NAT'L INST. OF STAND & TECH R I.C.

NBS

Publications

Aiiios asitia 31-2241

Engineering - Economic Analysis

of Improved Heat Pump

Performance for Minimum

Standards Development

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Washington, DC 20234

July 1981

Sponsored by

Office of Buildings and Community Systems

1 l.S. Department of Energy

-qq Washington, DC

100

. U56

81-2241

1981

NBSIR 81-2241

# *• ENGINEERING - ECONOMIC ANALYSIS

OF IMPROVED HEAT PUMP

PERFORMANCE FOR MINIMUM

STANDARDS DEVELOPMENT

Stephen R. Petersen

Kimberly A. Barnes

George E. Kelly

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Washington, DC 20234

July 1981

Sponsored by

Office of Buildings and Community Systems

U.S. Department of Energy

Washington, DC

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

NATIONAL fcUMEAi: OT 8TAKDABDS uiun

NOV 2 3 1381

;<??/
1 OH*-!**.T5 f

f>3£! : VOH
PREFACE

The work in this report has been conducted as an interdisciplinary research

project by the Building Economics and Regulatory Technology Division and the

Building Thermal and Service Systems Division within the Center for Building

Technology, National Engineering Laboratory, at the National Bureau of Standards (NBS). This effort has been supported by the Consumer Product Efficiency

Branch in the Office of Buildings and Community Systems, at the U.S. Department

of Energy (DoE).

The methodology outlined in this report employs a parametric analysis

technique. The numerical values resulting from this analysis are valid only

for the specified set of parameters selected by NBS. DoE is required by law

to consider many other factors in setting minimum efficiency standards.
ABSTRACT

This report provides a methodology and technical data for analyzing the

life-cycle cost effectiveness of energy efficiency improvements to residential

heat pump systems. This methodology could be used to develop a reference base

for establishing minimum efficiency standards for new heat pump systems that are economically justified in a prescribed percentage of installations. Criteria for economic optimization are outlined. The methodology used to compute

seasonal heating and cooling performance ratings and the annual energy savings

resulting from improvements in seasonal performance, by climate region, are detailed. The interdependence between efficiency ratings in the heating and

cooling modes is explored using statistical analysis. An example of the procedure for determining maximum cost-effective efficiency levels is demonstrated

for a 36,000 Btu/h heat pump.

Keywords: energy efficiency standards; engineering-economic analysis; heat

pump; mechanical equipment efficiency ratings; minimum efficiency standards;

space cooling requirements; space heating requirements.

iv
ACKNOWLEDGMENTS

The authors wish to thank the following people at the National Bureau of

Standards for their timely review and helpful comments: Harold E. Marshall,

David A. Didion, Peter Domanski, W. B. May, and Clinton W. Phillips. Errors

and omissions remain the responsibility of the authors.

v
TABLE OF CONTENTS

Page

LIST OF TABLES vii

LIST OF FIGURES viii

SI CONVERSION ix

1 . INTRODUCTION 1

2 . GENERAL METHODOLOGY FOR ESTABLISHING OPTIMAL PERFORMANCE LEVELS

FOR HEAT PUMPS 3

2.1 GENERAL ECONOMIC CRITERION FOR OPTIMIZATION 3

2.2 COMPUTATION OF INCREMENTAL SAVINGS AND COSTS FOR HEAT PUMP

SYSTEMS 5

3. CALCULATING THE SEASONAL PERFORMANCE OF HEAT PUMPS IN THE HEATING

AND COOLING MODES 9

3.1 COOLING MODE CALCULATIONS 9

3.2 HEATING MODE CALCULATIONS 11

3.3 INTERRELATIONSHIP BETWEEN PERFORMANCE CHARACTERISTICS IN THE

HEATING AND COOLING MODES 13

3.4 INTERRELATIONSHIP BETWEEN SEASONAL PERFORMANCE CHARACTERISTICS IN THE HEATING AND COOLING MODES 18

4 . ESTIMATING ANNUAL ENERGY SAVINGS 26

4 .1 GENERAL METHOD 26

4 .2 ANNUAL HEATING AND COOLING REQUIREMENTS FROM THE BEPS

PROGRAM 38

5. DETERMINATION OF MAXIMUM COST-EFFECTIVE EFFICIENCY LEVELS 46

6. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FURTHER RESEARCH .... 52

6.1 SUMMARY 52

6.2 CONCLUSIONS 52

6.3 RECOMMENDATIONS FOR FURTHER RESEARCH 53

REFERENCES 55

APPENDIX A - DERIVATION OF MODIFIED UNIFORM PRESENT WORTH FACTORS 56

vi
12

3

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5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

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22

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25

30

32

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35

36

37

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41

42

43

44

47

50

LIST OF TABLES

Major Heating Climate Regions in the Continental U .S .A HSPF by Heating Climate Region: 24,000 Btu/h Capacity (95°F),

Midpoint DHL

HSPF by Heating Climate Region: 24,000 Btu/h Capacity (95°F),

Minimum DHL

HSPF by Heating Climate Region: 24,000 Btu/h Capacity (95°F),

Maximum DHL

HSPF by Heating Climate Region: 18,000 Btu/h Capacity (95°F),

Midpoint DHL

HSPF by Heating Climate Region: 36,000 Btu/h Capacity (95°F),

Midpoint DHL

HSPF by Heating Climate Region: 48,000 Btu/h Capacity (95°F),

Midpoint DHL

Cooling Climate Regions

Combined Climate Regions

Annual kWh Usage for a 24,000 Btu/h Heat Pump by Combined

Climate Region (General Method)

Reduction in Annual kWh Usage Due to Increased Efficiency:

24.000 Btu/h Heat Pump (General Method)

Reduction in Annual kWh Usage Due to Increased Efficiency:

18.000 Btu/h Heat Pump (General Method)

Reduction in Annual kWh Usage Due to Increased Efficiency:

36.000 Btu/h Heat Pump (General Method)

Reduction in Annual kWh Usage Due to Increased Efficiency:

48.000 Btu/h Heat Pump (General Method)

Space Heating and Cooling Data from BEPS

Estimated Space Heating and Cooling Requirements for BEPS

House

Incremental kWh Savings: BEPS-Based; 12,000 Btu/h Heat

Pump

Estimated Space Heating and Cooling Requirements Corresponding to a 12,000 Btu/h Heat Pump

Incremental kWh Savings: General Method; 12,000 Btu/h Heat

Pump

Incremental Life-Cycle Savings Due to Increased Efficiency:

36.000 Btu/h Heat Pump

Estimated Incremental Retail Costs for a 36,000 Btu/h

Heat Pump

vii
LIST OF FIGURES

Figure Page

1 Life-Cycle Appliance-Related Costs 4

2 Economically Optimal Appliance Efficiency Varies with

Assumptions Governing Incremental Dollar-Value

Energy Savings 6

3 Distribution of Heating Load Hours Throughout the United

States 28

4 Distribution of Cooling Load Hours Throughout the United

States 29

5 Illustration of Incremental Savings and Costs of 0.5 Btu/Wh

Increase in SEER: 36,000 Btu/h Heat Pump 49

viii
SI CONVERSION

Because the energy analysis in this report is based directly on the NBS testing

and rating procedure for heat pumps operated in the heating and cooling modes

and on the capacities of heat pumps as typically rated by U S. manufacturers,

compatible U.S. units of measurement are used throughout this report. Since

the United States is a signatory to the Eleventh General Conference on Weights

and Measures, which defined and gave official status to the Metric SI system,

the following conversion factors are provided to assist users of SI units.

Metric Conversion Factors

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

1 foot (ft) = 0.3048 meter (m)

Area: 1 ft 2 = 0.092903 m

2

Volume:

Fluid Capacity:

Temperature

:

1 ft 3 = 0.028317 m

3

1 gallon (gal) = 3.78541 liters (L)

1°F = 9/5°C + 32

Temperature

Interval

:

1°F = 5/9°C or K

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

Mass per unit

Length: 1 lb/ft = 1.48816 kg/m

Mass per unit

Area: 1 lb/ft2 = 4.88243 kg/m2

Mass per unit

Volume

:

1 lb/ft3 = 16.0185 kg/m3

Energy:

Heat Flow Rate:

Specific Heat:

1 Btu = 1.05506 kilojoules (kJ)

1 Btu/h = 0.293071 Watt (W)

1 Btu/ (lb) (°F) = 4.1868 kJ/(kg)(K)

U-value

:

1 Btu/(ft2 )(h)(°F) = 5.67826 W/(m2 )(K)

R-value

:

1 (ft 2 )(h)(°F)/Btu = 0. I76ll0(m2

) (K)/W

ix

1 . INTRODUCTION

Minimum energy efficiency standards for air-to-air residential heat pumps are expected to be promulgated by the Department of Energy in the early 1980's.^

These standards will apply to all heat pumps manufactured in the United States

after the date of promulgation. It is likely that they will require that both

the seasonal performance factor for heating (HSPF) and seasonal energy efficiency ratio (SEER) for cooling by air-to-air residential heat pumps equal or exceed minimum specifications to be determined by DoE . Because these are performance standards, rather than prescriptive standards, the actual methods

and designs used to achieve these minimum efficiency levels will not be specified. However, the methodology and test procedures for calculating HSPF and

SEER for each heat pump model will be specified by DoE in order to assure

consistency

The energy efficiency standards for heat pumps are to be designed to achieve

the maximum improvement in energy efficiency which DoE determines to be technologically feasible and economically justified The purpose of this report

is to develop a benefit-cost methodology, based on engineering-economic analysis, that can be used to provide DoE with reference data for minimum standards

development that satisfies the criterion for economic justification. It will

be shown that this criterion is likely to constrain the standard from reaching

the energy efficiency level that is technologically feasible at this time.

Cost effectiveness is measured in this report in a life-cycle cost context. To

be economically justified, each improvement in energy efficiency must result in

additional life-cycle energy savings having a present dollar value greater than

or equal to the corresponding additional costs. The highest energy efficiency

levels (i.e., HSPF and SEER) which can be shown to be economically justified

would serve as the basis for the DoE minimum standards for heat pumps.

^ U .S . Department of Energy, "Advance Notice of Proposed Rulemaking and Notice

of Public Meetings Regarding Energy Efficiency Standards for Nine Types of

Consumer Products," Federal Register , Vol. 44, No. 1, January 2, 1979,

pp . 49-60

.

^ The procedures for calculating both HSPF and SEER are specified in "Test

Procedures for Central Air Conditioners, Including Heat Pumps," Department

of Energy Final Rule, Federal Register , Vol. 44, No. 249, December 27, 1979,

pp. 76700-76723. The procedure for calculating HSPF is specified in

W. Parken, G. Kelly, and D. Didion, Method of Testing, Rating, and Estimating

the Heating Seasonal Performance of Heat Pumps , NBSIR 80-2002, National

Bureau of Standards, Washington, D.C., April 1980. The procedure for calculating SEER is specified in G. Kelly and W. Parken, Method of Testing, Rating

and Estimating the Seasonal Performance of Central Air-Conditioners and Heat

Pumps Operating in the Cooling Mode , NBSIR 77-1271, National Bureau of

Standards, Washington, D.C., April 1978.

U .S . Department of Energy, "Advance Notice of Proposed Rulemaking," p. 52.

1
It should be recognized at the outset, however, that life-cycle savings, and

thus the cost effectiveness of increases in heat pump efficiency, will vary

significantly from installation to installation due to a number of factors,

including climate, house design, operational profile, energy prices, and the

discount rate used to convert future savings to present value. This wide

variation in projected dollar-value energy savings is important in light of

the high probability that DoE will establish a single standard for air-to-air

residential heat pumps, regardless of the geographic location and house design

in which the heat pump will be installed. As a result, the criteria for establishing minimum performance standards should seek to assure that such standards

are cost-effective in the greater majority of installations. A methodology for

estimating the approximate percentage of installations in which a given minimum

efficiency standard is economically justified is developed in this report.

Scope . This report is primarily intended to provide a methodology for the

engineering-economic analysis of air-to-air residential heat pumps in the

approximate range of 14,000 to 60,000 Btu per hour (Btu/h) output capacity in

the cooling mode. This corresponds to an output capacity of approximately

14,000 to 65,000 Btu/h in the heating mode. Only heat pumps which provide both

heating and cooling are examined. The analysis will consider installations in

all geographic regions in the United States where heat pumps are used in more

than token numbers. Energy savings will be calculated for improvements in

heat pump efficiency ranging from an SEER of 7.0 to 11.0 Btu/Wh, with corresponding changes in HSPF by heating region. The methodology for determining

the maximum heat pump efficiency levels that are cost-justified is demonstrated

for a 36,000 Btu/h heat pump.

Organization . In section 2, the economic criteria for determining the optimal

level of operating efficiency are outlined. In section 3, the methodologies

for calculating the seasonal performance of a heat pump in both the heating

and cooling modes are stated. In addition, the interrelationships between

both steady-state and seasonal heating and cooling efficiencies are quantified.

In section 4, annual energy savings due to specified improvements in heating

and cooling efficiencies are calculated for a wide range of climates. In

section 5, the methodology for determining maximum cost-effective levels of

efficiency is demonstrated for a 36,000 Btu/h heat pump. Conclusions and

recommendations for further research are discussed in section 6.

2
2. GENERAL METHODOLOGY FOR ESTABLISHING OPTIMAL PERFORMANCE LEVELS FOR HEAT

PUMPS

2 .1 GENERAL ECONOMIC CRITERION FOR OPTIMIZATION

The maximum improvement in energy efficiency which can be economically justified for any given appliance can be identified most readily in a life-cycle

cost context. Life-cycle costs include all costs incurred over the life of

an appliance resulting from its installation and use. These costs include not

only the initial installed cost, but energy, maintenance, and repair costs over

the useful life of the appliance, all evaluated on a time equivalent basis,

for example, discounted to present value^. The level of energy efficiency which

minimizes total life-cycle costs attributable to an appliance is considered to

be economically optimal. Any further increase in energy efficiency will not be

cost effective. This relationship between energy efficiency and economic

optimality is shown in figure 1 .

