NBSIR 85-3107

Field Performance of Three

Residential Heat Pumps in the

Cooling Mode

Walter H. Parken

David A. Didion

Paul H. Wojciechowski

Lih Chern

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Building Technology

Building Equipment Division

Gaithersburg, Maryland 20899

March 1985

Sponsored By:

U.S. Department of Energy

Office of Building Energy Research

and Development

Washington, D.C. 20585

• QC— ” H

130

. U56

35-3107

1985

National bureau

OF STANDARDS

.library

'2l£.-A)2 S

NBSIR 85-3107

FIELD PERFORMANCE OF THREE

RESIDENTIAL HEAT PUMPS IN THE

COOLING MODE

Walter H. Parken

David A. Didion

Paul H. Wojciechowski

Lih Chern

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Building Technology

Building Equipment Division

Gaithersburg, Maryland 20899

March 1985

Sponsored By:

U.S. Department of Energy

Office of Building Energy Research

and Development

Washington, D.C. 20585

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

ABSTRACT

This report presents the results of a field performance study of heat pumps

operating in the cooling mode. Hie objective of this study was to develop a

method for calculating seasonal field performance parameters as well as to

compare field performance and laboratory results. This comparison is

necessary to determine how well the testing and rating standards required of

heat pump and standard central air conditioning manufacturers predict actual

field performance. It was determined that the laboratory test procedures were

too high with respect to cycling rate and that a somewhat lower rate should be

employed. Field thermostat data was also collected and used to develop a

semi-empirical model.

Key Words: Central air conditioners; cooling seasonal performance; field

performance; field performance of heat pumps; heat pumps; heat

pump test methods; modelling; thermostat

/

iii
ACKNOWLEDGEMENTS

This study was sponsored by the U.S. Department of Energy, Office of Building

Energy Research and Development.

IV
TABLE OF CONTENTS

Page

ABSTRACT iii

ACKNOWLEDGEMENTS iv

LIST OF TABLES vii

LIST OF FIGURES viii

NOMENCLATURE x

SI CONVERSION FACTORS xi

1. INTRODUCTION 1

2. SELECTION AND DESCRIPTION OF FIELD DATA 3

3. FIELD DATA ACQUISITION SYSIEM 5 3.1. System Description 3

3.2. Measurements and Instrumentations 5 3.3. Data Scanning Requirements 8

3.4. Data Acquisition Format 8

4. DATA DISCRIMINATION AND FIELD TEST SUMMARY 11

5. STEADY-STATE FIELD PERFORMANCE 15

5.1. Weather 15

5.2. Steady-State Results 16

6. CYCLIC PERFORMANCE 23

6.1. Overview of Seasonal Cooling Requirements and Unit Sizing . 23

6.2. Comparison of Thermostat Model Prediction and Field Data . 28

6.3. Cyclic Performance Parameters 33

6.3.1. Data Organization 33

6.3.2. Determination of the Cooling Load and Part Load

Factors 33

6.3.3. Cyclic Performance Results 34

7. SEASONAL PERFORMANCE EVALUATION 45

7.1. Seasonal Degradation Coefficient 47

8. COMPARISON OF LABORATORY AND SEASONAL FIELD PERFORMANCE RESULTS . 51

9. CONCLUSIONS 57

v
10 . REFERENCES 61

APPENDIX 63

A.l. Thermostat Model 63

A. 2. Development of Method to Improve the Estimte for Steady^

State Capacity, Cooling Load Factor and Part Load Factor . 67

A. 3. Determination of Seasonal Part Load Factor 71

vi
LIST OF TABLES

Page

Table 3.1. Description of Data Recorded in Field Tests 7

Table 4.1. Overview of Seasonal Cooling Performance 12

Table 5.1. Fraction of Total Number of Temperature Bin Hours

During the Test Period 15

Table 6.1. Values for Part Load Performance Constants, p, q for

the Three Units 43

Table 7.1. Seasonal Field Performance Results 50

Table 8.1. Comparison of Laboratory and Field Cyclic Performance . . 54

vii
LIST OF FIGURES

Page

Figure 3.1. Schematic of instrumentation for typical field unit

showing location of 12 sensing chambers 6

Figure 5.1. Part load steady- state field performance [capacity vs. outdoor bin temperature, °F] 18

Figure 5.2. Part load steady-state field performance [power vs. outdoor bin temperature, ®F] 19

Figure 5.3. Part load steady-state field performance [EER and COP

vs. outdoor bin temperature, °F] 20

Figure 5.4. Steady-state capacity vs. fractional on-time. Unit 3 . 21

Figure 6.1. Percent seasonal cooling done vs. outdoor temperature . 24

Figure 6.2. Seasonal average cooling load profiles for three

field installations 25

Figure 6.3. Percent seasonal cooling done and percent of total

cycles vs. fractional on-time, . 27

Figure 6.4(a) Comparison of the thermostat model with field data

[Unit 1] 30

Figure 6.4(b) Comparison of the thermostat model with field data

[Unit 2] 31

Figure 6.4(c) Comparison of the thermostat model with field data

[Unit 3] 32

Figure 6.5. Cooling load factors and part load factors for selected

fractional on-time bins vs. outdoor temperature

typical results [Unit 1] 35

Figure 6.6. Cooling load factor versus fractional on-time for

Unit 3 (C = 0 min) 37

Figure 6.7. Comparison of empirical curve with the mean and

dispersion of data—typical data 38

Figure 6.8(a) Comparison of data and empirical curve fit [Unit 1] . . 39

Figure 6.8(b) Comparison of data and empirical curve fit [Unit 1] . . 40

Figure 6.8(c) Comparison of data and empirical curve fit [Unit 3] . . 41

Figure 8.1. Laboratory cyclic performance results 55

viii
NOMENCLATURE

CD

CLF

EER

N

Nmax PLF

v. q

Q

Q

time (minutes) after unit cycles on for condensate to form on coil

degradation coefficient

cooling load factor

energy efficiency ratio

cycling rate (cycles/h)

cycling rate at 50 percent on-time

part-load factor, PLF = EERC yC /EERss constants in the equation PLF = 1 - ©“P^CLF)*!

cooling done

capacity

l on " length of on-time in one cycle

t Q ff - length of off-time in one cycle

Tj - outdoor temperature, bin (Tout (°F))

W - energy input

W - power input

- fractional on-time, t / T on' x

- fractional on-time bin

x - total time period for a complete on-off cycle

IX
Subscripts

ss - steady-state

eye - cyclic

seas - seasonal

i - fractional on-time bin number

j - outdoor temperature bin number

k - a single on-off cycle

Superscripts

£ - latent

s - sensible

t - total

z
SI CONVERSION FACTORS

MULTIPLY BY TO OBTAIN

Btu/h, Btuh 0.293 W

Btu/lbm°F, ICp, specific heat] 4.19 kj/kg°i

°F °C = (°F - 32) /I .

ft 0.3048 m

ft/min, fpm 0.00508 m/ s

ft 3 /lbm 0.0623 m

3 /kg

ft3 /min, CFM 0.472 m

3 /s

gpm (US) 0.0631 L/S

inch 25.4 mm

inch of water 3 .38 kPa

kBtu/h 1055 kj

lbm/h 0.126 g/s

ton of refrigeration capacity 3516 W

/

xi

1 . INTRODUCTION

Methods of laboratory testing, rating and estimating the heating and cooling

seasonal performance of heat pumps have been established in research

previously performed and documented at the National Bureau of Standards

(NBS) [1,2]. This research became the basis for the development of test

procedures for central air conditioners and heat pumps issued by the United

States Department of Energy in December 1979 [3], In order to further verify

and refine the test procedures, reliable data from field installed heat pumps

were required in order to correlate their performance with independent

laboratory tests. To accomplish this, NBS began monitoring, in June 1980, the

field performance of three residential heat pumps located in the Washington,

D.C. area. A microprocessor-based data acquisition system, located at each

site, was used to gather, reduce, and analyze data during the cooling and

heating seasons of 1980 and 1981. A previous report describes the development

of the monitoring procedures, instrumentation, and microprocessor-related

hardware and software used in the heat pump performance monitoring and

evaluation [4] .

