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Economic Efficiency in the Sizing

of Residential Heat Pumps

I

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Economics and Regulatory Technology Division

Washington, DC 20234

July 1981

Prepared for: Office of Buildings and Community Systems

U.S. Department of Energy

hington, DC

NBSIR 80-2176

ECONOMIC EFFICIENCY IN THE SIZING

OF RESIDENTIAL HEAT PUMPS

Joel Levy

Stephen R. Petersen

MAR 4 1982

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U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Economics and Regulatory Technology Division

Washington, DC 20234

July 1981

Prepared for; Office of Buildings and Community Program

U.S. Department of Energy

Washington, DC

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director
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PREFACE

The work in this report was conducted by the Applied Economics Group of the

Building Economics and Regulatory Technology Division, in the Center for

Building Technology, National Engineering Laboratory, at the National Bureau of

Standards. This effort was supported by the Department of Energy (DoE) under

Interagency Agreement No. 77-A-01-6010 , Task Order A008-BCS.

iii
ABSTRACT

This report provides a methodology for determining the optimal heat pump size,

in terms of heating output capacity, for residential installations having

annual heating requirements significantly greater than annual cooling requirements. The optimal size heat pump is defined as the size for which total present value, life-cycle heating and cooling costs (including equipment costs) are minimized. Incremental energy savings from increasing the output capacity

of the heat pump are calculated using hourly simulation models of heat pump

and building performance developed at the National Bureau of Standards (NBS).

The dollar value of the incremental savings, in present -value, life-cycle

terms, is then calculated and compared with incremental costs to determine

the optimal heat pump size. A base case analysis of an 1800 square-foot house

in the Chicago climate shows that a slightly larger heat pump size than would

typically be selected for air conditioning purposes alone is optimal for the

assumptions specified. A number of sensitivity analyses are performed to show

the effects of changes in load size, degradation coefficients, power utilization efficiency, economic assumptions and geographic location on the optimal

heat pump size.

Key words: Benefit-cost analysis; energy conservation; equipment selection;

equipment sizing; heat pump; life-cycle costs.

iv
TABLE OF CONTENTS

Page

LIST OF TABLES vi

LIST OF FIGURES ix

SI CONVERSION x

1. INTRODUCTION 1

1.1 Purpose and Scope 1 1.2 Technical Background 2

1 .3 Organization A

2. MODELING HEAT PUMP PERFORMANCE 5

2 .1 Heating Mode 5 2.2 Cooling Mode 9

3. DETERMINATION OF AN OPTIMAL HEAT PUMP SIZE 13

3.1 Selection of Optimal Size Equipment 13

3.2 Energy and Dollar Savings as a Function of

Heat Pump Size lA

3.3 Heat Pump Costs as a Function of Size and the

Selection of an Optimal Size Heat Pump 21

A. SENSITIVITY OF OPTIMAL HEAT PUMP SIZE TO CHANGES IN

BASE CASE ASSUMPTIONS 2

A

A.l Effects of Changes in Load Size 2A

A. 2 Effects of Changes in Degradation Coefficients 2A

A. 3 Effects of Improvements in Steady-State

Efficiency 26

A. A Effects of Alternative Heat Pump Costs 26

A. 5 Effects of Alternative Energy Price Projections,

Discount Rates, and Life Expectancies 29

A. 6 Effects of Geographic Location 31

A. 6.1 Optimal Size Heat Pump for Base House 31

A. 6.

2

Optimal Size Heat Pump for House with

Increased Heating and Cooling Loads 37

5. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FURTHER

RESEARCH A3

REFERENCES A5

APPENDIX A Listing of Computer Program for Heat Pump Sizing

Analysis A-1

APPENDIX B Annual Heating and Cooling Energy Utilization

by Heat Pump Size; Sensitivity Analysis B-1

V
LIST OF TABLES

Table Page

3.1 Heat Pump Performance Characteristics Used in Base

Case Analysis 17

3.2 Physical Description of Base House 18

3.3 Annual Heating and Cooling Energy Utilization by Heat

Pump Size; Base Case (Chicago) 19

3.4 Energy and Dollar Savings Data by Heat Pump Size; Base Case

(Chicago) 19

3.5 Heat Pump Cost Data, Unadjusted 22

3.6 Heat Pump Cost Data, Adjusted 22

4.1 Energy and Dollar Savings Data by Heat Pump Size; Chicago;

Increased Loads 25

4.2 Energy and Dollar Savings Data by Heat Pump Size; Chicago;

Base Loads; Cp=0.925, Cjj=0.15 25

4.3 Energy and Dollar Savings Data by Heat Pump Size; Chicago;

Base Loads; Cp=0.850, Cq=0.25 27

4.4 Energy and Dollar Savings Data by Heat Pump Size; Chicago;

Base Loads; Cp=0.850, Cp=0.15 27

4.5 Energy and Dollar Savings Data by Heat Pump Size; Chicago;

Base Loads; Power Input Reduced by 10 Percent 28

4.6 Adjustment Factors for Alternative Economic Assumptions 30

4.7 Annual Energy Requirements for Base House 32

4.8 Energy and Dollar Savings Data by Heat Pump Size; Seattle;

Base Loads 33

4.9 Energy and Dollar Savings Data by Heat Pump Size; Atlanta;

Base Loads 33

4.10 Energy and Dollar Savings Data by Heat Pump Size; Washington,

D.C.; Base Loads 34

4.11 Energy and Dollar Savings Data by Heat Pump Size; Kansas

City; Base Loads 34

vi
LIST OF TABLES (Cont.)

Table Page

4.12 Energy and Dollar Savings Data by Heat Pump Size: Boston;

Base Loads 35

4.13 Energy and Dollar Savings Data by Heat Pump Size: Madison;

Base Loads 35

4.14 Energy and Dollar Savings Data by Heat Pump Size:

Minneapolis; Base Loads 36

4.15 Energy and Dollar Savings Data by Heat Pump Size: Seattle;

Increased Loads 36

4.16 Energy and Dollar Savings Data by Heat Pump Size: Atlanta;

Increased Loads 39

4.17 Energy and Dollar Savings Data by Heat Pump Size: Washington,

D.C.; Increased Loads 39

4.18 Energy and Dollar Savings Data by Heat Pump Size: Kansas

City; Increased Loads 40

4.19 Energy and Dollar Savings Data by Heat Pump Size: Boston;

Increased Loads 40

4.20 Energy and Dollar Savings Data by Heat Pump Size: Madison;

Increased Loads 41

4.21 Energy and Dollar Savings Data by Heat Pump Size:

Minneapolis; Increased Loads 41

B.l Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Chicago; Increased Loads; Cp=0.925, Cq=0.25 B-2

B.2 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Chicago; Base Loads; Cp=0.925, Cj)=0.15 B-2

B.3 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Chicago; Base Loads; Cp=0.850, Cp=0.25 B-3

B.4 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Chicago; Base Loads; Cp=0.850, Cq=0.15 B-3

B.5 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Chicago; Base Loads; Power Input Reduced by 10

Percent B-4

vii
LIST OF TABLES (Cont.)

Table Page

B.6 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Seattle; Base Loads B-4

B.7 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Atlanta; Base Loads B-5

B.8 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Washington, D.C.; Base Loads B-5

B.9 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Kansas City; Base Loads B-6

B.IO Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Boston; Base Loads B-6

B.ll Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Madison; Base Loads B-7

B.12 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Minneapolis; Base Loads B-7

B.13 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Seattle; Increased Loads B-8

B.14 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Atlanta; Increased Loads B-8

B.15 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Washington, D.C.; Increased Loads B-9

B.16 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Kansas City; Increased Loads B-9

B.17 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Boston; Increased Loads B-10

B.18 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Madison; Increased Loads B-10

B.19 Annual Heating and Cooling Energy Utilization by Heat Pump

Size: Minneapolis; Increased Loads B-11

vili
LIST OF FIGURES

Figure Page

1 Balance Point of Heat Pump as a Function of Heating

Output Capacity 3

2 Output Capacity of Heat Pump in Heating Mode as a Function of Outdoor Temperature 7

3 Output Capacity of Heat Pump in Cooling Mode as a Function of Outdoor Temperature 11

4 Life-Cycle Heating-Related Costs as a Function of

Output Capacity 15

ix
SI CONVERSION

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

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 ft2 = 0.092903 m2

Volume: 1 ft^ = 0.028317 m3

Fluid Capacity: 1 gallon (gal) = 3.78541 liters (L)

