7-C-i APPENDIX 7

- C. LCC ENERGY USE CALCU LATIONS

TABLE OF CO NTENTS

7-C.1 INTRODUCTION

....................................................................................................... 7-C-3

7-C.2 CLOTHES DRYERS

................................................................................................... 7-C-3

7-C.2.1 Number of Cycles

...................................................................................... 7-C-3

7-C.2.2 Energy Use Calculation

............................................................................. 7-C-4

7-C.3 ROOM AIR CONDITIONER S ................................................................................... 7-C-7

7-C.3.1 General Approach

...................................................................................... 7-C-7

7-C.3.2 Operating Hours ......................................................................................... 7-C-8

7-C.3.2.1 Residential

.................................................................................................. 7-C-8

7-C.3.2.2 Commercial

.............................................................................................. 7-C-12

LIST OF TABLES

Table 7 -C.2.1 Number of Loads Washed per Week Based on RECS Sample ................. 7-C-3

Table 7 -C.2.2 RECS Sample Clothes Dryer Usage .......................................................... 7-C-3

Table 7 -C.2.3 RECS Sample Clothes Dryers Utilization ................................................. 7-C-4

Table 7 -C.3.1 RECS Vintage Bins for Room Air Conditioner ......................................... 7-C-9

Table 7 -C.3.2 Fraction of Shipments of Room Air Conditioner by Product Class ........ 7-C-11

Table 7 -C.3.3 Average Room Air Conditioner EER by Product Class and Year Sold .. 7-C-12

Table 7 -C.3.4 Weather Stations Classified as Desert ..................................................... 7-C-17

Table 7 -C.3.5 Regressi on Equations ............................................................................... 7-C-19

Table 7 -C.3.6 Building Type and Abbreviation ............................................................. 7-C-20

Table 7 -C.3.7 Building Schedules and Abbreviation ..................................................... 7-C-20

Table 7 -C.3.8 Room Air Conditioner Operating Hour Equations By Building Type

and Schedule ............................................................................................ 7-C-21

Table 7 -C.3.9 Room Air Conditioner Operating Hour Equations By Building Type and Schedule (Desert) .............................................................................. 7-C-22

Table 7 -C.3.10 CBECS 2003 Building Code Match to Room Air Conditioner Equation Building Type ........................................................................... 7-C-23

LIST OF FIGURES

Figure 7 -C.3.1 1972–2008 Average Shipment Weighted EER for Room Air

Conditioners ............................................................................................. 7-C-10 Figure 7 -C.3.2 ANSI/SHRAE Standard 55 -2004: Thermal Environmental Conditions for Human Occupancy ............................................................................. 7-C-13 Figure 7 -C.3.3 National Solar Radiation Database (NSRDB) Stations ........................... 7-C-14 Figure 7 -C.3.4 Hours Above Comfort Zone in Palm Springs (1991) .............................. 7-C-16 Figure 7 -C.3.5 Hours Above the Standard 55 Comfort Zone Compared to CLDD ......... 7-C-17 Figure 7 -C.3.6 Hou rs Above the Standard 55 Comfort Zone versus CLDD with Different Regions Highlighted ................................................................. 7-C-187-C- ii Figure 7 -C.3.7 Hours Above ANSI/ASHRAE Standard 55-2004 as a Function of Cooling Degree- Days ............................................................................... 7-C-197

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- 3 APPENDIX 7

- C. LCC ENERGY USE CALCULATIONS

7- C.1 IN TRODUCTION

This appendix contains the calculation methodology for calculating the energy use of clothes dryers and room air conditioners (RAC) in the life

- cycle cost ( LCC ) a nalysis.

7- C.2 CLOTHES DRYERS

DOE determined the annual energy consumption by-products that would meet a potential future standard by multiplying the number of cycles per year by the energy use per cycle

.

7-C.2.1 Number of Cycles

DOE estimated the number of clothes dryer cycles per year for each sample home using data given by RECS on the number of laundry loads (clothes washer cycles) washed per week and the frequency of clothes dryer use. The responses in RECS fall into one of the bins shown in

Tables 7 -C.2.1 and 7-C.2.2. For each question, DOE assumed a uniform distribution within the boundaries of each bin and randomly assigned a value from within the appropriate range to each sample household.

Table 7 -C.2.1 Number of Loads Washed per Week Based on RECS Sample

Bin Loads per Week Derived Loads per Year*

Min Max

1 1 load or less 0 78

2 2 to 4 loads 78 234

3 5 to 9 loads 234 494

4 10 to 15 loads 494 806

5 More than 15 loads 806 1118
* The ranges reflect the inclusion of values in between the given bin boundaries.

Table 7 -C.2.2 RECS Sample Clothes Dryer Usage

Bin Description Fraction of Washer Cycles When Dryer is used

Min Max

1 Use it every time wash clothes 1 1

2 Use it for some, but not all, loads of

wash 0.50 1

3 Use it infrequently 0.00 0.50

The responses to the above questions vary among sample households using different clothes dryer products, so they yield somewhat different values for the average annual number of clothes dryer cycles for each product class (see Table 7 -C.2.3).7