This report presents the cooling performance results of three field-located

residential heat pumps for the 1980 cooling season. This program required the

examination, reduction and analysis of large amounts of data and this report

represents the summary of the results. The objectives of the cooling portion

of the field investigation were to:

(1) Provide manufacturers, modelers, government agencies and others with

accurate, complete and realistic field performance data;

(2) Present field thermostat data and develop a thermostat model to

predict cycling times;

(3) From the field performance data, develop a method for calculating

the seasonal field performance parameters;
(4) Present laboratory results for the steady-state and cyclic cooling

performance of a similar central air conditioner or heat pump model

as used in the field study;

(5) Compare field performance and laboratory results to determine how

well the testing and rating standards (Ref. 3) required of heat pump

and central air conditioning manufacturers predict actual field

performance ; and

(6) Evaluate and critically review the types of data and data

acquisition requirements needed for accurate and complete evaluation

for the field testing of heat pumps and central air conditioners.

/

2
2. SELECTION AND DESCRIPTION OF FIELD UNITS

The heat pumps monitored in this field study were units already operating in

residences of NBS employees who volunteered to participate in the program.

The heat pumps to be evaluated were selected on the basis of a number of

criteria, including the following: (1) the unit had to be an air-source heat

pump model available for procurement for additional laboratory testing;

(2) the unit must have been installed and operating in a manner recommended by

the manufacturer; (3) the unit had to be the only system providing heating and

cooling within the residence; (4) ductwork had to have straight sections long

enough for the proper installation of air flowrate and temperature sensing

devices; and (5) all dwellings had to be located close enough to NBS in

Gaithersburg, Maryland to permit frequent monitoring and to minimize travel

time and associated costs.

Three split system air-to-air heat pumps were eventually selected and

instrumented for the study. A brief description of the three installations is

given below:

Unit number one was a 2 1/2 ton, air-source, unitary heat pump. In the

cooling mode the unit utilized a non-bleed refrigerant thermal expansion

valve. Along with the indoor coil, the air handler contained 15 kW of

auxiliary heater elements. All ductwork (both return and supply) was

insulated on the inside. It was installed in a one-story, ranch-style

residence with brick exterior. A large part of the basement was used for

living quarters, with a total conditioned floor area of approximately

2900 ft 2

. The house was situated on an open, level plane and not shaded

by trees or other structures. Throughout the test period, the house was vacant during working hours (occupied on weekends during the day).

Unit number two, a 3 ton unitary, air-source heat pump, also contained 15

kW of auxiliary electric resistance heaters located in the indoor section. The unit utilized a constant area refrigerant expansion device.

Return ductwork was insulated on the inside while the supply ductwork, had

insulation on the outside. The unit was installed in a one- story, wood

frame structure with approximately 1800 ft^ of living space including a basement family room. The house was situated near many large trees, but

received direct sunlight from the south and west. The exterior was

3
painted a dark color. During the test period, the house was usually

occupied by two or more people throughout the day.

Unit number three also contained 15 kW of auxiliary electric resistance

heaters located in the indoor section and employed a constant area refrigerant expansion device. This unit, like unit number two, was a 3

ton air-source, unitary heat pump. Ductwork was not insulated. The unit was installed in a 1 1/2 story, wood frame house which had a light beige

exterior. The house was not shaded by trees or other structures. Total

living area is approximately 1600 ft^. The basement (another 1000 ft^) was not used as a regular living quarters. During the test period the

house was unoccupied during normal working hours on weekdays.

4
3. FIELD DATA ACQUISITION SYSTEM

3 . 1 System Description

The field instrumentation data acquisition system is described in a previous

report, NBSlR 81-2285, (Ref. 4). An on-line microcomputer at each field site

performed the following functions: (1) control of the data monitoring

strategy; (2) processing of data obtained from the analog and digital

instrumentation to engineering units; (3) performing computational analysis;

and (4) recording the results on magnetic (floppy) disks. Fie Id -located disks

were replaced every seven to ten days, at which time manual checks on field

unit operation and periodic instrument calibrations were made. A central

microcomputer located at NBS was used to further process the data contained on

disks recorded in the field. This central computer was a Z-80 based computer

with two 5 1/4 inch floppy disks and 64K of static RAM memory. Peripherals

included a CRT monitor and a printer.

3 . 2 Measurements and Instrumentations

Measurements of fourteen heat pump related functions—twelve analog and

digital inputs plus two on/off mode conditions—were made and recorded at each

field location. A schematic illustration of the nature and location of each

measurement is given in figure 3.1.

Outdoor ambient dry bulb temperature was monitored and recorded for the 1980

cooling season using a calibrated 1 inear ized-thermister sensor located in a

'bird house'—a vented wooden box mounted directly on the north-facing

exterior wall of the residence. Table 3.1 summarizes quantities which were

measured and the type of sensing element used for each measurement. A

5
c®3e

CO

u.ooO3O

®3

CO®ae®i 6

Figure

3.1.

Schematic

of

instrumentation

for

typical

field

unit

showing

location

of

12

sensing

elements.
Table 3.1 Description of Data Recorded in Field Tests

Data Acquisition —

Measured Quantity and Units Symbol Sensing Element (or Calculated) Scan Cyclic Daily Half Hour

1 Pitot tube differential pressure

(Inches HjO) DP Pitot tube with variable

capacitance AP cell

iv-/

2 Return air dew point temp. (F) TDPR LiCE/RTD dew point cell IV CTIA CTIA IV

3 Outdoor air dew point temp. (F) TDPO LiCl/RTD dew point cell IV HSA

4 Barometric pressure (inches H^O) PATH Pressure cell with diaphragm

potentiometer

IV IV

5 Return air dry bulb temp. (F) TRET Linear thermistor IV CTIA CTIA IV

6 Outdoor air dry bulb temp. (F) TOUT Linear thermistor IV EOC HSA IV

7 Differential temp, across indoor

coil DT Type-T thermocouple IV IV

8 Supply air dry bulb temp. (F) TSUP Linear thermistor IV IV

9 Compressor and outdoor fan energy

(pulse) DIG1 Watt-hour meter with magneticlatch pulse initiator

RT RT

10 Indoor fan and 1st stage heater

energy (pulse) DIG2 Watt-hour meter with magneticlatch pulse initiator

CIT RT

11 2nd stage heater energy (pulse) DIG3 Watt-hour meter with magnetic

latch pulse initiator

CIT RT

12 Condensate metering pump (pulse) DIG4 Positive displacement solenoid metering pump with optical

coupler

RT

13 Compressor ON-OFF MODE O-ON Opto-coupler IV IV

14 Outdoor Fan ON-OFF MODE 3-OFF Opto-coupler IV IV

15 Compressor on time for a cycle

(sec) CTIM Clock card CIT CIT

16 Defrost time for cycle (sec) DTIM Clock card CIT CIT

17 Volumetric flow rate in return

duct (ft J /min) FLOW Calculated IV IV

18 Sensible heat (Btu) QS Calculated TI CIT DIT

19 Latent Heat (Btu) QL Calculated CIT DIT

20 Compressor, outdoor fan and c.c. heater energy (Wh) ECXP Calculated CIT DIT

21 Indoor fan energy (Uh) EFAN Calculated CIT DIT

22 Auxiliary heaters (Uh) EHET Calculated CIT DIT

23 Coefficient of performance COP Calculated CIT DIT

—Refer to text y IV: instantaneous value HSA: average of the 48 half hour scans

CIT: cycle integrated total RT: running total for a cycle

CTIA: compressor time integrated average TI: value for the last time increment

DIT: daily integrated total

EOC: end-of-cycle value

7
complete description of the signal conditioning and computer interface system

is given in Ref. 4.

3 .3 Data Scanning Requirements

In order to evaluate cyclic performance it was necessary to integrate the

data. This required a high data acquisition rate (especially at the start of

the on-cycle) to insure accuracy. This would, however, require the storage of

large amounts of data if the high acquisition rate were maintained through the

cycle. Results from previous dynamic heat pump laboratory tests were reviewed

to determine the optimal sliding scale of intervals between data acquisition

scans. These intervals were established as (1) every 10 seconds for the first

2 minutes of a cycle, (2) every 30 seconds for the next 4 minutes, (3) every

60 seconds for the next 6 minutes, and (4) every 5 minutes until the

compressor is de-energized.

