Refrigerator Test Procedure Adjustments to Second Part of Test

12/9/11

Background: The Samsung waiver to adopt a te st procedure for multiple defros t cycle types, and the related discussion, have led to a reevaluation of the appropriate test period for the second part of a test for variable or long-time defrost products. See 76 FR 16760 (March 25, 2011) (request for comment and grant of interim test procedure waiver). This part of the test is used to determine the energy use associated with defrost, and a ll events associated with defrost, including precooling and temperature recovery.

The current (Appendix A1) test pe riod starts when the compressor stops, prior to or coincident with the defrost heater being energized, and fi nishes at the second tu rn-on of the compressor

after defrost.

The interim final Appendix A test pe riod refines this approach to re quire that the test period start prior to any precooling cycles. It adopts temperat ure-based requirements to confirm that the start has been selected to precede precooling, and th at the stop has been selected to follow all temperature recovery. However, th e procedure still ends the test pe riod for the second part of the test when the compressor starts.

Whirlpool commented on the Samsung waiver, sugge sting that the test period should stop when the compressor stops, rather than when it starts. This suggestion was first made in the test procedure NOPR public meeting presentation on June 22 (see page 53 of the presentation). Both the Whirlpool comment and the NOPR meeting pr esentation highlight the unusual result that energy use contribution associated with defrost sometimes is nega tive when determined using the Appendix A1 test procedure. This result occurs fo r some defrosts of an evaporator (i.e. a heat exchanger that cools the refrigerator’s air with refrigerant passing through its tubes) serving the fresh food compartment of specific refrigerator models. The Whirlpool co mments indicate that the Appendix A1 test procedure generally underestim ates the energy use asso ciated with defrost.

This memo presents a theoretical discussion de monstrating the merits of adopting Whirlpool’s suggestion to modify the test peri od of the second part of the te st so that it ends when the

compressor stops.

This issue applies only to produc ts with cycling compressors and long-time or variable defrost. Other products are not affected. For example, pr oducts with conventional automatic defrost are tested using a single test period that captures all product energy use, including the energy used for defrost, thus specifications for the second part of the test do not appl y. As another example, products with non-cycling compressors and long-time or variable defrost are not tested using test periods defined by compressor cycles.

The discussion presented in this memorandum assu mes that the test pro cedure for conventional automatic defrost as specified in Appendices A1 and A, section 4.2 accurately measures refrigerator energy use, properly capturing the ener gy use associated with defrost. This procedure2

for automatic defrost products has been in effect as part of the DOE test procedures since at least 1982 and its accuracy has not been questioned.

Potential questions about the accu racy of the two-part test prim arily (Appendix A1 or A, section 4.2.1) are associated with whether the second part of the test accurately ca ptures the contribution of defrost to overall energy use. The concept of the two-part test is that the first part of the test measures energy use during steady state operati on not including defrost events—this is the energy use to maintain particular temperature levels in the compartments, i.e. the average temperature levels measured for the first part of the test. Because the compartment temperatures fluctuate in products with cycling compressors, increasing when the comp ressor is not operating and decreasing when the compressor is operating, measured temperatur es for the first part of the test are averaged over a whole number of compressor cycles.

The defrost cycle, including all events associated with it, represent a de parture from steady state operation that is generally accepted to increase average energy use (i.e. energy consumption per elapsed time). This is because the defrost h eater itself expends energy and because the refrigeration system must remove from the comp artment(s) the heat added by the defrost heater. Compartment temperatures generally rise during de frost, hence the thermal load (i.e. heat that transfers into the refrigerator from outside) shou ld decrease during the defrost cycle. However, the reduction in energy use associated with this th ermal load reduction is sm all, if not negligible, when compared with the added energy use of th e defrost heater and the refrigeration system operation to remove the asso ciated heat addition.