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- 4 Table 7 -C.2.3 RECS Sample Clothes Dryers Utilization

Product Class

Electric

Standard Gas Vent

- less

Washer loads per

year 301 292 268

Clothes dryer frequency* 0.95 0.93 0.94

Clothes dryer loads

per year 283 274 251

* Fraction of washer loads ** Accounts for fraction of households that have a clothes washer, but no clothes dryer

7-C.2.2 Energy Use Calculation

For each considered efficiency level, DOE derived the field energy use by separately estimating the active mode and standby mode energy use and then adding them together. The DOE test procedure calculates active mode energy consumption by dividing the weight (lbs) of clothes dried per cycle (8.45 lbs for standard and 3 lbs for compact clothes dryers) by the Combined Energy Factor (CEF) (lbs/kWh) and subtracting standby power. a DOE adjusted the test procedure energy use to reflect field conditions by making an adjustment for

cl othes dryer load weight and moisture removal factor.

For each household, DOE determined the per- cycle test procedure clothes dryer energy use during active mode by using the following formula:

TP TP TP TP

Active Cycles CD Stby hrs Stby Cycles CD CEF ght avgLoadWei TP _/ 1000 *_ _* ** **  ** **  ** **  ** **  ** **  ** ** 

**− **  ** **  ** **  ****

**=**

Where:

avgLoadWeight TP = average l oad weight in the test procedure, lbs,

CEF = efficiency of the clothes dryer during active mode, lbs per kWh, CD_Cycles TP = test procedure clothes dryer cycles per year, Stby_hrs TP = test procedure standby hours, and, Stby = clothes dryers s tandby power usage, watts.

For each household, DOE determined the field adjustment for clothes dryer energy use during active mode by using the following formula:

a See chapter 5 for more information on how to convert from CEF to EF.7

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- 5 

## ( **)** Cycles CD RMC RMC RMC RMC RMC

ght avgLoadWei ght avgLoadWei RMC TP EnergyUse Adj

End TP TP Enc Field Field

TP Field adj Active Active

_

, , **∗ **  ** **  ****

** **  ** ** 

**+ **  ** **  ** **  ** **  ****

**− −**  **∗ **  ** **  ** **  ** **  ****

**∗−=**

Where:

TP Active = test procedure energy use per cycle, kWh per cycle,

RMC adj = RMC adjustment factor for the fixed energy use, kWh per cycle, avgLoadWeight TP = average load weight in the test procedure, lbs, avgLoadWeight Field = average load weight for each household, lbs,

RMC TP = remaining moisture content in the test procedure, 57.5 percent,

RMC TP,Enc = remaining moisture content at the end of the cycle in the test procedure, 5 percent,

RMC Field = remaining moisture content for the household, percent,

RMC Field,End = remaining moisture content at the end of the cycle for the household, percent, CD_Cycles = clothes dryer cycles per year

.

DOE assigned a fixed energy use adjustment ( RMC adj ) equal to 0.25 kWh/cycle to account for energy required to heat the clothes dryer cabinet.

To assign a field average load weight ( avgLoadWeight Field ) for each household, DOE developed a distribution of load weights by matching the listed tub sizes for models in the July 2010 California Energy Commission (CEC) directory with the correlations between tub size and average pounds in the DOE test procedure. To account for a wider distribution of households that do not wash the average pounds in the DOE test procedure, DOE added a ±25 percent adjustment factor. The average load weights for standard -size units range from 3.8 lbs. to 13.7 lbs., with a mean value of 8.45 lbs, which matches DOE’s proposed clothes dryer procedure

value.

To assign a field remaining moisture content (RMC Field ) value for each household, DOE used the 2008 shipment weighted values provided by AHAM for front loader and top loader washers. The shipment weighted value is 38.1 percent for front loaders and 51 percent for top loaders, with an overall shipment weighted RMC value of 47 percent . In 2008, front loaders represented 31 percent of shipments, while top loaders represented the remaining 69 percent, so the overall RMS shipment weighted value is 47- percent . This shipment weighted averag e RMC

value in the AHAM data is based on th e clothes washer RMC which uses a correction factor to normalize testing resu lts fr om different lots of test cloth. As a result, DOE determined that an initial clothes dryer RMC of 57.5 percent more accurately represents the moisture content of

current laundry loads after a wash cycle and therefore adjusted the shipment weighted va lue for front loaders and top loaders accordingly. In order to get a distribution of values, DOE used the number of models listed at each unadjusted RMC in the July 1010 CEC directory. 1 The adjusted RMC values used in the analysis range from 36 percent to 64 percent for front loaders, with an average of 47 percent, and from 42 percent to 75 percent for front loaders, with an average of 62 percent. The overall average value of 57.5 percent matches DOE’s proposed clothes dryer procedure value.7

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- 6 To assign a field remaining moisture content at the end of the cycl e (RMC Field,End ) value for each household, DOE used a uniform distribution of 0 to 5 percent. In comparison, the DOE test procedure uses 5 percent.

