~.-- ~.

3895

\ / EFFECT OF TIME RESOLUTION

ON STATISTICAL MODELING OF

COOLING ENERGY USE IN LARGE

COMMERCIAL BUILDINGS

Srinivas Katipamula, Ph.D., P.E. T. Agami Reddy, Ph.D. David E. Claridge, Ph.D., P.E.

Member ASHRAE Member ASHRAE

ABSTRACT predicting the peak consumption (demand). identifying opera-

Regression models of measured energy use in commercial tional and maintenance problems. or for real-time controls.

buildings are becoming an increasingly popLllar method of Higher resolution models, such as hourly or IS-minute mod-

determining retrofit savings or identifying operational and els, are needed.

maintenance (O&M) problems. When hourly monitored data A previous study (Katipamula et aJ. 1994) found that the

are available, an issue that arises is what time resolution to hourly models had higher coefficients of variation (CV) and

adopt for regression models to be most accurate. This paper lower coefficients of determination (R2) than the daily mod-

addresses this question by comparing monthly, daio', houri); els. The dai]y mode]s showed Jess variation because some

and individLtal hourly or hour-ofday (HOD) mLlltiple linear operational parameters (such as supply air temperatures,

regression (MLR) models when applied to measured cooling fresh air intake, internal gains. etc.), which change from hour

energy consumption (Ec) in commercial buildings. Ec con- to hour, are effective]y constant on a daily basis. Diamond

/ sumption in five large commercial buildings in Texas (both and Hunn (1981) compared simulated energy consumption

r under dual-duct constant-volume [DDCV] and dual-duct to the measured data and found that on a month]y time scale

~ variable-volume [VA V] operation) is modeled in all four time the deviations were higher than on an annual time scaie.

scales usingfimctionalforms based on engineering principles. They concluded that some effects average out over the year,

The relative advantages and disadvantages of all four types of reducing the deviations.

models are discLLSsed and compared. The outdoor dry-bulb One method to account for the hour-to-hour variation in

and dew-point temperatures accounted for most of the varia- the internal gains (which are influenced by the operational

lion (80% or more) in Ec. Although the monthly models had schedule of the building) is to sort the hourly data into sev-

higher model R2 than daily, hourly, and HOD models, the eral subgroups. A logical grouping would be to first sort the

daily and HOD models proved more accurate at predicting data into weekdays and weekends and then sort these into 24

Ec. Also, the HOD models had higher model R2 and /o}ver hourly data subgroups each.

coefficients of variation (CV) than the hourly models. The In this paper, measured data of cooling energy con-results of this study suggest that daily time scale models are sumption (Ec) in five large commercial buildings in central. .

most advantageous for retrofit savings detennination, }vhile Texas are used to develop the monthly, daily, hourly, and

HOD models are best for O&M purposes. hour-of-day (HOD) models for two commonly used heating,

INTRODUCT ON ventilating, and air-conditioning (HVAC) systems (namely

I the dual-duct constant-volume [DDCV] and the dual-duct

Regression analysis of measured data is becoming variable-air-volume [YAV] systems), based on engineering

increasingly popular for modeling the energy consumption in principles. They are then compared with one another.

commercial buildings to determine retrofit savings and to

identify operational and maintenance (O&M) problems. EFFECT OF TIME SCALE

Widely used regression models are either based on monthly To illustrate the effects of the time scale (monthly, dai1y,

(Fels 1986) or daily energy use (Ruch and Claridge ]992; hourly, and two typical hours [one during an occupied period

Kjssock et al. 1992). These models are appropriate for predict- and one during an unoccupied period] of the day) on regres-

ing mean energy consumption such as monthly or normalized sion mode]s, year-long monitored Ec data of a building with a

annual consumption (NAC). However, they are inadequate for DDCV system are ploned as a function of outdoor dry-bulb

,; V Srinivas Katipamula is a research scientist at Battelle PNL, Richland, WA. T. Agami Reddy is a research engineer at the Enetgy Systems

.. Laboratory and David E. Claridge is an associate professor in the Mechanical Engineering Department at Texas A&M University, College

Station.

THIS ?REPRINT IS FOR OISCUSSION PURPOSES ONLY. FOR INCLUSION IN ASH RAE TRANSAC1l0NS 1995. V. 101. Pt. 2. Not to be reprinted in whole or in

part without written permission of the Amencan Society of Heating. Refrigerating and Air-Conditioning Engineers. Inc.. 1791 Tul/ie Circle. ,~E. Atlanta. GA 30329.

Opinions. findings. conclusions. or recommendations expressed in this pacer are those of the author(s) and do not necessarily relect the vIews of ASHRAE. Wrinen

questions znd comments regarding this paper should be received at ASHRAE no later than July 5, 1995.

: "

temperature (To) in Figure I. The operational parameters (such MODEL DEVELOPMENT

\., as Tc, T h, outdoor air intake, qi' etc.) change from hour to hour P . d. h t d h . . I . I'--". " revlous stu les ave suQges e t at a pIecewise mu up ebut are effecuvely constant on a monthly or even a dally basis. I. . ( A' 1LR) d - I . . d Vmear regreSSion lV mo e IS more appropnate to mo e

Therefore, monthly and daily E:c, when compared to the predict the E:c of large commercial buildinos with either a

hourly E:c, show less scatter. The top plot in ~igure 1 shows DDCV or a VAV system (Reddy et al. 1993: Katiparnula et al.

. the average hour~y E:c f~r the m?nth as a function of the ~ver- 1994). Also, E:c in large commercial buildings operating 24

~ge ~o~thly To (I.e., taking a POI~t from the plot and m.ultlply- hours a day shows a segmented linear behavior as a function

Ing It With the nu~ber of hours In the ~onth would YIeld the of outdoor dry-bulb temperature (To) (Kissock et al. 1992;total monthly coolIng energy consumption). The second plot Katiparnula et al. 1994). The segmented linear behavior is a

shows the ~verage hourly E:c for rh: day ~ a function of ~he result of the compound effect of latent cooling and the hot

average dally To (total number of pOints being 365). The thIrd deck reset schedule in a DDCV system. In a VA V system the

plot presents hourly E:c as a function of hourly To, while the change in slope as a function of To occurs when the system

bottom two plots show hourly E:c as a function of hourly To reaches its minimum airflow condition.

for a typical unoccupied hour (5 a.m.) and a typical occupied In addition to To, the other variables that affect Ec are

hour (1 p.m.). outdoor dew-point temperature (T dp)' solar radiation (qsov,

The average hourly E:c values for the month seem to and internal gains (excluding gains from people) from lights

increase linearly with the average monthly To. Similarly, E:c and equipment (qi). In most large commercial buildings the

increases with To at the daily time scale, although there is major portion of the latent cooling energy is from ventilation,

more scatter in E:c for a given To when compared to the which is a strOng function of T dp. However. for performing

monthly time scale. Also, there appears to be a slight change regression analysis, it is better to use (T dp - Ts)+, where Ts is

in slope above an average daily To of 16°C (60°F) because of the mean surface temperature of the cooling coil and "+" indi-

latent loads. On the hourly time scale, the scatter in E:c is cates that the term is set equal to zero when T dp < Ts (Katipam-

much more pronounced and increases above To of 16°C ula et al. 1994; Reddy et aI. 1993).(60°F) because of the latent loads. Also, the scatter in E:c dur- Since E:c is a function of several variables, accurateing the occupied hour (1 p.m.) is greater than that at the unoc- regression modeling requires an MLR model. In regression

