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Energy 112 (2016) 1194e1206

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Energy

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Multi-objective optimization for thermal mass model predictivecontrol in small and medium size commercial buildings undersummer weather conditions

Xiwang Li a, b, *, Ali Malkawi a

a Center for Green Building and Cities, Graduate School of Design, Harvard University, Cambridge, MA 02138, USAb Department of Civil, Architectural and Environmental Engineering, Drexel University, Philadelphia, PA 19104, USA

a r t i c l e i n f o

Article history:Received 16 February 2016Received in revised form5 July 2016Accepted 5 July 2016

Keywords:Multi-objective optimizationModel predictive controlThermal mass controlDemand responseThermal comfort

* Corresponding author. Center for Green Building aDesign, Harvard University, Cambridge, MA 02138, US

E-mail address: xiwang_li@gsd.harvard.edu (X. Li)

http://dx.doi.org/10.1016/j.energy.2016.07.0210360-5442/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

Building thermal mass control has great potentials in saving energy consumption and cost. Optimalcontrol schemes are able to utilize passive thermal mass storage to shift the cooling load from peak hoursto off-peak hours to reduce energy costs. As such, this paper explores the idea of model predictive controlfor building thermal mass control. Specifically, this paper presents a study of developing and evaluating amulti-objective optimization based model predictive control framework for demand response orientedbuilding thermal mass control. This multi-objective optimization framework takes both energy cost andthermal comfort into consideration simultaneously. In this study, the developed model predictive controlframework has been applied in six commercial buildings at Boston, Chicago, and Miami, under typicalsummer weather conditions. Time-of-use electricity prices from these three locations are used tocalculate the cooling and reheating energy costs. Pareto curves for optimal temperature setpoints underdifferent thermal comfort requirements are calculated to show the trade-off between the cost saving andthermal comfort maintaining. Comparing with a typical “night setback” operation scheme, this modelpredictive control schemes are able to save energy costs from 20% to 60% at these three locations underdifferent weather and energy pricing conditions. In addition, the Pareto curves also show that the energycost saving potentials are highly dependent on the thermal comfort requirements, weather conditions,utility rate structures, and the building constructions.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Extensive studies have been focusing on building energy effi-ciency improvement, as buildings consume over 70% of the elec-tricity, and contribute over 40% of the greenhouse gas emissions [1].Within the total building energy consumption, heating, ventilationand air-conditioning (HVAC) systems are responsible for about one-third of the total energy consumption [1]. Besides the energyconsumption, the building energy costs are around $350 billion peryear in US [2], among which up to 40% of the building energy costcan be saved through proper control schemes [3]. Especially, thedevelopment of smart grids provides more opportunities for

nd Cities, Graduate School ofA..

buildings to save energy cost through demand response (DR),which encourages electricity users to alter their operation strate-gies in response to the DR signals [4]. Different advanced electricityrate structures are used in different utility companies to advocatethe development of DR, such as: time-of-use (TOU), on-off-peakpricing (OPP), and real-time pricing (RTP). To this end, buildingoptimal operation is not only to save energy but also cost withresponse to DR signals.

A great number of techniques have been utilized to helpbuilding sector reduce energy consumption and cost, such asspecial construction design [5,6], building retrofitting [7,8],optimal ventilation utilization [9,10], and on-site distributed en-ergy system integration [11e13]. These approaches which are noteasy to realize and need extra initial costs, require either equip-ment to be installed or replaced. Fortunately, the optimal controlof building thermal mass does not need any extra equipmentinstalling or replacement, which utilizes the existing building

