NBSIR 88-3781

Recommended Procedure for

Rating and Testing of Variable

Speed Air Source Unitary Air

Conditioners and Heat Pumps

Piotr A. Domanski

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Environment Division

Gaithersburg, MD 20899

May 1988

75 Years Stimulating Amerce*’* Progress 1913-1988 Sponsored by:

ILSo Department of Energy

Washington, DC 20585

NBSIR 88-3781

RECOMMENDED PROCEDURE FOR

RATING AND TESTING OF VARIABLE

SPEED AIR SOURCE UNITARY AIR

CONDITIONERS AND HEAT PUMPS

Piotr A. Domanski

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center For Building Technology

Building Environment Division

Gaithersburg, MD 20899

May 1988

Sponsored by::

U.S. Department of Energy

Washington, DC 20585

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

RECOMMENDED PROCEDURE FOR RATING AND TESTING OF

VARIABLE SPEED AIR SOURCE UNITARY AIR CONDITIONERS AND HEAT PUMPS

Abstract

A procedure is presented for testing and rating variable speed, residential

air conditioners and heat pumps. The procedure is derived in part from

existing procedures for single speed and two speed systems. The main

addition to the existing procedures is a new algorithm for representation

of variable speed unit performance in the intermediate speed operation

range. Analysis and background which led to the formulation of the

procedure are included as well as calculation examples for the cooling and

heating mode. This procedure has been prepared for the Department of

Energy for consideration in the rule making process.

Key Words: Air conditioner, heat pump, rating procedure, seasonal

performance, variable speed system.

ii
DISCLAIMER

In view of the presently accepted practice of the building industry in the

United States, common U.S. units of measurement are used in this report.

In recognition of the United States as a signatory to the General Conference

of Weights and Measures, which gave official status to the SI system of units

in 1960, appropriate conversion factors are provided in the table below.

The reader interested in making further use of the coherent system of SI

units is referred to: NBS SP330, 1972 Edition, "The International System

of Units," or E380-72, ASTM Metric Practice Guide (American National

Standard 2210.1).

METRIC CONVERSION FACTORS

Length 1 inch (in) = 25.4 millimeters (mm)

1 foot (ft) = 0.3048 meter (m)

Area 1 ft2 = 0.092903 m

2

Volume 1 ft3 = 0.028317 m

3

Temperature °F = 9/5 e C + 32

Temperature

Interval

1 °F = 5/9 e G or K

Mass 1 pound (lb) = 0.453592 kilogram (kg)

Mass Per Unit

Volume

1 lb/ft3 = 16.0185 kg/m3

Energy 1 Btu = 1.05506 kilojoules (kJ)

Specific Heat 1 Btu/ [lb • °F] = 4.1868 kJ/[kg • K]

Gallon 1 gallon 0.0037854 m

3

iii
TABLE OF CONTENTS Page

ABSTRACT ................... ii

DISCLAIMER .................. iii

TABLE OF CONTENTS. .............. . iv

LIST OF FIGURES. ............... ... vi

LIST OF TABLES ................. vii

LIST OF SYMBOLS. ................. . . viii

1. INTRODUCTION ................. 1

2. BACKGROUND OF THE PROCEDURE DEVELOPMENT 4

2.1 Intermediate Speed Test 4

2.2 Interpolation of the Intermediate Speed Power Input 8

2.3 Cyclic Test 12

2.4 Capacity and Power Input Lines at the Maximum Compressor

Speed in the Heating Mode 17

2.5 Building Load in the Heating Mode 19

2.6 Measurement of the Electrical Energy Input 21

2.7 Needed Research 23

3. RATING PROCEDURE FOR VARIABLE SPEED SYSTEMS IN THE COOLING MODE

3.1 Requirements for Testing Conditions and Testing Procedures . . 25

3.1.1 Tests and Testing Conditions 25

3.1.2 Cyclic Test. 25

3.1.3 Intermediate Speed Test. 27

3.1.4 Air Quantity Measurement 27

3.1.5 Power Measurement 28

3.2 Calculation of Seasonal Energy Efficiency Ratio, SEER .... 28

4. RATING PROCEDURE FOR VARIABLE SPEED SYSTEMS IN THE HEATING MODE

4.1 Requirements for Testing Conditions and Testing Procedures. . 36

4.1.1 Tests and Testing Conditions 36

4.1.2 Cyclic Test 36

4.1.3 Intermediate Speed Frost Accumulation Test 37

4.1.4 Maximum Speed Frost Accumulation Test 37

4.1.5 Nominal Speed High Temperature Test 37

4.1.6 Air Quantity Measurement 38

4.1.7 Power Measurement. 38

4.2 Calculation of Heating Seasonal Performance Factor, HSPF. . . 38

iv
5 . REFERENCES 49

APPENDIX A. EXAMPLE OF SEER CALCULATIONS 51

APPENDIX B. EXAMPLE OF HSPF CALCULATIONS 56

v
LIST OF FIGURES

1. Building cooling load and capacity of variable speed

air-conditioner . 2

2. System power at intermediate speed operation using different

interpolations 5

3. System EER at intermediate speed operation using different

interpolations. 10

4. Cyclic rate for a single speed system and a variable

speed system. .... .......... 14

5. Maximum theoretical SEER penalty at default Cd 16

6. Ratio of measured capacity to linearly interpolated

capacity (using 17°F and 47°F data) for the frost

accumulation test 19

7. Ratio of measured power to linearly interpolated power

(using 17°F and 47°F data) for the frost accumulation

test .20

8. Ratio of measured COP to linearly interpolated COP

(using 17°F and 47°F data) for the frost accumulation

test. . 21

9. Deformation of the current waveform at input to a three

phase inverter at 30 Hz output frequency 22

10. Building heating load and capacity of a variable speed

heat pump .42

11. Heating climatic regions and distributions of heating

load hours (HLH) for the United States. ........... 68

vi
LIST OF TABLES

Page

1. Summary of Test Conditions for Rating Variable Speed Systems

in the Cooling Mode 61

2. Distribution of Fractional Cooling Hours in Temperature Bins

for Calculation of SEER 62

3. Summary of Test Conditions for Rating Variable Speed Systems

in the Heating Mode 63

4. Distribution of Fractional Heating Hours in Temperature Bins,

Heating Load Hours and Outdoor Design Temperature for

Different Climatic Regions. ............ 64

5. Standard Design Heating Requirements. .............. 65

Al . Bin Calculation Worksheet for Evaluation of SEER. . . 66

B1 . Bin Calculation Worksheet for Evaluation of HSPF. ........ 67

o

vi i
LIST OF SYMBOLS

, k = 2

*9 5

BL( t)

Dk = 1 ^8 2

ok = 2 ^8 2

ok = 1 ^6 7

b

C

CD CFM

COP

DHR

D

k = i u6 7

E(t)

•EER

e (tj)

HSPF

steady state test in the cooling mode at conditions

specified in Table 1

coefficient used in eq. (3.17) and eq. (4.19), (-)

building load at outdoor temperature t, (Btu/h)

steady state test in the cooling mode at conditions specified

in Table 1

steady state test in the cooling mode at conditions specified

in Table 1

steady state test in the cooling mode at conditions specified

in Table 1

coefficient used in eq. (3.17) and eq. (4.19), (-)

0.77, an experience factor which improves the agreement

between calculated and measured building loads, (-)

cyclic degradation coefficient of performance, (-)

volumetric, flow rate of air, (ft3 /min)

coefficient of performance, (-)

cyclic test in the cooling mode at conditions specified in

Table 1

coefficient used in eq. (3.17) and eq. (4.19), (-)

design heating requirement, (Btu/h)

cyclic test in the cooling mode at conditions specified in

Table 1

power input to a system at outdoor temperature t during

steady state operation, different subscripts may be used, (W)

energy efficiency ratio, (Btu/W*h)

power usage in bin temperature t^ , (W)

heating seasonal performance factor, (Btu/W»h)

intermediate speed test in the cooling mode at conditions

specified in Table 1

sequential number of a temperature bin, (-)

viii
n

j

n8

PLF

Q(t)

q(tj)

RH(tj)

RPM

SEER

td

T0 f f

Ton

t3

to n

fractional bin hours in bin j, per Table 2 or Table 3, (-)

cycling rate of a single speed system, (1/h)

cycling rate of a variable speed system, (1/h)

part load factor, (-)

steady state capacity at outdoor temperature t, different

subscripts and superscripts may be used, (Btu/h)

cooling done in bin temperature tj , (Btu/h)

power input to the supplementary resistant heater required

in those cases when the heat pump automatically turns off

(tj < toff ), or when it is needed to meet the balance of the

building heating requirement, (W)

speed, (revolutions/min)

seasonal energy efficiency ratio, (Btu/(W®h))

outdoor design temperature as specified in Table 4, (°F)

compressor time-off, (h)

© compressor time-on, (h)

outdoor temperature, (°F)

representative outdoor temperature for temperature bin j (°F)

outdoor temperature in cooling at which the building load is

equal to capacity of the system operating at the minimum

compressor speed, ( e F)

outdoor temperature in cooling at which the building load is

equal to capacity of the system operating at the maximum

compressor speed, (

e F)

outdoor temperature in heating at which the building load is

equal to capacity of the system operating at the minimum

compressor speed, (°F)

outdoor temperature in heating at which the building load is

equal to capacity of the system operating at the maximum

compressor speed, (

e F)

outdoor temperature at which the compressor is automatically

turned on after low- temperature shut-off, (°F)

ix
tof f outdoor temperature at which the compressor is automatically

turned off to avoid operation at low temperatures, (°F)

"" outdoor temperature at which the building cooling load is

equal to system capacity while operating at the compressor

speed prescribed for the intermediate ?peed test, (°F)

Cvh = outdoor temperature at which the building heating load is

equal to system capacity while operating at the compressor

speed prescribed for the intermediate speed test, (°F)

X(tj) cooling or heating load factor at a bin temperature t i

, (-)

«( tj) heat pump low temperature cut-off factor, (-)

Superscripts

k=n = nominal compressor speed

k=l the minimum compressor speed

k=2 the maximum compressor speed

k=i = the intermediate speed specified for the intermediate

speed test

k=v = an intermediate speed at which the unit capacity matches the

building load at specified outdoor temperature

Subscripts

def = defrost

f indoor fan

i = intermediate speed test

max = maximum

min = minimum

s = single speed

ss = steady state

V = variable speed

x
‘
1 . INTRODUCTION

Most residential air conditioners and heat pumps employ single speed

compressors and single speed fans. Such systems can provide only one

level of capacity at given operating conditions. More advanced systems

employing two speed compressors can provide two levels of capacity at

given operating conditions. The distinguishing feature of variable speed

systems is that their compressors can operate at different speeds and

allow capacity to modulate within a certain range.

The interrelation between the building load and capacity of a variable

speed system in the cooling mode is shown graphically in Figure 1. The

diagonal line originating at the intersection of the ordinate and abscissa

is the building load line. The line defined by system capacities at the

maximum compressor speed, Qgg

2 (82) and Qgs

2 (95), provides a simplified

representation of system capacity at the maximum compressor speed at

different outdoor temperatures. Similarly, capacities Q^;:

1 (82) and

Qi^

1 (67) prescribe the system capacity line at the minimum compressor

speed.

