APPENDIX 7-B. HOT WATER DRAW MODEL
TABLE OF CONTENTS
7-B.1 INTRODUCTION ................................................................................................. 7-B-1 7-B.2 SEASONAL EFFECT ADJUSTMENTS.............................................................. 7-B-1 7-B.3 CLOTHES WASHER AND DISHWASHER ADJUSTMENTS ......................... 7-B-2 7-B.4 HOT WATER DRAW MODEL COEFFICIENTS AND VARIABLES.............. 7-B-2 7-B.5 SAMPLE CALCULATION USING THE HOT WATER DRAW MODEL ....... 7-B-4
LIST OF TABLES Table 7-B.2.1 Summary of EPRI Analysis Results for Seasonal Coefficients................. 7-B-1 Table 7-B.2.2 Summary of Seasonal Values .................................................................... 7-B-1 Table 7-B.3.1 Impact of Clothes Washer and Dishwasher Adjustments.......................... 7-B-2 Table 7-B.4.1 Variable Definition and Value Derivations ............................................... 7-B-3 Table 7-B.4.2 Coefficient Definitions............................................................................... 7-B-4 Table 7-B.5.1 Sample Hot Water Draw Model Calculation for a 40 gallon Water Heater......................................................................................................... 7-B-5
LIST OF FIGURES Figure 7-B.5.1 Average Daily Hot Water Use for Sample Calculation............................. 7-B-5

7-B-iAPPENDIX 7-B. HOT WATER DRAW MODEL
7-B.1 INTRODUCTION

1 DOE developed a modified Hot Water Draw Model as an improvement on a previously existing model. The Hot Water Draw Model estimates the average daily volume of hot water used by various households by accounting for the key characteristics described below.
DOE modified the Hot Water Draw Model to be able to calculate seasonal hot water use. DOE also adjusted hot water model to account for changes in hot water use by clothes washers and dishwashers due to the updated Federal energy conservation standards for this equipment. 7-B.2 SEASONAL EFFECT ADJUSTMENTS The seasonal coefficients for spring, summer, fall, and winter, where derived using the linear regression results in the EPRI study found in Appendix A of Modeling Patterns of Hot 1 Water Use in Households. Table 7-B.2.1 provides the detailed seasonal coefficients by hour. To obtain the total values, number of hours was multiplied by the coefficients. Table 7-B.2.1 Summary of EPRI Analysis Results for Seasonal Coefficients

hour # hours Weekday (I-P units) Weekend (I-P units) a10 a11 a12 a13 a10 a11 a12 a13 (spring) (summer) (fall) (winter) (spring) (summer) (fall) (winter) 11-6 7 0 0 0 0.1459 0.0907 0.1675 0 0.1696 6-8 2 0 -3.593 0 0 0 -1.569 -0.6553 0 8-11 3 0 0 -0.432 0.5654 1.2574 0 0 1.3516 11-1 2 0 0 -0.4447 0.4012 0 -1.2638 0 1.4804 1-5 4 0 0 0 0.683 0 -0.9405 0 1.1756 5-7 2 0 -0.9736 0 0.9658 0 -1.4838 0 1.6384 7-9 2 0 -2.1273 -0.8588 0 0.8262 -0.9764 0 0 9-11 2 0 -0.8922 -0.9381 0 0 0 -0.3788 0 Total 0 -15.1722 -5.7792 8.1835 6.0595 -13.1755 -2.0682 16.182 To obtain the daily average values (see Table 7-B.2.2) the coefficients were weighted by the number of days in the week which are weekend and weekday. Table 7-B.2.2 Summary of Seasonal Values

Seasonal Coefficient Average Value Standard Deviation Spring 1.731286 0.52 Summer -14.6017 4.35 Fall -4.71891 1.41 Winter 10.46879 3.12