Temperature: 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 Ib/ft = 1.48816 kg/m

Mass per unit

Area: 1 lb/ft2 = 4.88243 kg/m^

Mass per unit

V olume

1 lb/ft3 = 16.0185 kg/m3

Energy: 1 Btu = 1.05506 kilojoules (kJ)

Heat Flow Rate: 1 Btu/h = 0.293071 Watt (W)

Specific Heat: 1 Btu/(lb)(°F) = 4.1868 kJ/(kg)(K)

U-value: 1 Btu/(ft2)(h)(°F) = 5.67826 W/(m2)(K)

R-value: 1 (ft2)(h)(°F)/Btu = 0.176110(m2)(K)/W

X
1 . INTRODUCTION

1.1 PURPOSE AND SCOPE

The heat pump has become increasingly popular as a residential space heating

and cooling system since the oil embargo in the early 1970' s. In general,

heat pumps are significantly more energy efficient than electric resistance

heaters, although they have a considerably higher initial cost. Occasional

curtailments in the availability of new natural gas hookups, improved reliability of heat pump components, their ability to function as central air con- ditioners, a general trend toward electric heating in new houses, and rising

electricity prices have all contributed toward the increasing popularity of

the heat pump. While in 1965 only 20 percent of new single-family houses were heated with electricity and 25 percent had central air conditioning^, in 1978

approximately 50 percent had electric heat and 60 percent had central air

conditioning^. The use of heat pumps rose from insignificant levels in the

I960' s to 25 percent of new housing in 1978.2

The heating and cooling output capacities of a heat pump are closely related

due to the dual nature of the system. Traditionally, heat pumps have been

sized to properly match design cooling loads and indeed this requirement provides a minimum sizing constraint. Heating loads in excess of the heating

output capacity can be satisfied using supplemental electric resistance heating. However, this sizing procedure has been questionable from an economic

standpoint in geographic regions where annual heating requirements are significantly greater than annual cooling requirements. As will be demonstrated in

this report, the seasonal heating efficiency of a larger size heat pump is

generally somewhat greater, and operating costs somewhat lower, than of a smaller size heat pump in colder than average climates. Thus the purpose of

this report is to identify factors which make the use of a larger size heat

pump cost effective on a life-cycle basis and to determine the optimal size

heat pump from a life-cycle cost minimization viewpoint.

The scope of this report is limited to analysis of air-source, one-speed heat

pumps in the 2.0 to 5.0 ton^ output range. Supplementary electric resistance

heating is assumed to be used to assure a proper match with heating requirements.

Heating and cooling loads for a residential building and corresponding system

efficiencies are calculated hourly for an entire year in order to determine the

^ Bureau of the Census, Characteristics of New One-Family Homes: 1974 , Construction Reports - Series C25, U.S. Department of Commerce,

Washington, D.C., 1975.

2 Bureau of the Census, Characteristics of New Housing; 1978 , Construction

Reports - Series C25-78-13, U.S. Department of Commerce, Washington, D.C.,

1978.

^ One ton of heating or cooling output equals 12,000 Btu per hour (Btu/hr).

In this report the heating output capacity is designated at 47 °F outdoor

temperature.

1
!

annual energy use for each heat pump size examined. Some preliminary guidelines

for the optimal sizing of residential heat pump systems are developed. However,

more research will be required in order to provide a comprehensive set of guidelines that can be validated for field use.

1.2 TECHNICAL BACKGROUND

Basically, a heat pump is an air conditioner which can operate in a reverse mode in order to "pump" heat from the outside air to the inside air even though the outdoor temperature is lower than the indoor temperature. (While

the outside air may be cold relative to the inside air, it is still "warm"

relative to absolute zero.) The output capacity of a heat pump, in terms of

thermal units per hour, depends in part on the indoor-outdoor temperature

differential. For any given indoor temperature, the colder the outdoor temperature, the lower the heating capacity of the heat pump. Similarly, the higher

the outdoor temperature, the lower the cooling output capacity. The ratio of

the heat output to (or removed from) the conditioned space to the electrical

input, when expressed in common thermal units, is called the coefficient of

performance (COP). For any given indoor temperature, the lower the outdoor

temperature, the lower the COP in the heating mode. Similarly, the higher

the outdoor temperature, the lower the COP in the cooling mode.

Since the space heating requirements of a house increase as the outdoor

temperature decreases (given some Indoor temperature and fixed internal and

solar heat gains), the heat pump will not be able to satisfy all of the heating

requirements below some outdoor temperature. The outdoor temperature at which

the heat pump output just meets the space heating requirements is called the

"balance point" of the heat pump. This balance point concept is shown in

figure 1. In this figure the hourly heating load of a given house and the

hourly output capacity of a given heat pump system are shown on the vertical

axis as a function of the outdoor temperature on the horizontal axis. The

intersection of these two curves, Tg;^, determines the balance point for this

system. To the right of this point, the difference between heating requirements and output capacity must be provided by a supplementary heating system.

This supplementary system is usually made up of electric resistance strip

heaters in the indoor air handler. These strip heaters are less efficient,

and thus more costly in terms of electric energy per unit of heat output, than

the heat pump itself for outdoor temperatures above approximately -20°F. At

temperatures below -20°F the heat pump should be shut off and the entire heating load will be met by the supplementary system.

The balance point of a given heat pump, and thus the amount of supplementary

heat required, is a function of the rated output capacity of the heat pump at

any given outdoor temperature. Increasing the capacity of a heat pump for a given house will result in less supplementary heating, since the balance poiat

will be significantly lower. This is demonstrated in figure 1, where a secoid

heat pump of twice the capacity of the first is shown together with the

unchanged space heating requirements of the same house. T>ie balance point has

been reduced from Tg]^ to Tg2* No supplementary heating is required at all

between Tg]^ and Tg2

• In addition, those heating loads occurring below Tg2 can

be satisfied with less supplementary heat since the output of the larger heat

pump is greater, reducing seasonal kWh requirements further.

2
THERMAL

UNITS

Figure 1. Balance Point of Heat Pump as a Function of Heating Output Capacity

3
The actual seasonal reduction in kWh requirements, relative to electric

resistance heating, resulting from a heat pump in any given installation will

depend upon the heating load of the house, the performance characteristics of

the heat pump system used, and the local climatic conditions during the heating

season. Each of these factors will be explored in this report, using hourly

simulation data in all cases. In addition, the operation of the heat pump in

the cooling cycle will be considered, since oversizing of the heat pump with

respect to cooling loads will increase kWh consumption in the cooling mode and

may reduce its ability to control indoor humidity. While the Increase in kWh

consumption requirements in the cooling mode is estimated in this report, the

potential degradation of humidity control has not been quantified.

1.3 ORGANIZATION

This report has five sections. This introduction is section 1. In section 2, a model for simulating heat pump performance in both the heating and cooling

modes on an hourly basis is described. This model is based on the NBS heat

pump test procedure [3,5] and requires computer support for execution if more

than a few hours of performance are to be simulated. (The computer program

used to calculate the heat pump performance for each size examined is described

in Appendix A.) Section 2 can be skipped if the reader wishes to proceed

directly to the actual analytical results in sections 3 and 4.

In section 3 the procedure for determining the optimal heat pump size is

developed and demonstrated. The base case example is for a heat pump of known

performance characteristics in an 1800 square-foot house located in Chicago.

The heating and cooling loads for this house are calculated using the National

Bureau of Standards Load Determination Program, NBSLD [4]

,

and Test Reference

Year, TRY [6]

,

climate records. Specific assumptions are made as to the cost

per kWh and the incremental costs of heat pumps in the 2.0 to 5.0 ton range.

In section 4, sensitivity analyses are made with respect to load sizes,

degradation coefficients, steady-state efficiency characteristics, energy price

projections, heat pump costs, and climate location. In section 5, a summary,

conclusions, and recommendations for future research are provided.

4
2. MODELING HEAT PUMP PERFORMANCE

In this section the equations used to model the energy utilization of a heat

pump are presented. These equations are based on testing and rating procedures

developed at NBS by Parken, Kelly, and Didion [3,5] . Energy utilization is

modeled hourly based on the outdoor temperature and the coincident heating or cooling load in that hour. Energy utilization is then integrated for both

heating and cooling operations over the entire year. The equations for modeling

heat pump performance in the heating mode are modeled first, followed by those

for the cooling mode.