Because of the capacity range a variable speed system can provide, it has

two balance points in a given installation, and three modes of operation

as shown for the cooling mode in Figure 1. The low speed balance point,

depicted as t 1 , is the outdoor temperature at which the capacity line at

the minimum compressor speed intersects the building load line. The high

speed balance point, depicted as t2 , is the outdoor temperature at which

the capacity line at the maximum compressor speed intersects the building

1
Figure 1 . Building cooling load and capacity of a variable speed air

conditioner.

load line. These two balance points separate three outdoor temperature ranges

corresponding to three cases of operation of a variable speed unit:

65 e F to t. system cycles on and off at the minimum compressor

speed to match the building load, case I

t x to t2 system operates continuously at an intermediate

compressor speed to deliver the capacity that matches

the building load, case II,

t2 to 105 e F system operates continuously at the maximum compressor

speed, case III.

2
Operation of a variable speed system at the outdoor temperature ranges

from 65°F to t x (case I) and from t2 to 105°F (case III) is similar to the

operation of a two speed unit. As a result, appropriate portions of a two

speed unit rating procedure can be, with no or little modifications,

applied to represent performance of variable speed equipment. However,

for the outdoor temperature range between the two balance points (case II)

the existing U.S. Department of Energy (DoE) procedures [1] can not represent

adequately the performance of a variable speed system. Similarly, three

cases of operation of variable speed equipment can be identified in the

heating mode with no procedure available to account for performance in the

intermediate speed region. Consequently, new procedures are developed in

this report to allow rating of variable speed systems.

This report presents analysis and development of a rating procedure for a

variable speed system. At the time the analysis was performed no variable

speed system was available on the market, making it impossible to base the

procedure on NBS tests of actual units. The rating procedure was prepared

based on NBS experience with other residential heat pump products for

which rating procedures exist, and also based on industry waiver petitions

to DoE test procedures, and on comments on the DoE proposed procedure for

variable speed systems [2].

This procedure evolved from the existing DoE procedures for single speed

and two speed systems [1], Section 2 of this document describes, as a

background, only modifications and enhancements made to the existing

procedures to rate variable speed equipment. Reader's familiarity with the

3
existing procedures is assumed. This procedure has been prepared for DoE

as a NBS recommendation in the rule making process.

2. BACKGROUND OF THE PROCEDURE DEVELOPMENT

2.1. The Intermediate Speed Test

The main shortcoming of the existing rating procedure [1] with respect to

variable speed systems is that it cannot adequately represent performance

of variable speed equipment in the intermediate speed range. Consequently,

each manufacturer who planned to develop and market a variable speed

system formulated his own rating procedure and petitioned DoE for approval

as a waiver.

The first variable speed rating procedure was proposed by Borg-Wagner [3]

and was basically adopted in ARI Standard 210/240 [4]

.

As the major

concern was an accurate representation of a non-linear power input profile

in the intermediate speed operation range, the procedure introduced an

intermediate speed test in the cooling and heating mode at 87 °F and 35 °F

outdoor temperature, respectively. Taking into account bin hour distributions

and practical considerations, the selection of these outdoor temperatures

as test conditions was appropriate and was followed by other manufactures

in their waiver petitions.

The available points for power interpolation are shown for the cooling

mode in Figure 2. The two points at the edges of the intermediate speed

region, Eg“ 1 (t 1 ) and Egg 2 (t2 ), can be calculated from the minimum and

4
maximum speed capacity and power input equations, and the building load

algorithm. The point, E*" 1 ^?), is the additional datum obtained from the

intermediate speed test. This third point allows for a better representation

of the non-linear power input profile, which otherwise would have to be

prescribed by a straight line connecting Ej^Ctj.) and Eg” 2 (t2 ), as shown

by the short dashed line in Figure 2, overestimating the power input.

- linear interpolation of power using two points

linear interpolation of power using three points —

transposed from linear interpolation of EER using three

points; expected shape of typical characteristic curve

Figure 2. System power at intermediate speed operation using different

interpolations

.

5
The ARI procedure [4] requires the system capacities during the intermediate

speed tests to be equal to the respective building loads calculated for

the outdoor temperatures at which the cooling and heating tests are performed.

The matching of loads and capacities should be obtained by the proper

selection of compressor speeds. The matching requirement is much easier

to satisfy in cooling than in the heating mode. To avoid an iterative

testing at different speeds while searching for the speed at which

matching occurs, Urbs et al, [5], proposed an algorithm which allows use

of test data obtained when the capacity does not match the load. The

algorithm uses capacity slopes at the maximum and minimum compressor

speeds. By weighing these slopes, the capacity line for the intermediate

compressor speed at which the test was performed is determined. The power

line at the intermediate speed is similarly obtained. Having prescribed

capacity and the building load lines, the temperature can be found at

which both lines intersect, i.e. in which the system operating at the

tested intermediate speed matches the building load. The power input to

the system is then evaluated at this temperature, and this value is used

in interpolation of power for the intermediate speed operation range. For

details on this algorithm the reader may refer to the original publication.

NBS found this procedure adequate and highly practical, and adopted it in

this proposed rating procedure for variable speed systems.

Once it is accepted that a match between the building load and the system

capacity is not necessarily needed, the selection of the compressor speed

for the intermediate speed test had to be otherwise defined. A strict

prescription of the speed is preferable for rating verification.

6
Again, the objective of speed selection is to obtain capacity that would

match or be close to the building load. The task of prescribing such

speed for different systems in a standardized way appeared to be quite

difficult because different systems possess different capacity vs RPM

characteristics, dependent on electric drive and compressor characteristics,

control strategy relating fan speeds to the compressor speed, expansion

device characteristics, etc.

After a review of the waiver procedures for variable speed systems of two

manufacturers [6,7], the following equation is proposed for prescribing

the speed for the intermediate speed test in the cooling mode:

intermediate speed = minimum speed + (maximum speed - minimum speed)/3

(2.1)

For the heating mode, the same speed as for cooling is prescribed.

If the unit controls allow frequency to be changed only in discrete steps

such that the prescribed speed cannot be attained in the tested equipment,

the test should be performed at the next higher input frequency level

available in the system.

The above paragraphs identify the compressor speed at which the intermediate

speed test should be attempted to run. However, constant compressor speed

may be difficult to maintain and, therefore, the following variations from

the prescribed speed should be allowed:

7
those associated with variations of the input line frequency and

instability of controls. These variations should not result in

decrease of the compressor speed below the speed calculated by equation

(2.1); if this happened to be the case, the test should be performed

at the next higher available speed step.

those associated with control strategies which control speed in the

field during frosting/defrosting operation: during the initial period

after switching from defrosting into heating, in the final period of

the heating portion of the frost accumulation cycle, and during

defrosting. Variation of the compressor speed from the test value shall

be allowed in these instances to the same extent and for the same

period of time as such variations would occur in the field due to

control strategy.

2.2 Interpolation of the Intermediate Speed Power Input

The ART procedure for variable speed equipment [4] as well as waiver

procedures of individual manufacturers [3,6,7] evaluated the power input

in the intermediate speed range by applying linear interpolation between

the three known data points; the power at the minimum speed balance point,

Es s

1

(

1

1 ) » the power at the intermediate speed test, Ess

1 ^^), and the

power at the maximum speed balance point, E3 g 2 (t2 ). This method is shown

for the cooling mode in Figure 2 by the long dashed line.

It was recognized from the beginning that additional intermediate speed

tests at other than 87°F and 35°F temperatures would further improve the

rating of a variable speed product. However, because of the increased testing

8
burden, the manufacturers who submitted waver petitions for their variable

speed products opted for one intermediate test point and a lower rating.

An improved calculation procedure for seasonal performance of a variable

speed system (that would provide a rating closer to real system performance)

can be formulated by introducing two modifications to the existing

methods

1. instead of interpolating the power input, performing EER or COP

interpolation and then calculating the power input values by dividing

capacity by EER or COP, respectively,

2. using parabolic instead of a linear interpolation.

The advantage of interpolating EER rather than power can be deduced by

examining Figure 2 and Figure 3. The figures show system power and

efficiency lines in the intermediate speed operation range in the cooling

mode. The shape of the lines depends on the interpolation method used.

The short dashed line in Figure 2 connecting system power inputs, Eg 5

1 (t 1 )

and E* = 2 (t2 ) , at the minimum and maximum compressor speeds, respectively,

represents most conservative power input assessment. The long dashed line

connecting system powers at t 1 , 87 °F and t2 represents the interpolation

method used in ARI Standard 210/240. Experimental evidence has shown that

none of these lines prescribe adequately the system power but rather the

solid line provide a realistic representation of the power input.

As system power and EER are related through system capacity,

(EER = capacity/power) it is of interest to examine the shape of EER lines

(Figure 3) in the intermediate speed range in relation to selected

9
---- transposed from linear interpolation of power using two

points — — transposed from linear interpolation of power using three — points

linear interpolation of EER using three points

Figure 3. System EER at intermediate speed operation using different

interpolations

.

interpolating methods of the system power shown in Figure 2. There is a

direct relationship between the line pattern shown in Figure 2 and Figure

3; i.e. the short dashed line representing EER in Figure 3 corresponds to

the assumption that the system power changes linearly between and t2 as

shown by the short dashed line in Figure 2. Linear interpolation of power

between the three points results in an unrealistic shape of the EER line

in Figure 3. The continuous line in the intermediate region in Figure 3

represents a linear interpolation of EER between three points. This

linear interpolation of EER results in a realistic representation of the

system power as shown by the solid concave line in Figure 2.

10
In brief, the power input to a variable speed system in the intermediate speed

operating range, can be estimated by interpolating either system power or

system EER. The parameter selected for interpolation should be the one

which is more linear in the interpolation region. The experimental

evidence is that EER is a more linear parameter than power.

Having chosen EER for interpolation in the intermediate speed operation

range, it is not inconsequential which interpolation method is applied.

The parabolic interpolation method, as compared to the linear, has two

important advantages

unlike the power line, the EER line in the intermediate speed range may

be either convex or concave. The reason that this line may be concave

or convex is that, since it is nearly linear, a small deviation in system

characteristics in either direction will cause it to be either above

(convex) or below (concave) linearity. A straight line interpolation

of EER would unduly benefit systems with a concave EER line,

from the comments received from the industry on the proposed procedure

for variable speed systems it appears that the EER line is indeed of

a second or higher order. Although different systems may have different

characteristics, a parabolic fit should give the best estimate of the

EER line with three performance points available.

Although the above analysis refers to the cooling mode, the same conclusions

hold for the heating mode. Consequently, the recommended rating procedure

uses parabolic interpolation of an efficiency descriptor (EER or COP) for

representation of system performance over the intermediate speed range in

11
both cooling and heating. The recommended form of the interpolation

equation is y = a + b • x + b • x

2

.