3 .4 Data Acquisition Format

The microcomputer was programmed to record four types of data formats scan

data, cyclic data, daily data and half-hour data. 'Scan' data from each cycle

were used to evaluatec instantaneous as well as overall cycle performance. The

performance summary of each cycle is referrred to 'cyclic' data. Cyclic data

were recorded on disk for each cycle. In addition, a complete set of scan

data was recorded for every one out of ten cycles (i.e., 10 percent of all

scan results are available for further analysis). The purpose of this was to

provide disk space for other types of data and not fill it with redundant

information since only 'typical' cycles and accumulated data were of interest.

'Cyclic' data for each day were processed using summation and/or averaging

techniques. Results were recorded on disk at the end of each day. Daily

8
performance summaries are referred to as 'daily' data. Daily data include 24-

hour integrated totals of cooling done and electrical energy requirements as

well as average outdoor temperature for the 24-hour period. Half-hourly

measurements of the indoor and outdoor air temperatures were also recorded,

irrespective of the operation of the unit and referred to as 'half-hour' data.

Approximately twelve types of data were recorded for each of the four data

formats: scan, cyclic, daily, half-hour. These four data formats, the type of

data record in each format and a description of how each data value is

determined, are indicated in Table 3.1. Printouts and further analysis of

these data were made using the central microcomputer located at NBS.

9

4. DATA DISCRIMINATION AND FIELD TEST SUMMARY

An overview of the operation and thermal performance of each of the three

field-located heat pumps for the 1980 cooling season is given in Table 4.1.

The data recording period is presented in lines 2 and 3. Comparing the data

collection period in line 3 with the number of hours in which reliable data

were recorded and available for analysis (line 7) indicates a significant loss

in data collection, due to a number of factors. Early in the data collection

period, the condensate metering system was not functioning properly and the

cooling data, therefore, was not complete for that period. Also, the units

were turned off occasionally when cooling was not required. The time which

units 1, 2 and 3 were switched off were 9 percent, 30 percent, and 9 percent,

respectively, of the total cooling season data collection period. Some data

were also lost due to late replacement of data saturated disks. Lost data

amounted to 16 percent, 11 percent, and 6 percent of the total data collection

period for units 1, 2, and 3, respectively.

In the process of reviewing the data, additional cycles were excluded from

analysis. These excluded cycles included (1) cycles initiated manually by

adjustment of the thermostat setting to some value lower than that of the

previous cycle, (2) cycles aborted manually by adjustment of the thermostat

setting to some value higher than that which initiated the cycle, and (3)

other cycles in which manual adjustment did not alter the compressor operation

mode, but nonetheless resulted in detectable changes in return air temperature

in subsequent operation. These cycles were readily detected as they had

either (1) extended compressor-on periods relative to the preceeding cycle, or

(2) extended compressor-off periods relative to the preceeding cycle. It was

felt that the above cycles were unduly influenced by individual human

11
Table 4.1 Overview of Seasonal Cooling Performance

Comparison of Three Field Units

ITEM UNIT 1 UNIT 2 UNIT 3

1 Nominal Capacity 2 1/2 ton 3 ton 3 ton

2 Cooling season data

collection period

6/15/80 to 9/25/80 6/15/80 to 10/2/80 6/17/80 to 9/14/80

3 Day numbers 167 to 269 167 to 276 169 to 258

4 Total cycles n 1113 885 446

5 Total compressor time

TCTIM (hrs

)

221 287 168

6 Avg. Comp, time t (min/cyc)

11.9 19.5 21.6

7 Total cycle time TTIM

(hrs) 671 599 646

8 Avg. cycle time

(min/cyc)

36.2 40.6 83.2

9 TCTIM/TTIM = t /I on

.329 .479 .260

10 QS (Btu) x 10-6

, -6

4.823 5.433 3.670

11 QL (Btu) x 10 1.012 1.110 1.059

12 QS + QL = (Btu) x 10" 6 5.835 6.543 4.729

13 QS/Q .827 .830 .775

14 Avg. capacity

Q = Q/TCTIM (Btu/hr)

26400 22800 28200

15 Q/N (Btu/cycle) 5240 7390 10100

16 Avg. Load L = Q/TTIM

(Btu/hr)

8690 10900 7150

17 Compressor energy WCOMP

(kWh) 819 829 627

18 Indoor fan energy WFAN

(kWh) 115 197 81

19 Total Energy W (kWh) 934 1089 708

20 W = W/TCTLM (W) 4226 3794 3732

21 W/N (kWh /eye) .839 1.23 1.52

22 Seasonal EER 6.25 6.01 6.68

12
preference (such as windows and doors left open) which, if included, would

make generalizations difficult.

Early in the study, a method was developed to filter out the effects of manual

resets of the thermostat. A simple criterion which detected changes in return

duct air temperature, TRET, by an amount, ATRET, was established to determine

whether or not a given cycle, n, was affected by a manual reset of the

thermostat. If for each cycle, n, and subsequent cycle (n + 1):

TRET (n + 1) - TRET (n) > ATRET,

then cycles n and n + 1 were deleted. The magnitude of ATRET was established

by analyzing the values of TRET where manual changes in thermostat setting

were known not to have occurred. This analysis found specific thermostat

operating differentials for each unit resulting in the following limits for

ATRET:

UNIT ATRET

1 0 . 5°F

2 1 . 0°F

3 1 . 0°F

13
14
5. STEADY-STATE FIELD PERFORMANCE

5 . 1 Weather

Since field data for the three units were gathered over different portions of

the cooling season, the number of hours for a given outdoor temperature range

varied. Table 5.1 lists the fraction of temperature bin hours, n./N, for each

temperature bin, Tj, during the test periods for the three units.

Table 5.1 Fraction of Total Number of Temperature Bin Hours During

the Test Period

Range of Decimal Fraction of 1980 Cooling Season Hours

Tout ( °F) Unit #1 Unit #2 Unit #3

55-60 0 0 0

60-65 .0143 .0 .0553

65-70 .1047 .1150 .2267

70-75 .2014 .2545 .2501

75-80 .1557 .2366 .1855

80-85 .1292 .2656 .1682

85-90 .1806 .1272 .1024

90-95 .1647 .0011 .0119

95-100 .0494 0 0

Total Test period

hours, N 671.5 598.8 645.9

In subsequent discussions, the cooling performance results over the test

periods are referred to as seasonal cooling performance results. It should be

noted that intercomparison of seasonal performance results between units is

limited since the fraction of outdoor temperature bin hours are different.

15
5 .2 Steady-State Results

The steady-state part load performance results were obtained from the

(detailed) scan data. The term 'steady-state part-load' is used in the sense

that the unit is operating steadily but at less than peak capacity due to

variations in the indoor humidity and indoor and outdoor ambient temperatures.

The number of cycles of scan data available for steady-state analyses are

listed below along with the total number of cycles for the test periods of the

three units. To evaluate the part load steady-state sensible cooling capacity

and power from the scan data, data from the first 5 to 8 minutes after a unit

cycled on was disregarded. Data from the remaining time until unit shut-down

was found to be relatively unchanging and could be used to determine the

steady-state performance.

Total Number

Scan Data Cycles of Cycles

Unit 1 101 1113

Unit 2 77 885

Unit 3 40 466

Since condensate was collected only at the end of a complete on-off cycle, it

was necessary to estimate the steady-state latent capacity. Two different

methods were used in obtaining the estimate. The first method assumed that

the ratio of latent to sensible capacity was the same for the entire cycle and

steady-state portion of the cycle. This is expressed as follows:

^ = -~y— = constant

Qss ^cyc

(5.1)

16
The quantities and denote latent and sensible steady-state capacities

respectively and and Q* _ the latent and sensible cooling done over a cy c cy

complete cycle.

Steady-state performance results versus outdoor temperature for the three

field units are presented in figures 5.1, 5.2 and 5.3. The results are

averaged values over all the scan cycles for a given temperature bin.