X. Li, A. Malkawi / Energy 112 (2016) 1194e1206 1195

control systems to adjust the operation of HVAC system to stor-age/release thermal energy to/from building thermal mass.Currently, two different HVAC operation strategies have beenwidely used in most of the buildings. The first one is “on and off”control, in which HVAC systems are turned on at occupied hoursand turned off at unoccupied hours. The other one is “nightsetback” operation, in which “looser” temperature setpoints areused at unoccupied periods. Since the deadband between heatingand cooling setpoint is relatively large, the HVAC system is off atmost of the time of the unoccupied periods and will be turned onwhen the room temperature is out of the setpoint deadband.However, neither of these two operation strategies fully utilizesthe building thermal mass energy storage or the DR electricityprices. Previous studies have illustrated high potentials for energyand cost saving through building thermal mass control. InRefs. [14e16], real field case studies using heuristic pre-coolingschemes are conducted for building thermal mass control. Up to40% reduction in total cooling costs from using those thermalmass control strategies have been demonstrated in those studies.Yin et al. [17] achieved 15e30% peak demand reduction in 11 realfield buildings during auto DR days in California. Similarly, heu-ristic pre-cooling schemes have also been applied in simulationstudies for residential buildings in 12 US DOE climate zones [18].Even though these studies have proved the energy cost savingopportunities from thermal mass control, the passive thermalmass control, however, is hard to predict and control through thetraditional control schemes, such as how to determine when tostart store thermal energy, and how to determine the temperaturesetpoints. Therefore, a few studies started to develop more effi-cient operation strategies to control the building thermal massrecently. In the existing literature, the model predictive control(MPC) has been proven to be a feasible method for HVAC systemoptimal control [19]. MPC utilizes system forecasting models topredict the system operation under proposed operation strategiesand determines the optimal control strategies over a recedinghorizon [20]. As the basis of MPC, building energy forecastingmodel is critical to its performance. The existing forecastingmodels can be categorized into white box models, black boxmodels, and grey box models. Most of the existing studies useblack box or grey box models for building operation MPC due totheir merits in calculation speed. Resistance and capacitance (RC)model, as one of the most popular grey box models, has beenutilized in several building temperature control studies, such as[21e23]. Similarly, a lot of black box models, such as: autore-gressive with exogenous (ARX), artificial neural network (ANN),and support vector machines (SVM), have also been utilized forbuilding operation and thermal mass control [24e26]. Other thanthe typical black box and grey box models, a number of studiesdeveloped new modeling approaches for building energy man-agement and control, by combining different modeling ap-proaches together. Lü et al. [27] developed a combined RC andautoregressive-integrated-moving-average (ARIMA) model forheterogeneous building energy forecasting. Fux et al. [28] com-bined RC models with extended Kalman filters to improve themodel accuracy and robustness. Hu [29] proposed a feed-forwarddecision framework for building operation MPC using data-drivenmodels and particle filters. Li et al. [30,31] developed a proactivesystem identification methodology for building energy fore-casting by combining system excitation and frequency domainmodeling approaches. All these studies made significant contri-bution to building energy forecasting. However, we have to admitthat even though different advanced parameter identificationmethods have been implemented to identify the parameters forgrey box models, the parameter identification process still needs along calculation time and the model simplification process also

requires expert knowledge. On the other hand, the black modelsrequire long training periods and the model extensibility is alwayslimited to the quality of training data. The reasons why white boxmodels have rarely been used for building operation MPC are: (1)the difficulty in connection white box models with optimizationtools; (2) the calculation speed of white box models which is nothigh enough for heuristic searching based optimizationalgorithms.

Fortunately, with the improvement of computing power and theinvention of optimizationmiddleware, these two limitations can beresolved today. Recently, a building control virtual test bed (BCVTB)is developed and released by Lawrence Berkeley National Labora-tory (LBNL) [32]. BCVTB is able to couple several different simula-tion programs, including EnergyPlus, MATLAB/SIMULINK, TRNSYS,and BACnet which allows data exchange between simulation pro-grams and real Building automation system (BAS). MultipleEnergyPlus-MATLAB co-simulation framework have been devel-oped to test new HVAC control methods based on BCVTB [33,34].For example, a new HVAC control scheme using Predicted MeanVote (PMV) of each occupant as feedback and provides the oppor-tunity to act on their own comfort level had been reported inRef. [33]. Another important control optimization middleware,GenOpt, is also developed by LBNL, which can iteratively executeany text input/output based simulation program, such as Ener-gyPlus until optimal solutions are found [35]. GenOpt was used byCoffey et al. [36] to incorporate a modified genetic algorithmmodelpredictive control with an EnergyPlus model to study the temper-ature control optimization in office buildings and its effect buildingenergy demand. Rackes and Waring developed a multi-objectiveoptimization framework to determine the building dynamicventilation strategies to save energy and improve indoor air quality,using EnergyPlus and GenOpt [37]. To this author's best knowledge,there is no study which investigated the potentials of using Ener-gyPlus and GenOpt for thermal mass MPC as well as thermalcomfort control.

Based on the current research statutes and the urgent need forbuilding energy efficiency improvement, this study proposes todevelop a MPC framework for building thermal mass control withconsidering the energy cost saving and thermal comfort main-taining simultaneously. To test the performance of this multi-objective optimization scheme, this MPC framework will beimplemented in six commercial buildings at Boston, Chicago, andMiami under typical summer weather conditions from August 1stto 5th. The reason why only summer cases are studied is that gasprices are usually constant throughout the day. So the thermalmass control for heating cost reduction is not applicable. To thisend, this study targets on the operation optimization in summerconditions. In order to evaluate this MPC framework in thosebuildings, EnergyPlus models for small size and medium sizecommercial buildings are used in lieu of real building. In thefollowing sections, Section 2 introduces the methodology formulti-objective MPC framework development, EnergyPlus simu-lation model modification, and optimization algorithm imple-mentation. Section 3 discusses and analyzes the thermal massMPC results for all the tested cases. Finally, Section 4 summarizesthe findings from this study and puts forward the directions offuture work.

2. Multi-objective MPC framework development

The first objective of this study is to develop a multi-objectiveoptimization framework for building thermal mass MPC for en-ergy cost reduction and thermal comfort control. The optimizedthermal massMPC scheme is intended to fully utilize pre-cooling atthe off-peak hours when electricity price is low. This section will

X. Li, A. Malkawi / Energy 112 (2016) 1194e12061196

introduce the development of the optimization framework and thebuilding energy simulation models in detail.

