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Analysis of HVAC System Oversizing inCommercial Buildings through FieldMeasurementsDenchai WoradechjumroenUniversity of Nebraska - Lincoln

Yuebin YuUniversity of Nebraska–Lincoln, yyu8@unl.edu

Haorong LiUniversity of Nebraska-Lincoln, hli3@unl.edu

Daihong YuUniversity of Nebraska-Lincoln, daisy.yu926@gmail.com

Huojun YangUniversity of Nebraska - Lincoln

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Woradechjumroen, Denchai; Yu, Yuebin; Li, Haorong; Yu, Daihong; and Yang, Huojun, "Analysis of HVAC System Oversizing inCommercial Buildings through Field Measurements" (2014). Architectural Engineering -- Faculty Publications. 87.http://digitalcommons.unl.edu/archengfacpub/87

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Energy and Buildings 69 (2014) 131–143

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Energy and Buildings

j ourna l ho me page: www.elsev ier .com/ locate /enbui ld

Analysis of HVAC system oversizing in commercial buildings throughfield measurements

Denchai Woradechjumroena, Yuebin Yua,∗, Haorong Lia, Daihong Yub, Huojun Yanga

a Durham School of Architectural Engineering and Construction, University of Nebraska-Lincoln, Omaha, NE, USAb Architectural Engineering Department, Lawrence Technological University, MI, USA

a r t i c l e i n f o

Article history:Received 15 January 2013Received in revised form 19 July 2013Accepted 11 October 2013

Keywords:Over-sizingRooftop unitsRetail storesReal-time measurementsCyclingOversizing capacityEnergy penaltyOptimizationSmart building management

a b s t r a c t

This study analyzes the oversizing issues of HVAC equipment in commercial buildings based on thedata from long-time field measurements. Specifically, retail stores are selected as the typical commercialbuildings to evaluate the status of equipment oversizing and its effect on energy consumption. Rooftopunits (RTUs) in 12 retail stores located in different climatic regions are analyzed in terms of the over-sizing status in both cooling and heating mode. The proposed method utilizes three parameters, namelycycling number (N), run time fraction (RTF), and maximum cycling number (Nmax) to jointly determinethe performance of a RTU based on the annual design condition. The accuracy of the methodology isevaluated by self-validation in terms of uncertainty and compared with previous studies. The resultscan be used to evaluate the oversizing level of RTUs and quantify the average energy penalty of sam-ple buildings. Designers can also use the findings as a reference to evaluate building load design. Moreimportantly, the analytical process presented in this article can be automated and applied in the smartbuilding management system for the advanced soft repair of an oversizing issue with RTUs.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Commercial buildings accounted for 19% of total energy con-sumption in the U.S. in 2009 [1]. From the survey in 2003 [2], 4.9million commercial buildings covered 72 billion sq ft of floor space– an increase of 28% in buildings and 40% in floor space since 1979.According to the estimation [3], commercial building floor space isexpected to reach 109.8 billion sq ft in 2035 – a 53% increase over2003 level. From this estimation of the commercial building expan-sion, this building type would significantly consume more energythan today. Specifically, based on U.S. Commercial Sector PrimaryEnergy in 2006 [4], heating, ventilation, air-conditioning and refrig-eration systems (HVAC&R) accounted for about 50% of the totalenergy use in commercial buildings. Approximately, 30% of totalenergy was consumed on space cooling and space heating by HVACsystems. Thus, HVAC&R systems are considerably important areasto be analyzed in order to reduce energy use waste in commercialbuildings. Among them, rooftop units (RTUs) consumed approxi-mately 62% of total energy to heat and cool commercial buildingsin the U.S. [5]. Specifically, for small commercial offices and retailstores, RTUs accounted for 50% of total energy use [6].

∗ Corresponding author. Tel.: +1 402 554 2082; fax: +1 402 554 2080.E-mail addresses: yuebinyu@gmail.com, yuebin.yu@unl.edu (Y. Yu).

Proper sizing of RTUs is one of the important processes in termsof appropriate energy use in small commercial offices and retailstores. In the main results of previous interviews [7] and surveys[8], a number of designers size RTUs based on estimated inter-nal load or related safety factors by software tools for commercialbuildings. Regarding these reasons, it could lead to oversizing RTUsand eventually result in waste of energy. Since the compressor andgas furnace of a RTU is manipulated by an on–off controller, theoversizing may lead to the short-time cycle of a RTU operationat a peak design condition instead of running continuously. Overusage of the induction in the compressor motor and of gas supply-ing to gas furnace incur waste of energy. This problem also results inhigher operation cost due to the lower efficiency from the improperoperation of the RTU machine.

The energy penalty of RTUs has been significantly concernedsince 1998. Previous researchers (e.g., [7–9]) evaluated and/or sur-veyed the performance of RTU in terms of oversizing at field tests.Only two of the prior studies [7,10] processed data from the engi-neering design point of view; however, no previous study analyzedand evaluated the performance of a RTU in terms of the level ofoversizing and average energy penalty based on annual design con-dition for both cooling and heating mode. The right-sizing capacityof RTUs should be identified and then utilized to optimize the oper-ation without RTU replacements.

In order to increase the equipment efficiency and reduce theenergy waste, in this study, the analysis of commercial buildings is

0378-7788/$ – see front matter © 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.enbuild.2013.10.015

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Nomenclature

Roman letter symbolsAFUE annual fuel utilization efficiency (%)AOAT annual design condition of OAT (◦C)EDBT the effect of a dead band temperature (◦C)EER energy efficiency ratio (Btu/W-h)l duration of a compressor or gas furnace operation

(h)N cycles in one hour (cycle per hour)OAT average outdoor air temperature (◦C)PLR part load ratioQ capacity of a RTU (W or Btu/h)RTU rooftop unitRTF runtime fraction� time constant (s)

Subscriptscycle cycle of a compressor or gas furnaceon on-status of a compressor or gasoff off-status of a compressor or gas furnaceover oversized capacitypnt energy penalty

carried out on the data obtained by the advanced internet protocol,i.e., BACnet, a Data Communication Protocol for Building Automa-tion and Control Networks. The weather data and RTU performancedata from 12 retail stores at different climates are analyzed bythe program described below to compute the waste energy con-sumption occurring from the over-sized RTUs. The accuracy of theproposed programming calculation is evaluated using N-analysismethod to validate PLR (part load ratio) in terms of uncertainty(within ±16.99% for all RTUs).

The accuracy of PLR ensures the robustness of quantified averageover-sized capacities. Using EER (energy efficiency ratio) and AFUE(annual fuel utilization efficiency), average peak energy penaltycan be computed for a cooling and heating mode, respectively.HVAC designers can use the method as a tool to evaluate the siz-ing calculation of building load for both renovation work and newcommercial buildings. Also, average peak energy penalty can beused to estimate yearly optimum energy consumption in com-mercial buildings; more importantly, the analytical process can beautomated and applied in smart building management system foradvanced soft repair of over-sizing issue.