Using the above approach, DOE calculated a unique value for the clothes dryer annual active mode energy c onsumption for each sample household with an electric clothes dryer using the number of dryer cycles specified for that household. For gas clothes dryers, DOE used a similar approach as for electric clothes dryers, but added an estimate of the energy use of the electric components. An estimate of 0.107 kWh per cycle, which was derived from tests done by DOE, was applied for all efficiency levels except for the max

- tech level. For the latter, which has a more efficient motor, the tests found a value of 0.091 kWh.

For each household, DOE determined the field-adjusted clothes dryer energy use during standby mode by using the following formula:

Power Standby Time CD Cycles CD e erEnergyUs ClothesDry Standby

_ 60 _ _8760 **∗ **  ** **  ** **  ** **  ** **  ** **  ****

**∗ −=** 

Where:

8760 = number of hours in one year, hrs,
CD_Time = clothes dryer time to complete one cycle, min/cycle,

60 = number of minutes in one hour, min/hr, Standby_Power = standby power, kW, and CD_Cycles = clothes dryer cycles per year

.

DOE assumed that clothes dryers take 60 minutes on average to complete a cycle. Standby power varies by efficiency level as discussed in chapter 5.

DOE also considered the impact of clothes dryer operation on home heating and cooling loads. A clothes dryer releases heat to the surrounding environment. If the dryer is located indoors, its use will tend to slightly reduce the heating load during the heating season and slightly increase the cooling load during the cooling season. To calculate this impact, DOE first estimated whether the clothes dryer in a RECS sample home is lo cated in conditioned space (referred to as indoors) or in unconditioned space (such as garages, unconditioned basements, outdoor utility closets, or attics). Based on the 2005 RECS 2 and the 2009 American Housing

Su rvey (AHS) 3 , DOE assumed that 50 percent of vented standard electric and gas dryers are located indoors, while 100 percent of compact and ventless clothes dryers are located indoors. For these installations, DOE utilized the results from a Eu ropean Union study about the impacts of clothes dryers on home heating and cooling loads to determine a the appropriate factor to apply to the total clothes dryer energy use. 4 This study reported that for vented dryers there is a factor of negative 3 to 9 percent (average 6 percent) and for ventless dryers there is a factor of positive 7 to 15 percent (average 11 percent). DOE believes that t his effect is the same for all of the considered efficiency levels because the amount of air passing through the clothes dryer does

not vary.7

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- 7 7- C.3 ROOM AIR CONDITIONER S

7-C.3.1 General Approach

DOE calculated the annual energy consumption of a room air conditioner using the following equation:

IEER OH Capacity RAC ENERGY **∗**

**=**

Where:

RAC ENERGY = Room air conditioner annual energy consumption (kWh/year), Capacity = rated capacity in Btu/h,

O H = operating hours per year,

CEER = Combined Energy Efficiency Ratio in Btu/h/W.

DOE used the same representative capacities for each product class (PC) as it did in the engineering analysis : 5 kBtu/h for < 6000 Btu/h product classes (PC 3 and 8), 8 and 12 kBtu/h

for 8000–13,999 Btu/hr product class (PC 1) b , and 24 kBtu/h product class (PC 5). The CEER is also determined in the engineering analysi s and is a new energy factor descriptor that incorporates standby power. The CEER is calculated as capacity times active mode hours (equal to 750) divided by the sum of active mode annua l energy use and inactive mode annual energy use. The number of hours associated with this standby mode for room air conditioners is 5,115 hours per year. See chapter 5 for details.

For residential room air conditioners, the operating hours of the R AC are determined using the data reported by RECS 2005 on the annual energy consumption ( field energy consumption) for room air conditioning , as well as assumed EER and capacity values for the existing room air conditioner. For commercial

- sector room air conditioners, CBECS does not report annual energy consumption for room air conditioning, so DOE estimated the energyconsumption using variables specific to each building in the sample and data on cooling degreedays. The following section provides a detailed explanation of the methodology for estimating the number of room air conditioner operating hours for each household or commercial building in the samples.

b The fraction of 8 and 12 kBtu/h units was assumed to be equal, so each are assigned to a specific household 50 percent of the time.7

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- 8 7-C.3.2 Operating Hours

7-C.3.2.1 Residential

DOE calculated the annual room air conditioner operating hours for each residential sample unit using the following formula:

CDDAdj dj BldgShellA Capacity EER FEC OH RECS RECS * * **∗**

**=**

Where:

OH = operating hours per year,

FEC RECS = field energy consumption for a room air conditioner,

EER RECS = the estimated EER of the room air conditioner in the sample home,

Ca pacity = the room air conditioner capacity in Btu/h, BldgShellAdj = adjustment to building shell efficiency in 2014, precent, CDDAdj = cooling degree days (CDD) adjustment in Btu/h.

DOE used the same representative capacities for each class as it did in the engineering analysis. c

To ensure that the estimated operating hours are representative of future conditions, DOE used the building shell index factor from AEO2010 in 2014 for space cooling in all homes of 0.96 and 115 year historical average CDD by census division. The building shell index factor decreased energy use by 4 percent, while the CDD adjustment factor decreased energy use by 10

percent on average.

