7.7-i

APPENDIX 7.7. GAS AND ELECTRICITY USE FOR MODULATING FURNACES TABLE OF CONTENTS 7.7.1 INTRODUCTION ................................................... 7.7-1 7.7.2 SINGLE STAGE EQUIVALENT BURNER OPERATING HOURS ............. 7.7-1 7.7.2.1 Annual Average Heating Energy (E M ) ................................ 7.7-2 7.7.3 BURNER OPERATING HOURS AT REDUCED AND HIGH FIRING MODES ... 7.7-2 7.7.3.1 Fraction of Heating Load ......................................... 7.7-3 7.7.3.2 Balance-Point Temperature (TC ) .................................... 7.7-3 7.7.3.3 Oversize Factor ( " ) ............................................. 7.7-3 7.7.3.4 Heating Capacity at Maximum Input Rate (Q OUT ) ....................... 7.7-4 7.7.3.5 Reduced Fuel Input Rate Heating Capacity ............................ 7.7-5 7.7.3.6 Design Heating Requirement ....................................... 7.7-5 7.7.4 FAN MOTOR ELECTRICITY CONSUMPTION ........................... 7.7-6 LIST OF TABLES Table 7.7.3.1 Q OUT and Corresponding DHR values ............................... 7.7-5 LIST OF FIGURES Figure 7.7.3.1 X Rand X

H versus Balance-Point Temperature for Modulating Furnaces and Boilers .................................................... 7.7-47.7-1

APPENDIX 7.7. GAS AND ELECTRICITY USE FOR MODULATING FURNACES 7.7.1 INTRODUCTION The Department modeled two-stage modulating furnaces with both high and reduced firing rates. The two different firing rates change the amount of gas and electricity consumed by the furnace burner and circulating air blower motor. This appendix describes how DOE calculated the gas consumed by the burner and electricity consumed by the circulating air blower motor at the two firing rates. This calculation method is based on the procedure in the ASHRAE Standard 103. 1 The gas consumed by the burner during the two firing rates depends on the amount of time the burner is firing at each mode and the gas consumption rates. The first section of this appendix discusses the calculation for burner operating hours and firing rates. The six variables for the burner operating hours calculation are: fraction of heating load, balance-point temperature, oversize factor, heating capacity at high rate, heating capacity at reduced rate, and the design heating requirement. The second section describes the circulating blower motor electricity consumption calculation. 7.7.2 SINGLE STAGE EQUIVALENT BURNER OPERATING HOURS The Department calculated equivalent single-stage burner operating hours as;



# [ ] BOH HHL Q AFUE BE y PE y R SS IN IG IG = × × × + × × × × × 1000000 1000 3 412 . where: HHL = the annual household heating load (kBtu/yr), BE = blower motor electrical power consumption, y = ratio of blower on-time to average burner ontime, as defined in the

ASHRAE test procedure, 1 PE IG = electrical input rate to the interrupted ignition device on burner, yIG = ratio of ignition device on-time to average burner ontime, as defined in

10.2.1 of DOE test procedure, 2 R = 2.3 for two-stage modulation, 3.0 for step-modulating controls when the

ratio of minimum-to-maximum output is less than 0.5. (For non-weatherizedgas furnaces, the ratio of minimum-to-maximum output is 40% for stepmodulating, indicating R = 3.0.), and AFUE = Annual Fuel Utilization Efficiency.7.7-2

For non-weatherized gas furnaces, with electronic ignition, AFUE is the same as steady-state efficiency. This equation for BOH SS is similar to the equation from the DOE test procedure. The main difference is that the LCC spreadsheet has a house heating load for each house, while the test procedure equation uses average heating load hours and design heating requirement (DHR). 7.7.2.1 Annual Average Heating Energy (EM) For furnaces and boilers equipped with two-stage or step-modulating controls, the average annual energy used during the heating season, E M , from ASHRAE Standard 103, is defined as: 

### E Q Q BOH Q M IN P SS P 

### = − × + − × ( ) ( )

8760 4600 where:
= steady-state nameplate maximum fuel input rate, 

### Q IN
= national average number of burner operating hours, and 

### BOH SS = fuel input from pilot light. 

### QP For non-weatherized gas furnaces, there is no pilot light, so QP= 0, and E Mbecomes: 

### E Q BOH M IN SS 

### = ×
7.7.3 BURNER OPERATING HOURS AT REDUCED AND HIGH FIRING MODES The Department calculated burner operating hours ( BOH ) as shown below for reduced firing (R) and high firing (H). 

