Journal Identification = ENB Article Identification = 3178 Date: May 19, 2011 Time: 12:42 am

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Energy and Buildings

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ncorporation of latent loads into the cooling degree days concept

orazd Krese, Matjaz Prek ∗, Vincenc Butalaniversity of Ljubljana, Faculty of Mechanical Engineering, Askerceva 6, 1000 Ljubljana, Slovenia

r t i c l e i n f o

rticle history:eceived 27 December 2010eceived in revised form 31 January 2011ccepted 20 March 2011

eywords:

a b s t r a c t

The cooling degree days concept is a tool to estimate and analyze weather related energy consumptionin buildings, i.e. the cooling system electric energy consumption. The main problem with applying thismethod is that it disregards latent cooling loads. This paper deals with an approach for monitoring electricenergy consumption due to cooling in buildings based on cooling degree days, which allows an estimationof latent loads. In addition to applying methods for determining base temperature to base humidity, a

ooling degree dayooling loadatent loadase temperature-testerformance surface

new technique is introduced, which is based on a significance test of the enthalpy latent days partialregression coefficient. Analogous to the performance line concept, the influence of latent loads can bepresented in the form of a “performance surface” graph. The performance surface is a plot of electricenergy consumption as a function of cooling degree days and latent enthalpy days. The above methodsare tested on data sets consisting of electric energy consumption data obtained from two buildings andhourly meteorological data.

. Introduction

In times when energy prices are continuously reaching neweights and rising electric energy consumption due to air condi-ioning in buildings as a consequence of global warming, an analysisf electric energy consumption in buildings is crucial, because thenergy savings potential of HVAC systems is estimated to be up to5%. While computer simulations are becoming more and moreccurate, other simpler methods for energy estimation are stillmportant as is shown by Day et al. [1]. One of these simple meth-ds is the cooling degree day method. Cooling degree days (CDD)re the summation of temperature differences between the outside0 and a reference temperature �b:

DD =∑(

�0 − �b

)(1)

The reference temperature is known as the base temperature,hich is a balance point temperature at which the cooling sys-

em does not need to run to maintain comfortable conditions. Itepresents the set indoor temperature, lowered due to internalnd external heat gains and is, as such, specific for each build-ng. Therefore, base temperature should be determined for each

uilding individually instead of using degree days calculated to atandard reference temperature as is given in [2] and described byli et al. [3].

∗ Corresponding author. Tel.: +386 1 4774 312; fax: +386 1 2518 567.E-mail address: matjaz.prek@fs.uni-lj.si (M. Prek).

378-7788/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.enbuild.2011.03.042

© 2011 Elsevier B.V. All rights reserved.

The main disadvantage of the degree day method is that itneglects the influence of latent loads, which become more signifi-cant at higher outdoor temperatures. Huang et al. [4] and Sailor [5,6]introduced the use of enthalpy latent days (ELD) to incorporate theinfluence of humidity on energy consumption. Enthalpy latent daysare the summation of enthalpy differences between the outdoor airenthalpy h0 and enthalpy at the outdoor air temperature �b and areference absolute humidity xb:

ELD = 124

×24∑i=1

[h0(�0, x0) − hb(�0, xb)

](2)

Ihara et al. [7] used a similar concept to determine the sensitivityof electricity consumption to air temperature and air humid-ity in selected business districts of Tokyo, but with referencehumidity determined for each district separately and with momen-tary temperature/humidity differences instead of summations oftemperature/humidity differences over time (i.e. CDD and ELD).Principal component analysis (PCA) was used in a study carriedout by Lam et al. [8] to investigate seasonal variations in electricityuse in 20 air-conditioned office buildings in Hong Kong as a func-tion of dry-bulb temperature, wet-bulb temperature, global solarradiation, wind speed and clearness index. Since the new variablesderived by PCA (i.e. principal components) are linear combinationsof original ones, their physical meaning is obscure and one cannotdetermine the sensible/latent portion of the buildings cooling load

or even a threshold temperature/humidity at which the coolingsystem starts to operate.

In this paper a new approach for monitoring electric energyconsumption based on the concept of degree and latent enthalpy

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1758 G. Krese et al. / Energy and Buildings 43 (2011) 1757–1764

ature;

dd

2

cdt

2

etbdcacp(cbsl

Fig. 1. (a) Energy sign

ays is presented and tested on real building performanceata.