2.3 Cyclic Test

The cooling cyclic test for single speed systems and two speed systems is

prescribed at an outdoor 82°F temperature [1]. The cyclic test for

variable speed systems is specified in ARI Standard 210/240 [4] at an outdoor

temperature of 67 °F. Although the 67 °F temperature constitutes a departure

from the standard cyclic test 82°F condition, it has been adopted in the

procedure contained in this report. This selection is based on the

practical consideration of assigning a cyclic test at the same outdoor

temperature as one of the wet coil tests. Because variable speed systems

are expected to operate at the minimum speed in the outdoor temperature

range from 65°F to approximately 80°F (depending on the capacity modulation

ratio) , minimum speed wet coil test outdoor temperatures were selected to

be 82°F and 67°F. Since a variable speed system is not likely to cycle in

the field at an outdoor temperature above 80° F, the temperature of 67 °F

seems to be the better selection for the cyclic test. For similar

reasons, the ARI Standard 210/240 62 e F outdoor temperature for heating

cyclic test was also adopted.

It should be pointed out that NBS laboratory cyclic tests performed on a

single speed system showed insignificant dependence of the CD value on the

outdoor temperature as long as the compressor time-on and time-off are

preserved. The CD values for tests at outdoor temperatures of 95 9 F, 82°F,

and 70° F were the same within the experimental error.

12
Another departure from the single speed cyclic test is the length of the

time-on and time-off. Since a variable speed system will start to cycle

"on” and "off" at a much lower outdoor temperature than a single speed

system, the variable speed unit should be allowed more than 6 minutes

time-on during the cyclic test. An analysis using simple thermostat

equations will allow derivation of appropriate time-on, time-off, and

cycling rate values for variable speed equipment.

Figure 4 presents a typical parabolic curve representing the compressor

cycling rate as a function of the cooling load. The upper graph describes

the compressor cycling rate for a single speed system whose capacity line

coincides with the capacity of a variable speed system operating at the

maximum speed. The lower graph describes the cycling rate of the variable

speed system. Cycling starts at the building load equal to Qss (t2 ) for

the single speed system (which is equal to Q^s

2 (t2 ) of the equivalent

variable speed system), and at the building load equal to (^^(tj.) for t^rie

variable speed system.

In order to find the cycling rate of the variable speed system, the

relationship between the time-on and time-off periods for the variable and

single speed systems must be first determined. Since both units would be

installed in the same structure, the same building load would have to be

satisfied. Also, assuming that the thermostat band is the same for both

systems, the same amount of heat would have to be transferred to the house

(independently of the outdoor temperature) to trigger a compressor in each

system, i.e. BL(tj) • Toff (tj) = const.

13
Figure 4. Cycling rate for a single speed system, ns , and a variable

speed system, .

In order to find time-off for the variable speed system, we may write this

equation for both systems for the same load fraction and equate both

sides; for example, for a 20% fraction,

14
0.2 • Qi;

2 (t2 ) = ToffiV • 0.2 • (S;l off, s (t!) ( 2 . 2 )

where: Toff s and Toff v are time-off of single speed and variable speed

systems, respectively.

Consequently,

T T off , v

A of f , i

• ^ss <£: '^2 2 (t2 ) / (2.3)

Assuming the start-up characteristics of both systems are similar and the

percentages of time-on and time-off are preserved, time-on for the

variable speed system, Ton v , may be expressed as a function of the time-on

of the equivalent single speed system, Ton s

Ton.v = Ton , s

• QS:

2 (t2 ) / qj;1 ^) (2.4)

Employing equations (2.3) and (2.4), the cycling rate of the variable

speed system, , in relation to the cycling rate of the single speed

system, ns , is determined.

"v = • Qg s

^ ( t, ) / Q5;

2 (t2 ) (2.5)

The above equations, although derived with some simplifications, could

serve as an algorithm for determining time-on and time-off during the

cycling test of a variable speed system. The equations would allow a

variable speed system with a greater capacity modulation ratio,

Q^ 2 (t2 ) / s

1

( t ! )

,

to have longer compressor time-on during the test

which would result in a lower value of the cyclic degradation coefficient,

CD

. However, applying these equations could result in a long and costly

15
cyclic test. For a capacity modulation ratio of 2, the cyclic test would

last one hour, but two hours would be required for a system having a

capacity modulation ratio of 3. Conversely, the benefit of a lower CD value is smaller for systems with a higher capacity modulation ratio since

the systems cycles less often. The decreasing effect of CD on the

Seasonal Energy Efficiency Ratio, SEER, is shown in Figure 5. The figure

shows the maximum theoretical penalty in SEER which we define as a

difference in the SEER value calculated with CD =0.25 and CD = 0. The

figure shows that, from a practical standpoint, there is no reason to run

long cyclic tests for high capacity modulation systems since the CD improvement will not justify the increased burden of a prolonged test. As

a result, a fixed time-on equal to 12 minutes is prescribed in the

proposed procedure for systems having a capacity modulation ratio of 2 or

1 1.5 2.0 2.5 3.0 3.5

CAPACITY MODULATION RATIO (-)

Figure 5. Maximum theoretical SEER penalty at default CD.

16
more. The equations presented above are recommended for systems having

capacity modulation ratio smaller than 2.

As was done for the cooling mode, a similar analysis can be repeated for

the heating mode. The situation in the heating mode is more complicated

because of a range of building loads (between the maximum and minimum)

prescribed by the DoE rating procedure [1]. If the steps of the cooling

mode analysis are followed rigorously, different values for time-on and

time off could be prescribed for different building heating loads. A heat

pump with a capacity modulation ratio of 2 in the cooling mode could have

a compressor time-on between 9 minutes and 12 minutes in the heating mode,

depending on the design heating requirement. For simplicity, the proposed

procedure prescribes the heating mode time-on and time-off to be the same

as for cooling cycling test.

2.4 Capacity and Power Input Lines at the Maximum Compressor Speed in the

Heating Mode

The rating procedure for variable speed equipment contained in ARI

Standard 210/240 [4] prescribes the capacity and power lines based on

results of two tests at temperatures of 17°F and 47°F. The same method

was proposed in two waiver procedures [6,7] submitted to DoE. This

prescription of the capacity and power lines does not include degradation

due to frost accumulation and, therefore, is inconsistent with reality and

the rating procedures already in place for other equipment. The simplification

of the linear representation of capacity and power characteristics based

on 17°F and 47°F points, however, does not affect the Heating Seasonal

17
Performance Factor (HSPF) value calculated for the minimum heating design

requirement. This is due to the intersection between the minimum building

load line and the maximum speed capacity line occurring in the neighborhood

of 14°F for region V, and in the neighborhood of 19°F for the other

regions. Thus, the method of representation of capacity and power used in

previous procedures [4,6,7] does not affect the HSPF value for the minimum

design heating requirement in region IV which is prominently used for

marketing purposes. For higher design heating requirements, the linear

representation underestimates the power input required to the electric

heater and, as a result, overestimates the efficiency descriptor.

NBS believes that comparability of variable speed equipment and single

speed equipment ratings should be maintained by including the frost

accumulation test results at the maximum speed, Q^g|(35) and Ejjef(35), in

prescription of the capacity and power input lines. Since results of this

test affect HSPF values derived for lesser used design requirements, NBS

recommends that, as an alternative to test, the use of equations (2.6) and

(2.7) be allowed to obtain the values for Q^e|(35) and E^ef(35).

Qdef (35) = 0.90 • [Q5 =| (17) + [Qdef (47) - Q

k

d =J ( 17) ] [ 35- 17 ] /

[47- 17 ] ] (2.6)

Ede? (35) = 0.985 - [E$;| (17) + [E5;2(47) _ E{jef( 17)] [35-l 7]/[ 47-17] ] (2.7)

Correction factors of 10 percent for capacity and 1.5 percent for power in

these equations were selected based on review of test data of ten single

speed heat pumps [8] equipped with demand defrost (Figure 6 and 7). These

18
correction factors result in COP degradation of 8.6% which is in line with

COP degradation observed in the tested systems, as is shown in Figure 8.

2.5 Building Load in the Heating Mode.

It is likely that some variable speed systems which will be available

commercially will be able to run at a higher compressor speed in the

heating mode than in the cooling mode. As sizing of heat pumps is usually

performed based on the cooling load, the ability to run at a higher

maximum speed in the heating mode lowers the balance point - the temperature

at which the electric heater is turned on by system controls. The

efficiency benefit associated with the higher compressor speed in the

heating mode depends on the relative position of the building load line

Figure 6. Ratio of measured capacity to linearly interpolated capacity

(using 17°F and 47°F data) for the frost accumulation test.

19
and the capacity line. The building load line, as prescribed in the

existing procedures [1], is a function of capacity at 47°F outdoor

temperature. If the system capacity at the maximum compressor speed,

0^ 5 2 (47), were used for the building load calculations, the calculated

HSPF value would not be much different from the HSPF value calculated for

a system operating at the same maximum speed in both heating and cooling.

In order to allow for an appropriate credit, the proposed procedure

prescribes an optional, nominal capacity test at 47 °F outdoor temperature.

This test is applicable only if controls of the unit allow the compressor

to run in the heating mode at a higher speed than in the cooling mode.

The nominal capacity test should be performed at the compressor speed

Figure 7. Ratio of measured power to linearly interpolated power (using

17°F and 47 e F data) for the frost accumulation test.

20
Figure 8. Ratio of measured COP to linearly interpolated COP (using 17°F

and 47 °F data) for the frost accumulation test.

equal to the compressor speed during the cooling test at 95°F temperature.

The system capacity obtained in the nominal capacity test is to be used

exclusively for evaluation of the design heating requirement.

2.6 Measurement of the Electrical Energy Input

The existing DoE rating procedure [1] requires measurement of the energy

input to a system within 0.5 percent uncertainty. This requirement is not

difficult to meet for single and two speed systems and, most likely, can

be satisfied with an induction (rotating disc) type watthour meter.

Among the various types of variable speed drives possible, drives employing

some kind of a solid state inverter are expected to be used in heat pumps.

21
An undesirable feature of electric inverters is that they may inject large

amounts of harmonic currents into the utility system. The amount of

current wave distortion from its sinusoidal shape depends on the type of

the inverter and its detailed design. For illustration, Figure 9 presents

deformations of a current waveform recorded at the input to a three phase

inverter. An informative presentation of different types of solid state

inverters and their input and output current waveforms may be found in [9].

MILLISECONDS

Figure 9. Deformation of the current waveform at input to a three phase

inverter at 30 Hz output frequency (two voltage and one current

waveforms are recorded)

.

Distortion of the current waveform on the line side makes the measurement

of the energy input more difficult. Significant errors may occur if an

inductive watthour meter if used. Baldwin et al. [10] conducted a series

22
of tests on commercially available, self-contained, induction watthour

meters. When exposed to current waveform distortion due to a variable-speed

controller (three-phase) , the meters over registered even if the voltage

was undistorted at 60 Hz. The average error was 2 percent with an

individual meter over registering by as much as 6.7 percent.