At the top of figure 1, the generalized relationship between increased

efficiency (on the horizontal axis) and life-cycle energy costs (measured in

present-value dollars on the vertical axis) is shown for a given appliance

operated in a specified manner. As the efficiency increases linearly, the

life-cycle energy costs decrease, but at a decreasing rate, since energy usage

is inversely proportional to the efficiency rating. In addition, both the

installed cost and life-cycle maintenance and repair costs of the appliance

are shown in figure 1 as a function of appliance energy efficiency. As energy

efficiency is upgraded, the installed appliance cost rises at an increasing

rate due to the more intensive design changes needed to achieve each additional

improvement. Life-cycle maintenance and repair costs may be constant or may

change (upward or downward) as a function of appliance efficiency ratings.

The total life-cycle cost (TLCC) curve is shown at the top of figure 1 . This

is the sum of the installed cost and life-cycle energy, maintenance, and repair

costs for any given level of appliance efficiency. As is typical of most

energy using systems, improvements in energy efficiency at first reduce TLCC.

At the optimal efficiency level, designated fj in figure 1, TLCC is minimized.

At any point beyond h, TLCC is increasing so that no increase in energy

efficiency beyond rj can be cost justified to the consumer.

This same optimal efficiency level can be identified by evaluating only incremental savings and costs attributable to small increases in efficiency as shown

in the bottom of figure 1 . Incremental savings (in present-value dollar terras)

correspond to the reduction in life-cycle energy costs for each additional unit

of efficiency improvement. Incremental costs include both the increase in

installed cost plus the change in maintenance and repair costs (if any)

attributable to the same efficiency improvement.

^ Alternatively, an equivalent annual cost can be determined. However, in the

methodology presented all costs will be evaluated in present-value terms.

For an in-depth examination of alternative economic optimization methods and

discounting procedures, see H. Marshall and R. Ruegg, Simplified Energy

Design Economics , NBS SP 544, National Bureau of Standards, Washington, D.C.,

January 1980.

3
(b)

INCREMENTAL

SAVINGS

AND

COSTS

(a]

TOTAL

COSTS

(

PRESENTVALUE

DOLLARS)

(PRESENT-VALUE

DOLLARS)

4
At any point to the left of n, an increase in appliance efficiency will

result in incremental life-cycle savings greater than incremental costs; to

the right of n, an increase in efficiency will result in incremental costs

greater than incremental savings. Thus the maximum cost-effective level of

efficiency, again identified as n, is achieved where incremental savings

just equal incremental costs. Incremental savings and costs are used for

identifying the economically optimal level of heat pump efficiency in this

report because they are often more accurately estimated than total life-cycle

savings and costs.

Projected life-cycle dollar savings will vary significantly with changes in

assumptions related to projected energy prices, operational profile, useful

lifetime, and discount rate. Each of these factors is therefore relevant in

determining the optimal level of energy efficiency. Given a known useful

appliance life and discount rate, an increase in energy prices or operating

hours will shift the incremental savings curve to the right, increasing the

optimal efficiency level. This is shown in figure 2, where a shift in the

incremental savings curve from IS to IS* raises the optimal efficiency level

from n to n'. Similarly, a decrease in energy prices or operating hours will

shift the incremental savings curve to the left (IS"), with a corresponding

decrease in the optimal efficiency level (to n" in figure 2).

2.2 COMPUTATION OF INCREMENTAL SAVINGS AND COSTS FOR HEAT PUMP SYSTEMS

The determination of an optimal efficiency level for a heat pump is somewhat

more complicated than for most other appliances because its efficiency in the

heating mode (HSPF) is measured differently than its efficiency in the cooling

mode (SEER)*. While these different efficiency parameters are specified

separately, they are functionally interdependent. (This interdependent relationship will be examined further in section 3.3.) While a composite annual

efficiency measurement could be specified for a particular unit in a particular

application, it would have little meaning in other applications since the ratio

of heating requirements to cooling requirements is quite variable. As a result,

there is little purpose in evaluating the annual efficiency of a heat pump

system. Instead, the HSPF and SEER that can be economically justified for a given set of assumptions will be specified separately.

The reduction in annual heating energy use due to an increase in HSPF, from

HSPF-^-i to HSPF^, can be calculated as follows:

AHR (HSPF. - HSPF. ,)

AHEU,- 1" 1 1 (2.1) (3413)(HSPF

i )(HSPF

i :

)

* HSPF is defined as the total heating season heat output in Btu divided by

total heating season energy input in Btu (3413 Btu = 1 kWh). SEER is defined

as the total cooling season heat removed (in Btu) divided by total cooling

season energy input in Wh.

5
INCREMENTAL

SAVINGS

AND

COSTS

(PRESENT-VALUE

DOLLARS)

Figure 2

APPLIANCE EFFICIENCY

Economically Optimal Appliance Efficiency (n) Varies With

Assumptions Governing Incremental Dollar-Value Energy Savings (IS).

6
where: MEU^ = reduction in annual heating energy use (in kWh) due t© an

increase in HSPF from HSPF^-i to HSPF-^,

AHR = annual heating requirements in Btu, and

3413 = Btu per kWh.

The reduction in annual cooling energy requirements due to an increase in SEER,

from SEER^-i to SEER^, can be calculated as: ACR (SEER i - SEER±_ 1

) ACEUi ~ (1000)(SEERi )(SEER

i _ 1

)

( 2 . 2 )

where: ACEU^ = reduction in annual cooling energy requirements (in kWh) due

to an increase in SEER from SEERj__i to SEER-^,

ACR = annual cooling requirements in Btu, and

1000 = Watts per kWh.

Annual energy savings (AAEU^) due to an increase in HSPF from HSPF^_i to

HSPF^ and a simultaneous increase in SEER from SEER^_j to SEER^ are therefore

the sum of the seasonal energy savings, i.e.,

AAEUi = AHEUjl + ACEl^. (2.3)

Incremental present-value, life-cycle dollar savings (IS) corresponding to AAEU^ can be calculated as:

IS = (AAEU i )(P)(UPWk ), (2.4)

where: P = purchase price of energy in kWh at the beginning of the

heat pump operating life, and

UPWfc = modified uniform present worth factor.

The modified uniform present worth factor is a function of the useful life of

the system, the projected rate of kWh price increase, and the appropriate

discount rate. Procedures for calculating UPW* are discussed in Appendix A.

For an individual homeowner, the most appropriate price per kWh to use in an economic analysis is the marginal cost of the last kWh purchased. However, the

appropriate price per kWh to be used in an analysis of an appliance for standards development purposes is better based on the cost of the new electrical

generation and distribution capacity, since this is the energy that will actually be saved due to a large scale conservation effort. The Department of

Energy has been estimating these costs and should soon be able to provide them

for use in economic analyses supporting minimum standards development. Similarly, discount rates, projected rates of increase for kWh prices, and useful

lifetime assessments should be consistent with the assumptions used in other

analyses supporting DoE minimum efficiency standards for appliances and

building energy standards .

As stated in section 2.1, incremental costs include all costs incurred as a result of a given increase in HSPF or SEER. These incremental costs include

not only any increase in purchase and installation costs, but any increase in

maintenance and repair costs as well, discounted to present value. Most of the

7
increase in heat pump cost due to improvements in efficiency are likely to be

in the purchase cost. However, higher efficiency heat pump equipment may have

slightly higher installation costs than lower efficiency equipment because it

will typically have a larger outdoor condenser unit. Maintenance and repair

costs are not likely to be significantly higher for higher efficiency heat

pumps than lower efficiency heat pumps unless the compressor must be replaced.

The expected occurrence of compressor replacement depends to some extent on the

useful life assigned to the heat pump in the life-cycle cost analysis.

In the following section, a methodology for calculating the annual energy

savings from improvements in heat pump design will be presented. Since these

savings vary significantly by region, house design, and operational profile, a general methodology that can be used in establishing minimum heat pump efficiency standards is developed.

8
3. CALCULATING THE SEASONAL PERFORMANCE OF HEAT PUMPS IN THE HEATING AND

COOLING MODES

3.1 COOLING MODE CALCULATIONS

The seasonal energy efficiency ratio (SEER) in Btu/h output per Watt input

(Btu/Wh) for a single-speed heat pump operating in the cooling mode is determined using the NBS testing and rating method.1 This method requires that

the steady-state energy efficiency ratio of the heat pump at 82°F outdoor

and 80°F indoor dry bulb temperature (EERg2 ) and a degradation coefficient

for part-load performance due to cycling on and off (Cp) be measured as prescribed by the test method. The SEER is then determined by the equation:

SEER = [PLF (0.5)] [EERg2 ] > (3.1)

where

0.5

PLF (0.5)

EERg2

cooling load factor (i.e. the ratio of total cyclical cooling

done during a complete cycle (including off-time) to steadystate cooling capacity over the same time period at the same ambient conditions),

the part-load factor for a cooling load factor of 0 .5

1 - Cj) (1-0.5), and

(output capacity in Btu/h at 82°F)/(power input in W at 82°F).

A Cp of 0.25 is assumed to be representative of heat pumps operating in the air

conditioning mode, based on NBS testing.2

It should be noted that this method for estimating SEER is not dependent on

geographic region since average cooling temperatures tend to be reasonably

similar in different regions of the United States. In addition, this method

assumes that the heat pump is properly sized for the design cooling load^ in

order to ensure proper dehumidification, and that cooling loads are proportional to (t Q -65 0 F), where t Q is the outdoor dry-bulb temperature. (This

rating procedure thus assumes that natural ventilation is not used to any

significant degree for cooling when the outdoor temperature is above 65°F.)

1 G. Kelly and W. Parken, Method of Testing, Rating and Estimating the Seasonal

Performance of Central Air-Conditioners.

2 Ibid .

O Proper heat pump sizing is defined in the NBS testing and rating procedures

to be 10 percent greater than the design hourly cooling load, the cooling

load exceeded in only 2 1/2 percent of all cooling hours.

9
The Air Conditioning and Refrigeration Institute (ARI) Directory* regularly

reports certain performance parameters for heat pumps manufactured in the

United States. This Directory provides an important and extensive data base

which will be referenced at several points in this report. At present, however, neither SEER nor EER82 are reported for heat pumps in the ARI Directory . Instead, the energy efficiency ratio measured at 95°F outdoor and 80°F indoor

dry-bulb temperature (EER95 ) is reported. In order to maintain consistency

with the data base in the ARI Directory , it was necessary to estimate EER82

as a function of EER95 .

The Ray W. Herrick Laboratories at Purdue University, under contract to ARI,

have recently reported EER95 and EER32 for 148 central air conditioners, based

on the DoE testing and rating procedures . 2 Since the steady-state operation of

a heat pump in the cooling mode is quite similar to that of a central air conditioner, this data base can provide the basis for determining a statistical

relationship between these two performance parameters. Several alternative

regression (i.e., least-squares) equations were analyzed in order to determine

how well EERg2 could be estimated as a function of EER95 . The following simple

linear regression gave the best results:

EER82 = 0.8123 + 1 .0206 EER

gs

(R2 = 0.915) (3.2)

(4 .38) (39 .77)

The R^ (or "coefficient of determination") of 0.915 means that 91.5 percent of

the variation in the dependent variable (EERg2 here) can be "explained" by the

regression equation. The closer the R

2 approaches 1.0, the more completely

the variation in the dependent variable is identified. The numbers in parentheses beneath the regression equation are t-ratios, which test the significance

of each of the independent variables. A t-ratio greater than 2.33 is significant at the 99 percent confidence level; that is, the probability that the

independent variable does not affect the dependent variable is less than one percent

.

Since measured EER data are not generally available for heat pumps, this

relationship will be used in the calculation of EERg2 for the determination

of SEER in this report.

* Directory of Certified Unitary Air-Conditioners, Air-Source Unitary Heat

Pumps, Sound-Rated Outdoor Unitary Equipment, and Central System Humidifiers , January 1 - June 30, 1980, Air-Conditioning and Refrigeration Institute,

Arlington, Virginia, 1980.

2 S. Thomas, D. Tree, and V. Goldschmidt, "A Study of the Prediction and

Measurement of Air Conditioning System Seasonal Performance Characteristics - Compilation of Data and Analysis of Test Procedure for SEER," Ray W. Herrick

Laboratories, Purdue University, Lafayette, Ind., sponsored by the

Air-Conditioning and Refrigeration Institute, 1979.

10
3.2 HEATING MODE CALCULATIONS

The seasonal performance factor for heating (HSPF), in Btu output per

equivalent Btu input (1 Btu/h = 0.293 W), can be approximated by using the NBS

method for testing and rating heat pumps in the heating mode.^ This method

is more complex than the rating method for heat pumps in the cooling mode

since the hourly outdoor temperature profile and the corresponding heating

loads of the house must be considered. As a result, the HSPF varies

significantly with geographic region, house design, and heat pump size.

The measured performance characteristics of a given heat pump model needed to

calculate HSPF are the output capacity and power input at outdoor dry-bulb

temperatures of 47°, 35°, and 17 °F, plus a degradation coefficient for partload performance (Cp). The capacity and power parameters are measured at an indoor temperature of 70°F. Ideally, the hourly heating load of the house and

the corresponding outdoor temperature are known for each hour of the heating

season

.

The output capacity corresponding to the outdoor temperature in any given hour

is estimated by extrapolating below 17 °F and above 45°F, using a linear equation fitting published capacity measurements for 17 °F and 47 °F. Between outdoor temperatures of 17 °F and 45°F, capacity is estimated using a linear

equation fitting 17°F and 35°F in order to account for performance degradation

due to frosting of the outdoor coils. Input power requirements corresponding

to the outdoor temperatures are estimated using an equation fitting published

power requirements measured at 17 °F and 47 °F. Above 47 °F, power input is

modified by a part-load factor calculated as a function of Cp in order to

model losses due to cycling.

Rather than using hourly load and temperature data for each hour in the heating

season to estimate HSPF, the NBS method for testing and rating heat pumps

divides the outdoor temperature profile into 5°F temperature "bins,” starting

at 65 °F. Hourly heating loads are assumed to be proportional to (65 - tj),

where tj is the representative (midpoint) outdoor temperature for each bin.