2.1. Optimization formulation

As this MPC framework needs to consider energy cost andthermal comfort simultaneously, the optimization framework hastwo objectives included: energy cost (Ccooling/reheating) and thermalcomfort (CPMV). This multi-objective optimization problem can beformulated as:

J�Tstp; i; Wk

� ¼ Ccooling=reheating þ CPMV

¼XNi¼1

Re;iEclg;i þXNi¼1

Rg;iGrhtg;i þWk

XNi¼1

ðIiPMViÞ2

(1)

Subject to : Eclg;i ¼ f�Tstp; i; Tout; i; Qsol; i; Qin; i; COPcl;i…

�(2)

Tmin < Tstp; i < Tmax (3)

Ii ¼�1; for i ¼ 8 am to 6 pm0; for i ¼ others

(4)

where Re,i ($/kWh) is the electricity price at time, i, Eclg,i is thebuilding electricity consumption (kWh) at time, i, Rg,i ($/kJ) is thegas price at time, i, Grhtg,i is the building reheating energy con-sumption (kJ) at time, i, Ii is the occupancy indicator. From 8:00 a.m.to 18:00 p.m., Ii ¼ 1, otherwise, Ii ¼ 0. PMVi is the thermal comfortindex at time, i. Here, multiplying Ii is to only consider the thermalcomfort during occupied periods. Neutral thermal comfort prefer-ence is assumed here, and the optimization algorithm will try tomove the PMV close to zero. Since PMV is usually between �3 and3, the total summation of squared value is used in the objectivefunction. As there are over 100 time steps in the occupied periods,the total summation of the thermal comfort cost term is thencompetitivewith the energy cost term, and the optimization enginewill derive the minimization of both energy cost and thermalcomfort.

On the left hand side of Eq. (1), Tstp, i (�C) is the temperaturesetpoint at time, i, and Wk is weighting factor for thermal comfortobjective and the objective function is deterministic once thisweighing factor is determined. This study targets on the summeroperation, the heating system is turned off at most of the studyingperiods. So only reheating gas consumption Grhtg.i is considered inthe objective function. The constraint shown in Eq. (2) representsthe building cooling energy forecasting model in EnergyPlus, whichis a complex forecasting model with respect to temperature set-point, Tstp, i, weather conditions: outdoor air temperature, Tout,i, andsolar irradiance, Qsol,i, as well as internal heat gains, Qin, i, and thechiller coefficient of performance, COPcl,i, etc. Tmin and Tmax in Eq. (3)are lower and upper limits of the temperature setpoints, which are15 �C and 28 �C in this study.

2.2. Building simulation: energy cost and thermal comfort

The second objective of this study is to utilize and evaluate thedeveloped MPC framework in different buildings under varyingweather and energy pricing conditions. As a result, two types ofcommercial building EnergyPlus models from the DOE post-1980office reference building database are used in this study [38].

2.2.1. Simulation modelsThe first building is a small office building with 511 m2

floorarea. This building has four perimeter zones and one core zone,with each served by a packaged constant air volume (CAV) airhandling unit (AHU) using a direct expansion cooling coil. Thenominal coefficient of performance (COP) of the direct expansioncooling coil is 3.07. The second building a three-story office build-ing, and each floor has five conditioned zones. The total floor area is4982 m2. This building uses multi-zone variable-air-volume (VAV)systems with water reheat. The VAV system is served by a basechiller with capacity as 414 kW and nominal COP as 2.8 Table 1 andTable 2 summarizes the general building geometries and key con-struction features of these two buildings used in this paper. Thesimulation time step is chosen as 15min for the accuracy and speedpurpose. In order to link the EnergyPlus models with the developedMPC framework, several modifications have been made on theoriginal simulation models. The details about this modification areprovided in Section 2.2.4.

In order to evaluate the performance of the developed thermalmass MPC framework, it has been applied at different locations:Boston, Chicago, and Miami, under typical summer weather con-ditions from August 1st to 5th. Typical meteorological year (TMY3)weather data during the studying period from all of these threelocations are used in this study. Fig. 1 shows the outdoor air tem-perature during the study period at these three locations, whichshows that the temperature at Miami is higher than that of othertwo, followed by the temperature at Chicago. TOU electricity pricesfrom these three locations are plotted in Fig. 2.

2.2.2. Optimization approachThe multi-objective optimization framework uses Genopt to

connect EnergyPlus simulation model and optimization algorithm.The Hooke-Jeeves Particle Swarm Optimization (HJPSO) is selectedin this study, which uses heuristic searching methods and is suit-able for the simulation based optimization where derivatives ofobjective function are unavailable [36]. The details about the HJPSOalgorithm are introduced in Section 2.2.3.

Considering the hubristic searching optimization approach usedin this study, the total calculation time can be estimated as:

Tcal ¼ tsimNuNit (5)

Where, Tcal is the estimated total calculation time, tsim is the Ener-gyPlus simulation time of each run, Nu is the total number of de-cision variables, and Nit is the number of iterations in theoptimization.