To estimate the energy consumption of a single room air conditioner, referred to as

FEC RECS

, DOE divided the RECS 2005 reported annual energy consumption ( field energy consumption) for room air conditioning , referred to as FEC (all) RECS , by the reported numb er of room air conditioners. Although in reality the utilization of each of the room air conditioners in a home may vary, DOE has no way to estimate such variation. The reported RECS 2005 end

- use quantities were not based on metering of individual appliances, rather, EIA used a regression technique to estimate how much of the total annual electricity consumption for each household

can be attributed to each end

- use category. d

c In conducting the analysis of energy use by

- products that would meet some future standard, DOE effectively

substitute d the room air conditioners in the sample residential and commercial buildings with a new product of identical product class (capacity) that the household or buildin g owner would purchase if their room air conditioner

failed. The reported field energy consumption refers to the

d The desire to use a large number of independent variables without using a large number of interaction terms and the desire to adapt the regression procedures to account for heteroscedastic error terms led to the use of a nonlinear regression technique. For more information, see: h ttp://www.eia.doe.gov/pub/consumption/residential/append_c.pdf7

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- 9 consumption of all of the room air conditioners in a ho me . RECS also reports the number of

room air conditioners in the home. Of all homes that use a room air conditioner, 35 percent have

two room air conditioners and 14 percent have three or more room air conditioner s.

In RECS 2005, some households are identified as having purchased ENERGY STAR air conditioners in the last 4 years. For these households, DOE applied the appropriate ENERGY

STAR EER. For the rest of the sample, DOE estimated the EER of the existing room ai r conditioner in each sample household by matching the age of the room air conditioner given by RECS with the average EER for the specific product class in the year of its vintage. In RECS, the age of a room air conditioner is given in one of th e five bins shown in Table 7-C.3.1 . DOE assumed a uniform distribution within each vintage bin and assigned an age to the room air conditioner in each sample household. Once the vintage year was determined, DOE assigned an EER to the unit equal to the average EER for the appropriate capacity for that year.

Table 7 -C.3.1 RECS Vintage Bins for Room Air Conditioner

Bin Age of unit

1 Less than 2 years old

2 2 to 4 years old

3 5 to 9 years old

4 10 to 19 years old

5 20 years or older

To derive a time series of average EER by capacity, DOE began with data from AHAM on total shipment- weighted average EER for 197 2–2008 ( See Figure 7-C.3 .1 ). AHAM also provided average EER data by product class (capacity) for 2005–2007. 5 To develop the EER values by product class (capacity) for earlier years, DOE first assumed that all of the products shipped in each product class had the minimum efficiency required by the standard in each particular year.7

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- 10 Figure 7 -C.3.1 1972–2008 Average Shipment Weigh ted EER for

Room Air Conditioners

DOE then estimated the shares of total shipments by product class in each year using data for 1989, 1992, and 2005–2007, and calculated a total shipment- weighted EER (See Table 7

- C.2.2). DOE then calculated scalars for each year from the ratio of the actual total shipment

weighted EER to the calculated EER, and then applied the scalars to the minimum efficiency required for each prod uct class in each year. 5 6 7 8 9 10 11

1970 1975 1980 1985 1990 1995 2000 2005 2010

YearAverage Shipment Weighted7

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- 11 Table 7 -C.3.2 Fraction of Shipments of Room Air Conditioner by Product Class

P roduct Class 2007 2006 2005 199 2 1989

1

Without reverse cycle and with

louvered sides Less than 6,000 Btu/h 32.0% 23.0% 37.0% 26.7% 27.7%

2 6,000 to 7,999 Btu/h 16.0% 19.0% 19.0% 14.4% 17.7%

3 8,000 to 13,999 Btu/h 36.0% 34.0% 30.0% 32.8% 29.7%

4 14,000 to 19,999 Btu/h 6.0% 5.5% 3.0% 13.1% 13.2%

5 20,000 Btu/h and more 2.6% 3.9% 2.0% 6.3% 7.0%

6

Without reverse cycle and without

louvered sides Less than 6,000 Btu/h

7.0% 12.0% 7.0% 7 6,000 to 7,999 Btu/h 2.1% 3.2%

8 8,000 to 13,999 Btu/h 2.1%

9 14,000 to 19,999 Btu/h

10 20,000 Btu/h and more

11 With reverse cycle and with

louvered sides Less than 20,000 Btu/h **
1.0% 0.7%
2.1% 1.5%

12 20,000 Btu/h and more 0.1%

13 With reverse cycle and without

louvered sides Less than 14,000 Btu/h **
0.6% 0.4% 0.5%

14 14,000 Btu/h and more

15 Casement Casement Only 0.4% 0.6% 0.4% 16 Casement Slider

Table 7 -C.3.3 shows the AHAM data on total shipment- weighted average EER and the average EER estimated for the representative product classes.7

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- 12 Table 7 -C.3.3 Average Room Air Conditioner EER by Product Class and Year Sold

