2111 Wilson Boulevard | Suite 500 | Arlington | Virginia | 22201-3001 USA

PHONE 703 524 8800 | FAX 703 562 1942 | www.ahrinet.org

December 17, 2012

Dr. David Danielson

Assistant Secretary for Energy Efficiency and Renewable Energy

United States Department of Energy

1000 Independence Avenue SW

Washington, D.C. 20585

Re: Revision of AFUE Calculation in U.S. Department of Energy Test Procedures

for Two Stage or Modulating Condensing Boilers

Dear Assistant Secretary Danielson:

Following up our November 19, 2012 letter regarding the subject noted above, we have 

developed a calculation to determine the annual fuel utilization efficiency (AFUE) of two-stage 

and step-modulating condensing boilers when the heat-up and cool-down tests are not conducted. 

As we have explained, the DOE efficiency test procedures for residential furnaces and boilers 

allows the option of omitting the heat-up and cool-down tests for condensing furnaces or boilers 

which have no measurable air flow through the model during the off cycle. Yet, the calculation 

section only provides an alternative calculation to determine the AFUE when this option is 

implemented for condensing models that operate at a single input rate (Section 11.3.11.3 of 

ASHRAE 103-1993).

We have used the concept reflected in the calculations in 11.3.11.3 and the direction in Section 

9.10 to “use the losses determined during the steady state test described in 9.1 when calculating 

heating seasonal efficiency (EffyHS)” to develop the corresponding alternative calculations for 

two-stage and step-modulating condensing boilers. In this case, alternative calculations are 

needed in Section 11.5 to determine part load efficiencies at both maximum input and reduced 

input rates, EffyU,H and EffyU,R, when option 9.10 is employed. These values along with the 

average part load efficiency for the modulating mode, EffyU,M, then are used to determine EffyHS. 

Note, the calculation of EffyU,M is unaffected by option 9.10 so the existing calculation is 

appropriate.

The calculation for EffyU,R which should be included in subsection 11.5.11.1 to apply when 

option 9.10 is employed is:

EffyU,R = 100 – LL,A + LG – LC – CJLJ – [tON/( tON + (QP / QIN) tOFF)] (CS)(LS,SS)

The calculation for EffyU,H which should be included in subsection 11.5.11.2 to apply when 

option 9.10 is employed is:

EffyU,H = 100 – LL,A + LG – LC – CJLJ – [tON/( tON + (QP / QIN) tOFF)] (CS)(LS,SS)
The calculations of EffyHS for modulating boilers are provided in subsection 11.5.11.3:

For two stage units:

EffyHS = (XH)EffyU,H + (XR)EffyU,R 

For step modulating units:

EffyHS = (XH)EffyU,M + (XR)EffyU,R 

The terms XH and XR are the heating load fractions which are not affected by the option of 9.10. 

The values for EffyU,H and EffyU,R resulting from the calculations described above and EffyU,M 

would be used to determine EffyHS when the option of 9.10 is used. That heating seasonal 

efficiency value then would be used in 11.4.12 to determine the AFUE. We believe this process 

results in a conservative rating of the model.

Attached is an explanation of the derivation of these equations, including information as to why 

the equations result in a conservative rating. We request that this be reviewed by DOE’s 

technical staff to confirm the validity of these alternative calculations.

As we had noted, the test procedures clearly allow the option of omitting the heat-up and cooldown tests for condensing models. The flaw which we uncovered is the lack of appropriate 

equations that address this option of the test methodology for other than single stage condensing 

models. Fundamentally, the calculations in any efficiency test procedure are a subordinate part 

of the procedure; they do not define the procedures. That is, the calculations provide a 

mathematical process to convert the data generated during the conduct of the test procedure into 

the specified efficiency metric. The title of Section 11, “Calculations of Derived Results from 

Test Measurements,” reflects this principle. Consequently, we consider the calculations provided 

in this letter to be a clarification of the current DOE efficiency test procedures for residential 

furnaces and boilers rather than a change to the actual test procedures. 

Therefore we request DOE to review these calculations, confirm that they are appropriate for

determining the AFUE of two-stage and modulating condensing boilers and furnaces when the 

heat-up and cool-down tests are not conducted, and allow the use of these calculations as soon as 

possible. We are ready to meet with DOE at your convenience to provide additional explanation 

on the derivation of these calculations, as necessary, and to answer any other questions that DOE 

may have on this matter. We look forward to your response. 

Sincerely,

Frank A. Stanonik

Chief Technical Advisor

Cc: John Cymbalsky, DOE

Attachment
Attachment 

DOE Danielson Letter

Dec. 17, 2012

AHRI Derivation of Alternative Calculations When Applying Section 9.10 of 

ASHRAE 103-1993 to Condensing, Modulating Furnaces and Boilers

This document explains the derivation of alternative calculations to be used in determining the annual fuel 

utilization efficiency (AFUE) for modulating, condensing boilers and furnaces when heat-up and cool down tests are 

omitted as permitted by Section 9.10. This derivation follows the general instructions for calculating heating 

seasonal efficiency that are provided in Section 9.10 and is consistent with more detailed calculations provided in 

ASHRAE 103 for non-modulating, condensing boilers and furnaces. (Unless otherwise noted, the nomenclature 

used, and sections referred to, herein are those in the standard ASHRAE 103-1993.)