2.1 HEATING MODE

In this report, the known heat pump characteristics used in simulating the

heating performance of a typical one-speed heat pump on an hourly basis are the

f ollowingl

:

Output Capacity at 17 °F (CAP17) in Btu/hr,

•• 47 °F (CAP 47) in Btu/hr,

Input Power " 17°F (P0W17) in kW,

'* " 47 °F (POW47) in kW,

a coefficient of degradation (less than 1.0) resulting from cycling

when heating load is less than heat pump capacity (Cp), and a coefficient of degradation due to frosting (Cp).

In addition, it is convenient to have symbols for capacity at 35°F (CAP35), and

power at 35°F (POW35) . These values are calculated in terms of the heat pump

characteristics given above by linear interpolation and (in the case of capacity) adjustment by Cp. Thus,

CAP35 = (0.4 * CAP17 + 0.6 * CAP47) * Cp, and

POW35 = (0.4 * P0W17 + 0.6 * POW47).

The procedure for modeling the hourly energy utilization of a heat pump is based

on three elementary functions of the outdoor temperature in hour j (Tj) and the

corresponding hourly heating load of the house (HL^). These three functions

determine the output capacity (in Btu) , the power input (in Watts), and the

part-load factor of a heat pump in each hour that a heating load exists.

(a) Capacity Function. The capacity function, denoted CAP(Tj), is piecewise

linear! At Tj = 17°F the function has a change in slope, but is continuous.

At Tj = 45°F the function has a change in slope and a discontinuity. The

parameters used in defining the function are;

^ These characteristics are typically rated by the manufacturer using a standardized testing and calculation procedure.

5
CAP17

,

Ai = [CAP47 - CAPl7]/30, and

Bi = [CAP35 - CAP17]/18.

The domain of the function, T j , is divided into three intervals:

for Tj £ 17°F, CAP(Tj) = CAP17 + A^ (Tj-17°F),

for 17°F < Tj _< 45°F, CAP(Tj) = CAP17 + (Tj-17°F), and

for Tj > 45°F, CAP(Tj) = CAP17 + A^ (Tj-17°F).

The functional relationship between capacity in the heating mode and Tj is

shown in figure 2 for specified values of CAP17 , CAP 47 , and Cp.

(b) Part-Load Factor . The power function is defined in terms of the part-load

factor for heating (PLF^^). Thus the latter function is described first.

For the outdoor temperature in hour j (Tj), the heating output capacity of a given heat pump (CAP(Tj)) can be calculated using the formula in paragraph

(a) above. Now define for hour j the heating load factor (Xj):

HL.— or 1.01 whichever is less,

J CAP(Tj)

where HLj is the heating load in Btu for a given house in hour j.

The part-load factor for heating in hour j is then defined in terms of the

known parameter Cp (which will always be less than one) and the value of Xj:

PLFh(Xj) = 1 - Cd (1-Xj).

The part-load factor is used only when Tj > 45°F.^

(c) Power Function . The power function (POW(Tj)) is continuous and piecewise

linear for Tj £ 45*F. The function undergoes a change in slope at Tj = 17°F;

for Tj > 45°F power is a nonlinear function of Tj and PLF^^(Xj).

The parameters used in defining the function POW(Tj) are:

P0W17

,

A2 = [POW47 - P0W17]/30,

B2 = [POW35 - P0W17]/18, and

PLFv,(Xj).

The domain of the power function is determined by both the outdoor temperature

(Tj) and the heating load factor (Xj), the second component entering only when

^ In the final version of the testing and rating procedure, the part-load

factor was extended to outdoor temperatures below 45°F as well. However, the

analysis in this report was completed before the testing and rating procedures

were finalized.

6
OUTPUT

CAPACITY

|Btu/hr)

OUTDOOR TEMPERATURE TF)

Figure 2. Output Capacity of Heat Pump in Heating Mode as a Function of

Outdoor Temperature

7
Tj > 45°F through its effect on the value of PLFy^. The Tj component of

the domain is divided into three intervals:

for Tj _< 17°F, POW(Tj) = P0W17 + A2 (Tj-17°F)

for 17°F £ Tj 45°F,

for Tj > 45°F,

POW(Tj) = P0W17 + B 2 (Tj-17°F), and

POW(Tj,Xj)

P0W17 + A2 (Tj-17°F)

PLF^ (Xj)

]•

The electrical energy requirements and coefficient of performance (COP) for

a given heating load, outdoor temperature and heat pump installation can be

determined using the functions described above, given that the heat pump

characteristic parameters are known.

Note that when the electricity required to operate the heat pump is greater

than that of operating the supplementary electric resistance heating strips

to provide the same output, it is assumed that the heat pump will automatically shut off and the entire heating load will be satisfied with the electric resistance strips. In other words, it is assumed that the heat pump

will not be operated at temperatures for which

POW(Tj) > CAP(T j)

3413 >

where 3413 is the number of Btu per kWh.

Denote by Ej the electricity in kWh required to meet the heating load in

hour j. For any hour j at which the temperature is so low that

POW(Tj) > CAP(T^)

3413

set

HL.

E . = —

J 3413

That is, the space heating load in hour j is met entirely by electric

resistance heating. Otherwise

and

Ej = POW(T^) +

HLj - CAP(Tj)

3413

for Xj = 1,

Ej = (Xj) [POW(Tj)] for Xj < 1.

The heating COP of the heat pump for any hour j in which there is a heating

load is calculated as: HL.

COP i = J

J (E,)(3413)

8
Annual electricity requirements for heating are obtained by summing Ej over all

hours of the year for which HLj > 0. The heating seasonal performance factor

(HSPF) is calculated as:

8760

S HLj

HSPF = 3=^ for all HL . > 0.

8760 3 E (Ej)(3413)

3=1

2.2 COOLING MODE

Section 2.1 provides the methodology used to model the energy-related

performance of a heat pump in the heating mode. In this section the corresponding methodology for determining the performance of the same heat pump in

the cooling mode is presented.

The parameters of the equation used to calculate energy utilization in the

cooling mode are a function of the design characteristics of the heat pump, and

thus will be different for different heat pumps. The characteristics that are used in this report to model the cooling performance of a one-speed heat pump

on an hourly basis are as follows:

1

Output Capacity at an outdoor temperature of 75°F (CAP75) in Btu/hr,

85°F (CAP85) in Btu/hr,

95°F (CAP95) in Btu/hr,

115°F (CAP115) in Btu/hr,

75°F (POW75) in kW,

95®F (POW95) in kW, and

a coefficient of degradation resulting from cycling when cooling load

is less than heat pump capacity (Cp).

The procedure for modeling energy utilization with a heat pump in the cooling

mode is based on three elementary functions of the outdoor temperature in hour

j (Tj) and the hourly cooling load of the house (CLj). As for the heating mode,

these three functions determine the output capacity, the power input, and the

part-load factor of the heat pump in each hour that a cooling load exists.

(a) Capacity Function . The capacity function, denoted CAP(Tj), is piecewise

linear. At Tj = 85°F and Tj = 95°F the function has a change in slope, but Is

continuous. The parameters used in defining the function are:

Input Power

1 These characteristics are sufficient to model the performance of a specific

heat pump in the cooling mode in that the capacity and power functions can

be approximated using these rating points. Other rating points may be more

appropriate for other heat pump systems but the underlying model will be the same

.

9
CAP75,

CAP85,

CAP95,

CAP115,

SCi = [CAP85 - CAP75]/10,

SC2 = [CAP95 - CAP85]/10, and

SC3 = [CAP115 - CAP95J/20.

The domain of the function, Tj , is divided into three intervals:

for 65 °F < Tj

for 85°F < Tj

for 95 °F < Tj

£

85 °F, CAP(Tj)

< 95 °F, CAP(Tj)

_< 115®F, CAP(Tj)

= CAP75 + SCi

= CAP85 + SC2 = CAP95 + SC3

(Tj-75°F),

(Tj-85°F), and

(Tj-95°F).

The functional relationship between capacity in the cooling mode and Tj is

shown in figure 3.

(b) Part-Load Factor . The power function is defined in terms of the part-load

factor for cooling (PLF^,) . Thus, the latter function is described first.