Each temperature bin is weighted as a percentage of the total number of heating

hours in the heating season below 65°F. These weights vary by geographic

region. Table 1 shows the weights used for the six major U .S

.

heating climate

regions used in the NBS heat pump testing and rating procedure.

Supplementary electric resistance heating is assumed to be used to maintain an

indoor temperature of 70°F when the output capacity of the heat pump falls

below the heating load of the house. Electrical input for the heat pump and

supplementary heating system are integrated over the heating season, and the

total input divided into the total coincident heating output (in consistent

thermal units) to arrive at HSPF.

1 W. Parken, G. Kelly, and D. Didion, Method of Testing, Rating and Estimating

the Heating Seasonal Performance of Heat Pumps .

11
Table 1. Major Heating Climate Regions in the Continental U.S.A.a

Region

Heating Load Hours, HLH 750

II

1250

III

1750

IV

2250 2750

VI

2750b

Outdoor Design Temperature,

Tqd for the region 37 27 17 -10 30

Fractional Hours:

Bin # Tj(°F)

1 62

rr

II .291

T

I .215

1

1 .153

T

1 .132

T

1 r

.106 | .113

2 57 1 | .239 1 .189 1 .142 1 .111 1 .092 | .206

3 52 II .194 I .163 1 .138 1 .103 1 .086 | .215

4 47 II .129 I .143 1 .137 1 .093 1 .076 | .204

5 42 1 | .081 1 .112 1 .135 1 .100 1 .078 | .141

6 37 II .041 | .088 1 .118 1 .109 1 .087 | .076

7 32 II .019 1 .056 1 .092 1 .126 1 .102 | .034

8 27 I | .005 1 .024 1 .047 1 .087 1 .094 | .008

9 22 1 | .001 | .008 1 .021 1 .055 1 .074 | .003

10 17 1 1 o 1 .002 1 .009 1 .036 1 .055 | 0

11 12 1 1 o 1 o 1 .005 1 .026 1 .047 | 0

12 7 1 1 o 1 o 1 .002 1 .013 1 .038 | 0

13 2 1 1 o 1 o 1 .001 1 .006 1 .029 | 0

14 -3 1 1 o 1 o 1 0 1 .002 1 .018 | 0

15 -8 1 1 o 1 o 1 0 1 .001 1 .010 | 0

16 -13 1 1 o 1 o 1 0 1 0 1 .005 | 0

17 -18 1 1 o 1 o I 0 1 0 1 .002 | 0

18 -23 I 1 o

II

1 o

1

1

I

0 1

1

0 1

1

.001 |

1

0

a Source: W. Parken, G. Kelly, and D. Didion, Method of Testing, Rating , and Estimating the Heating Seasonal Performance of Heat Pumps , p. 35.

See figure 3 for a map of the heating load hours in the United States.

b In Pacific Coast Region.

12
Heat pump performance parameters (capacity and power) are both reported in the

ARI Directory at 47 °F and 17 °F outdoor temperatures. The data in the Directory

are used to provide consistency between estimates of the heating and cooling

performance of heat pumps in this report. However, no measurements of capacity

at 35°F outdoor temperature are reported. Since these are needed to calculate

the capacity of a heat pump at outdoor temperatures between 17°F and 45°F, this

parameter must be estimated. This can be adequately performed by reducing the

interpolated value for capacity at 35°F (Cap 35 ) by a degradation coefficient

due to coil frosting ( Cp ) ; that is:

Cap35 = (0.4 Capi7 + 0.6 Cap47) Cp. (3.3)

The value for used in this report is 0.85^.

3.3 INTERRELATIONSHIP BETWEEN PERFORMANCE CHARACTERISTICS IN THE HEATING AND

COOLING MODES

The purpose of this subsection is to develop an empirical model which quantifies the interrelationship between the steady-state performance characteristics

of currently produced air-to-air residential heat pump systems in the heating

and cooling modes. ^ A typical air-to-air heat pump system provides both space

cooling and space heating functions using the same basic system components (an

outdoor coil, compressor and fan, and an indoor coil and blower) in both operational modes. As a result, the steady-state performance characteristics

(capacity and power) for the heating and cooling modes of a given heat pump

design are closely related. It follows, therefore, that most modifications

which increase heat pump efficiency in the cooling mode can be expected to

result in increases in efficiency in the heating mode as well.^

Since heat pumps are typically sized to match design cooling loads rather than

design heating loads, the empirical model of heat pump performance developed in

this report is based on performance characteristics measured in the cooling

mode. For given increases in steady-state cooling efficiency, corresponding

increases in steady-state heating efficiency are estimated. Based on the

methodology outlined in subsections 3.1 and 3.2, seasonal efficiency estimates

can then be calculated in order to better determine corresponding reductions

in annual energy usage.

1 Based on the NBS testing of heat pump systems.

Oc It is important to note that the empirical model developed in this report is

not meant to represent the theoretical relationship between heat pump performance in the heating and cooling modes and is therefore not necessarily valid

in estimating the heating performance of new heat pump systems based on their

cooling performance parameters.

Consideration of adequate dehumidification during the cooling cycle does

place physical constraints on certain efficiency improvement options, notably

on the indoor coil size.

13
The ARI Directory lists several hundred outdoor heat pump units under 41

different trade names having cooling output capacity (rated at 95 °F outdoor

and 80°F indoor temperatures) in the range of 14,000 to 62,000 Btu/h. These

units have EER95 ratings ranging from 6.07 to 8.55 Btu/Wh with a mean of 7.33.

Heating output capacities rated at 47 °F and 17°F outdoor temperatures (at 70°F

indoor temperature) are listed in the Directory for each unit. Power input

requirements for each of these three ratings are also listed. No other rating

points are published in the Directory .

The reported performance characteristics of each outdoor unit depend to some extent on the indoor coil size selected. For this report the indoor coil size

which most closely matched the outdoor unit in output capacity was selected for

each outdoor unit listed. The capacity and power measurements used in this

report therefore correspond to this matched set of components. Variations in

indoor coil size are not considered in this report because it is assumed that

the indoor coil size is selected to properly match dehumidification requirements and indoor blower characteristics rather than to increase seasonal

efficiency.

Close inspection of the Directory reveals that many of the models included are actually the same equipment, with only a difference in manufacturer name used

for marketing purposes. All duplicate models that could be detected were

eliminated, leaving a data base with 217 distinct models representing 24

different manufacturers. All models are air-to-air, split systems with

single-speed compressors (ARI code HRCU-A-CB).

An initial plotting of the cooling capacities at 95° and heating capacities at

47°F (Cap 95 and Cap 47 , respectively) suggested that these two variables were linearly related. The least-squares linear regression equation that best fit

this data is:

Cap (Btu/h) = -1,053.3 + 1.09364 Cap 95 (Btu/h). (R2 = 0.985) (3.4)

(3.0) (177.5)

Alternative regression forms were examined. Since initial data plotting

indicated that Cap 47 may be reduced slightly from the level predicted by equation (3.4) when EER95 (Cap 95 /Pow95 ) is greater than 7.0 Btu/Wh, a multiple

regression equation was calculated with both Capg 5 and EER95 as independent

variables. However, the inclusion of EER95 did not prove to be statistically

significant (t-ratio = 0.33). As a result, equation (3.4) is used to model

Cap 47 as a function of Cap 95 » However, it should be noted that the highest

EER95 in t he data sample is 8.55 Btu/Wh. Thus it is quite possible that for new units with EER95 greater than 8.55 Btu/Wh, EER95 may become a significant

variable in determining Cap 47 , and estimates of Cap 47 based on equation (3.4)

may be overestimated for high efficiency units.

Similarly, regression equations were calculated to determine the functional

relationship between power requirements at 95 °F and 47 °F (P0W95 and P0W47,

respectively). Initial data plotting indicated that P0W95 and P0W47 are also

linearly related, but that EER95 may also explain some of the variation.

14
Several multiple-variable regression equations were calculated. The best of

these is:

P 0W47 (W) = -488.5 + 0.8337 Pow95 (W) + 91.38 EER95 (Btu/Wh). (3.5)

(2 .44) (105.32) (3.55) (R2 =0.981)

Note that in this case, P0W47 is shown to be partially dependent on the

efficiency of the heat pump in the cooling mode (EER95 ). Each independent

variable is shown to be statistically significant at the 99 percent confidence

level and thus is included in the empirical model developed here.

Equations (3.4) and (3.5) can be used to calculate the degree to which steadystate heat pump efficiency in the heating mode varies with a given change in

steady-state efficiency in the cooling mode. As an example, consider a 0.5

Btu/Wh improvement in EER95 , from 8.0 to 8.5 Btu/Wh, for a heat pump with a Cap 95 of 24,000 Btu/h. First, calculate the input power in W before and

after improvement (P0W95 and Pow' 95 , respectively):

24,000 Btu/h

Powqc = --- 7 = 3,000 W, and 95 8.0 Btu/Wh

24,000 Btu/h

P°W

95 8.5 Btu/Wh

2,824 W.

Using equation (3.4), the capacity of the heat pump at 47°F can be calculated

based on its capacity at 95°F:

Cap 47 = -1053.3 + 1.09364(24,000) = 25,194 Btu/h.

This is assumed to be held constant as the EER47 increases. Using equation

(3.5), the power input can be calculated before and after the improvement in

EER95 (P 0W47 and Pow' 47 , respectively):

P0W47 = -488.5 + 0.8337(3,000) + 91.38(8.0) = 2743.6 W, and

Pow '47 = -488.5 + 0.8337(2,824) + 91.38(8.5) = 2642.6 W.

Now calculate the steady-state efficiency of the heat pump at 47°F before and

after the increase in efficiency at 95°F (EER47 and EER' 47 , respectively):

EER47 = (25,194 Btu/h)/2743.6 W = 9.18 Btu/Wh, and

EER '47 = (25,194 Btu/h) /2642 . 6 W = 9.53 Btu/Wh.

Thus the 0.5 Btu/Wh increase in steady-state efficiency at 95 °F (EER95 ) corresponds to a 0.35 Btu/Wh increase in steady-state efficiency at 47°F

(EER47 ) or an equivalent increase in steady-state coefficient of performance

of 0.10 Btu output/Btu input at 47 °F (COP 47 ).

As a check on the accuracy of the estimates obtained from equations (3.4) and

(3.5), a comparison was made of the published ratings in the ARI Directory

15
with the predicted values for capacity and power and the corresponding COP

based on those equations. The absolute percentage difference (% DIFF) between

the actual value (ACT) and the predicted value (PRED), calculated from the

corresponding regression equation, was computed as follows:

ACT - PRED

% DIFF = x 100 (3.6)

ACT

The percentage was determined for each of the three variables for all 217 heat

pump units in the sample. The mean absolute percent error 1 was then calculated

for each variable as follows:

Variable Mean Absolute Percent Error

Cap47 3 .44%

P0W47 3.73%

COP47 3.61%

Equations (3.4) and (3.5) establish a statistical model of steady-state heat

pump performance at 47°F, based on its performance at 95°F. However, in order

to estimate the seasonal efficiency of a heat pump system, the output capacity^

and power input at 17 °F outdoor temperature (Capjj and Powjj) are also needed.

The same approach described above was taken, using the same 217 outdoor heat

pump units in the ARI Directory .

As might be expected, it was found that Cap47 and P 0W47 were better predictors

of Capi 7 and P 0W17 than Capg 5

an<1 1

* 0^95 . The equation which bests fits the

heating capacity data is:

Capi 7 (Btu/h) = 3705 .3 + 0.6011 Cap47 (Btu/h) - 537 .70 EER47 (Btu/Wh). (3.7)

(3.0) (81 .42) (3.65)

(R2 = 0.972)

The R

2 for this equation again indicates a highly satisfactory explanation

of the variation in the independent value. Note that in this case the estimate

of Capi 7 is reduced as EER47 is increased. This has important consequences

in the seasonal efficiency calculation because it means that more supplementary

heat will be needed at the lower outdoor temperatures, offsetting some of the

increase in EER in the heating mode

.

1 For a description of the use of mean absolute percent error and similar

quantities to test the performance of a simulation model, see Section 10.2

of R. Pindyke and D. Rubinfeld, Econometric Models and Economic Forecasts , McGraw-Hill Book Company, New York, 1976.

In addition, the heating output capacity at 35°F is also needed. However,

this parameter is not published in the ARI Directory . Estimation of this

parameter is discussed in section 3.4.

16
The equation which best fits input power data is:

Pow17 (W) = 206.0 + 0.8287 Pow47 (W).

(4.98) (103.64)

(R2 = 0.980) (3.8)

When EER47 was introduced as an independent variable in the regression

analysis, it was found to be statistically insignificant in this case (t-ratio

= 0.89). However the negative coefficients estimated for EER47 in this case implies that it may tend to reduce P0W17 slightly.

The mean absolute percent error between the calculated and actual values for

Capi 7 , P0W17 and COP17 were computed as follows:

It was shown above that a 0.5 Btu/Wh increase in EER95 results in an 0.35

Btu/Wh increase in EER47 . This can be extended to show the effect of this

change on EER17 (Cap^/Pow^) and the corresponding COP17 .

Using equation (3.7), the heat pump output capacity at 17°F, before and after

the improvement in EER95 (Cap ^7 and Cap'j^, respectively), can be calculated

based on Cap 47 and EER47 :

Cap 17 = 3705.3 + 0.6011 (25,194) - 537.7 (9.18) = 13913.3 Btu/h, and

Cap ' 1

1

= 3705.3 + 0.6011 (25,194) - 537.7 (9.53) = 13725.1 Btu/h.

Using equation (3.8), the power input at 17°F (P0W17 and Pow'^) can be

calculated based on P0W47 and Pow'47, respectively:

Pow17 = 206.0 + 0.8287 (2743.6) = 2479.6 W, and

Pow' 17 = 206.0 + 0.8287 (2642.6) = 2395.9 W.

Now the steady-state efficiency of the heat pump at 17 °F before and after the

increase in efficiency at 95°F (EER17 and EER'^ 7 , respectively) can be

calculated:

EER17 = (13913.3 Btu/h)/2479.6 W = 5.61 Btu/Wh, and

EER ’ 17 = (13725.1 Btu/h)/2395 .9 W = 5.73 Btu/Wh.