To tackle barriers from calculation time, several simplificationsand modifications are conducted to improve the simulation andoptimization speed. For the MPC framework in this study, if all thetemperature setpoints at each time step are decision variables, thetotal calculation time will be around 80 h. In order to reduce thecalculation time, only cooling temperature setpoints are optimizedin this study. The heating setpoints are defined as three degreeslower than the cooling setpoints at occupied periods and eightdegrees lower at unoccupied periods, using the setpoint overriddenprogram in EnergyPlus. By review the building temperatureoptimal control strategies from previous projects, the temperaturesetpoints before 4:00 a.m. is usually not optimized and the tem-perature setpoints are not necessary to change every 15 min[14,24]. Therefore, the temperature setpoints between 4:00 a.m. to10:00 p.m. at every 30 min are optimized. From 10:00 p.m. to 4:00a.m., the zone temperature is allowed to float within the deadbanddefined by the nighttime setback setpoints [14], which are 26.7 �Cand 19.4 �C. After all these modification, the total number of deci-sion variables is then reduced to 36, and total calculation time is

Table 1Small and medium building view and floor plan.

ISO view Floor plan

Small office 1 floor with attic 1 core zone and 4 parameter zones

Medium office 3 floors 1 core zone and 4 parameter zones

Table 2Building construction and HVAC features.

Feature Small reference Medium reference

Floors 1 3Total floor area (m2) 511 4982Floor to floor height (m) 3.05 3.96Window to wall ratio 0.21 0.33Glazing U-factor (W/(m2$K)) 3.35 3.35Glazing SHGC 0.36 0.36Roof construction Attic roof Built-up roofOccupant Density (m2/person) 18.6 18.6Lighting Power Density (W/m2) 19.5 16.89Equipment Power Density (W/m2) 10.8 10.8HVAC Packaged CAV Packaged multi-zone VAV

Fig. 1. Outdoor air temperature. Fig. 2. Electricity TOU prices. Electricity TOU prices are obtained from utility com-panies. Boston: https://www.nationalgridus.com/masselectric/home/rates/4_tou.asp.Chicago: https://hourlypricing.comed.com/. Miami: https://www.fpl.com/rates/pdf/Jan2016-Residential.pdf.

X. Li, A. Malkawi / Energy 112 (2016) 1194e1206 1197

less than 3 h.Before running the optimization program, determining the

initial conditions is a crucial step to guarantee the convergence ofthe optimization. The initial temperature setpoints used in thisstudy are adopted from the “light precool” strategy reported inRef. [14]. In this “light pre-cooling” strategy, the temperature set-points are 26.7 �C from 0:00 a.m. to 4:00 a.m., 19.4 �C from 3:00a.m. to 6:00 a.m., 22.8 �C from 6:00 a.m. to 6:00 p.m., and 26.67 �Cfrom 7:00 p.m. to 12:00 a.m. In order to evaluate the performanceunder different thermal comfort requirements, five different

weighting factors, 0, 1, 5, 10 and 50 are used for different thermalcomfort requirements. In addition to these five optimized strate-gies, the night setback “light pre-cooling” operation strategy is alsosimulated as the baseline for comparison.

2.2.3. Optimization algorithmAs introduced before, the HJPSO algorithm is used in this study.

Table 3Key parameters for PSO algorithm.

Variable Value

Number of particles 100Number of generations 1000Cognitive acceleration 3Social acceleration 1

X. Li, A. Malkawi / Energy 112 (2016) 1194e12061198

The two critical factors, particle velocity vip, and particle position,xip, are updated using the following equations:

viþ1p ¼ wpVi

p þ c1riþ11;p �

�Pip � xip

�þ c2r

iþ12;p �

�Pig � xig

�(6)

xiþ1p ¼ xip þ viþ1

p (7)

where Vip is the velocity of the pth particle at time i, xip is the po-

sition of the pth particle at time i, Pip is the best position found so farby the pth particle, Pig is the best position found so far by the swarm,ri1;p and ri2;p are two independent random numbers uniformlydistributed between 0 and 1. c1 and c2 are the cognitive accelerationand social acceleration factors. wp is the inertia weight. The keyparameters for the HJPSO optimization are listed in Table 3. Thedetails about the implementation of HJPSO algorithm in GenOptcan be found in Ref. [39].

2.2.4. EnergyPlus modification for GenOpt connectionThe concept of the connection between EnergyPlus and GenOpt

is that GenOpt reads in the EnergyPlus simulation results from“eso” file and modifies the decision variables in “idf” file based onthe optimization results [35]. Specifically, the whole MPC

