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-iAPPENDIX 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 equation 1 yields average daily water heater energy consumption (Q in ), and is expressed as follows:

7-C-1⎛
1

− UA × ( T tank − T amb ) ⎟ + ⎞

⎟ ⎠ ( T

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

on

Where:

Q in = total water heater energy consumption, Btu/day,

RE = recovery efficiency, %,

P

on = rated input power, Btu/h,

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

T

tank = thermostat setpoint temperature, o F,

T

in = inlet water temperature, o F,

T

amb = 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

C

p = 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:

Q electricity = Q in = P ON = P

aux = P standy = in Q = Q

× 

# ( P

− P 

# )

− P × 24

electtricity aux s tan dy s tan dy P

ON

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-2Gas and Oil StorageWHs has both Fueland Elec UseAverage Yearly TankTemperature(Distribution)Average MonthlyInlet WaterTemperatureAverage Daily HotWater UseAverage MonthlyAmbientTemperatureDraw ModelModeEnergyConsumptionDuring WaterHeatingEnergyConsumptionDuring StandbyWater HeatingStandbyAverage DailyTotal Energy Usefor MonthREUAWHAM CalculationPonHeat Capacity ofWaterDensity of WaterAverage Monthly Temperature DifferenceWater HeaterHeating LoadTest ProcedureParametersWH ON = 24 hrsEFFuel UseElec UseFigure 7-C.2.2 Methodology for Calculating Storage Water Heater Energy Consumption using WHAM Equation7-C-3DOE calculated gas consumption by subtracting electricity consumption from total water heater energy consumption (Q in ). 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 o F. 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 o F and 100 o F, 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-4Average Daily HotWater UseAverage MonthlyAmbientTemperatureDraw ModelMode ofOperationWHAM (ElectricResistance Mode)WHAM (HeatPump Mode)ElectricResistanceModeHP ModeHeat Pump LoadFactor (% EnergyUse at HP Mode)Monthly EnergyUseREElectric. Res.= 98%EF = 2.2 @ 50 GalTankECR ModelDataREHeat Pump.= 242%UA = 1.82RECS SampledHouseholdRE AdjustmentFactorTest Data(JohnMaxwell)Monthly REHeat Pump.Calculation ofHPWH RuntimeFraction1% ER runtime per9500 Btu of DailyHot Water LoadEngineeringSpreadsheetTest Data/AssumptionPON,Electric. Res.= 4.5kWPON,HPWH= .5 kWAbove 32 F?YES(Calculate)HP Load =Adjusted RE *PONER Load = RE *PONNO (0% HP Mode)ECR ModelDataECR ModelDataFigure 7-C.2.4 Methodology for Calculating HPWH Energy Consumption using Modified WHAMEquation7-C-5The 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 

### ) ( T 

### )

− − + 24 × UA × Q vol den C T T × × × = in P k Tank amb tan ⎛ ⎜ ⎜ ⎞ ⎟ ⎟ 

### ( T

− T 

### )

k amb UA × tan 1

− × RE P ⎝ ⎠ ⎣ ⎦ ER ON

, ER

Where:

Q in = total water heater energy consumption, Btu/day,

vol = daily draw volume, gal/day,

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

C

p = specific heat of water, set constant at 1.000743 Btu/lb- o F,

T

tank = tank thermostat set point temperature, o F,

T

in = inlet water temperature, o F,

RE HPWH = recovery efficiency of heat pump mode, %,

RE ER = recovery efficiency of electric resistance mode, %,

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

T

amb = temperature of the air surrounding the water heater, o F,

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

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

PA hwh = 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:

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

vol × den × C 

### ( T

− T 

### )

P tan k in ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ , when T amb >32oF and 0 when T amb <32 oF. 100

− 9500

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

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

RE HPWH = recovery efficiency of heat pump mode, %,

RE ER = recovery efficiency of electric resistance mode, %,

PA hwh = performance adjustment factor, %,

0

. 00019738 × T 2

- 0

. 01842 × T + 1

. 3222625 , and amb amb
T

amb = temperature of the air surrounding the water heater, o F.

7-C-67-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 Q
in = EF × (1 + PA )

Where:

Q in = total water heater energy consumption, btu/day,

vol = daily draw volume, gal/day,

den = density of water, lb/gal,

C

p = specific heat of water, Btu/lb- o F,

T

tnk = tank thermostat set point temperature, o F,

T

in = 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 + 0.0011 × T

− 0.4833 × T + 0.0857, when > 32 F amb amb amb 

### T amb



### 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

− ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ × ⎜

⎜ ⎝ P
HP 

### ( T in 

### ) ( T 

### )

− − + 24 × UA × Q vol den C T T × × × = in P k Tank amb tan 

### ( T

− T 

### )

k amb ⎛ ⎞ UA × tan 1

− × ⎜

⎜ ⎝ ⎟ ⎟ ⎠ EF P ⎣

r r Where:

Q in = total water heater energy consumption, Btu/day,

Vol = daily draw volume, gal/day,

den = density of water, lb/gal,

C

p = specific heat of water, Btu/lb- o F,

7-C-7T tank = tank thermostat set point temperature, o F,

T

in = inlet water temperature, o F,

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

T

amb = temperature of the air surrounding the water heater, o F,

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

P

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

EF

r = resistance mode energy factor,

EF hpa = 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-8Determination of HPWH Operating HoursTank ThermostatTemperatureAverage MonthlyInlet WaterTemperatureAverage Daily HotWater Use(Draw Model)Heating orCooling MonthCooling Outputinto ConditionedSpaceNo Heating/CoolingDecerasedCooling LoadPon(1,700 Btu/hr)Average MonthlyIndoor Temperature(thermostat)Thome <(Toutdoor + 5)= CoolingWater HeatCapacityWaterDensityAverage Monthly Temperature DifferenceThome >(Toutdoor + 10)= HeatingAverage Daily WaterHeater Heating LoadCooling Capacity(3,500 Btu/hr)Additional HeatingLoadNo AdditionalHeating/CoolingRE(rated vol depedantand Adjusted forTamb)Average MonthlyOutdoor TemperatureInstallationLocationConditionedspaceNon-conditioned spaceRECS SampledHouseholdOvercooling Effect(Decreases Loadby 1/3)Heating Fuel andEquipment TypeCooling EquipmentTypeHeatingEquipmentEfficiencyCooling EquipmentEfficiencyAEO 2007*RECSSample*No AdditionalHeating/CoolingSpace Heating & Cooling Eqp ImpactsDetermination of Heating or Cooling MonthFigure 7-C.2.5 Methodology for Calculating HPWH Cooling Effect7-C-9For 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,

C

p = specific heat of water, Btu/lb- o F,

T

tank = tank thermostat set point temperature, o F,

T

in = indoor air temperature, o F,

P ON,HPWH = rated input power, Btu/h,

RE = recovery efficiency, %,

PA hwh = performance adjustment factor, %, and CoolingCap HPWH = cooling capacity of heat pump water heater, Btu/h.

For the P ON 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 2005 5 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-10The 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-11Efficiency (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 × Q

− vol den C T × × 

## ( T amb 

## ) P k tan 1

− − Q
in = T × ⎜

⎜ ⎝ Tank RE × (1 + PA iwh ) P ON

Where:

Q in = 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,

T

tank = tank thermostat set point temperature, o F,

Tin = inlet water temperature, o F,

RE = recovery efficiency, %,

PA iwh = performance adjustment factor, %, Q

p = pilot input rate, Btu/h,
Q out = heat content of the water drawn from the water heater, Btu/h, and

Pon = rated input power, Btu/h,.

7-C-12Average Yearly TankTemperature(Distribution)Average MonthlyInlet WaterTemperatureAverage Daily HotWater UseAverage MonthlyAmbientTemperatureDraw ModelModeEnergyConsumptionDuring WaterHeatingEnergyConsumptionDuring StandbyWater HeatingStandbyAverage DailyTotal Energy Usefor MonthREQpModified WHAM CalculationPonHeat Capacity ofWaterDensity of WaterAverage Monthly Temperature DifferenceWater HeaterHeating LoadWH ON = 24 hrsFuel UseElec UsePerformanceAdjustment FactorFigure 7-C.2.7 Methodology for Calculating Instantaneous WH Energy Consumption using Modified WHAM Equation7-C-13The performance adjustment factor for instantaneous water heaters ( PA iwh ) 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, E F , using the DOE test
procedure: 12

E F = BOH × Q
IN − ( 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 = × E Q
IN t Where:

BOH = burner operating hours, h/year,

PHHL = pool heater heating load, btu/year, (see Appendix G),
Q in = pool heater input rate, kBtu/h, and

E t = 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

PE stby = electrical consumption of the heater when the burner is off.

7-C-147-C.4 DIRECT HEATING EQUIPMENT

DOE calculated the average annual fuel energy, E F , for single-stage direct heating equipment using the following formula from the current revision of DOE’s test procedure: 13

E = BOH × ( Q

− Q ) + 8760 × Q

F SS IN P P

Where:

BOH = burner operating hours, h/year,
Q in = input capacity (at the max input rate), kBtu/h, 8760 = hours per year, and
Q

p = 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:

BOH SS = burner operating hours, h/year,
100,000

341,000 × PE + 

## ( Q

− Q 

## ) × η in P U A = , HHL = house heating load (see Appendix G), btu/year,

PE = maximum electric power, kW,

4160 = average heating season hours,
Q P = pilot light input rate, kBtu/h,

2950 AFUE × η × Q

SS in 2950 × η × Q

− AFUE × 2.033 × 4600 × Q

SS in P η U = , and

η SS = steady state efficiency, %.

The steady state efficiency ( η SS ) is calculated by solving for η SS in the equation given in section 4.1.17 of the DOE test procedure using the following equation and the values for the

parameters D F , D S , P F , and L J 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 ) × P stby Where:

7-C-15ElecUse = DHE electricity consumption, kWh/year,

BOH = burner operating hours, h,

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

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

7-C-16REFERENCES

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

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

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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.

7-C-1712. 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".

7-C-18