh-budget MPC update gain.The common data-driven predictor is an hourly refitted adaptive ARX model; the reported configuration table summarizes case, predictor, disturbance setting, and tested parameters.Source: §3.2.1 · pp. 5–6, Table 1 · p. 7

3.2.2. V1: Kh-budget response

  • V1 sweeps prescribed Kh budgets for the adaptive-ARX controller and compares the response with nominal MPC slack-weight tuning and DAD-DPC violation-rate targets.DAD-DPC's target specifies the allowed fraction of time steps outside the temperature bounds.Source: §3.2.2 · p. 6

3.2.3. V2: Predictor portability

  • V2 tests whether the Kh-budget response transfers across adaptive and fixed predictors, including DeePC, a gray-box RC model, and NNARX.The Kh-budget MPC formulation remains unchanged across these predictor classes.Source: §3.2.3 · p. 6

3.2.4. V3: Disturbance sensitivity

  • V3 tests budget response under three stronger combinations of measurement noise and weather-forecast error than the baseline setting.The adaptive ARX predictor is used with prescribed budgets of 0.02 and 0.05 Kh/step.Source: §3.2.4 · p. 7

3.2.5. V4: Coupled two-zone budget operation

  • V4 tests separate zone budgets in a coupled two-zone system whose zones share a heat pump and supply-water temperature.The equal-budget setting is paired with two asymmetric settings, placing the tighter budget on each zone in turn.Source: §3.2.5 · p. 7

3.3. Field deployment configuration

The field configuration deploys Kh-budget MPC in an occupied Swiss home using retrofit sensing and heat-pump controls. The controller targets delivered heating power and converts its 15-minute target into minute-level supply-water-temperature setpoints.

3.3. Field deployment configuration

  • The occupied-home deployment monitors and controls a living-area floor in a Swiss house heated by a Mitsubishi Ecodan heat pump.The residents' feedback informed the operative-temperature measure and solar-dependent lower temperature bounds.Source: §3.3 · p. 7
  • A Home Assistant hub gathers room and floor temperatures and heat-pump measurements, while an off-site computer runs MPC and returns setpoints through the hub.Weather forecasts are retrieved from Open-Meteo.Source: §3.3 · p. 7
  • The field comparison includes the residents' default Weather Compensation mode, nominal MPC, and Kh-budget MPC; the MPCs optimize delivered heating power rather than heat-pump electricity.The supervisory layer updates supply-water-temperature setpoints each minute so measured 15-minute heating energy tracks the MPC target.Source: §3.3 · p. 7

4. Simulation results

The simulations test whether prescribed Kh budgets yield clear running-average responses across controller settings, predictors, disturbance conditions, and coupled zones. The results show budget tracking in Case 1, portability with a finite-relaxation caveat, and zone-specific responses in Case 2.

4.1. Case 1: Kh-budget response and controller mechanism

  • Across 20 runs, achieved final average Kh violation stays close to the prescribed budget, unlike nominal MPC’s nonlinear slack-weight response and DAD-DPC’s indirect, saturating response.DAD-DPC targets violation rate rather than Kh severity, so its target cannot directly specify a Kh budget.Source: Figure 3 · p. 8, §4.1 · p. 8
  • The proposed controller’s running-average Kh violation stays mostly below its budget; nominal MPC can reach a similar final value after a large early transient.Scheduled unoccupied daytime bounds can reduce the running average for all controllers.Source: Figure 4 · p. 8, §4.1 · p. 8
  • When running-average violation is well below budget, bound relaxation increases; as it approaches budget, relaxation decreases, while a looser budget permits more relaxation.DAD-DPC’s equivalent adaptation is nonpositive, limiting it to reducing tightening toward zero rather than relaxing beyond nominal temperature bounds.Source: §4.1 · pp. 8–9, Figure 5 · p. 9, Figure 6 · p. 9
  • At α = 0.005 Kh/step, Kh-budget MPC saves 31.9% energy and reduces Kh violation by 36.2% relative to the default controller.Figure 7 compares relative energy use with achieved Kh violation across controller-parameter sweeps.Source: Figure 7 · p. 9, §4.1 · p. 9

4.2. Case 1: portability and disturbance checks

  • Across V2 predictor variants, final average violations are generally close to budgets; stronger V3 disturbance groups retain similar responses, except G3 at α = 0.05 Kh/step.The G3 response is weaker and more variable because the finite relaxation cap prevents further temperature-bound relaxation; average energy use falls 30.8%–35.7% at α = 0.02 and 0.05 Kh/step versus default.Source: §4.2 · p. 9, Table 2 · p. 10

4.3. Case 2: coupled two-zone budget operation

  • Across tested two-zone settings, energy use falls 18.9%–20.5% and zone-level mean Kh violations fall 9.4%–64.3% versus the default controller.Kh reductions are smaller in looser-budget zones and larger in tighter-budget zones.Source: Table 3 · p. 10, §4.3 · p. 10
  • In the coupled two-zone case, asymmetric budgets produce zone-specific running-average violations and bound adaptations, with Zone 2 realizing more violation under its looser budget.For (α1, α2) = (0.02, 0.05), first-step adaptations are often saturated at the relaxation limit; the 24th-step signals show the asymmetry more clearly.Source: Figure 8 · p. 10, §4.3 · p. 10

5. Occupied-home field results

In the occupied-home runs, the Kh-budget MPC completed all three six-day deployments, with running-average violations close to or below prescribed budgets. The trajectories show how temperature and heating use varied across the three budgets under field conditions.