. Theory

In this section approaches for monitoring electric energyonsumption in existing buildings and statistical methods foretermining base temperatures are described. In addition, a newechnique for determining base humidity is presented.

.1. Monitoring electric energy consumption

There are two common approaches for monitoring electricnergy consumption in existing buildings by means of outdooremperature. One approach is to plot an energy signature for auilding, which is a plot of daily energy consumption against meanaily temperature as shown in Fig. 1a. Since cooling degree daysapture both the extremity and duration of outdoor temperatures,better way to analyze electric energy consumption for building

ooling is to use performance lines. A building performance line is alot of monthly energy consumption against monthly degree daysFig. 1b). The main advantage of performance lines, apart from using

ooling degree days instead of outdoor temperatures, is that they,ecause of using monthly values, require significantly smaller dataets than equivalent daily energy signatures and so exhibit muchess scatter [2].

Fig. 2. Performan

(b) performance line.

To include the influence of latent loads on energy consumptionwe defined the performance surface analogously to the perfor-mance line concept. The performance surface is a plot of monthlyelectric energy against monthly cooling degree and latent enthalpydays as shown in Fig. 2. In contrast to the building power line, theperformance surface E makes it possible to observe building’s elec-tric energy consumption regarding both sensible and latent loadsin the form of CDD and ELD:

E = E0 +(

�E

�CDD

)× CDD +

(�E

�ELD

)× ELD (3)

E0 the intercept with the z-axis represents the building baseload, while the cooling degree day’s partial regression coefficient(�E/�CDD) is lower compared to the regression coefficient of theperformance line obtained from the same data because latent loadsare included in the regression model.

2.2. Determination of base temperature

Because analytical determination of base temperatures is com-plex and time-consuming mainly statistical methods are used [9].We can obtain a building’s base temperature from energy sig-natures by using piecewise linear regression to determine theintercept of weather dependent and independent electric energy

consumption. Another statistical method for determining basetemperature of a building is based on the performance line.Instead of using linear regression we use second order polyno-mial regression and determine the base value by a variation of

ce surface.

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G. Krese et al. / Energy and Buildings 43 (2011) 1757–1764 1759

) via e

bcl

2

toc

wpsf

C

E

cm

(

Fig. 3. Base temperature determination: (a

ase temperature so that the quadratic term’s regression coeffi-ient becomes zero or the polynomial best fit is almost equal toinear. Both methods are shown in Fig. 3.

.3. Determining base humidity with the F-test method

In addition to applying methods for determining base tempera-ure to base humidity (Fig. 4) we developed a new technique basedn a significance test of the enthalpy latent day’s partial regressionoefficient.

First, we need to calculate monthly/weekly cooling degree daysith the base temperature determined via the energy signature orerformance line method (Section 2.2) and the latent enthalpy daystarting at a random base humidity, e.g., average absolute humidityor a given time interval.

DD =N∑

j=1

(�0,j − �b)

�0,j>�b

(4)

LD = r0 ×N∑

j=1

(x0,j − xb)

�0,j>�b;x0,j>xb

(5)

From electric energy consumption data and the correspondingooling degree and latent enthalpy we construct two regressionodels for the treated building:

(a) performance surface:

E = E0 +(

�E

�CDD

)× CDD +

(�E

�ELD

)× ELD (6)

b) performance line:

E∗ = E0 +(

�E

�CDD

)∗− CDD (7)

We formulate two statistical hypothesizes:

Fig. 4. Applied methods for determining base humidity: (a) e

nergy signature, (b) via performance line.

(a) Null hypothesis: latent enthalpy day’s partial regression coef-ficient is insignificant

H0 :(

�E

�ELD

)= 0 (8)

(b) Alternative hypothesis: latent enthalpy day’s partial regressioncoefficient is significant

H0 :(

�E

�ELD

)/= 0 (9)

The null-hypothesis is tested with F-test:

F = SSE∗ − SSE

MSE(10)

where SSE* is the performance line’s residual sum of squares, SSE isthe performance surface’s residual sum of squares and MSE is theperformance surface’s residual mean square.