Year Shipment Weighted EER Derived Average EER*

< 6000

Btu/h 8000

– 13,999

Btu/hr (PC 3) ≥ 20,000

Btu/hr 8000

– 13,999

Btu/hr (PC 8)

2007 9.81 9.80 10.10 9.10 9.50

2006 10.02 9.80 10.40 9.20 9.50

2005 9.95 9.80 10.10 9.10 9.40

2004 9.71 9.70 9.86 8.83 9.15

2003 9.75 9.70 9.92 8.89 9.21

2002 9.75 9.70 9.92 8.88 9.21

2001 9.63 9.70 9.80 8.50 8.73

2000** 9.3 9.03 9.70 8.50 8.73

1999 9.07 8.56 9.63 8.50 8.73

1998 NA 8.56 9.63 8.50 8.73

1997 9.09 8.57 9.64 8.50 8.73

1996 9.08 8.55 9.62 8.50 8.73

1995 9.03 8.49 9.55 8.50 8.73

1994 8.97 8.42 9.47 8.50 8.73

1993 9.05 8.50 9.56 8.50 8.73

1992 8.88 8.31 9.35 8.50 8.73

1991 8.8 8.24 9.27 8.45 8.73

1990** 8.73 8.18 9.20 8.39 8.69

1989 8.48 7.95 8.95 8.15 8.45

1988 8.23 7.72 8.68 7.91 8.20

1987 8.06 7.56 8.51 7.75 8.03

1986 7.8 7.32 8.23 7.50 7.77

1985 7.7 7.22 8.13 7.40 7.67

1984 7.48 7.02 7.89 7.19 7.45

1983 7.29 6.84 7.69 7.01 7.27

1982 7.14 6.70 7.53 6.86 7.12

1981 7.06 6.62 7.45 6.79 7.04

1980 7.02 6.58 7.41 6.75 7.00

1978 6.72 6.44 7.25 6.60 6.85

1972 5.98 6.30 7.09 6.46 6.70

* Shaded area values were provided by AHAM 5

** Years in which standards became effective

7-C.3.2.2 Commercial

DOE calculated the annual operating hours for each sample commercial

- sector room air conditioner by establishing a relationship between cooling degree-days and operating hours for a7

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- 13 number of building type and building schedule combinations. DOE assumed that the room air conditioner is operated when the outdoor air conditions are above the comfort zone described by

ANSI/ASHRAE Standard 55 -2004 Thermal Environmental Conditions for Human Occupancy (see figure 7 -C.3.2). 6 To estimate how often this occurs, DOE used the following general equation:

OH 55 = (a * CDD) + b

Where:

OH55 = Average annual hours when the outdoor air conditions are above the ASHRAE Standard 55 comfort zone;

CDD = the number of annual cooling degree -days (65 F) for a given location;

a and b are linear fit parameters.

Figure 7 -C.3.2 ANSI/SHRAE Standard 55 -2004: Thermal Environmental Conditions for Human Occupancy

ANSI/ASHRAE Standard 55 assumes that metabolic rates of 1.1 met, (engaged in near

sede ntary physical activity) , 0.5 clo of clothing insulation, insulation levels typical of clothing worn when the outdoor environment is warm, air speeds are not greater than 0.20 m/s (40 ft/min) , upper recommended humidity limit, and 0.012 humidity ratio. The range of operative temperatures presented in Figure 7-C.3.2 are for 80 percent occupant acceptability. This is based

on a 10 percent dissatisfaction criteria for general (whole body) thermal comfort based on the

PMV -PPD index, plus an additional 10 percen t dissatisfaction that may occur on average from local (partial body) thermal discomfort. Predicted mean vote (PMV) index is an index that predicts the mean value of the votes of a large group of persons on the seven point thermal7

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- 14 sensation scale. The predicted percentage of dissatisfied (PPD) index is an index that establishes a quantitative prediction of the percentage of thermally dissatisfied people determined from PMV. The room air conditioner is assumed to operate if the outdoor conditions are outside

comfort zone if W (humidity ratio) >0.012 or T>Tcomf for that humidity ratio. Tcomf is given by the following equation: 2 28.2549142 7081.117 **+×−=** W Tcomf , where W is the humidity ratio

at the outdoor conditions for that hour.

DOE used data on cooling degree-days from the National Solar Radiation Database
(NSRDB). 7 The 1991–2005 NSRDB is an update of the 1961–1990 NSRDB. This updated NSRDB dataset is an hourly ground-based data set of solar and meteorological fields for 1454

stations , which are subdivided into three c lasses of stations (see figure 7

- C.3 .3). A total of 858 sites have a complete 15 -year period of record.

Figure 7 -C.3.3 National Solar Radiation Database (NSRDB)

Stations

Stations are identified with a USAF number as follows:

**•** Class I Stations have a complete period of record (all hours 1991–2005) for solar and key meteorological fields and have the highest

- quality solar modeled data (221 sites).

**•** Class II Stations have a complete period of record but significant periods of interpolated, filled, or otherwise low er -quality input data for the solar models (637 sites).