Better accuracy of energy input measurement for distorted wave forms can

be obtained with an electronic- type watthour metering device. However, our

review of specifications of a number of electronic meters of different

manufacturers showed that the measurement uncertainty of 0.5 percent

cannot be obtained even with an electronic meter unless an excessively

priced meter is used. Therefore, the proposed rating procedure specifies

a relaxed uncertainty of 1 percent of the energy input measurement of

systems employing a solid state inverter.

2.7 Needed Research

Numerous assumptions were made in the development of the proposed testing

and rating procedure described in this report. Some assumption were

related to performance characteristics in the intermediate speed region.

One of the unknown aspects of system operation is its ability to closely

follow the building load in the intermediate speed range. The proposed

procedure assumes that the heat pump capacity exactly matches the building

load at all times in the intermediate speed operation range. The penalty

due to the compressor speed hunting in search of the matching capacity has

not been evaluated.

23
The frost accumulation test at the intermediate speed, as prescribed by

the procedure, represents a significant departure from the intermediate

speed operation in the field. To simplify the procedure, a constant

compressor speed during the test is prescribed, while in field operation

the compressor speed would increase with accumulation of frost to provide

capacity matching the building load. Accumulation of frost provided

significant complexity to the rating procedure for single speed systems;

accurate representation of variable speed system performance when frosting

of the outdoor coil occurs is even more difficult.

Since there was no variable speed equipment available on the market at the

time of formulation of this rating procedure, NBS did not have its own

laboratory data for support of the procedure development and relied on

data and information made available by others [11,12,13,14]. It is

believed that the proposed procedure captures the major performance

characteristics common to most of the forthcoming variable speed products.

It has to be realized, however, that continuous developments in electronics,

sensors and control strategies will provide future systems with performance

advantages that might not be accounted for within the presently proposed

rating methodology. Thus the impact of system controls, frosting and load

matching capability are all issues for further investigations.

24
3. RATING PROCEDURE FOR VARIABLE SPEED SYSTEMS IN THE COOLING MODE

3.1

Requirements for Testing Conditions and Testing Procedures

Requirements regarding instruments and data acquisition systems, test

apparatus, methods of test, test procedures, and data analysis are as

prescribed in ASHRAE Standard 116-1983 [15] with the exception to the

provisions specified in the following sections.

3.1.1 Tests and Testing Conditions

The tests and test conditions are presented in Table 1. The required

tests include five wet coil tests (Ag| 2

, Bg^ 2

, Bg^ 1, Bg? 1

, I^ 1

) and two

dry coil tests (Cg" 1

, D^" 1 ).

3.1.2 Cyclic Test

The cyclic test, Dg? 1 (see Table 1), shall be conducted by cycling the

unit "on" and "off" by manual or automatic operation of the normal control

circuit of the unit. The unit shall cycle "on" and "off" with the

compressor time-on, Ton , and time-off, Toff , determined as follows:

r c£: 2 (95)

Q^ 1 (82)

6 6 or (3.1)

To n

12, whichever is smaller

(3.2)

25
The indoor fan and outdoor fan shall also cycle "on" and "off"

;

the

duration of the fans "on" and "off" periods shall be governed by the

automatic controls which the manufacturer normally supplies with the unit.

The installation shall be designed to prevent air flow through the indoor

unit due to natural or forced convection while the indoor fan is "off".

This may be accomplished by installing dampers upstream and downstream of

the test unit to block the "off" period air flow. Capacity integration

shall be performed during the indoor fan "on" period. Power integration

shall be performed over the total period of the cycle (time-on and timeoff) .

During "on" time the compressor shall operate at the minimum speed unless

the system controls have a preprogrammed start-up routine which causes the

compressor to run at other than the minimum speed during the initial

portion of the start-up period. In such a case, the compressor may follow

the start-up routine during the test for the time and to the degree this

would happen in the field.

The results of the cyclic test, Dgy 1

, shall be used in conjunction with

the results of test Cg? 1 to evaluate the cyclic degradation coefficient,

CD

. Evaluation of CD shall be performed by using the algorithms prescribed

in section 9.2.2 of ASHRAE Standard 116-1983 [15]. An assigned value of

0.25 may be used for the degradation coefficient, CD , in lieu of conducting

tests Cg" 1 and Dg" 1

.

26
3.1.3 Intermediate Speed Test

The intermediate speed test, Igy 1 (see Table 1), shall be conducted at the

compressor speed evaluated by the equation:

RPMi = RPM^ + [ RPMj,, a

x

- RPHmin ]/3 (3.3)

where: RPMi = compressor speed during the intermediate speed test,

(revolutions/min)

RPM^h = minimum compressor speed in the cooling mode,

(revolutions/min)

RPMjjjgx = maximum compressor speed in the cooling mode,

(revolutions/min)

The compressor input frequency may be used in lieu of the compressor speed

to evaluate the compressor speed for the intermediate speed test. If the

system controls allow varying the compressor speed only in discrete steps

such that the calculated RPMi cannot be attained by the system, the

intermediate speed test shall be performed at the next higher compressor

speed available. Variations from this speed are not allowed with the

exception of those associated with line frequency variations and instability

of the system controls. If these variations result in a decrease in the

speed below the calculated RPMi value, the compressor speed selected for

the test shall be increased.

3.1.4 Air Quantity Measurement

The air flow through the indoor and outdoor sections at any test shall be

governed by system controls. The air flow shall meet the requirements of

sections 5. 1.3. 3, 5. 1.3.4, and 5. 1.3.

6

of ARI Standard 210/240-84 [4].

The minimum external pressure requirement (section 5. 1.3. 6 of [4]) applies

27
only to tests with the maximum indoor air flow. The indoor air flow at

lower than the maximum fan speed shall be determined by the equation:

CFM = CFMraax

where: CFM

CFM, a x

RPM*

RPMf , m a x

• RPMf /RPMf , max (3.4)

= volumetric flow rate at a lower than the maximum fan

speed, (ft3 /min)

= volumetric flow rate at the maximum fan speed, RPM*-

(ft3 /min)

= indoor fan speed during a test, (revolutions/min)

= maximum fan speed, (revolutions/min)

3.1.5 Power Measurement

The power input to a system which employs an electrical inverter shall be

measured with the aid of an instrument which is accurate to within + 1.0

percent of the quantity measured.

Due to the possibility of distorted voltage and current waveforms when an

inverter is employed, an induction (rotating disc) type watthouf meter may

not provide the required accuracy for energy measurement for a variable speed

system. The instrument which most likely can satisfy this accuracy

requirement would cover a bandwidth of at least to 1 kHz. Because of the

possibility of small dc-currents resulting from nonsymetrical switching,

the use of current transformers may contribute additional errors.

3.2 Calculation of Seasonal Energy Efficiency Ratio, SEER

The building cooling load in bin temperature t

1

, BL(tj )

,

shall be calculated

by the following equation:

28
BL(tj) = 05;

2 BL(tj) = (95) (Btu/h) (3.5)

where : 1.1

^

-65

2 (95) (Btu/h) (3.5)

1 . 1 [95-65]

= size factor for 10% oversizing

The seasonal Energy Efficiency Ratio, SEER, shall be found by the following

equation:

8

i

j=l

SEER = —

8

I

j=l

n

j

• qVj)

(3.6)

n

j

• e ( tj>

where: t,

J = representative outdoor dry-bulb temperature for temperature

bin j, (°F)

n

j = fractional cooling bin hours in bin j, per Table 2.

q(tj) - cooling done in bin temperature tj , (Btu/h)

e(tj) = power input in bin temperature tj , (W)

The terms q(t, ) and e(t.) are evaluated at each bin temperature, shown in

Table 2, by the following equations:

q ( tj ) = x(tj )

• Q(tj (3.7)

)

e ( tj ) = X(tj) • E(tj)/PLF(X) (3.8)
where : Q( tj )

E( tj )

X(tj)

system cooling capacity at bin temperature t^ at the speed

at which capacity matches the building load, (Btu/h)

system power input at bin temperature tj during steady

state operation, (W)

cooling load factor, (-)

X(tj)

' BL(tj )/Q(tj ) if BL(tj)/Q(tj) < 1

1 otherwise

(3.9)

PLF(X) = part load factor, (-)

PLF(X) = 1 - CD [ 1 - XCtj)] (3.10)

CD = cyclic degradation coefficient, (-)

Quantities Q(t^ ) and E(tj ) shall be evaluated according to three possible

cases depending on compressor operation, as shown in Figure 1. These

three cases can be identified in terms of the three outdoor temperature

ranges or the two temperatures, t 2 and t2 , which separate them.

The outdoor temperature, t x , at which the building load equals system

capacity with the compressor operating at the minimum (k=l ) speed shall be

calculated by the equation:

975 • Q^“ 2 (95) + 495 • “ 1 (67) + 2211 • [Q^

1 (67) -Q^1 (82)

]

15 • Qi;

2 (95) + 33 •

[ Qj

“ 1 (67)- Qj

” 1 ( 82 ) ]

30
The outdoor temperature, t2 , at which the building load equals system

capacity with the compressor operating at the maximum speed (k=2) shall be

calculated by the equation:

845 • Qi;

2 (95) + 429 • Q^;2 (82) + 2706 • [Q^ 2 (82) -Q^* 2 (95) ] t2 = (3.12)

33 • oj; 2 (82) - 20 • Q*: 2 (95)

The equations for , and t2 were derived by equating the building load

(eq. (3.5)) with system capacities at the minimum and maximum speeds,

respectively (eqs. (3.13) and (3.32)).

Case I, BL(tj) < g

1 ( tj ) , (

t

d < t 1 )

Capacity of the unit at the minimum compressor speed is greater than or

equal to the building load. The unit cycles on and off.

Q(tj) =Q*: 1 (67) + [Q^ 1 (82) - Qi;

1 (67) ]

•

[ tj - 671/15 (3.13)

E(tj) = Ej” 1 (67) + [Ej* 1 (82) - “ 1 (67) ]

•

[ tj - 67J/15. (3.14)

CASE II. QS^tj) < BL(tj) < Q*; 2 (tj), (t, < tj < t2 )

The unit is able to match the building load by modulating compressor speed

between the minimum (k=l) and maximum (k=2 ) speed.

Q(tj) = BL(tj) (3.15)

Q(tj)

E(tj ) = (3.16)

eerJ“ v

(tj

)

31
where: EERg" v (tj) = a + b • tj + e • (3.17)

steady state energy efficiency ratio at temperature t^ and at

an intermediate speed at which the unit capacity matches the

building load, (Btu/W»h)

a, b, c = coefficients to be calculated

The following is a procedure for evaluation of coefficients a, b, and c.