. CO cupied hour (5 a.m.). Apart from the scatter induced by the modeling, a change in slope can be handled by introducing an

r-. latent loads, some of the scatter on the hourly time scale is indicator variable. The value of the indicator variable, I, is set

\-I probably due to a change in the operational parameters, such equal to 1 for To values to the right of the change point, indi-

as the system setpoint temperatures, and also due to the chang- cating the presence of the change point. For the rest of the dataing internal loads from hour to hour. Since most of these varia- (To values to the left of the change point), the indicator is set

tions average out on monthly and daily time scales, the scatter equal to zero (Daniel et aI. 1980). Thus the regression model

in E:c tends to be small. for both the DDCV and the VA V systems assumes the follow-

F . 2 h h .. f E . .th T " .1 . ing functional form:19ure sows t e vanatlon 0 c WI 0 lor a but ding

with a VAV system. Again, the scatter in E:c increases as the E:!3 T 13

time scale changes from monthly to hourly. The apparent c = a. + 0 0 + (I (1)

change of slope on the monthly time scale is due to the + 13 IT +~. T+ + 13 q + 13-1;

increase in latent cooling. The change in slope, due to 2 0 .) dp 4 sol )

increase in latent cooling both on the daily and the hourly h J3 J3 n B J3 d J3 . ffi .'. . . w ere a., 0, I' u." 3, 4, an 5 are regression coe IClents.

ume scales, IS much more pronounced than In FIgure 1. The Th ffi . J3- th ff th . d. d b. e coe Iclent 1 represents e 0 set e m Icate 0 serva-Increase in scatter above To of 16°C (60°F) on the hourly t .

(T aI t th . ht fth h .t) h e from theIons 0 v ues 0 e nQ 0 e c anQe porn avscale is primarily because of changes in internal and latent value a.. The coefficien; J3., indicates ilie extent to which the

ventilati~n loads. The effect of the int~rnalloads can clea:ly right-hand slope is larger-than the slope to the left of thebe seen In the botto~ plot. where E:c IS plotted as a ~uncuon change point If the change point does not exist in the data.of To for an unoccupied hour (4 a.m.) and an occupied hour then the coefficients 8( and ~ will not be statistically signifi-

(1 p.m.). cant (i.e., both 81 and 62 will be near zero).

It is clear from both Figures 1 and 2 that as the time scale The MLR analysis assumes that the regressor variables

is increased from hourly to monthly the scatter in E:c are independent of each other. Multicollinearity betWeen the

decreases. The approach adopted in this paper to determine regressor variables results in large uncertainty bounds for thethe effect of time-scale resolution on regression models regression coefficients, leading to model uncertainty. A rule of

involves three phases: (i) model development based,on engi- thumb (Draper and Smith 1981) is that multicollineari£y

r--. neering principles of how HVAC systems operate, (b) model effects may be important if the simple correlation be~'een two

\ /.. identification based on goodness of fit, and (iii) testing the variables is larger than the correlation of one or either variable \. predictive capability of the model, i.e., how well the model with a dependent variable. Earlier studies by Wu et al. (1992)

predicts future energy use. and Katipamula et al. (1994) showed (at daily and hourly time

2 3895

'0

~IO

'"

:;)

~9 MONTHLY

~,

L=:37 0

00 0 0 0

~, c: 0

:,::::..:: ~: 0 00 0 0 0

.?;o4 0

...

A -

; 03

:I:

" V 2.

00

EI

c:J

>

. <0

: -10 -S 0 5 10 15 20 2.S 30 35 40

Average Monthly Ourdoor Dry-Bulb Temperature ('C)..

;i QIO

, '"

~ :;)

,~ 6:(;9 DAILY

, ...

., ~ '

L=:37

00c:

-- 6

85

C)

': -§' 4 If2J [1:J DO?

- 03 0

, X

()2.

00

el

()

>

;; < 0

-10 -5 0 5 10 15 20 2.S 30 35 40

Average Daily Ourdoor Dry-Bulb Temperature ('C)

10

.':. ~ 9 HOURLY

. "'-", j :;) ,

, .,-,;.' >-00

, ... 7

, ~

,:; ~ 6

: 00

j c: 5

, :=

. 0

04

; ~: ~~

. 0

XI

: 0

; -10 -5 0 5 10 15 20 2.S 30 35 40

...: Hourly Outdoor Dry-Bulb Temperature ~C)

'~E -

:' ..;10 E:IO

0.

.- ~9 -9

--' ~

<, ~,

() c:J

'" '"

:;)7 ::J7

>-6 >-

6~ ~

c:J ~

- ~5 c:5

:. tI3 ~

, 004 004 ~

c: ~ ~

--3 --3

G-"0 "0 G G

... 0 G o GU2. UZ

:.?;ol ;:'1

... ...

= ;:;

/- 00 00

loT" -10 -S 0 S 10 IS 20 2S 30 35 40 :I: -10 -S 0 S 10 15 20 2S 30 35 40

~:_.; Hourly Ourdoor Dry-Bulb Temperature ('C) Hourly Outdoor Dry-Bulb TemperatUre ('C)

Figure 1 Ec (GJ/h) as afunction o/T%r different rime scales at the EC building under DDCV operation.

3895 3

-; :

()10

::J'

~9 MONTHLY58c:

, ~7I \ t:Q .-I --- c: 0

(I '- 6

! -0 0 00 ,

.~ 0 S

i (J

j:>o-. ~

. - 0I ...-, ~

. 03 0 0

.,:1: 0 0

'. 0

, ()2.

,i ~

, () 1

: ;..

: <0

; -10.S 0 S 10 15 20 2S 30 3S 40

.1 Average Monthly Outdoor Dry-Bulb Temperature (C)

:~ ()10

,.j ::J'

j ~9 DAILY

'1 t 8I c:

1 ~7

t:Q 0

.~ C:6

,.. = ; 8 S

u

, .?;o.

I ...

~ ~: 0 ~D

: cQ 1, ...()

, ;..

~ <0

; -10 -S 0 S 10 IS 20 2S 30 3S 40

j Average Daily Outdoor Dry-Bulb Temperature (C)

10, i ~ ~9 HOURLY (..

f ~8

: :>0-: ~7

i ()

,I c:: ~6

1 , tIQ: .S S

. -0.

, 0

~ (J

~ :>0-3

. -

, ...