The paper is organized as follows: the fundamental of build-ing load design and the control of a RTU are briefly described atfirst. Secondly, methodology and store information including RTUoperations are succinctly mentioned. Then, data analysis and per-formance evaluation of RTUs are systematically conducted for bothcooling and heating mode. The results (Nmax and PLR) are validatedby N-analysis and are compared with previous studies in literature.In the final implementation of the program, the study presents theevaluation of RTUs in terms of average over-sized capacities andenergy penalty with the accuracy of solutions. The contribution andfuture work are discussed as well at the end to conclude this study.

2. Background

A RTU is typical packaged air-conditioning equipment mountedon the roof. It comprises all components built into one unit includ-ing a vapor compression cycle and/or a furnace for cooling andheating the space. The performance of a RTU can be evaluated byanalyzing the operation of the compressor and gas furnace. Select-ing this device is conducted in the process of building load design.

After installation, the unit is automatically operated by a controller.This section briefly explains the essential process and control relat-ing to the evaluation of a RTU in commercial buildings.

2.1. Typical process of building load design

In the process of building load calculation, the indoor and out-door temperature of each location should be specified before sizingcapacities of HVAC equipment. The capacity of a machine shall beable to supply adequate cool in the hottest condition and adequateheat in the coldest period. These principles are referred to peakdesign conditions classified in daily, monthly and annual-baseddesign. At different locations, the conditions are not identical. Thecondition of each location can be found in ASHARE Handbook –Fundamentals [11]. At a conditioned space, the temperature is con-trolled by a HVAC controller to comfort occupants in buildings.Normally, the set point temperatures are 24 ◦C for a cooling modeand 20 ◦C for a heating mode when buildings are occupied. For otherconditions, these set points can be adjusted by the program of aHVAC controller for appropriate ambient conditions (e.g., set-up,set-back) in buildings.

Selection of an outdoor and indoor design condition mainlyquantifies the sensible load. For a cooling mode, the sensible loadis determined by the heat transfer through the components of abuilding and the sensible heat gain from the indoor occupants,equipment, lighting, etc., whereas the latent load is determinedby the latent heat gain from the indoor moisture sources. In thedesigning process, many factors may result in improper load calcu-lation and HVAC equipment sizing. For instance, if external shadingis neglected, calculated sensible cooling load increases and leads toover-sizing issue of a cooling mode. From an interview of mechani-cal design engineers [7], three possible reasons creating over-sizedcapacities were: (1) insufficient communication with a design teamand owner resulting in too much internal load, (2) using safetyfactor in sizing calculation without experience, and (3) neglect ofexternal shading for sensible load. Moreover, in a survey aboutwidely used tools for load calculation, Jacobs and Colon [8] foundthat 51% of the designers in California used manufacturing softwareand 17% used rules of thumb (e.g., 28–32.5 m2 per ton for generaloffice) and previous experiences. All examples and reasons lead toover-sizing load calculation.

2.2. Control of a RTU

Fig. 1 illustrates the typical control of a RTU with two-stage heat-ing at Boise, Idaho, with the room temperature, stage status, andoutdoor temperature depicted. The annual heating design condi-tion at 1% dry-bulb (DB) of this city is −11.94 ◦C. Two set points forthe RTU are assumed as 20 ◦C and 18.89 ◦C. When the temperatureof a space drops below 20 ◦C due to the decrease of outdoor tem-perature, the first-stage electrical valve of a gas furnace is turnedon to supply gas for heating. After that, it is automatically turnedoff when the temperature of the space gets higher than 21.11 ◦C. Onthe other hand, if the space condition is at a peak condition, withoutdoor air temperature (OAT) being −11.94 ◦C as shown in thelower chart of Fig. 1, the first-stage gas furnace remains on. Sinceindoor temperatures are still below 18.89 ◦C, the second-stage gasfurnace is turned on to supply auxiliary heat until the temperaturesin the zone are higher than 18.89 ◦C or out of the operating differ-ential range, denoted as A in Fig. 1. This stage is off while the firststage runs continuously in the operating differential range B andthen it is stopped when the zone temperature is out of the range B.This figure illustrates the on and off operation, called the cycle ofa gas furnace. Furthermore, it is desired that both first and second

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Fig. 1. On–off control action of 2-stage heating versus outdoor temperature.

stage of gas furnaces should automatically and continuously run ata peak condition, when both stages are sized properly.

3. Overview of methodology and system

3.1. Methodology

Fig. 2 shows the methodology for this study. It includes foursteps. First of all, for data collection, the field measurement dataare obtained by BACnet Protocol from 12 retail stores. The set ofdata in retail stores are composed of timestamps, the on-off sta-tus of cycles and outdoor temperatures from local weather station.Secondly, a program is applied to process and extract the data foranalysis based on annual design conditions. In the process, run-time fraction (RTF), cycle per hour (N), maximum cycle per hourat RTF being 0.5 (Nmax), and part load ratio (PLR) are obtained. Theaccuracy of results in terms of uncertainty is affected by a dead-band temperature in a RTU controller. For the next step, results arecompared against the previous studies [7,12,13] and validated byusing N-analysis. Finally, PLR is utilized to evaluate RTUs in the retailstores in terms of average over-sized capacities and average peakenergy penalty. The final results can be applied in the process ofbuilding load design and to optimize RTU operation in retail stores.Moreover, smart building management strategy will be developedby applying the program in a future study.

R e al t im e t r e nde d data f r o m the B u i ld ing A u to m at io n S ys t e m

C lim ate c o nd i t io n ands to r e and s ys te m in f o

R e l a te d in f o :T im e s ta m p ,O n - O f f s ta tu s ,O u td o o r a i r t e m p

D e ve lo p ing p r o gr amf o r au to m ate d analy s i s

P r e vio us s tud ie s b as e d o n :A n n u a l co n d i t io n ,M e a s u r e m e n t d a y s

A nalys ing ke y var i ab le s :E D B T , N , R T F , P L R , N m a x ;O v e r - s i z e d ca p a ci ty ;E n e r g y p e n a l t y

R TU c o n t r o l in f o :s ta g e s ,d e a d - b a n d ,cy cl in g

A pp ly ing the f ind ings ins m ar t bu i ld ing m anage m e n tand ve r i f y the r e s u l t s

D a ta c o l le c t ion

P r og r a m m in g

A n a l ys i s

F u tu r e s tu d y

Fig. 2. Flowchart of methodology in this study.

3.2. Description of the retail stores and machine operations

Data in 45 Big-box retail stores, being the same brand andlocated in the United State of America, were downloaded fromOctober 2010 to October 2011 through BACnet protocol. The storesare in 7 different climatic regions categorized in DOE 2010 [14]. Forthis study, 12 stores out of the total, as given in Table 1, are selectedas samples.