The unit performance has to be evaluated first at the compressor speed

(k=i) at which the intermediate speed test was conducted. The capacity of

the unit at any temperature t with the compressor operating at the

intermediate speed (k=i) shall be determined by:

^‘(t) = OS;

1 (87) + Mq[t - 87] (3.18)

where: Q^ s

i (87) = capacity of the unit at 87°F determined by the

intermediate speed steady state test, (Btu/h)

Qs s

1 (82) - Qji

1 (67)

Kq = • (1 - Nq) + (3.19)

82 - 67

Qs s 2 (95) - Q^s

2 (82)

95 - 82

QJs' (87) - Q^;

1 (87)

Nn = -

Q (3.20)

s 2 (87) -s

1 (87)

32
Qg S

1 (87) and Qg S 2 (87) shall be calculated by equations (3.9) and (3.28),

respectively

.

Once the equation (3.18) for Q^g

1 (t) has been determined, the temperature

at which Q^g

1 (t) = BL(t) can be found. This temperature, designated as tvc ,

shall be calculated by the equation:

33 » Q^ i (87) - 2871 « Mq + 65 • Q^ 2 (95)

tvc = _______ ———— — (3.21)

Qs s 2 (95) - 33 . Mq

The electrical power input for the unit operating at the intermediate

compressor speed (k=i) and the temperature (tvc ) is determined by:

E*-‘(tvc ) = Egg 1 (87) + ME [tvc - 87] . (3.22)

where: Egg 1 (87) = electrical power input of the unit at 87°F determined

by the intermediate speed, steady scate test, (W)

Egs

1 (82) - E5; 1 (67)

Me = —• [1 - Ne ] (3.23)

82 - 67

Ess

2 (95) - E^ 2 (82)

+ ——— — — • Ne 95 - 82

Ess

1 (87) - Eg

g

1 (87)

Ne = — — (3.24)

E5

s

2 (87) - Eg

g

1 (87)

Egg 1 (87) and Eg S 2 (87) shall be calculated by equations (3.14) and (3.33),

respectively

.

33
The energy efficiency ratio of the unit, EERj" 1 (tvc ) , at the speed (k=i)

and temperature tvc shall be calculated by the equation:

Q^Ctvc)

EER^Ct^) = (3.25)

Similarly, energy efficiency ratios at temperatures, t x and t2 shall be

calculated by the equations:

EERk = 1

s s (tj) = -

EERk = 2

s s o^: 2 (t2 ) (t2 ) =

Esl

2 (t2 )

(3.26)

(3.27)

where : EERg s

1 (

t

x ) steady state energy efficiency ratio at the minimum

compressor speed at temperature t 1 , (Btu/W*h)

EER$; 2 (t2 ) steady state energy efficiency radio at the maximum

compressor speed at temperature t 2 , (Btu/W«h)

Qj;

1 ^) = Q(t x ), steady state capacity at the minimum

compressor speed at temperature t 1 , calculated by

eq„ (3.13), (Btu/h)

34
Qss

2

( t2 ) = Q(t2 ), steady state capacity at the maximum

compressor speed at temperature t2 , calculated by

eq. (3.32), (Btu/h)

E(t 1 ), electrical power input at the minimum

compressor speed at temperature t x , calculated by

eq. (3.14), (W)

E^; 2 (t2 ) E(t2 ), electrical power input at the maximum

compressor speed at temperature t2 , calculated by

eq. (3.33), (W)

Finally, coefficients a, b, and c shall be calculated using equations

(3.28) through (3.$1):

d =

Cvc

(3.28)

b =

EERg s

1

( tl ) - EER3 s

(

t

2 ) - d • [EER^g 1 (t,

)

- EERg g

1

(

t

v c )

]

tj. " t2- d • [ti - tvc ]

(3.29)

EERgs 1 (ti

)

- EERg

g

2

(

t

2 ) - b • [t, - t2 ] c =

t

2 - t2 C 1 c2

(3.30)

a = EERg s 2(

t

2 ) - b • t2

- c • t| (3.31)

35
CASE III, BL(tj) > (tj > t2 )

Capacity of the unit at the maximum (k=2) compressor speed is equal to or

smaller than the building load.

Q(tj) = Q^s

2 (82) + [05;2 (95) - Q^" 2 (82) ] [ tj - 82 ]/13 (3.32)

E(tj) = Ej" 2 (82) + [Eg“ 2 (95) - E^ 2 (82)][ tj - 82J/13 (3.33)

4. RATING PROCEDURE FOR VARIABLE SPEED SYSTEMS IN THE HEATING MODE

4.1 Requirements for Testing Conditions and Testing Procedures

Requirements regarding instruments and data acquisition systems, test

apparatus, methods of test, test procedures, and data analysis are as

prescribed in ASHRAE Standard 116-1983 [15] with the exception to the

provisions specified in the following sections.

4.1.1 Tests and Testing Conditions

The tests and test conditions are presented in Table 3.

4.1.2 Cyclic Test

The cyclic test shall be conducted according to provisions specified in

section 3.1.2 of this document and with the compressor time-on and timeoff specified for the cyclic test in the cooling mode. Results of the

heating mode cyclic test shall be used with results of the maximum

temperature heating test to evaluate the cyclic degradation coefficient,

CD , as specified in section 9.2.4 of ASHRAE Standard 116-1983 [15]. An

36
assigned value of 0.25 may be used for the degradation coefficient, CD , in

lieu of conducting the heating cyclic test.

4.1.3 Intermediate Speed Frost Accumulation Test

The compressor speed shall be the same as during the intermediate speed

test in the cooling mode. Compressor speed variations are allowed as

specified in section 3.1.3. Also, variations associated with control

strategies (if employed) during the initial period after switching from

defrosting to heating, in the final period of the heating cycle, and

during defrosting are permitted. Variations of the compressor speed from

the prescribed speed are allowed to the same extent and for the same

period of time as such variation would occur in the field due to control

strategy

.

e

4.1.4 Maximum Speed Frost Accumulation Test

In lieu of conducting the test the following equations may be used to

obtain heat pump capacity and power at the test conditions:

05:1(35) =0.90 • [05:1(17) + [Q5:|(47)-Q5;|(17)][35-17]/[47-17]] (4.1)

E5:|(35) = 0.985 • [E5;| (17) + [E5:| (47) -E5:f (17) ] [ 35-17 ] /[47-17 ] ] (4.2)

4.1.5 Nominal Speed High Temperature Test

This test is applicable if the maximum compressor speed in the heating

mode is greater than the maximum speed in the cooling mode. In such a case

the nominal speed is the maximum speed the compressor may run in the

cooling mode. The heating capacity obtained during the nominal speed high

37
temperature test shall be used only to calculate design heating requirements.

This test is optional. If this test is not opted to be performed or is not

applicable, capacity obtained during the maximum speed high temperature

heating test shall be used for design heating requirement calculations.

4.1.6 Air Quantity Measurement

Air flow quantity and measurement method shall comply with provisions

specified in section 3.1.4.

4.1.7 Power Measurement

Power measurement shall be performed as prescribed for the cooling mode in

section 3.1.5.

4.2 Calculation of Heating Seasonal Performance Factor, HSPF

The Heating Seasonal Performance Factor, HSPF, shall be calculated by the

following equation:

l nJ

• “•<«:,)

j

HSPF = — (4.3)

l rij • [e(t. ) + RH( tj ) ] j

where: t, = representative outdoor dry-bulb temperature for

J temperature bin j, (°F)

n, - fractional heating bin hours in bin j , per Table 4

«J

BL(tj

)

= building load at bin temperature tj , (Btu/h)

38
e(tj ) = power input to the system (excluding the supplemental

resistance heater) operating in temperature t, , (W)

RH(tj

)

= power input to the supplementary resistance heater

required in those cases when the heat pump automatically

turns off (tj < ton ), or when it is needed to meet the

balance of the building heating requirement, (W)

The building load, BL(tj ) , shall be calculated by the following equation:

BL(tj) C • DHR (4.4)

where : C

Td

DHR

0.77, an experience factor which improves the agreement

between calculated and measured building loads, (-)

outdoor design temperature (shown for different regions

in Table 4) , (°F)

design heating requirement, (Btu/h)

The minimum and maximum design heating requirements, DHRmin and DHRmax , of

a residence in which a heat pump is likely to be installed shall be

obtained by evaluating the following two equations and rounding off the

results to the nearest standardized values given in Table 5.

DHR,„ in

' C£-"(47) • [65 - Td ]/60,

. c£: n (47),

for regions I, II, III,

for region V

IV, and VI

(4.5)

for regions I

,

for region V

II, III, IV and VI

(4.6)

2 • Q^"(47)[65 - Td ]/60

2.2 • Q^" n (47)

,

39
where

Q^"(47)

system capacity during the optional nominal speed high

temperature test

Q^" 2 (47) if the nominal speed high temperature test

was not performed, (Btu/h)

The quantities e(tj

)

and RH(t^ ) shall be calculated by the following

equations

*(tj) • X(tj) • E(tj)

e(tj) = (4.7)

PLF(X)

- 8 (tj) • X(tj) • Q(tj ) RHCt.) = — —- (4.8)

3.413

where: 5(t.) = heat pump low temperature cut-off factor, (-)

0 if tj < toff or Q(tj)/(3.413 • E(tj)) < 1

<S(tj) = < 0.5 if toff < tj < ton and Q(tj)/(3.413 • E(tj)) > 1

l 1 if tj > ton and Q(tj )/ (3 .413 • E( tj )) > 1 (4.9)

toff = outdoor temperature at which the compressor is

automatically stopped to avoid operation at low temperatures

ton = outdoor temperature at which the compressor is

automatically turned on after low- temperature shut-off

X(t i ) = heating load factor, (-)

X(t,) = < BL(tj )/Q(tj ) if BL( tj )/Q( tj ) < 1

1 otherwise (4.10)

40
PLF(X) = part load factor

PLF(X) = 1 - CD [1 - X(tj)] (4.11)

CD = cyclic degradation coefficient, (-)

Q(tj) = system capacity at temperature tj during continuous

compressor operation at the speed needed to match the

building load, (Btu/h)

E(tj

)

- power input to the system at temperature tj (excluding

the supplemental resistance heater) during continuous

compressor operation at the speed needed to match the

building load, (W)

Quantities Q(tj ) and E(tj) shall be calculated according to three possible

cases depending on compressor operation, as shown in Figure 10. These three

cases can be identified in terms of the three outdoor temperature ranges

or the two temperatures, t3 and t 4 , which separate them.

The outdoor temperature, t3 , at which the building load equals system

capacity with the compressor operating at the minimum (k=l) speed shall be

calculated by the equation:

975 • C • DHR + 47 • [65-TD ][Q^" 1 (62)-Q*" 1 (47)] - 15 • Q*' 1 (47) [ 65-TD J

15 • C • DHR + [65-TD ][Q5;

1 (62)-Qi;;1 (47)]

(4.12)

41
Figure 10. Building heating load and capacity of a variable speed heat pump.

The outdoor temperature, t4 , at which the building load equals system

capacity with the compressor operating at the maximum speed (k=2) shall

be calculated by either equation (4.13) or (4.14), as appropriate:

If the calculated value for t4 is smaller than or equal to 17

1950 • C • DHR+17[65-Td ] [Q^ 2 (47)-Q5 s 2 (17)]-30 • Q^ 2

( 17) [ 65-TD ] =

30 • C • DHR+[65-Td ][Q^ 2 (47)-Q^ 2 (17)]

(4.13)

If the calculated value for t4 is greater than 17, t4 shall be calculated

by the following equation:

42
1170 • C • DHR + 17[65-TD ][Qg = |(35)-Q^ = ^(17)] - 18 Q*; 2 (17) [ 65-TD ]

,k = 2 )k = 2

*4 =

18 C • DHR + [65-Td ] [Qdef (35) - Q^ 2 (17)]

(4.14)

The equations for t 3 and t 4 were derived by equating the building load

(eq. (4.4)) with respective system capacities and the minimum and. maximum

speeds (eq. (4.15) and eq. (4.34) or (4.36)).

