An integrated model predictive control approach for optimal HVAC and energy storage operation in large-scale buildings

1. Introduction

• About half of buildings’ total energy consumption is devoted to HVAC, motivating efficient control of building devices.The introduction connects efficient operation with lower energy consumption, emissions, and energy bills.Source: §1 · p. 1
• Demand-response programs let buildings adjust consumption to advance aggregator requests and receive monetary rewards, while storage can add consumption flexibility.The paper also notes storage’s roles in self-sufficiency and system resiliency.Source: §1 · p. 2

1.1. Paper contribution

• The proposed centralized MPC manages heat pumps, heater actuators, storage, and PV generation to minimize a large building’s electricity bill under price-volume demand-response signals.The aggregator’s signals specify rewards for meeting energy-consumption constraints during a stated period.Source: §1.1 · p. 2
• The control problem uses an LP-based framework whose DR binary-variable count is independent of building size, supporting applications with hundreds of zones.The number of binary variables is at most a few units, determined by DR intervals in the optimization horizon.Source: §1.1 · p. 3
• A two-step optimization first minimizes comfort-bound violations, then solves the overall problem with modified constraints, avoiding the need to select penalty weights.The approach is intended to recover quickly when original comfort constraints cannot be satisfied.Source: §1.1 · p. 3

Zone Thermal model

• Zone notation includes indoor temperatures, heat flows, and time-varying thermal comfort ranges.The symbols also distinguish vectors of zone temperatures and heat flows.Source: Zone Thermal model · p. 6
• HVAC notation distinguishes heating and cooling constraint sets, heat-pump commands, and electrical energy consumption.The glossary also identifies heat-exchanger air-flow actuation signals.Source: Zone Thermal model · pp. 6–8
• The optimization notation covers battery state of charge, PV energy, grid energy, DR requests and rewards, and forecasts of exogenous inputs.It also defines a binary variable for fulfillment of each DR request.Source: Zone Thermal model · pp. 7–8

2. System architecture overview

• Heating and cooling power comes from electrical heat pumps, with thermal storage coupled to the heating pump but not the cooling pump.Thermal storage is used for heating in this setup to illustrate control both with and without storage.Source: §2 · p. 9
• Each zone exchanges heat through a fan coil, whose air mass flow is regulated, while the building also has electrical storage, PV generation, and demand-response participation.The fan coils exchange heat with the thermal storage at constant water throughput.Source: §2 · p. 9
• A digital centralized control unit regulates the heat pumps, thermal storage, fan-coil flow, electrical storage, and PV in discrete time.Each zone is equipped with a temperature sensor.Source: §2 · p. 9

3.1. Zone thermal model

• Each zone has a temperature sensor and independently regulated heat-exchanger airflow, with time-varying comfort constraints on room temperature.The heat-flow and temperature variables are defined per zone.Source: §3.1 · p. 9
• The zone model represents indoor temperature dynamics as depending on heat flows and exogenous variables such as outdoor temperature, solar radiation, appliances, lighting, and occupancy.Available measurements or forecasts of these variables are collected in an input vector.Source: §3.1 · p. 10

3.2. HVAC system model

• The HVAC model links heat flow to heat-exchanger airflow and performance, yielding linear constraint sets for heating and cooling operation.The heat-exchanger performance coefficient is specific to each device.Source: §3.2 · p. 11

3.2.1. Heating mode operation with thermal storage

• In heating mode, the heat pump is coupled to thermal storage, and the heat exchangers’ inlet temperature is assumed equal to the TES outlet temperature.The paper states that the modeling assumptions are satisfied by the real-world devices emulated in EnergyPlus.Source: §3.2.1 · pp. 11–12

0. Therefore, the condition

• The thermal storage temperature depends on heat-pump temperature and total heater-level heat exchange, and zone temperatures and stored energy are controlled through heat-pump and zone-flow variables.The storage temperature is represented with a regressive model.Source: §0 · pp. 12–13

3.2.2. Cooling mode operation

• Cooling heat-pump dynamics use a regressive model whose inputs include supply temperature and total zone heat flow, with model orders specified for the temperature and heat-flow terms.The cooling heat pump’s electrical consumption is zero when it is switched off.Source: §3.2.2 · p. 13

3.3. Electrical storage model

• The battery model tracks state of charge and charge/discharge energy, with efficiency, capacity, and maximum charge/discharge rates constraining operation.The charge and discharge signals represent energy fed to and drawn from the battery during each time interval.Source: §3.3 · p. 14

3.4. PV generation model

• PV generation is modeled using PVUSA as a function of irradiance and outside-air temperature, yielding a static linear-in-the-parameters model when exogenous inputs are specified.The model is described as accurate when its parameters are fit to measured data.Source: §3.4 · pp. 14–15

3.5. Energy consumption and Demand-Response model

• The DR model represents requests with a time horizon, energy threshold, and reward; a request is satisfied when building consumption over that horizon does not exceed its threshold.The operating cost accounts for energy cost minus rewards for satisfied requests.Source: §3.5 · pp. 15–16

4. Optimal HVAC and storage operation problem

• The overall problem minimizes the building electricity bill under a DR program while preserving comfort, and becomes linear when zone heat flows replace heater control variables as decisions.The optimal heat-exchanger actuation is recovered from the optimal zone heat flows.Source: §4 · p. 16

4.1. Heating mode operation with thermal storage

• Heating operation with thermal storage is formulated as a MILP that minimizes total energy cost over the prediction interval using sensor measurements.The formulation assumes sensor measurements of building, storage, and heat-pump states are available.Source: §4.1 · p. 17

