APPENDIX 7-C. WLIFE-CYCLE COST ENERGY USE CALCULATIONS
 

TABLE OF CONTENTS
 

7-C.1 INTRODUCTION ................................................................................................. 7-C-1 

7-C.2 WATER HEATERS .............................................................................................. 7-C-1 

7-C.2.2 WHAM Equation................................................................................................... 7-C-1 

7-C.2.3 WHAM Equation for Heat Pump Water Heaters .................................................. 7-C-4 

7-C.2.3.1 Comparison of energy use calculations for heat pump water heaters.. 7-C-7 

7-C.2.3.2 Calculating HPWH Cooling Effects .................................................... 7-C-8 

7-C.2.4 WHAM Equation for Gas Instantaneous Water Heaters ..................................... 7-C-11 

7-C.3 POOL HEATERS ................................................................................................ 7-C-14 

7-C.4 DIRECT HEATING EQUIPMENT .................................................................... 7-C-15 

LIST OF TABLES 

Table 7-C.2.1 Comparison of HPWH Energy Use Results .............................................. 7-C-8
 

LIST OF FIGURES 

Figure 7-C.2.1 Methodology for Calculating Energy Consumption for Water Heaters .... 7-C-1 

Figure 7-C.2.2 Methodology for Calculating Storage Water Heater Energy 

Consumption using WHAM Equation....................................................... 7-C-3 

Figure 7-C.2.3 Methodology for Calculating Electricity and Fuel Consumption for 

Gas and Oil Storage Water Heaters ........................................................... 7-C-4 

Figure 7-C.2.4 Methodology for Calculating HPWH Energy Consumption using 

Modified WHAM Equation ....................................................................... 7-C-5 

Figure 7-C.2.5 Methodology for Calculating HPWH Cooling Effect ............................... 7-C-9 

Figure 7-C.2.6 Efficiency versus Hot Water Usage for Instantaneous Gas Water 

Heater rated at 0.82 EF ............................................................................ 7-C-12 

Figure 7-C.2.7 Methodology for Calculating Instantaneous WH Energy Consumption 

using Modified WHAM Equation ........................................................... 7-C-13
 

7-C-i 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

APPENDIX 7-C. LIFE-CYCLE COST ENERGY USE CALCULATIONS 

7-C.1 INTRODUCTION 

This appendix contains the methodology for calculating the energy use of residential 

water heaters, direct heating equipment, and pool heaters in the life-cycle cost (LCC) analysis. 

7-C.2 WATER HEATERS 

Water heater energy consumption is calculated using the Water Heater Analysis Model 

(WHAM) equation.1 Figure 7-C.2.1 shows the WHAM methodology. 

Engineering 

Analysis 

Average Yearly Tank 

Temperature 

(Distribution) 

Average Monthly 

Inlet Water 

Temperature 

Average Daily Hot 

Water Use 

Operating 

Conditions 

Contractor 

Survey 

Weather 

Data 

Average Monthly 

Ambient 

Temperature 

Draw Model 

RECS 

Sample 

Equipment 

Type 

Modified WHAM 

for HPWHs 

Storage WH 

HP WH 

Monthly Energy 

Use 

Data Sources 

RECS Household 

Sampled 

WHAM Calculations depedent on 

Equipment Type 

Inlet Water 

Temp 

Methodolog 

y 

Well? 

Equipment Parameters 

Pon 

WHAM 

RE 

EF 

UA 

Modified WHAM 

for Tankless WHs 

Figure 7-C.2.1 Methodology for Calculating Energy Consumption for Water Heaters 

7-C.2.2 WHAM Equation 

The WHAM equation1 yields average daily water heater energy consumption (Qin), and is 

expressed as follows: 

7-C-1 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

⎛

1
−
 

UA
 ×
 (T
tank −
 Tamb )
 

⎟ +

⎞

⎟

⎠

(T
tank −
 Tin vol den C
 ×
 ×
 × )
 P ∗
 24 (T
tank −
 Tamb Q
 )
 in =
 ⎜ ×
 UA
 × ⎜ RE
 ⎝ P on 

Where: 

Qin = total water heater energy consumption, Btu/day, 

RE = recovery efficiency, %, 

Pon = rated input power, Btu/h, 

UA = standby heat-loss coefficient, Btu/h-oF, 

Ttank = thermostat setpoint temperature, oF, 

Tin = inlet water temperature, oF, 

Tamb = temperature of the air surrounding the water heater, o

F, 

vol = volume of hot water drawn in 24 hours, gal/day, 

den = density of stored water, set constant at 8.29 lb/gal, and 

Cp = specific heat of stored water, set constant at 1.000743 Btu/lb-o

F. 