Fig. 3. Thermal mass control optimization results: temperature setpoint

framework developed in this study is divided into three layers. Thefirst layer is the simulation software, which is EnergyPlus model inthis study. The second layer is the optimization layer, which exe-cutes optimization algorithms to find out the optimal solutions fordecision variables. The third layer is the organization layer, whichinterfaces with the first two layers. This organization layer passesthe simulation results to the optimization layer and provides de-cision variables back to the simulation layer. Unfortunately, theoptimization objectives in Eq. (1) are not direct output variablesfrom EnergyPlus. Therefore, certain minor modifications areneeded in the reference EnergyPlus models to obtain those vari-ables. Firstly, two scheduled values, “Gas_price” and “TOU”, arecreated for gas and electricity prices. A new meter, named “Ener-gy_cost”, is also created to measure the total energy cost, which isthe sum of “Cooling_cost” and “Heating_cost”. The “Cooling_cost” isthe product of cooling electricity consumption, “cooling_electricty”and electricity price, “TOU”. At the same time, “Heating_cost” is theproduct of reheating gas consumption, “reheating:gas” and gasprice, “Gas_price”. In this study, only the PMV in occupied period isconsidered, therefore a new measurement for “PMV_occuplied” isalso created. Then “Energy_cost” and “PMV_occuplied” are passedfrom simulation layer to optimization layer for temperature set-point optimization. The details about the EnergyPlus modificationand GenOpt declaration can be found in Appendix A.

3. Optimization results

3.1. Thermal mass MPC results

Fig. 3 illustrates the temperature setpoint optimization resultsfor the two commercial buildings in Boston. Comparing with thebaseline control scheme, the basic logic for the optimal control

for small building (upper) and medium building (lower) in Boston.

Table 4Energy savings for small and medium buildings under different optimization schemes.

H/C cost, $ Saving Average Temp �C Peak Temp �C Average PMV, - Peaka PMV, - Off-peak rate, $/kWh Peak rate, $/kWh Peak price ratio

Boston SmallBaseline 104.8 e 22.8 22.9 �0.60 �0.63 0.06 0.21 3.5Opt w ¼ 0 16.9 83.9% 27.7 28.0 0.67 0.78Opt w ¼ 1 28.3 73.0% 25.9 26.7 0.18 0.40Opt w ¼ 5 32.9 68.6% 25.3 25.5 0.08 0.15Opt w ¼ 10 54.9 47.6% 25.2 25.4 0.04 0.13Opt w ¼ 50 55.5 47.0% 25.1 25.3 0.04 0.13Chicago SmallBaseline 85.3 e 23.1 23.7 �0.59 �0.68 0.02 0.05 2.5Opt w ¼ 0 25.2 70.5% 27.8 28.0 0.70 0.98Opt w ¼ 1 40.8 52.2% 26.2 26.8 0.14 0.27Opt w ¼ 5 42.1 50.7% 25.8 26.5 0.07 0.18Opt w ¼ 10 45.3 46.9% 25.7 26.4 0.07 0.14Opt w ¼ 50 58.3 31.2% 25.1 25.4 0.03 0.11Miami SmallBaseline 135.8 e 23.9 24.3 �0.19 �0.30 0.03 0.10 2.97Opt w ¼ 0 71.2 47.6% 27.1 28.3 0.80 1.13Opt w ¼ 1 100.7 25.8% 25.9 27.9 0.30 0.85Opt w ¼ 5 102.9 24.2% 25.2 26.1 0.09 0.44Opt w ¼ 10 113.0 16.8% 24.9 25.6 0.09 0.20Opt w ¼ 50 119.7.0 11.9% 24.7 25.1 0.06 0.11Boston MediumBaseline 207.0 e 22.8 23.8 �0.72 �1.17 0.06 0.21 3.5Opt w ¼ 0 110.4 46.7% 24.6 26.2 0.88 0.92Opt w ¼ 1 148.1 28.5% 24.9 26.0 0.30 0.39Opt w ¼ 5 154.7 25.3% 24.9 25.6 0.01 0.28Opt w ¼ 10 160.0 22.7% 25.1 25.5 0.01 0.25Opt w ¼ 50 171.0 17.4% 24.9 25.2 0.00 0.11Chicago MediumBaseline 168.4 e 22.2 22.8 �0.90 �1.83 0.02 0.05 2.50Opt w ¼ 0 102.0 39.4% 26.6 27.6 0.80 0.98Opt w ¼ 1 132.0 21.6% 25.2 26.1 0.14 0.34Opt w ¼ 5 134.0 20.4% 24.9 25.6 0.07 0.25Opt w ¼ 10 137.0 18.6% 25.1 26.0 0.07 0.17Opt w ¼ 50 142.0 15.7% 25.0 25.5 0.05 0.12Miami MediumBaseline 550.8 e 22.9 24.7 �0.47 �0.93 0.03 0.10 2.97Opt w ¼ 0 365.0 33.7% 27.5 27.9 0.80 1.14Opt w ¼ 1 388.0 29.6% 25.7 26.7 0.30 1.04Opt w ¼ 5 400.2 27.3% 25.1 25.9 0.13 0.56Opt w ¼ 10 410.5 25.5% 24.5 25.2 0.08 0.27Opt w ¼ 50 422.0 23.4% 24.2 24.9 0.02 0.19

a Peak absolute values.