Although the steady-state part load capacity and efficiency would be expected

to decrease smoothly with increasing outdoor temperature, the results of

figures 5.1 and 5.3 show erratic behavior. This behavior is due in part to

variations in the return air wet-bulb and dry-bulb temperatures which must

also be considered (Carnot effect due to changes in source and sink

temperatures)

An example of typical results presented in figure 5.4 provide a clue for

another cause for the erratic behavior in the steady-state part load

performance results. As the figure demonstrates at a given outdoor

temperature, the steady— state capacity tends to increase with increasing cycle

on-time. This behavior was found to occur for all three units.

The reason for the dependence of the steady-state performance on length of

cycle on-time may be traced back to the assumption discussed earlier and

embodied by equation (5.1). An improved estimate for the steady-state latent

capacity can be obtained by noting that condensate will generally not be

generated at a steady-state rate until several minutes after the cooling unit

17
CAPACITY

c\j o co

N-' CD

z iiNn

OJ

CD o

CD $

CDJC

T q -<t CD CD T T e s I siiNn

2 UNfl

o

18

Figure

5.1.

Part

load

steady-state

field

performance

[Capacity

vs.

outdoor

bin

temperature

results,
4500

N-O

CM

O)

N>

00

CM

00

hCM

CD

CM

CD

o o o o

in o in o

CM o h- in

00 CO

LU

DC3

H*

<

DC

LU

0.

LU

h*

CO

CC

o

o

Q

H3

O

(M) U3MOd

19

Figure

5.2.

Part

load

steady-state

field

performance

results

[Power

vs.

outdoor

bin

temperature,

°F],
dOO

CO

3 - CO fa

ai o u

CO

LO

<u

i-i 3

00

•H

fa

fc!33

OUTDOOR

BIN

TEMPERATURE

(°F)
Outdoor temperature=82°F

o

< ~

< o 0 *- LU *

h-

^

< CD

h- w

CO to

1 to £-°

5j

b

31 h

30

29

28

27

26

25

c

C0O

CO

1

COc

COO

CO CO

COc

COo

CO 5

d)

>

CO

COc

COo

CO CO

r~ CO £ C *0

CO O

o w

CO

IT) ~

w U

1

.05 .15 .25 .35 .45 .55 .65 .75 .85 .95

FRACTIONAL ON-TIME BIN, Tj

Figure 5.4. Steady-state capacity versus fractional on-time, unit 3.

21
cycles on. To account for this, equation (5.1) is modified to the following

form:

= O£yc/(t

on - c)

( 5 . 2 ) Qss Q*y c /t on

where t denotes the total cycle on-time and c is the time required (ranging

from 2 to 4 minutes as found in laboratory tests) after the unit cycles on,

for condensate to form on the coil and to be generated at a steady-state rate.

A more complete discussion is given in Appendix A.2 and subsequent results

include the assumptions summarized by equation (5.2).

It is worth noting that the above expression predicts higher latent and total

steady-state capacities than would be obtained by equation (5.1) for short ontime and exhibiting negligible difference for larger on-times.

22
6. CYCLIC PERFORMANCE

6 . 1 Overview of Seasonal Cooling Requirements and Unit Sizing

The percentage of total seasonal cooling requirements versus outdoor

temperature of the residences associated with the three field units is

presented in figure 6.1. For the residences associated with units 2 and

3 the histogram is bell-shaped, centering around an outdoor temperature of

82°F. Unit 1 has a flatter profile with the greatest percentage of cooling

occurring in the range of 87°F to 92 # F. The shape of the histograms reflect

several factors including outdoor temperature-generated heat gains, solar heat

gain, occupancy usage patterns (internal heat gains) as well as the building

sh e 1 1

Seasonal building cooling load curves can be derived from the data presented

in figure 6.1 together with the temperature bin hours presented in Table 5.1.

These curves are shown in figure 6.2. The figure demonstrates that a heat

pump unit may encounter a wide range of cooling load profiles. Since the

relationship between building load and outdoor temperature varies from house

to house, the seasonal energy efficiency ratio of a given unit can also vary

even if the temperature bin hours and sizing are identical.

In order to fully account for the building seasonal cooling load profiles

presented in figure 6.2 a detailed (computerized) analyses is required and is

beyond the scope of this report. Nevertheless, several factors can be

identified which qualitatively explain the curves. One obvious factor

affecting the shape of the curves is the strategic location of the thermostat

and the placement and operation of the registers which can lead to significant

23
40 r

30

20

10

0

Unit 1

j

OUTDOOR TEMPERATURE BIN, Tj

Figure 6.1. Percent seasonal cooling done versus outdoor temperature.

24
22 rFigure 6.2. Seasonal average cooling load profiles for three

field installations.

25
indoor air temperature stratification and false indications of the total

honsehold cooling requirements.

The building load associated with unit 1 exhibits a somewhat flat profile with

the outdoor temperature. The structure was of a relatively heavy brick

construction with an underground and frequently used basement. This

construction would tend to act as a heat sink, minimizing the instantaneous

effects of solar and outdoor temperature generated heat gains. The two

remaining residences (units 2 and 3) show a steeper cooling load slope up to

an outdoor temperature of 87°F beyond which the load tends to level off or

decrease. The residences were of a lighter wood frame construction and with

walk-out basements. In one case the basement was not used as living quarters.

With the relatively light construction the observed drop in the cooling load

beyond an outdoor temperature of 87°F could be due in part to the short

thermal response delay from that time in the afternoon when outdoor

temperatures are highest to a later time when outdoor temperatures would be

expected to be lower and occupancy rates and (instantaneous) internal heat

gains higher.

Figure 6.3 presents results of the percent seasonal cooling done and the

percentage of total cycles as a function of fractional on-time. Of the three

units, unit 1 is the most oversized since it exhibits the greatest percentage

of seasonal cooling and cycling at fractional on-times below .45. During the

test period the unit never exceeded a fractional on-time beyond .65. Unit 2

appears to be properly sized with a large percentage of cooling done at

fractional on-times exceeding .55. The relative sizing for unit 3 lies

between units 1 and 2 with the greatest amount of cooling provided at

26
PERCENT

OF

SEASONAL

COOLING

DONE

Figure 6. 3. Percent seasonal cooling done and percent of total versus fractional on-time, T.

UNIT 1

UNIT 2

UNIT 3

cycles

27
fractional on-time ranging from .45 to .65. Oversizing on cooling will

degrade unit cyclic performance as well as providing less control in

maintaining proper dehumidification.

6 . 2 Comparison of Thermostat Model Predictions and Field Data

The development of the thermostat model is given in Appendix A.1. The model

predicts a cycling rate, N, as a function of the fractional on-time, T,

through the following expression:

ru-ri ( 6 . 1 )

where Nmax

= cycling rate at F = 0.5

Since the cycling rate is the inverse of the total cycle time, x, the above

expression may be used to find the on-time, t on

:

t on i - r> (6.2a)

The off-time, t Q££, is then given by the expression

fc off “ x t on

(6.2b)

In order to obtain a good fit of equation (6.1) to the data, it was necessary

to obtain a good estimate for the value of N . This was accomplished by

calculating Nffiai from equation (6.1), utilizing values of N and T obtained

from the data. The data used in calculating Nfflai ranged from T = .25 to

28
r = .75 to incorporate the statistically more significant number of cycles.

An average value of Nfflax was then determined for each unit.

As seen in figures 6.4(a), (b) and (c) the model is in excellent agreement

with the data. Values of N_._ for the three units are given below along with

SI cl X

corresponding on-off times for T - 0.2.

F = 0.2

Nmax

( cycle s/hr) t on

(min) t off (min)

Unit 1 2.13 8.8 35.2

Unit 2 2.28 8.2 32.9

Unit 3 1.64 11.4 45.8

The above results indicate a significant increase in the on-time at T = 0.2 as

compared to the on-off time (6/24) used in the test procedures for cyclic

cooling performance (3).

Figure 6.4 presents a comparison of the semi-empirical thermostat model with

experimental results. The average values of fractional on-times, T, and

cycling rates, N, were obtained by averaging over the total number of cycles

in the test period for each fractional on-time bin. Also illustrated in the

figure is the standard deviation of the data, obtained by assuming that all

cycles falling within a given fractional on-time and outdoor temperature bin

have approximately equal fractional on-times and cycling rates.