For the outdoor temperature in hour j (Tj) the output capacity of the heat

pump under consideration (CAP(Tj)) can be calculated using the formula in

paragraph (a) above. Now define for hour j the cooling load factor (Xj):

CL^

Xa = or 1.0, whichever is less,

J CAP(Tj) ’ ’

where CLj is the cooling load in Btu of the house in hour j.

The part-load factor for cooling in hour j is then defined in terms of the

parameter Cj) (which will always be less than one) and the value of Xj:

PLFc(Xj) =1 - Cp (1-Xj).

(c) Power Function . The power function, denoted P0W(Tj,Xj), is a nonlinear

function of Tj and PLF(,(Xj).

The parameters used in defining the function P0W(Tj,Xj) are:

POW75,

SP = [POW95 - POW75]/2 0, and

PLFc(Xj).

The domain of the power function is determined by both the outdoor temperature

and the cooling load factor (Xj), the second component entering through its

effect on the value of PLF^.:

P0W(Tj,Xj)

POW75 + SP (T-j-75°F)

PLF<^(Xj)

10
OUTPUT

CAPACITY

(Btu/hr)

Figure 3. Output Capacity of Heat Pump in Cooling Mode as a Function

of Outdoor Temperature

11
The electric energy requirement in hour j (Pj) and coefficient of performance

(COP) for a given cooling load, outdoor temperature and heat pump installation

can be expressed in terms of the functions described above as follows:

If CLj > CAP(Tj) then

set

Pj = POW(Tj,l).

(Note that the cooling load is not fully met in such an hour.)

Otherwise

Pj = (Xj) POW(Tj,Xj).

The cooling COP of the heat pump for any hour j in which there is a cooling

load is calculated as;

(X.)CAP(T:j)^

COP

j = _J! L

• (34l3)(Pj)

Annual electricity requirements for cooling are obtained by summing the Pj over

all hours in the year at which CLj > 0. The cooling seasonal performance

factor (CSPF) is calculated as:

8760

I (Xj)CAP(Tj)

rspi? = for all CLj ^ 0

.

8760

Z (3413)(Pj)

j=l

12

k
3. DETERMINATION OF AN OPTIMAL HEAT PUMP SIZE

In section 2 , a methodology was described for calculating the electric energy

needed to meet the annual heating and cooling requirements of a house when a one-speed heat pump of known performance characteristics is to be installed.

In this section, the optimal size heat pump (in terms of output capacity) is

determined for a given set of assumptions, including performance characteristics, geographic location, annual heating and cooling requirements, energy

costs, heat pump costs, and the expected useful lifetime of the heat pump. In

the following section these assumptions will be varied in order to determine

the sensitivity of the results to these assumptions.

3.1 SELECTION OF OPTIMAL SIZE EQUIPMENT

The general economic objective in selecting equipment to perform a given task

is to choose equipment capable of achieving that task at minimum total present

value, life-cycle cost.^ This objective is valid both for selecting equipment

size as well as for selecting among qualitatively different types of equipment

(e.g., heat pumps from different manufacturers or of different efficiency

ratings). However, this report focuses entirely on the selection of the optimal size heat pump in terms of its thermal output capacity, given specific

operating conditions and economic assumptions. (In all cases, the heat pump

must be large enough to match the design cooling load. However, supplementary

electric resistance heat strips will be used to assure that any heating load

in excess of the heat pump capacity is fully satisfied.)

For a heat pump, total present-value life-cycle cost (TC) can be calculated

as:

n n TC = IC + Z EC^/(1+D)’^ + Z MC^/(1+D)’^ - S^/(l+D)’^

t=l t=l

where IC = initial Installed equipment cost,

EC(- = energy cost in year t,

MC^^ = maintenance cost in year t, n = study period, i.e. the expected life of the heat pump,

D = discount rate, and

= salvage value at the end of the study period.

In evaluating the life-cycle cost of a given heat pump type, the expected life

and maintenance cost are not assumed to vary significantly with variations in

output capacity only. In addition, the salvage value of the heat pump at the

end of its useful life is assumed to be insignificant. As a result, the two key

parameters that will determine the optimal size heat pump are the difference

^ In order to properly compare the life-cycle costs of such alternatives, a common time horizon or study period must be used. If the alternatives considered have different expected lives, cost adjustments (e.g., prorating)

must be made to bring them to a common life.

13
in initial installed cost for alternative output capacities and the change in

life-cycle energy costs. Changes in energy costs are in turn a function of

the change in seasonal heat pump performance for both heating and cooling due

to selecting a heat pump of different output capacity, the annual heating and

cooling requirements of the house, the projected price of electricity over

the life of the heat pump, and the discount rate.

The initial installed cost of a heat pump is a function of heat pump size,

typically increasing at a constant or slightly increasing rate as capacity

increases, as shown in the top of figure 4. Therefore, when a given size heat

pump is acceptable in a particular application, the alternative of a larger

heat pump need only be considered if the net amount of electricity saved by

the heat pump increases with the heat pump size. It will be shown that in

colder than average geographical locations, annual electricity consumption

typically decreases as the heat pump size is Increased, but at a decreasing

rate, as shown at the top of figure 4. Therefore, as long as the present

dollar value of the additional (or "incremental”) energy savings attributable

to a given increase in heat pump size exceeds the additional (or incremental)

heat pump costs incurred, total life-cycle costs will be reduced by increasing

the heat pump size, as seen to the left of output capacity C figure 4. These

incremental savings and costs are shown graphically at the bottom of figure 4.

However, because Incremental heat pump costs are constant or increasing while

incremental energy savings are declining as the heat pump size is increased,

beyond some point the Incremental costs will exceed the corresponding incremental dollar savings, resulting in an increase in total life-cycle costs. Thus

the optimal size heat pump (C)is that size for which the incremental presentvalue dollar energy savings (compared to the next smaller size) just equals

the corresponding incremental cost of that size increase. Note that at C in

figure 4, the ratio of Incremental savings to incremental costs is 1.0.

In practice, heat pump sizes do not vary continuously as shown in figure 4. An

optimal size heat pump from the set of available sizes is therefore the largest

one for which the ratio of present -value incremental savings to incremental

heat pump cost (both measured from the immediately smaller size heat pump available) is larger than or equal to 1.0. This incremental savings-cost approach

will be used to identify the optimally sized heat pump in each case examined

in the report because incremental costs and savings can often be more accurately

identified than total costs and savings.

3.2 ENERGY AND DOLLAR SAVINGS AS A FUNCTION OF HEAT PUMP SIZE

In this subsection an example of the effects of heat pump size on annual energy

requirements is discussed and the resulting energy savings are translated into

present -value dollar terms. The example is based on specified design characteristics representative of a product line of six commercially available onespeed heat pumps ranging in size from 2.0 tons (24,000 Btu/hr output capacity

at 47 °F outdoor temperature) to 5.0 tons (60,000 Btu/hr). The capacity and

power characteristics have been adjusted so that (1) the increments of size

follow a regular pattern, and (2) small variations in the coefficient of performance (COP, the ratio of energy output to energy input) at any given temperature

are eliminated, thereby isolating the effects of changes in size from changes in

COP characteristics.

14
TOTAL LIFE-CYCLE COST

-Cycle Heating-Related Costs as a Function of Output Capacity

15
The given performance characteristics related to capacity and power at specified

outdoor temperatures, used in calculating the annual energy requirements of the

six heat pump sizes, are shown in table 3.1. Note that for the base case, the

coefficient of degradation resulting from cycling, C]^, is 0.25 and the coefficient of degradation due to frosting, Cp, is 0.925. Sensitivity of the results

to variation in the degradation coefficients and the power input will be

examined in section A.

The annual energy utilization (in kWh) of each of the six heat pump sizes was calculated for both space heating and cooling of an 1800 square-foot house,

based on the methodology outlined in section 2. The computer program used in

this heat pump simulation is listed in Appendix A. Chicago was selected as the geographic location for the base case analysis, as it has a reasonably

typical climate for the northern half of the continental United States. Hourly

heating and cooling loads were simulated for a well insulated and tightly

constructed one-story house using the NBS Load Determination Program, NBSLD

[4]

,

and hourly Test Reference Year, TRY [6] , climate records for Chicago.

Table 3.2 provides the physical description of the house, including relevant

operational assumptions. Table 3.3 shows the annual energy utilization for

heating and cooling and the corresponding seasonal performance factors for

each heat pump size.