5. Occupied-home field results

  • The controller completed all three six-day deployments; final average violations were 0.0145 and 0.0278 Kh/step at α = 0.015 and 0.030, and 0.0284 Kh/step at α = 0.050.The α = 0.050 run ended well below its budget; the default controller ended at 0.0020 Kh/step. Table 4 summarizes the field runs.Source: §5 · pp. 10–11, Table 4 · p. 11
  • After the initial transient, the α = 0.015 and 0.030 running-average violations stayed close to and mostly below budget, while α = 0.050 stayed well below budget.The default controller remained close to zero; nominal MPC slack-weight changes altered violation levels but were not referenced to a prescribed Kh budget.Source: §5 · p. 11, Figure 9 · p. 11
  • The α = 0.015 run kept operative temperature near the lower bound and used heating frequently, while α = 0.030 allowed larger deviations and ended near budget.The α = 0.050 run's measured heating fell nearly to zero during its final three days, while mild conditions limited further Kh accumulation; a temperature drop around day four followed a window-opening event.Source: §5 · p. 11
  • The occupied-home results show running-average Kh violations responding to prescribed budgets under real sensing, actuation, weather, and occupancy conditions.Source: §5 · pp. 10–11

6. Discussion and conclusion

The study proposes user-specified running-average Kh budgets with step-by-step signed bound adaptation, evaluated in high-fidelity simulations and an occupied-home deployment. Simulation results report energy and violation reductions, while the field runs show budget responses under real operating conditions.

6. Discussion and conclusion

  • The controller adapts temperature bounds step by step according to realized Kh violation relative to the user's running-average budget.The study evaluates budget response, predictor portability, disturbance sensitivity, and coupled two-zone operation in simulation, as well as occupied-home deployment.Source: §6 · p. 11
  • At α = 0.005 Kh/step, the one-zone simulation reduced energy use by 31.9% and Kh violation by 36.2% relative to the built-in default controller.In the coupled two-zone simulation, separate budgets produced zone-level responses, with 18.9%–20.5% energy reduction and 9.4%–64.3% zone-level Kh violation reduction.Source: §6 · pp. 11–12
  • In the occupied-home deployment, α = 0.015 and 0.030 Kh/step runs ended close to budget, while the α = 0.050 Kh/step run ended below budget.Source: §6 · p. 12
  • Field comparator runs covered different time windows and weather, so weather-matched quantitative energy comparisons were not possible.The authors identify broader validation across buildings, climates, seasons, occupancy patterns, and disturbance conditions as future work.Source: §6 · p. 12

Appendix A.1. Weather-forecast error emulator

The appendix describes settings for the BOPTEST weather API forecast-error emulator. It identifies different error distributions for outdoor temperature and GHI, and notes nighttime and smoothing treatment for GHI.

Appendix A.1. Weather-forecast error emulator

  • The low and high forecast-error levels are generated by the BOPTEST weather API using the forecast-error emulator reported in.Source: Appendix A.1 · p. 12
  • The outdoor-temperature forecast-error settings use a normal distribution, while the GHI settings use a Laplace distribution.The passage identifies the distributions but does not provide the numerical settings in the supplied text.Source: Appendix A.1 · p. 12
  • For GHI, nighttime forecasts are set to zero and nonzero forecasts receive smoothing post-processing.Source: Appendix A.1 · p. 12

Appendix A.2. Two-zone implementation and COP-aware ob-

The two-zone implementation uses an adaptive ARX predictor with zone temperature inputs and shared supply-water temperature and zone valve duty. Its fitted COP model contributes to the MPC energy objective, and the optimized control is translated into BOPTEST setpoints and valve commands.

Appendix A.2. Two-zone implementation and COP-aware ob-

  • The adaptive ARX predictor uses room and floor temperatures for both zones, with shared supply-water temperature and zone valve duty as zone inputs.Equivalent zone-level virtual variables avoid putting the product of supply temperature and valve duty directly in predictor constraints.Source: Appendix A.2 · p. 13
  • A fitted COP model uses supply-water and outdoor temperatures in the MPC's electrical-energy objective.Its coefficients were fitted once from the same 10-day bang-bang-control data as the initial Case 2 ARX model and held fixed during the V4 episode.Source: Appendix A.2 · p. 13
  • The optimized supply-water temperature is sent as the BOPTEST setpoint, and each on/off valve's on-duration approximates its optimized duty fraction over the sampling period.Source: Appendix A.2 · p. 13

Appendix A.3. Modeling details for V2

Appendix A.3 describes four V2 predictors and a shared SCP residual-calibration protocol for their temperature-bound tightening margins.

Appendix A.3. Modeling details for V2

  • The V2 predictors are adaptive ARX, adaptive DeePC, fixed 4R3C RC, and fixed NNARX models.DeePC uses a rolling five-day data buffer; the RC and NNARX models are fitted offline.Source: Appendix A.3 · p. 13
  • The DeePC predictor uses a bilevel adaptive formulation and rebuilds its Hankel representation hourly.Its initial-step length is dinit = 6.Source: Appendix A.3 · p. 13
  • The fixed RC and NNARX predictors are trained offline using 30 days of bang-bang-controller data.NNARX additionally uses 30 days of PRBS data.Source: Appendix A.3 · p. 13
  • All four predictors use open-loop N-step residuals from forecast weather on a held-out five-day dataset to calibrate tightening margins.The 98% quantile of absolute residuals is computed at each horizon step and held fixed during each episode.Source: Appendix A.3 · p. 13

CRediT authorship contribution statement

The contribution statement assigns conceptualization to both authors, while their other listed roles differ.

CRediT authorship contribution statement

Loading 2609.06698v1…