The energy use contribution associat ed with defrost is determined from the test measurements by subtracting from the energy use of the second part of the test the energy use that would have been expended during the same pe riod of time if the product had in stead continued to operate in steady state mode as it does during the first part of the test. The energy use equation (e.g. Appendix A1 section 5.1.2.3) adjust s this energy use per defrost ba sed on defrost frequency per day. Conceptually, to assure that energy use associ ated with defrost is not “lost from” (or “added to”) the measurements of the sec ond part of the test, the second pa rt of the test should start and end with the product operating in its steady-state mode with the compresso r cycling as it does in the first part of the test. Furthe r, the start and end should ideally be at times when the product is in the same time during a compressor cycle: ju st as achieving proper te mperature and energy use averages for the first part of the test requires th at the test period for the first part of the test includes a whole number of compressor cycles, th e second part of the test should represent a period of time for which, had there been no defrost cycle, there would have been a whole number of compressor cycles. This means that the test period should start and end at the same time during a compressor cycle, as suggested by Whirlpool.

The discussion that follows is presented first fo r products that operate such that there is a complete regular compressor cycle prior to the defros t cycle, since this scen ario more readily fits the presented theoretical analysis. The memorandum ends with a discussion of how the analysis would be affected by situations in which there is a truncated compressor cycle prior to the defrost cycle. This latter scenario generally occu rs for timer-based defrost initiation.3

Operation in Which There is a Full Regu lar Compressor Cycle Before Defrost This section shows that, for those cases where th e compressor “on” cycle prior to the defrost is not truncated (e.g., through the use of timer-based defrost initiatio n), the test period should end when the compressor stops in order to more accurately capture the energy consumption of refrigeration products with cycling compressors and long-time or va riable defrost.

When testing products with long-time or va riable defrost, the test is split into steady-state and defrost portions (first part and second part) to reduce test burden. For long-time automatic defrost, the energy equation (section 5.2.1.2 of both Appendices A1 and A) is,

ܧܶ ൌ 1440 ൈ ܲ1ܧ

ܶ1 ൅ ൬ ܧܲ2 െ ܧܲ1 ൈ ܶ2

ܶ1 ൰ ൬ 12

ܶܥ ൰

where ET is the total energy in kWh/day; EP1 an d EP2 are the energies of the first and second parts of the test, respectively (in kWh); T1 and T2 are the leng ths of time of the two parts (in minutes); and CT is the compressor run time betw een defrosts (in hours). The first term on the right side of the equation repres ents the energy use during steady ope ration without defrost. The second term represents the energy use associ ated with defrost.

The energy equation for variable defrost, in se ction 5.2.1.3, is identical to the above equation except that in that case CT is a representative compressor run time between defrost cycles, calculated as prescribed in the test procedur e, as a weighted average of the minimum and maximum values that the control algorithm can select for it.

In this analysis, the test peri od provided in Appendix A1, secti on 4.2 is assumed to result in an accurate measure of the averag e energy use for a time period from one defrost to a second:

4.2 Automatic Defrost. If the model being te sted has an automatic defrost system, the test time period shall start afte r steady-state conditions have been achieved and be from one point during a defrost period to the sa me point during the ne xt defrost period.

Figure 1 shows a representative power input and fr eezer temperature history of a generic variable defrost refrigerator.4

Figure 1: Representative Power and Te mperature Histories for a Generic Cycling Compression Scenario

The section 4.2 test period is shown as T full . The two test periods asso ciated with long-time or variable defrost products, T1 and T2, are labeled so that they correspond to the allocation of time that Whirlpool suggested should apply. Specifi cally, the end of the T2 period is shown as occurring at the end of the compressor “on” cycle after th e recovery compressor cycle, rather than at beginning of that “on” cycle (as is shown in Figure 1 of Appendix A1 or A).