Note that an increase of 0.5 Btu/Wh in EER95 and the corresponding 0.35

Btu/Wh increase in EER47 results in 0.12 Btu/Wh increase in EER17 , or a 0.035

Btu output/Btu input increase in the coefficient of performance at 17 °F (COP]^).

Variable Mean Absolute Percent Error

Cap 17

Pow^7

COP17

5.26%

4.47%

5.99%

17
3 .4 INTERRELATIONSHIP BETWEEN SEASONAL PERFORMANCE CHARACTERISTICS IN THE

HEATING AND COOLING MODES

Using the methods for calculating seasonal energy performance for cooling

(SEER) and heating (HSPF) outlined in sections 3.1 and 3.2, and the functional

relationships shown between the steady-state capacity and power performance

characteristics in section 3.3, the HSPF corresponding to any given SEER can

be estimated for a given heat pump size in a given building located in a specified climate region. However, since the highest EER95 for any residential,

air-to-air base heat pump system listed in the ARI Directory is 8 .55 Btu/Wh

(SEER =8.4 Btu/Wh), any estimate of HSPF corresponding to an SEER greater than

approximately 8.5 is based on extrapolation.

Since a heat pump is typically sized to match design cooling loads rather than

heating loads, and since there is no general relationship between heating

loads and cooling loads in houses, it is impossible to calculate an HSPF cor- responding to a given SEER without specification of both the climate profile

and the corresponding building heating loads. Six major U .S . heating climate

regions are defined in the NBS heat pump testing and rating procedure. The

heating load hours, outdoor design temperatures, and fractional hours for each

of the 5°F temperature bins used in the calculation procedure are shown in

table 1 for each of these six regions.

As explained in subsection 3.1, the SEER of a given heat pump, properly sized

for the air conditioning loads of a house, is assumed to be the same in all

regions of the country. However, in each climate region shown in table 1, the

HSPF corresponding to a given SEER and change in HSPF corresponding to a given

change in SEER, will be different. Table 2 shows the HSPF corresponding to

nine levels of SEER, in 0.5 Btu/Wh increments from 7.0 to 11.0 Btu/Wh, for the

six climate regions indicated, based on a 24,000 Btu/h (Capg 5 ) heat pump. It

is important to note that a 0 .5 Btu/Wh increase in SEER (equivalent to a 0.56

Btu/Wh increase in EER95 ) from 8.0 to 8.5 Btu/Wh results in increases in HSPF

ranging from 0.087 Btu output/Btu input (0.300 Btu/Wh) in region I (the warmest

region) to 0.024 Btu output/Btu input (0.082 Btu/Wh) in region V (the coldest

region) . It is apparent that improvements in a heat pump design that increase

its overall performance will have significantly more effect on seasonal cooling

performance than seasonal heating performance, especially in the colder climates.

As a result, the greatest potential energy savings due to improvements on heat

pump design are likely to occur in houses where annual cooling requirements

clearly dominate annual heating requirements. (This is, of course, most likely

to occur in southern climates.)

The design heating loads (DHL) shown in table 2 correspond to the midpoint

between the minimum and maximum design heating loads as defined in the NBS

testing and rating methodology.^ (It will be shown in section 4.2 that the

midpoint provides a reasonable estimate of design loads in certain cases.) As

noted above, the increase in HSPF due to a 0.5 Btu/Wh improvement is not only

a function of climate but of the size of the design heating load relative to

the output capacity of the heat pump at that same temperature. Tables 3 and 4

show the HSPF of a heat pump corresponding to the same nine levels of SEER in

the same six climate regions as table 2 , but in this case the design heating

18
Table 2. HSPF by Heating Climate Region : 3 24,000 Btu/h

Capacity (95°F), Midpoint DHL

Heating Climate Region II III IV VI

Design Heating Load

(kBtu/h) 17 .6 23.9 30.2 37 .8 40.3 22.0

Annual Heating

Requirements

(10° Btu/yr)

10.19 23.03 40.73 65.47 85.34 46.68

SEER

(Btu/Wh)

EER95

(Btu/Wh)

HSPF

7.0

1

1 7.04

II

|| 1.948

1

1 1 .862

1

1 1 .773

T

1 1 .612

T

1 1 .453

T

1 1 .904

1

1 7.5 1 7.60 | | 2 .056 1 1 .958 1 1 .854 1 1 .666 1 1 .488 1 2.007 1 8.0 I 8.16 II 2.153 1 2.043 1 1 .925 1 1 .712 1 1 .517 1 2.099 1 8.5 | 8.72

1

| | 2.240

II

1

1

2 .118 1

1

1 .987 1

1

1 .750 1

1

1 .541 1

1 2.182 1

1 b

9.0

1

I 9.28

Ti~

II 2.316

1

1 2.184

1

1 2.041

1

1 1 .783

1

1 1 .560

1

1 2.255

1

1 9.5 I 9.84 | | 2.383 1 2.241 1 2 .087 1 1 .810 1 1 .575 I 2.318 1 10.0 | 10.40 II 2.440 1 2.290 1 2.126 1 1 .832 1 1 .586 1 2.372 1 10.5 | 10.96 II 2.489 1 2.331 1 2.158 1 1 .850 1 1 .596 1 2.418 1 11 .0 I 11.52

1

| | 2.529

II

1

1 2.364 11 2.184 1

1

1 .864 1

1

1 .603 1

1 2.455 11

a Calculated using methodology described in section 2.

b Calculations of HSPF's corresponding to given SEER's are based on statistical relationships that were estimated from a data base with no observed SEER greater than 8.55 Btu/Wh. Thus any HSPF below this line

is extrapolated from the data base.

19
loads are those corresponding to the minimum and maximum, respectively, defined

in the NBS testing and rating methodology. Table 3 shows that while the HSPF

corresponding to a given SEER is smaller than those in table 2, the increase in

HSPF due to a 0 .5 Btu/Wh increase in SEER tends to be slightly larger (except

in climate regions I and VI). Table 4 generally shows the opposite results,

except that the increase in HSPF tends to be slightly smaller than those in

table 2 in all regions. The smallest increase in HSPF is in climate region V

for the case with the maximum design heating loads: an increase in SEER from

8.0 to 8.5 Btu/Wh results in a 0.016 Btu output/Btu input increase in HSPF

(0.055 Btu/Wh). The largest increase in HSPF due to an increase in SEER from

8.0 to 8.5 Btu/Wh is in climate region I with the midpoint design heating loads:

0.087 Btu output/Btu input (0.30 Btu/Wh). At the same time, it must be recognized that the annual heating requirements in climate region I are typically

so small that the increase in HSPF in this region will result in relatively

little actual energy savings.

This same procedure was used to estimate the HSPF corresponding to the same SEER levels for three additional heat pump sizes. Tables 5, 6, and 7 show the

HSPF's corresponding to unit capacities of 18,000, 36,000, and 48,000 Btu/h

(Cap95 ), respectively. In all three cases the midpoint design heating loads were used. Note that the increase in HSPF due to a 0.5 Btu/Wh increase in SEER

(from 8.0 to 8.5 Btu/Wh) increases significantly as the output capacity is

increased. For example, in climate region III, this increase in HSPF is 0.046

Btu output/Btu input (0.16 Btu/Wh) for the 18,000 Btu/h heat pump, but 0.094

Btu output/Btu input (0.32 Btu/Wh) for the 48,000 Btu/h heat pump. This is

because the steady-state performance characteristics of the heat pump in the

heating mode, as modeled empirically in section 3.3, improve as Capg 5 is

increased

.

Since the energy savings are related to the increase in HSPF, this relationship

between capacity and increase in HSPF may be a significant factor in determining optimal heat pump efficiencies. It implies that for larger size heat pumps

higher efficiency levels (both steady-state and seasonal) will be more readily

economically justified than those for smaller size heat pumps. However, additional factors must be considered before this can be verified: the size of

the annual heating and cooling requirements expected to be encountered and the

relative cost of the improvements in efficiency for larger units compared to

smaller units. In the next section, annual heating and cooling requirements

will be estimated and projected energy savings will be calculated.

1 The DHL is assumed to be a function of the heat pump heating capacity at 47°F

(Cap47 ) in the NBS methodology:

Minimum DHL = (Cap47 ) (65°F-TOD )/60

Minimum DHL = Cap47

Maximum DHL = (2)(Cap47 )(65 °F-Tq{))/ 60

Maximum DHL = (2.2)(Cap47)

for regions I, II, III, IV and VI.

for region V . for regions I, II, III, IV and VI.

for region V

20
Table 3. HSPF by Heating Climate Region : 3 24,000 Btu/h

Capacity (95°F), Minimum DHL

Heating Climate Region II III IV VI

Design Heating Load

(kBtu/h) 11 .8 16.0 20.2 25.2 25.2 14 .7

Annual Heating

Requirements

(10^ Btu/yr)

6.79 15.36 27 .16 43.64 53.36 31 .12

SEER

(Btu/Wh)

EER95

(Btu/Wh)

HSPF

7.0

1

I 7.04

il

|| 1.879

T

1 1 .797

!

1 1 .731

T

1 1 .635

1

1 1.468

T

1 1 .827

7.5 | 7.60 || 1.984 1 1 .892 1 1 .817 1 1 .701 1 1 .512 1 1 .927

8.0 I 8.16 || 2.078 1 1 .979 1 1 .894 1 1 .759 1 1 .550 1 2.017

8.5 I 8.72

1

|| 2.163

II

1

1 2.055 1

1

1 .962 1

1

1 .809 1

1

1 .581 1

1

2.097

9.0

T

I 9.28

tr

II 2.237

1

1 2 .123

1

1 2.021

1

1 1 .851

1

1 1 .607

1

1 2.168

9.5 I 9.84 | | 2.303 1 2.182 1 2.072 1 1 .887 1 1 .628 1 2.230

10.0 j 10.40 II 2.359 1 2.232 1 2.116 1 1 .917 1 1 .645 1 2.283

10.5 | 10.96 || 2.406 1 2.274 1 2.152 1 1 .942 1 1 .659 1 2.328

11 .0 1 11.52

1

|| 2.445

II

1

1

2.309 1

1

2.182 1

1

1 .961 1

1

1 .670 1

1 2.365

a Calculated using methodology described in section 2.

k Calculations of HSPF's corresponding to given SEER's are based on statistical relationships that were estimated from a data base with no observed SEER greater than 8.55 Btu/Wh. Thus any HSPF below this line

is extrapolated from the data base.

21
Table 4. HSPF by Heating Climate Region : 3 24,000 Btu/h

Capacity (95°F), Maximum DHL

Heating Climate Region

71

1

1

1

1 !

II III IV V VI

Design Heating Load

II

II (kBtu/h) II 23.5

11

31 .9 40.3 50.4 55.4 29.4

Annual Heating

II

II Requirements II 13.58 30.71 54 .31 87 .31 117 .36 62.24

(10^ Btu/yr) IIII

SEER EER95

II

II HSPF

(Btu/Wh) (Btu/Wh) II

II

7.0

r

! 7.04 II 1.984 1 .857 1 .733 1 .531 1 .387 1 .939

7.5 I 7.60 || 2.089 1 .942 1 .800 1 .571 1 .413 2.038

8.0 I 8.16 II 2.183 2.016 1 .858 1 .604 1 .434 2.126

8.5 | 8.72

1

jj 2.266

II

2 .082 1 .908 1 .632 1 .450 2.203

9.0

1

I 9.28

II

| | 2.339 2.138 1 .950 1 .655 1 .464 2.271

9.5 1 9.84 II 2.403 2.186 1 .986 1 .674 1 .475 2.330

10.0 j 10.40 II 2.457 2.227 2.015 1 .689 1 .483 2.380

10.5 | 10.96 II 2.502 2.261 2.040 1 .701 1 .490 2.422

11 .0 1 11.52

1

II 2.540

II 2.288 2.059 1 .711 1 .495 2.456

a Calculated using methodology described in section 2

.

k Calculations of HSPF's corresponding to given SEER's are based on statistical relationships that were estimated from a data base with no observed SEER greater than 8.55 Btu/Wh. Thus any HSPF below this line

is extrapolated from the data base.

22
Table 5. HSPF by Heating Climate Region : 3 18,000 Btu/h

Capacity (95°F), Midpoint DHL

Heating Climate Region II III IV VI

Design Heating Load

(kBtu/h) 13.0 17.7 22.4 28.0 29.8 16.3

Annual Heating

Requirements

(10^ Btu/yr)

7 .53 17.03 30.12 48.43 63.12 34 .53

SEER

(Btu/Wh)

EER95

(Btu/Wh)

HSPF

7.0

1

| 7.04

1 1 || 1.889

1

1 1 .802

1

1 1 .715

1

1 1 .562

1

1 1 .411

1

1 1 .843

7.5 I 7.60 II 1.980 1 1 .881 1 1 .781 1 1 .604 1 1 .438 1 1 .930

8.0 1 8.16 I | 2.058 1 1 .949 1 1 .837 1 1 .639 1 1 .459 1 2.004

8.5 I 8.72

1

II 2.125

II

1

1 2.006 11

1 .883 1

1

1 .667 1

1

1 .475 1

1 2.067

9.0 j 9 .28

IIII 2.181

1

1 2.053

1

1 1 .921

1

1 1 .689

1

1 1.487

1

1 2.120

9.5 | 9.84 II 2.226 1 2.092 1 1 .951 1 1 .706 1 1 .496 1 2.162

10.0 | 10.40 j | 2.262 1 2.121 1 1 .975 1 1 .719 1 1 .502 1 2.196

10.5 | 10.96 II 2.288 1 2.144 1 1 .992 1 1 .729 1 1 .507 1 2.221

11 .0 I 11.52

1

|| 2.307

1 1

1

1 2.159 11

2 o 004 1

1

1 .735 1

1

1 .510 1

1 2.238

a Calculated using methodology described in section 2

.

k Calculations of HSPF's corresponding to given SEER's are based on statistical relationships that were estimated from a data base with no observed SEER greater than 8.55 Btu/Wh. Thus any HSPF below this line

is extrapolated from the data base.