**•** Class III Stations have some gaps in the period of record but have at least 3 years of data that might be useful for some applications (596 sites).7

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- 15 The NSRDB has complete measured hourly Dry Bulb Temperature, Dew Point Temperature, Relative Humidity, and Atmospheric Pressure for all Class I & Class II Stations.

The Dry Bulb Temperature, Relative Humidity, and Atmospheric Pressure fields were used to calculate the humidity ratio for each hour. The humidity ratio was calculated using procedures

from the 2005 ASHRAE Handbook-Fundamentals, Chapter 6 Psychrometrics. Under the section

on Numerical Calculation of Moist Air Properties , Situation 3 describes the process to calculate humidity ratio (W) from Dry Bulb Temperature, Relative humidity , and Pressure. The saturation pressure for the dry bulb temperature is calculated using the following equation:

)ln( )ln( 13 3 12 2 11 109 8 TCTCTCTCC T C Pws **×+×+×+×++=**

where:

C8 = -5.8002206 E+03

C9 = 1.3914993 E+00

C10 = -4.8640239 E-02

C11 = 4.1764768 E-05

C12 = -1.4452093 E-08

C13 = 6.5459673 E+00 Pws = saturation pressure, Pa T = absolute temperature, K = °C + 273.15

The water vapor partial pressure is the saturation pressure multiplied by the relative humidity.

Pws Pw **×= φ** 

The humidity ratio, W, is defined as the ratio of the mass of water vapor to the mass of dry air contained in the sample. It can be calculated from the pressure and the water vapor partial pressure as:



## ( ) Pw P Pw W

- 0.62198 **×=**

The testing the conditions for that hour against the criteria from Std 55, we can determine

if the room air conditioner would have operated during that hour.

Figure 7

- C. 3.4 shows the hours (2281 hours) in 1991 that were above the comfort zone for Palm Springs.7

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- 16 Figure 7 -C.3.4 Hours Above C omfort Z one in Palm Springs (1991)

Figure 7 -C.3.5 shows hours above the Standard 55 comfort zone compared to CLDD for 15 years (1991-2005) for all Class 1 & II weather stations. Hours above comfort zone Palm Springs, 1991

0 0.005 0.01 0.015 0.02 0.025 0.03

0 5 10 15 20 25 30 35 40 45 50

dry bulb temperaturehumidity ratio 100%RH

90%RH

80%RH

70%RH

60%RH

50%RH

40%RH

30%RH

20%RH

10%RH7

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- 17 Figure 7 -C.3.5 Hours A bove the Standard 55 C omfort Z one Compared to CLDD

The lower ‘b ranch’ in the ‘hours above Std 55’ vs ‘CLDD 65’ is from low desert

locations. After examining the data, the following sites were classified as desert.

Table 7 -C.3.4 Weather Stations Classified as Desert

STATION ST

DAVIS MONTHAN AFB AZ

DEER VALLEY/PHOENIX AZ

DOUGLAS BISBEE

- DOUGLAS INTL A AZ KINGMAN (AMOS) AZ

LUKE AFB AZ

PHOENIX SKY HARBOR INTL AP AZ

SCOTTSDALE MUNI AZ

TUCSON INTERNATIONAL AP AZ

YUMA INTL ARPT AZ

YUMA MCAS AZ

BAKERSFIELD MEADOWS FIELD CA

BLYTHE RIVERSIDE CO ARPT CA

CHINA LAKE NAF CA

DAGGETT BARSTOW

- DAGGETT AP CA

EDWARDS AFB CA

IMPERIAL CA

LANCASTER GEN WM FOX FIELD CA

NEEDLES AIRPORT CA

PALM SPRINGS INTL CA Room AC Operating Hours

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0 500 1000 1500 2000 2500 3000 3500 4000

CLDD 65hours above Std 557

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- 18 PALM SPRINGS THERMAL AP CA

PALMDALE AIRPORT CA

TWENTYNINE PALMS CA

CARLSBAD CAVERN CITY AIR TERM NM

DEMING MUNI NM

HOLLOMAN AFB NM

LAS CRUCES INTL NM

ROSWELL INDUSTRIAL AIR PARK NM

TRUTH OR CONSEQUENCES MUNI AP NM

LAS VEGAS MCCARRAN INTL AP NV MERCURY DESERT ROCK AP [SURFRAD] NV

NELLIS AFB NV EL PASO INTERNATIONAL AP [UT] TX SAINT GEORGE (AWOS) UT

In F igure 7 -C.3.6, the desert and tropical sites are shown. The uppermost points on the original chart ( F igure 7 -C.3.5) represent data from stations in Hawaii, Guam and the Caribbean.