Table 3.3 shows that the annual energy utilization for heating decreases while

the energy utilization for cooling increases as the capacity of the heat pump

is increased. Accordingly, the seasonal performance factor (SPF) for heating

increases while the SPF for cooling decreases. (Cooling energy requirements

increase because cycling losses increase as the air conditioning capacity is

increased relative to cooling loads.) It will be demonstrated in section 4.6

that increasing the heat pump capacity beyond the basic capacity needed to

satisfy the cooling requirements of a house will not always reduce total energy

consumption, especially if annual cooling requirements exceed annual heating

requirements.

Table 3.4 provides the incremental annual kWh savings for each increase in heat

pump size, based on the difference between total annual energy utilization for

each heat pump size and the next smaller size from table 3.3 As expected, equal

increases in heat pump size result in positive, but increasingly smaller, energy

savings as the overall size is increased.

The corresponding present -value life-cycle dollar savings are shown in the third

column. These savings are calculated using a base year price of $0.04 per kWh,

a 10-year life, a nominal rate (i.e., including inflation) of kWh price increase

of 12 percent per year, and a 15 percent nominal discount rate.^

^ A 15 percent nominal discount rate is approximately equal to a four percent

real discount rate if the rate of general inflation averages 11 percent. A

12 percent nominal increase in electricity prices is approximately equal to a one percent real increase in electricity prices if the rate of general inflation averages 11 percent. The four percent real discount rate and one percent

real price increase in electricity prices are consistent with other residential energy conservation reports prepared for DoE by NBS.

16
Table 3.1 Heat Pump Performance Characteristics used in Base

Case Analysis

Nominal Performance Characteristics^:

Size Heating Cooling

2 .0 tons

CAPl 7=1 3,254 Btu/hr

CAP47=24,000

P0W17=2.157 kW

P0W47=2.705

CAP75=22,615 Btu/hr

CAP85=22,313

CAP 95=2 1,600

CAP115=19,138 " POW75=2 .29 kW

P0W95=2.70

CAPl 7=1 6, 567 Btu/hr CAP75=28,269 Btu/hr

CAP47=30,000 •t CAP85=27,891

POW17=2 .697 kW CAP 95 =2 7, 000

2 . 5 tons POW47=3.381 CAPl 15 =2 3, 922 " POW75=2.87 kW

POW95=3.38

CAPl 7=1 9, 880 Btu/hr CAP75=33,923 Btu/hr

CAP47=36,000 CAP85=33,469 tt POW17=3.236 kW CAP95=32,400

3.0 tons P0W47=4.057 " CAPl 15=2 8, 706 • • POW75=3.43 kW

P0W95=4.05 •t

3.5 tons

CAPl 7=2 3, 194

CAP 47 =42, 000

P0W17=3.775

POW47=4.733

Btu/hr

ft kW

M

CAP75=39,577

CAP85=39,047

CAP95=37,800

CAPl 15=3 3, 491

POW75=4.01

POW95=4.73

Btu/hr

II

•1

II kW

•1

CAPl 7=2 6, 507 Btu/hr CAP75=45,230 Btu/hr

CAP47=48,000 M CAP85=44,626 II

4.0 tons

POW17=4.315 kW CAP95=43,200 II P0W47=5.409 CAP115=38,275

POW75=4.58

P0W95=5.40

1 kW

II

CAPl 7=33, 134 Btu/hr CAP75=56,538 Btu/hr

CAP47=60,000 •I CAP85=55,782 II POW17=5.393 kW CAP95=54,000 " 5 . 0 tons POW47=6.761 II CAPl 15=47, 844 If POW75=5.72 kW

POW95=6.75 II

a Cp = 0.25 and Cj. = 0.925 for all sizes (base case).

17
Table 3.2 Physical Description of Base House

° Single-family detached house - one story over crawl space.

° 1800 square feet floor and ceiling areas.

° Other surface areas:

Areas by or ientation (ft2)

Component S W N E

Wall 292 294 322 294

Windows /sliding 100 - 50 - glass door

Door 20

Windows/ sliding

“ Insulation Ceiling Walls Floor glass door

levels: R-38 R-13 R-19 Double Glazed

® Infiltration rates = approximately 0.6 air changes/hr at At = 25°F and

7.5 MPH windspeed; 1.0 air changes/hr at At = 50°F

and 15 MPH windspeed.

° Thermostat settings: 68°F heating, 78°F cooling.

° Natural ventilation used when sufficient to keep house below 78°F.

° Windows are 50 percent shaded during summer months.

° Occupants: 2 adults, 2 children.

° Lights and equipment heat output scheduled hourly.

° Annual heating requirements computed for Chicago: 51.1 million Btu = 14,972 kWh at an efficiency of 1.0 (i.e. , electric resistance heating).

° Annual cooling requirements computed for Chicago: 8.0 million Btu.

18
Table 3.3 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Base Case^ (Chicago)

Heat Pump Annual Energy Seasonal Performance

Size (Tons) Utilization (kWh) Factors (SCF)

Heating^ Cooling^ Total Heating Cooling

2.0 8722 1008 9729 1.72 2.33

2.5 8399 1040 9439 1.78 2.26

3.0 8196 1057 9253 1.83 2.23

3.5 8069 1074 9143 1.86 2.19

4.0 7989 1085 9075 1.87 2.17

5.0 7905 1102 9007 1.89 2.14

^ 1800 square-foot house, C^ = 0.25, Cp = 0.925.

^ Annual heating requirements = 51.1 million Btu; electric resistance

equivalent = 14,972 kWh.

^ Annual cooling requirements =8.0 million Btu.

Table 3.4 Energy and Dollar Savings Data by Heat Pump

Size: Base Case (Chicago)

(1) (2) (3) (A) (5)

Hours Cooling

Heat Pump Incremental Savings Total Heating Savings ^ Load Exceeds

Size (Tons) (kWh/yr) ($, Life Cycle)^ ($, Life Cycle) Capacity

2.0 .. $2169 6

2.5 290 $101 2281 0

3.0 186 65 2351 0

3.5 110 38 2395 0

4.0 69 24 2423 0

5.0 68 24 2452 0

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

19
(Sensitivity analyses of kWh price projections, discount rates, and expected

lifetimes is discussed in section 4., 5).

The present dollar value (P.V.) over a given study period (10 years in this

case) of each unit of energy used or saved annually was evaluated using the

following formula:^

(

12

)

(. -

(11^

1

)

where P = annual rate of energy price increase

D = discount rate, and

L = lifetime or study period

Thus the present dollar value of a kWh saved each year over ten years is

(oa^)

As with kWh savings, the dollar-valued savings attributable to equal increases

in heat pump capacity are positive but decline as the overall capacity is

increased.

Table 3.4, column four, provides the present -value, life-cycle dollar savings

for each heat pump size (heating only) relative to the use of electric resistance heat only. For any heat pump size selected, these savings must be at

least as great as the difference between (1) the total installed cost of the

heat pump, including expected maintenance, and (2) the cost of separate air

conditioning equipment (if needed) and conventional electric resistance heating

equipment. Including expected maintenance and repairs in both cases. ^ If they

do not exceed this difference, the heat pump is not a cost-effective alternative to separate central air conditioning and electric resistance heating

equipment. (In such a case the economically optimal heat pump size is zero.)

Table 3.4, column five, displays the number of hours per year in which the

cooling load is not fully satisfied by the heat pump size shown. Typically,

central air conditioners and heat pumps are sized so as to satisfy the entire

cooling load of a house 97.5 percent of the hours in which there is a cooling

load. According to the cooling load analysis performed with NBSLD and the TRY

climate data for Chicago, there are approximately 800 hours per year in which

a cooling load exists (i.e., the space temperature will rise above 78°F unless

the air conditioner is turned on). Thus the 2.0 ton heat pump will apparently

satisfy the criterion typically used in selecting an appropriate heat pump

size. Again note that this is a well-insulated and tightly constructed house.

^ If P=D, the formula is modified to P.V. = ($/unit) (L).

2 In comparing alternative equipment costs, it is important to adjust

these costs in order to reflect the same expected lifetimes.

20
3.3 HEAT PUMP COSTS AS A FUNCTION OF SIZE AND THE SELECTION OF AN

OPTIMAL SIZE HEAT PUMP

In the previous subsection calculations of incremental energy and dollar-value

savings were shown for a wide range of heat pump sizes in Chicago. In this

section we will discuss how to use this information together with information

on the incremental cost of additional heat pump capacity in order to determine

an optimum heat pump size, i.e., the heat pump size which will minimize total

life-cycle costs.