For convenience, T1 is set to be the entire steady- state period rather than a short portion of that period. Note that T2, the test period of the seco nd part (defrost portion) of the test, is divided into separate periods T pcB (precooling B) and T drB (defrost/recovery B). The energy use associated with each of these periods is represented by the terms EP full , EP1, EP2, EP pcB , and

EP drB ; for example, EP full is the energy use expended during time period T full ,

Note that the figure shows two separate time periods for defrost and recovery, T drA and T drB

. While products may not always operate in a repeatab le fashion, the fact that a laboratory test that measures only one (or two) defrost cycles is co nsidered to be repres entative of field use presupposes a reasonable degree of repeatab ility in product oper ation. Therefore, T drB should be considered to be equal to T drA . Similarly, the energy use measured during these time periods should also be considered equal, EP drB equal to EP drA

.PRECOOLDEFROST ARECOVERYPOWERTEMPERATUREDEFROST BRECOVERY T full

T drA T drB T1 (steady) T pcB

T2

Same Temperature Before and After T25

Considering the T full time period, the total energy use for the period starting when the defrost heater is energized for the fi rst time (i.e., for defrost A) and ending the second time it is energized (for defrost B) is:

ܲܧ ௟௟ ௨௙ ܲܧ 	 ൌ ஺௥ௗ ܲܧ ൅ ܲ1ܧ	 ൅ ஻௖௣

Alternatively, the total energy use de termined by the two-part method is:

ܲܧ ൌ ܲ2ܧ	 ൅ ܲ1ܧ ஻௥ௗ ܲܧ	൅ ܲ1ܧ ൅ ஻௖௣

Because EP drB and EP drA are equal, EP full is expected to be exactly equal to EP1 + EP2, when T1 is defined as indicated in the figure to include the entire steady-state period.

The following discussion will show that th e two-part energy equation (section 5.2.1.3 of Appendix A1 or A) calculates energy use in a manner consistent with the single-test-period equation of section 4.2 only if the test period of th e second part of the test ends at the end of a compressor “on” cycle. The meaning of the “ 12” in the two-part en ergy equation is that compressor run time is half of the clock time from one defrost initiation to the next. In other words, the equation defines CT to be equal to half of T full /60.

The daily energy use calculated based on EP full is determined by multiplying average energy use per hour for the test period by 24 hours.

ܧܶ ൌ 	24 ൬ ா௉ ೑ೠ೗೗

் ೑ೠ೗೗ /଺଴ ൰ ൌ ቀ ଶସ

ଶ஼் ቁ ܧܲ ௙௨௟௟ ൌ	ቀ ଶସ

ଶ஼் ቁ ሺ ܧܲ1 ൅ ܧܲ2 ሻ

ൌ ቀ ଶସ

ଶ஼் ቁ ሾ ܧܲ1 	൅ ሺ ܧܲ2 െ ܧܲ1 ൈ ܶ2/ܶ1 ሻ ൅ 	ܧܲ1 ൈ ܶ2/ܶ1 ሿ
ൌ ቀ ଶସ

ଶ஼் ቁ ሾሺ 1 ൅ ܶ2/ܶ1 ሻ ܧܲ1 	 ൅ ሺ ܧܲ2 െ ܧܲ1 ൈ ܶ2/ܶ1 ሻሿ
ൌ 24 ቀ ்ଵା்ଶ

ଶ஼் ቁ ܧܲ1/ܶ1 ൅ ቀ ଵଶ

஼் ቁ ሺ ܧܲ2 െ ܧܲ1 ൈ ܶ2/ܶ1 ሻ

Because T drA = T drB and CT = 0.5 × T full /60, it follows that

2ܥܶ ൌ ் ೑ೠ೗೗

଺଴ ൌ ቀ ் ೏ೝಲ ା்ଵା் ೛೎ಳ

଺଴ ቁ

ൌ ቀ ் ೏ೝಳ ା்ଵା் ೛೎ಳ

଺଴ ቁൌቀ ்ଵା்ଶ

଺଴ ቁ

Plugging this into the first term of the ri ght side of the above equation for ET gives6

ܧܶ ൌ 24 ቀ ்ଵା்ଶ
ሺ ்ଵା்ଶ ሻ /଺଴ ቁ ܧܲ1/ܶ1 ൅ ቀ ଵଶ

஼் ቁ ሺ ܧܲ2 െ ܧܲ1 ൈ ܶ2/ܶ1 ሻ

ൌ 1440 ൈ ܧܲ1/ܶ1 ൅ ቀܧܲ2 െ ܧܲ1 ൈ ்ଶ

்ଵ ቁ ቀ ଵଶ

஼் ቁ

Hence, for the time periods as defined in Figure 1, ET calculated using the full-period calculation is identically equal to ET calculate d using the two-part calculation.