,j g 2., :: ""1

I

:' 0

} -10 -S 0 S 10 15 20 2S 30 3S 40

:, Hourly Outdoor Dry-Bulb TemperaUJre (C)

'~e:10 e:101 = 0-

"1 ""-9 -,

t - ; < 8 :' cQ I

1 (). ' ;, ~I .,. - GJ ~7 " :-, ~7

j :>0- - :>0-

j t:Q6 -' -,' -- ~6

... C)

'

\ ~S C:S ~. ~

00. eo'

c: c:

! =3 :g3j 82 GG , 82 G

1:>0-1 .?;o1

I - ..., ... -; go 00

; :1: -10 -s 0 S 10 IS 3) 2S 30 3S 40 :1: -10 .S 0 S 10 IS ~ 2S 30 3S 40 \

i ~ Hourly Outdoor Dry-Bulb Temperature (C) Hourly Outdoor Dry-Bulb Temperature (C) ",.o-

j ,

Figure 2 Ec (GJ/h) as a function 01 To lor different time scales at the EC building tinder VA V operation.

4 3895

~-

_.~I..II.

i

scales) that colline:1rity is not significant between To, T dp"', and HOD models (24 \veekday and 24 weekend) was regressedV'. qi. using Equation 1. The results from the stepwise regression

are presenced in Table 1. The contribucion of qsol is stacisci-MODEL IDENTIFICATION OF DDCV SYSTEM cally insignificanc in all cases and has not been included.

;' In this section, the results from monchly, daily, hourly, and Since rhe EC buildi~g ~as only ab.ouc 22% glazing area. the

. HOD regression models of Ec for an engineering center (EC) solar loads are noc signIficant (Katlpamula er al. 1994).

. with a DDCV system are presenced. The physical characteris- The concribucion of each independent variable to the

. : tics and operational decails of the EC are given in che appen- model can be assessed by comparing rhe parcial values of R2.

; dix. The measured daca used for the analysis included hourly A parcial R2 of 95.9% for the independenc variable To on the

values of To, T dp' qsol (global horizontal solar radiacion), qi, monthly time scale (column 2) means rhat To explains 95.9%

and Ec from September 1989 through August 1990. Monthly of the variacion in Ec. On the monthly time scale, qi and T dp+

values were obtained by sununing the hourly values of qsol' qi- are also statistically significant. explaining 1.3% and 0.3%

i and Ec over the monch. and daily values were obtained by of the variation in Ec, respecrively. Alchough the same num-

i summing the hourly values over the day. The independent ber of independent variables is statistically significant for

variables, To and T dp+, were averaged over the month and over both daily and momhly models, the daily model explainsthe day for monthly and daily values, respectively. only 91.6% of the variation in Ec, compared to 97.5% in the

In most commercial buildinas in hot and humid cli- momhly model.0)

mares. che cold deck supply temperature (Tc) is held cons cant For the weekday hourly model. the independent vari-throughout che year such that the average surface rempera- abIes To and T dp+ explain 77.6% and 5.7% of rhe variacion in

ture of the coil, Ts, is approximately 12.8°C (55°F). Ec, respecrively. The contribution of To did noc change much

However, in the EC a control problem resulted in Ts varying for the weekend hourly model, but the concribution from

between 10°C (50°F) and 21°C (70°F) (Katipamula and T dp+ almost doubled. Also, the model R2 for the weekend

Claridge 1992, 1993). Therefore, for the EC with the DDCV hourly model is three percemage points higher than the

system, a mean coil surface temperacure of 15.6°C (60°F) weekday hourly model. The contribution of qi to boch week-

was assumed. day and weekend hourly models is stacistically insignificanc.

For hourly and HOD modeling, the measured hourly The partial R2 for two typical \veekday and weekenddata were first sorted inco weekday and weekend groups hours (one during unoccupied hours and one during occupied

~ (holidays are treared as weekends). For HOD modeling, hours) are also surmn:1rized in Table 1. The general trend of

. these two groups were further sorted imo 24 subgroups, each che independent variables is similar co that of the hourly mod-

represeming the individual hour of the day (hour 0 midnight, els, except the model R2 is higher for HOD models. The

hour 100, ..., hour 2200, and hour 2300). model R2 values for the unoccupied hours on both weekdays

When developing an Iv1LR model, "stepwise" regression and weekends are higher compared to those of the occupied

is useful in identifying the contribution of each individual hours. Also, che model R2 values for the weekend models

variable in the model. Therefore. Ec for monthly, daily, two (both occupied and unoccupied) are higher compared to the

; - types of hourly models (weekday and weekend), and 48 weekday HOD models. The variation of the regression coeffi-

: TABLE 1

. : Summary of Stepwise Regression Analysis for DDCV Operation at the EC Building

; ;

Montnly Daily Hourly HOD

:: WO WE WO . WE

;

':.: ? 2 2? ? '2 22 2 2 2 2'; v~ PR- MR PR MR- PR- MR PR MR PR MR PR MR

.~.' U/O t lUO lUO UIO

~ . ("f.) ("10) ("f.J ("f.) (%) ("10) ("10) ("to) (%) (%) ("to} ("10)

To 95.9 95.9 87.1 87.1 77.6 77.6 74.7 I 74.7 82.2174.2 I 82.2/74.2 84.1/80.8 I ~.1/80.8

I 0.0 95.9 0.0 87.1 0.0 I 77.6 0.0 I 74.7 O.C/O.O I 82.2174.2 0.010.0 I 84.1/80.8

I * To 0.0 95.9 0.0 87.1 0.0 77.6 0.0 74.7 O.C/O.O I 82.2174.2 0.010.0 I ~.1,'80.8

r TZ 0.3 96.2 3.6 I 90.7 5.7 I 63.3 10.9 85.6 4.514.5 I SO.7na.7 3.SI 5.3 I 57.9186.:

V qi 1.3 I 97.5 0.9 91.6 0.0 I a3.3 0.6 I 86.2 0.3/0.2 I a7.0I7a.9 0.SlO.1 I 58.7i50.2

PR ~ :s Panla! R 2 and MR 2 is ,'Aodel R 2; WD is Weekday and WE is Wee.end. t u: U~oc=;pieo nour (500): 0: C=oied ,,:our (:"CC).

3895 5

;--

cient at individual hours for HOD models is shown in Figure £c. Both these loads are a strong function of To, which varies

"--' 3. The slope of To changed from 20% on weekdays to about from hour to hour, from day to day, and from month to month.

40% on weekends. while the slope of Tdp+ changed from This variation in To causes most of the change in £c. There-100% on weekdays to about 70% on weekends. fore. the partial R2 for To is high on all time scales. T dp+

Since the hot deck temperature (Th) is almost a constant explains about 5CJo to 10% of the variation in £c for hourly

" and very high in the EC building with the DDCV system, both models and about 4% for the dai1y model. As the time scale

I and ITo are statistically insignificant at all time scales. The increases from hourly to monthly, the correlation between To

envelope and ventilation loads account for more than 50% of and T dp+ also increases; therefore, the contribution of the inde-: :; pendent variable To to the mOdel is inflated and

: ~ ,:0 0.06 the contribution of T dp + is deflated.