Table 3.5 provides representative cost data^ for a heat pump with approxmately

the same performance characteristics as those shown in table 3.1. These costs

include both the outdoor compressor and Indoor coil units plus the refrigerant

tubing. No change in cost for the thermostat is expected so this cost is

not needed. Installation costs are expected to be similar for each size as well, although a slightly larger concrete pad would be needed for the larger

sizes and the heavier weight may require additional lifting capability at the

site. In addition, no change in duct size is attributed to the increased

heat pump sizes. On the other hand, no savings from potential reductions in

supplementary heating strips is credited to the larger heat pump sizes. In

general, these latter assumptions will be reasonable if the optimal heat pump

size does not greatly exceed the heat pump size that would be selected using

more conventional procedures.

Based on the cost data shown in table 3.5, a 24,000 Btu/hr heating output

capacity heat pump would cost approximately $1150, uninstalled. The average

incremental cost per 1000 Btu/hr heating output capacity above 24,000 Btu/hr is

approximately $17 up to 36,000 Btu/hr ($200/(36-24. 5)=$17) . Above 36,000 Btu/hr

the average incremental cost per 1000 Btu/hr is $25 ($705/(64-36)=$25) . Table

3.6 shows the estimated cost of the six heat pump sizes examined in section 3.2,

calculated using this incremental cost data and rounded to the nearest ten

dollars. In addition, table 3.6 shows the incremental cost estimated for each

heat pump size above the 2.0 ton unit.

This incremental cost data can now be compared with the incremental dollar

savings for identical Increases in heat pump size. The incremental savings

attributable to the 2.5 ton heat pump over the 2.0 ton heat pump in table 3.4

($100) is slightly larger than the Incremental cost of that change. A further

increase in size generates incremental savings less than incremental costs,

making the 2.5 ton heat pump the optimal heat pump size in this example. At

higher Incremental costs or lower kWh costs, the 2.0 ton size would be optimal.

(This is the size that would likely have been selected if the heat pump size was selected to satisfy the cooling criterion only.) In order for the 3.0 ton

heat pump size to be optimal, the price per kWh would have to be increased to

$0,062 (100/65 X $.04) given the other assumptions made in this example.

^ These costs were taken from the Sears, Roebuck, and Co., "Spring-Summer 1979"

catalogue

.

21
I

Table 3.5 Heat Pump Cost Data, Unadjusted^

Heating Output Capacity Cost (1979 $)

(1000 Btu/hr at 47 °F) (Rounded to nearest dollar)

24.5 1155

30 1255

36 1355

42 1500

49 1730

64 2060

^ These costs include outdoor unit, indoor coils, and connecting

tubing only. Installation costs are not included here, but are assumed to remain relatively constant as the capacity increases.

Table 3.6 Heat Pump Cost Data, Adjusted^

Heating Output Capacity Total Incremental

Nominal 1000 Btu/hr at 47°F Cost ($) Cost ($)

2.0 tons^ 24 1150

2.5 tons 30 1250 100

3.0 tons 36 1350 100

3.5 tons 42 1500 150 ? 4.0 tons 48 1650 150 } 5.0 tons 60 1950 300

^ Based on table 3.5.

b 1 ton = 12,000 Btu/hr.

22
section 4 the

heating and cool

r costs , energy^ co#l

examined In more detail.

II

l^natlve assumptions regarding the size of

characteristics;' Incremental heat pump

|ilc location on optimal heat pump sizes will be

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4. SENSITIVITY OF OPTIMAL HEAT PUMP SIZE TO CHANGES IN BASE CASE ASSUMPTIONS

The previous sections describe a model of heat pump performance and show how to use the results of the model to select a heat pump that will minimize the lifecycle cost of the heat punq) . In this section the variation in heat pump energy

utilization with respect to changes in load conditions, changes in degradation

coefficients, and increases in steady-state efficiency will be investigated.

Incremental energy and dollar savings will then be recalculated in each case in

order to determine the effects of these changes on the optimal heat pump size.

In addition, the effects of alternative heat pump costs and energy price projections on the optimal heat pump size will be considered. Finally, the effects

of changes in geographic location on both energy utilization and optimal heat

pump sizes will be examined. All calculations of total kWh utilization and

seasonal performance factors are shown in Appendix B.

4.1 EFFECTS OF CHANGES IN LOAD SIZE

The heat pump simulation analyses described in section 3 were repeated for a house with a 100 percent increase in hourly heating loads and a 50 percent

Increase in hourly cooling loads relative to the base case. A doubling of

hourly heating loads can be attributed to a combination of factors, including

a larger house, less insulation, greater air infiltration rates, more (nonsouth facing) glass area, less solar gains through windows, and smaller internal loads than were modeled in the base house. Except for increased glass

area on east and west walls, these factors will have significantly less effect on increases in cooling loads than on heating loads. While a computer simulation could be used to quantify these interrelationships, the proportion of

increase in cooling requirements to heating requirements is quite sensitive to

the assumptions made about each of these modeling parameters. The outdoor

temperature profile, performance characteristics and economic assumptions were

the same as used in the base case in section 3. Incremental reductions in

annual kWh consumption and present-value , life-cycle energy costs were then

calculated for each of the five heat pump sizes greater than the basic 2 .0 ton

unit. The results of this analysis are reported in table 4.1.

In comparing table 3.4 with the new data reported in table 4.1, one can see that the incremental savings in energy and dollars for each increase in heat

pump size are significantly greater in the latter. These Incremental dollar

savings from increasing the size of the heat pump are greater than the incremental heat pump costs (reported in table 3.6) through the 4.0 ton heat pump

size. The optimal size heat pump for the larger house in Chicago under the

energy and equipment cost assumptions made is thus the 4.0 ton heat pump. Had

the heat pump size been based on the cooling load criteria only, the 2.5 ton

heat pump would have been selected.

4.2 EFFECTS OF CHANGES IN DEGilADATION COEFFICIENTS

In describing the model of heat pump performance in section 2 , two degradation

coefficients were identified among the given heat pump characteristics: (1)

the coefficient of degradation that results from cycling when heating or cooling

loads are less than the heat pump capacity during that hour (Cj)); and (2) the

24
Table 4.1 Energy and Dollar Savings Data by Heat Pump

Size: Chicago; Increased Loads^

(1) (2) (3) (4) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size (Tons) (kWh/yr) ($ , Life Cycle )

($ , Life Cycle) Capacity

2.0 _ $3182 76

2.5 1152 $400 3609 14

3.0 885 307 3931 6

3.5 640 222 4165 0

4.0 471 163 4336 0

5.0 613 213 4561 0

a A 100 percent increase in hourly heating loads and a 50 percent increase

in cooling loads relative to the base case. See table B.l in Appendix B

for corresponding annual energy utilization and seasonal performance

factors.

^ Based on $0.04 per kWh price in base year , 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

Table 4.2 Energy and Dollar Savings Data by Heat Pump

Size: Chicago; Base Loads; Cp=0.925, Cp=0. 15^

(1) (2) (3) (4) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size (Tons) (kWh/yr) ($, Life Cycle)

($ , Life Cycle) Capacity

2.0 $2182 6

2.5 307 $106 2294 0

3.0 197 68 2366 0

3.5 119 41 2410 0

4.0 74 26 2438 0

5.0 78 27 2468 0

^ See table B.2 in Appendix B for corresponding annual energy utilization and

seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent annual

increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

25
I

the coefficient of degradation due to frosting (Cp) of the outdoor coils when

the outdoor temperature is between 17 and 47 °F . For the computations of heat

pump energy utilization reported in section 3 the values of these parameters

were taken as Cp = 0.25 and Cp = 0.925.

Other conditions held constant, a decrease of Cp would result in a heat pump

yielding smaller energy savings, and a decrease in Cp would result in a heat

pump yielding larger energy savings. However, the magnitude of the effect of

given changes in the degradation coefficients on the total and incremental

energy savings from larger size heat pumps is not immediately apparent. To get

some indication of how sensitive heat pump energy utilization is to variation

in these degradation coefficients, the energy savings for heat pumps with

coefficients different from those used in section 3 were calculated. The same climate data, load data and heat pump performance characteristics (other than

degradation coefficients) described in section 3 were used. Results are shown

in table 4.2 for a Cp of 0.15 and a Cp of 0.925, in table 4.3 for a Cp of 0.25

and a Cp of 0.850, and in table 4.4 for a Cp of 0.15 and Cp of 0.850.