RTUs are HVAC equipment used to provide thermal comfort inretail stores. They can operate in either heating or cooling mode.Each RTU may have multi-stage compressors or furnaces in orderto reduce energy consumption at part load conditions. For instance,RTU No. 5 given in Table 3 was designed with two-stage compressorfor a cooling mode operation. The first-stage compressor is used toprovide cool air for part load conditions, whereas auxiliary coolair can be provided by the second-stage compressor for peak loadconditions.

Conversely, if one RTU is oversized, it can incur power con-sumption waste. For instance, a 2-stage RTU No.5 is operated fora cooling mode at peak load conditions; both two stages may bestarted together and/or be cycled frequently instead of continu-ously running. The machines with various capacities in the analyzedbuildings can be categorized into three different models: (1) onestage compressor for cooling and two-stage gas furnace for heating;(2) two-stage compressor for cooling and two-stage gas furnace forheating; and (3) one-stage compressor for cooling and one-stagegas furnace for heating.

In the studied stores, each one has 20–25 RTUs, which aremanipulated by on–off controllers. A thermostat per one RTU isused to detect temperatures at a conditioned space. Typically athermostat is set with a dead band temperature, which can causearound 5–10 min time delay for residential air conditioners afterstarting and before stopping RTUs to avoid frequent on–off cycleson compressors and gas furnaces.

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Table 1Geography and climate information of 12 stores.

Store City State Built year Floor area (m2) DOE climateclassification

Annual design conditionof outdoor temperatureat 1% DB cooling and 99%DB heating (◦C)

Weather type

A Saint Augustine FL 2002 11,907 2A 30.6 5.1 Hot-humidB Phoenix AZ 1998 11,384 2B 42.3 6.6 Hot-dryC Macon GA 2001 11,683 3A 34.6 −2.6 Warm-humidD Irvine CA 1999 11,632 3B 32.3 6.0 Warm-dryE San Leandro CA 2002 13,653 3C 25.4 4.2 Warm-marineF Louisville KY 2002 11,680 4A 32.8 −4.2 Mixed-humidG Gig WA 2001 11,664 4C 27.1 0.3 Mixed-marineH Mansfield OH 2001 11,654 5A 29.7 −14.6 Cool-humidI Boise ID 2001 11,968 5B 33.6 −11.9 Cool-dryJ Northfield MN 2000 11,662 6A 30.2 −22.5 Cold-humidK Billings MT 2001 11,649 6B 33.0 −20.8 Cold-dryL Silverthorne CO 2003 11,835 7 29.6 −18.9 Very cold

Fig. 3 illustrates the effect of a dead-band temperature occurringin a cooling mode operation of RTU No.1 in Store I. This effect is high-lighted in Area 1. Whereas the RTU compressor ran continuouslyuntil the outdoor temperature was out of the design temperature at35 ◦C, the compressor did not stop until the outdoor air temperaturedropped to 30.83 ◦C, approximately. This different temperature,4.17 ◦C between the design temperature and the temperature atthe stopped time, was the effect of a dead-band temperature forconsidering the cycle of a compressor operation versus outdoortemperatures. The sizing capacity analysis can be impacted by theselection of the dead-band temperature. With this example, if thedead-band temperature of this RTU is chosen less than 4.17 ◦C, thiscycle becomes incomplete without off status. In contrast, if thistemperature is considered more than 4.17 ◦C, another cycle couldbe included in the calculation of number of cycle N due to a longerduration as marked in Area 2. Regarding these two situations, thedifference of dead-band temperatures may significantly vary thenumber of cycles and lead to the variation of results in the analysis.Thus, two dead-band temperatures (i.e., 1.39 ◦C and 4.17 ◦C) anduncertainty analysis are conducted in this study to minimize thepotential bias. The two temperatures are the examples of EDBT (theeffect of dead-band temperature) defined to reflect the impact onthe operation of RTU by the dead-band temperature of a thermostat.

4. Implementation of real application

4.1. Data analysis

In the analysis, the quantification of oversizing is evaluatedthrough the on/off status data of compressors and gas furnaces.At peak conditions, properly sized equipment should run contin-uously without cycling during this period. Fig. 4 illustrates theproper-sized one-stage compressor for a cooling mode of RTU No.1in Store I. Two areas are marked out to explain the cycles of acompressor. At a design condition, the design outdoor tempera-ture is selected as 35 ◦C based on annual design 1% DB. Area 1 and2 show the ranges of outdoor temperatures that are higher thanthe design temperature on 7/24, 2011 and 7/25, 2011, respectively.Within these ranges, an on-status compressor was continuouslyactivated until the temperatures were below 33.6 ◦C for Area 1and 29.4 ◦C for Area 2, approximately. It can be seen that thetemperature differences between the design temperature and thetemperature at the stopped time of these 2 areas are 1.39 ◦C and5.56 ◦C. 1.39 ◦C is assigned for this RTU because the fluctuation ofoutdoor temperatures occurred in Area 3. Also, 5.56 ◦C is too highfor appropriate quantification of over-sized RTUs as mentioned inSection 3.2.

Fig. 3. Effect of dead band temperature occurred in a cooling mode of RTU No.1 in Store I.

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Fig. 4. Example of a proper-sized RTU compressor, No.1 in Store I.

Conversely, for the same day but with a different RTU, RTU No.5, Fig. 5 illustrates the operation of an over-sized first-stage com-pressor in a cooling mode. Compared Fig. 5 with Fig. 4 for the sameperiod on 7/25, 2011, it can be seen that the compressor cycles morefrequently in Area 4 at the peak design temperature, 35 ◦C, whichcan be regarded as the signature of oversize.

Therefore, to evaluate a compressor using the data based on anannual design condition at this location, the design temperature at35 ◦C is used to identify the new set of data. This set is calculatedfor the cycles of a compressor at the annual design temperature.Similarly, two-stage compressors can be calculated by the samemethod to determine the cycles as well as the evaluation of gasfurnaces in a heating mode, since both 2 stages can continuouslyrun together if they are properly sized. Also, as mentioned in Section3.2, the effect of a dead-band temperature (EDBT) in a thermostatresulting in the cycles of a compressor or gas furnace is includedin this analysis program. The range of the different temperaturesinfluenced by EDBT is defined between 1.39 ◦C and 4.17 ◦C for this

study. The accuracy of the analysis can be evaluated in terms ofuncertainty using EDBT 4.17 ◦C against EDBT 1.39 ◦C. 4.17 ◦C is alsoclose to studies in the literature on RTU oversizing based on a peakday condition. The analysis of oversizing with EDBT 4.17 ◦C can alsobe used to compare with those studies.

Fig. 6 illustrates the detailed data analysis process applied inthis study. The trended data were filtered first with only relatedvariables remained. Table 2 gives the equations and definitions forthe critical variables used in the analysis. Following procedures areimplemented in the program.

Step 1: Selecting AOAT from Table 1 for the given store location;Step 2: Selecting EDBT 1.39 ◦C and 4.17 ◦C to obtain the solution ofset-1 (S1) and -2 (S2), respectively;Step 3: Comparing average RTF of S1 with S2 in term of uncertainty;Step 4: Calibrating lon and lcycle of cycles from S1 and S2; S3and S4 are the calibrated sets of S1 and S2 by using N-analysis,respectively;

Fig. 5. Example of an over-sized RTU compressor, No.5 in Store I.