For gas-fired storage water heaters, gas-fired instantaneous water heaters, and oil-fired 

storage water heaters, it is necessary to disaggregate electricity and fuel consumption. Figure 7­

C.2.2 shows the methodology for calculating electricity and fuel consumption using WHAM. 

DOE calculated electricity consumption as follows: 

Where: 

Qelectricity =
 

Qin =
 

PON =
 

Paux =
 

Pstandy =
 

in Q = Q × (P − P )− P × 24 electtricity aux s tan dy s tan dy PON 

electricity consumption, kWh,
 

total water heater energy consumption, Btu/day,
 

rated input power, kW,
 

electricity demand when burner is on, kW, and
 

electricity demand when burner is off, kW.
 

7-C-2 

EE-2006-STD-0129 COMMENT 56.10
Gas and 

WHs has 

and E

Average Yearly Tank 

Temperature 

(Distribution) 

Average Monthly 

Inlet Water 

Temperature 

Average Daily Hot 

Water Use 

Average Monthly 

Ambient 

Temperature 

Draw Model 

Mode 

Energy 

Consumption During Water 

Heating 

Energy 

Consumption 

During Standby 

Water Heating 

Standby 

Average Daily 

Total Energy Use 

for Month 

RE 

UA 

WHAM Calculation 

Pon 

Heat Capacity of 

Water Density of Water 

Average Monthly Temperature Difference 

Water Heater Heating Load 

Test Procedure 

Parameters 

WH ON = 24 hrs 

EF 

FueEle

Figure 7-C.2.2 Methodology for Calculating Storage Water Heater Energy Consumption using W

7-C-3 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DOE calculated gas consumption by subtracting electricity consumption from total water 

heater energy consumption (Qin ). Figure 7-C.2.3 shows the methodology for calculating 

electricity and fuel consumption for gas and oil storage water heaters. 

Pstandby 

Mode 

Electricity 

Consumption Due 

to Water Heating 

Energy 

Consumption 

During Standby 

Water Heating 

Standby 

Paux 

(electronic ignition, 

controls, fan use) 

Pon 

Average Daily Elec 

Use for Month 

Average Daily 

Total Energy Use 

for Month 

Fuel Use 

Figure 7-C.2.3	 Methodology for Calculating Electricity and Fuel Consumption for Gas 

and Oil Storage Water Heaters 

7-C.2.3 WHAM Equation for Heat Pump Water Heaters 

For heat pump water heaters, energy efficiency and consumption are dependent on 

ambient temperature. To account for this factor, DOE expanded the WHAM to utilize the 

calculation approach used in the New York State Energy Research and Development Authority 

(NYSERDA) heat pump water heater site screening tool and DOE’s weatherization assistance 

program. 2, 3 The equation for determining the energy consumption of heat pump water heaters is 

similar to the WHAM equation, but a performance adjustment factor that is a function of the 

average ambient temperature is applied to adjust RE. A heat pump water heater operates either in 

heat pump or in electric resistance mode. DOE assumed that the electric resistance mode of 

operation is used 100 percent of the time when the monthly ambient temperature is less than 32 

o

F or more than 100 oF. A heat pump water heater also operates in the electric resistance mode 

for part of the time even when the monthly ambient temperature is between 32 oF and 100 oF, 

because this product has a slower recovery rate than an electric resistance water heater. DOE 

determined that, depending on household hot water consumption patterns, the electric resistance 

mode of operation occurs for as much as 10 percent of the unit’s operating time. Figure 7-C.2.4 

shows the methodology for calculating the energy consumption of HPWHs using the modified 

WHAM equation. 