The base humidity is determined by a variation such that theF-number of significance test is larger than the critical value Fcrit ofthe F-statistics at the chosen significance level ˛:

xb = x → F > Fcrit (11)

3. Evaluation

The approach using the performance surface and base humiditywas tested on two buildings from which electric energy consump-tion and meteorological data was obtained.

3.1. Data

3.1.1. BuildingsThe selected buildings are located in Ljubljana, the capital

of Slovenia. Building A is 13 story office building built in 1973with 7200 m2 of air-conditioned offices, while building B is a 5story hotel and congress center built in 2004 with 844 m2 of air-conditioned spaces. Both buildings are equipped with multiple

nergy signature method, (b) performance line method.

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1760 G. Krese et al. / Energy and Buildings 43 (2011) 1757–1764

Table 1Considered buildings overview.

Building A Building B

Location Ljubljana, Slovenia Ljubljana, SloveniaBuilding type Office building Hotel and conference roomsGross net area [m2] 7200 9500Number of floors 13 5Area conditioned [m2] 3970.6/1893.3 844Volume conditioned [m3] 15,483/7383.8 3376Occupation schedule 7:00–17:00 7:00–24:00Maximum number of occupants 480 450Installed lighting and appliances power [W/m2] 12 12Other equipment [kW] 22 2External wall area [m2] 1950 1960External wall U-value [W/m2 K] 2.4 0.98–1.37Roof/ceiling area [m2] 553.8 –Roof/ceiling area U-value [W/m2 K] 0.8 0.36Floor area [m2] 553.8 –Floor area U-value [W/m2 K] – 0.36Window area [m2] 2340 2070Glazing type Double DoubleWindow (frame + glazing) U-value [W/m2 K] 2.4 1.1 (Ar); 1.4Window g-value 0.75 0.8Shading device Internal shade Internal shadeHVAC system Air and water 4-pipe induction system/CAV system Air and water 4-pipe fan-coil systemChiller type 2× water cooled vapor-compression liquid chiller Water cooled vapor-compression liquid chillerCooling capacity [kW] 2 × 550 342

cviai

3

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fJta

3m

asiisr

E

wcxtvc

Table 2.For all three datasets, the global irradiance and wind velocity

were proven to be statistically insignificant. The confidence lev-els for partial regression coefficients of temperature and absolute

Table 2Regression analysis of an unrestricted regression model.

ˇ t 1 − p(t)

Building A 2007� 0.71 10.69 1x 0.33 5.57 1Iglob −0.06 −1.02 0.69v −0.05 −1.09 0.72

Building A 2009–2010� 0.50 6.83 1x 0.50 7.96 1Iglob 0.08 1.45 0.85v −0.05 −1.10 0.72

Building B

Nominal electrical power [kW] 2 × 219Moisture control YesHumidifier type Water spray

entralized HVAC systems. The air conditioning in building A is pro-ided by a 4-pipe air and water induction system, while building Bs equipped with a 4-pipe fan-coil system. Additional informationbout the tested buildings and the installed HVAC systems is listedn Table 1.

.1.2. Electric power consumption and meteorological dataElectric power consumption data for each building was obtained

n the form of 15-min total electric power readings from Elektrojubljana, a local electricity distribution company, with permissionrom the buildings owners. Hourly meteorological data was pro-ided by The Environmental Agency of the Republic of SloveniaARSO).

For building A, data for the two time intervals was gatheredor 2007 and for the period from February 2009 to the end ofanuary 2010 (1 year). In contrast, for building B only data forhe interval from May 2009 to the end March 2010 was avail-ble.

.2. Sensitivity test of electric energy consumption for selectedeteorological variables

To find out if the given data was appropriate for testing the newpproach, a sensitivity test of electric energy consumption to out-ide air temperature (dry-bulb) and absolute humidity plus globalrradiance and wind velocity was made. For an easier comparison ofndividual meteorological variables impact on electric energy con-umption, all the variables were standardized and the followingegression model was constructed:

stand = ˇ1 × �stand + ˇ2 × xstand + ˇ3 × Iglob,stand + ˇ4 × vstand (12)

here Estand is the buildings predicted standardized electric energyonsumption, �stand is standardized outdoor dry-bulb temperature,

stand is the standardized outdoor absolute humidity, Iglob, stand ishe standardized global irradiance, vstand is the standardized windelocity and the coefficients ˇ1–ˇ4 are standardized regressionoefficients, i.e. the so-called beta weights.