4.2. Cooling mode operation

• Cooling operation is formulated to minimize total energy cost over the prediction interval using measured states and cooling-mode control variables.The formulation is presented as Problem 2 for combined cooling and storage control under DR.Source: §4.2 · p. 17

4.3. Managing constraint violations and uncertainty

• When uncertainty or disturbances make hard comfort constraints infeasible, the method first minimizes the 1-norm of comfort violations, then optimizes operation using the resulting relaxed bounds.The second-step substitution is stated to ensure feasibility of the subsequent problems.Source: §4.3 · p. 18

4.4. MPC algorithm

• The MPC runs an LP and a MILP at each step, but its formulation omits the constraint preventing simultaneous battery charging and discharging.The MILP’s integer-variable count depends on DR requests within the horizon.Source: §4.4 · p. 19
• The optimization scales linearly with building zones, and realistic scenarios require only a few integer variables, supporting application to buildings with hundreds of zones.The MILP’s binary-variable count equals the number of DR requests in the prediction horizon.Source: §4.4 · p. 19

• The stated EES condition is always met because battery efficiency satisfies η < 1.Source: i.e., that W EES · p. 19
• At a battery state-of-charge bound, W_EES(l) can be set according to equations (19) and (20).The supplied passages do not specify the setting itself.Source: i.e., that W EES · p. 19

5. Test cases

• The test structure is an 8-floor building in Turin with 126 zones, comprising commercial, office, and residential floors.It includes PV, electrical storage, two heat pumps, and thermal storage for heating; EnergyPlus simulations used a 10-minute sampling time and 12-hour MPC horizon.Source: §5 · p. 20

5.1. Winter season simulation - heating operation

• Zone-model FIT averaged 75%, 68%, and 66% for 1-, 6-, and 12-hour-ahead predictions; TES FIT exceeded 90% at 12 hours.Zone models were identified using 14 estimation days and validated on 4 days; each zone model coupled neighboring zones.Source: §5.1 · p. 23
• The worst-performing zone averaged about 0.13°C of comfort-bound violation over three days, attributed to modeling errors despite exact input forecasts.The bound-relaxation technique pushed temperatures back within prescribed bounds shortly after violations; strict comfort bounds at all times were described as infeasible under modeling errors or unpredictable disturbances.Source: §5.1 · p. 24, Table 4 · p. 26
• 25.49% lower total cost than the thermostatic benchmark was achieved in the winter comparison without DR.The comparison is for the considered days; the benchmark simulations omitted DR requests for fairness.Source: §5.1 · pp. 26–27, Table 5 · p. 27

5.2. Summer season simulation - cooling operation

• The cooling-mode heat-pump inlet-fluid model achieved FIT above 80% for 12-hour-ahead predictions; heating did not need this separate step because its inlet temperature equals TES temperature.The cooling setup has no TES.Source: §5.2 · p. 27
• 35.67% lower cost than the thermostatic benchmark was achieved in cooling while maintaining similar zone comfort.The comparison summarizes a three-day cooling simulation.Source: §5.2 · p. 27, Table 6 · p. 27, Table 7 · p. 29

5.3. Performance analysis under uncertainties

• Uncertainty tests perturbed outdoor temperature, solar irradiance, and internal gains, while treating energy price and the daily DR program as known one day ahead.Forecast scenarios were considered individually and in combination.Source: §5.3 · pp. 29, 31
• Inaccurate forecasts could raise overall cost by up to 7.79% relative to the nominal case, while comfort differences were negligible, indicating the control algorithm could minimize thermal discomfort during unexpected situations.Twenty heating-mode simulations were generated for each uncertain input, and inaccurate forecasts were considered individually and combined.Source: §5.3 · p. 31

6. Discussion

• Prediction performance declines as the horizon grows but remains acceptable, and receding-horizon updates let the controller adapt to inaccuracies in long-term forecasts.Source: §6 · p. 32
• 25.49% lower total cost than standard thermostatic rules, with mostly satisfied comfort bounds; the benchmark excludes DR for a fair comparison.The average bound violation in the worst zone is less than 0.14°C.Source: §6 · p. 32
• The EES and TES charge and discharge twice daily to exploit price fluctuations and help satisfy DR requests, but the controller skips the last request when reduction is not profitable.Source: §6 · p. 32
• Under inaccurate forecasts, maximum cost is less than 8% above the exact-forecast result, and only a slight increase in discomfort occurs.The receding-horizon strategy limits the effect of prediction errors because near-future errors matter most; the MPC implementation mitigates comfort impacts.Source: §6 · p. 33
• The authors report similar considerations for cooling operation in summer as for the winter simulation.Source: §6 · p. 33
• For the 126-zone building, each 10-minute control step takes about 20 seconds to compute on a standard PC.Source: §6 · p. 33

7. Conclusion and future research

• The proposed receding-horizon MPC optimizes building electricity costs by solving an LP and an MILP at each step, with integer-variable count equal to DR requests in the prediction horizon.Source: §7 · p. 33
• The approach was evaluated through experimental validation in a realistic simulation framework and is described as applicable to large buildings.Source: §7 · p. 33
• Future work will model the building as a microgrid including electric vehicles, appliances, and other loads, with attention to active/reactive power-flow constraints.Source: §7 · p. 33
• Further studies will consider DR incentives for keeping consumption above a minimum and compare chance-constrained or scenario-based uncertainty methods with the proposed method.Source: §7 · p. 34