7-C-4 

EE-2006-STD-0129 COMMENT 56.10
Average Daily Hot 

Water Use 

Average Monthly 

Ambient 

Temperature 

Draw Model 

Mode of 

Operation 

WHAM 

Resista

WHA

Pum

Electric 

Resistance 

Mode 

HP Mode 

Heat Pump Load 

Factor (% Energy 

Use at HP Mode) 

REElectri

EF = 2.2 @ 50 Gal 

Tank 

ECR Model 

Data 

REHeat Pump. = 242% 

UA = 1.82 

RECS Sampled 

Household 

RE Adjustment 

Factor 

Test Data 

(John 

Maxwell) 

Monthly 

Calculation of 

HPWH Runtime 

Fraction 

1% ER runtime per 

9500 Btu of Daily 

Hot Water Load 

Engineering 

Spreadshee 

t 

Test Data/ 

Assumption 

PON,Electric. Res. = 4.5 

kW 

PON,HPWH = .5 kW 

Above 32 F? YES (Calculate) 

HP Load = 

Adjusted RE * 

PON 

ER Load = RE * 

PON 

NO (0% HP Mode) 

ECR Model 

Data 

ECR Model 

Data 

Figure 7-C.2.4 Methodology for Calculating HPWH Energy Consumption using Modified W

Equation 

7-C-5 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The HPWH WHAM equation is as follows:
 

⎡ HP frac
 ⎛ UA ⎞ ⎤ (T − T ) × k amb 
 _ tan 

RE HPWH × PA 

(1 − HP _ frac ) 

⎢

⎢

⎢

⎢

⎢

⎥

⎥

⎥

⎥

⎥

×
 1 − +
 P
 

⎜

⎜

⎝

⎟

⎟

hpwh ON ,HPWH ⎠ (T in Q vol den C
 =
 ×
 ×
 −
 T
 )× +
 24
 ×UA
 × (T − T
 ) in P tan k Tank amb ⎛

⎜

⎜

⎞

⎟

⎟

(T − T ) UA
 × k amb 
 tan ×
 1 − RE
 P
 ⎣ ⎝ ⎠ ⎦ ER ON ,ER 

Where: 

Qin = total water heater energy consumption, Btu/day,
 

vol = daily draw volume, gal/day,
 

den = density of water, set constant at 8.29 lb/gal,
 

Cp = specific heat of water, set constant at 1.000743 Btu/lb-oF,
 

Ttank = tank thermostat set point temperature, o

F,
 

Tin = inlet water temperature, o

F,
 

REHPWH = recovery efficiency of heat pump mode, %,
 

REER = recovery efficiency of electric resistance mode, %,
 

UA = standby heat-loss coefficient, Btu/h-oF,
 

Tamb = temperature of the air surrounding the water heater, oF,
 

PON,HPWH = rated input power of heat pump mode, Btu/h,
 

PON,ER = rated input power of electric resistance mode, Btu/h,
 

PAhwh = performance adjustment factor,
 

0.00019738 × T 2 -0.01842 ×T +1.3222625 , and amb amb 

HP_frac = fraction of water heating load that is satisfied by heat pump mode. 

HP_frac is calculated using the following equation: 

HP × P × RE × PA on ON ,HPWH HPWH hpwh HP _ frac = HP × P × RE × PA + (1 − HP ) × P × RE on ON ,HPWH HPWH hpwh on ON ,ER ER 

Where: 

HPON = fraction of time when heat pump mode is operating, %, 

vol × den ×C (T − T ) P tan k in ⎞

⎟

⎠

⎛

⎜

⎝

100 −
 , when Tamb>32oF and 0 when Tamb<32 oF. 

9500
 

PON,HPWH = rated input power of heat pump mode, Btu/h,
 

PON,ER = rated input power of electric resistance mode, Btu/h,
 

REHPWH = recovery efficiency of heat pump mode, %,
 

REER = recovery efficiency of electric resistance mode, %,
 

PAhwh = performance adjustment factor, %,
 

0.00019738 × T 2 -0.01842 ×T +1.3222625 , and amb amb 

Tamb = temperature of the air surrounding the water heater, oF. 