X. Li, A. Malkawi / Energy 112 (2016) 1194e1206 1199

strategies is to pre-cool the building at early morning and in-crease the temperature setpoints during the peak hours to reduceelectricity consumption at peak hours. Especially for the caseswith smaller weighting factors for thermal comfort (w ¼ 0 andw ¼ 1) in the small building (Fig. 3 upper), the temperaturesetpoints are close to the lower bounds at unoccupied periodsand close to the upper bounds at occupied periods. Similarfindings are also observed in the medium building optimizationresults (Fig. 3 lower). The building is also pre-cooled at earlymorning, but the room temperature setpoints do not go to thelower limits at the early morning. This is because that the me-dium building has heavier thermal mass and requires morecooling energy to precool the building. However, the price dif-ference between unoccupied and occupied periods is not so largethat the energy savings at the peak period are able to make up theenergy cost at off-peak period. Similar phenomenon is also foundin the cases at other two locations. For the simplification of thepresentation, they are not plotted here, but they are summarizedin Section 3.3.

3.2. Building thermal mass control under optimized temperaturesetpoint

The summary of the optimization results regarding the cost

savings, occupied hour average temperature and PMV indexes forall the cases are tabulated in Table 4. In order illustrate to theperformance of the thermal control optimization more clearly,Fig. 4 plots the temperature simulation results for small and me-dium buildings in Boston under all the thermal mass controlschemes. According to the temperature setpoint results shownFig. 3, the MPC schemes decrease the room temperature at earlymorning to store thermal energy in the building thermal masswhen electricity prices are relatively low and release it at the peakhours when electricity prices are high. Large temperature fluctua-tions are found during the unoccupied hours in the small buildingcases with weight factors as 0,1, and 5 (Fig. 4 upper). This is becausethe building cooling load exceeds the capacity of the cooling systemat certain periods when the temperature setpoints are too low.Comparing the temperature in the small and medium building, themedium building temperature at unoccupied hours is higher thanthat in the small building, which is in accordance with the tem-perature setpoints results in Section 3.1. Another finding from Fig. 4is the temperature under all the optimal control schemes are higherthan that under baseline operation scheme. This is because theMPCframework increase the cooling setpoints to save cooling energy.Even though the room temperature is increased, the buildings arestill under ASHRAE comfort range at most of the MPC operationcases, as shown in Fig. 5.

Fig. 4. Average room temperature of small building (upper) and medium building (lower) in Boston.

X. Li, A. Malkawi / Energy 112 (2016) 1194e12061200

In order to show the performance of the thermal mass MPC interms of the thermal comfort, the average room PMV for buildingsin Boston are plotted in Fig. 5. As shown in Fig. 5 (upper), only whenthe weighing factor is 10, the PMV indexes are within the ASHRAEcomfort limits in all of the 5 days. The averaged PMV are above theupper limits at the occupied periods in all of these five days withthe weighting factor as 0. For the optimal control case with weightfactors as 1 and 5, the PMV indexes are above than the upper limitsat the afternoon in the last three days when outdoor air tempera-ture is higher. When the weight factor is 10, the energy cost andthermal comfort objectives are competitive, therefore the averagePMV are very close to zero in all the 5 days. The average PMV in-dexes under the baseline operation scheme are below the ASHRAElower limits at the occupied period. In the results from the mediumbuilding studies shown in Fig. 5 (lower), except the results from thebaseline operation scheme, all the average PMV indexes are withinthe ASHRAE limits at the occupied hours from all the MPC schemes.Similar to the temperature simulation results presented in Section3.2, the PMV decreases at the early morning at the building is pre-cooled and increases at the peak hours when temperature setpointsare higher.

3.3. Optimization objectives and Pareto curves

The key results from all the cases in all of these three locationsunder different operation schemes are summarized in Table 4. Theresults should be considered together with the Pareto curves inFig. 6, where the objective of energy cost and thermal comfort areplotted together. These Pareto curves graphically illustrate thetradeoff between these two objectives with weighting factor as 0, 1,5, 10 and 50. In addition to those optimal control schemes, the

results under baseline cases are also plotted. This figuremakes clearthat the PMV indexes from control schemes with smaller weightingfactors are higher than those from control schemes with higherweighting factors. With looser requirements for thermal comfort,the MPC scheme is able to save more energy cost. This is becausethe HVAC system can sacrifice certain thermal comfort to reducethe energy consumption at occupied periods. For example, theenergy cost for Boston medium building with weighting factor as50 is $171, comparing to $160 with weighting factor as 10, and $148with weighting factor as 1. Another finding from the Pareto curvesis that the results fromoptimal schemeswithweighting factor as 10and 50 are very close, which means that the objectives for thermalcomfort and energy cost are competitive and both of them areconverged to the minimum simultaneously with these twoweighting factors. Similar to the studies for buildings in Boston, theaveraged PMV indexes at other two locations are within the ASH-RAE limits under the optimal control strategies with weightingfactors as 5, 10, and 50. What's more, the peak PMV indexes are alsowithin the ASHRAE limits, which means the zone temperature isunder control without too large fluctuations during the occupiedperiods.

