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 (EM) ................................ 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 (QOUT) ....................... 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 QOUT and Corresponding DHR values ............................... 7.7-5

LIST OF FIGURES

Figure 7.7.3.1 XR and XH versus Balance-Point Temperature for Modulating Furnaces 

and Boilers .................................................... 7.7-4
7.7-1

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

PEIG = 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-weatherized

gas 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 BOHSS 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, EM, from ASHRAE Standard 103, is defined as:

EM = (QIN − QP) × BOHSS + (8760 − 4600) × QP

where:

QIN = steady-state nameplate maximum fuel input rate,

BOHSS = national average number of burner operating hours, and

QP = fuel input from pilot light.

For non-weatherized gas furnaces, there is no pilot light, so QP = 0, and EM becomes:

EM = QIN × BOHSS

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:

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

EM = average annual energy used during the heating season (kBtu), and

QIN, R = steady-state reduced fuel input rate (kBtu/h).

BOHH

XH E M

QIN

=

×
7.7-3

where:

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

and

Q = steady-state high, or maximum, fuel input rate (kBtu/h). IN

7.7.3.1 Fraction of Heating Load

The Department determined XH and XR, 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 (TC)

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:

TC

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 TC = 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

1
7.7-4

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 to 

Reduced Operating Mode (XR)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Fraction of Total Annual Heating Load Applicable to 

Maximum 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 XH versus Balance-Point Temperature for

Modulating Furnaces and Boilers

7.7.3.4 Heating Capacity at Maximum Input Rate (QOUT)

The QOUT is expressed to the nearest 1000 Btu/h and is calculated for non-condensing and

condensing furnaces as:

QOUT = QIN × (0.7247 × AFUE + 22.346) for non-condensing and
7.7-5

QOUT = QIN × (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 QOUT 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 130
7.7-6

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 0775 0 375

30 05667 325

195 05879 01364

130

For induced draft units,

A

yIG PEIG y BE R QIN QP EffyHS

=

× × + × × + − ×

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

BOHH and the BE at reduced firing rate times the BOHR and 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.