RESULTS AND METHODOLOGY OF THE LIFE-CYCLE COST ANALYSIS FOR RESIDENTIAL WATER HEATER EFFICIENCY STANDARDS

Submitted to the U.S. Department ofEnergy Office ofCodes and Standards (OCS) November 3, 1998

ADDENDUM

pages 73-86Temperature Derivations The temperatures for water heater thermostat setpoint, inlet water temperature, and temperature ofthe air surrounding the water heater are based on the outdoor airtemperature. RECS provides data on heating and cooling degree days, but not airtemperatures, for each household in the sample. To assign a physical location to each RECS household from which outdoor air temperatures could be derived, three steps were taken: 1.The continental United States was divided into 42 different climate zones. Each zone is associated with a particular city.22 Figure 5.5.3 shows the 42 climate zones. The cities are listed below. Birmingham, AL Chicago, IL Las Vegas, NV Nashville, TN Phoenix, AZ Lake Charles, LA Reno, NV El Paso, TX Fresno, CA Boston, MA Buffalo, NY Ft. Worth, TX Los Angeles, CA Portland, ME New York, NY San Antonio, TX San Diego, CA Minneapolis, MN Cincinnati, OH Salt Lake City, UT San Francisco, CA St. Louis, MO Oklahoma City, OK Burlington VT Denver, CO Great Falls, MT Portland, OR Seattle-Tacoma, WA Miami, FL Raleigh, NC Philadelphia, PA Cheyenne, WY Jacksonville, FL Bismarck, ND Pittsburgh, PA Washington DC Atlanta GA Omaha, NE Charleston, SC Boise, ID Albuquerque, NM Memphis, TN 

## Climate Zonesfor LCC Analysis

Sealtq

San FrOmeh

LosA.. > Id li )/rh 3 Sanb- \»fAluenieI M oms Bminlhm

Figure 5.5.3 Map ofClimate Zones

-73-2. NOAA provides daily outdoor airtemperatures and cooling and heating degree days for each ofthe 42 cities. Cooling degree days are the number ofdegrees the average temperature is above a base temperature. Heating degree days are the number ofdegrees the average temperature is below abase temperature. The base temperature used in this study is 65°F. 3. RECS reports heating and cooling degree days for each housing record. Every RECS household was assigned to the climate zone within its reported census region with the closest number ofheating and cooling degree days for 1993. Once each RECS household is associated with a climate zone, other temperature assignments are made from the 30year average annual temperatures from NOAA. To assignthermostat setpoints for RECS households, an equation was derived from a California Energy Commission (CEC) study that measured hot and cold water temperatures. 3 The CEC study examined single-family houses built between 1984 and 1988 to assess the accuracy ofthe California Title 24 Energy Efficiency Standards modeling assumptions. As apart ofthe study, hot and cold watertemperatures were measured. The CEC assumed that hot water temperatures were equal to the water heater thermostat setpoint and the cold water temperatures were equal to the inlet water temperatures. The graph ofthe CEC data displayed in Figure 5.5.4 shows the correlation between the thermostat setpoint and the inlet water temperature. The data show that people with colder inlet water tend to set their water heaters to higher setpoint temperatures to avoid using a greater proportion ofhot water to cold to get their desired water temperature. Often what motivates people to increase the setpoint is frequently running out ofhot water. The equation that was derived from the CEC data is shown below. Ifthe inlet water temperature for the household is 58°F, then the water heater's setpoint temperature is 134.1°F. As the inlet water temperature gets warmer, the setpoint temperature decreases. Ttank = 

### 134.1 + 0.55* (58

- 

### T7n)
RECS households were given setpoint temperatures based on their inlet water temperatures using this equation. Since individual households maintain a wide range ofthermostat settings, a random error with a mean of0OF and a standard deviation of 13°F was added to account for this variability.

-74-Hotvs ColdWater Temperature from CEC data for California 200-

u 180 1 G I o 1 160- I140 -"'''
.......... ......... 