23
Table 6 . HSPF by Heating Climate Region : 3 36,000 Btu/h

Capacity (95 °F), Midpoint DHL

Heating Climate Region II III IV VI

Design Heating Load

(kBtu/h) 25.8 36.4 46.0 57.5 61 .3 33.5

Annual Heating

Requirements

(lO^ Btu/yr)

14 .92 35.04 61 .94 99.58 129 .78 70.98

SEER

(Btu/Wh)

EER95

(Btu/Wh)

HSPF

r M T T T T T

7.0 I 7.04 1 1 2.010 1 1 .927 1 1 .837 1 1 .669 1 1 .502 1 1 .967

7.5 I 7.60 || 2.136 1 2.040 1 1.935 1 1 .737 1 1.548 1 2.089

8.0 I 8.16 II 2.254 1 2.146 1 2.025 1 1 .798 1 1 .588 1 2.202

8.5 I 8.72

1

II 2.364

II

1

1 2.244 11 2.107 11

1 .851 1

1 1.623 1

1 2.308

9.0

1

1 9.28

n

1 1 2 .466

1

1 2.333

1

1 2.181

1

1 1.897

1

1 1.652

1

1 2.405

9.5 I 9.84 II 2.559 1 2.414 1 2.248 1 1.938 1 1.677 1 2.494

10.0 | 10.40 II 2.645 1 2.488 1 2.307 1 1 .973 1 1 .698 1 2.575

10.5 | 10.96 || 2.722 1 2.554 1 2.360 1 2.004 1 1.715 1 2.649

11 .0 I 11.52

1

II 2.791

II

1

1 2.614 11 2.407 1

1 2.031 11 1.729 11 2.715

3 Calculated using methodology described in section 2.

b Calculations of HSPF’s corresponding to given SEER's are based on statistical relationships that were estimated from a data base with no observed SEER greater than 8.55 Btu/Wh. Thus any HSPF below this line

is extrapolated from the data base.

24
Table 7. HSPF by Heating Climate Region : 3 48,000 Btu/h

Capacity (95°F), Midpoint DHL

Heating Climate Region II III IV VI

Design Heating Load

(kBtu/h) 36.0 48.9 61 .7 77 .2 82.3 45.0

Annual Heating

Requirements

(106 Btu/yr)

20.79 47 .04 83.20 133.71 174 .30 95.33

SEER

(Btu/Wh)

EER95

(Btu/Wh)

HSPF

7.0

TI 7.04

II'

| | 2.042

1

1 1 .960

1

1 1 .870

T

1 1 .701

T

1 1 .530

T

1 2.000

7.5 I 7.60 II 2.178 1 2.084 1 1 .979 1 1 .777 1 1 .583 1 2.132

8.0 ! 8.16 | | 2.308 1 2.202 1 2 .079 1 1 .846 1 1 .631 1 2.257

8.5 1 8.72

1

II 2.431

II

1

1 2.312 11 2.173 1

1

1 .909 1

1

1 .672 1

1 2.375

9.0

T

I 9 .28

II

II 2.547

1

1 2.415

1

1 2.260

1

1 1 .965

1

1 1 .708

1

1 2.487

9.5 ! 9.84 II 2.656 1 2.512 1 2.340 1 2.015 1 1 .740 1 2.592

10.0 | 10.40 II 2.758 1 2.601 1 2.413 1 2.059 1 1 .768 1 2.689

10.5 | 10.96 11 2.853 1 2.684 1 2.480 1 2.099 1 1 .792 1 2.780

11 .0 1 11.52

1

II 2.941

II

1

1

2 .760 1

1 2.541 1

1 2.135 11

1 .813 1

1 2.864

a Calculated using methodology described in section 2.

k Calculations of HSPF's corresponding to given SEER's are based on statistical relationships that were estimated from a data base with no observed SEER greater than 8.55 Btu/Wh. Thus any HSPF below this line

is extrapolated from the data base.

25
4. ESTIMATING ANNUAL ENERGY SAVINGS

In order to estimate the annual energy usage of a heat pump, estimates of the

annual heating and cooling requirements (AHR, ACR) of the house in which it is

to be installed are needed. These two design variables can be calculated for

a given house using any one of a number of load determination programs (e.g.

BLAST, DOE-2, NBSLD) , representative climate data and an operational profile.

Equations (2.1), (2.2), and (2.3) provide a calculation methodology that can be

used to estimate annual energy savings attributable to given improvements in

HSPF and SEER once the values of the AHR and ACR are known for a given house.

These AHR and ACR are thermally independent of the type and efficiency of the

heating and cooling equipment installed. However, typical values of AHR and

ACR associated with heat pumps of different output capacities are not available

to serve as the basis for estimating typical energy savings from increased

heat pump efficiency.

As an alternative to typical AHR and ACR data, the NBS testing and rating

procedures for heat pumps can be used to provide a generalized method for estimating AHR and ACR in different regions of the United States, based on the size

of the heat pump installed rather than for specific building designs and operational parameters. This general method, examined in section 4.1, provides a good starting point for the estimation of annual heat pump energy usage and

potential savings. However, these estimates appear to be somewhat high for

the more tightly constructed housing that is likely to be built in the years

to come. Thus a further analysis, based on DoE Building Energy Performance

Standards (BEPS) data, is presented in section 4.2.

4. 1 GENERAL METHOD

The NBS procedures for testing, rating and estimating the seasonal performance

of heat pumps in the heating and cooling modes provide a general method for

estimating the annual energy usage of a heat pump and the energy savings due

to specified improvements in its steady-state efficiency ratings. Since the

energy usage and energy savings will vary with the local climate profile, the

annual heating and cooling requirements (AHR, ACR), and the design heating

load (DHL) of a house, these must be specified as well.

Based on the general method for calculating heat pump energy utilization in the

heating mode, AHR can be calculated using:

AHR = (DHL) (C) (HLH) , (4.1)

where

DHL = the design heating load of a house, i.e., the heating load at the outdoor

design temperature, Tqd,

C = a correction factor, defined in the NBS testing and rating procedure for

heat pumps to be 0.77, and

26
HLH = heating load hours.

A map of HLH for the continental United States is shown in figure 3 The six

major heating climate regions, including the corresponding t 0D and the midpoint HLH, as specified in the NBS testing and rating procedure for heat pumps

in the heating mode, are shown in table 1 .

Based on the general method for calculating heat pump energy utilization in the

cooling mode, ACR can be calculated using:

ACR = (Cap95 >(CLH) (4.2)

where:

Cap95 = the output capacity of a heat pump in the air conditioning mode when

the outdoor temperature is 95°F and the indoor temperature is 80°F,^

and

CLH = cooling load hours, which are based on the number of annual compressor

hours, a zero cooling load at 65°F outdoor temperature, and an indoor

temperature in the range of 75°-80°F.

A map of CLH by region for the continental United States is provided in figure

4 Based on this map, six major cooling climatic regions are proposed here,

as shown in table 8. Table 8 also includes the annual cooling requirements

calculated for each of these regions, as defined in the NBS method for estimating annual energy usage of heat pumps in the cooling mode. These ACR are based

on the midpoint CLH for each cooling region. (2600 CLH are used for region F)

Given six heating regions and six cooling regions, 36 potential combined

climate regions can result. However, only about 16 of these combined regions

actually exist in the continental United States. Moreover, based on a comprehensive 1977 heat pump sales report by ARI,^ which identified heat pump sales

in 615 trading areas, 98.5 percent of all heat pump sales occurred in only ten

Jim = (24)(Heating Degree Days, base 65°F)

(65°F - Tod )

^ This map is taken directly from W. Parken, G. Kelly, and D. Didion, Method of

Testing, Rating and Estimating the Heating Seasonal Performance of Heat Pumps .

^ Wet bulb temperatures are 75°F outdoors and 65°F indoors.

^ The CLH map was prepared under contract to NBS by York Division, Borg-Warner

Corporation, and was based on results calculated in R.R. McConnell,

J.R. Tobias, and L.W. Nelson, "Reducing Energy Consumption During the Cooling

Season," ASHRAE Journal , June 1976, pp . 61-65. It is included in G. Kelly

and W. Parken, Method of Testing, Rating and Estimating the Seasonal

Performance of Central Air-Conditioners.

27
2500

28

Figure

3.

Distribution

of

Heating

Load

Hours

Throughout

the

United

States
29

Distribution

of

Cooling

Load

Hours

Throughout

the

United

States
Table 8. Cooling Climate Regions

Annual Cooling Requirements3

CIO6 Btu)

Btu/h Output Capacity (95°F)

Region 1 Load

1

1

Hours 1

1

1 18,000 24,000 36,000 1 48,000

A

1

1 o - 400

1

1 0 0 0 1 o

B | 400 - 800 1 10.8 14.4 21.6 1 28.8

C | 800 - 1200 1 18.0 24.0 36.0 I 48.0

D | 1200 - 1800 1 27.0 36.0 54.0 1 72.0

E | 1800 - 2400 1 37.8 50.4 75.6 I 100.8

F | 2400

1

- 3000 1

1 46.8 62.4 93.6 1 124.8

a ACR = CLH x Capg^: Midpoints of CLH intervals are used (2600 CLH

are used for region F); no cooling is assumed

in region A.

30
of these regions. These ten regions are identified in table 9, which also

shows the midpoint HLH and CLH in each combined climate region and the percent

of 1977 heat pump sales in those regions, based on the ARI data.

Annual kWh usage in each of these ten regions was then calculated for a 24,000

Btu/h (Cap95 ) heat pump, based on the AHR and ACR data shown in tables 2 and 8,

respectively, and the SEER and corresponding HSPF data shown in table 2.

These annual kWh usages are shown in table 10 . The reduction in annual kWh

usage due to each 0.5 Btu/Wh increase in SEER (and corresponding increase in

HSPF) are shown in table 11 . Ultimately it is these savings (evaluated in

terms of present-dollar values over the life of the heat pump) which must

justify any cost increase related to the increased heat pump efficiency.

Examination of table 11 provides some preliminary information regarding the

effects of climate regions on the kWh savings due to increases in efficiency.

The annual kWh savings in the five combined regions having the lowest savings,

II-D, III-C, IV-B, V-B, and VI-B are all quite similar for an increase in SEER

from 8.0 to 8.5 Btu/Wh, ranging from 352 to 382 kWh per year. These five zones represent approximately 45 percent of all heat pump sales in 1977 . The largest

savings occur in regions II-E and I-F, the regions with the greatest cooling

requirements and smallest heating requirements. Note that these largest savings

are only about 50 percent greater than the lowest savings.

Tables 12, 13, and 14 provide the annual kWh savings, based on the same methodology, for an 18,000, 36,000, and 48,000 Btu/h heat pumps. Note that

the incremental savings for the larger units tend to be more than proportionally larger than the change in size alone would account for. This is because

the increase in HSPF corresponding to a given size increase in SEER tends to

be significantly greater for the larger units than for the smaller units. For

both the 18,000 and 24,000 Btu/h heat pumps, regions II-D, III-C, IV-B, V-B,

and VI-B have the smallest savings. For the 36,000 and 48,000 Btu/h units,

I-E replaces V-B in the list of the five regions having the lowest savings.

There is surprisingly little variation in the savings calculated for any given

change in SEER within these five regions. For all but the 18,000 Btu/h unit,

the savings vary by less than 10 percent; for the 18,000 Btu/h unit savings

vary by 25 percent.

Again these results for HSPF, energy utilization, and energy savings are based

on the general methods outlined in the NBS testing and rating procedures. They

are not based on a given house with known heating and cooling requirements.

Moreover they give results which appear to be significantly higher than what

might be expected for newer housing built to more stringent insulation specifications than most older housing. For this reason it is useful to reevaluate

these same factors, based on the use of a heat pump in a better defined

operational context.

1 This regional analysis was based on unpublished data provided by the AirConditioning and Refrigeration Institute for the sales of 33 companies in 615

trading areas during 1977

.

31
Table 9 . Combined Climate Regions

Region

1

1 Designator I HLH

1

1

1 CLH |1

% Salesa

1

1

1 1 1 I-E

1

| 750

1

1

1 2100 | 2.13

1

1 2 1 I-F 750 1 2600 | 3.30 1 3 1 II-D | 1250 1 1500 j 8.26 1 4 1 II-E | 1250 1 2100 | 6.43 1 5 | III-C | 1750 1 1000 | 16.29 1 6 1 III-D | 1750 1 1500 | 12.62 1 7 | IV-B | 2250 1 600 | 11 .75 1 8 1 IV-C | 2250 1 1000 | 28.73 1 9 1 V-B | 2750 1 600 | 5.85 1 10 i

1 VI-Bb

| 2750

1

1

1 600 |1

3.11 1

1

a Based on ARI report of 1977 sales. (1 .53% of sales

are outside these 10 regions.)

b Pacific coast region.

32
Table 10. Annual kWh Usage for a 24,000 Btu/h Heat Pump

by Combined Climate Region (General Method)

SEER

Combined Climate Region

(Btu/Wh)

|

1 T T

I I-E

1

1

1 I-F 1

1 II-D 1

1 ii-e i III-C

7.0

1

| 8732

1

1 10446

T

1 8767

1

1 10824 | 10160

7.5 | 8172 1 9772 1 8248 1 10168 | 9639

8.0 | 7686 1 9186 1 7804 1 9604 | 9200

8.5 | 7262

1

1

1

8674 1

1

7422 1

1 9116 | 8830

9.0

T1 6888

T

1 8222

1

1 7090

1

1 8690 | 8515

9.5 | 6557 1 7821 1 6801 1 8317 | 8246

10.0 | 6263 1 7463 1 6548 1 7988 | 8015

10.5 | 5999 1 7142 1 6325 1 7696 | 7817

11 .0 | 5762

1

1

1 6853 11 6128 11 7437 | 7647

1

| III-D

1

1

1

1 IV-B

1

I

1 IV-C

T

1

1 V-B i VI-B

7.0 | 11875

1

1 13957

1

1 15329

1

1 19274 I 9241

7.5 | 11239 1 13435 1 14715 1 18727 | 8736

8.0 I 10700 1 13007 1 14207 1 18283 | 8315

8.5 | 10242

1

!