CASE I, Q^Vtj) > BL(tj), (tj > t3 )

Capacity of the unit at the minimum compressor speed (k=l) is greater than

or equal to the building load. The unit cycles on and off.

Q(tj) =Qk

I

1 (47) + [Q5" 1 (62) - Q5;1 <4-7) ] [ t

j

- 47]/15 ’ (4.15)

E(tj) = Eg^ 1 (47) + [Egg 1 (62) - E

k

J

1 (47) ] [ t., - 47J/15. (4.16)

CASE II, Qg g 1( tj

) < BL(tp < Q

k " 2

(

t

j

) , (t4 < tj < t3 )

The unit is able to match the building load by modulating compressor speed

between the minimum (k=l ) and maximum (k=2) speed.

Q(tj) = BL(tj) (4.17)

E(tj) = Q(tj)/(3.413 • C0Pk "''(t

j )) (4.18)

where: C0Pk=v (C.) - coefficient of performance at an intermediate speed

at which the unit delivers capacity matching the

building load at temperature tj

43
COPk=v (tj ) = a + b • t_, + c • (4.19)

a, b, c = coefficients which have to be calculated

separately for each design building requirement

The following is a procedure for evaluation of coefficients a, b, and c.

Before the coefficient of performance, COPk = v (tj), can be calculated, the

c unit performance has to be evaluated at the compressor speed (k=i) at

which the intermediate speed test was conducted. The capacity of the unit

at any temperature t when the compressor operates at the intermediate

speed (k=i) shall be determined by:

QS:J(t) = Q§:J(35) + Mq

[

t - 35] (4.20)

where: Qdef(35) = capacity of the unit at 35°F determined at the

intermediate compressor speed (k=i) in the frost

accumulation test, (Btu/h)

OS!

1 (62) - Q^;1 (47)

Mq = • (1 - Nq) (4.21)

62 - 47

Q$:?(35) - Q^2 (17)

+ —

35 - 17

Nq

Qd^f (35) - Q

1" 1 (35)

Nq = (4.22)

Qd^f (35) - Q

1 '- 1 (35)

44
Q* 1

( 3 5 ) = Q(35) , capacity of the unit at 35°F at the minimum

compressor speed, calculated by equation (4.15), (Btu/h)

Once the equation for Q def(t) has been determined, the temperature at which

Qdef(t) = BL(t) can be found. This temperature, designated as tvh , shall

be calculated by the equation:

65 • C • DHR + [65 - TD ][35 • Mq Q§ =

1 05) ] tvh = ———— ——— — — (4.23)

C • DHR + Mq [65 - TD ]

A separate tvh shall be determined for each design heating requirement.

The electrical power input for the unit operating at the intermediate

compressor speed (k=i) and at the temperature tvh shall be determined by:

E$:Htyh> = Edil<35) + ME [tvh - 35] (4.24)

where: E^g£(35) - electrical power input of the unit at 35°F determined

at the intermediate compressor speed (k=i) in the

frost accumulation test, (W)

Ess

1 (62) - Eg" 1 (47)

Me = • (1 - Ne ) (4.25)

62 - 47

E$:f(35) - Egg 2 (17)

+ ——————— — ° Np

35 - 17

45
E*jef (35) - E

k = 1 (35)

ne = (4.26)

E

k = |(35) - Ek = 1 (35)

The coefficient of performance, COP^f (tvh ) , at the intermediate speed

(k=i) and temperature tvh shall be calculated by the equation:

Qd e f ( Cv h ) C oPkd:Htvh ) = (4.27)

3.413

. E*:‘(tvh )

Similarly, coefficients of performance at temperature t3 and t4 shall be

calculated by the equations

Q

k = 1

(

t

3 ) COPk = 1 (t3 ) =-— (4.28)

3.413

- E

k = 1 (t3 )

Q

k = 2 (t 4 ) COPk = 2 (t 4 ) = — (4.29)

3.413

• E

k = 2

(

t

4 )

where: COPk = 1 (t3 ) = coefficient of performance at the minimum compressor

speed at temperature t 3 , (-)

COPk = 2 (t 4 ) = coefficient of performance at the maximum compressor

speed at temperature t 4 , (-)

Q

k=1 (t 3 ) = Q(t3 ), system capacity at the minimum compressor

speed at temperature t3 , calculated by eq. (4.15), (Btu/h)

46
Q

k=2 (tA ) = Q(t4 ), system capacity at the maximum compressor

speed at temperature t 4 , calculated by eq. (4.34) for

t 4 >17, or by eq. (4.36) for t4 <17, (Btu/h)

Ek=1 (t3 ) = E(t3 ), power input at the minimum compressor speed at

temperature t 3 , calculated by eq. (4.16), (W)

Ek=2 (t 4 ) = E(t4 ), power input at the maximum compressor speed at

temperature t 4 , calculated by eq. (4.35) for t 4 > 17,

or by eq. (4.37) for t 4 < 17, (W)

Finally, coefficients a, b, and c shall be calculated using equations

(4.30) through (4.33):

(4.30)

b

copk - 2 (t 4 ) - copk ' 1 (t 3 ) - d • [C0Pk - 2 (t 4 ) - copk ;j(tvh )]

- t3

- d • [t4 - tvh ]

(4.31)

C0Pk * 2 (t„) - C0Pk - 1 (t3 ) - b . [t 4 - t3 ] c = —— (4.32)

a = C0Pk 2

(

t

4 ) - b ° t 4 = c ° t 4 (4.33)

47
CASE III, BL(tj) > Q

k - 2 (t

J ), (tj < t4 )

Capacity of the system at the maximum (k=2) compressor speed is equal to

or less than the building load. Evaluation of Q(t.) and E(t-) depends on

the value of tj as prescribed in equations (4.34) through (4.37).

If tj > 1 7

‘ ’F

Q(tj) = Q* =

s: 2 (i7) + [QS:l (35) - Q^2 (17)] [tj - 17]/18 (4. 34)

E( tj ) = E

k =

s; 2 (i7) - [E^ 2 (35) - E^ 2 (17) ] [ tj. - 17]/18 (4. 35)

If C

j

< 17'’F

Q(tj) = £; 2 (i7) + [Q^ s 2 (47) - q^:

2 (17)] [ t

j

- 17]/30 (4,,36)

E(tj) = E

k =

; 2 (i7) + [E^ 2 (47) - Ej- 2 (17)] [ t

j

- 17]/30 (4. 37)

48
5

.

REFERENCES

1. Federal Register, Test Procedures for Central Air Conditioners,

Including Heat Pumps, Vol. 44, No. 249, p. 76700, U.S. Government

Printing Office, Washington, DC, December 27, 1979.

2. Federal Register, Proposed Rulemaking and Public Hearing Regarding

Test Procedures for Central Air Conditioners, Including Heat Pumps,

Vol. 51, No. 194, p. 35736, U.S. Government Printing Office,

Washington, DC, October 7, 1986.

3. Borg-Warner Corporation, Application for Exception from Central Air

Conditioner Test Procedures, DoE Office of Hearings and Appeals,

Case BEE- 1338 , January 13, 1981.

4. Air Conditioning and Refrigeration Institute, Standard 210/240 for

Unitary Air-Conditioning and Air-source Heat Pump Equipment,

Arlington, VA, 1984.

5. Urbs , D.G., Bullock, C.E. and Voorhis , R.J., New Testing and Rating

Procedures for Seasonal Performance of Heat Pumps with Variable Speed

Compressors, ASHRAE Transactions, Vol. 92, Part 2, 1986.

6. Federal Register, Petition for Waiver of Central Air Conditioner Test

Procedures from Carrier Corporation, (Case CAC-001), Vol. 51,

No. 31, p. 5587, U.S. Government Printing Office, Washington, DC,

February 14, 1986.

7. Federal Register, Petition for Waiver of Central Air Conditioner Test

Procedures from The Trane Co., (Case CAC-002) , Vol. 51, No. 192,

p. 35410, U.S. Government Printing Office, Washington, DC,

October 3, 1986.

8. Horak, B.F., of ETL Testing Laboratories, Cortland, NY, letter of

June 3, 1987.

9. Mohan, N. and Ramsey, J.W., Comparative Study of Adjustable-Speed Drives

for Heat Pumps, Electric Power Research Institute, EM-4704,

Palo Alto, CA, 1986.

10. Baldwin, A.J., Planer, N.G., Nordell, D.E. and Mohan, N. , Evaluation of

Electrical Interference to the Induction Watthour Meter, Electric

Research Power Institute, EL-2315, Palo Alto, CA, 1982.

11. Miller, W.A. of Oak Ridge National Laboratory, Oak Ridge, TN, private

communication, April, 1987.

12. Urbs, D.G. of Carrier Corporation, Syracuse, NY, private communication,

J une , 1987.

13. Kirkpatrick, K. of Trane Co., Tyler, TX, private communication,

June, 1987.

49
14. Nelson, L.W. of Honeywell Inc., Golden Valley, MN , private communication,

July, 1987.

15. The American Society of Heating, Refrigerating, and Air-Conditioning

Engineers, Inc., ANSI/ASHRAE Standard 116-1983,

Atlanta, GA, 1983.

50
APPENDIX A. EXAMPLE OF SEER CALCULATION

This appendix contains an example of calculations required for determination

of the Seasonal Energy Efficiency Ratio, SEER.

Table Al presents a summary of calculations performed for each temperature

bin. Calculation steps required for the 92 °F temperature bin are shown in

detail below.