: ~ ~ While the contribution of the internal gains

. : .~ 0.055 from lights and equipment to the cooling load is

'. . ;; ~ significant (30CJo and more), their contribution to

.' :. co:: : ~ 0.05 the model is small (1 % or less) because the diur-

.j ~ nal variation in qi is small compared to the diur-

.~ 0.045 nal variation in To or T dp' Therefore. qi explains

~ very little of the variation in £c for a building

8 0.04 0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19202122 23 with a DDCV system.

'" ~ Hour ofthc Day

. : f 0.08 MODEL IDENTIFICATION.£ OF YAY SYSTEM

j . g 0.07 .: : .z; In early 1991, the DDCV system In the EC

: ~ 0.06 bui1ding was retrofitted with a VAV system.

"= 0.05 Concurrencly, the hot and cold deck controls~ were corrected, and T c was fixed at l2.8°C

~ "~ 0.04 (55°F). Therefore. Ts was sec ac 12.8°C (55°F)

. ] 0.03 when idencifying models using Equation I.. ~ u 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2122 23 The data used for this analysis were from

" HourofthcDay January 1992 through December 1992. Analo-" (a) gous to the DDCV case. stepwise regression of

measured £c at mond1ly, daily, hourly, and0 HOD were performed using Equation 1 (Table

'.2 0.061//~~ ! 2). For the monthly model To, Tdp+' and qi are

.2 statistically significanc, explaining 95.1 %, 2.2CJo,

. 5 0.055 and 0.6% of the variacion in £c, respectively.

: . ~ 005 The model R2 is slightly higher than in thei :::. monthly DDCV syscem model. At the daily! ~ 0.045 level, all variables in the model, including I and

] I. TO' are staciscically significanL The stacistical

:":-: : g 0.04 significance of I and I.To means thac the VAV; '.1 u 0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20 2122 23 system in the EC reaches a minimum flow con-

'i . +~ HourofthcDay ".d T 2l 0 C(70 °F)Ex ti T

_.; '": ,.:: 0 1 diuon ac aroun lO = . cepc or 10'

. 1.' ~ .9:' all other variables explain more variacion in £c

"':".. ; g 0.09 on a daily time scale than on a monthly time" 'z;

..";~ ~ 0 08 scale.

. ~ . All variables entered in the two hourly

: ~

; ;" : '0 0.07 models (weekday and weekend) and 48 HOD

.. ." ~ ~ 006 models were statiscically significanL The gen-

. . ".; ]' era! trends across all models are similar, with

~~.. i ~ 0.050 1 2 3 4 5 6 7 8 91011121314151617181920212223. oneexception:thehou:lyweekendmodelan~a

: Hourofthc Day few HOD models (T dp ) account for more van~-

(b) cion in £c than does To. To and T dp+ explaIn

'-.t . most of the vari~tion in £c at all tIme scalesFiuure 3 VariaTion of the regression coefficient at each hollr of the day (about 90%). UnlIke the DDCV models, both I

.. forDDCVoperation: (a) weekday. (b) Iveekend. and I.To are statistically significant for all the

6 3895

. '0I .

TABLE 2

""-/ .. Summary of Stepwise Regression Analysis for VAV Operation at the EC Building

- r I

~onlhly Daily Hourly HOD

WD WE WD WE

2 ? ? ? 2 ? ? ? ? ? 2 ?VM PA MR- PR- MA- PR MR- PR- MR- PR- MR- PR MR-

.

U/oi u/o UfO u.'O

("I.J ("t.) (",) (%) (".J ("t.J <".) (".) ("to) <".J (".) (";'0)

To 95.1 95.1 83.2 I 83.2 01.0 81.0 13.7 13.7 6.0/79.6 I 6.0/79.6 81.1fl8.0 I 01.lfl8.0

I 0.0 95.1 0.7 83.9 0.9 81.9 0.5 I 14.2 0.511.3 I 6.5100.9 0.&0.5 I 81.6178.5

I * To 0.0 95.1 1.0 I 84.9 1.2 I 83.1 0.6 14.8 1.4/0.6 I 7.9/01.5 6.210.7 87.6179.2

T~ 2.2 I 97.3 7.2 I 92.1 6.6 I 89.7 77.0 I 91.8 85.6/9.7 I 93.7/91.2 2.2113.7 I 90.0192.9

qi 0.6 I 97.9 4.1 I 96.2 3.5 I 93.2 0.5 I 92.3 0.8/3.1 I 94.5194.3 1.4/0.1 I 91."'~3.0

? ? ?? t

?R - is ParuaJ R - and MR - is .Yodel R -; WD is Wee'day and WE is Weekend. U: UnCC:oJpied hour (500); 0: O=pied hour (1400).

VAV models (except on the monthly time scale). Also, qi is The general trend in the model R1 ofbo(h the WEL and

statistically significant for all models and explains more varia- MSB monmly models is similar (0 mat of me EC DDCV

tion during weekdays and occupied hours than during unoccu- monmly model except ma( T dp+ explains more variation in

pied hours. The reason for this is that there is more variation in £c. The model R1 for all three monthly DDCV models is high

me internal gains from lightS and equipment during occupied (more man 94%). In me case of the EC daily DDCV model. Tor- hours than during unoccupied hours. The variation of the explained 87.1 % of the variation in £c compared (0 onl y

'-.It' regression coefficient at each hour of day for HOD models is 6.6% and 4.5% by the WE- and MSB daily models, respec-

, . '. -' shown in Figure 4. All the coefficientS show significant tively. T dp+ explains 90.3% and 88.6% of the variation in £c

change over the 24-hour period (more (han 100%). on the daily time scale for WEL and MSB, respectively. There

In oeneral the coolino enero y us e of a bu ' ld ' 0 w.o\. a are two main reasons why T dp+ explains more of me variationO' ~ 0 I m~ Iul . £ . . .

VAV system is a stronger function of the therrnalloads on me m c: (I) both WEL..and M~B have outdoor air m.~es ofb .

ldi o\. 'oL DDCV b oL';'. more than 80% and (II) there IS more day-to-day vanauon ofUI ng Ulan one Wlul a system ecause Ule aIrIlOW IS .

. . . T dp'" than of To. The trends of the hourly and HOD models for

modulated (0 meet the comfort condluons. The modulauon of both .L "n::-T d MSB b .Idi . .1 . T +

. '1

d .

I h . I. d Ule yy L;.J- an UI ngs are SIffi1 ar. Again. dpaJrTIOW re uces slmu taneous eaung and coo m~, an thus I . .,. '" -d oL h I d.' .. - . exp aJns more varIatIon m Lc compare to Ule our y an

the coolIng energy IS a stronger functIon of Independent VarI-

HOD d I fro h EC ( d DDCV . ). -. mo e s m t e un er operat(on .

abIes. Therefore. the Independent variables T dp+ and qi - . . .

account for tWice as much variation in £c wim the VAV sys- . T~les :> and 6 show the regressIon results f~r ~wo bulld-tern (han wim (he DDCV system. mgs WIth the VA V systems (BUR and Wn'f buIldings). The

trends of all models for born BUR and WIN are similar toMODEL IDENTIFICATION mose of the EC models (underVAV operation).