### I X- *- B * *m E · E- *nn I B *" **-*.......

- 20 ..... O 100- 80--

40 45 50 55 60 65 70 75 80 Cold WaterTemperature(deg F) Figure 5.5.4 Comparison ofSetpoint and Inlet Water Temperatures
Inlet water temperature was assumed to equal the ground water temperature, which varies according to geographic region. Ground water temperatures are assumed to be slightly warmer than air temperatures. Two degrees were added to theNOAA average annual outdoor air temperature data2 4

. The estimates were compared to theNational Well Water Association's published annual average ground water temperatures forvarious regions in the country25

. The comparison shows that, in themajority ofcases, the difference between the two estimates is lessthan 2°F. A set ofassumptions to determine air temperature around the water heater was developed based on calls tofifty waterheater installers from around the country regarding thetypical locations for water heater installation. 1. RECS reports the presence or absence ofbasements and, ifthere is abasement, whether or not it is heated. Ifthe house had abasement, itwas assumed the water heater was located in the basement. For unheated basements, the assigned temperature was the average between the outdoor air temperature for that climate zone and a house air temperature of72°F (22.2°C). 2. Ifthe basement is reported as a heated space, then thetemperature ofthe air around the water heater is assumed to be the temperature ofthe house: 72°F (22.2°C).

-75-3. Ifthe house had no basement but did have a garage or carport, itwas assumed that the water heater was in the garage or carport. The temperature assigned was 5°F (2.8°C) higher than the outside air temperature for that house. 4. In the absence ofabasement, garage, or carport, it was assumed that the water heater was in thehouse (in the kitchen or autility closet) and a temperature of72°F (22.2°C) was assigned. Table 5.5.6 shows thepercentages ofassigned water heater locations. Table 5.5.6 Water Heater Location Percentages Water Heater Location Percentage (%) unheated basement 20.9



### heated basement 26.0 garage 24.7 house 28.3 The volume ofhot water drawn in 24 hours is calculated using the Hot Water Draw Model discussion in Section 5.6. 5.5.5 Energy Analysis Results ElectricWaterHeaterEnergy Use Table 5.5.7 lists the average annual energy use for electric waterheaters and the average daily energy savings for each design option.

-76-Table 5.5.7 Energy Consumption for Electric Water Heaters Design Option Average Electricity Use Average Energy Savings (kWh/yr) (Btu/day) 0 Analytic Baseline 3503 1 0+ Heat Traps 3408 884 2 1+ 2" Jacket Insulation 3362 1312 3 1+ 2.5" Jacket Insulation 3318 1726 4 3+ Plastic Tank 3276 2121 5 3 + Insulated Tank Bottom 3296 1936 Figure 5.5.5 shows, for each design option, the cumulative frequency ofthe difference of energy consumption compared to analytic baseline electric water heaters.

-77-Delta Daily Energy Consumption of HeatTrap Delta Daily Energy Consumption of2' Jacket Water Heater comparedtoAnalytic Baseline Insulation Water Heater compared toAnalytic (Btu/Day) Baseline (Btu/Day) 3000 100 % 1 2500 - -..100% ! S.80% s " 2000 80% S 2000 60% I 1500 60% 10 _iB Z |L X20% E 500 1 20% 20% 2- : 0 0% 0 _==::::I
_ 0% o o o n o 0000000000 oOOO O COD N 0 a-O CD 0 0 ' O0 NC 0 O CDCN 0COD CD - o v a 0 e14 .o o i c - ou o * to

_ BTU/Day BTU/Day

Delta Daily Energy Consumption of2.5" Jacket Delta Daily EnergyConsumption of Plastic Tank Insulation Water Heater comparedtoAnalytic Water Heater comparedtoAnalytic Baseline Baseline (Btu/Day) (Btu/Day) 2500 100% 2000 100% > 2000 80% 3 i 1500 

### o -80% 

### o s1500 60% 60%

- lOO1000. n40% ! 10 0 0 ~1000 40%5~ ~ C 40% o500 20% = 500 20% E 00000000000)oooo~~~~ !O l)o ioo CD

.....