The unit performance data needed by the calculation procedure are listed

below:

Q*; 2 (95) = 27000 Btu/h E*; 2 (95) = 3288

q5;

2 (82) = 28397 Btu/h E^g 2 (82) = 3082

Q^;

1 (82) = 13130 Btu/h E^= x (82) = 958

Q^” 1 (67) = 14492 Btu/h Eg

g

1 (67) = 859

Q^ 1 ^) = 17888 Btu/h Ess

1 (87) = 1450

CD = 0.2

Step 1. Determine the minimum and maximum speed balance points, t ± and

975 • 27000 + 495 • 14492 + 2211 • (14492-13130)

tl = ———————— — = 81 . 14° F

15 • 27000 + 33 • (14492-13130) (eq. (3.11))

845 » 27000 + 429 ° 28397 + 2706 - (28397-27000)

t2 = — —— _____ - _____ = 97 „ 65 °f

33 - 28397 - 20 • 27000 (eq. (3.12))

Since tj = 92, t 1 < t^ < t2 , Case II applies

51
Step 2. Calculate tvc .

qS;

1 (87) = 14492 + (13130-14492) (87-67) /I 5 = 12676.0 Btu/h

5 2 (87) = 28397 + (27000-28397) (87-82)/13 = 27859.7 Btu/h

17888 - 12676

N

q = = 0.34326

27859.7 - 12676

13130 - 14492

Mq = - (1-034326) +

82 - 67

27000 - 28397 — o 0.34326 = -96 . 519

95 - 82

33 • 17888 - 2871 • (-96.519) + 65 .« 27000

tvc = ——— —— ———

86 . 88 °F

27000 - 33 • (-96.519)

(eq. (3.13))

(eq. (3.32))

(eq. (3.20))

(eq. (3.19))

(eq. (3.21))

Step 3. Calculate power at temperature tvc .

E^g 1 (87) = 859 + (958-859) (87-67) /I 5 = 991.0 W

Ess

2 (87) = 3082 + (3288-3082) (87-82)/13 = 3161.2 W

1450 - 991

Ne = —— = 0.21150

3161.2 - 991

958 - 859 3288 - 3082

ME = — (1.-0.21150) + - 0.21150 = 8.556

82 - 67 95 - 82

Ess

1 (86.88) - 1450 - 8.556 ° (86.88-87.0) = 1451.0 W

(eq. (3.14))

(eq. (3.33))

(eq. (3.24))

(eq. (3.23))

(eq. (3.22))

52
Step 4. Calculate EER at temperatures t 1 =81.14, tvc =86.88, and t2 =97.65 .

Qgg

1 (81.14) = 14492 + (13130-14492) (81 . 14-67)/15 = 13208.

Eg

g

1 (81 . 14 ) = 859 + (958-859)(81.1-67.0)/15 = 952.1 W

EERg

g

1 (81 . 14) = 13208.1/952.1 = 13.87 Btu/(W«h)

g

1 (86.88) = BL(86 . 88) = 27000 - (86 . 88-65)/(l . 1 • 30) =

E*; 1 (86.88) = 1451.0 W

17901.8

EERg

g

1 (86.88) = = 12.34 Btu/(W-h)

1451.0

g 2 (97.65) = 28397 + (27000-28397) (97 . 65-82)/13 = 26715.:

Ess

2 (97.65) = 3082 + (3288-3082) (97 . 65-82)/13 = 3330.0 W

EERg

g

2 (97.65) - 26715.2/3330.0 = 8.02 Btu/(W-h)

Step 5. Evaluate parameters for a parabolic fit.

d = (97. 652 - 81 . 142 )/(86 . 88 2 - 81. 142

) = 3.0607

13.87 - 8.02 - 3.0607 • (13.87-12.34)

b =

• = 1.1027

81.14 - 97.65 - 3.0607 • (81.14-86.88)

13.87 - 8.02 - 1.1027 • (81.14-97.65)

c = —— ——————— = - 8 . 1494° 10" 3 81. 142 - 97. 65 2

a = 8.02 - 1.1027 • 97.65 - ( -8 . 1494- 10“ 3

)

• 97. 65 2 = -21

Btu/h

(eq. (3.13))

(eq. (3.14))

(eq. (3.26))

17901.8 Btu/h

(eq. (3.5))

(step 3)

(eq. (3.25))

Btu/h

(eq. (3.32))

(eq. (3.33))

(eq. (3.27))

(eq. (3.28))

(eq. (3.29))

(eq. (3.30))

950

(eq. (3.31))

53
Step 6. Calculate capacity and energy input at 92°F temperature.

Q ( 9 2 ) = BL(92) = 27000 (92-65)/33 = 22090.9 Btu/h (eq. (3.5))

EERg

v (92) = -21.950 + 1.1027-92 - 8.1494-10' 3 • 92 2 = 10.52 Btu/(W-h)

(eq. (3.17))

22090.9

E(92) = = 2099.9 W (eq. (3.16))

10.52

Step 7. Calculate seasonally weighted capacity and energy input at 92 °F

temperature bin.

X(92) = 1 (eq. (3.9))

PLF(l) = 1 (eq. (3.10))

q(92) = 1

• 22090.9 = 22090.9 Btu/h (eq. (3.7))

n6 = 0.052 (Table 2)

n6

• q(92) = 0.052 • 22090.9 =: 1148.7 Btu/h (eq. (3.6))

e (92) = 1

• 2099.9/1 = 2099.9 W (eq. (3.8))

n6

o e (92) = 0.052 • 2099.9 = 109.2 W (eq. (3.6))

54
It should be noted that some values in the above example differ from the

respective values shown in Table Al due to smaller number of carried

digits and the round-off error of hand-done calculations.

While performing calculations for all temperature bins, Steps 1 through 5

have to be followed one time. Once coefficients a, b and c are evaluated,

calculations for Case II start at Step 6.

55
APPENDIX B. EXAMPLE OF HSPF CALCULATIONS

Example of HSPF Calculations.

This section contains an example of calculations required for determination

of the Heating Seasonal Performance Factor, HSPF. The example calculations

were performed for the minimum design heating requirement in region IV.

The following are the unit performance data needed for calculating HSPF:

QL 2 (47) = 30838 Btu/h E5' 2 (47) = 3236 W

Q5:f(35) = 22930 Btu/h E5:?(35) = 2900 W

Q5- 2 (17) = 17112 Btu/h e5: 2 (17> = 2544 w

oi:

1 (62) = 13274 Btu/h E5: 2 (62) = 1101 w

= 10355 Btu/h e5: 1 (47) = 960 w

q5:I(35) = 10233 Btu/h ES:? (35) = 1106 w

Q5:

n (47) = 25670 Btu/h

CD = 0.25

toff = O'F ton = 10°F

First, the minimum and maximum heating requirements have to be determined.

Since the nominal speed test was performed, capacity from this test,

Qi;

n (47), will be used in calculations. For region IV after rounding off

to the standardized values we obtain:

DHRmin = 25670 - (65 - 5)/60 = 25670 ~ 25000 Btu/h

DHRtnax = 50000 Btu/h

(eq. (4.5)

and Table 5)

(eq . (4.6)

and Table 5)

56
Table B1 presents a summary of calculations performed for each temperature

bin for minimum heating design requirement. Calculation steps required

for 27°F temperature bin are shown in detail below.

Step 1. Determine the minimum and maximum speed balance points, t 3 , and t 4

.

975 • 0.77 * 25000 + 47 • (65-5) (13274-10355) - 15 • 10355 • (65-5)

t3 = —— — —

15 • 0.77 • 25000 + (65-5) ( 13274- 10355)

t3 = 38 . 11 °F (eq. (4.12))

1950 • 0.77 • 25000 + 17(65-5) (30838-17112) - 30 • 17112 • (65-5)

t A =

30 * 0.77 • 25000 + (65-5) (30838-17112)

t4 = 14. 80°F (eq. (4.13))

Since calculated t 4 is smaller than 17, the applied equation is the right

one. If obtained value were greater than 17, equation (4.14) would be

used.

Since t A < tj = 27 < t3 we have Case II.

Step 2. Evaluate tvh .

Q

k=

1

(35) = 10355 + (13274-10355) (35- 47 )/15 = 8019.8 Btu/h (eq. (4.15))

N

q = (10233-8019. 8)/(22930-8019. 8) = 0.14844 (eq. (4.22))

Mq = (13274-10355) (1-0. 14844) /I 5 + (22930-17112) - 0.14844/18 = 213.69

(eq. (4.21))

57
65 - 0.77 • 25000 + (65-5) (35 • 213.69-10233)

tvh = = 33 . 86 °

F

0.77 • 25000 + 213.69 • (65-5)

Step 3. Calculate power at temperature tvh

(eq. (4.23))

E

k ^ 1 (35) = 960 + (1101-960) (35- 47) /1 5 = 847.2 W (eq. (4.16))

Ne = (1106-847. 2)/(2900-847. 2) = 0.12607 (eq. (4.26))

Me = (1101-960)(1-0.12607)/15 + (2900-2544) • 0.12607/18 = 10.708

(eq. (4.25))

Edef(33.86) = 1106 + 10.708 - (33.86-35) = 1093.8 W (eq. (4.24))

Step 4. Calculate COP at temperature t3 =38.11, tvh =33 . 86

,

and t 4 =14.8 .

Q

k “ 1 (38.11) = BL(38.11) = (65-38.11) • 0.77 • 25000/(65-5) = 8627.2 Btu/h

(eq. (4.4))

Ek=1 (38.11) = 960 + (1101 -960) (38.11-47)/! 5 = 876.4 W (eq. (4.16))

8625.0

C0Pk ' 1 (38. 11) = = 2.883

3.413 • 876.4

(eq. (4.28))

Qdef(33.86) = BL(33 . 86) = (65-33.86) ° 0.77 « 25000/(65-5) = 9990.8 Btu/h

(eq. (4.4))

9990.8

C0Pk "

| (33.86) = = 2.676

3.413 • 1093.8

(eq. (4.27))

Q

k=2 (14.80) = BL( 14 . 80) = (65-14.80) - 0.77 ° 25000/(65-5) = 16105.8 Btu/h

(eq. (4.4))

E

k==2 (14 . 80) = 2544 + (3236-2544) (14 . 80-17)/30 = 2493.3 W (eq. (4.37))

(If t4 were greater than 17, equation (4.35) would be used)

58
16105.8

C0Pk = 2 (14.80) = — = 1.893 (eq. (4.29))

3.413 • 2493.3

Step 5. Evaluate parameters for a parabolic fit.

d = (38.11 2 -14.802 )/(33.862 -14.802

) = 1.3298 (eq. (4.30))

1.893 - 2.883 - 1.3298 • (1.893-2.676)

b = — —— = 2 . 5164® 10" 2 (eq. (4.31))

14.80 - 38.11 - 1.3298 • (14.80-33.86)

1.893 - 2.883 - 2.5164°10~ 2

• (14.80-38.11) — _____ = 3,2711° 10" 4 14. 802 - 38. II 2 (eq. (4.32))

a = 1.893 - 2.5164* 10" 2 * 14.8 - 3.2711-10-4

• 14.

8

2 = 1.4489

(eq. (4.33))

Q(27) = BL(27) = (65-27) • 0.77 « 25000/(65-5) = 12191.7 Btu/h

(eq. (4.4))

C0Pk=v (27) = 1.4489 + 2.5164-10' 2 * 27 + 3.2711-10" 4

° 27 2 = 2.367

(eq. (4.19))

E(27) = 12191.7/(3.413 ° 2.367) = 1509.1 W (eq. (4.18))

Step 7. Calculate seasonally weighted capacity, the energy input to the

heat pump, and energy input to the electric heater.