7-C-6 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7-C.2.3.1 Comparison of energy use calculations for heat pump water heaters 

The energy use calculation used by DOE in this analysis is slightly different from either 

the NYSERDA Heat Pump Water Heater Site Screening Tool or DOE’s weatherization 

assistance program. 

DOE’s weatherization assistance program calculates HPWH energy use by using the 

following formula: 

vol × den ×C (T − T ) P tan k in Qin = EF × (1 + PA ) 

Where: 

Qin = total water heater energy consumption, btu/day,
 

vol = daily draw volume, gal/day,
 

den = density of water, lb/gal,
 

Cp = specific heat of water, Btu/lb-o

F,
 

Ttnk = tank thermostat set point temperature, o

F,
 

Tin = inlet water temperature, o

F,
 

EF = energy factor, and
 

PA = performance adjustment factor, %.
 

The performance adjustment factor is calculated by using the following formula: 

3 2 o PA = 0.00008 ×T amb + 0.0011 ×T amb − 0.4833 ×T amb + 0.0857, when Tamb > 32 F

1 PA = −1, when T amb ≤ 32 o F 

EF 

The New York State Energy Research and Development Authority (NYSERDA) Heat 

Pump Water Heater Site Screening Tool calculates HPWH energy use by using the following 

formula: 

⎡

⎢

⎢

⎢

⎢

⎢

hpa 

(1 − lfhp ) 

UA (T − T ) ⎤ k amb ⎛ ⎞

⎟

⎠

⎟ + lfhp 

EF 

×
 tan 1 − ⎥

⎥

⎥

⎥

⎥

⎦

× ⎜

⎜

⎝ PHP (T in Q vol den C
 =
 ×
 ×
 −
 T
 )× +
 24
 ×UA
 × (T − T
 ) in P tan k Tank amb (T − T ) k amb ⎛ UA
 ×
 ⎞ tan × ⎜1 − ⎜

⎝

⎟

⎟ ⎣ EF
 r P
r ⎠

Where: 

Qin = total water heater energy consumption, Btu/day,
 

Vol = daily draw volume, gal/day,
 

den = density of water, lb/gal,
 

Cp = specific heat of water, Btu/lb-o

F,
 

7-C-7 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ttank = tank thermostat set point temperature, oF,
 

Tin = inlet water temperature, o

F,
 

UA = standby heat-loss coefficient, Btu/h-o

F,
 

Tamb = temperature of the air surrounding the water heater, o

F,
 

PHP = rated input power of heat pump mode, Btu/h,
 

PR = rated input power of electric resistance mode, Btu/h,
 

EFr = resistance mode energy factor,
 

EFhpa = heat pump mode adjusted energy factor,
 

2 EF × (0.00019738× T -0.01842 ×T +1.3222625), and hp amb amb 

lfhp = fraction of water heating load that is satisfied by heat pump mode, %, 

rthp × P × EF HP hpa 

rthp × P × EF + (1 − rthp ) × P × EF HP hpa R R 

rthp = fraction of run time by heat pump mode (96.4%). 

Table 7-C.2.1 shows a comparison of energy use results for the DOE modified WHAM 

method used in this analysis, the NYSERDA Heat Pump Water Heater Site Screening Tool 

method, and DOE’s weatherization assistance program method. 

Table 7-C.2.1 Comparison of HPWH Energy Use Results 

Calculation Methodology Average Annual 

Energy Use (kWh/y) 

% Diff from method 

used in this analysis 

DOE modified WHAM 1343 -

NYSERDA method 1445 +7.6% 

Weatherization program 1095 -18.4% 

7-C.2.3.2 Calculating HPWH Cooling Effects 

Heat pump water heaters draw heat from the space in which they are located. Thus, when 

such a water heater is located in a conditioned space, its use affects the load that the home’s 

space heating and air conditioning equipment must meet. When the home is being heated, use of 

the heat pump water heater increases the heating load, and when the house is being cooled, its 

use decreases the cooling load. 