1

12654 1

1

13783 1

1

17921 | 7963

9.0

1

| 9848

1

1 12360

1

1 13427

1

1 17631 | 7667

9.5 j 9509 1 12116 1 13127 1 17398 | 7417

10.0 | 9215 1 11912 1 12872 1 17205 | 7206

10.5 I 8960 1 11742 1 12656 1 17045 | 7029

11 .0 | 8738

1

1

1 11599 1

1

12472 1

1 16913 | 6880

a Annual kWh usage for a heat pump with an SEER greater

than 8.5 Btu/Wh is based on extrapolation of the

technical relationship between SEER and HSPF.

33
Table 11. Reduction in Annual kWh Usage Due to Increased Efficiency

24,000 Btu/h Heat Pump (General Method)

Combined Climate Region

(Btu/Wh) 1

| I-E

1 T

| I-F

1 r

1 II-D

1

1

| II-E

1 III-C

7.0 7 .5 r

| 560

1

| 674

1

| 519

1

| 656 522

7.5 - 8.0 | 486 | 586 | 444 | 564 438

8.0 8.5 | 424

1

| 513

1

| 382

1

| 488

1 370

8.5 _ 9.0

r

| 374

1

| 452

1

| 332

1

| 426 315

9.0 - 9.5 | 331 | 401 | 289 | 373 269

9.5 - 10.0 | 295 | 358 | 253 i 329 231

10.0 - 10.5 | 264 | 321 | 223 | 292 198

10.5 11 .0 | 237

1

| 289

1

| 197

1

| 259

1

170

1

| III-D

1

1

I IV-B

1

1

| IV-C

1

1

I V-B

1 VI-B

7.0 7.5

1

| 636

1

| 522

1

| 614

I

| 547 505

7.5 - 8.0 | 538 | 428 | 508 | 444 421

8.0 8.5 | 459

1

| 353

1

| 424

1

| 362

1

352

8.5 _ 9.0

T~

| 393

T~

| 293

r

| 356

1

| 290 296

9.0 - 9.5 | 339 | 244 | 300 | 233 250

9.5 - 10.0 | 294 | 204 | 255 | 193 211

10.0 - 10.5 | 255 1 171 | 216 | 160 177

10.5 11 .0 | 222

1

| 143

I

| 184

1

| 133

1

149

a Annual kWh usage for a heat pump with an SEER greater

than 8.5 Btu/Wh is based on extrapolation of the

technical relationship between SEER and USPF.

34
Table 12. Reduction in Annual kWh Usage Due to Increased

Efficiency: 18,000 Btu/h Heat Pump (General Method)

Combined Climate Region

(Btu/Wh) 1

| I-E

1

1

I I-F

1

i ii-d

T

| I I-E

1

i in-c

7.0 _ 7.5

1

| 414

1

| 499 | 374

1

| 477 | 362

7.5 - 8.0 | 358 | 433 | 317 | 407 | 301

8.0 8.5 | 312

1

| 378

1

| 272 | 351

1

| 251

8.5 _ 9.0

I

| 274

1

| 332 | 234

1

| 304 | 210

9.0 - 9.5 | 242 | 294 | 202 | 265 1 177

9.5 - 10.0 | 215 | 262 | 176 | 232 | 149

10.0 - 10.5 | 191 | 234 | 153 I 204 | 125

10.5 11 .0 1 171

1

| 210

1

| 134 | 180

1

| 105

1

| III-D

1

1

| IV

1

I IV-C

!

| V-B

1

| VI-B

7.0 _ 7.5

1

| 448

1

| 344 | 413

!

| 349 | 348

7.5 - 8.0 | 376 | 277 | 337 | 277 | 285

8.0 8.5 | 317

1

| 224

1

| 277 | 218

1

| 234

8.5 9.0

1

| 269

1

| 182 | 229

1

| 169 | 192

9.0 - 9.5 | 229 | 148 | 190 | 136 | 157

9.5 - 10.0 | 196 | 120 | 158 | 110 | 128

10.0 - 10.5 | 168 1 97 | 132 | 90 | 103

10.5 11 .0 | 144

1

1 78

1

| 109 1 74

1

| 82

Annual kWh usage for a heat pump with an SEER greater

than 8.5 Btu/Wh is based on extrapolation of the

technical relationship between SEER and HSPF.

35

i
Table 13. Reduction in Annual kWh Usage Due to Increased

Efficiency: 36,000 Btu/h Heat Pump (General Method)

Combined Climate Region

(Btu/Wh) 1

| I-E

1 i-f i II-D | I I-E i III-C

7.0 7.5

T"

| 853 1025 | 811 | 1017 | 845

7.5 - 8.0 | 741 891 | 698 | 878 | 717

8.0 8.5 | 650

1

782 | 605 | 764 I 613

8.5 _ 9.0

r

| 573 691 | 528 | 670 | 528

9.0 - 9.5 | 509 615 | 464 | 591 j 458

9.5 - 10.0 | 455 550 | 410 | 524 | 399

10.0 10.5 | 409 494 | 364 | 467 | 349

10.5 11 .0 | 359

1 447 | 325 | 418 | 306

1

| III-D

1 IV-B | IV-C i V-B i VI-B

7.0 7.5

1

| 1016 891 | 1028 | 969 | 820

7.5 - 8.0 | 867 743 | 863 | 800 | 693

8.0 8.5 | 746

1

625 | 731 | 665 | 591

8.5 9.0

1

| 646 528 | 623 | 557 | 506

9.0 - 9.5 | 563 450 | 534 | 469 | 436

9.5 - 10.0 | 493 384 | 460 j 393 | 377

10.0 - 10.5 | 434 330 | 398 | 322 | 327

10.5 11 .0 | 384

1

284 | 346 | 274 | 284

a Annual kWh usage for a heat pump with an SEER greater

than 8 .5 Btu/Wh is based on extrapolation of the

technical relationship between SEER and HSPF.

36
Table 14. Reduction in Annual kWh Usage Due to Increased

Efficiency: 48,000 Btu/h Heat Pump (General Method)

Change in SEER

(Btu/Wh)

1 Combined

1 Climate Region

1

| I-E

1

i i-f II-D II-E III-C i

7.0 7.5 | 1146 1375 1104 1378 1169 | 7.5 - 8.0 | 997 | 1197 952 1192 998 | 8.0 8.5 | 875

1

| 1051 828 1040 859 |

8.5 9.0

1

| 773 | 930 726 914 744 | 9.0 - 9.5 | 688 | 828 640 809 649 | 9 .5 - 10.0 1 615 | 742 568 719 569 | 10.0 - 10.5 | 554 | 668 506 643 502 | 10.5 11 .0 | 500

1

| 604 453 578 444 |

1

| III-D

1

| IV-B IV-C V-B VI-B i

7.0 7.5

1

I 1398 | 1267 1450 1406 1136 | 7.5 - 8.0 | 1198 | 1066 1226 1173 966 | 8.0 8.5 | 1035

1

| 904 1046 987 829 |

8.5 9.0

1

j 901 | 773 898 836 716 | 9.0 - 9.5 | 790 | 664 776 713 622 | 9.5 - 10.0 | 696 | 574 675 610 544 | 10.0 - 10.5 | 616 | 498 589 525 477 | 10.5 11 .0 | 548

1

| 434 517 454 419 j

a

a

a Annual kWh usage for a heat pump with an SEER greater

than 8.5 Btu/Wh is based on extrapolation of the

technical relationship between SEER and HSPF.

37
4 .2 ANNUAL HEATING AND COOLING REQUIREMENTS FROM THE BEPS PROGRAM

A limited amount of data from the DoE Building Energy Performance Standards

(BEPS) development program was obtained in order to provide a basis for estimating the AHR and ACR of new houses built to the relatively tight insulation

standards expected. Table 15 shows the AHR, ACR, and the maximum hourly heating and cooling loads for the 1200 square foot "prototype" house insulated to

the levels assumed in the BEPS development program in nine locations. ^ Note

that the ACR were calculated only during hours when the outdoor dry-bulb

temperature is 78°F or greater. As a result, these ACR can be expected to be

considerably less than those calculated in the general seasonal efficiency

estimating methodology, in which cooling loads are assumed to exist whenever

the outdoor temperature exceeds 65°F.

Also shown in table 15 are the heating degree days base 55°F (HDD 55 ) and

cooling degree hours base 75°F (CDH 75 ), which were computed from the same climate data^ used in the calculations of the AHR and ACR shown. These two

climate variables are provided because they correlate well with the AHR and

ACR shown, and thus can be used to interpolate AHR and ACR to other locations

Maximum hourly heating and cooling loads are shown rather than design heating

and cooling loads (DHL, DCL) since the latter were not available. These maxi- mum loads indicate that an appropriately sized heat pump (i.e., one sized to

provide about 10 percent more cooling at 95°F than the design cooling load)

would be approximately 12,000 Btu/h except in Fresno and Phoenix, where it

would be considerably higher. It is recognized that such a low capacity heat

pump is not commercially available at this time. However, in order to provide

a basis for comparison of the general method for estimating AHR and ACR with

the AHR and ACR based on the available BEPS research data, a 12,000 Btu/h heat

pump size will be assumed. It was necessary to adjust the BEPS data to

correspond to the heating and cooling climate regions used in the general

method. This was accomplished by plotting HDD 55 and CDH 75 data on the maps

shown in figures 3 and 4, respectively, and determining the HDD55 and CDH 75

that best represent an approximate midpoint in each of the heating and cooling

climate regions. AHR and ACR were then interpolated from the data in table 15

^ These data were calculated at Lawrence Berkeley Laboratories using the DOE-2

computer program, and served as the basis for the development of the proposed

energy budgets for single-family detached residences published in the DoE

Notice of Proposed Rulemaking on BEPS for new buildings, Nov. 28, 1979.

Insufficient data was made available for larger houses. Further information

regarding the prototype house and energy analysis can be found in the BEPS

"Technical Support Documents" available from the Department of Energy.

^ Test Reference Year climate data, which consist of measured hourly weather

data for an entire year and are considered to be reasonably representative of

the long-run climate for a given location, were used in the calculation of

the AHR and ACR

38
Table 15. Space Heating and Cooling Data from BEPS a

! Location

1

| AHR

I (106 Btu/yr)

1

I 1

| MAX H. L. |

| (kBtu/h) |

1 1

ACR

(106 Btu)

MAX C. L.

(kBtu/h)

I HDD55

b

1

1 CDH„b

1

| Atlanta

1

I 10.5

1 1

1 20.0 | 7.5 11 .2

1

| 1370

1

| 8264

I Burbank ! 1.5 | 11.7 | N/A 13.1 82 | 1050

1 Chicago I 27.4 | 29.5 | 4.3 12.5 | 3768 | 5124

I Fort Worth I 7.0 1 18.9 | 17 .2 13.0 | 1048 | 24761

| Fresno I 6.9 I 13.3 | 13.4 14 .6 | 1044 | 21268

| Houston I 3.9 1 18.1 | 16.9 12 .3 | 601 | 21379

| Minneapolis 1 43.0 | 44 .6 | 6.0 13.3 | 5934 | 7654

I Phoenix I 1.8 1 11.6 | 25.4 18.3 404 | 47746

I Washington, D.C. I 14.1

1

1 24 .4 |

1 1

9 .3 12.3 | 2185

1

| 12025

1

a Based on data received directly from Lawrence Berkeley Laboratories.

k Computed directly from the Test Reference Year (TRY) climate data used in

establishing AHR and ACR

.

39
to correspond to those midpoints. These are shown in table 16. In addition,

design heating loads (DHL) corresponding to these midpoint AHR were estimated,

based on the maximum heating loads shown in table 15, adjusted to correspond

to the regionally specified outdoor design temperature (from table 1). These

DHL are needed in order to calculate the hourly heating loads so that the

seasonal heat pump efficiency can be estimated.

Since the heating balance point (the average outdoor temperature below which

space heating is required) of the BEPS house tends to be approximately 55°F,

rather than 65°F used in the general method, the seasonal heat pump performance

calculation procedure was adjusted to make heating loads proportional to 55°F

minus the outdoor temperature, and to eliminate the two temperature bins

between 55°F and 65°F. This results in a somewhat lower HSPF because these

two bins contain the temperatures for which the COP of the heat pump is the

highest. The calculated incremental annual kWh energy savings for each 0.5

Btu/Wh increase in SEER (and corresponding increase in HSPF) are shown in

table 17 for each combined climate region, based on the use of a 12,000 Btu/h

heat pump.

In order to provide comparable results using the general method described in

subsection 4.1, the AHR, DHL, and ACR based on the general method were also

estimated for a 12,000 Btu/h heat pump. The results are shown in table 18.

Note that the AHR which were calculated for the same heating climate regions

using the general method tend to be significantly higher in the milder climates

but reasonably similar in the colder climates. The ACR tend to be about 50-70

percent higher in all regions. Conversely, the DHL for both methods tend to

be quite similar for the milder climates but somewhat low for the two coldest

climates using the general method. (This confirms that the use of the midpoint

DHL described in subsection 4 .1 is a reasonable assumption except in the coldest regions. However, use of a higher DHL would result in an even higher

estimate of annual energy usage and energy savings in those regions.)

Annual kWh savings corresponding to the AHR, DHL, and ACR based on the general

method are shown in table 19 . The order of increasing savings by combined

climate region estimated for both the BEPS data and the general method is quite

similar. However, the general method results in savings which tend to be about

50-100 percent greater than those estimated using the BEPS data. (In region

IV-B, along the Pacific Coast, the savings from the general method tend to be more than twice those based on the BEPS data.)

While additional BEPS data for larger houses are not available, simple linear

scaling of the AHR, ACR, and DHL was used to estimate annual kWh savings for

the larger heat pump sizes (18,000, 24,000, 36,000, and 48,000 Btu/h). (The

BEPS energy budgets implicitly assume proportionality of heating and cooling

requirements with house size. In fact, it is unlikely that cooling requirements will increase proportionately with heating requirements unless internal

and solar loads increase with house size). Comparison of these results with

the results based on the general method for the larger heat pump sizes shows

that the relative ordering of savings by climate region is quite similar in

all cases. In addition, the relative size of the savings for the two methods

is nearly identical to those reported for the 12,000 Btu/h heat pump size.