. ACROSS SEVERAL BUILDINGS The trends across buildings for both the DDCV and VAV. . . . models appear to be consistent. except for T dp+' which

~ A general cha:actenzaClon of monmly, daily, hourly, and explains more variation in t::c for buildings with high outdoor

HOD models requIres more man one example. Therefore. t::c air intake. Fioure 5 shows me chanoe in the coefficient ofvari-'. models for four oilier buildings (two wim DDCV and tWo ation (CV) (as defined in Equati~n 3) with the addition of

:. with VAV systems) have been developed. more independent variables to the model. The trends of the

.' Tables 3 and 4 show me regression results for the tWO CV are similar to me model R1.

buildings wim the DDCV system (WEL and MSB buildings). The monmly models for both DDCV and VAVoperation

In both WEL and MSB buildings a major portion of the condi- had higher model R1 and lower CV than the other models,

tioned area is made up of laboratories; therefore. rfleir outdoor with only tWO independent variables-To and T dp+~xplain-

air intake is more than 80%. Since both WEL and MSB build- ing most of the variation in £c. The daily models had slightly

V;' ings are located in hot and humid climates (Austin and Hous- lower model R2 (2% (05%) and higher CV than the monmly

. ~.. ton. respectively), a major portion of their £c is from latent models. For me daily VAV models. all independent variables

ventilation. were statistically significant. which is in contrast to daily

3895 7

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3895

-, -

..TABLE 5

, Summary of Stepwise Regression Analysis for VAV Operation (BUR)

"'-/""""

, ':

,: ',~~!;!

Monthly Daily Hourly HOD

WD WE WD WE

I VM PR2 MR2 PR2 MR2 PR2 MR2 PR2 MR2 PR2 MR2 PR2 MR2

~ u,ct UJO UJO UJO

("I.) ("t.} ("I.) ("I.) ("!O) ("I.) ("!O) ("I.) ("t.) ("I.) ("t.) ("t.)

To 95.2 95.2 6.6 6.6 8.7 8.7 7.3 7.3 2.3/11.2 2.3/11.2 4.Ql8.1 4,0/8.1

; I 0.0 95.2 0.0 6.6 0,0 8.7 0.0 7.3 0.0/0.0 2.3/11.2 0.0/0.1 4.0/8.2

1* To 0.0 95.2 0.0 6.6 0.0 8.7 0.0 7.3 0.310.1 2.6111.3 O.QlO.2 4.0/8,4

TIn 3.6 98.8 90.3 96.9 85.4 94.1 86.3 93.6 93.6184.1 96.2195.4 92.9/88.0 I 96.9/96.4

I

Iq i 0.2 99.0 0.0 96.9 0.0 94.1 0.0 93.6 0.0/ 0.0 96.2195.4 0.0/ 0.0 96.9/96.4

: PR2 is PaniaJ R2 and MR2 is Model R2; WD is Weekday and WE is Weeksnd. t U:Uno=pied hour (SOO);O:Dccupied hour (1400).

. TABLE 6

~ Summary of Stepwise Regression Analysis for VAV Operation (WIN)

I

.

: Monthly Daily Hourty HOD

..: WO WE WD WE

,,-

,. ":. 2 ? 2 2I. j"'. 2 2 2 2 2 2 2 2 " R -PR .",

: ~ c.,; Var PR MR PR MR PR MR PR MR PR... Mn

; '..":..."." u,ct U/O U/O UfO

: ("!O) ("!O) ("to) ("/.) ("!O) {"I.} ("!O) ("t.) ("!O} ("!O) ("t.) ("to)

::j To 87.0 87.0 4.5 4.5 12.1 12.1 10.2 10.2 1.5/8.9 1.5/8.9 3.4/12.9 3.4/12.9

.1 I 0.0 87.0 0.1 4.6 0.6 12.7 0.0 10.2 1.0/0.2 2.5/9.1 0.9/0.0 4.3112.9

: I * To 0.0 87.0 0.9 5.5 0.0 12.7 0.0 10.2 0.1/0.0 2.619.1 0.2/0.0 4.5/12.9

,

; TIn 6.9 93.9 88.6 94.1 78.0 90.7 80.3 90.5 91.9177.5 94.5/86.6 91.3171.3 95.S/84.2

i qi 0.0 93.9 0.9 95.0 1.3 92.0 0.7 91.2 1.2/0.0 95.7/86.6 0.8/2.6 I 96.6186.8

PR2 is PaniaJ R2 and MR2 is Model R2; WD is Weekday and WE is Weeksnd. t U: Unoccupied hour (SOO); 0: Occupied hour (1400).

.i

.1 DDCV models, wherein only To and T dp + were significant and hour to hour, but t~ey are effectively constant from month

; The HOD models had higher model R2 and lower CV than the to month. However, over time there may be a change in qi or

; hourly models, but both models had lower model R2 and the system operation, which may affect the monthly Ec. Also

; higher CV than the corresponding monthly and daily mDdels. on the monthly time scale, the correlation between To and T dp+

.~ is stronger than on the daily or hourly time scale. Therefore, if

: MODEL EVALUATION there is a sicrnificant chancre in T d + from the modeled data set

0 0 p

j Although the monthly models show lower CV than daily, ~o the pr~diction data set, then the predicted Ec ~ay h<: signif-

~ hourl

y and HOD models the uncertainty in E P redicted with Icantly different from the measured value. In thiS section, the

.; , , c

d ,. ab . l . . f thl dail hId HOD

i the use of monthly models can be high. Because the engineer- pre ICtive cap I I ties 0 mon y, y. our y. an

.: ing equations (Reddy et al. 1993; Katiparnula et al. 1994) models are presented and compared to one another.

i show that Ec is a function of several independent ~ariables Accuracy and reliability of regression models are gener-

(To. T dp +, q j, I. I. To)' some of the information content in the ally assessed by comparing statistical indices such as coeffi-

~~ .~: data is probably lost in the process of averaging the variables cient of determination (R2). RMSE (root mean square errDr).

"'-(. -..' over the month. The independent variables that are not statisti- CV (coefficient Df variation), and MBE (mean bias error).

cally significant in the monthly models vary from day to day Such a comparison is reasonable, provided the models are all

3895 9

, .

TABLE 5

. Summary of Stepwise Regression Analysis for VAV Operation (BUR) ,

,:~ (; '."

! Monthly Daily Hourly HOD-: WO WE WD WE

i

,", 2 2 2 2 ? 2 22 ? ? ? ?

