APPENDIX 7-E. DERIVATION OF HEATING LOAD FOR DIRECT HEATING EQUIPMENT AND POOL HEATERS

TABLE OF CONTENTS

7-E.1 INTRODUCTION ................................................................................................. 7-E-1 7-E.2 DIRECT HEATING EQUIPMENT ...................................................................... 7-E-1 7-E.2.1 Derivation of House Heating Load for Direct Heating Equipment ....................... 7-E-1 7-E.2.2 Adjustment to Direct Heating Equipment Energy Consumption using RECS...... 7-E-2

7-E.3 POOL HEATERS .................................................................................................. 7-E-3 7-E.3.1 Derivation of Pool Heaters Heating Load for Pool Heaters .................................. 7-E-3 7-E.3.2 Adjustment of Energy Consumption from RECS.................................................. 7-E-4

LIST OF TABLES

Table 7-E.2.1 Adjustment of RECS Energy Consumption for Secondary DHE........ 7-E-3 Table 7-E.3.1 Assignment of Existing Pool Heater Thermal Efficiency by RECS

Year...................................................................................................... 7-E-4 Table 7-E.3.2 Adjustment of RECS Energy Consumption for Pool Heaters ............. 7-E-4

7-E-iAPPENDIX 7-E. DERIVATION OF HEATING LOAD FOR DIRECT HEATING

EQUIPMENT AND POOL HEATERS

7-E.1 INTRODUCTION

RECS 2005 provides variables for the energy consumption for direct heating equipment and pool heaters. DOE used this information to determine the annual house heating load (HHL) and pool heater heating load (PHHL).

7-E.2 DIRECT HEATING EQUIPMENT

7-E.2.1 Derivation of House Heating Load for Direct Heating Equipment

Annual house heating load (HHL) is determined using the DOE’s test procedure 1, 2

approach as follows. First, from the test procedure the average annual fuel energy for gas or oil vented heaters, E F , for single-stage direct heating equipment is given by the following equation:

E = BOH × ( Q

− Q ) + 8760 × Q

F SS IN P P

Then the burner operating hours (BOH SS ) can be rewritten as follows using DOE’s test procedure equation for BOH SS and substituting in the HHL:

BOH = HHL × A

− 4160 × A × Q × η SS P U

Finally, the HHL is determined by replacing E F with the RECS 2005 calculated annual energy consumption ( Q YR,RECS ) and adding an adjustment factor to account for future improvements to the building shell and increases in home area:

⎛

U ⎞ ⎟ ⎠

⎟ ∗ Q

− 8760 × Q

YR

, RECS P + 4160 × × η HHL = Q Adj Factor ⎜ ⎜ ⎝ P _ A × ( Q IN − Q P )

Where:

Q YR,RECS = annual heating fuel use from RECS 2005, kBtu/yr, Q P = pilot input rate, Btu/h, Q IN = rated input capacity of direct heating equipment, Btu/h,

8760 = hours in a year, h,

4160 = average heating season hours according to test procedure, h,

A = test procedure factor, h/kBtu,
100,000

341,000 × PE + 

## ( Q

− Q 

## ) × η in P U

, PE = DHE power consumption while the burner is on, W,

η U = part load utilization efficiency (%),

7-E-12950 AFUE × η × Q

SS in 2950 × η × Q

− AFUE × 2.033 × 4600 × Q

SS in P

, η SS = steady state efficiency (%), and Adj_Factor = adjustment factor.

The average pilot input rate for the above calculation is 400 Btu/h for gas wall fan DHE and gas wall gravity DHE, 450 Btu/h for gas floor DHE, and 350 Btu/h for gas room DHE. 3

Chapter 7 describes the input capacity ( Q IN ) values.

The PE value reflects a design with electrical components. DOE used values for PE given in the 1993 technical support document. 3

The adjustment factor ( Adj_Factor ) takes into account future improvements to the building shell and increases in home area based on EIA’s 2009 Annual Energy Overview ( AEO

2009 ) projections for retrofit and new construction in 2013. 4

The steady state efficiency ( η SS ) is calculated by solving for η SS in the equation given in section 4.1.17 in the DOE test procedure as follows:

AFUE + 1.78 × D + 189 × D

− 129 × P

− 2.8 × L + 1.81
F S F J η

SS = 0

. 968

The DOE test procedure gives values for the parameters D F , D S , P F , and L J

.

7-E.2.2 Adjustment to Direct Heating Equipment Energy Consumption using RECS

For the households for which it is clear that the natural gas use for heating is associated solely with use of the direct heating equipment as primary or secondary heating equipment, DOE used the annual heating fuel consumption variable for the housing unit from RECS 1993-2005. 1,

5, 6, 7

For the households that use direct heating equipment as secondary heating equipment and also use primary gas heating equipment other than direct heating equipment, DOE made adjustments to the household heating load by using a RECS 1993-2005 variable which reports the fraction of heating energy consumption provided by the primary heating system. Using this variable, DOE estimated the fraction of heating provided by the secondary direct heating equipment (see Table 7-E.2.1) using a triangular distribution.