0..l 0 ~ 0 C?

- :D0 0 ;! T I? I? Cm CN(C? CNN BTU/Day BTU/Day

Delta Daily Energy Consumption ofTank Bottom Insulation Water Heater compared to Analytic Baseline (Btu/Day) 2000 _- 100% 1500 80% * | 1000 BH60% e 500 20% " o 0 0% o

0 OON OO o ooo BTU/no Day BTU/Day

, Frequency Cumulative %

Figure 5.5.5 Differences in Energy Consumption by Design Option

- Electric Water Heaters

-78-Gas-firedWaterHeaterEnergy Use Table 5.5.8 lists the average annual energy use for gas-fired water heaters and the average daily energy savings for each design option. Table 5.5.8 Energy Consumption for Gas-Fired Water Heaters Design Option Average Energy Use Average Energy Savings (MCF/yr) (kWh/yr) Btuday) (Btu/day) 0 Analytic Baseline 22.32 0 1 0 + Heat Traps 21.72 0 1671 2 1+ 2" Jacket Insulation 20.58 0 4886 3 1+ 2.5" Jacket Insulation 20.34 0 5567 4 3+ Side Arm Heater 17.37 23 13719 5 2 + Improved Flue Baffle 20.04 0 6422 Figure 5.5.6 shows, for each design option, the cumulative frequency ofthe difference of energy consumption compared to analytic baseline gas-fired waterheaters.

-79-Delta Daily Energy Consumption of HeatTrap Delta Daily Energy Consumption of2' Jacket Water Heatercompared toAnalytic Baseline Insulation Water Heater compared toAnalytic (Btu/Day) Baseline (Btu/Day) 1000 100% : 5000 100% 800 80% > 4000 80% 600 660%Z : 3000- 60% Z " 400 40% & 2000 40% e 200 20% " E 1000 0 20% 0 0% L 0 0%

C(0 _" N C(D 1- 0 ON 0
_ N ( ( 0 0 0N 0 I r _ 1 N 00 o N
_ N 0 N N N N N N Nr N
_ ' r BTU/Day BTU/Day

Delta Daily Energy Consumption of 2.5' Jacket Delta Daily Energy Consumption ofSide-Arm InsulationWater Heater compared to Analytic Design (w/ Metal Tank) Water Heatercompared Baseline (Btu/Day) toAnalytic Baseline (Btu/Day) 5000 100% 3000

- - - 100% ; 4000 -80% , I 2500- 80 0 3000 60%
_ c 2000 60% i 1000 20% 500 20%

. 0 0% 0 _ .... 0% % 

# oL___ ooo o 0CD 0C N (0 0( N (0 N 0(0 NC 0CD >0 N0 NC N Nt - , , N N N N - ' ' BTU/Day BTU/Day

Delta Daily Energy Consumption of Improved Flue Baffle Water Heater compared to Analytic Baseline (BtulDay) 4000 100% ' 3000 80% 1 80% I; 200060% a.o~~~ 4-~~40% 1000 20% E L 0 0%

o o to oo o o 0 N

- N 'q (0
_ 0, ON BTU/Day

r-- Frequency Cumulative % Figure 5.5.6 Differences in Energy Consumption by Design Option

- Gas-fired Water Heaters

-80-5.6 Hot Water DrawModule 5.6.1 Introduction to Hot Water Use Hot water use varies widely between households because it is dependent on the household and water heater characteristics including: the number and age ofthe people who live in the home, the presence ofhot water-using appliances, thetank size and thermostat setpoint ofthe water heater, and the climate in which the home is situated. By accounting for these five types of characteristics, the draw model estimates average daily hot water draw volume26