"1 Vat PR MR PR MR PR- MR PR MR PR- MR- PR- MR-

::,; UfO t u/O u/~ ' u/O

,. ,

.,.: (%) ('Yo) ("/0) ("10) (Of.) (%) ("/0) {"/oj ("10) ("10) {"/oj ("10)

:~] To 93.7 93.7 79.1 79.1 74.5 74.5 9.6 9.6 2.7/65.3 2.7/65.3 2.3/74.3 2.3/74.3

:.;j I 0.0 93.7 2.3 81.4 1.7 76.2 1.0 10.6 0.4/ 0.3 3.1/65.6 0.012.6 2.3/76.9'/

~'I 1* To 0.0 93.7 0.8 82.2 1.0 77.2 0.4 11.0 1.4/4.1 4.5169.7 0.010.4 2.3/77.3

~1 -r:

c; T dp 3.8 97.5 8.1 90.3 4.3 81.5 73.8 84.8 79.3/6.1 83.8/75.8 82.0112.2 84.3/89.5

"

"~ q i 0.0 97.5 2.3 92.6 2.0 83.5 0.1 84.9 0.1/2.8 83.9178.6 0.1/0.4 84.4/89.9

;j PR2 is Paniaj R2 and MR2 is Model R2; WD is Weekda~and WE is Weekend. t U: Uno=.pied hour (SOO); 0: Occ.Jpied hour (1400).

.;

~ TABLE 6

:.:~ Summary of Stepwise Regression Analysis for VAV Operation (WIN)"j

.

.j

'! Monthly Daily "Hourly HOD

~

i WD WE WO WE

. ,.-- 2 ? ? 2 2 ? 2 2 ? ? ? 2 ,

Vat PR MR- PR- MR PR MR- PR MR PR- MR- PR- MR {

~ "'-'" UfO t U/O u/o u/o ";::

I

"1

, ("I.) ("10) ("/0) ("/0) (%) ('Yo) ("/0), ("10) ("10) ("/0) ("10) ("/oj

i

-i '7'

" .L 0 94.7 94.7 84.1 84.1 77.3 77.3 76.8 76.8 76.8/74.0 76.8/74.0 80.3/74.4 80.3/74.4

1 I 0.0 94.7 0.2 84.3 0.0 77.3 0.1 76.9 1.010.9 77.8/74.9 0.010.1 80.3/74.5

:; I*To 0.0 94.7 0.9 85.2 1.4 78.7 0.4 77.3 1.010.4 78.8/75.3 0.010.1 80.3/74.6

"

:i Tk 2.5 97.2 5.5 90.7 3.9 82.6 6.9 84.2 5.3/5.6 84.1/80.9 4.9/7.8 85.2182.4

~i qi 0.0 972 0.6 91.3 1.5 84.1 1.0 85.2 0.011.1 84.1/82.0 0.012.6 85.2185.0

-j

.j

j PR2 is Partial R2 and MR2 is Model R2; WDis Weekday and WE is Weekend. t U: Unoa:upied hour (SOO); O:O=Jpied hour (1400).

;j

:) based on the same time scale. For models with a different time where j represents a month and n representS the total number,,;1 scale, it would be more meaningful to compare the predictive of months in the second data set For daily models, /!;c,j is

capability of the models, i.e., identify the regression models k = 31

; from a data set and then use the model to predict energy use I !::c,j, k,

~ for a second data period during which measured energy use is k = 1

1 also available. The predictive capability of models with differ- h k .th be fd '

th F h I cd I . t. " ..

E w ere 1S e num r 0 ays In a mon . or our y m e s 1

J ent tIme scales 1S compared by pred1ctJng c on the monthly, .

i daily, and hourly time scales; summing the daily, hourly, and IS k = 31[ g = 24 ]i HOD predictions to a monthly value; and then computing the I IE.

k . . .

k 1 1 C,)"g ; CV and the MBE on the monthly tJme scale. 0= g =,J The RMSE is computed as The CV is defined as

1

I

: IE CV=~ (3) . )= 2 E l- IE. - /!;c j - C ,: \.,.../ j = Il C,) , I (2) where Ec is the mean monthly cooling energy use of the sec- "--.

RMSE = n ond data set. The MBE is computed as

10 3895

. .. -

.

I

2D 25

V ~" - MonIhly , - Malth!y

..". 18., Daily .', "..Daily.. . , H . ,

'. ': , -- OO1ly . , - Hoozl

y, . 16' "" --, . "..-" . , . . - HOD ~. . - HOD

:., .".".,. "'"'-i 14' \ . . . . . . . .~ - .

. "'- r.. .. ,",,' . -, .

; ~ '" '---~ ".

12 ", , IS ".'. ""..'. . . ".""."""..

. '-" 10 ' '-" '.""".'.

, > 8 ~ .' > 10 """...'U6 U

i 4 5, --

: 2

.J 0 0

, To Tdp+ ~ I*To I qsol To TdP+ qi I*To I ~ol

.~ (C) (f)

.; 25 2D ,; - MonIhly ',- Malth1y

: Daily 18, Dail

y. 0 0 ,0 - Hourly ° " - Hourly

". 2D ° ...HOD 16'. ' ". ".HOD

" ' 0 . "... . . . ", 14 . ". - -

" ~ \ ~ '0. ".- .:; ~ IS "

\ ~ 12 "".",., . . . . . .

"-" '-" '."

~., 10 '.: > "" - . . . .'.'_..:.: ' . . ...'.'-..:.: ' > " 10 8

"". r , U. \:;~ U 6

Y'::..:.;t 5 4

i 2

! 0 0

: To TdP+ ~ I*To I qsol To TdP+ qi I*To I qsol

~

~ (b) (e)

,

: 2D; 14 - Ma11h1y " - Malth!yj Daily 18', Daily': - Hourly ',- HOJrly, 12 . . . HOD 16 ." . . . HOD, . "

,: '. ,j 14 '. . "

1 ~10 ~ '0.0. ""1 ~ ' ~ o '..'

., 12 ..."-\ . .'- .. '-".' ., -j - . - '-" 8 . "'-:--:-:-:-:-:-:-:-:-:-:-:-:--:-:-: '-" 1 0 .'..' . . . . . . ---

"I> :. '. > ". ."""

1 6 '."' ". 8 " ",,~--~=:="".'..'.'."I

U """""""""""" U " 6

. 4I 4

:1 2"I 2.,1 0 0

1 ' To TdP+ ~ I*To I qsol To TdP+ qi I*To I ~ol

'; -. : (a) (d).; ~-,' Figure 5 Change in CVwith addition ojindependenrvariables to the model (Eq!tation 1). (a) ECDDC\-:- (b) WELDDC'v; (c)

MSB DDC'v; (d) EC VA V). (e) BUR VA'v; and if) WIN VA\-:

3895 II

. .-. .

TABLE 7 TABLE 8

Comparison of the Predictive Ability of Different Models Advantages and Disadvantages of Different Models

'"-,,,Site I Modeling Penod

I Indices I lknthly I Daily I Hourly I HOC I I-'"'nthly i Daily Hourly

I HOC

IdentificatIon! PrediCtIon I ' !