7-E-2Table 7-E.2.1 Adjustment of RECS Energy Consumption for Secondary DHE

RECS Value for RECS Value Definition (How much Fraction of DHE Heating (%)
EQMAMT heat main heating equipment provides) Min Avg Max

1 Almost all 5 15 25

2 About three-fourths 15 25 35

3 Close to half of all your heat 35 40 45

6 Don't know 5 25 45

7-E.3 POOL HEATERS

7-E.3.1 Derivation of Pool Heaters Heating Load for Pool Heaters

Annual pool heaters heating load (PHHL) is determined using the DOE test procedure as

follows. 8 First, from the test procedure the average annual fuel energy for gas pool heaters, E F , is given by the following equation:

E = BOH × Q + ( POH

− BOH ) × Q

F IN P

Then the burner operating hours ( BOH SS ) can be written as follows:

PHHL BOH SS = Q IN × E

t

1, 5, 6, 7 DOE determined the PHHL by replacing E F with the RECS 1993-2005 calculated annual energy consumption ( Q RECS ):

⎛ ⎞ Q IN ( Q

− ) PHHL = Q POH × E × ⎜ ⎜ ⎝ ⎟ ⎟ ⎠ RECS P t Q IN − Q P

Finally, because Q P is much smaller than Q IN for pool heaters, DOE approximated the PHHL using the following formula:

PHHL = ( Q

− Q × POH ) × E RECS P t Where:

Q RECS = Pool heater annual fuel consumption (kBtu/yr), Q P = pilot light input rate (kBtu/yr),

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

E t = thermal efficiency of the household’s existing pool (%).

For units with a pilot light, DOE assigned a pilot light input rate of 1,000 Btu/h. 3, 9 DOE assigned pool heaters with pilot lights to 26.5 percent of households based on the fraction of

7-E-3models in the May 2008 FTC pool heater directory. 10 DOE estimated the remaining 73.5 percent were equipped with electronic ignition.

The DOE test procedure uses an average value for pool operating hours (POH) of 4,464 hours per year. DOE used a distribution around this average to assign POH to the sample households. The distribution ranges from 235 h/yr to 8760 h/year (100 percent of the time). The value of 235 h/year is the minimum value that fits the function used to calculate the distribution, and is close to the minimum number of hours that a pool heater burner can operate.

DOE assigned the sample households an existing pool heater having thermal efficiency based on the survey year. Thus, for example almost all pool heaters associated with RECS 2005 households were installed after 1989 (based on a maximum lifetime for pool heaters of 16 years), which was after EPCA mandated the 78-percent energy conservation standard. For every previous survey the thermal efficiency is assumed to be 1-percent less. See table below for the thermal efficiency assigned to each households RECS year.

Table 7-E.3.1 Assignment of Existing Pool Heater Thermal Efficiency by RECS Year

RECS Year Thermal Efficiency (%)

RECS 2005 78

RECS 2001 77

RECS 1997 76

RECS 1993 75

7-E.3.2 Adjustment of Energy Consumption from RECS

Pool heater annual fuel consumption ( Q RECS ) for each household with a pool heater comes from RECS 1993-2005. In most cases the fuel energy consumption in RECS 1993-2005 includes other gas appliances such as gas clothes dryers and/or gas cooking equipment. For households having a pool heater and gas clothes dryers and/or gas cooking equipment, DOE subtracted the average value that represents the energy use of this equipment from the fuel energy consumption provided in RECS (see Table 7-E.3.2).

Table 7-E.3.2 Adjustment of RECS Energy Consumption for Pool Heaters Gas equipment in households with pool heaters Annual Energy Consumption Subtracted (kBtu/h)

RECS2005 RECS2001 RECS1997 RECS1993 Cooking Equipment Only 6805 4315 6667 4128 Clothes Dryer Only 7354 7235 8555 6878 Cooking Equipment and Clothes Dryer 13,521 10,892 12,345 9389

7-E-4REFERENCES

1. 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 >

2. 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".

3. U.S. Department of Energy-Office of Codes and Standards, Technical Support Document: Energy Efficiency Standards for Consumer Products: Room Air Conditioners, Water Heaters, Direct Heating Equipment, Mobile Home Furnaces, Kitchen Ranges and Ovens, Pool Heaters, Fluorescent Lamp Ballasts & Television Sets , 1993. Washington, DC Vol. 1 of 3. Report No. DOE/EE-0009.

4. Energy Information Administration, Annual Energy Outlook 2009 with Projections to

2030 , 2009. Washington, DC. Report No. DOE/EIA-0383(2009).

< http://www.eia.doe.gov/oiaf/aeo / >

5. U.S. Department of Energy - Energy Information Administration, Residential Energy Consumption Survey: 2001 Public Use Data Files, 2001.

< http://www.eia.doe.gov/emeu/recs/recs2001/publicuse2001.html >

6. U.S. Department of Energy - Energy Information Administration, Residential Energy Consumption Survey: 1997 Public Use Data Files, 1997.

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

7. U.S. Department of Energy - Energy Information Administration, Residential Energy Consumption Survey: 1993 Public Use Data Files 1993.

< http://www.eia.doe.gov/emeu/recs/93publicuse.html >

8. Department Of Energy, Appendix P to Subpart B of Part 430-Uniform Test Method For Measuring The Energy Consumption Of Pool Heaters . filed as "PH Test Procedure 10 CFR 430 subpart B, Appendix P".

9. Hamos, R., Consultant Report - Pool Heater Pilot Size , 2008.

10. Federal Trade Commission, Appliance Energy Data - Pool Heaters, 2008.

< http://www.ftc.gov/bcp/conline/edcams/eande/appliances/data/2008/pool/index.htm >

7-E-5