. There is a degree ofuncertainty in this estimation ofhot water use. Uncertainty is caused not only by variability in the demographic and climatic inputs but also by uncertainties attached to the weighting factors, i.e., the estimated coefficients in the equation. The uncertainties in the coefficients are defined using normal distributions with the parameters provided in the original regression analysis 2 7

. 5.6.2 Equation forHot Water Use The Hot Water Draw Model equation is expressed as follows: vol = {sea_coef + (peroef* per) + (agel_coef* agel) + (age2_coef* age2) + [age34_coef* (age3 + age4)] + (T,ancoef * (Tank + Ttanerr))+ (Tankszcoef* Tanksz) + T7,coef * T) + (Tarcoef*Tar) + (home_coef* athome)

- [(0.692 *per + 1.335 * /(per) * no_dw]

- [(1.1688 *per+ 4.7737 * /(per)) * no_cw } * (senior_mf* no_pay)
where:
vol = hot water consumption, gal (L)/day per = total number ofpersons in household agel = number preschool children, age 0-5 yrs age2 = number ofschool age children, age 6-13 yrs age3 = number ofadults, age 14-64 yrs age4 = number ofadults, age 65 yrs and over

-81-Tank = water heater thermostat setting, °F (°C) Tanksz = water heater nominal tank size, gal (L) Tn = water heater inlet water temperature, °F (°C) Tair = outdoor air temperature, °F (°C) athome = presence ofadults at home during day nodw = absence ofa dishwasher
no cw = absence ofa clothes washer senior_mf = senior-only household in a multi-family building no_pay = household does not pay for hot water Ttankerr =estimation error for the thermostat setpoint (normal distribution) sea_coef =coefficient for seasonal effects (normal distribution) per_coef =coefficient for total number ofpersons in household (normal distribution) agel_coef =coefficient for "agel" (normal distribution) age2_coef =coefficient for "age2" (normal distribution) age34_coef =coefficient for "age3" + "age4" (normal distribution) home_coef =coefficient for "athome" (normal distribution) Tanksz_coef =coefficient forwater heater tank size (normal distribution) Tankcoef =coefficient forwater heater setpoint (normal distribution) 

### Te,_coef =coefficient forwater heater inlet temperature (normal distribution) 

### Tircoef =coefficient for average outdoortemperature (normal distribution)

-82-5.6.3 General Description ofKey Variables Numberof People in Household (per). The total number ofhousehold members. Numberof Preschool Children (agel). The number ofinfants and young children up through age 5. Number of School-Age Children (age2). The number ofchildren age 6 through 13. Number ofAdults 14-64 (age3). The number ofadults age 14 to 64. Number of Adults 65+ (age4). The number ofadults age 65 or more. Thermostat Setpoint (Tank). The thermostat setting ofthe heating element ofthe water heater. WaterHeater TankSize (Tanksz). The nominal size ofthe water heater tank. Outside Air Temperature(Tair). The average annual outdoor airtemperature. Inlet Water Temperature(Tn). The temperature ofthe water entering the waterheater. Unemployed Household Member (athome). The presence ofa household member at home during the day. Dishwasher (no_dw). Absence ofa dishwasher in thehousehold. Clothes Washer (no_cw). Absence ofa clothes washer in the household. Senior Only (senior_mf). A senior-only (age 65 or more) household in amulti-family building. No-Pay Household (no_pay). A household that does not pay to heat water.

5.6.4 General Description ofSources ofData RECS provides data on the number, age, and employment status ofhousehold occupants, presence ofa clothes washer or dishwasher, and form ofpayment to fuel utilities. The derivations ofthe three temperature variables are discussed in Section 5.5.4.