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Fig. 6. Diagram for developing program.

Step 5: Computing the final solution of set-3 (S3) in terms of uncer-tainty by comparing S3 with S4 ((S3-S4)/S3 is the uncertainty ofthe final solution);Step 6: Applying S3 to compute over-sized capacities and aver-age energy penalties using PLR because the calibrated S4 is usedto compute the uncertainties of the final solution, S3. The resultscan be fed directly into a smart building management for optimalcontrol.

The cleaned data are as follows:

1. Recorded timestamps, in the form as MM/DD/YYYY HH:MM:SS.2. Average outdoor air temperatures (OAT), obtained in English

unit (F).3. The status records of RTU compressors and gas furnaces at times-

tamps (1 = turned on, 0 = turned off).

From the cleaned one-year data (2010–2011), the followingvariables are further prepared for analysis:

1. The start time (tstart) of all compressor and gas furnace cycles ofboth cooling and heating mode along the year.

2. The stop time (tstop) of all compressor and gas furnace cycles ofboth cooling and heating mode along the year.

3. The selected design condition of an outdoor temperature in eachlocation based on ASHARE Fundamentals, annual heating 99% DBand 1% cooling DB/WB [11].

4. The effect of a dead-band temperature (EDBT, ◦C) as the lowestlimited temperature for a cooling mode, whereas the maximumlimited temperature for a heating mode. Both the assigned valuesare affected by the dead-band temperature of a thermostat asmentioned in Section 3.2.

With above information, the calculation is carried out for thecycles of each stage compressor and gas furnace in peak design con-ditions. The following parameters as detailed in Table 2 are definedfor the calculation.

As tabulated in Table 2, lon and loff are the duration of on-statusand off-status per cycle, respectively. They are used to derive lcycle,N, and RTF. Using identified AOAT at 99% heating DB and 1% coolingDB/WB for the stores collected in Table 1. EDBT is applied to specify

Table 2Definition of parameters for calculation of compressor cycle.

Parameters Equations or conditions Units

lon (duration of on-status of a compressor) lon = |tstart − tstop| (1) Hourloff (duration of off-status of a compressor) loff = |tstart,next cycle − tstop| (2) Hourlcycle (total duration for a cycle) lcycle = lon + loff (3) Hour

N (a number of cycles occur in a hour) N = 1lcycle

(4) Cycle per hour

RTF (runtime fraction) RTF = lon

loff(5) Dimensionless

PLR (part load ratio [13]) PLR = RTF − �

lcycle(1 − e(−lon/�)) (6) Dimensionless

� (time constant, duration) � = 60 SecondAOAT (annual design condition of outdoor air temperature) 99% heating DB 1% cooling DB/WB ◦CEDBT (the effect of dead band temperature) Cooling condition≥AOAT − EDBT (7) ◦C

Heating condition ≤ AOAT − EDBT(8) ◦C

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the range of temperatures out of AOAT in each day along a year.It implies that measurements are preceded through the annualdesign temperature for various days in both cooling and heatingseason. Therefore, AOAT and EDBT can be utilized as the indepen-dent variables to study RTU performance for the year in this typeof commercial buildings.

To assess energy penalty, PLR is used to quantify the actual loadof RTU performance at peak load conditions. The over capacities ofa RTU are then used for computing over-sized capacity and energypenalty in each store. To obtain PLR, time constant (�) is one of theparameters as shown in Eq. (6). It is referred to how rapid a pieceof equipment reaches the steady state output when a compressoror gas furnace is cycled. Henderson et al. [13] used 80 s, whereasDjunaedy et al. [7] compared the results using � = 30 and 60 s. Inthe present article, we decide to select the time constant of 60 s,which can be used to compare our results with [7] and [13]. In ouropinion, � = 30 is too fast for RTUs built in 2001.

4.2. Implementation of the developed program

The results implemented through the flowchart in Fig. 6 aredemonstrated in Tables 3, 4 and 6. 22 RTUs in Store I at Boise,Idaho, are the examples of the implementation of our methodol-ogy. Firstly, AOAT being 35 ◦C is selected for step 1. Next step on theflowchart, lon and loff of all cycles in the range of specific temper-atures (e.g., for cooling mode, OAT ≥ AOAT-EDBT, OAT ≥ 35–1.39 ◦Cat Store I) are calculated to obtain RTF and N of S1 and S2, whenEDBT is 1.39 ◦C and 4.17 ◦C, respectively.

Compared RTF of S1 with that of S2 in step 3, the uncertainty ofresults occurs due to the selection of different EDBTs from the ther-mostat of a RTU as mentioned in Section 3.2. Again, the uncertaintycould lead to incomplete cycles because the developed programdoes not calculate RTF and N of a cycle which is out of the spe-cific range of temperatures. Moreover, the variation of cycles couldaffect N and RTF and lead to the variation of evaluation on RTUs inthe analysis. This uncertainty can be used as a self-validation mea-sure to evaluate the accuracy of the proposed methodology whenEDBT 4.17 ◦C is selected in the program.

Figs. 7 and 8 illustrate the results (On–off status and lon) for thecooling mode of compressor in RTU No. 5 located in Store I by usingEDBT 1.39 ◦C and 4.17 ◦C, on 7/25, 2011, respectively. The differ-ent results are demonstrated through comparing Fig. 7 with Fig. 8.Area 1 in Fig. 7 shows the 5 complete cycles occurring between time15:36 and 19:12. The results in this area can be approximated thesame as the results of Area 3 in Fig. 8 for the same period becauselon of those cycles did not vary. This comparison shows there is novariation due to the different EDBTs for this period. On the otherhand, a cycle is affected by the selection of EDBT in Area 2 sincethe same cycle is longer in Area 4 when EDBT is 4.17 ◦C as shownin Fig. 8. As a result of this variation, lon of this cycle is approxi-mately changed from 2 h to 4 h, so this difference between Area 2and 4 leads to the variation of an average maximum RTF. Since therange of specific temperatures is longer for EDBT 4.17 ◦C, Area 5 inFig. 8 shows two more cycles which do not exist with EDBT 1.39 ◦C.Similar incidences as Area 4 and Area 5 also result in the varia-tion of the average maximum RTF at the peak condition in termsof uncertainty. Area 6 is another example of the difference affectedby the dead-band temperature. However, the cycle of this area isnot included because it cannot be computed by the program due tothe incomplete cycle. Consequently, Area 6 does not count in thefinal calculation of the average maximum RTF. The comparison ofRTF between EDBT 1.39 ◦C and 4.17 ◦C is tabulated in Table 3 for allRTUs in Store I.