### BOH X E Q R R M

IN R 

### = ×

, where:
= fraction of heating load at reduced fuel input rate operating mode, 

### X R = average annual energy used during the heating season (kBtu), and 

### E M = steady-state reduced fuel input rate (kBtu/h). Q IN R , BOHH X H E M QIN = ×7.7-3

where: = fraction of heating load at high, or maximum, fuel input rate operating mode, X H and

= steady-state high, or maximum, fuel input rate (kBtu/h). QIN 7.7.3.1 Fraction of Heating Load The Department determined X H and X R , the fraction of heating load at the maximum and reduced fuel input operating modes, from a correlation with the balance-point temperature according to ASHRAE Standard 103. Figure 7.7.3.1 shows this correlation. 7.7.3.2 Balance-Point Temperature (T C) The balance-point temperature (TC ) apportions the annual heating load between the reduced cycling mode and maximum cycle mode. The Department calculated the balance-point temperature as:

T C QOUT R QOUT = − × − ×       65 60 1 ( ) ( ) ,

a where: 65 = typical average outdoor temperature at which a furnace or boiler starts

operating (°F), 60 = the difference between 65 / F and the typical outdoor design temperature of 5

/ F (°F), " = oversize factor, QOUT , R = heating capacity at reduced fuel input rate (kBtu/h), and QOUT = heating capacity at maximum fuel input rate (kBtu/h). If the balance point temperature is less than zero, the Department used T C= 0 . 7.7.3.3 Oversize Factor ( " ) The oversize factor, " , is a ratio between the heating capacity at the maximum fuel input rate and the DHR, less 1, as defined in ASHRAE Standard 103.



### a = − Q DHR OUT 

### 17.7-4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 20 40 60 Balance Point Temperature, TC (°F)Fraction of Total Annual Heating Load Applicable toReduced Operating Mode (XR) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Fraction of Total Annual Heating Load Applicable toMaximum or Modulating Mode (XH)

This figure is based on 5200 degree-days and 5°F outdoor design temperature. Figure 7.7.3.1 XR

and X

Hversus Balance-Point Temperature for Modulating Furnaces and Boilers 7.7.3.4 Heating Capacity at Maximum Input Rate (Q OUT ) The Q OUT is expressed to the nearest 1000 Btu/h and is calculated for non-condensing and condensing furnaces as:

Q OUT = Q IN × (0.7247 × AFUE

+ 22.346) for non-condensing and7.7-5 Q OUT = Q IN × (0.7247 × AFUE

+ 22.346) for condensing furnaces. The Department derived these equations by fitting a linear function of input capacity and AFUE to the heating capacity of the furnace models listed in the GAMA directory. 7.7.3.5 Reduced Fuel Input Rate Heating Capacity For QOUT,R , the Department assumed that the steady-state efficiency at the reduced input rate is the same as a maximum input rate. Thus, the reduced fuel input heating capacity is: 

### Q Q Q

Q OUT R IN R OUT IN , , 

### = × 7.7.3.6 Design Heating Requirement Table 7.7.3.1, taken from ASHRAE Standard 103, shows DHR for boilers and furnaces with different output capacities. Table 7.7.3.1 Q OUT and Corresponding DHR values

Output Capacity (Btu/h) DHR (kBtu/h) 5000 - 10,000 5 11,000 - 16,000 10 17,000 - 25,000 15 26,000 - 42,000 20 43,000 - 59,000 30 60,000 - 76,000 40 77,000 - 93,000 50 94,000 - 110,000 60 111,000 - 127,000 70 127,000 - 144,000 80 145,000 - 161,000 90 162,000 - 178,000 100 179,000 - 195,000 110 196,000 and over 1307.7-6

The Department used the following piece-wise linear equation to determine DHR in the LCC analysis. This avoids discontinuities of DHR as Qout changes bins.



### DHR if Qout Qout

if Qout Qout if Qout Qout

else = < = × −

< = × − ≤ = × −

=               ( ) . . ( ) . . ( ) . .

15 0 775 0 375 30 0 5667 3 25 195 0 5879 0 1364

130 For induced draft units, 

### A y PE y BE R Q Q Effy IG IG IN P HS 

### = × × + × × + − × 100000 341300 ( ) ( )

7.7.4 FAN MOTOR ELECTRICITY CONSUMPTION In modulating furnaces, the circulating blower motor operates at two different rates. At the high firing rate, the blower motor speed is equal to the non-modulating blower speed. At reduced firing rate, the blower motor operates at the lowest speed. The fan motor electricity consumption (BE) for these operating modes is determined as explained in Chapter 7. The burner and the fan motor are coordinated so that when the burner is operating at a particular rate, the blower motor operates at the appropriate speed. Total electricity use is calculated by multiplying the BE at high firing rate times the BOH H and the BE at reduced firing rate times the BOH Rand summing to get total winter blower electricity consumption.7.7-7 REFERENCES 1. American Society for Heating Refrigeration and Air-Conditioning Engineers, Method of Testing for Annual Fuel Ultilization Efficiency of Residential Central Furnaces and Boilers , 1993, ANSI/ASHRAE. Atlanta, GA. Report No. Standard 103-1993. 2. Title 10, Code of Federal Regulations, Chapter II Part 430 Appendix N, Subpart BUniform Test Method for Measuring the Energy Consumption of Furnaces, January 1, 2001.