Illustrated in Table 4, the energy cost savings are also relatedwith the ratio of peak to off-peak rate. The buildings in Bostonachieve the highest cost saving percentages, followed by thoseMiami and then Chicago. The reason behind this situation is thatmore benefits can be obtained from the stored thermal energyduring the off-peak hours if the peak price ratio is higher. Thebuilding capacity of the thermal mass also affects the cost savingpotentials. However, the effect of the thermal mass capacity is alsohighly related to the capacity of the HVAC systems, which cannot beevaluated in detail using the information captured in this study. The

Fig. 5. Average PMV: small building (upper) and medium building (lower) in Boston.

X. Li, A. Malkawi / Energy 112 (2016) 1194e1206 1201

results from this study show that the thermal mass MPC has higherenergy cost saving potentials in the small buildings than that inmedium buildings. Nevertheless, this observation may change un-der different conditions.

Besides the energy costs shown in Fig. 6, the total coolingelectricity and reheating energy consumption is also plotted inFig. 7. This figure clearly makes clear that those optimal thermalcontrol schemes do not reduce energy consumption in some of thecase, comparing with the energy consumption under the baselineoperation scheme, because of the unintended energy loss of thestored thermal energy. For example, the electricity consumption atthe optimal control strategies with weighing factors as 1, 5 and 10 ishigher than that consumed in the baseline operation case. Thissituation does not happen in those two buildings in Miami, as thecooling energy consumption is relatively high under the baselineoperation scheme when the outsider temperature is high. Anotherobservation from this figure is that the energy consumption ishigher when weighting factor is larger, as more energy is neededmaintain the thermal comfort, which is the same trend as that inthe energy cost results.

4. Discussion and future work

Different to the existing studies using simplified building energyforecasting models, this study uses validated detailed energysimulation models in EnergyPlus for building thermal mass MPC.The results obtained from this study are more reliable and closer tothe real field situation. Amulti-objective optimization framework is

developed to exploit the energy cost saving potentials withconsidering the thermal comfort under typical summer weatherconditions and energy pricing structures, using hybrid HJPSO al-gorithm resided in GenOpt. The findings from this study show thatsignificant energy cost can be saved from optimal thermal masscontrol with still maintaining thermal comfort within ASHRAElimits. To be more specific, comparing with a typical night setbackcontrol scheme, the optimal thermal control schemes show thecapability to save cooling and reheating energy costs by over 40%,30% and 15% in the small office buildings in Boston, Chicago andMiami from August 1st to 5th. They are also able to reduce the costsby over 20%, 18% and 25% for the medium office buildings in thesethree locations.

The deep analysis of the results shows that the energy savingpotentials are affected by a lot of factors, such as thermal comfortrequirements, weather conditions, utility rate structures, and thebuilding constructions. As studied in this paper, the weightingfactor for thermal comfort requirement is the most critical factor tothe performance of the MPC schemes. The higher the thermalcomfort requirement, the more energy cost will be needed. Theresults with weighting factors as 10 and 50 are very similar, as thethermal comfort objective is competitive with the energy costobjective. The cost saving potentials are also highly relatedwith theenergy rate structures. The cases with higher peak rate to off-peakratio are able to achieve higher cost saving percentages. Forexample, the electricity peak rate ratio at Boston is 3.5, which ishigher than that at Chicago and Miami. The energy cost savings forthe two buildings at Boston are higher than the buildings at other

Fig. 6. Pareto curve for thermal mass control in small buildings (upper) and medium buildings (lower).

Fig. 7. Energy consumption in small buildings (left) and medium buildings (right).

X. Li, A. Malkawi / Energy 112 (2016) 1194e12061202

two locations. Other factors, such as building occupancy schedule,HVAC system capacity, detailed building construction, are alsoimportant to the performance of thermal mass control. Movingforward, all these factors will be evaluated using the developedframework.

In this paper, only three locations are studied. Even though theyhave different weather conditions and electricity pricing structures,more locations from different areas are also worthwhile to study inthe future. For the issues with calculation speed, the deadband

between cooling and heating setpoints are defined as 3 degrees atthe occupied periods and 8 degrees at the unoccupied periods. It isa reasonable assumption, but future work should also address theeffects of the deadband on thermal mass MPC.

5. Conclusion

This paper investigates the application of MPC in buildingthermal mass control to reduce energy costs and maintain thermal

X. Li, A. Malkawi / Energy 112 (2016) 1194e1206 1203

comfort. Specifically, a MPC framework using detailed physicsbased building energy simulation models and HJPSO algorithms inGenOpt is developed and demonstrated in six commercial build-ings at three different locations. The results from this study provethat this MPC framework is able to reduce a significant amount ofenergy costs. This study also presents Pareto curves for eachbuilding under different thermal comfort requirements, which canprovide guidelines for building operators to choose suitable ther-mal mass optimal control schemes according to their requirements.In addition, this MPC framework can also be used as a basis forother building thermal mass control projects.