To conclude RTF of Step 3 for Store I, as shown in Table 3, theuncertainties of RTF are from −9.50% to 13.43% for a first-stagecooling mode, from −20.90% to 24.62% for a second-stage coolingmode, and from 0% to 24.71% for a first-stage heating mode. Theuncertainty of a second-stage heating mode cannot be evaluatedbecause only RTU No. 5 has the related result for RTF. It can be seenthat the uncertainty of first-stage cooling mode is within ±13.43%,because half of RTUs, whose RTF is more than 0.771 based on EDBT1.39 ◦C, were properly sized for the first-stage cooling mode in thisstore. Conversely, only 2 RTUs of both second-stage cooling andfirst-stage heating modes have RTF more than 0.771 based on EDBT1.39 ◦C. The evaluation of results processed through RTF fluctuatesbecause RTF depends on the selected outdoor air temperatures.

Table 3Results of RTF and uncertainty in Store I.

Store I (RTF) Cooling mode Heating mode Uncertainty of 2 stages (St) in both modes (%)

RTU no. Stage1 (EDBT, ◦C) Stage2 (EDBT, ◦C) Stage 1 (EDBT, ◦C) Stage 2 (EDBT, ◦C) Cooling mode Heating mode

1.39 4.17 1.39 4.17 1.39 4.17 1.39 4.17 St 1 St2 St1 St2

1 0.995 0.921 * * 0 0 0 0 7.44 – – –2 0.679 0.655 * * 0.397 0.356 * * 3.53 – 10.33 –3 0.640 0.610 * * 0 0 * * 4.68 – – –4 0.604 0.590 * * 0.378 0.322 * * 2.30 – 14.81 –5 0.631 0.691 0.261 0.235 0.519 0.445 0.483 0.519 −9.50 9.96 14.26 −7.456 0.937 0.948 0.642 0.642 0.165 0.151 0 0 −1.17 0 8.48 –7 0.600 0.540 0.659 0.550 0 0 0 0 10.00 16.51 – –8 0.967 0.928 0.452 0.345 0 0 0 0 4.03 23.67 – –9 0.996 0.998 0.904 0.742 0.350 0.286 0 0 −0.2 17.92 18.29 –10 0.808 0.729 0.680 0.592 0.505 0.398 0 0 9.77 12.94 21.08 –11 0.997 0.980 0.605 0.450 0 0 0 0 1.71 24.62 – –12 0.591 0.603 0.413 0.325 0.805 0.734 0 0 2.03 21.31 8.82 –13 0.771 0.665 0.878 0.873 0.112 0.072 0 0 13.75 0.57 24.71 –14 0.818 0.808 0.425 0.538 0 0 0 0 1.22 −20.9 – –15 0.394 0.349 – 0.197 – 0.973 0 0 11.42 – – –16 0.423 0.400 0.321 0.297 – 0.311 0 0 5.44 7.48 – –17 0.999 0.996 0.831 0.633 0.382 0.292 0 0 0.30 23.83 23.56 –18 0.960 0.929 0.539 0.474 0.603 0.530 0 0 3.23 12.06 12.11 –19 0.693 0.655 0.249 0.269 0.631 0.550 0 0 5.48 -8.03 12.84 –20 0.613 0.679 * * 0.537 0.406 * * −10.7 – 24.39 –21 0.581 0.503 * * 0.704 0.620 0 0 13.43 – 11.93 –22 * * * * 0.704 0.614 * * – – 12.78 –

Note: The symbol, –, means RTF cannot be computed due to no completed cycle at EDBT 1.39 ◦C and symbol * means without a mode operation, whereas – refers to nouncertainty due to – and *.

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Fig. 7. The cycles of a cooling mode of RTU No.5 in Store I with EDBT = 1.39 ◦C.

Whenever EDBT is changed, more cycles and/or the longer dura-tion of cycles could occur as demonstrated in Figs. 7 and 8. Thus,more oversized capacity leads to higher RTF uncertainty. This self-validation is more accurate when more RTUs are properly sized. Theuncertainties of all stores are within ±30% for all mode operations.The implementation of RTF results till Step 3 can be used as the cor-rection factor for typical load calculation in commercial buildingsbecause many HVAC designers normally amplify the load calcula-tion by 20–5% for safe and acceptable practice [9]; however, theseresults till step 3 are not accurate enough to implement in smartbuilding management. In the next section, lon and lcycle, which areless than 6 h, are used to calibrate solution 1(S1) and 2 (S2) forsolution 3 (S3) and 4 (S4) to process Nmax analysis. This step is thevalidation of final results for real applications.

4.3. Application of N-analysis

Step 4 is applied to validate the results by using N-analysis.Based on the calibrated results with EDBT 4.17 ◦C (S4) in the pre-vious section, this range of OAT is approximately equivalent to thefield measurements in previous studies, which analyzed the data onpeak day conditions only for one day. The relation between N andRTF was processed by two equations (i.e., Eqs. (9) and (10)), whichwere proposed by several researchers [12,13]. These two equationsare also applied to compute maximum cycle rate per hour, Nmax, inthis section in order to validate the results.

In previous studies, researchers processed the problem of RTUsin terms of oversized capacities similar to this study; howeverthey only did small size experiments in the cooling mode of RTUs

Fig. 8. The cycles of a cooling mode of RTU No.5 in Store I with EDBT = 4.17 ◦C.

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Fig. 9. N and RTF in cooling mode of RTU No.2 in Store I.

[7,13] or the heating mode of heat pump [12] due to limitedmeasurements. Field tests of both two modes require long-termmeasurements, and are difficult to process without an advancedcommunication network such as BACnet protocol. Thus, they mea-sured data based on outdoor temperatures at peak day conditionson site by data loggers; RTF and N were computed from the cyclesof those data obtained in one day. Therefore, characteristics ofcompressor or machine performance were not based on annualtemperature condition and not conclusive in their studies.

Fortunately, using BACnet protocol in this study, all limitationsof measurement can be solved on not only extending the periodto study in a year, but also processing both cooling and heatingseason in many stores for the same period. The two equations usedto evaluate the performance of RTUs, and to validate results in thissection are described below.

Firstly, Henderson et al. [13] proposed Nmax which is themaximum cycle per hour occurring at RTF = 0.5 to describe the per-formance of a thermostat of an air-conditioner. This parameter isfitted from the equation:

N = 4NmaxRTF(1 − RTF) (9)

Second equation was proposed by Miller and Jaster [12]. The cor-relation between N and RTF of 9 heat pumps was described by theproposed variables called Beta (ˇ) and Alpha (˛) in the differentpattern as Eq. (10).

N = 4 ̌ · RTF(1 − RTF)1 + ̨ · RTF

(10)

where ̌ is equivalent to Nmax when ̨ is zero. The productionterm with ̨ and RTF is essential since it represents the uncountedstochastic factors that may also largely influence the operation ofan RTU sporadically, including sharp building load change, extremeoutdoor temperature fluctuation, etc.; meanwhile RTF shows theon-time operation of a RTU.