Section 9.10 states that when the cool-down and heat up tests are omitted, “the tester may use the losses determined 

during the steady state test described in 9.1 when calculating heating seasonal efficiency (EffyHS)”. The 

calculations for steady-state efficiency, heating seasonal efficiency and annual fuel utilization efficiency (AFUE) for 

condensing gas or oil furnaces and boilers are provided in Section 11.3. The following calculations of EffyHS for 

single stage, condensing boilers and furnaces are provided in Subsection 11.3.11.3: 

If heat-up and cool down are run:

EffyHS = 100 − LL,A + LG − LC − CJLJ – [tON /( tON+(QP / QIN)tOFF)] (LS,ON + LS,OFF + LI,ON + LI,OFF) 

If heat-up and cool down test are omitted as permitted by 9.10:

EffyHS = 100 − LL,A + LG − LC − CJLJ – [tON /( tON+(QP / QIN)tOFF)] (CS)(LS,SS). 

When the Section 9.10 option is used the sum of the cyclic sensible and infiltration losses (LS,ON + LS,OFF + LI,ON + 

LI,OFF) in the first equation is replaced with the adjusted steady state sensible heat loss (CS x LS,SS). This follows the 

direction of Section 9.10 to use the losses determined during the steady state test described in 9.1. This appears to be 

a conservative assumption based on the fact that there is no measurable off-cycle flow through the unit and therefore 

negligible off-cycle sensible and infiltration losses. Furthermore for systems numbered 9 or 10, Section 11.2.10.5 

(referenced by 11.3.10.5) indicates that CS x LS,SS must always be greater than or equal to LS,ON.

 

Note that CS is a correction factor used to scale LS,SS when outdoor air is used for combustion. Also, for models 

without a continuous pilot, QP=0 and the second equation simplifies to:

EffyHS = 100 − LL,A + LG − LC − CJLJ – (CS)(LS,SS) 

 

The calculations for steady-state efficiency, heating seasonal efficiency and AFUE for condensing, modulating gas 

or oil furnaces and boilers are provided in Section 11.5. The following calculations of EffyHS for modulating, 

condensing boilers and furnaces are provided in Subsection 11.5.11.3: 

For two stage units:

EffyHS = (XH)EffyU,H + (XR)EffyU,R 

For step modulating units:

EffyHS = (XH)EffyU,M + (XR)EffyU,R 

The heating load fractions, XH and XR, are determined by the balance point temperature and are unaffected by the 

use of the 9.10 option. Therefore there is no alternative calculation required in this subsection. However the partload efficiencies calculated in subsections 11.5.11.1 and 11.5.11.2 are the analogous versions of the first equation of 

subsection 11.3.11.3 for modulating models operating at the reduced and maximum input rate. It is in these two 

subsections that an alternative calculation should be provided when the option in 9.10 is employed.
ASHRAE 103 assumes that cyclic operation of step-modulating appliances only occurs when the output at the 

reduced input is greater than the heating load. Accordingly, the structure of the calculation for part-load efficiency at 

reduced input rate in 11.5.11.1 parallels the first equation in 11.3.11.3. Following the concept established in that 

subsection, when Section 9.10 is used the sum of the cyclic sensible and infiltration losses (LS,ON + LS,OFF + LI,ON + 

LI,OFF) is replaced with the adjusted steady state sensible heat loss (CS x LS,SS), resulting in the following equation: 

EffyU,R = 100 − LL,A + LG − LC − CJLJ – [tON /( tON+(QP / QIN)tOFF)] (CS)(LS,SS) 

Where:

LS,SS = Sensible steady state loss at reduced input, %

CS = Adjustment factor used when outside air is used for combustion based on the “standard” outdoor air 

temperature at reduced input (TOA,R) as described in 11.3.10.1 (referenced by 11.5.10.1).

All other nomenclature is the same as shown in 11.5.11.1.

For models without a continuous pilot, QP=0 and the equation simplifies to: 

EffyU,R = 100 − LL,A + LG − LC − CJLJ – (CS)(LS,SS) 

This equation can be used to calculate EffyU,R for condensing boilers and furnaces equipped with either two stage or 

step-modulating controls.

The structure of the calculation for part-load efficiency at maximum input rate for two-stage condensing models in 

11.5.11.2 also parallels the first equation in 11.3.11.3. So we again apply the concept established in that subsection. 

When Section 9.10 is used the sum of the cyclic sensible and infiltration losses (LS,ON + LS,OFF + LI,ON + LI,OFF) is 

replaced with the adjusted steady state sensible heat loss (CS x LS,SS), resulting in the following equation: 

EffyU,H = 100 − LL,A + LG − LC − CJLJ – [tON /( tON+(QP / QIN)tOFF)] (CS)(LS,SS) 

Where:

LS,SS = Sensible steady state loss at maximum input, %

CS = Adjustment factor used when outside air is used for combustion based on the “standard” outdoor air 

temperature at maximum input (TOA,H) as described in 11.3.10.1 (referenced by 11.5.10.1).

All other nomenclature is the same as shown in 11.5.11.2.

For models without a continuous pilot, QP=0 and the equation simplifies to: 

 

EffyU,H = 100 − LL,A + LG − LC − CJLJ – (CS)(LS,SS) 

 

For step modulating condensing boilers and furnaces, EffyU,M (average part load efficiency for the modulating 

mode) is calculated in accordance with 11.4.9.2.3 (referenced by 11.5.9.2.3). EffyU,M is purely a function of steady 

state efficiency and steady state infiltration losses. Therefore this calculation is not affected by use of the 9.10 

option and no alternative calculation is necessary.

When the option of 9.10 is used, the values for EffyU,H and EffyU,R calculated using these alternative calculations 

would be inserted into the equations provided in 11.5.11.3 to determine EffyHS. The AFUE for modulating 

condensing boilers and furnaces is calculated in 11.4.12 (referenced by 11.5.12). For boilers and furnaces not 

equipped with a standing pilot, this equation reduces to:

AFUE = EffyHS