In some cases, a household will choose to install a venting system to deal with the above 

situation. DOE believes this would occur to 40% of the houses where the cooling load produced 

by the heat pump water heater in the heating season is large (greater than 4 MMBtu/year). In the 

remaining cases, DOE believes the household would not want to incur the cost of a venting 

system, and would instead operate their heating and cooling systems to compensate for the 

effects of the heat pump water heater. To account for these indirect effects of heat pump water 

heaters on home energy use, DOE estimated the impact on space heating and air conditioning 

energy consumption for some of the homes in the RECS electric water heater subsample that 

have the water heater in the conditioned space. 

7-C-8 

EE-2006-STD-0129 COMMENT 56.10
Determination of HPWH Operating Hours 

Tank Thermostat 

Temperature 

Average Monthly 

Inlet Water 

Temperature 

Average Daily Hot 

Water Use 

(Draw Model) 

Heating or 

Cooling Month 

Cooling Output 

into Conditioned 

Space 

No Heating/Cooling Decerased Cooling Load 

Pon 

(1,700 Btu/hr) 

Average Monthly 

Indoor Temperature 

(thermostat) 

Thome < 

(Toutdoor + 5) 

= Cooling 

Water Heat 

Capacity 

Water 

Density 

Average Monthly Temperature Difference 

Thome > 

(Toutdoor + 10) 

= Heating 

Average Daily Water 

Heater Heating Load 

Cooling Capacity 

(3,500 Btu/hr) 

Additional Heating 

Load 

No Additional 

Heating/Cooling 

RE 

(rated vol depedant 

and Adjusted for 

Tamb) 

Average Monthly 

Outdoor Temperature 

Installation 

Location 

Conditioned 

space 

Non-conditioned space 

RECS Sampled 

Household 

Overcooling Effect 

(Decreases Load 

by 1/3) 

Heatin

Equipm

Efficien

Cooling Equ

Efficien

AEO 20

No Additional 

Heating/Cooling 

Space He

Determination of Heating or Cooling Month 

Figure 7-C.2.5 Methodology for Calculating HPWH Cooling Effect
 

7-C-9 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

For each such home, DOE estimated the impact on space heating in heating months only 

(when indoor temperature is 10 degrees greater than the average outdoor temperature), and the 

impact on air conditioning for cooling months only (when indoor temperature is 5 degrees less 

than the average outdoor temperature). Figure 7-C.2.5 shows the methodology DOE used to 

calculate the amount of cooling added (i.e., heat removed) by the heat pump water heater. 

DOE calculated the amount of cooling added (heat removed) by the heat pump water 

heater as follows: 

vol × den ×C (T − T ) p tan k in CoolingInput = CoolingCap HPWH ×

P × RE × PA ON ,HPWH HPWH HPWH 

Where: 

CoolingInput = amount of cooling added by the HPWH, Btu/h,
 

vol = daily draw volume, gal/day,
 

den = density of water, lb/gal,
 

Cp = specific heat of water, Btu/lb-oF,
 

Ttank = tank thermostat set point temperature, oF,
 

Tin = indoor air temperature, oF,
 

PON,HPWH = rated input power, Btu/h,
 

RE = recovery efficiency, %,
 

PAhwh = performance adjustment factor, %, and
 

CoolingCapHPWH = cooling capacity of heat pump water heater, Btu/h.
 

For the PON and cooling capacity of the heat pump water heaters DOE created 

distributions that apply for a range of possible HPWH designs. Based on a consultant report, 

cooling capacity for HPWHs was determined to vary from 3200 to 4200 Btu/h.4 A uniform 

distribution was used to describe this range (with a mean value of 3700 Btu/h). The cooling 

capacity is estimated to be 2/3 of heating capacity (e.g., for mean cooling capacity value of 3700 

Btu./h this results in 5550 Btu/h heating capacity). Pon is calculated using heating capacity and 

the COP of the HPWH. DOE used a COP value of 3.0 for this calculation. DOE used this COP 

value for HPWH having efficiencies of 2.0 EF (e.g., for mean cooling capacity value of 3700 

Btu./h and 5550 Btu/h heating capacity, this results in Pon of 1850 Btu/h = 542 Watts). To 

account for the increase in efficiency for HPWHs at 2.2 EF, DOE adjusted the Pon value by 

multiplying by a fraction equal to the ratio of RE between 2.0 HPWH and 2.2 HPWH (e.g. 

continuing with the example, Pon of the 2.2 HPWH would be 93 percent of the 2.0 HPWH = 

1719 Btu/h = 504 Watts). 

DOE used RECS 20055 data for each household to determine the primary heating system, 

type of heating fuel used, and cooling system type. DOE then assigned an energy efficiency to 

each type of equipment to determine the energy use loss (from heating) or gain (from cooling). 