In comparing these three tables with table 3.4, note that incremental savings

due to increasing the output capacity of the heat pump are slightly greater in

all three cases. The cost-effectiveness of each heat pump size is increased

assuming no change in the cost of the heat pump. However, given the heat pump

cost data shown in table 3.6, in no case is this increase large enough to

increase the optimal size heat pump above 2.5 tons.

4.3 EFFECTS OF IMPROVEMENTS IN STEADY-STATE EFFICIENCY

In this subsection the effects of increasing the overall steady-state heat pump

energy utilization efficiency are examined. This is accomplished by changing

the performance characteristics of the heat pump so that it will achieve the same output capacity at any given outdoor temperature with a smaller power

input. Specifically, the power inputs for each heat pump size and outdoor

temperature shown in table 3.1 are reduced by 10 percent and the simulation

analysis described in section 2 is repeated. The results of these new simulations are shown in table 4.5.

Incremental energy and dollar savings for each heat pump size are increased

significantly (from 16 to 35 percent) relative to the base case. However, as

in the previous sensitivity analyses with respect to degradation coefficients,

the increase in incremental savings is not sufficient to change the optimal

heat pump size from the 2.5 ton unit. On the other hand, an increase in the

cost of the higher efficiency heat pump, relative to the retail cost data used

in the base case analysis, may reduce the optimal size heat pump to 2.0 tons.

4.4 EFFECTS OF ALTERNATIVE HEAT PUMP COSTS

In subsection 3.3, retail price data from a major department store catalog were

used to estimate the costs of the six heat pump sizes examined. By comparing

the incremental heat pump cost for each increase in output capacity with the

corresponding incremental dollar savings, the optimal size heat pump for the

base case example was found to be 2.5 tons. Thus the incremental cost of

26
Table 4.3 Energy and Dollar Savings Data by Heat Pump

Size: Chicago; Base Loads; Cj.=0.850, Cj^=0.25^

(1) (2) (3) (4) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size (Tons) (kWh/yr) ($, Life Cycle)^ ($, Life Cycle) Capacity

2.0 - - $2023 6

2.5 318 $110 2144 0

3.0 196 68 2218 0

3.5 115 40 2264 0

4.0 71 25 2293 0

5.0 68 24 2322 0

3 See table B.3 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate,

^ Total heating savings relative to electric resistance heating.

Table 4.4 Energy and Dollar Savings Data by Heat Pump

Size; Chicago; Base Loads; Cp=0.850, Cp=0.15^

(1) (2) (3) (4) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size (Tons) (kWh/yr) ($, Life Cycle)^ ($, Life Cycle) Capacity

2.0 - - $2036 6

2.5 334 $116 2159 0

3.0 208 72 2233 0

3.5 124 43 2280 0

4.0 78 27 2309 0

5.0 78 27 2338 0

® See table B.4 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

27
Table 4.5 Energy and Dollar Savings Data by Heat Pump

Size: Chicago; Base Loads; Power Input

Reduced by 10 Percent^

(1)

Heat Pump

Size (Tons)

(2)

Incremental

(kWh/yr) ($,

(3)

Savings

Life Cycle)^

(4)

Heat Pump Savings*^

($, Life Cycle)

(5)

Hours Cooling

Load Exceeds

Capacity

2.0 _ _ $2379 6

2.5 337 $117 2506 0

3.0 218 76 2588 0

3.5 133 46 2639 0

4.0 86 30 2672 0

5.0 90 31 2708 0

^ See table B.5 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

28
additional output capacity is an important determinant of the optimal heat pump

size, as long as increasing the heat pump size reduces annual energy costs. In

general, the higher the cost per additional unit of output capacity, the smaller

the optimal size heat pump tends to be; the lower the cost per additional unit

of output capacity, the larger the optimal size heat pump tends to be. However,

variation in the heat pump size is constrained by the need to satisfy the space

cooling and dehumidification requirements of the dwelling unit as well. These

lower and upper size constraints, respectively, are best determined on a siteby-site basis by an experienced air-conditioner installer. In addition, since

heat pump sizes vary by discrete units of capacity, relatively small changes in

unit capacity costs may not be sufficient to change the optimal heat pump size

in many instances.

4.5 EFFECTS OF ALTERNATIVE ENERGY PRICE PROJECTIONS, DISCOUNT RATES, AND LIFE

EXPECTANCIES

In computing the present -value, life-cycle savings in dollars due to each kWh

hour saved annually, the current price per kWh was assumed to be $0.04. In

addition, a 12 percent per year increase in electricity prices, a 15 percent

discount rate and an expected lifetime of 10 years were assumed. Using equation 3.1, these assumptions resulted in a 10-year present -dollar-value of

$0,347 for each kWh saved per year. The effects of an increase or decrease in

this life-cycle kWh price factor on the incremental dollar savings shown in

tables 3.4 and 4.1 through 4.5 can be readily computed by multiplying the

annual incremental energy savings in kWh by the new f actor.

The life-cycle dollar savings are directly proportional to the price per kWh in

the base year, i.e., a doubling of the price per kWh would result in a doubling

of dollar savings. However, due to the exponential nature of equation 3.1, the

life-cycle dollar savings are not directly proportional to the rate of kWh

price increase, the discount rate, nor the expected lifetime. Table 4.6 provides constants of proportionality derived using equation 3.1 for selected

variations in these factors. The life-cycle kWh price factor based on the 12

percent kWh price increase, 15 percent discount rate, and 10-year life can then

be adjusted by simple multiplication to reflect changes in these three factors

(e.g., $0,347 X 0.91 = $0,316 for a 10 percent Increase in annual kWh price

instead of a 12 percent increase).

Note that a 15 percent decrease in the life-cycle kWh cost factor (from $0,347

to $.29) will reduce the optimal heat pump size by one-half ton in all cases

examined in sections 3 and 4. A 56 percent increase in the life-cycle kWh

price factor (to $0.54) is needed to raise the optimal heat pump size to 3.0

tons in the base case example in table 3.3. A 42 percent increase in the same factor (to $0.49) is needed to made the 5.0 ton heat pump size cost effective

in the example shown in table 4.1 (increased heating and cooling loads).

^ The total dollar savings relative to electric resistance heating can be

recomputed by dividing the figure shown by $0,347 and multiplying by the new life-cycle kWh price factor.

29
Table 4.6 Adjustment Factors for Alternative

Economic Assumptions^

I. 10 Percent Discount Rate

Expected Life (years)

Price

7 10 12 15

Escalation

Rate (%) 8 0.75 1.04 1.23 1.50

10 0.81 1.15 1.38 1.73

12 0.87 1.27 1.56 2.00

14 0.93 1.41 1.76 2.33

16 1.00 1.56 1.99 2.72

II. 15 Percent Discount Rate

Expected Life (years)

Price

7 10 12 15

Escalation

Rate (%) 8 0.63 0.83 0.94 1.09

10 0.68 0.91 1.05 1.23

12 0.73 1.00 1.17 1.41

14 0.78 1.10 1 .31 1.61

16 0.84 1.21 1.46 1.86

^ Base case = 10-year life, 12 percent kWh price increase

15 percent discount rate, UPW* = 9.672.

30
4.6 EFFECTS OF GEOGRAPHIC LOCATION

In this section heat pump energy utilization will be calculated for the same six heat pump sizes examined in sections 3 and 4 in seven additional geographic

locations in the United States where calculated annual heating requirements

exceed calculated annual cooling requirements.^ NBSLD [4] and Test Reference

Year [6] climate data tapes were used to calculate annual heating and cooling

requirements and the hourly heating and cooling load profile for the same 1800

square-foot house in each location. The heat pump energy utilization is then

computed for each size heat pump in each house using the corresponding outdoor

temperature data. The heat pump performance characteristics shown in table 3.1 are used for these simulations. Incremental energy and dollar savings for each

increase in heat pump output capacity are calculated and the optimal heat pump

size is identified for each location.

No sensitivity analyses for changes in degradation coefficients nor power input

will be performed since these have relatively small effects on Incremental

savings. However, incremental savings and optimal heat pump sizes for a house

with significantly increased heating and cooling loads will be calculated.

