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### 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

R e: 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 efficienc y (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 t he option of omit ting the heat

- up an d 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

heatin g seasonal efficiency (Effy HS 

### )” 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 determ ine part load efficiencies at both maximum input and reduced input rates, Eff y U,H 

### and Eff y U,R 

### , when option 9.10 is employed . These values along with the average part load efficiency for the modulating mode

, Effy U,M 

### , then are used to determine Effy HS



### . Not e, the calculation of Effy U,M 

### is unaffected by option 9.10 so the existing calculation is appropriate.

The calculation for Eff y U,R 

### which should be included in subsection 11.5.11.1 to apply when option 9.10 is employed is :

Effy U,R 

### = 100

– L L,A 

### + L G



### – L C



### – C J 

### L J



### – [t ON 

### /( t ON 

### + (Q P 

### / Q IN 

### ) t OFF 

### )] (C S 

### )(L S,SS 

### )

T he calculation for Eff y U, H 

### which should be included in subsection 11.5.11. 2 to apply when option 9.10 is employed is :

Effy U,H 

### = 100

– L L,A 

### + L G



### – L C



### – C J 

### L J



### – [t ON 

### /( t ON 

### + (Q P 

### / Q IN 

### ) t OFF 

### )] (C S 

### )(L S,SS 

### )

### The calculations of Effy HS 

### for modulating boilers are provided in subsection 11.5.11.3:

For two stage units:
Effy HS 

### = (X H 

### )Effy U,H 

### + (X R 

### )Effy U,R



### For step modulating units: Effy HS 

### = (X H 

### )Effy U,M 

### + (XR)Effy U,R



### The terms X H 

### and X R 

### are the heatin g load fractions which are not affected by the option of 9.10.

The values for Effy U,H 

### and Eff y U,R 

### resulting from the calculations described above and Effy U,M 

### would be used to determine Effy HS 

### when the option of 9.10 is used. That heating seasonal

efficie ncy 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 cool

down tests for con densing 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 subord inate 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

- do wn 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 que stions 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 Calculation s When Applying Section 9.10 of

ASHRAE 10 3

- 19 93 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 wh en heat

- up and co ol 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

, here in are those in the standard ASHRAE 103

- 1993. )

Section 9.10 states that when the cool

- down and heat up tests are omitted, “t he tester may use the losses determined during the steady state test described in 9.1 when calculating heating seasonal efficiency (Effy HS )”. 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 Effy HS for single stage, condensing boilers and furnaces are provided in Subs ection 11.3 .11.3:

If heat

- up and cool down are run:

E f f

y H S = 100 − L L

, A + L G − L C − C J L

J

– [ t O N /( t O N +( Q P / Q I N ) t O F F )] ( L S

, O N + L S

, O F F + L I

, O N + L I

, O FF )

If heat

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

E f f y H S = 100 − L L

, A + L G − L C − C J L

J

– [ t O N /( t O N +( Q P / Q I N ) t O F F )] (C S )(L S,SS ).

W hen the Section 9.10 option is used the sum of the cyclic sensible and infiltration losses ( L S

, O N + L S

, O F F + L I

, O N +
L I

, O FF ) in the first equation is replace d with the adjusted steady state sensible heat loss (C S x L S,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 th ere 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, Secti on 11.2.10.5 (referenced by 11.3.10.5) indicates that C S x L S,SS must always be greater than or equal to L S,ON

.

Note that C S is a correction factor used to scale L S,SS when outdoor air is used for combustion. Also

, for models without a continuous pilot, Q P =0 and the second equation simplifies to:

E f f y H S = 100 − L L

, A + L G − L C − C J L

J

– (C S )(L S,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 Effy HS for modu lating, condensing boilers and furnaces are provided in Subsection 11.5.11.3:

For two stage units:

Effy HS = (X H )Effy U, H + (X R )Effy U,R

For step modulating units:

Effy HS = (X H )Effy U,M + (X R )Effy U,R

T he heating load fractions, X H and X R , 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 part

load 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 em ployed.ASHRAE 103 assume s that cyclic operation of step

- modulating appliances only occurs when the output at the reduced input is greater than the heat ing 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 ( L S

, O N + L S

, O F F + L I

, O N +
L I

, O FF ) is replaced wi th the adjusted steady state sensible heat loss (C S x L S,SS ), resulting in the following equation:

E f f y U,R = 100 − L L

, A + L G − L C − C J L

J

– [ t O N /( t O N +( Q P / Q I N ) t O F F )] (C S )(L S,SS )

Where:

L S,SS = Sensible steady state loss at reduced input , %

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

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

All other nomenclature is the same a s shown in 11.5.11.1.

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

E f f y U,R = 100 − L L

, A + L G − L C − C J L

J

– (C S )(L S,SS )

This equation can be used to calculate Effy U,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 ( L S

, O N + L S

, O F F + L I

, O N + L I

, O FF ) is replaced with the adjusted steady state sensible heat loss (C S x L S,SS ), resulting in the following equation:

E f f y U,H = 100 − L L

, A + L G − L C − C J L

J

– [ t O N /( t O N +( Q P / Q I N ) t O F F )] (C S )(L S,SS )

Where:

L S,SS = Sensible steady state loss at maximum input , %

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

temperature at maximum input (T OA, 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, Q P =0 and the equation simplifies to:

E f f y U,H = 100 − L L

, A + L G − L C − C J L

J

– (C S )(L S,SS )

For s tep modulating condensing boilers and furnaces, Effy U,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)

. Effy U,M is purely a function of steady state efficiency and s teady state infiltration losses. Therefore this calculation is not affect ed by use of the 9.10 optio n and no alternative calculation is necessary.

When the option of 9.10 is used, the values for Effy U, H and Effy U,R calculated using these alternative calculations would be inserted into the equations provided in 11.5.11.3 to determine Effy HS

. 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 e quation reduces to:

AFUE = Effy HS