29
,

cycles/hr

2 . 50

-

Figure 6.4(a). Comparison of the thermostat model with field data [Unit 1].

30
,

cycles/hr

Figure 6.4(b). Comparison of the thermostat model with field data [Unit 2].

31
,

cycles/hr

r , fractional on-time

Figure 6.4(c). Comparison of the thermostat model with field data [Unit 3].

32
6 .3 Cyclic Performance Parameters

6.3.1. Data Organization

The field data were organized into 5°F outdoor temperature bins, Tj, and .10

fractional on-time bins, T The types of data organized in this manner were

cooling consumption, energy used, cycle period, number of cycles, cooling load

factors and part-load factors. These data were summed or averaged over the

number of cycles, k (as appropriate) for each i, j bin.

As discussed in Section 3.4, two major types of data were collected and

primarily used in the data analyses. The first type is referred as cycle data

• • in which only the total capacities, Q__. a and power used, W___ were

cy cy c# lj

recorded. The cycle data consisted of all cycles undergone by the units which

were used for evaluating seasonal performance. The second (a subset of the

first type) is referred to as scan data. These data include portions of a

• • cycle from which steady^-state capacities, Q_ e power W__ cooling load

S S| 1J S S i 1

factors, CLF^j and part-load factors, PLF^j could be calculated.

6.3.2 Determination of the Cooling Load and Part Load Factors

As discussed in Section 5.2, steady-state sensible capacity and power could be

evaluated from scan data by using only those data collected after

approximately the first 5 to 8 minutes after unit start-up. For each cycle

falling within a given fractional on-time bin I\ and outdoor temperature bin,

Tj , the part load and cooling load factors were obtained by the expressions:

CLFi i = Q

gZgjlJ- —L_ (6.3)

A T .

Qss,ij

33
(6.4)

EER

PLF-. = eye, U

J EERss>ij

where t .

denotes the length of the on-off cycle.

As noted in Section 5.2, two methods were used to estimate the steady-state

latent capacity from the total condensate collected in a cycle. The steadystate latent capacity could be determined from the following expression:

tfL _ Qcyc, ij/ (t on, ij uss,ij = Qss,ij ucyc , 1 j

l on, xj

(6.5)

where the superscripts s and £ denote sensible and latent respectively and t

is the total on-time for a given cycle. All the quantities on the right-hand

side of equation (6.5) (except the value c) are measured. The value c is the

time required after unit start-up for condensate to form on the coil and be

generated at a steady-state rate. Values of c = 0,2, 3, 4 minutes are used

throughout this report. Results obtained from laboratory tests indicate that

a reasonable estimate is c = 2 minutes. Appendix A. 2 outlines the derivations

in obtaining PLF and CLF for c /= 0 from values obtained for c = 0.

6.3.3 Cyclic Performance Results

In reviewing the scan data for the three field units it was noted that for any

given frational on-time bin, ^ j, the cooling load factor, CLF

^ j

aQd part load

factor, PLF^j, were insensitive to the outdoor temperature bin, Tj. A typical

example of the results is given in figure 6.5. This result simplified

34
CLF

PLF

CLF

PLF

CLF

PLF

Fractional

on time bin

.25

1.0

0.9

0.8

0.4 r

0.3

O O o O O O

O

O

O o o

1.0

0.9

0.8

0.5

0.4

O o o ° o

I

I I I I I I I 62 67 72 77 82 87 92 97

OUTDOOR TEMPERATURE (°F)

.35

.45

Figure 6.5. Cooling load factors and part load factors for selected fractional

on-time bins versus outdoor temperature; typical results (unit 1).

35
subsequent seasonal field performance calculations. In addition, the result

is in agreement with previous laboratory results and implicit in the seasonal

performance calculations required of heat pump and central air-conditioners

manufacturers [3], This result may also be stated as follows:

CLFij = CLF £ » and

PLF i j = PLF i

and is employed in later sections.

( 6 . 6 )

Figure 6.6 illustrates typical results of cooling load factor versus

fractional on-time. Due to part load losses, the curve deviates from the

ideal curve: CLF = T. As expected, at the end points T = 0,1, CLF tends to 0

and 1, respectively.

Results for PLF versus CLF are given in figures 6.7 and 6.8. Figure 6.7 shows

typical results of PLF versus CLF for unit 3. As seen in the figure, the part

load data are very consistent, exhibiting a small standard deviation of + .02.

Some data do not show deviation marks since they contain only one or two data

points. The standard deviations in PLF for units 1 and 2 averaged + .02 and

+ .035, respectively. These deviations remain approximately the same for

values of c = 0, 2, 3, and 4 minutes.

Figures 6.8(a), (b) and (c) contains graphs of PLF versus CLF for the three

units for c = 0, 2, and 4 minutes. It is evident from the graphs that at a

constant CLF, PLF decreases for increasing values of c. This is expected

36
CLFj

Figure 6.6. Cooling load factor versus fractional on-time

for Unit 3 (c = 0 min)

37
PLF

Figure 6.7. Comparison of empirical curve with the mean and

dispersion of data—typical data.

3 8
3 9

X

=

CLF

Figure

6.8(a).

Comparison

of

data

and

empirical

curve

fit

[Unit

1].
<D c CDc

TO * * c

k_ o T“

a) k-k. co c\j CM CM LU CO T3

CO CM

Tf o o o X X >

CD CM

*—

O 05 o 00

s- Tj- o

co CO CO I I CD 0> CD

O)• O

00oo

CDo

IDoo

00o

CM6 o

II X c

CLE

GJ T3c«

«8

4-1 Q

T3comH

C4

reaEOu

.DCO• vO

0)Li3

eo

did

40
PLF

Figure 6 . 8 (c)

Comparison of data and empirical curve fit [Unit 3].

41
since increasing values of c result in increasing values of the steady-state

latent and total capacities. The resulting ratio of EERcyc and EERSS

therefore decreases.

Empirical curves were fitted to the data of figure 6.8 and had the following

form:

PLF = 1 - e -

P (CLF)<l (6.7)

In evaluating the constants p and q the above equation was linearized to the

form:

1i = a + q ej (6.8a)

where p

= e a (6.8b)

(6.8c)

e

i = In [CLFil (6.8d)

A least square fit of the data (denoted by the subscript i) in the form of

equation (6.8) was taken over a selected range (generally over the range

CLF = .1 to CLF = .6) to evaluate the constants p, q. Table 6.1 contains

values for p and q for the three units.

42
Table 6.1 Values for Part Load Performance Constants, p, q for the Three

Units*

UNIT 1 UNIT 2 UNIT 3

P q P q P q

c = 0 min 4.0774 .34 3.7019 .40 3.644 .40

c = 2 min 3.4822 .34 3.4702 .43 3.0855 .35

c = 3 min 3.265 .35 3.320 .44 3.1997 .415

c = 4 min 3.0811 .37 3.0897 .42 2.973 .40

*PLF = 1 - e “P(CLF)q

43
It is evident from figure 6.8 that the curves fit the data surprisingly well.

For values of CLF ranging from .1 to .8 the average deviation of the curve

from the data was 0.5 percent with a maximum error of 2.9 percent. For values

of CLF less than .1, the error ranged from 2 percent to 14 percent. In this

range, however, very little data were available to obtain an accurate value for

PLF. For values of CLF ranging from .8 to 1.0, the error averaged

approximately 3 percent with a maximum of 4.8 percent. These errors occurred

mostly at the value of CLF = 1 where equation (6.7) predicts a value less than

unity for PLF.

The above curves were used in the seasonal performance calculation of the

three units. Although the error for very small values of CLF appeared

significant, it was considered unimportant since very little cooling was done

in this part of the range. For values of CLF ranging from .7 to 1.0, a

straight line was used, joining the curve fit at CLF - .7 and having a value

of PLF equal to 1 at CLF = 1. This piecewise curve fit was used since the

exponential portion resulted in values of PLF slightly less than 1 at CLF = 1.

44
7. SEASONAL PERFORMANCE EVALUATION

The seasonal part load factor is defined as:

PLF = - SEER

seas SEER__

ss

(7.1)

where

SEER = §

(7.2)

(7.3)

and Q = the total cooling done over the test period

W - the total electrical energy used over the test period

W

gs = the total electrical energy that would have been used over the

test period had the unit operated with no part load losses.