'AS8 I Jan. . Cec. '92 I Jan. . Cec. '931 CV I 8.4 4.8

I 5.8 I 5.1 Mode.ng I I

I I: (CCCY) J ,M8E -2.2 00.6 00,7 00.9 Effon Mnimum I Mnimum Ikderate . Difficult

8UR

I Jan..cec.'92 I Jan..Dec. 93 1 CV I 9,9 7.5 1 9.1 I 9.1 Melenngand I I I(VAY) M8E -8.2 -6.5 -6.4 -7.7 Monrtoring None' ReQuired Required ReQUired

WIN

I Jan..Dec.'92 I Jan..CeC-'93 1 CV I 15.3 15,2 1 15.7 1 15.5 DataNeeoed '. '

I(VAY) M8E .12.6 -12.0 -10,7 -11.8 for Robust ! 12months

I 3.6momhs 3-6 months'

I 3-6 months'

Modeling 1 or more or more or more or more

ApplicaDtlily

I I I '

. . to Savings In some In most .oJ1 .oJ1

; j = /I MeasurementS, cases cases cases I cases

: L. (E . - !::c,V PrediCtIon I Hign I Low I Ikderate I Low

1 . - I C,)

(4) Uncenalnty

)- O&M

I I I; MBE = -. Opponuni1les Umiled Possible Appropriate MoS!

. nEc Det8C\1on aopropriare

j DynamIC

I I I, The second data set which is different from me one used Control No Possible Ves Best

. '

, to identify me model. also has one calendar year's worth of , If monthly billing data available. - If only 3 months 01 data are available then the, data. Onl y three of me five buildinas have one additionalY ear data should not ce soneo IntO WC and WE groups be~se regresSjon models is such: 0 Instances have ceen found to be lnappropnate lor prediCtIng annual energy use.

: of data because me oilier two buildings were retrofitted. Table

: , 7 compares me CV and the MBE between me models for the daily and HOD models were more accurate at predicting

: MSB, BUR, and WIN buildings. The daily models have lower future energy use,

CV values, followed by HOD, hourly, and monmly values, 5. The HOD models had higher R2 and lower CV than the

respectively. For the MSB building, the difference between hourly models because some of the scheduling effects

monthly and daily (and HOD) models is high because it is were minimized by modeling the energy consumption

located in the hot and humid climate of Houston and takes in by the HOD method.

more than 80% outdoor air. Since To and T d + are highly cor- 6. Compared to the base model (£c = a + BoT 0' Tables I

related at the monmly level, the predicted tc is significantly through 6), the MLR models showed a decrease in CV

different from the measured energy use. There is no clear of between 12% and 54%. The range for the DDCV

trend in the MBE for the three sites. The MBE for the MSB models was between 12% and 47%; for the VAV mod-

\-! building is less than 1% for daily, hourly, and HOD models, els, it was between 17% and 54%. The average decrease

while it is about-2.2% for the monthly model. The MBE of - in the CV with VAV MLR models was 33%,-which was

2.2% means that the predicted £c is less than the measured higher than that of the DDCV MLR models (30%).

I value over the year by 2.2%. In early 1993, the air-handling

unitS at both BUR and WIN were rolled back durin a the Table 8 sununarizes me advantages and disadvantages of

unoccupied hours of the day; this is probably why the ~E the different modeling approaches. Modeling on a monthly or

~ for both buildin!!S is neoative and rather high. daily time scale requires minimum effort, while the HOD

: 0 ° modeling requires the maximum effort because it involves

CONCLUSIONS developing 48 models (24 weekday and 24 weekend models).

A piecewise multiple linear regression model that essen- In ~ost cases, the data re~~ire~ for m~nthly ~alysis can. be: ; tially captures most of the physical interactions taking place in obtained !ro~ ~onthly. uullty bills, whl~e dedicated metenng

,.1 an actual HVAC system was used to model me cooling energy and momtonng I~ required ~ collect daily, ho~rly, and HOD: consumption of five larae commercial buildinos in Texas energy consumpuon. An earlier study by Rachlm et al. (1986)

, : (three with DDCV and three with VA V systems) °on monthly, suggested .mat ~ight months of mon~ly data are sufficien: to

; daily hourly and HOD bases. The major conclusions from model resldenual or small commerCIal energy consumpuon.

i

thi ' tud ' ti 110 S However, to model large commercial buildings on a monthly

J ss yareas 0 w.

; time scale requires 12 months or more of data. In order to

:1 1. To and T dp + accounted for more than 90% of the varia- accurately predict annual energy use using daily regression

~ tion in the cooling energy consumption on all time models, at least three to six months of data are required

'; scales for both DDCV and VAV systems. (Kissock et al. 1993), while no analysis has yet been done to

,1 2. On a monthly time scale, only tWo independent vari- determine how much data are required for hourly or HOD

'; abIes (To and T dp+) explained most of the variation for regression models. Since the daily models require three to six

both DDCV and VA V systems. months of data, this period may be valid for hourly or HOD

3. For daily VAV models. all independent vari~bles were models as well.significant, while only To and T dp+ were significant for Currently, monthly models are being used to evaluate ret-

, the daily DDCV models. rofit savings in residences and small commercial buildings '.

'--! 4. Although the monthly models had higher R2 and lower (Fels 1986). However, their usefulness to measure savings

CV values than the daily, hourly, and HOD models, the from retrofitS in large conunercial buildings has not yet been

12 3895

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""

°. . ..':*.,

thoroughly investigated. This study suggests that the daily REFERENCES. .- models are better than monthly and hourly models at predict-. .

\, ) ing Ec over a year. Since the effort required to develop and Clandge, D.E.. J.S. Ha?erl, ~. ;IU. J. Houcek. and A. Athar.

use the daily model is less than that for HOD models. the daily 1994. Can you ~chleve 1)9. ACEEE 1994 Summer Study

model is probably most appropriate for measuring savings .on Energy EfficIency: pp. ):73-5.88.from retrofits in larae commercial buildinas if sufficient data Darnel, C., F.S. Wood, WIth assIstance of J. W. Gorman. 1980.are available. For p;edictina the annual e;eray consumption Fitting eqLlations to data: Computer analysis of multifac-

hourly and HOD models sh~uld be considered instead of dail; . tor data, 2d ed. New York: John Wiley and. Sons.or monthly models only if less than six months of hourly data DIamond, S.C., and B.D.. Hunn: 1981. Companson of DOE-2

are available. In any case, HOD models have been found to be computer program slmulauons to metered data for seven

superior to hourly models. commercial buildings. ASHRAE Transactions 87(1):

AIth gh . d . 12??-1?31ou metenng an momtoring are general1y used for -- -'. . . .b.il1ing, measuring retrofit savings, and evaluating demand- Dra~r, N., and H. S~th. 1981. ApplIed regressIon analysIs,

sIde management programs, monitoring can be a powerful _d ed. New York. John \Viley & Sons.

tool to help detect O&M opportunities. To identify O&M Fels, M., ed. 1986. Special issue devoted to measuring energy

opportUnities and to measure savings from O&M opportUni- savings, the Princeton scorekeeping method (PRISi\ll).

ties, hourly and HOD modeling are the most appropriate Energy and BLlildings 9( I &2).

approaches because of their higher time resolution (Claridge Katipamula, S., and D.E. Claridge. 1992. Monitored air han-

et al. 1994; Liu et aI. 1994). Daily modeling can be used if the dler performance and comparison with a simplified sys-

level of savings from the O&M changes is high (5% or more tern model. ASHRAE Transactions 98(2): 341-351.

of the energy consumption). At the monthly level, it may be Katipamula, S., and D.E. Claridge. 1993. Use of simplified

difficult to detect any O&M opportunities. Also, hourly and system models to measure retrofit energy savings. Jour-

~I HOD models can be used for real-time control of the building. nal of Solar Energy Engineering 116(2).