Fig. 9 illustrates the application of Eqs. (9) and (10) for a coolingmode of RTU No.2 in Store I obtained with EDBT 1.39 ◦C. The bluecurve is fitted in the pattern of ̌ and ˛, obtained from Eq. (10),where ̌ = 1.58 and � = (−K/N), K = 0.45 for RTU No. 2 in Store I. Theblack curve is then fitted by using the RTF and new N obtained fromEq. (10) with the deduction of the term with ̨ and RTF.

The above process for reducing the uncertainty and improve therobustness in analyzing the oversizing issue of RTUs is termed N-analysis. Results of Nmax for RTUs in store I are finally tabulated inTable 4.

Fig. 10 illustrates the analysis of RTU performance through thefitted curves between N and RTF for RTU No. 2 in Store I in heating

Fig. 10. N and RTF in heating mode of RTU No.2 in Store I.

mode; the thick blue curve is a plot based on original data and theblack curve excludes the impacts from uncounted factors, includingOAT and internal load fluctuation. The parameter Nmax, togetherwith N and RTF, from the fitted black curve is used to explain thelevel of over-sized capacity.

In the previous study [7], low Nmax and high maximum RTF wereproposed to be the signature of a right-sizing RTU under a peak dayoperation. On the other hand, high Nmax and low maximum RTFwere the signature of an over-sized RTU. However, the red points inFig. 10 are composed of the cycles under many peak day operations.Thus, only Nmax and maximum RTF cannot be used to sufficientlyquantify the level of oversize of a RTU along a year. This study pro-poses the combination of RTF, N, and Nmax to identify the over-sizinglevel of RTU performance. The combination can be used to classifythe points in 5 levels as follows:

Oversizing level 1, 0 < RTF < 0.2 and 0 < N < Nmax/2. It is the sig-nature of severely over-sized capacity because low N and very lowRTF mean the system seldom cycles in a hour, and lon is of a veryshort duration. Extreme fluctuation of OAT or load, or short periodsof specific OAT or load can also lead to this situation occasionally.Whenever an over-sized RTU at level 1 is activated, it never runscontinuously and is turned off in short time (e.g., ton 12 min andtcycle 60 min).

Oversizing level 2, 0.2 < RTF < 0.5 and Nmax/2 < N < Nmax,. It is sim-ilar to level 1, but lon and lcycle are longer; lon is more close to loff.This level is less over-sized than first case.

Oversizing level 3, 0.2 < RTF < 0.7 and Nmax < N. It is at the peakof the curve. With N being higer than Nmax, the operation phe-nomenon of an over-sized RTU in this area is that the system cyclesmore frequently.

Oversizing level 4, 0.5 < RTF < 0.8 and Nmax/2 < N < Nmax. When-ever RTF is higher, the system stays on much longer. It is cycledless frequently because the fluctuation of load change and OAT isweaker than Level 2. The oversizing severity of a RTU operating inthis range is much lower than Level 1 and 2.

Oversizing level 5, 0.8 < RTF < 1 and 0 < N < Nmax/2. This levelshows the signature of a properly sized/right-sized capacity. Whenmost points of (N, RTF) are in this range, the RTU is right for theapplication.

Although some points may be found out of the 5 areas withthe proposed evaluation method, the number of these outliers aremuch less than those in the 5 areas. Therefore, the application ofthis method can be used to quantify the oversizing level of a RTUbased on data along a year. Table 4 tabulates all values relating to N-analysis of all RTUs in Store I. The comparison between EDBT 1.39 ◦Cand 4.17 ◦C is in terms of uncertainty of Nmax. Also, Nmax at EDBT

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Table 4The comparison of Nmax between EDBT 1.39 ◦C and 4.17 ◦C by step 4 in Store I.

Store I (Nmax) Cooling mode (cycle per hour) Heating mode (cycle per hour) Uncertainty of 2 stages (St) in both modes (%)

RTU no. Stage1(EDBT, ◦C) Stage2(EDBT, ◦C) Stage 1 (EDBT, ◦C) Stage 2(EDBT, ◦C) Cooling mode Heating mode

1.39 4.17 1.39 4.17 1.39 4.17 1.39 4.17 St 1 St2 St1 St2

1 2.15 2.38 * * 0 0 0 0 9.67 – – –2 1.58 1.72 * * 1.98 2.16 * * 8.23 – 9.09 –3 2.22 2.35 * * 0 0 * * 5.86 – – –4 1.31 1.33 * * 1.90 1.74 * * 1.53 – −8.42 –5 1.75 1.62 0.22 0.24 0.51 0.56 0.04 −7.43 9.09 9.80 –6 0.14 0.15 0.15 0.16 0.26 0.28 0 0 7.14 6.67 7.70 –7 0.17 0.18 1.12 1.12 0 0 0 0 5.88 0 – –8 0.12 0.13 1.01 1.09 0 0 0 0 8.33 7.92 – –9 – – 0.12 0.13 0.68 0.76 0 0 – 8.33 8.82 –10 1.70 1.53 0.59 0.65 2.10 2.33 0 0 10.00 10.17 10.95 –11 0.17 0.18 1.05 1.09 0 0 0 0 5.88 3.81 – –12 0.165 0.173 0.931 1.039 0.505 0.452 0 0 4.85 11.60 10.50 –13 2.45 2.25 0.49 0.51 0.29 0.30 0 0 8.16 4.08 3.33 –14 3.09 2.97 1.50 1.34 0 0 0 0 −3.97 −10.67 – –15 0.16 0.17 – 0.17 – 0.37 0 0 6.25 – – –16 0.35 0.25 1.05 1.15 – 0.24 0 0 −2.86 9.52 – –17 – – 0.235 0.214 0.85 0.77 0 0 – −8.94 −9.42 –18 0.261 0.286 0.91 1.01 0.51 0.52 0 0 9.56 10.99 1.96 —19 – – 0.178 0.197 0.266 0.281 0 0 – 10.67 5.64 –20 1.51 1.65 * * 1.25 1.27 * * 9.27 – 1.6 –21 1.89 2.09 * * – 0.28 0 0 10.58 – – –22 * * * * 0.88 0.83 * * – – −5.68 –

Note: The symbol, –, means Nmax cannot be computed by data due to not enough points and * is also without a mode operation, whereas – means no uncertainty due to –and *.

4.17 ◦C can be used to compare with previous studies because theduration of OAT in this range in one day is approximately closeto the duration used by the previous researchers for oversizinganalysis based on one peak day condition measurements.

The calibrating criteria, lon and lcycle being less than 6 h, of step4 are used for EDBT 4.17 ◦C. This adjusted duration is calculatedfor solution 4(S4) using the proposed analysis. The Nmax for EDBT4.17 ◦C is used to validate the results of EDBT 1.39 ◦C for the uncer-tainty of calculation due to the effect of OAT and/or load variation.After that, PLR is computed in Step 5 for all RTUs and is used toquantify over-sized capacities and energy penalties as the final step.