148.5No–

For analysis only hourly values at 12.00 local standard time (CET)were taken. Weekend, holiday and other data that stood out werefiltered out and energy signatures for each time period and mete-orological variable were plotted (Fig. 5).

From the energy signatures for both buildings it was evidentthat the highest correlation among all meteorological variables wasbetween temperature and electric energy consumption. Thereforeonly those sampling units (�i, xi, Iglob,i, vi) were included in theregression models where the temperature was higher than the basetemperature as shown in Fig. 6.

E = f(

�, x, Iglob, v)

�>�b(13)

Base temperatures for each building and the observed time spanwere determined using piecewise linear regression. A t-test at a0.05 level of significance was performed to check the significanceof individual regression coefficients. The results are summarized in

� 0.77 7.32 1x 0.10 1.09 0.72Iglob −0.08 −0.96 0.66v −0.07 −1.10 0.73

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G. Krese et al. / Energy and Buildings 43 (2011) 1757–1764 1761

res of

hwicicg˛

E

tf

3

ip

3

dnibw

TR

We were not able to select an appropriate time interval or deter-mine the base temperature and humidity for building B, due to highbuilding base load fluctuation, which was seen in the form of highly

Fig. 5. Energy signatu

umidity were high (i.e. higher than minimal confidence level),ith the exception of the regression coefficient of absolute humid-

ty in the regression model for building B, which had a similar lowonfidence to wind velocity and global irradiance. In order to verifyf the low confidence level of humidity’s partial regression coeffi-ient for building B was the consequence of the interaction withlobal irradiance and wind velocity, another test of significance (at= 0.05) for a restricted regression model was made:

stand = ˇ1 × �stand + ˇ2 × xstand (14)

The results are listed in Table 3. The confidence levels for the par-ial regression coefficients of temperature and absolute humidityor all datasets were above the minimal level of 0.95.

.3. Determination of base values

Base values (i.e. base temperature and humidity) for each build-ng and given time period were determined by the energy signature,erformance line and F-test method.

.3.1. Via energy signaturesBecause internal and external heat gains vary throughout the

ay, hourly base values were calculated from hourly energy sig-

atures (already filtered) to establish the most appropriate time

nterval for determination of base values. Further daily progress ofase dry-bulb �b, wet-bulb �w,b and dew point �d,b temperaturesere plotted as shown in Figs. 7–10.

able 3egression analysis of a restricted regression model.

ˇ t 1 − p(t)

Building A 2007� 0.67 14.26 1x 0.37 7.87 1

Building A 2009–2010� 0.55 11.36 1x 0.47 9.57 1

Building B� 0.68 9.88 1x 0.16 2.25 0.97

building A for 2007.

From building’s A daily progress for both periods it was clear,ignoring the extreme values (i.e. between 4 and 6 a.m.), which werethe consequence of poor correlation, that the lowest base temper-atures were achieved in early morning and late evening hours. Thisis absurd from the theoretical point of view, since heat gains werethe lowest at that time, thus the base temperatures should havebeen the highest. Further investigation showed that the anoma-lies were the effect of available electric energy consumption data.Because total electric energy consumption was used, the buildingbase load also affected the determination of base values. Low basevalues early in the morning and late in evening were the result ofa 50% reduction in the ventilation rate between 8 p.m. and 6 a.m.during winter operation. For this reason there is a jump in buildingbase load between the transitions from winter to summer regime,therefore the determined base value is lower than the actual basetemperature (see Fig. 9).

The most appropriate time interval should then lie between6 a.m. and 8 p.m., however a different interval from 7.00 (transitionfrom standard to summer time) to 15.00 was chosen due to higherscatter after 15.00. The base values obtained from the selected timeinterval are listed in Table 4.

negative slopes of regression lines on the left side of base values, i.e.

Fig. 6. Data included in the regression model.

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1762 G. Krese et al. / Energy and Buildings 43 (2011) 1757–1764

Fig. 7. Daily progress of building A base values for the period January 2007–December 2007.

Fig. 8. Daily progress of building A base values for the period February 2009–January 2010.