~. Katipamula, S.. T.A. Reddy, and D.E. Claridge. 1994. Devel-

ACKNOWLEDGMENTS opment and application of regression models to predict

This work was funded by the Texas State Energy Con- ~ooling energy cons~mption in large commercial build-

servation Office of the Inter2overnmental Division of the mgs. ASME-Internatlonal Solar Energy Conference, San

V :" General Services Commissio; (State Agencies Pro2ram) as Fransico, CA, March.

. '~., part of the LoanSTAR monitoring and analysis proiram. We Kissack, J.K., J.S. Haberl, D.E. Claridge, and T.A. Reddy.

would like to thank Aamer Athar and Curtis Boecke,for pro- 1992. Measuring retrofit savings for the Texas Loan-

viding timely information regarding the metering and site- STAR program: Preliminary methodology and results.

related information. Also we thank Ron Chambers and Rob- Proceedings of the ASl\1E/JSES/KSES International Solar

ert Sparks for maintaining the measured data and providing Energy Conference, Maui, HI, pp. 299-308.excellent data base support. Finally, we thank the technical Kissack, J.K., T.A. Reddy, D. Fletcher, and D.E. Claridge.support group and Dean Wil1is in particular. 1993. The effect of short data periods on the annual pre-

diction accuracy of temperarure-dependent regressionNOMENCLATURE models of commercial buildings' energy use. Proceedings

E = energy use (GJ/h) of the AS1\1E/~SES/SED Inre~tional Solar~Energy Con-

GJ . J I 10 9 J I ference, WashIngton, DC, Apnl, pp. 455-46-,.= gIg a ou es = ou es. .

. . .., LIU, M., J. Houcek, A. Athar, T.A. Reddy, and D.E. Clandge.

qsol = global honzonral solar radlauon (GJ/m-/h) 1994. Identifying and implementing improved operation

T = dry-bulb temperature (OC) and maintenance measures in Texas LoanSTAR build-

T' = dry-bulb temperature at minimum flow condition ings. ACEEE 1994 Summer SrLldy on Energy Efficiency,(OC) pp. 5.153-5.166.

Tc = cooling coil leaving air dry-bulb temperature (OC) Rachlin, J., M. Fels, and R. Sacolow. 1986. The stability of

T h = heating coil leaving air dry-bulb temperature (OC) PRISM estimates. Energy and Buildings 9( I &2).

. Reddy, T.A., S. Katipamula, and D.E. Claridge. 1993. The

Subscripts functional basis of air-side thermal energy use in

c = coolina HVAC systems. Energy Systems Laboratory, Reportd td :0 d . t ( O C) No. ESL-PA-94/01. Col1e2e Station: Texas A&M Uni-

p = ou oar ew-pom temperature .-. verslty.

~1 = ~eaung . Ruch, D., and D.E. Claridge. 1992. A four parameter change-

\-.) L = Internal gaIns (GJ/h) point model for predicting energy consumption in com-o = outdoor dry-bulb temperature (OC) mercial buildings. Journal of Solar Energy Engineerings = surface temperature (OC) 114(2): 77-84.

3895 13

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,.~' ..,;.. --

Ruch. D.. L. Chen. l.S. Haberl. and D.E. Claridge. 1993. A Wu. l.X:, T.A. Reddy. and D.E. Claridge. 1992. Statistical..:\; change point principal component analysis (CP/PCA) m~d~ling o~ daily ~nergy con~umption !n .commercial ,~.

:"'-'"method fior pred .ct .na e e a . . I b .ld buIldings USing multIple regressIon and pnnc1pal compo- :

I I n r y usaae In commercIa U1 - . -. . . '..

, . ~ .,., . nent analysIs. Proceedings of the EIghth SymposIum on

Ings: The PCA model. Journal of Solar Energ)' Engmeer- Improving Building Systems in Hot and Humid Climates,. ; ing 115(2): 77-84. Dallas, May, pp. 155-164.

, .,

, i

;; APPENDIX

.j TABLE A1 (51)

;~ Building Characteristics

I

i Building Roor ExternaJ Area ConStruction~ Iazing % of Glazing Type O~door Supply Building Operation

; fType Area (m2 NaJl+Glass (m2 xternaJ Ar~ ~a Intake Temp. (oC) PeoplelHVAC (hrs/day)

; (%) 7'c/Max.Th

: EC/1 30,150 3.810 Insulated I 22 Single 10-20 15.6/40.6 12/24

I" (DDCV) Cement Blodt Pane

.'~ EC/1 30,150 3.810 Insulated I 22 Single 10-20 12.8/40.6 12/24

I:' (VAV) Cement Blodt Pane

...: WEll1 40.850 6,230 Red Face Brid<j 17 Single 90 12.8135 12/24

II on Blodt I Pane

-; MSB/1 82,400 NlA Cementatious

I NA Single 70 12.8/20.4 9/24

IPlaster Pane

BUR/2 9,610 3,250 Pre-Cast I 7 Single 10-15 12.8135 12/24I (

; "-" Cement Blodt Pane .~..-1 WIN12 10.130 4.000 Cement Blodtl 10 Single 10-15 12.8135 12/24

I: ~th Face Bri~ Pane

.,

1 :Class/Lab'Ottice; 2.-CIass/Ottice,

, TABLE A2 (IP)

~ Building Characteristics

.J

:"1

~

.1 . .:i Building Floor External Area ConStruction Glazing % of Glazing Type Outdoor Supply Building Operation" I. /Type fArea (ft2 NaJl+G1ass (ft2 ExternaJ Are. Jia Intake Temp. (° F) Peopie/HVAC (hrs/day)

. (%) TclMax. Th

~ EC/1 324,500 41,000 Insulated. 22 Single 10-20 601105 12/24

I-:j (DDCV) Cement Blodt Pane ,

:1 EC/1 324.500 . 41,000 Insulated 22 Single 10-~ 551105 12/24

I1 (VAV) Cement Bloc!< Pane

::1 WW1 440,000 68.000 ~ed Face Brid 17 Single 90 55195 12/24

I,I on Bloc!< Pane

;1 MSB/1 887,000 NlA Cementatious NA Single 70 55185 9/24

I~ Plaster PaneI

I.1 BUR/2 103,500 35,000 Pre-Cast 7 Single 10-15 55/95 12/24

. i Cement Bloc!< Pane

'; WIN12 109,000 43,000 Cement Blodt 10 Single 10-15 55195 12/24

I: Hith Face Brid Pane

IiV 1 :C1ass/Lab/Ottice; 2:Class/0ttice \,.-

14 3895

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