40
Table 16. Estimated Space Heating and Cooling Requirements for BEPS House3

Heating Region | I | II | III | IV | V | VI

AHR (106 Btu) I 2.0 | 5.0 | 12.5 I 25.0 | 43.0 | 7.0

DHL (kBtu/h) | 8 .5 | 12 .5 | 17 .5 | 24.0 | 33.0 | 11.5

Cooling Region | A | B| C| D| E| F

ACR (106 Btu) | 0 | 4.2 | 8 | 11.6 | 15.0 | 20.0

a 1200 sq. ft. one-story, single-family house.

41
Table 17. Incremental kWh Savings: BEPS-Based; 12,000 Btu/h Heat Pump

Combined Climate Region

(Btu/Wh)

| I-E | I-F | II-D i ii-e III-C

1

7.0 7.5 | 153 | 201 | 133 | 165 123

7.5 - 8.0 | 132 | 174 | 113 | 141 100

8.0 8.5 | 116 | 152 1 97 | 122 82

8.5 9.0 | 101 | 134 | 83 | 105 67

9.0 - 9.5 | 90 j 119 1 72 | 92 55

9.5 - 10.0 | 80 | 106 | 63 | 80 45

10.0 - 10.5 1 71 1 95 1 54 1 71 36

10.5 11 .0 ! 64 | 85 | 48 | 62 29

| III-D I IV-B

1

I IV-C

1

I V-B VI-B

7.0 7.5 1 157 1 97

r

| 134 1 95 75

7.5 - 8.0 | 130 1 74 | 106 1 72 61

8.0 — 8.5 | 109 1 57 1 85

1

1 56 49

8.5 9.0 91 | 44

V

I 69 1 43 39

9.0 - 9.5 I 76 1 34 | 56 | 33 31

9.5 - 10.0 | 64 1 25 1 45 1 25 24

10.0 - 10.5 1 54 1 18 1 36 j 18 19

10.5 ““ 11 .0 45 1 12 | 28

1

1 13 14

a Annual kWh usage for a heat pump with an SEER greater

than 8 .5 Btu/Wh is based on extrapolation of the

technical relationship between SEER and HSPF.

42
Table 18. Estimated Space Heating and Cooling Requirements

Corresponding to a 12,000 Btu/h Heat Pump a

Heating Region | I | II | III | IV | V | VI

AHR (106 Btu) | 4.9 | 11.0 | 19.5 | 31.4 | 40.9 | 22.4

DHL (kBtu/h) | 8 .4 | 11 .4 | 14 .5 | 18.2 | 19.4 | 10.5

1

1 I I 1 I Cooling Region | A | Bl C| D| E| F

ACR (106 Btu) | 0 | 7.2 | 12.0 | 18.0 | 25.2 | 31.2

a Based on general method described in section 4 .1

.

43
Table 19. Incremental kWh Savings: General Method; 12,000 Btu/h Heat Pump

Change in SEER

Combined Climate Region

(Btu/Wh) 1

| I-E

1

i i-f | II-D I II-E III-C

7.0 - 7.5

r

| 267 | 324 | 229 | 298 206

7.5 - 8.0 | 230 | 280 | 192 | 252 167

8.0 - 8.5 | 199

1

| 243 | 162 | 215 135

8.5 - 9.0

T~

| 174 | 213 | 137 | 184 109

9.0 - 9.5 | 153 | 188 | 116 | 158 87

9.5 - 10.0 I 134 | 166 | 99 | 136 69

10.0 - 10.5 | 119 | 148 | 84 | 118 54

10.5 - 11 .0 | 106

1

| 132 1 71 | 102 41

1

| III-D

1

I IVI IV-C I V-B VI-B

7.0 - 7.5

1

| 263 1 177 | 223 | 173 191

7.5 - 8.0 | 217 | 137 1 177 | 133 150

8.0 - 8.5 | 179

1

| 106 | 142 | 103 116

8.5 - 9.0

r

| 148 1 81 | 113 1 76 88

9.0 - 9.5 | 122 | 61 | 89 1 58 65

9.5 - 10.0 | 101 1 45 1 70 1 43 46

10.0 - 10.5 | 82 1 31 1 53 1 31 30

10.5 - 11 .0 1 67

1

1 18 | 39 1 21 16

a Annual kWh usage for a heat pump with an SEER greater

than 8.5 Btu/Wh is based on extrapolation of the

technical relationship between SEER and HSPF.

44
The results of the BEPS data analysis imply that the general method for

estimating annual kWh savings may be useful for estimating order-of-magnitude

savings in a consistent manner, but that these savings tend to be, on the average, about 75 percent larger than those based on the BEPS data. Since the BEPS

heating and cooling load data are based on more tightly insulated new houses

than the existing stock of housing and a more conservative operating profile,

it is not surprising that the general method estimates higher kWh savings than

those based on the BEPS data reported above.

j

j

I

45
5. DETERMINATION OF MAXIMUM COST-EFFECTIVE EFFICIENCY LEVELS

Determination of the economically optimal HSPF and SEER for a heat pump system

in a given installation requires that each of these efficiency measures be

increased up to the point where incremental life-cycle dollar savings equals

incremental costs, as shown in section 2, figure 1. There are a number of

important variables which determine economic optimality, including annual

heating and cooling requirements, kWh prices, time horizons, and discount

rates. Since many of these variables vary widely from place to place or person

to person, it is not possible to identify a universal level of HSPF and SEER

that can be considered to be optimal for the United States. However, the same optimality criterion can be used to determine maximum efficiency levels which

can be economically justified from a more generalized (or "social") viewpoint

in a prescribed percentile of installations. This requires that a social

discount rate and an incremental (i.e., new capacity) kWh price be established

either regionally or nationwide. The Department of Energy will likely establish such assumptions for analyses of other appliances and building energy

standards. Ideally, these same assumptions will be used for all analyses

pertaining to standards development. In addition, a useful system lifetime

and all costs associated with improvements in heat pump efficiency must be

quantified for the analysis.

In this section a generalized methodology will be demonstrated for establishing

maximum HSPF and SEER levels for heat pumps that are economically justified

in a given percentile of installations. Examples shown are based on the annual

kWh savings determined in section 3; an incremental electricity price of $0.05/

kWh, increasing in real terms at two percent per year; and a real discount rate

of four percent. A 10-year life is assumed for the heat pump with no compressor replacement during that time period. However, further analysis using

assumptions specified by DoE would be required to establish the reference

basis for actual standards development.

In table 20, incremental present-value, life-cycle dollar savings are shown

for a 36,000 Btu/h capacity (95°F outdoor temperature) heat pump. These

savings are calculated for 0.5 Btu/Wh increases in SEER (and corresponding

increases in HSPF) over a range of SEER's from 7.0 to 11.0 Btu/Wh for each of

the 10 climate regions identified in section 4. The savings are based on the

reductions in annual kWh usage shown in table 13. However, these kWh savings

have been adjusted to correspond more closely with the results derived from the

BEPS data analysis by dividing each value by 1.75, as suggested in section 4.2.

Thus, each data point shown in table 20 was calculated as: AkWh * IS = (Y77jJ( p )(upw )

where: IS

AkWh

1.75

incremental present-value life-cycle savings,

reduction in annual kWh usage (from table 13),

adjustment factor,

46
Table 20. Incremental Life-Cycle Savings Due to Increased

Efficiency: 36,000 Btu/h Heat Pump

Change in SEER

(Btu/Wh)

1

! Combined

1 Climate Region

1

| I-E

1

i i-f II-D II-E III-C

7.0 - 7.5

1

| $219 | $264 $209 $262 $217

7.5 - 8.0 | 190 | 229 179 226 184

8.0 - 8.5 | 167 | 201 156 196 158

8.5 - 9.0 | 147 | 178 136 172 136

9.0 - 9.5 | 131 | 158 119 152 118

9.5 - 10.0 ! in | 141 105 135 103

10.0 - 10.5 | 105 | 127 94 120 90

10.5 - 11 .0 1 95

1

1 115 84 107 79

1

| III-D

1

| IVB

1

1

1 IV-C

1

1

1 V-B

1

1

1 VI-B

1 7.0 -7.5

1

1 $261 | $229

1

1 $264

1

1 $249

1

1 $211

1 7.5 - 8.0 | 223 | 191 1 222 1 206 1 178

I 8.0 -8.5 | 192 | 161 1 188 1 171 1 152

I 8.5 -9.0 | 166 | 136 1 160 1 143 1 130

1 9.0 -9.5 | 145 j 116 1 137 1 121 1 112

1 9.5 - 10.0 | 127 ; 99 1 118 1 101 1 97

1 10.0 - 10.5 | 112 1 85 1 102 1 83 1 84

1 10.5 - 11 .0 | 99

1

73 1

1

89 1

1

70 1

1

73

47
P = price per kWh in base year (assumed to be $0.05), and

UPW* = modified uniform present worth factor (assumed to be 9.00^).

These incremental savings are shown graphically in figure 5, plotted at the

midpoint of each 0.5 Btu/Wh increase in SEER from 7.0 to 11.0 Btu/Wh. Note

that there is relatively little spread among the savings, considering the wide

range of geographic locations included. Note also that there is some shifting

in the relative ranking of climate regions (in terms of savings) as the SEER

is increased over the range shown. In general, climate regions with the lowest

annual cooling requirements and the highest annual heating requirements have

the lowest savings as the heat pump efficiency is increased at the upper end of

the SEER range examined. (This is because the empirical model used to relate

HSPF to SEER produces relatively small changes in HSPF at the upper end of the

SEER scale examined.)

Incremental heat pump cost data developed explicitly for higher efficiency

equipment have not yet been refined to the point where they can be used for

standards development purposes. In general, such data can be derived from two

distinct sources: (1) a statistical analysis of retail cost data and corresponding published efficiency data; and (2) a cost engineering analysis of the

design changes needed to improve heat pump efficiency.

Statistical analysis was attempted by the authors using retail cost data

collected by Oak Ridge National Laboratory for 41 heat pumps. ^ While a positive correlation between EER and cost is clearly established, the correlation

is too weak to provide a meaningful basis for estimating incremental costs.

While no cost engineering data specific to residential size heat pumps is

readily available, a technical report from the Carrier Corporation^ provides an engineering cost analysis of efficiency improvements to central air conditioners. Since the basic changes that were incorporated into the outdoor unit

in that study (increased heat exchanger size and improved compressor efficiency)

are the same changes that would likely be made to improve seasonal heat pump

efficiency, this cost data will be representative of heat pump improvements as well. These Carrier data, adjusted to represent the estimated change in 1980

retail cost (from 1978 estimates) for a 36,000 Btu/h central air conditioner,

10

1 1 .02 1 .02

UPW* = { ) 1 - f 1 ) = 9.00.

^0.02 n 4.04 J J

See Appendix A for derivation of UPW* calculation.

^ J. K. Martin and D. L. O'Neal, "An Energy and Cost Analysis of Residential

Heat Pumps in Northern Climates," Oak Ridge National Laboratory, Oak Ridge,

Tenn., 1980.

O f Unpublished technical report entitled "Analysis to Determine Minimum

Efficiency Levels," 1979, obtained through private communication.

48
Figure 5. Illustration of Incremental Savings and Costs of 0.5

Btu/Wh Increase in SEER: 36,000 Btu/h Heat Pump

49
are shown for 0.5 Btu/Wh increases in SEER from 7.5 to 9.5 Btu/Wh in Table 21

These data are presented for purposes of example only and are not intended to

be used for actual standards development purposes.

Table 21. Estimated Incremental Retail Costs (1980 dollars)

for a 36,000 Btu/h Heat Pumpa

SEER Incremental

(Btu/Wh) Cost

7.5 - 8.0 $ 27

8.0 - 8.5 54

8.5 - 9.0 105

9.0 - 9.5 153

a Based on a Carrier Corporation technical report

obtained through private correspondence. 1978

costs were increased to 1980 costs using a GNP

deflator change of 19.2 percent.

These incremental costs were plotted on figure 5 as curve "IC" in order to

allow visual comparison between incremental costs and savings. The maximum

cost-effective level of SEER corresponding to the assumptions made above is

found at the intersection of the incremental cost curve and the incremental

savings curve for each climate region. In this example, the points of intersection range from 8.9 Btu/Wh for the region with the lowest savings (VI-B) to

9.25 Btu/Wh for the region with the highest savings (I-F). This remarkably

narrow range is due to both the relatively narrow range of kWh savings by

region and the steepness of the incremental cost curve. Since the technologically feasible SEER for a new heat pump system is likely to be higher than

10.0 Btu/Wh, it is unlikely that the maximum level of efficiency that can be

justified economically will reach this level. Thus the economic constraint

would likely prevail in the development of minimum performance standards for

heat pumps.

Since the percentage of heat pump sales can be determined for each climate

region (see table 9 for 1977 figures), the cumulative percentage of sales which

fall into regions where a given efficiency level is cost effective under the

conditions assumed can be calculated. For example, suppose that a heat pump

1 Indoor coil size was held constant in order to assure adequate

dehumidification performance. However, increasing the size of the indoor

coil can provide a less costly means of increasing HSPF and SEER than shown

in table 21. In addition, improved defrosting procedures, and two-speed or variable speed compressors may also lead to lower incremental costs for

higher heat pump performance.

50
Figure 5. Illustration of Incremental Savings and Costs of 0.5

Btu/Wh Increase in SEER: 36,000 Btu/h Heat Pump

49
are shown for 0.5 Btu/Wh increases in SEER from 7.5 to 9.5 Btu/Wh in Table 21

These data are presented for purposes of example only and are not intended to

be used for actual standards development purposes.

Table 21. Estimated Incremental Retail Costs (1980 dollars)

for a 36,000 Btu/h Heat Pump a

SEER Incremental

(Btu/Wh) Cost

7.5 - 8.0 $ 27

8.0 - 8.5 54

8.5 - 9.0 105

9.0 - 9.5 153

a Based on a Carrier Corporation technical report

obtained through private correspondence. 1978

costs were increased to 1980 costs using a GNP

deflator change of 19.2 percent.