Figure 7 -C.3.6 Hours A bove the Standard 55 Comfort Z one

v ersus CLDD with D ifferent Regions H ighli ghted

After removing the sites in Hawaii, Guam, and the Caribbean islands, regressions were done to predict the hours per year above Standard 55 from the number of cooling degree- days for each year. The data points and regression lines are shown in Figur e 7-C.3.7 for all hours of the year. This represents 842 sites for 15 years each in the continental United States. Room AC Operating Hours

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0 500 1000 1500 2000 2500 3000 3500 4000

CLDD 65hours above Std 55

all

HI & Guam

Caribbean

desert7

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- 19 Figure 7 -C.3.7 Hours Above ANSI/ASHRAE Standard 55 -2004 as a Function of Cooling Degree-Days

As can be seen in the graph above, the data patterns are different for desert locations, where humidity is not a present factor affecting comfort. The regression equations used to derive the average annual hours when the outdoor air conditions are above the ASHRAE Standard 55 comfort zone (OH55) are shown in Ta ble 7 -C.3.5.

Table 7 -C.3.5 Regression Equations Region Equation R 2 # sites

Non

- desert OH55 = 2.759 x CLDD + 127.99 0.9224 809

Desert OH55 = 1.153 x CLDD + 574.04 0.8714 33

The number of annual hours above the ASHRAE Standard 55 comfort zone varies by schedule, which refers to the time that a building is open. Thus, DOE performed the regression for a number of combinations of building type and building schedule, yielding some what different equations for each combination. The building types included are: Assembly, Education, Food Service, Office, Retail, and Warehouse. For each building type, DOE estimated operating hours for each of the following building schedules: (1) open 24 hours a day and seven days a week (24/7); (2) open business hours Monday through Friday; (3) open business hours Monday through Saturday; (4) open business hours Monday through Friday and Sunday; (5) open business hours all week. The building types and schedule abbrev iations are shown in table 7- C.3.6 and 7-C.3.7. An assumption was made that if the occupancy rate was greater than 20% of CLDD vs #hours > ASHRAE Std55 all day, all year 1991-2005

y = 2.7592x + 127.99

R 2 = 0.9224

y = 1.153x + 574.04

R 2 = 0.8714

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0 500 1000 1500 2000 2500 3000 3500

CLDD (base 65F)hours/year above ASHRAE Std 55

non-desert

desert

Linear (non-desert)

Linear (desert)7

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- 20 full occupancy, the room air-conditioner would operate if the outdoor air conditions were above

the ASHRAE standard 55 comfort zone.

Table 7 -C.3.6 Building T ype and Abbreviation Building Type Abbreviation Assembly ASM

Education EDU

Food Service FDS Lodging LOD

Medical MED

Office OFF

Outdoor OUT

Retail RET

Warehouse WHS

Table 7 -C.3.7 Building S chedules and Abbreviation Building Schedules Abbreviation

24/7 hours 247 Monday

- Friday M

- F Monday

- Friday and Saturday and Sunday ALL

The equations to predict the hours per year the outdoor air conditions are above the ASHRAE Standard 55 comfort zone for various building types and schedules for non- desert

locations are shown table 7 -C.3.8.7

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- 21 Table 7 -C.3.8 Room Air Conditioner Op erating H our E quations By B uilding T ype and

S chedule
building

type open schedule equation R2

ALL 247 ROH55 = 2.759 x CLDD + 127.99 0.9224

OUT M_F ROH55 = 1.974 x CLDD + 93.29 0.9458

OUT ALL ROH55 = 2.759 x CLDD + 127.99 0.9430

ASM M_F ROH55 = 0.751 x CLDD + 119.67 0.9458

ASM ALL ROH55 = 1.396 x CLDD + 169.18 0.9430

EDU M_F ROH55 = 1.001 x CLDD + 117.11 0.9412

EDU ALL ROH55 = 1.398 x CLDD + 163.52 0.9424

FDS M_F ROH55 = 1.243 x CLDD + 112.91 0.9354

FDS ALL ROH55 = 1.510 x CLDD + 166.44 0.9408

LOD M_F ROH55 = 1. 471 x CLDD + 17.11 0.9428

LOD ALL ROH55 = 2.206 x CLDD + 40.94 0.9408

MED M_F ROH55 = 1.001 x CLDD + 128.06 0.9428

MED ALL ROH55 = 1. 151 x CLD D + 148.72 0.9408

OFF M_F ROH55 = 0.918 x CLDD + 119.76 0.9428

OFF ALL ROH55 = 1.510 x CLDD + 166.44 0.9408

RET M_F ROH55 = 0.751 x CLDD + 119.67 0.9458

RET ALL ROH55 = 1.281 x CLDD + 170.57 0.9450

WHS M_F ROH55 = 0.836 x CLDD + 109.17 0.9422

WHS ALL ROH55 = 1.514 x CLDD + 178.06 0.9419

The highlighted rows are the same. This is because the occupancy rates were above 20

percent for 24 hours per day for all building types operating under the 24/7 schedule. The analysis does not account for differences in building operation schedules due to holidays.