Table 4 illustrates the results obtained from N-analysis to vali-date the accuracy in terms of uncertainty. This method is morerobust than the validation by RTF uncertainty because RTF is largelyproportional to OAT and load, whereas Nmax is obtained excludingthe effect of those stochastic factors. Thus, Nmax is more accurateand reliable to evaluate RTU oversizing than RTF; the uncertainty ofNmax is within ±11.6% for this store and within 17.9% for all stores.However, N-analysis cannot be used to compute Nmax if RTUs areof right-sizing capacities (i.e., RTFs are approximately closed to 1)and/or RTUs are of much oversizing capacities (i.e., RTFs are lowerthan 0.01). Under this circumstance, the uncertainly of RTF is usu-ally smaller and can be used in stead.

Table 5 shows the comparison of results for Store I with the 3prior studies. For the cooling mode of RTUs, both stage 1 and 2are approximately in the similar range of [7,13]. Furthermore, onlythe heating mode of stage 1 is approximately close to that of [12].

Table 5Comparision of Nmax at Store I with the previous studies.

Comparing Nmax(Cycle/hour) Cooling modeUsing EDBT 4.17 ◦C

Heating modeUsing EDBT 4.17 ◦C

RTUs in Store I: Stage 1 0.13–2.97 0.28–2.33RTUs in Store I: Stage 2 0.13–1.15 0.00–0.04Henderson et al. [13] 0.15–4.07 –Djunaedy et al. [7] 0–8.78 –Miller and Jaster [12] – 0.6–2.1

Note: The symbol, –, means without consideration.

Stage 2 of this store is not considered because only one RTU canbe computed for Nmax and other RTUs are oversized with stage 2never being triggered. Results of other stores are concluded in nextsection.

4.4. Validation of PLR using N-analysis

Last section obtains the validation of results by using Nmax. Thismethod shows more accurate results than using RTF with uncer-tainty within ±17.9% for all stores. In this section, N-analysis isfurther applied to validate the uncertainty of PLR for the calcula-tion of average over-sized capacities and peak energy penalty inSection 4.5.

Based on the results in Table 3, all percentages of RTF uncer-tainty, which are higher than 14%, will result in high PLRuncertainties. These uncertainties can be decreased by using thecalibrated solution (S3) from the N-analysis process to calculateaccurate PLR. The results are given in Table 6. RTF uncertainties ofother operation modes or RTUs are not demonstrated because theiroriginal RTF uncertainty values are less than 14%. As it can be seen,whenever N-analysis is used to calculate the uncertainty of PLR, itsvalue will only decrease. For example, the second stage of a cool-ing mode in RTU No. 7, the RTF uncertainty of this mode is 16.51%(in Table 3). After applying N-analysis, the uncertainty of PLR isreduced to 11.59% (PLR = 0.663 for EDBT 1.39 ◦C and PLR = 0.586 forEDBT 4.17 ◦C).

Table 6 shows the improvement of the accuracy using N-analysisto calibrate the possible duration of cycles for RTUs in store I. Theaccuracy of PLR results is with ±14.88% for Store I, whereas ±16.99%is the accuracy of PLR results for 12 stores.

4.5. Average energy penalty analysis along a year

The validated results from Section 4.4 can be utilized to evalu-ate the overall performance of RTUs in terms of average over-sizedcapacities and energy penalty for retail stores. PLR is the parameterto quantify the actual load of a RTU in a peak condition. Since var-ious cycles may occur in peak conditions, RTF is an averaged value

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Table 6More accuate PLR in terms of uncertainty based on RTF results in Store I.

Store I (PLR) Cooling mode Heating mode Uncertainty of 2 stages (St) in both modes (%)

RTU No. Stage1(EDBT, ◦C) Stage2(EDBT, ◦C) Stage 1 (EDBT, ◦C) Stage 2(EDBT, ◦C) Cooling mode Heating mode

1.39 4.17 1.39 4.17 1.39 4.17 1.39 4.17 St 1 St2 St1 St2

4 * * * * 0.345 0.310 * * * * 9.98 *5 * * * * 0.299 0.297 * * * * 0.80 *7 * * 0.663 0.586 * * * * * 11.59 * *8 * * 0.441 0.381 * * * * * 13.60 * *9 * * 0.874 0.740 0.342 0.391 * * * 14.19 −14.52 *10 * * * * 0.454 0.403 * * * * 11.15 *11 * * 0.417 0.356 * * * * * 14.70 * *12 * * 0.361 0.310 * * * * * 14.02 * *13 * * * * 0.112 0.072 * * * * – *14 * * 0.427 0.491 * * * * * −14.88 * *17 * * 0.729 0.626 0.374 0.323 * * * 14.05 13.70 *20 * * * * 0.509 0.439 * * * 13.82 * *

Note: The symbol, –, means without consideration because Nmax cannot be computed, whereas * means the mode operation which RTF uncertainties are less than 14%.

Table 7Summary of over-sizing capacity and peak energy penalty for 12 retail stores.

Store Range of Nmax (cycle/hour) Over-sized capacities (%) Total capacities (Tons, MBH) Peak energy penalty (kW) Scharn’s results (%)

Cooling Heating Cooling Heating Cooling Heating Cooling Heating Cooling Heating

A 0.57–5.75 0.64–4.05 100.11 398.69 320 3778.8 192.16 1106.12 43.88 632.84B 0.48–3.95 * 39.19 * 209 2753.2 70.62 * 24.39 *C 0.59–2.77 0.51–4.14 14.65 224.29 235 2449.5 34.66 620.30 5.28 313.28D 0.61–3.07 0.48–1.61 88.89 631.45 218 2741.1 123.11 872.66 57.33 1018.48E 0.24–4.65 0.68–4.05 247.19 261.43 289 3611.0 226.41 802.44 216.98 384.02F 0.58–3.22 0.27–1.63 71.47 198.15 241 2903.0 120.54 635.44 45.25 275.37G 0.48–4.05 0.72–5.63 87.90 367.41 172 2685.2 90.94 772.81 49.14 488.71H 0.85–3.17 0.44–1.97 67.52 199.99 197 2928.2 91.89 593.74 31.83 225.64I 0.13–2.97 0.00–2.33 50.43 236.49 177.5 2848.0 71.41 732.87 38.98 302.99J 0.61–3.85 0.29–2.04 94.12 383.38 177 4738.4 102.98 1375.99 55.16 476.63K 0.52–3.22 0.37–3.29 70.09 225.16 226 3326.7 111.76 25.14 64.70 241.06L * 0.19–3.08 * 166.62 185 3997.4 * 914.66 313.73 152.89

Note: The symbol, *, means without consideration due to temperatures which are not in the range of design temperature. (1 MBH = 1000 Btu/h = 292.91 W and 1 Ton = 3519 W).

for these conditions and each one RTF is used to compute PLR byusing Eq. (6). As a result, PLR is also an averaged value of the sameconditions. Similar processing is proposed by Henderson et al. [13].The equations used to quantify the over-sized capacity and energypenalty are given as

Qover = Q · (1 − PLR) (11)

Qpnt = Q · (1 − PLR)EER

(12)

where Q is the capacity of a RTU, W or Btu/h, EER (Btu/W-h) is theenergy efficiency ratio of a RTU. The subscripts over and pnt denotethe over-sized capacity and energy penalty, respectively.