DOE based the energy efficiency of the heating and air conditioning equipment on the stockaverage values for 2015 given in EIA’s Annual Energy Outlook 2008.

6 To account for the times 

during the summer months when the air conditioner is not operating (e.g., at night), DOE 

reduced the estimated cooling benefits from the water heater by one-third (8 out of 24 hours). 

7-C-10 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The analysis results that the HPWH cooling effect affects 46.4 percent of households for 

an average of 6.1 months in the heating season and 29.6 percent of households for an average of 

4.7 months in the cooling season. Overall 49.8 percent of households are affected either in 

cooling and/or heating season. The average net cost from heating is about $82 per year, while the 

average net benefit for cooling is about $10 per year. These impacts are accounted for in the 

LCC and NIA analysis. 

Alternatively, as explained above, the household can install a venting system to vent the 

cold air out of the conditioned space. DOE estimates that the average cost for this installation 

would be similar to the average cost of adding a new plastic venting system for condensing 

furnaces which is found in the 2007 Furnace and Boilers Rulemaking.7 (See Appendix 8-A for 

more details) 

7-C.2.4 WHAM Equation for Gas Instantaneous Water Heaters 

For instantaneous water heaters, DOE calculated the energy use using a similar approach 

to storage water heaters, but modified to account for the absence of storage tank and adjusted for 

the performance observed in the field compared to that measured with the DOE test procedure. 

Figure 7-C.2.7 shows the methodology for calculating the energy consumption of instantaneous 

water heaters using the modified WHAM equation. 

For instantaneous water heaters, DOE utilized the approach used for storage water 

heaters to calculate the energy use, modified to account for the absence of storage tank. DOE 

applied a performance adjustment factor to account for results from studies of instantaneous 

8, 9, 10, 11 water heater performance under field conditions. Preliminary results from a study of 

instantaneous water heater installations conducted for the California Energy Commission (CEC) 

under field conditions at single-family two-occupant residence indicated higher energy use than 

under the test procedure conditions. The report concludes that the discrepancy is due to the extra 

losses at small draw volumes.8 The other studies have shown a similar effect. DOE’s approach 

used data from GTI and CEC studies to derive the adjustment factor as a distribution of values as 

a function of the household hot water use. 

To account for this phenomenon, DOE used test data from TIAX to come up with a 

relationship between hot water consumption and decreased performance as shown in the figure 

7-C.2.6 for the 0.82 EF unit tested using typical U.S. household draw patterns. DOE set an upper 

limit on the performance factor equal to the CEC recommended Energy Factor (EF) reduction for 

gas-fired instantaneous water heaters of 8.8 percent and a lower limit of 0%. 

7-C-11 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Efficiency (Qout/Qin)

0.83 

0.82 

0.81 

0.8 

0.79 

0.78 

0.77 

0.76 

0.75 

0.74 

0.73 

0.72 

TIAX Test Data for 0.82 IGWH 

DOE Performance Adjusted Efficiency 

0 10 20 30 40 50 60 70 80 90 100 

Hot Water Usage (gallons) 

Figure 7-C.2.6	 Efficiency versus Hot Water Usage for 

Instantaneous Gas Water Heater rated at 0.82 EF 

The instantaneous water heater WHAM equation is as follows: 

(T in ) ⎛ p ⎞

⎟

⎠

⎟ + 24
 ×Q
p 

×
 vol den C
 ×
 ×
 −T
 Q
 (T amb ) P tan k Qin =
 ×⎜1
−
 −T
 ⎜

⎝ Tank RE ×(1+ PA iwh ) PON 

Where: 

Qin = total water heater energy consumption, Btu/day,
 

vol = daily draw volume, gal/day,
 

den = density of water, lb/gal,
 

Cp = specific heat of water, Btu/lb-oF,
 

Ttank = tank thermostat set point temperature, oF,
 

Tin = inlet water temperature, oF,
 

RE = recovery efficiency, %,
 

PAiwh = performance adjustment factor, %,
 

Qp = pilot input rate, Btu/h,
 

Qout = heat content of the water drawn from the water heater, Btu/h, and
 

Pon = rated input power, Btu/h,.
 