1. EnergyPlus modification: “energymanageEnergyManagementSystem:Sensor,

CoreZonePMV, !- NameCORE_ZN PEOPLE, !- Output:VariaZone Thermal Comfort Fanger Model PMV

EnergyManagementSystem:Sensor,Perimeter1ZonePMV, !- NamePerimeter_ZN_1 PEOPLE, !- OutputZone Thermal Comfort Fanger Model PMV

EnergyManagementSystem:Sensor,Perimeter2ZonePMV, !- NamePerimeter_ZN_2 PEOPLE, !- OutputZone Thermal Comfort Fanger Model PMV

EnergyManagementSystem:Sensor,Perimeter3ZonePMV, !- NamePerimeter_ZN_3 PEOPLE, !- OutputZone Thermal Comfort Fanger Model PMV

EnergyManagementSystem:Sensor,

Acknowledgement

Part of the work presented in this paper was conducted when X.Li was at Drexel University. X. Li would like to acknowledge theGraduate Research Fellowship from Drexel University. X. Li is alsograteful the Postdoctoral Fellowship from The Center for GreenBuildings and Cities (CGBC) at Harvard University. The authorswould also like to thank Adams Rackes for his insightful commentson GenOpt and PSO settings.

Appendix A

mentsystem” define

ble or Output:Meter Index Key Name; !- Output:Variable or Output:Meter Name

:Variable or Output:Meter Index Key Name; !- Output:Variable or Output:Meter Name

:Variable or Output:Meter Index Key Name; !- Output:Variable or Output:Meter Name

:Variable or Output:Meter Index Key Name; !- Output:Variable or Output:Meter Name

Perimeter4ZonePMV, !- NamePerimeter_ZN_4 PEOPLE, !- Output:Variable or Output:Meter Index Key NameZone Thermal Comfort Fanger Model PMV; !- Output:Variable or Output:Meter Name

EnergyManagementSystem:Sensor,OCCIndex, !- NameREAL_OCC, !- Output:Variable or Output:Meter Index Key NameSchedule Value; !- Output:Variable or Output:Meter Name

EnergyManagementSystem:Sensor,ElectricityConsuption, !- Name, !- Output:Variable or Output:Meter Index Key NameElectricity:Building; !- Output:Variable or Output:Meter Name

EnergyManagementSystem:Sensor,ElectricityPrice, !- NameTariff, !- Output:Variable or Output:Meter Index Key NameSchedule Value; !- Output:Variable or Output:Meter Name

EnergyManagementSystem:ProgramCallingManager,CalculatePMVOPT, !- NameEndOfZoneTimestepBeforeZoneReporting, !- EnergyPlus Model Calling PointCalculatePMV; !- Program Name 1

EnergyManagementSystem:ProgramCallingManager,CalculateTotalCost, !- NameEndOfZoneTimestepBeforeZoneReporting, !- EnergyPlus Model Calling PointCalculateCost; !- Program Name 1

EnergyManagementSystem:Program,CalculatePMV, !- NameSet Real_OCC_PMV=((CoreZonePMV+ Perimeter1ZonePMV + Perimeter2ZonePMV+Perimeter3ZonePMV + Perimeter4ZonePMV )/5)* ((CoreZonePMV+ Perimeter1ZonePMV +Perimeter2ZonePMV+ Perimeter3ZonePMV + Perimeter4ZonePMV )/5) *OCCIndex; !- Program Line 1

EnergyManagementSystem:Program,CalculateCost, !- NameSet Real_Cost=ElectricityConsuption*ElectricityPrice; !- Program Line 1

EnergyManagementSystem:GlobalVariable,Real_OCC_PMV; !- Erl Variable 1 Name

EnergyManagementSystem:GlobalVariable,Real_Cost; !- Erl Variable 1 Name

EnergyManagementSystem:OutputVariable,Real_OCC_PMV, !- NameReal_OCC_PMV, !- EMS Variable NameAveraged, !- Type of Data in VariableSystemTimestep; !- Update Frequency

EnergyManagementSystem:OutputVariable,Real_Cost, !- NameReal_Cost, !- EMS Variable NameSummed, !- Type of Data in VariableSystemTimestep; !- Update Frequency

X. Li, A. Malkawi / Energy 112 (2016) 1194e12061204

2. GenOpt declaration

CallParameter { Suffix = USA_MA_Boston-Logan.Intl.AP.725090_TMY3;

}ObjectiveFunctionLocation{

Name1 = Obj;Function1 = "add(%E_Cost_dollar%, multiply(0,%PMV_All%), multiply(0,%Gas_Cost_dollar%))";

Name2 = PMV_All;Function2 = "multiply( %PMV_Overall%, 240)";

Name3 = E_Cost_dollar;Function3 = "divide( %E_Cost%, 3600000)";

Name4 = Gas_Cost_dollar;Function4 = "divide( %Gas_Overall%, 150419000)";

Name5 = E_Cost;Delimiter5 = "725,";FirstCharacterAt5 = 1;

Name6 = PMV_Overall;Delimiter6 = "723,";FirstCharacterAt6 = 1;

Name7 = Gas_Overall;Delimiter7 = "603,";FirstCharacterAt7 = 1;

}} // end of section Simulation

X. Li, A. Malkawi / Energy 112 (2016) 1194e1206 1205

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