The energy penalty using Eq. (12) is for cooling mode only.When heating mode is concerned, EER should be replaced by AFUE(Annual Fuel Utilization Efficiency).

Qpnt = Q · (1 − PLR)AFUE

(13)

For simplicity, EER and AFUE are assumed as 10 Btu/W-h and 80%,respectively, for all RTUs in order to conveniently evaluate theenergy penalties. As a result, these two assumed values can resultin the minor error of the total energy penalties in each store. Addi-tionally, the results of this section are compared with a prior study[10], which used the same set of data to calculate the percent-age of over-sized capacities for all RTU machines in 45 stores witha preliminary method. Only RTF was used in their process. Thatpreliminary method is mathematically reasonable to apply, but itcannot be used to accurately describe the performance and char-acteristics of a RTU. More information is provided in the Appendix.

Table 7 tabulates the results of 12 retail stores with 268 RTUs intotal. The range of Nmax varies from 0.13 to 5.75 cycle per hour fora cooling mode, while the range of a heating mode is between 0.00and 5.63 cycle per hour. The over-sized capacity of the RTUs has anaverage value of 84% for cooling and 299% for heating. The lowestpeak energy penalty for the 12 stores is 34.66 kW in a cooling modeand 25.14 kW in a heating mode, while the highest peak energypenalty goes to 226.41 kW in a cooling mode and 1375.99 kW in aheating mode. Compared the results in terms of average over-sizedcapacities with Scharn’s evaluation [10], the current results showrelatively higher oversized capacity for a cooling mode and loweroversized capacities for a heating mode in the 12 stores. For thisstudy, the accuracy of oversized capacities for both heating andcooling are within ±16.99%, for all twelve stores including aver-age peak energy penalty, because both 2 sets of final results areevaluated based on PLR with N-analysis.

5. Conclusion and discussion

This study presents the systematic analysis of oversized capaci-ties and energy penalties of RTUs for 12 retail stores. The data werecomprehensively obtained by BACnet protocol for one year, from2011 to 2012. Both narrow and wide EDBTs are applied to minimizethe potential bias in evaluating the RTUs. The average maximumRTF (run time fraction) of each store is assessed by self-validationin terms of uncertainty. The range of RTF uncertainty is between±30% for all RTUs. The study finds that the validation of RTF is quitefluctuated because RTF of an RTU changes under different peak OATand load distribution. They could be used as references to adjust the

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load calculation for new retail stores; however, they are not accu-rate enough for future study, such as real-time optimization of astore where the oversized RTUs are installed.

N-analysis is proposed to calibrate the solution and uncer-tainty. Nmax at annual design condition is introduced to excludethe uncounted stochastic effect of OAT and/or load in evaluatingthe compressor’s and gas furnace’s performance. Compared Nmax

obtained from EDBT 1.39 ◦C with EDBT 4.17 ◦C, the uncertainty ofthis value is within ±17.9% for all RTUs. Since Nmax describes theperformance of a RTU based on both N and RTF, this validationdemonstrates the improved accuracy of the methodology. In addi-tion, N-analysis is further applied to compute PLR as a function ofN and RTF. The high uncertainty based on RTF can be improved byusing PLR instead. The average over-sized capacities and penaltyenergy of RTUs can be computed by PLR for both cooling and heat-ing mode. These accurate and robust results can be used as a toolto enhance the process of building load calculation.

For N-analysis, five levels are proposed to classify the oversizingdegree of a RTU. This proposed analysis could be used to optimizethe performance of a RTU. For example, RTU at Level 1 can be opti-mized by increasing the dead-band of a thermostat to avoid shortcycling and reduce waste power consumption. The RTUs with afeature close to Level 1 can be turned off accordingly. The detailedoptimization methodology of Level 2 to Level 4 requires more anal-ysis by the smart build management.

In terms of the average oversized capacities and energy penal-ties, PLR value can be used as a safety factor to adjust building loadcalculation and avoid excessive energy waste for new buildingsand renovation work. For example, the PLR results of Store I canbe used to evaluate load calculation of RTUs for renovation work inthis store. Also, they can be used as the criteria to design or evaluateRTUs for the new building of the same brand or similar constructionof commercial buildings.

Due to the robustness of the identified oversized capacities,an average peak energy penalty can be calculated and appliedto estimate yearly optimum energy consumption in commercialbuildings. The numbers of hours associated with the EDBTs can beused to transform the average energy penalty (kW) to kWh. Wecan estimate how optimum energy use is in commercial buildingsby comparing the calculated energy with the yearly billed powerconsumption.

Additionally, the oversized capacities lead to the concept ofsmart building management within which we aim to developinnovative supervisory control on multiple RTUs. The supervisoryfunction will include the accurate RTF for estimating the actual RTUcapacity performing at part and peak load conditions of a building.Then, this program will automatically assist and adjust the oper-ations of each RTU to meet the actual load in stores. The aim of

this future study is to minimize waste energy consumption con-sumed by RTUs in retail stores without extra investment such asRTUs replacement and retrofitting of an advanced local RTU control(e.g., variable feed drive and economizer control). The findings, inaddition to the virtual sensors [15] and improved algorithms [16],can be grouped as smart building technologies for improving thebuilding operation visibility and efficiency [17].

Appendix A.

This appendix shows the artificial data to explain Scharn’smethodology and the equations.

Fig. 11 illustrates the mathematical methodology of Scharn’sstudy [10] to quantify the over-sized capacity of RTUs along oneyear by the artificial data. This method first identifies the range ofdesign temperature. lon is defined as B1 through B5 for the specifyrange, whereas lcycle is defined as A1 through A4 for a cycle. RTF issimply calculated by

RTF = (B1 + B2 + B3 + B4 + B5)(A1 + A2 + A3 + A4)

(14)

Instead of using PLR, RTF is directly used to calculate the over-sized capacities:

Qover = Q · (1 − RTF) (15)

This lumped method is only suitable for rough quantifying over-sized capacity of RTUs. It ignores the potential bias for countingcycles included in each time period.

Appendix B.

AFUE is a thermal efficiency measure of combustion that showsthe performance unit of gas furnace efficiency.

AOAT is a design temperature proposed by ASHRAE for calculat-ing the peak conditions of building load in a year for cooling andheating seasons.

EDBT is the value uncertainties of computational programaffected by a thermostat operation and the outdoor air tempera-ture.

EER is the performance unit of compressor efficiency, which isthe ratio of compressor input power over a compressor capacity.

N demonstrates how many cycles the on-off controller of air-conditioning system performs in one hour.

PLR is the ratio of actual building load over air-conditioning loadcapacity.

RTF is the ratio between an on-time operation and a cycle-timeoperation.

Fig. 11. Illustration of the mathematic methodology by Scharn [10].

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� refers to how rapid equipment reaches the steady state outputwhen a compressor or gas furnace is cycled.

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