TBf

Fig. 9. Daily progress of building B base value

able 4ase values determined using the energy signature method for the time interval

rom 7:00 to 15:00.

Building A 2007 Building A 2009–2010

R2 R2

�b (◦C) 13.38 0.80 17.10 0.79xb (g kg−1) 5.96 0.62 8.47 0.76

s for the period May 2009–April 2010.

on the weather independent side of the energy signatures (Fig. 11).Therefore building B was excluded from further analysis.

3.3.2. Via performance lines and F-test

As stated previously, the base temperature and humidity were

also calculated using the performance line method (see Section2.2). For each given time period for building A (B was droppedout) the base values were determined twice, once with CDD and

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G. Krese et al. / Energy and Buildings 43 (2011) 1757–1764 1763

Fig. 10. Variation of base load due to mode of operation changes.

F

Ed

C

E

C

E

ttmil

TB

Table 6Base values determined using the F-test method.

Hourly values Daily values

Building A 2007�b (◦C)a 14.77 12.90xb (g kg−1) 13.42 13.1

Building A 2009–2010�b (◦C)a 21.46 16.08

−1

ig. 11. Example of building B hourly energy signature with dry-bulb temperature.

LD calculated from daily averaged hourly temperature/humidityifferences and once with daily differences:

DDhour =∑24

j=1(�0,j − �b)�0,j>�b

24(15)

LDhour = r0 ×

∑24j=1(x0,j − xb)

(�0,j>�b, x>xb)

24(16)

DDday =(∑24

j=1�0,j

24− �b

)(�0,j>�b)

(17)

LDday = r0

(∑24j=1x0,j

24− xb

)(�0,j>�b, x0,j>xb)

(18)

The results are listed in Table 5.Base temperatures determined using hourly values were higher

han their counterparts determined using daily values, which is due

o the fact that hourly values do not capture the effect of the thermal

ass. The situation with base humidity was exactly the opposite,.e. values determined with hourly differences were considerablyower. The reason for this lies in the definition of ELD used (Eq. (5)).

able 5ase values determined using the performance line method.

Hourly values Daily values

Building A 2007�b (◦C) 14.77 12.90xb (g kg−1) 1.09 5.14

Building A 2009–2010�b (◦C) 21.46 16.08xb (g kg−1) 1.02 7.14

xb (g kg ) 4.04 7.43

a Base temperatures determined using the performance line method.

Since we calculate ELD only for those days/hours when the externaltemperature is higher than the base, a higher base temperatureresults in a lower base humidity.

As the F-test method is only used for determining base humidityat known base temperature, we used base temperatures deter-mined from performance lines with CDD calculated by samemethod as the CDD and ELD used in the F-test, e.g. if we used CDDand ELD calculated from daily differences to determine base humid-ity, we took the base temperature determined using daily values.Therefore, the base humidity was determined twice for each periodwith an F-test at a 0.05 level of significance (Table 6).

3.3.3. AnalysisTo check the suitability of base values determined by individ-

ual methods, performance surfaces were created for each pair ofbase values; once using CDD and ELD calculated from hourly valuesand once with CDD and ELD calculated from daily differences. Forevery performance surface equation a partial t-test at a 0.05 levelof significance was made.

The results are summarized in Tables 7 and 8.A t-test for the performance line method was unnecessary, since

we had already checked the correctness of the base values indi-rectly by using the base temperatures determined by performancelines for the determination of base humidity values using the F-testmethod. Because base humidity values determined by performancelines are significantly different from the equivalent values deter-mined by the F-test, they are automatically inadequate since thenull hypothesis of F-test (�E/�ELD = 0) cannot be rejected at theselected significance level (i.e. 0.05).

For 2007, the confidence levels of the ELD partial regressioncoefficients were below the minimal level of 95% regardless of themethod; therefore ELD was statistically insignificant for monitoringbuilding electric energy consumption. The situation for the periodbetween January 2009 and February 2010 was reversed, i.e. con-fidence levels of the CDD regression coefficients were below 95%,while confidence levels of ELD were above the minimal value. Theonly exception was with base values determined by F-test with CDDand ELD calculated from hourly temperature/humidity differences,where all partial regression coefficients had confidence levels above95%, but with CDD values for months when no cooling was needed(e.g. January, February). Due to the above facts, further analysiswith the available data (i.e. total electric energy consumption) wasimpossible.