BL(27) = (65-27) » 0.77 • 25000/(65-5) = 12191.7 Btu/h (eq. (4.24))

n8 = 0.087 (Table 4)

n8

- BL(27) = 0.087 • 12191.7 - 1060.7 Btu/h (eq. (4.3))

5(27) = 1 (eq. (4.9))

59
X(27) = 1 (eq. (4.10))

PLF (27) = 1 - 0.25 • (1-1) = 1 (eq. (4.11))

e(27) =1*1 o 1509.1/1 = 1509.1 W (eq . (4.7))

n8

• e (27) = 0.087 • 1509.1 = 131.3 W (eq. (4.3))

RH(27) = (12191.7 - 1 • 1 • 12191 . 7)/3 .413 = 0 W (eq. (4.8))

n8

- RH(27) = 0

It should be noted that calculations steps related to evaluation of the

minimum and maximum speed balance points, and evaluation of coefficients

for the parabolic fit of COP in the intermediate speed range (Steps 1

through 5) have to be performed one time for each design heating requirement

and climate region for which seasonal performance of a heat pump is

evaluated. Once the parabolic fit is determined for a given region and

DHR, calculations for succeeding temperature bins in the intermediate

speed range include only steps 6 and 7.

60
03 OJ

a)

H

y v£> 3 3 3 vO v—/ : o a /-N /^N /^S /~s S-/ >%

J) c ^ lH Csl CsJ >s

M

T3

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U

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CL 3 n <a 1 «3

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<uC o C O Cl

tu tJJ U3 UJ U3

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75

—i o O' O' O' O' O' <3 s3= 3 p 3 © 9—4 9—=) 4 S—V

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05 AJ 0 0 O 0 O /-> 9-\ •3

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-o 1-1 3 sO S0 so sO A—- 3 3 3 a. 3 U 3 V4 CL C0 0

C/5 l-i 3 4-1 o r- r^. f'A r^- i 3 3 a u • • • • • • 9 3 Li E o sO SO iO SO so sO so 3 O

JZ1 <y J3 CM CM CM CM CM CM CM CL

CO &-> 3 3

°H 3 -C >

S-t -Q 4-1—4 Q)

03 • L •H > 3 O t o O O O O O O O

Li

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00 0

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OO

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L e f"“4 M T3 00 00 CO 00 00 00 00 3 0 C u 00 E O * O

cO

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C 33

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0-1 o •—- o 0 9 • * 9 « 9 CL 3 4-4 o co 0 00 00 9—4

9—4 JZ 3 3 JD CM CM f—1 9—4 9-4 9—4 3 4-1 3 C -C <—4 JZ Li O AJ 3 O 3

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C

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°i-4

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1-1

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C/1

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Li CO 3 3 3 5 C -H •L "3

u 1 1 1 1 3 «M -4 CM 9-4 5*4 <H 3 1 9 r» 8 CM 1 ess a B a i>* /—» -»-<9 /—9 9 A H „* ffl J<ffl M<0 M <£' HP H CM CO ^ t-1 OQ 03 CQ CJ v-y V-99 w

61
Table 2.

Distribution of Fractional Hours in Temperature Bins

to be Used for Calculation of SEER.

Bin

number

j

Bin

temperature

tj(°F)

Fraction of total

temperature bin hours

1 67 0.214

2 72 0.231

3 77 0.216

4 82 0.161

5 87 0.104

6 92 0.052

7 97 0.018

8 102 0.004

62
m—I J-a x ,°

cO 4-(

cn 03 §5X C

x-s /''s /-N CN CN m m r- VO vO <* cn cn

'w' 'W N-/ N-/ V-/ H —» o H N CN 4-3 -H«M (M 1 « 1 >» 1 a 1 «fl H ® 1 9 II WJ J4 «* •« O M <n J* V) J*T3 MT3 x* a w U U U3 w CO CO o X a

03 3

5-)

X 3 AJ

03 03 « X 3 E 0) 0) a X E

Cfl 03 H e/5 x

"0 o X 0) o «—H 0) X 3

Q* c X C/3 t—i i

03 & »H X XcO •Ox

03 • > -8 b0 o C X

X °rl r—

x b0 03 3 c0 C X X 05 -X 3 1 AJ AJ U oo

0) H o uoO X O XX 3X Cn X ~ o ~

cnw

cn

X

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cn0) H

CN

vD

CN

AOX

CO

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r^

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r^ lOCO N<M H ©m

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CNJI <0 V oA©

CNo

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<0

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03X

03

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AJ

a •S3

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cno

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X £ £ b0C

°MX

co0) xX

c0

)-a 0)

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bOC

°r^ x

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0)

(Uo.

C/3 Xc

cO s

bOC

a© V“J 03 °r^ • • c • s c—4

cn ao <7—4 OV c o »—i 1 1 o o

am

y

J-*

U

ID 03 03 w X CN X

m o o O • X a 0 • • 03 aO cn o m X • C

lH <t cn <r c— i

,—i c

•—* c o X

03

O 03

X

K 03

f*'* cn p^ cn cn aj s X o o 0 O o Q cn v© oo 5“} 00 cn 03 5—a i x cn CAJ p

cn

O 3

03

C

p

U .M

C 3 O ><

O o O o X

X »M co

a • 0 O 03 03

X E

CN

m p^ 03 cn <0 AS cn c*=S cu cn -H

y

cn 3 3 X „ o y X 6 cn 2 c0 am E X y 0 H CN CO >} in vO

N

fi3

the

specified

temperature

isa

dew-point

selection

of

the

speed

is

prescribed

in

section

4.1.3
Table 4. Distribution of Fractional Heating Hours in Temperature Bins,

Heating Load Hours and Outdoor Design Temperature for Different

Climate Regions.

Region* I II III IV V VI

Heating Load Hours, HLH 750 1250 1750 2250 2750 2750

Outdoor Design Temperature,

Td for the region 37 27 17 5 -10 30

Fractional Hours:

Bin # tj(°F)

j = i 62 .291 .215 .153 .132 .106 .113

2 57 .239 .189 .142 .111 .092 .206

3 52 .194 .163 .138 .103 .086 .215

4 47 .129 .143 .137 .093 .076 .204

5 42 .081 .112 .135 . 100 .078 . 141

6 37 .041 .088 .118 .109 .087 .076

7 32 .019 .056 .092 .126 .102 .034

8 27 .005 .024 .047 .087 .094 .008

9 22 .001 .008 .021 .055 .074 .003

10 17 0 .002 .009 .036 .055 0

11 12 0 0 .005 .026 .047 0

12 7 0 0 .002 .013 .038 0

13 2 0 0 .001 .006 .029 0

14 -3 0 0 0 .002 .018 0

15 -8 0 0 0 .001 .010 0

16 -13 0 0 0 0 .005 0

17 - 18 0 0 0 0 .002 0

18 -23 0 0 0 0 .001 0

*Heating domestic regions are shown in Figur<e 11.

64
Table 5

Standard Design Heating Requirements

(Btu/h)

5,000 25,000 50,000 90,000

10,000 30,000 60,000 100,000

15,000 35,000 70,000 110,000

20,000 40,000 80,000 130,000

65
Table Al . Bin Calculation Worksheet for Evaluation of SEER.

j n

j BL( tj ) Q(tj) m rt

C-t. X( tj ) PLF n

j -q n

j

* e

1 67. .214 1636. 14492. 859.0 .113 .8 350.2 25.2

2 72. .231 5727. 14038. 892.0 .408 ,9 1323.0 95.4

3 77. .216 9818. 13584. 925.0 .723 .9 2120.7 152.9

4 82. .161 13909. 13909. 1017.0 1.000 1.0 2239.4 163.7

5 87 .104 18000. 18000. 1461.6 1.000 1.0 1872.0 152.0

6 92 .052 22091. 22091. 2096.7 1.000 1.0 1148.7 109.0

7 97 .018 26182. 26182. 3139.5 1.000 1.0 471.3 56.5

8 102 .004 30273. 26248. 3398.9 1.000 1.0 105.0 13.6

TOTALS9630.3 768.3

SEER (Btu/(W®h)

)

= 9630. 3/768.3 = 12.53

66
Table B1 . Bin Calculation Worksheet for Evaluation of HSPF.

j BL(tj) Q(tj) X(td

) PLF <(tj) BL*n,

J e « n^ RH 0 nj

1 62. .132 963. 13274. .073 .768 1.0 127.0 13.7 .0

2 57. .111 2567. 12301. .209 .802 1.0 284.9 30.4 .0

3 52. .103 4171. 11328. .368 .842 1.0 429.6 45.4 .0

4 47. .093 5775. 10355. .558 .889 1.0 537.1 56.0 .0

5 42. .100 7379. 9382. .787 .947 1.0 737.9 75.9 .0

6 37. .109 8983. 8983. 1.000 1.000 1.0 979.2 101.4 .0

7 32. .126 10588. 10588. 1.000 1.000 1.0 1334.0 151.0 .0

8 27. .087 12192. 12192. 1.000 1.000 1.0 1060.7 131.3 .0

9 22. .055 13796. 13796. 1.000 1.000 1.0 758.8 102.9 .0

10 17. .036 15400. 15400. 1.000 1.000 1.0 554.4 82.4 .0

11 12. .026 17004. 14824. 1.000 1.000 1.0 442.1 63.1 16.6

12 7. .013 18608. 12537. 1.000 1.000 .5 241.9 15.0 47.0

13 2. .006 20213. 10249. 1.000 1.000 .5 121.3 6.6 26.5

14 -3. .002 21817. 7961. 1.000 1.000 .0 43.6 .0 12.8

15. -8. .001 23421. 5674. 1.000 1.000 .0 23.4 .0 6.9

TOTALS7675.9 875.2 109.8

HSPF (Btu/ (W»h)

)

= 7675 .9/(875.2 + 109.8) = 7.793

67
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MBS»1 14A 1REV- 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

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

NBSIR 88-3781 MAY 1988

4. TITLE AND SUBTITLE

Recommended Procedure For Rating and Testing Of Variable Speed Air Source Unitary

Air Conditioners And Heat Pumps

5. AUTHOR(S)

Piotr Domanski

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)

DoE

Washington, DC 20585

10. SUPPLEMENTARY NOTES

] 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 si gn i fi cant

bi bl iography or literature survey, mention it here)

A procedure is presented for testing and rating variable speed, 'split residential

air conditioners and heat pumps. The procedure is derived in part from existing

procedures for single speed and two speed systems where these procedures could be

applied, and introduces a new algorithm for representation of variable speed unit

performance in the intermediate speed operation range. Analysis and background which

led to the formulation of the procedure are included as well as calculation examples

for the cooling and heating mode. This procedure has been prepared for the Department

of Energy for consideration in the rule making process.

12. KEY WORDS (Six to twelve entries ; alphabetical order; capitalize only proper names; and separate key words by semicolons)

air conditioner; central air conditioner; heat pump; rating procedure;

variable speed system

13. AVAILABILITY

[~yl Uni imited

| j For Official Distribution. Do Not Release to NTIS

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

20402.

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

14. NO. OF

PRINTED PAGES

$13.95

USCOMM-DC 6 0 4 3 -P 80
''

'