7-C-12 

EE-2006-STD-0129 COMMENT 56.10
Average Yearly Tank 

Temperature 

(Distribution) 

Average Monthly 

Inlet Water 

Temperature 

Average Daily Hot 

Water Use 

Average Monthly 

Ambient 

Temperature 

Draw Model 

Mode 

Energy 

Consumption During Water 

Heating 

Energy 

Consumption 

During Standby 

Water Heating 

Standby 

Average Daily 

Total Energy Use 

for Month 

RE 

Qp 

Modified WHAM Calculation 

Pon 

Heat Capacity of 

Water Density of Water 

Average Monthly Temperature Difference 

Water Heater Heating Load 

WH ON = 24 hrs 

Perfor

Adjustme

Figure 7-C.2.7 Methodology for Calculating Instantaneous WH Energy Consumption using Modified 

7-C-13 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The performance adjustment factor for instantaneous water heaters (PAiwh) was derived 

from a study conducted for the California Energy Commission (CEC) in 2006.8 According to this 

report, current DOE test procedure energy factor calculations for gas-fired instantaneous water 

heaters overvalue their performance by neglecting the impact of small hot water draws and heat 

exchanger “cool down” on overall performance. The DOE test procedure measures six 

successive draws of approximately 10 gallons, while actual field use has many more small 

draws. The 8.8 percent adjustment factor is derived using average hot water use profiles and 

weighting by more efficient “hot starts” and less efficient “cold starts”. 

7-C.3 POOL HEATERS 

DOE calculated the average annual fossil fuel energy, EF, using the DOE test 

procedure:12 

EF = BOH ×QIN − (POH − BOH ) ×Qp 

Where: 

BOH = burner operating hours, h/year,
 

Qin = pool heater input rate, kBtu/h,
 

POH = pool operating hours, h/yr, and
 

Qp = pilot light input rate, kBtu/yr.
 

The burner operating hours are calculated using the pool heater heating load (PHHL) for 

each sample household. The equation for BOH is as follows: 

LOAD BOH = QIN t × E

Where: 

BOH = burner operating hours, h/year,
 

PHHL = pool heater heating load, btu/year, (see Appendix G),
 

Qin = pool heater input rate, kBtu/h, and
 

Et = thermal efficiency.
 

DOE calculated the electricity consumption using the following formula 

E = BOH × PE − (POH − BOH ) × PE F s tan by 

Where: 

BOH = burner operating hours,
 

PE = electrical consumption of the heater,
 

POH = pool operating hours (h/yr), and
 

PEstby = electrical consumption of the heater when the burner is off.
 

7-C-14 

EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7-C.4 DIRECT HEATING EQUIPMENT
 

DOE calculated the average annual fuel energy, EF, for single-stage direct heating 

equipment using the following formula from the current revision of DOE’s test procedure:13 

E F = BOH SS IN P × (Q − Q ) + 8760 ×QP 

Where: 

BOH = burner operating hours, h/year,
 

Qin = input capacity (at the max input rate), kBtu/h,
 

8760 = hours per year, and
 

Qp = pilot light input rate, kBtu/h.
 

The burner operating hours are calculated using the calculated house heating load (HHL) 

for each sample household (see Appendix G). The equation for BOH is as follows: 

BOH = A× HHL − 4160 ×Q ×η , SS P U 

Where: 

BOHSS = burner operating hours, h/year,
 

100,000
 

341,000 × PE + (Q in P U − Q )×η A = ,
 

HHL = house heating load (see Appendix G), btu/year,
 

PE = maximum electric power, kW,
 

4160 = average heating season hours,
 

QP = pilot light input rate, kBtu/h,
 

2950 AFUE ×η SS in ×Q

η

2950 ×η SS in ×Q − AFUE × 2.033 × 4600 ×QP U = , and
 

ηSS = steady state efficiency, %.
 