4. Discussion

In cases where a quick insight into the operation of an HVAC sys-tem is more important than accuracy, cooling degree days are usedfor monitoring electric energy consumption dependent on meteo-

rological conditions. The idea of cooling degree days is derived fromheating degree days (HDD) and, as such, assumes only linear depen-dence between cooling energy consumption and sensible coolingloads and so neglects latent loads.

Journal Identification = ENB Article Identification = 3178 Date: May 19, 2011 Time: 12:42 am

1764 G. Krese et al. / Energy and Buildings 43 (2011) 1757–1764

Table 7Analysis of base values determined using the energy signature method.

Building A 2007 Building A 2009–2010

Hourly values Daily values Hourly values Daily values

E0 (kWh) 144,112 145,477 153,197 153,255t 50.96 54.64 43.99 51.471 − p(t) 1 1 1 1

�E/�CDD (kWh/K day) 151 169 87 −8.4t 2.61 2.49 0.55 −0.051 − p(t) 0.97 0.97 0.4 0.04

�E/�ELD (kWh/kJ kg−1 day) 43 28 238 295t 1.01 0.56 1.88 2.391 − p(t) 0.66 0.41 0.91 0.96

Table 8Analysis of base values determined using the F-test method.

Building A 2007 Building A 2009–2010

Hourly values Daily values Hourly values Daily values

E0 (kWh) 145,307 145,418 152,498 151,851t 67.59 65.73 50.13 52.411 − p(t) 1 1 1 1

�E/�CDD (kWh/K day) 201 177 −1017 11t 7.9 9.72 −1.39 0.071 − p(t) 1 0.99 0.8 0.06

−1 120

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[[

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[

[8] J.C. Lam, K.K.W. Wan, K.L. Cheung, L. Yang, Principal component analysis ofelectricity use in office buildings, Energy and Buildings 40 (2008) 828–836.

�E/�ELD (kWh/kJ kg day) 16,919t 2.811 − p(t) 0.98

In this study a new approach based on CDD for monitoring elec-ric energy consumption due to cooling in buildings in dependencef external air temperature and absolute humidity the so-callederformance surface was developed and applied to the meteredata. Energy signatures and performance lines were not only usedor determining base temperatures, but were also applied for deter-

ining base humidity in addition to the new method with the-test.

Electric energy consumption and hourly meteorological dataere obtained from two buildings located in Ljubljana; building, an office building, and building B, a hotel. For building A, data for

wo time periods was available. For each time interval completelyifferent results were got. In the first period, it appeared that onlyensible cooling loads affected electricity use, while in the seconderiod only latent loads had an effect on electric energy consump-ion. Base values for building B could not be determined from theiven data.

The cause of these problems lies in the total electric energy con-umption data, because we cannot know when the change in totalnergy consumption is a consequence of cooling load variation andhen is it due to building base load modification. Another problem

s the assumption of constant internal conditions.

. Conclusion

The concept of the cooling degree days was introduced to deter-ine the energy consumption of HVAC systems. The CDD method is

erived from the heating degree day method and therefore the lin-ar dependence between cooling energy and sensible cooling loads considered. The latent cooling load is significant in the case of hotnd humid climate conditions when controlled indoor humidity isaintained.Regarding the energy balance of buildings, the problems associ-

ted with use of the degree day method are mainly seen in theon-constant internal temperature and the variation of internalnd external heat gains. Therefore an appropriate definition of baseemperature and base humidity is essential. In this paper, a new

[

14,318 463 211.16 2.57 2.31.94 0.97 0.95

technique for determining the base humidity based on a signifi-cance test of the enthalpy latent day’s partial regression coefficientis shown. The base humidity is determined using the F-test statis-tics. This method was applied to the metered data for two differentbuildings and compared to the results obtained by energy signatureand performance line methods.

Absolute humidity was proven to have an effect on electricenergy consumption not only for building A, but also for build-ing B, which had no moisture control (Section 3.2). Despite that,further analysis revealed that the new approach for monitoringelectric energy consumption in buildings using performance sur-face and base humidity cannot be evaluated with building totalelectric energy consumption data. Therefore our aim for the futureis to test the newly developed approach directly on chiller powerconsumption data obtained from existing buildings.

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