7-B-17-B.3 CLOTHES WASHER AND DISHWASHER ADJUSTMENTS The Hot Water Draw Model incorporates the parameters for clothes washer and dishwasher hot water use. These parameters reflect assumptions about clothes washer and dishwasher water use as they existed in the 1990s. Since that time, there has been a considerable change to clothes washer and dishwasher technology that has resulted in lower hot water use. In particular, updated Federal energy conservation standards for clothes washers that became 2 3 effective in 2007 and for dishwashers that will become effective in 2010 have a significant impact on clothes washer and dishwasher hot water use. The baseline water use for clothes washers in the 1990’s was 39.2 gallons/cycle and the 2 water use calculated based on the 2007 standard is 21.0 gallons/cycle. The baseline water use for dishwashers in the 1990’s was 8.2 gallons/cycle and the water use calculated based on the 4 2010 standard is 6.5 gallons/cycle. Therefore, DOE updated the draw model to account for the reduced hot water use by adjusting the dishwasher and clothes washer water use variables to account for the new standards. The results are shown in Table 7-B.3.1. For example, the impact on gas-fired storage water heaters was a reduction of the average daily water use by 10.7% Table 7-B.3.1 Impact of Clothes Washer and Dishwasher Adjustments Product Classes Average Hot Water Use (not Adjusted) Average Hot Water Use (Adjusted) Change in Hot Water Use Percent Change

gal gal gal % Gas-fired (Storage) Water Heater 50.7 45.3 -5.4 -10.7 Electric Water Heater 47.5 43.1 -4.4 -9.3 Oil-fired Water Heater 48.2 43.0 -5.2 -10.8 Gas (Instantaneous) Water Heater 51.3 46.4 -4.9 -9.6
7-B.4 HOT WATER DRAW MODEL COEFFICIENTS AND VARIABLES The Hot Water Draw Model uses an equation that is expressed as follows:
vol = { sea
_ coef + ( per
_ coef * per ) + ( age1

_ coef * age1 ) + age 2

_ ceof * age 2 + [ age 34 _ coef *( age 3 + age4) + ( T tank _ coef * T tank ) + ( Tanksz

_ coef * Tanksz ) + ( T

in _ coef * T in ) + ( T air _ coef + T air ) + (hom e
_ coef * at hom e )

− [(0.6 92 * per + 1.335* per ) * dw

_ adj

− [(1.1688* per + 4.7737 * per ) * cw
_ adj ]}* ( senior

_ mf

_ coef * senior

_ mf ) *( no
_ pay
_ coef * no
_ pay ) Table 7-B.4.1 lists the variables used in the equation as well as the definition and derivation of the value for each RECS household

7-B-2Table 7-B.4.1 Variable Definition and Value Derivations Variable Definition Value Derivation per total number of persons in household =NHSLDMEM* age1 number of preschool children, age 0-5 yrs =YEARS1* (RECS value significantly underestimates) age2 number of school age children, age 6-13 yrs =YEARS2* (RECS value significantly overestimates) age3 number of adults, age 14-64 yrs =YEARS5* (RECS value slightly overestimates) age4 number of adults, age 65 yrs and over =YEARS3*
T

tank water heater thermostat setting, oF Uniform distribution from contractor survey (See Ch. 7) Tanksz water heater nominal tank size, gal Derived using WHEATSIZ and methodology described in Ch. 7 T

in water heater inlet water temperature, oF Calculated (See Ch.7)
T

air outdoor air temperature, oF Calculated (See Ch.7) athome presence of adults at home during day =ATHOME* dw_adj adjustment factor to account for the differences due to the current energy conservation standard for dishwasher and for the cases of households with no dishwasher = IF DISHWASH*=1 then .207 IF DISHWASH* ≠ 1 then 1

cw_adj adjustment factor to account for the differences due to the current energy conservation standard for cloth washers and for the cases of households with no cloth washers = IF CWASHER*=1 then .464 IF CWASHER* ≠ 1 then 1

senior

_mf senior-only household in a multifamily building = IF TYPEHUQ*=4 or 5 AND NHSLDMEM*=YEAR4*, then 1; = IF TYPEHUQ* ≠4 or 5 OR

NHSLDMEM* ≠YEAR4*, then 0 no_pay household does not pay for hot water = IF (PGASHTWA, LPGPAY, PELHOTWA, or FOPAY)*=1 then 0 = IF (PGASHTWA, LPGPAY,