A straight-forward method for determining Y_. would be to use the steady-state

s s results presented in figure 5.2 for each temperature bin, Tj. W cc z could

then be determined from the following expression:

ss (7.4)

and

(7.5)

j

45
It was noted, however, that EERSS varied not only with Tj but with fractional

on-time, 1^. This method results in estimates of the steady-state F.F.R that

were less than the cyclic EER for a significant number of cycles. The above

mentioned variations were due in part to variation on the return air and

return dew point temperature.

An alternative method for determining the steady— state seasonal performance

was therefore used, incorporating the results of the previous section. It was

noted that the part load performance factor, PLF^j, and cooling load factor,

CLFjj, obtained from the scan data are a strong function of the fractional ontime, r. (i denotes the fractional on-time bin) but insensitive to the outdoor

temperature, Tj. It is assumed that PLF^j and CLFjj obtained from the scan

data for each i, j bin are representative of all the cycles in that bin. From

the analyses given in the Appendix, the seasonal part load performance factor

is determined from the following expression:

^F

seas

“ ^ W-Fi (7.6)

Where W

cyc ^ = the energy used in a given fractional on-time bin, i.

In some instances scan data was totally lacking or insufficient to determine

PLF^ for a given fractional onrtime bin. In addition, the fractional on-time

in each fractional on-time bin determined from the scan data varied slightly

from the total (cycle) data for that bin.

In order to account for the above deficiencies in the data, the PLF^ were

therefore determined by the following method. From the scan data, CLF was

46
plotted against fractional on-tine, T and a smooth curve vas drawn. An

example of the plot is given in figure 6.6. The fractional on-time determined

from all the data was then determined for each i-bin and, using graphs similar

to the one illustrated in figure 6.6, a CLF^ characteristic of that bin vas

read off it. The PLF^ were then determined from the performance curves given

in figure 6.8, Section 6.3.3.

7 . 1 Seasonal Degradation Coefficient

The seasonal degradation coefficient is defined by the following expression:

°Dseas

1 PLF seas

1 - CLF(PLFsea$ ) (7.7)

where the quantity CLF(PLF

seas ) is the cooling load factor obtained from the

part load performance curves of figure 6.8 at PLF = PLF_.... Ov A S

A 'seasonal cooling load factor', CLF e _ a. may be defined as: Sv & s

CLF SCaS ^ss,i

i

(7.8)

where

i E Bgjcul

^ CLF ,

(7.9)

The quantity Q . is the sum of the steady-state cooling over all cycle* for 0 0)1

a given i-bin. The steady-state cooling is that which would have occurred if

47
the unit operated steadily for the entire cycle time, x, and at the same

ambient condition existing during t Qn .

It should be noted that in general CU? and CLF(PU? are not

equivalent. The former quantity is obtained by weighting with the fractional

amount of cooling done whereas the latter value is dependent on the unit part

load performance curve, weighted with the fractional amount of energy input.

The difference between CU? as given by equation (7.8) and CLF(PU? is S€aS S6SS

more clearly seen by assuming a linear relationship for the part load

performance curve:

Applying equation (7.6) to equation (7.10) results in the following expression:

The value of CLF(PLF ) is obtained by substituting the expression for

S" a S PLF c

. oc , given by equation (7.11) into equation (7.10), which yields: Sv&S

By comparing CLF(PLF

geas ) as given by equation (7.12) and CLFseas

as defined

through equations (7.8) and (7.9), it is evident that the two expressions are

not equivalent.

PLF = 1 - CD

(1 - CLF) (7.10)

(7.11)

i

(7.12)

48
Seasonal performance results of the three units are presented in Table 7.1.

As discussed in Section 6.3, the factor ’c’ appearing in the Table is a

correction factor for the estimate of the steady-state latent capacity, which

strongly influences the estimate for PLFseas

* correction time, c = 2 min

assumes that condensate does not start to form until 2 minutes after the unit

cycles on, whereas c = 0 minutes assumes the unit is creating condensate at a

steady-state rate as soon as the unit cycles on.
Table

7.1

Seasonal

Field

Performance

Results

50
8. COMPARISON OF LABORATORY AND SEASONAL FIELD PERFORMANCE RESULTS

Hie extensive data obtained from the field study were used to determine how

well the present procedures [1,3] for determining the seasonal cooling

performance of central air conditioners and heat pumps agree with actual field

data. To this end, laboratory tests were conducted with an identical model as

field unit number 3.

The following tests were conducted in the laboratory (as called for in the

Test Procedures (1)).

Indoor Dry-Bulb-Wet

Bulb, °F

Outdoor Dry-Bulb

Temperature, # F Cycling Rate

Test A 80/67 95 steady-state

Test B 80/67 82 steady-state

Test C 80/dry-coil 82 steady-state

Test D 80/dry-coil 82 6 min-on, 24 min-off

(T = .2)

Tests C and D are used to determine the cycling degradation coefficient, C^, as

follows

PLP = EER(Test D)

’ EER(Test C)

( 8 . 1 )

CLF

QCV c< Test D)

Qss (Test C) ((6 + 24))

( 8 . 2 )

51
r = 1 - PLF

1 - CLF

(8.3)

Because of the differences in cycling rates as required in the test procedures

and the actual rate encountered in the field. Test D was also conducted at the

typical field cycling rate for unit 3. The cycling rate was found to be

closely approximated by the following relationship:

N = 6.55 r (1 - n

(cycles per hour)

(8.4)

The laboratory unit was charged with refrigerant R22 at the same outdoor

temperature and supply air quantity that occurred for a typical scan (detailed

data) cycle of the field unit. Refrigerant charge was added or subtracted

until the temperature difference across the coil agreed with the temperature

difference that occurred for that cycle. Latent capacity was also checked to

ensure agreement with the field performance for that 'typical' cycle. The

ambient conditions of the selected cycle were:

IDB = 76°F where

IDP = 60.6°F

ODB = 81 °F

CFM = 1182 (1148 used in

the laboratory tests)

IDB Indoor dry bulb temp.

IDP Indoor dew point temp.

ODB Outdoor dry bulb temp.

CFM Cubic feet per minute

A comparison of the steady-state capacity and power of the laboratory-tested

unit and the field unit at an outdoor temperature of 82°F is given below:

52
(Btu/h)

6ss <82>

(watts)

Wss (84) EERSS (82)

Laboratory Unit 32,030 4021 7.97

Field Unit 30,144 4143 7.3 c = 2 min

(28,550) 4143 (6.9) (c = 0 min)

Field data at an outdoor temperature of 95°F is not reported since no direct

scan data were available.

Tbe capacity and energy efficiency ratio results for the field unit were

obtained through an estimate of the steady-state latent capacity. The results

for c = 0 were obtained by assuming that the ratio of steady-state latent to

steady-state sensible capacities are the same as in cyclic operation. As can

be seen, there is a significant difference in results. Laboratory

investigations, however, have indicated that in cyclic operation, condensate

is not generated until 2 to 4 minutes after the unit cycles on. Hence, for

short on-times the ratio of steady-state latent to steady-state sensible

capacity is greater than the cyclic ratio. Using this new estimate, the

results are reported in the above table for c = 2 minutes. Other factors

which contribute to the variations in results are the lower entering dry-bulb

and wet-bulb temperatures (approximately 76°F and 66°F, respectively) for the

field unit than the laboratory test conditions (80°F/67°F).

A comparison of the field and laboratory cyclic performance results can be

made with the aid of Table 8.1 and figure 8.1. As discussed earlier, the

constants c = 0, 2, 4 minutes appearing in the field performance results art

53
Table 8.1 Comparison of Laboratory and Field Cyclic Performance

Fractional On-Time T,

Thermostat Setting,

N (cycle/hr) max J

On-Off Times

(Min)

t /

on of f Laboratory Results Nmax

= 3

max

= 1.64

6/24

10/10

11.5/46

11/18

.36

31

,21

,23

Field Results

(Seasonal Values)

c = 0 min

c = 2 min

c = 4 min

(N

max

= 1.64)

,14

,18

,22

54
Qss7

”

Figure 8.1. Laboratory cyclic performance results.
estimates of the time required after the unit cycles on for condensate to form

on the coil, and as a result, affect the estimate for total steady-state

capacity. Based on previous laboratory tests, a value of c = 2 is judged to

be a reasonable (conservative) estimate. This value should therefore be used

in comparing the field results with laboratory results.