The equations to predict the hours per year the outdoor air conditions are above the ASHRAE Standard 55 comfort zone for various building types and schedules for desert locations

are shown table 7 -C.3.9.7

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- 2 2 Table 7 -C.3.9 Room Air Conditioner O perating H our E quations By B uilding T ype and

S chedule (Desert)
building

type open

sc hedule equation R2

ALL 247 ROH55 = 1.153 x CLDD + 574.04 0.9224

OUT M_F ROH55 = 1.974 x CLDD + 93.29 0.8353

OUT ALL ROH55 = 2.759 x CLDD + 127.99 0.8925

ASM M_F ROH55 = 0.289 x CLDD + 546.12 0.8353

ASM ALL ROH55 = 0.600 x CLDD + 721.20 0.8925

EDU M_F ROH55 = 0.409 x CLDD + 532.56 0.8723

EDU ALL ROH55 = 0.572 x CLDD + 741.06 0.8794

FDS M_F ROH55 = 0.553 x CLDD + 449.33 0.8914

FDS ALL ROH55 = 0.663 x CLDD + 690.02 0.8985

LOD M_F ROH55 = 0. 642 x CLDD + 40.06 0.8260

LOD ALL ROH55 = 0.951 x CLDD + 157.74 0.8985

MED M_F ROH55 = 0.402 x CLDD + 603.12 0.8260

MED ALL ROH55 = 0. 458 x CLD D + 706.19 0.8985

OFF M_F ROH55 = 0.353 x CLDD + 573.23 0.8260

OFF ALL ROH55 = 0.663 x CLDD + 690.02 0.8985

RET M_F ROH55 = 0.289 x CLDD + 546.12 0.8353

RET ALL ROH55 = 0.534 x CLDD + 749.00 0.8813

WHS M_F ROH55 = 0.317 x CLDD + 524.97 0.8087

WHS ALL ROH55 = 0.612 x CLDD + 837.58 0.8682

To estimate the room air conditioner operating hours for each of the buildings in the

CBECS 2003 room air conditioner sample, DOE identified the building type (see T able 7

- C.3.10) and the building schedule using information provided by CBECS, and used the appropriate equation (non-desert or desert) combined with the number of cooling degree- days for the location of the building. It adjusted the results with a scaling factor to account for the

difference between the number of building operating hours assumed to derive the equations and the actual building operating hours reported by CBECS.7

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- 23 Table 7 -C.3.10 CBECS 2003 Building Code Match to R oom Air Conditioner Equation Building Type

CBECS

2003 PBA

Code Definition Building Type Match Fraction of

CBECS 2003 RAC Sample

1 Vacant Not Applicable

2 Office OFF 18.3%

4 Laboratory MED 0.2%

5 Nonrefrigerated warehouse WHS 5.9%

6 Food sales RET 2.9%

7 Public order and safety OFF 4.1%

8 Outpatient health care MED 0.6%

11 Refrigerated warehouse WHS 0.0%

12 Religious worship ASM 8.7%

13 Public assembly ASM 5.5%

14 Education EDU 12.7%

15 Food service FDS 4.5%

16 Inpatient health care MED 0.2%

17 Nursing MED 1.4%

18 Lodging LOD 3.5%

23 Strip shopping mall RET 0.0%

24 Enclosed mall RET 0.0%

25 Retail other than mall RET 11.8%

26 Service RET 17.3%

91 Other OFF 2.3%

The above approach provides a ‘best guess’ of the room air conditioner operating hours for a particular CBECS building. However, operating hours are affected by some factors not included in the analysis, such as interior heat gains from equipment or people and solar gains. To develop a distribution of the number of operating hours for each sample building, DOE added an error band to the value derived using the regression equation. The error band includes values that are ± 10% from the regression line for the appropriate building type/schedule combination.

The commercial sector operating hours were estimated based on the cooling climate in 2003. To match the 115 year CDD average values, DOE decreased the estimated commercial sector operating hours by 2 percent on average.7

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- 24 REFERENCES

1. California Energy Commission, California Energy Commission Appliance Efficiency
Database, 2010. (Posted July) < http://www.energy.ca.gov/appliances/database/ >

2. U.S. Department of Energy: Energy Information Administration, Residential Energy Consumption Survey: 2005 Public Use Data Files . 2008: Washington, DC. http://www.eia.doe.gov/emeu/recs/recspubuse05/pubuse05.html

3. U.S. Census Bureau: Housing and Household Economic Statistics Division, American Housing Survey National Data . 2009, HUD. http://www.huduser.org/portal/datasets/ahs/ahsdata09.html

4. Rüdenauer, I. and C.

- O. Gensch, Energy demand of tumble dryers with respect to differences in technology and ambient conditions, January 13, 2004. European Committee of Domestic Equipment Manufacturers (CECED). < http://www.aib

deutschland.de/das_institut/mitarbeiterinnen/dok/630.php?id=40&dokid=202&anzeige=d

et&ITitel1=&IAutor1= >

5. Association of Home Appliance Manufacturers (AHAM), Trends in Energy Efficiency

2008

6. American National Standards Institute & American Society of Heating, R., and AirConditioning Engineers, Inc.,, ANSI/ASHRAE 55 -2004 Thermal Environmental Conditions for Human Occupancy , 2004.

7. National Renewable Energy Laboratory, National Solar Radiation Database 1991–2005 Update: User’s Manual, 2007. < http://www.nrel.gov/docs/fy07osti/41364.pdf >