PELHOTWA, or FOPAY)* ≠ 1 then 1 * RECS 2001 variable. See Appendix 7-A for definitions. Table 7-B.4.2 lists the coefficients used in the equation as well as the definition and normal distribution parameters for each RECS household

7-B-3Table 7-B.4.2 Coefficient Definitions Coefficient Definition Normal Distribution Parameters Average

Value Standard Deviation sea_coef coefficient for seasonal effects See Table D.2.2 per_coef coefficient for total number of persons in household 0.974 0.09 age1_coef coefficient for age1 6.393 0.71 age2_coef coefficient for age2 10.518 0.63 age34_coef coefficient for age3 + age4 15.305 0.67 home_coef coefficient for athome 10.219 1.44 Tank sz_coef coefficient for tank size 0.144 0.03 T

tank _coef coefficient for water heater setpoint -0.128 0.02 T

inlet _coef coefficient for water heater inlet temperature -0.179 0.05 T

air

_coef coefficient for average outdoor temperature 0.512 0.06 senior_mf_coef coefficient for senior-only household in a multifamily building 1.00 0.2 no_pay_coef coefficient for household does not pay for hot water 1.00 0.2
7-B.5 SAMPLE CALCULATION USING THE HOT WATER DRAW MODEL Table 7-B.5.1 and Figure 7-B.5.1 provide a sample calculation and results for a 40 gallon water heater and common values for the hot water draw model variables.

7-B-4Table 7-B.5.1 Sample Hot Water Draw Model Calculation for a 40 gallon Water Heater Variable Values Coefficients GallonsSpringSummerFallWinterSpringSummerFallWinterSpringSummerFallWinter

Sea_coef 1.73 -14.60 -4.72 10.46 1.7 -14.6 -4.7 10.5 per 3 0.974 2.9 age1 0 6.393 0 age2 1 10.518 10.5 age3 2 15.305 30.6 age4 0 15.305 0 T

tank 120 oF -0.128 -15.4 Tanksz 40 gal 0.144 5.8 T

in 56.0 68.7 64.2 51.2 -0.179 -10.0 -12.3 -11.5 -9.2 T

air 55.3 74.1 57.9 37.5 0.512 28.3 37.9 29.7 19.2 athome 1 10.219 10.2 dw_adj 1 -.207 *(0.692 * per + 1.335 * √per) -0.9 cw_adj 1 -.464*(1.1688*per +4.7737 * √per) -5.4 senior

_mf 0 1 1 no_pay 0 1 1 Total Gallons per Day 58.3 49.4 51.8 58.8

48 50 52 54 56 58 60

1 2 3 4 5 6 7 8 9 10 11 12 MonthDaily Hot Water Use (gallons / day)

Figure 7-B.5.1	 Average Daily Hot Water Use for Sample Calculation

7-B-5REFERENCES
1. Lutz, J. D., X. Liu, J. E. McMahon, C. Dunham-Whitehead, L. J. Shown, and Q. T. McGrue, Modeling Patterns of Hot Water Use in Households , 1996. Lawrence Berkeley National Laboratory. Berkeley, CA. Report No. LBNL-37805 Rev.
2. U.S. Department of Energy-Office of Building Research and Standards, Final Rule Technical Support Document (TSD): Energy Efficiency Standards for Consumer Products: Clothes Washers , 2000. U.S. Department of Energy. Washington, DC. Report No. LBNL-47462. <http://www.eren.doe.gov/buildings/codes_standards/reports/cwtsd/index.html >
3. United States Cong. House. 110th Congress, H. R. 6 Energy Independence and Security Act of 2007. 2007. http://frwebgate.access.gpo.gov/cgibin/getdoc.cgi?dbname=110_cong_bills&docid=f:h6enr.txt.pdf
4. U.S. Department of Energy - Energy Efficiency & Renewable Energy, Technical Support Document: Energy Efficiency Program for Consumer Products and Commercial and Industrial Equipment, Residential Dishwashers, Dehumidifiers, and Cooking Products, and Commercial Clothes Washers , 2007. Washington, DC.

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