The laboratory results presented in Table 8.1 have been divided into two

operating regions: the first (Nmax = 3 cph) corresponds to a thermostat

setting which results in a maximum cycling rate of 3 cycles/hr at l - 0.5 and

the second (Nmax = 1.64 cph) is the thermostat setting approximating the field

measurements. The present test procedure calls for a thermostat setting of

Nmax

= ^ cPk an<* T = 0.2 which results in on-off times of 6 minutes and 24

minutes, respectively.

The laboratory results indicate a relatively high value of the degradation

coefficient for Nmax = 3 cph, T = 0.2 (6 min on, 24 min off). A slightly

lower value was obtained for F = 0.5 (10 min on, 10 min off) but still high

compared to field performance results.

Much better agreement in the degradation coefficient is shown for a thermostat

setting equal to 1.64 cph. A slightly anomolous trend is observed in the

laboratory results for F= 0.2 (Cp = .21) and F = 0.5 (Cp = .23). This is

most probably due to the rounding of the on-off times for convenience in

testing.

56
9 . CONCLUSIONS

Field data were collected and the cooling performance of three heat pomp units

evaluated. Two major types of data were collected and used to evaluate the

cyclic performance parameters and seasonal performance. The first type

consisted of scan data collected at various intervals during the on portion of

a cycle. The second type consisted of cycle data in which data was averaged

or summed, as appropriate, for an entire on-off cycle. Cycle data was

collected for every cycle throughout the test period.

Scan data for every tenth on-off cycle was collected and used to evaluate the

cyclic performance parameters. The results confirmed laboratory findings that

the cooling load and part load factors are independent of the outdoor

temperature and dependent only on the cycling rate and fractional on-time.

From the scan data, part load performance curves were generated and in

conjunction with the cycle data, seasonal part load factors and cyclic

degradation coefficients determined. The methodology utilized performance

data from the units and therefore did not require incorporating a building

cooling load assumption.

Field thermostat data were collected and a semi-empirical model was developed.

The model was found to be in excellent agreement with the data. Peak cycling

rates, occurring at fractional on-times of 0.5 were found to range from

approximately 1.6 cph to 2.3 cph. The predicted cycling rate at a fractional

on-time of 0.5 resulting from cycling at the rate called for in the standard

test and rating procedures [1,3] is 3 cph, higher than observed for the three

field units. It is believed that factory settings for the cooling antieijater

57
and commonly used mercury bulb electromechanical thermostats result in peak

cycling rates ranging from approximately 2 cph to an upper limit of 3 cph [5],

Cooling performance tests were conducted in the laboratory on an identical

model heat pump as was tested in the field. At an outdoor tempeature of 82°F,

the steady-state capacity, power, and EER of the laboratory unit were within 6

percent, 3 percent, and 9 percent, respectively of the field unit. The above

differences were attributed to a) lower average return-air dry-bulb (76°F) and

wet-bulb (66°F) temperatures for the field unit as compared to laboratory

conditions (80°F dry-bulb, 67°F wet-bulb temperature), b) approximation used

in determining the steady-state latent (and hence) total capacity of the field

unit, and c) manufacturing tolerances listed in order of importance.

Cycling tests were also conducted in the laboratory in accordance with the

standard test and rating procedures [1,3] in order to compare and evaluate the

cyclic degradation coefficient, CD

» with field results. Cycling the unit at

the standard rate of 6 minutes-on, 24 minutes-off resulted in a value of Cp =

0.36. The result is significantly different than the field result, Cj) = 0*18.

The laboratory unit was then cycled at the same avarage rate as the field unit

corresponding to a fractional on-time, T, equal to 0.2 (11.5 minutes-on, 46

minutes-off). The cyclic degradation coefficient resulting from this rate was

found to be in much better agreement (Cp = *21) with the field results. The

remaining disparity between laboratory and field results are attributed to a)

differences in the amount of refrigerant charge in the two units, and b)

approximations used in the field results for evaluating the steady-state

latent capacity.

58
The laboratory test procedures [1,3] used to determine the cyclic degradation

coefficient from dry coil tests appear to accurately reflect the degradation

coefficient found in actual practice, as long as comparable thermostat

charcteristics (reflected by the peak cycling rate Nmax at 0.5 fractional

on-time) are employed. It is apparent that the standard laboratory cycling

rate is too high and that a somewhat lower rate, ranging between Nmax = 2 and

N

nai = 3 should be employed.

59
60
10. REFERENCES

1. Kelly, G.E., and Parken, W.H., "Method of Testing, Rating and Estimating

the Seasonal Performance of Central Air-Conditioners and Heat Pumps

Operating in the Cooling Mode," National Bnreau of Standards, M3SIR 77-

1271 (April 1978).

2. Parken, W.H., Kelly, G.E., and Didion, D.A., "Method of Testing, Rating

and Estimating the Heating Seasonal Performance of Heat Pumps," National

Bureau of Standards, NBSIR 80-2002 (April 1980).

3. Federal Register, Part III, Department of Energy, Office of Conservation

and Solar Energy, Test Procedures for Central Air Conditioners, Including

Heat Pumps, Thursday, December 27, 1979.

4. Hurley, C.W., Kelly, G.E., and Kopetka, P.A., "Using Microcomputers to

Monitor the Field Performance of Residential Heat Pumps," National Bureau

of Standards, NBSIR 81-2285 (June 1981)

5. Private ccxnmunica tions with Lome Nelson of Honeywell.

61

APPENDIX

A. 1 THERMOSTAT MODEL

The development of the thermostat model rests on several simplifying

assumptions so that only a brief discussion is justified.

The building cooling load, BL, is assumed to be met over the cycle time

period, x, by the cooling done (by the unit) during the on time, t This is

expressed as:

Ion = BL A. 1(1)

where the fractional on time, t on/r is dominated by variations in BL. The

variation in unit cyclic capacity, QCyC due to outdoor temperature and cycling

rate is small in comparison to changes in BL so that the former is considered

constant. Equation A. 1(1) is therefore written as: — = K1 BL A. 1(2)

x

1

A thermostat has a built-in temperature differential, T* - T. which is

normally on the order of 3°F. When the indoor air temperature reaches a

value T* above the set point, Tse t» the thermostat calls for cooling. The

indoor air temperature decreases while the unit is on, to a value, Tcr ^ t b( . lo

Tco + before turning off. The following figure illustrates the indoor air Set

temperature variation as the cooling unit goes through a complete on-off

cycle

63
Air temperature

near thermostat

A second simplifying assumption made is that the building cooling load is

proportional to the rate of increase in the indoor air temperature when the

unit is off. This is expressed as:

BL = K2

T* - Tcrit

off

A. 1(3)

The quantity K(T* - T

cr ^ t

) incorporates heat transfer and storage effects of

the building interior surfaces to the indoor air as well as the thermostat

differential. The above quantity can be adjusted to any desired value by

means of a thermostat anticipator circuit. The anticipator heats the air near

the bimetallic element during the unit off period. The following figure

illustrates ideally how the anticipator regulates the length of the unit offtime.

Air temperature

near thermostat

64
The above discussed quantity, I^OT* - Tcr i*) is herein considered constant

with respect to changing building loads and fractional on-times. Equation

A.l(3) is then written as:

BL = —L_ A. 1(4)

t of f

Combining the following definitions:

T = t on + toff

N « I

x

with equations A. 1(2) and A. 1(4) the

t t N = K (i - _on)

X X

Recognizing that the maximum cycling

above expression is written as:

N = 4 Nmai r (j - D

where Nmax is the cycling rate at 50

on-time (t on/ x )

A. 1(5)

A. 1(6)

following expression is obtained

A. 1(7)

rate, N

fflax> occurrs as t on/r = .5, the

A. 1(8)

percent on time and T is the fractional

6 5
66
A. 2 DEVELOPMENT OF METHOD TO IMPROVE THE ESTIMATE FOR STEADY- STATE CAPACITY

COOLING LOAD FACTOR AND PART LOAD FACTOR

Observations made daring laboratory tests indicate that condensate starts to

form from 2 to 4 minutes after unit start-up.