The steady state efficiency (ηSS) is calculated by solving for ηSS in the equation given in 

section 4.1.17 of the DOE test procedure using the following equation and the values for the 

parameters DF, DS, PF, and LJ given in the DOE test procedure: 

AFUE +1.78 × D +189 × D −129 × P − 2.8× L +1.81 F S F J η SS = 0.968 

The electricity consumption is calculated as follows: 

ElectUse = BOH × PE + (8760 − BOH ) × Pstby

Where: 

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EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

ElecUse = DHE electricity consumption, kWh/year,
 

BOH = burner operating hours, h,
 

PE = electricity demand when the product is firing, kW, and
 

Pstby = DHE standby power draw (when the burner is OFF), kW.
 

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EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

REFERENCES 

1.	 Lutz, J., C. D. Whitehead, A. Lekov, D. Winiarski, and G. Rosenquist, WHAM: A 

Simplified Energy Consumption Equation for Water Heaters., in 1998 ACEEE Summer 

Study on Energy Efficiency in Buildings. 1998: Asilomar, CA. p. 1.171-1.183. 

2.	 Kelso, J., Incorporating Water Heater Replacement into The Weatherization Assistance 

Program, May 2003, 2003. D&R International, Ltd. Information Tool Kit. 

3.	 Maxwell, J., Heat Pump Water Heater Economic Model, personal communication. 

NYSERDA. 2004. 

4.	 Hiller, C., Consultant Report - Residential Heat Pump Water Heater Ratings. 2009 

5.	 U.S. Department of Energy - Energy Information Administration, Residential Energy 

Consumption Survey: 2005 Public Use Data Files, 2005. 

<http://www.eia.doe.gov/emeu/recs/recspubuse05/pubuse05.html> 

6.	 U.S. Department of Energy - Energy Information Administration, Annual Energy 

Outlook 2008 (Revised Early Release) with Projections to 2030, 2008. Washington, DC. 

Report No. DOE/EIA-0383(2008). 

7.	 U.S. Department of Energy - Energy Efficiency & Renewable Energy, Technical Support 

Document: Energy Efficiency Standards for Consumer Products: Residential Furnaces 

and Boilers, 2007. Washington, DC. 

8.	 Davis Energy Group, Measure Information Template: Tankless Gas Water Heaters, May 

18, 2006. Docket # 07-BSTD-1. 

<http://www.energy.ca.gov/title24/2008standards/prerulemaking/documents/2006-05­

18_workshop/2006-05-11_GAS_WATER.PDF> 

9.	 Gas Technology Institute, Literature Review of Tankless Water Heaters, January 3, 2007, 

2007. Des Plaines, Illinois. Report No. CEC# 500-05-011/ GTI# 20272. 

10.	 Bradford White Inc., Tankless vs. Tank Type Storage Water Heater Efficiency 

Comparison Testing, 2005. PM Engineer. (Last accessed 8/17/2007, 

<http://www.pmengineer.com/copyright/8cf9e86f7c298010VgnVCM100000f932a8c0> 

11.	 Entchev, E., F. Szadlowski, L. Yang, J. Gusdorf, M. Swinton, D. Mackenzie, M. 

Manning, C. Zaloum,, Benchmarking the Performance of Natural Gas Combination 

Systems - Project #5: Tankless Water Heater in Domestic Hot Water Application. 

CETC/SBE/IES project #00300-05, 2005. 

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EE-2006-STD-0129 COMMENT 56.10
 

 

 

 

 

 

12.	 Department Of Energy, Appendix E to Subpart B of Part 430-Uniform Test Method For 

Measuring The Energy Consumption Of Water Heaters. filed as "WH Test Procedure 10 

CFR 430 subpart B, Appendix E". 

13.	 Department Of Energy, Appendix O to Subpart B of Part 430-Uniform Test Method For 

Measuring The Energy Consumption Of Vented Home Heating Equipment. filed as "WH 

Test Procedure 10 CFR 430 subpart B, Appendix E". 

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EE-2006-STD-0129 COMMENT 56.10