In contrast, suppose that T2 ends at the start of the compressor “on” cycle that follows the recovery compressor cycle, as in Figure 1 of the the current Appendix A, instead of at the end of that “on” cycle. In that scenario, T drB is now unequal to T drA , and, significantly, the energy consumption during T drB is now less than that of T drA by the amount of a full compressor “on” cycle. Since T drB ≠ T drA , we no longer have 2CT = (T1 + T2)/60 and the section 5.2.1.3 equation for ET is no longer valid. Defining both T drA and T drB to end at the second compressor start after the defrost, and defining T1 to start at the end of T drA would resolve this inequality. However, in this case, T1 does not include a whole number of compressor cycles, as required by the test procedure. This situation illustrates that esta blishing equality of the full-cycle energy use calculation and the two-part energy use calcula tion requires that T2 end at the end of a compressor “on” cycle.

The temperature history may be further examined to support ending the se cond part of the test when the compressor stops. The defrost part of the test is intended to capture the energy use associated with temperature recovery from defrost. However, at the time of the second compressor start after defrost B, the temperatur e has recovered only to the maximum level it normally reaches during the steady state portion of the test (i.e. the upper horizontal line in the temperature plot of Figure 1) – but the test period starts when th e compartment temperature is at the minimum level normally reached during steady state (i.e. the lower horizontal line in the temperature plot). The test, as currently writ ten, would be missing both the energy use and time associated with additional recovery of the compartment temperature to its level at the start of the second part of the test. By extending the test th rough this additional compressor “on” cycle, the product is brought back to the thermal state it was in at the start of the second part of the test, thus assuring full temperature recovery.

Operation in Which There is Not a Full Regular Compressor Cycle Before Defrost In some circumstances the compressor “on” cycl e before the defrost cycle may be truncated. This may occur in products with timer-based long-time defrost and in tests involving initiation of instant-defrost. Instant-defrost testing is used by manufacturers in which they can force a defrost to occur, rather than waiting for the variable defrost algorithm to initiate the next defrost. This approach is used to reduce test time.

In the extreme case where the compressor stops immedi ately after it started prior to defrost, the steady portion of the test between defrosts coul d be selected to incl ude a whole number of complete compressor cycles from a compressor star t to a compressor start. The second part of the test could be selected under Appendix A1 sec tion 4.2.1 at the instant the compressor turns on and

back off and the defrost heater turns on (with all three events c onsidered for the purposes of the discussion to be occurring within the same inst ant). In this case, the logic of the previous7

discussion is reversed: in or der to avoid improper inclusi on of the energy use and time associated with a compressor “on” cycle, the end time for the second part of the test would be

selected to occur at the start rather than at th e end of a compressor “on” cycle. This approach also holds true when considering the temperature- based view of the test period: the compartment temperature would have been at its steady-state maximum level at the start of the second part of the test, since the compressor was just restarti ng. Hence, temperature recovery would involve returning to this steady-state maximum, which is coincident with a compressor start, for example, the second compressor start after defrost.

In practice, the timer-based de frost control would stop the co mpressor at a random time during the compressor “on” cycle. Hence, achieving strict equality of E full and E 2part would require using an approach that measures the energy c onsumption of the tested unit by ending the second part of the test at a time during a regular compressor “on” cycle after defrost when the compartment temperature matches its level at the st art of the test, which would be at some point between the steady-state maximum and minimum temperatures. Extending the test period through to the end of a compressor “on” cycle would add to the test the energy use and time associated with the additional compressor operati on to bring the compartment temperature to its steady-state minimum.

However, by modifying Appendix A’s te st period of the second part of th e test so that it starts at

the “termination of the last re gular compressor “on” cycle,” it causes a truncated compressor “on” cycle to be considered part of the defros t cycle. Accordingly, by modifying the procedure in this manner, the procedure addresses any issues associated with the ra ndom nature of timerbased initiation of defrost wh en using the two-part test.