In the field, condensate was measured only over a complete cycle. In the

initial calculations of the steady-state latent capacity the following

relationship was assumed:

6^ ft 8 6

8 -S3£. = -l8 or equivalently

AT AT qT qT

ucyc uss ycyc uss

A.2 ( 1)

where the superscripts £, s, T denote latent, sensible and total,

respectively. For small on-times it is evident that equation A.2(l)

underestimates the steady-state latent capacity.

To improve the estimate of the latent steady-state capacity the following

relationship was assumed:

s s _ Q

s USS

^cyc

(t on

" °>

A. 2(2)

where c denotes the delay time (ranging from two to four minutes) before

condensate starts to form after the unit has cycled on.

Using the relationship:

67
<4c

Q

s ^cyc

eye

Q

s wcyc

1.

and combining with equations A.2(l) and A.2(2), the following equation

appl ies

6

s

s s

qLc _ j 1

Q|yc 1 " c/ton

A. 2(3)

Equation A. 2(3) is further rearranged to the form:

. , 1

o 1

1

1 + D

A.2(4a)

where

D = -c/t

on A . 2 ( 4b

)

The steady-state total capacity is expanded to the form:

6T = 6

s ss uss 1 + A. 2(5)

Combining equation A.2(4a) and A.2(5) results in the following expression for

the total steady-state capacity:

68
_ As

ss uss rhs A. 2(6)

QT

1 +\-PZ°

,QS

k eye

- 1

The above expression is rearranged to:

•T + D 6*

Ql _ s s s s SS 1 + D

A. 2(7)

where Qj s denotes the 'uncorrected' total steady-state capacity as determined

from equation A. 2(1). In the subsequent derivations, all variables written

with a ~ (telda) denote quantities uncorrectd for the improved estimate in the

latent steady-state capacity.

The steady-state energy efficiency ratio, EERss can be evaluated in terms of

the uncorrected estimate EERSS using equation A. 2(7) as:

Q

T

EER = -AA =

o d rrr "SS

ws s

1 + D

A. 2(8)

The part-load factor, PLF is expressed in terms of the uncorrected PLF and the

uncorrected ratio of steady-state sensible and steady-state total capacity

using equation A. 2(8)

1 _ EER

ss EERSS 4- 1 f D *ls

PLF EERC y C EERgyg EERgyg /

1 + D

Equation A.2(9a) can be simplified to the following expression:

69

A . 2 ( 9a

)
1 PLF

4- i PLF

+ D<S

]

A . 2 ( 9b

)

where as noted is equation A. 2(1):

jjs = Mzc

6Js *lyc

The cooling load factor, CLF, can be evaluated from the uncorrected estimate,

CLF by using the following relationship:

-1- = _I_ A. 2(9)

CLF ton

6jyc

toAd +

Using the above relationship equation A.2(9) can be reduced to the following

expression:

70
A. 3 DETERMINATION OF SEASONAL PART LOAD FACTOR

The seasonal part load performance, 1PLF is defined by the following

• OoS

expression:

PLFseas SEER

seerS8

where SEER = Q/W

SEERss = Q/Wss

A.3 ( la)

A.3 ( lb)

A.3( lc)

Q = total measured seasonal cooling

W = total measured seasonal energy used

The term W__ is the seasonal energy usage that would have occurred if the unit

operated with no part load losses. This term is evaluated by first

considering a single cycle, k, in temperature bin j with fractional on time,

i. The steady-state (ideal) energy input for a single cycle, W $$ — ^ may be

expressed as:

V =4

s s , ij k s s , ij t on, ijk A. 3(2)

» where ton = the 'ideal' time the unit would have been on to satisfy the

cooling load if the unit had no part load losses.

W ss, ij the steady-state power input of the unit for temperature

bin j and fractional on-time, i

71
The 'ideal' on-time, t^ n jjj. is determined by the oooling load balance

equations:

BL x ijk ®cyc,ij * on, ijk A. 3(3)

BL T ijk “ ^ss,ij t on, ijk A. 3 ( 4)

where BL = building cooling load

x = total time for one complete cycle.

A one-to-one correspondence between 'ideal' and actual cycle times can be

maintained if in the ideal case the anticipator is readjusted. This

equivalence is stated here for convenience:

T ijk " T ijk A.3 ( 5)

Thus in the 'ideal' case and actual case, the building load is met over the

same time periods.

Using equations A. 3(3), A. 3(4) and A. 3(5), the 'ideal' on time is written as:

t

' = Qcyc, ij t t on,ijk on, ijk A.3 (6)

l ss, ij

Using the expression with equation A. 3(2), gives:

Q,

^ss,ijk ^ss,ij . t on,ijk

Qss, ij

A.3 ( 7)

72
the above expression is expanded as follows:

vss, ijk

*ss,ij ^cyc.ij ^ss.ij j. [~^gjca ij

• • • eye , ij i . *cyc,ij ®ss,ij ®cyc,ij L®ss,ij

-on .Jjkj

A. 3 ( 8)

Equation A. 3(8) reduces to:

W

ss,ijk PLFij Vcyc,ijk A. 3(9)

where

EERCVC PLF • - = SISj IA

*J EER a

- ss , ij

A.3 ( 10)

Vcyc,ijk ^cyc,ijk t on,ijk A. 3(11)

Ihe seasonal energy usage that would have occurred if the unit had no partload losses is the sum over all cycles, m jj* in each, i, j bin. This is

written as:

i j k

W

ss

m . . HE1J

PLF-.

i j k

J V

cyc, ijk

A. 3(12)

As discussed in the text, the part load factor, PLF^ j

, is relatively

insensitive to outdoor temperature. A mean value is determined from the data

73
for all cycles for a given fractional on-time bin, i. Hie above expression

therefore reduces to

Wss I PLFj

i Wcyc,i A.3( 13)

where ^cyc,i ^ ^cyc,ij

j

A.3 ( 14)

Combining equations A.3 (13) with equation A.3(la), A.3 (lb) and A.3(lc) results

in the following expression:

^seas =1^1 »cyc.i A.3 ( 15)
NBS-' 14A (REV. 2-80

U.S. DEPT. OF COMM. 1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

BIBLIOGRAPHIC DATA

SHEET (See instructions) NBSIR 85-3107 March 1985

4. TITLE AND SUBTITLE

Field Performance of Three Residential Heat Pumps in the Fooling Mode

5. AUTHOR(S)

Walter Parken, David Didion, Lih Chern and Paul Woiciechowsk]

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State, ZIP)

U.S. Department of Energy

1000 Independence Avenue, S.W.

Washington, D.C. 20585

10.

SUPPLEMENTARY NOTES

f

1 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Field data was acquired for three residential heat pumps and the part load

performance factor and seasonal cooling energy efficiency ratio were evaluated.

Laboratory tests were conducted on a unit identical to one of the field-tested heat

pumps and performance results compared. Thermostat data was also acquired and a semi-empirical model developed.

The thermostat model was found to be in excellent agreement with the field data

for all three field units and could be characterized by a peak cycling rate, N

occuring at a fractional on-time of 0.5. The value of N was found to range

from 1.64 cycles per hour to 2.28 cycles per hour.

The laboratory test results indicated a higher cyclic degradation coefficient

than found for the field unit when cycled at a rate of 6 minutes on, 24 minutes off

(corresponding to N =3 cycles per hour) . However, when the laboratory unit was cycled at the same ^fower) rates as found for the field unit (corresponding to N 1.64 cycles per hour), the cyclic degradation coefficient and seasonal part load

factors were in good agreement.

max 12.

KEY WORDS (S/x to twelve entries; alphabetical order; capitalize only proper names; and separate key word-, b, •'••• central air-conditioning; cooling field performance; energy conservation; field

data acquisition; heat pumps; thermostats

13. AVAILABILITY

[~xl Unlimited For Official Distribution. Do Not Release to NTIS

1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

[X Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTEO PAGE

86

15. Pn

ill. SO
’