These incremental costs were plotted on figure 5 as curve "IC" in order to

allow visual comparison between incremental costs and savings. The maximum

cost-effective level of SEER corresponding to the assumptions made above is

found at the intersection of the incremental cost curve and the incremental

savings curve for each climate region. In this example, the points of intersection range from 8.9 Btu/Wh for the region with the lowest savings (VI-B) to

9.2 5 Btu/Wh for the region with the highest savings (I-F). This remarkably

narrow range is due to both the relatively narrow range of kWh savings by

region and the steepness of the incremental cost curve. Since the technologically feasible SEER for a new heat pump system is likely to be higher than

10.0 Btu/Wh, it is unlikely that the maximum level of efficiency that can be

justified economically will reach this level. Thus the economic constraint

would likely prevail in the development of minimum performance standards for

heat pumps.

Since the percentage of heat pump sales can be determined for each climate

region (see table 9 for 1977 figures), the cumulative percentage of sales which

fall into regions where a given efficiency level is cost effective under the

conditions assumed can be calculated. For example, suppose that a heat pump

1 Indoor coil size was held constant in order to assure adequate

dehumidification performance. However, increasing the size of the indoor

coil can provide a less costly means of increasing HSPF and SEER than shown

in table 21. In addition, improved defrosting procedures, and two-speed or variable speed compressors may also lead to lower incremental costs for

higher heat pump performance.

50
efficiency standard requires SEER to be no less than 9.1 Btu/Wh (with

corresponding HSPF determined for a specified operating profile as outlined in

section 3).* The standard would then be cost- justified under the conditions

assumed in regions IV-C, III-D, II-E, and I-F, or a total of 51 percent of

sales (based on 1977 sales data tabulated in table 9). As the minimum SEER

and corresponding HSPF are reduced, the percentage of sales for which the standard will be cost- justified will increase. At an SEER of 8.9 Btu/Wh the mini- mum standard would be cost effective under the conditions assumed for 99 percent

of all sales.

It must be stressed that the determination of cost effectiveness in each region

is based on a number of assumptions which may not be valid for each individual

installation. Conservative estimates of annual heating and cooling requirements will reduce the number of installations where savings are overestimated.

However, the use of kWh prices attributable to new generating capacity and a social discount rate will result in present-value savings that may be greater

than can be anticipated by many individual homeowners.

In addition, a number of other economic factors must be considered in minimum

standards development that fall outside the scope of this report. These

include the economic impact of the standard on manufacturers as well as consumers, lessening of product performance, the effect on industry competition,

the impact on export and import shipments, and the magnitude of potential

energy savings and their significance in meeting national energy conservation

goals

.

1 Using table 6, which provides the HSPF corresponding to specified SEER levels

for a 36,000 Btu/h heat pump in each heating climate, the HSPF corresponding

to an SEER of 8.75 Btu/Wh can be determined for any heating region. For

example, if region III were specified in evaluating heat pump performance,

the HSPF of 2.144 would correspond to an SEER of 8.75 Btu/Wh.

51
6. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FURTHER RESEARCH

6.1 SUMMARY

The Department of Energy has been mandated by Congress to develop energy

efficiency standards for new heat pumps which will result in the maximum

improvement in energy efficiency that is both technologically feasible and

economically justified. The purpose of this report is to provide a methodology

for determining, in a life-cycle cost context, the maximum improvement that is

economically justified. In general, economic justification is likely to con- strain a minimum standard from achieving the level of efficiency that is

technologically feasible.

In section 2, economic criteria for establishing an optimal efficiency level

for an appliance were outlined. Since the optimal efficiency level will vary

significantly as a function of a number of key factors, including climate,

operating profile, projected energy prices, and discount rate, it is impossible

to establish an economically optimal basis for minimum standards development.

However, these same economic criteria can be used to determine minimum efficiency levels that can be cost- justified from a national (or societal)

viewpoint in an estimated percentage of installations.

In section 3 the dual nature of heat pump efficiency is explored. Since the

efficiency in the heating mode (HSPF) is measured differently than the efficiency in the cooling mode (SEER), separate efficiency ratings must be established. However, these efficiency ratings are technically interrelated and

this interrelationship is quantified using a statistical analysis of currently

available heat pump units. In section 4, incremental annual energy savings were calculated in ten different climate regions for 0.5 Btu/Wh increases in

SEER and corresponding increases in HSPF.

In section 5, the benefit-cost methodology for establishing maximum levels of

heat pump efficiency that can be cost justified is demonstrated. However, the

results of that analysis are for purposes of example only; certain key assumptions regarding energy costs, discount rates, useful appliance life, and incremental heat pump costs would need to be defined by the Department of Energy to

be consistent with the other appliance efficiency programs that they

administer

.

6 .2 CONCLUSIONS

A number of conclusions can be drawn from this report that may have direct

relevance to minimum standards development for heat pumps. (1) The technical

interrelationship between steady-state heat pump performance in the heating

and cooling modes can be quantified to a degree that is quite satisfactory

from a statistical standpoint. This statistical relationship is based on the

entire list of commercially available residential air-to-air heat pumps certified by the Air-Conditioning and Refrigeration Institute, edited to remove identical units with different brand names. This statistical relationship

included heat pumps having energy efficiency ratios (EER at 95°F) ranging from

a low of 6.0 to a high of 8.55 Btu/Wh. However, the relationship estimated

52
from this data base may not be accurate outside this range. Moreover, the fact

that the highest efficiency heat pump listed has an EER of 8.55 Btu/Wh would

imply that several years will likely be required before the industry could

comply with a minimum EER requirement higher than that point. As more units

are added to the list, especially units with an EER greater than 8.0 Btu/Wh,

the statistical relationship should be recalculated.

(2) A given improvement in EER generally results in a significantly smaller

increase in heating efficiency, especially in the colder regions of the United

States. As a result, the annual kWh savings from improved heat pump design in

those colder climates tend to be smaller than the kWh savings realized in

regions with substantial air conditioning requirements. Research in improving

heat pump performance in the heating mode relative to the cooling mode may be

useful in developing heat pumps for northern climates.

(3) In general, the annual kWh savings due to a given increase in heat pump

efficiency tend to be reasonably similar in most regions of the United States.

The two regions where kWh savings are lowest are the coastal areas of Washington State and extreme southern California. The highest savings are in Florida

and along the Gulf Coast. In the examples of economically justified maximum

efficiency levels calculated in this report, there is relatively little variation by climate region. The selection of projected energy prices, discount

rate, useful life, and incremental heat pump costs will likely have considerably more impact on the final outcome of the analysis than regional

considerations .

(4) The current testing and rating procedures used to determine annual heating

and cooling requirements and design heating requirements for a typical heat

pump installation will likely significantly overstate these parameters in new,

better insulated and more conservatively operated houses. As a result, the

kWh savings calculated using these general methods will likely be overstated

as well.

(5) The increase in heating efficiency due to a given increase in cooling

efficiency tends to increase significantly as output capacity is increased.

Thus the maximum level of heat pump efficiency that can be economically justified may be greater for larger capacity heat pumps than for the smaller sizes.

This may encourage the use of larger heat pumps for use in northern climates

than would be selected based on cooling requirements alone.

6 .3 RECOMMENDATIONS FOR FURTHER RESEARCH

Several key areas of research become apparent in establishing a reference basis

for minimum standards development. These largely revolve around the problem of

calculating expected annual kWh savings that correspond to given increases in

heating and cooling performance. More work is required to extend the statistical model of heating and cooling interdependence beyond an EER rating of 8.5

Btu/Wh. An improved methodology must also be developed for estimating annual

heating and cooling requirements and design heating and cooling loads since

these are critical determinants of kWh usage (and thus savings) and since they

appear to be overestimated by the testing and rating procedures for tightly

53
constructed, BEPS-type houses. Another area of significant concern is the

development of a reliable data base of incremental heat pump costs for all

sizes of heat pumps. This is a major determinant of maximum cost-justified

improvements in heat pump efficiency for which little data are currently

available

54
REFERENCES

Carrier Corporation, unpublished technical report entitled "Analysis to

Determine Minimum Efficiency Levels," 1979.

Directory of Certified Unitary Air-Conditioners, Air-Source Unitary Heat

Pumps, Sound-Rated Outdoor Unitary Equipment, and Central System Humidifiers , January 1 - June 30, 1980, Air-Conditioning and Refrigeration Institute,

Arlington, Va., 1980.

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 , NBSIR 77-1271, National Bureau of Standards,

Washington, D.C., April 1978.

Marshall, Harold E. and Ruegg, Rosalie T., Simplified Energy Design Economics , NBS SP 544, National Bureau of Standards, Washington, D.C., January 1980.

Martin, J .K . and O'Neal, D.L., "An Energy and Cost Analysis of Residential Heat

Pumps in Northern Climates," Oak Ridge National Laboratory, Oak Ridge, Tenn.,

1980.

McConnell, R.R., Tobias, J .R . and Nelson, L.W., "Reducing Energy Consumption

During the Cooling Season," ASHRAE Journal , June 1976.

Parken, Walter H., Kelly, George E., and Didion, David A., Method of Testing,

Rating and Estimating the Heating Seasonal Performance of Heat Pumps , NBSIR

80-2002, National Bureau of Standards, Washington, D.C., April 1980.

Pindyck, Robert S. and Rubinfeld, Daniel L., Econometric Models and Economic

Forecasts , McGraw-Hill Book Company, New York, 1976.

Thomas, Steven B., Tree, David R., and Goldschmidt, Victor W., "A Study of the

Prediction and Measurement of Air Conditioning System Seasonal Performance

Characteristics - Compilation of Data and Analysis of Test Procedure for SEER,"

Ray W. Herrick Laboratories, Purdue University, Lafayette, Ind., sponsored by

the Air-Conditioning and Refrigeration Institute, 1979.

U .S . Department of Energy, "Advance Notice of Proposed Rulemaking and Notice

of Public Meetings Regarding Energy Efficiency Standards for Nine Types of

Consumer Products," Federal Register , Vol. 44, No. 1, January 2, 1979.

U ,S . Department of Energy, "Test Procedures for Central Air Conditioners,

Including Heat Pumps," Department of Energy Final Rule, Federal Register , Vol. 44, No. 249, December 27, 1979.

55
APPENDIX A

DERIVATION OF MODIFIED UNIFORM PRESENT WORTH FACTORS

One of the most critical aspects of a life-cycle cost analysis is that of

evaluating a flow of future benefits or costs associated with some design

change in present-value terms. In general, this requires that future benefits

or costs be discounted to present value using an appropriate discount rate.

The purpose of this appendix is to show the derivation of modified uniform

present worth (UPW*) factors that can be used to evaluate the present value of

energy savings over the life of an appliance.

Dollar-valued energy savings can be calculated for each year over the life of a design modification and discounted to present value. However, if the physical

energy savings are assumed constant from year to year, it is generally easier

to calculate a modified uniform present worth factor which, when multiplied by

the annual energy savings calculated at the cost of energy in the initial time

period, will produce the same results.

That is:

present value \ / annual \ / price of energy

\

life-cycle

J = UPW x I energy 1 x I at initial time

savings

j

l savings

j

\ period

J The UPW* factor is a function of the life over which the savings are expected

to be realized, the discount rate, and the rate at which energy prices are expected to increase over the life of the modification. If the discount rate

and the rate of energy price escalation are constant over the life of the

appliance the modified uniform present worth factor can be calculated using:

1 + P1 + D'

y

where L = the lifetime of the appliance (in years),

P = the annual rate of price increase for energy, and

D = the discount rate.

(A-l

)

Note that if P = D, the increase in fuel prices just offsets the discount rate

so that the UPW* is equal to the lifetime in years, i.e., the savings are simply added each year at initial year energy prices.

* The term "modified" is used to describe a uniform present worth factor which

incorporates an increasing cash flow over time rather than a conventional UPW

factor which is based on a constant cash flow over time.

56
(A-2)

If P does not equal D, equation A-l can be reformulated as:

UPW = c

1 + P

D - P

) (l - ( 1 + P

1 + D

n

Alternatively, if the rate of energy price increase is not constant over the

life of the appliance, but is expected to change n-1 times at specified points

in time, the UPW* can be evaluated as

where

n 1+p . 1+p . 1+p . ^

uw )

n = number of time intervals,

T-£ = length of time interval i,

Tj = length of time interval j (Tq =0), and

Pj = rate of price increase in time interval j (Pq = 0).

(A-3)

57
SBS-114A (REV. 2-8C) U.s. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date NBSIR 81-2241

ENGINEERING - ECONOMIC ANALYSIS OF IMPROVED HEAT PUMP PERFORMANCE FOR

MINIMUM STANDARDS DEVELOPMENT

5. AUTHOR(S)

Stephen R. Petersen, Kimberly A. Barnes, and George E. Kelly

6. PERFORMING ORGANIZATION (If joint or other than NBS. see in struction s) NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8 . Type of Report & Period Covered

Final

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

U.S. Department of Energy

Washington, D.C. 20461

10. SUPPLEMENTARY NOTES

J 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

bi bl iography or literature survey, mention it here)

This report provides a methodology and seasonal performance data that could be

used in the development of a reference basis for minimum efficiency standards

for heat pumps that are economically justified on a life-cycle basis. Criteria

for economic optimization are outlined. The methodology used to compute seasonal

heating and cooling performance ratings and the annual energy savings resulting

from efficiency improvements, by climate region, is detailed. The interdependence

between efficiency ratings in the heating and cooling modes is explored using

statistical analysis. An example of the procedure for determining maximum costeffective efficiency levels is demonstrated for a 36,000 Btu/h heat pump.

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

Energy efficiency standards; engineering-economic analysis; heat pump; mechanical

equipment efficiency ratings; minimum efficiency standards; space cooling requirements: space heating requirements.

13. AVAILABILITY

fy-yj Unlimited

[ j For Official Distribution. Do Not Release to NTIS

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

20402.

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

14. NO. OF

PRINTED PAGES

85

15. Price

$9.5q

USCOMM-DC 6043-P80