-83-RECS reports three ranges ofwater heater tank size -- small, medium, and large; for this analysis however, specific sizes are needed. Bymatching the three RECS ranges with the standard sizes, an exact water heater size was assigned to each RECS house. Table 5.6.1 shows, by fuel type, the RECS water heater volumes and the corresponding selections for this analysis. Table 5.6.1 Water Heater Volumes Selected for LCC Analysis RECS Selection forLCC Analysis (gal) (liters) Electric Small 30 (110) Medium 40 (150)

Large 50 (190) 65 (250) 80 (300) Gas Small 30(110) Medium 40 (150)

Large 50 (190) 75 (280) Oil Small Medium 32 (120)

Large 50(190)
Terms and values for no_dw, no_cw, senior_mf, and no_pay were developed by LBNL for the draw model. Standard errors for the coefficients used in the equation were reported in the original hot water consumption model. These values were used to develop the normal distributions for the coefficients. 5.6.5 Results ofHot Water Use Calculations Figure 5.6.1 shows estimated daily hot water use forhouseholds with electric water heaters

-84-asa histogram. For these households average daily use is44.3 gallons. Figure 5.6.2 shows the equivalent chart for households with gas-fired water heaters. For those households the average daily use is 48.9 gallons ofhotwater.

Daily Hot Water Use (Gal/Day) 2500

----- A--- 100% >, 2000 

### t - t80% 

### ! c g1500]- 60% 1000o 40% E 500 20%



### 0 !__In La 20Hann___ -0% Gal/Day Figure 5.6.1 Frequency Chart ofHot Water Use

- Households with Electric Water Heaters Daily HotWater Use (gal/day) 3000
. ......- 100% >2500 

### t-80% * 2000 , E- 2 1000 4 0% E [L 500 20% 0 :In I__ 0% Gal/Day Figure 5.6.2 Frequency Chart for Hot Water Use

- Households with Gas-Fired Water Heaters

-85-References 1. Lawrence Berkeley National Laboratory (LBNL), 1998. Engineering Analysis MethodologyandResults forResidentialWaterHeaterEfficiency Standards, 1998. Intermediate report to U.S. DOE, Berkeley, CA. October 1. 2. LBNL, 1998. LBNL WaterHeaterCostDatabase.[Microsoft Excel spreadsheet.] Berkeley, CA. August. 3. Lutz, J.D., C.D. Whitehead, A. Lekov, D. Winiarski, G.J. Rosenquist, 1998. "WHAM: A Simplified Energy Consumption Equation for Water Heaters." In: Proceedingsof the ACEEE 1988Summer Study on EnergyEfficiency inBuildings,August23-28, 1998. American Council for an Energy-Efficient Economy, Washington, DC. 4. Gas Appliance Manufacturers Association (GAMA), 1998. Consumers'Directoryof CertifiedEfficiencyRatings forResidentialHeatingand WaterHeatingEquipment. Prepared for GAMA by Intertek Testing Services, Cortland, NY. April. 5. U.S. DOE, Energy Information Administration, 1997.Annual EnergyOutlook1998. DOE/EIA-0383(98). Washington, DC. December. 6. Gas Research Institute (GRI), 1998. 1998Editionof the GRIBaselineProjection. Arlington, VA. 7. U.S. DOE, Energy Information Administration, 1995. HouseholdEnergy ConsumptionandExpenditures1993. DOE/EIA-0321(93), Washington, DC. October. 8. Whirlpool Corporation comments to theDepartment ofEnergy, December 12, 1990, Docket No. CE-RM-90-201, p. 1&2, Attachment #1. 9. "The Life Expectancy/Replacement Picture." 1998. ApplianceMagazine.55:9, 71. September. 10. National Oceanic and Atmospheric Administration (NOAA), 1998. <http://www.ncdc.noaa.gov/ol/climate/online/ccd/meantemp.html > (last accessed: July 17, 1998). 11. Stanonik, F., 1998. Manufacturing Cost Data forResidential Gas and Electric Storage Water Heaters. GAMA, Arlington, VA. Letters to DOE, June 19 and July 17.

-86-