4.6.1 Optimal Size Heat Pump for Base House

Table 4.7 shows the annual heating and cooling requirements for the base house

(see table 3.2) in eight U.S. cities, including Chicago, based on NBSLD analysis and the TRY climate records in each case. The kWh-equivalent heating

requirements are shown for each location, corresponding to the 1.0 efficiency

of electric resistance heating. In addition, the number of hours annually in

which a cooling load occurs in the base house is shown. Tables 4.8 through

4.14 show the incremental energy and dollar savings attributable to increasing

the output capacity of the heat pump as indicated for each location (except

Chicago). In all cases, the 2.0 ton heat pump will satisfy the space cooling

requirements in 97.5 percent of the cooling hours. In all locations except

Seattle, increasing the output capacity beyond 2.5 tons increases the seasonal

performance factor for heating (HSPF) thereby reducing electricity demand for

heating. In Seattle, because approximately 85 percent of the heating degree

days are above 45°F, increasing the heat pump output capacity causes severe penalties with regard to part-load (cycling) performance. The 2.0 ton heat

pump size appears to be optimal in this case. (Coincidentally, Seattle has much

lower electricity prices than most other locations in the United States as well,

which also tends to hold the optimal heat pump size to the minimal acceptable

size .

)

In both Washington, D.C. and Atlanta, decreases in the seasonal performance

factor for cooling along with relatively high annual cooling requirements result

in little or no net energy savings on an annual basis. As a result, increasing

^ In installations where annual cooling requirements exceed annual heating

requirements, increasing the heat pump size typically results in no net

annual energy savings because of the increase in part-load performance

losses

.

31
Table 4.7 Annual Energy Requirements for Base Housed

Annual Heating

Requirements

Annual Cooling

Requirements

Annual

Cooling Hours

Location (kWh) (million Btu) (million Btu)

Seattle, Washington 10990 37 .5 2.2 240

Atlanta, Georgia 5403 18.4 17 .4 1491

Washington, D.C. 8786 30.0 16.8 1561

Kansas City, Missouri 12706 43.4 20.5 1711

Chicago, Illinois 14972 51.1 8.0 811

Boston, Massachusetts 15229 52.0 6.6 632

Madison, Wisconsin 19518 66.6 6.0 633

Minneapolis, Minnesota 25527 87.1 10.9 1013

^ Based on NBSLD analysis using TRY climate data and assumptions shown in

table 3.2.

32

i.
Table 4.8 Energy and Dollar Savings Data by Heat Pump

Size; Seattle; Base Loads^

(1)

Heat Pump

Size (Tons)

(2)

Incremental

(kWh/yr) ($,

(3)

Savings

Life Cycle)^

(4)

Heat Pump Savlngs^^

($ , Life Cycle)

(5)

Hours Cooling

Load Exceeds

Capacity

2.0 $2044 0

2.5 - 6 -$ 2 2049 0

3.0 -11 - 4 2047 0

3.5 -12 - 4 2045 0

4.0 - 9 - 3 2042 0

5.0 -13 - 4 2039 0

^ See table B.6 In Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price In base year, 10-year life, 12 percent

annual Increase In kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

Table 4.9 Energy and Dollar Savings Data by Heat Pump

Size: Atlanta; Base Loads^

(1) (2) (3) (4) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size (Tons) (kWh/yr) ($, Life Cycle)^ ($ , Life Cycle) Capacity

2.0 $ 961 1 2.5 -21 -$ 7 979 0

3.0 -23 - 8 985 0

3.5 -34 - 12 987 0

4.0 -24 - 8 987 0

5.0 -38 - 13 987 0

^ See table B.7 In Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price In base year, 10-year life, 12 percent

annual Increase In kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

33
Table 4.10 Energy and Dollar Savings Data by Heat Pump

Size: Washington, D.C.; Base Loads^

(1)

Heat Pump

Size (Tons)

(2) (3)

Incremental Savings

(kWh/yr) ($, Life Cycle)^

(4)

Heat Pump Savings^

($, Life Cycle)

(5)

Hours Cooling

Load Exceeds

Capacity

2.0 _ $1498 1 2.5 47 $ 16 1538 0

3.0 25 9 1561 0

3.5 -1 0 1573 0

4.0 -4 - 1 1580 0

5.0 -20 - 7 1586 0

^ See table B.8 in Appendix B for corresponding annual energy

and seasonal performance factors.

utilization

^ Based on $0.04 per kWh price in base year, 10-year life, 12

annual increase in kWh price, 15 percent discount rate.

percent

^ Total heating savings

Table 4.11

relative to electric resistance heating.

Energy and Dollar Savings Data by Heat Pump

Size: Kansas City; Base Loads^

(1) (2) (3) (4) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size (Tons) (kWh/yr) ($, Life Cycle) ° ($, Life Cycle) Capacity

2.0 $1730 33

2.5 245 $ 85 1848 0

3.0 153 53 1920 0

3.5 86 30 1967 0

4.0 53 19 1997 0

5.0 44 15 2030 0

^ See table B.9 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

34
Table 4.12 Energy and Dollar Savings Data by Heat Pump

Size: Boston; Base Loads^

(1)

Heat Pump

Size (Tons)

(2)

Incremental

(kWh/yr) ($,

(3)

Savings

Life Cycle)^

(4)

Heat Pump Savings^

($, Life Cycle)

(5)

Hours Cooling

Load Exceeds

Capacity

2.0 $2398 0

2.5 387 $134 2541 0

3.0 207 72 2618 0

3.5 97 34 2657 0

4.0 42 15 2674 0

5.0 20 7 2686 0

a See table B.IO in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

b Based on $0.04 per kWh price in base year, 10-year life. 12 percent

annual increase in kWh price, 15 percent discount rate.

c Total heating savings relative to electric resistance heating.

Table 4.13 Energy and Dollar Savings Data by Heat Pump

Size: Madison; Base Loads^

(1) (2) (3) (4) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size: (Tons) (kWh/yr) ($, Life Cycle)^ ($, Life Cycle) Capacity

2.0 $2420 1 2.5 416 $144 2572 0

3.0 262 91 2667 0

3.5 172 60 2731 0

4.0 124 43 2776 0

5.0 166 58 2838 0

^ See table B.ll in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

35
Table 4.14 Energy and Dollar Savings Data by Heat Pump

Size: Minneapolis; Base Loads^

(1) (2) (3) (A) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size (Tons) (kWh/yr) ($, Life Cycle)^ ($ , Life Cycle) Capacity

2.0 - - $2316 6

2.5 573 $199 2531 0

3.0 420 146 2685 0

3.5 302 105 2799 0

4.0 214 74 2879 0

5.0 260 90 2977 0

^ See table B.12 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

Table 4.15 Energy and Dollar Savings Data by Heat Pump

Size: Seattle; Increased Loads^

(1)

Heat Pump

Size (Tons)

(2)

Incremental

(kWh/yr) ($,

(3)

Savings

Life Cycle)^

(4)

Heat Pump Savings^

($ , Life Cycle)

(5)

Hours Cooling

Load Exceeds

Capacity

2.0 $3661 13

2.5 633 $220 3888 6

3.0 331 115 4007 0

3.5 161 56 4066 0

4.0 61 21 4089 0

5.0 21 7 4099 0

^ See table B.13 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

^ A

36
the heat pump output capacity above 2.0 tons in these two locations does not

appear to be either an energy conserving nor cost-effective procedure.

In Kansas City, the incremental energy savings for increasing the heat pump

from 2.0 to 2.5 tons ($84) are less than the $100 cost calculated in section

3.3. The 2.0 ton system appears to be optimal here. However, higher energy

costs (e.g., $0.05/kWh), a more efficient heat pump, larger annual heating

requirements, or lower incremental heat pump costs would likely increase the

optimal size to 2.5 tons.

In the remaining locations (Boston, Madison, and Minneapolis) the incremental

savings for the 2.5 ton heat pump are all significantly higher than the incremental cost. The optimal size for Boston and Madison is shown to be 2.5 tons

under the assumptions made. For Minneapolis, the 3.0 ton heat pump size is

optimal. (While the dollar savings from increasing the heat pump size from 3.0

to 3.5 tons in Minneapolis is approximately $104, the corresponding incremental

cost is assumed to be $150.)

Based on the analysis of heat pump sizing effects in these seven locations, plus

the base case example for Chicago in section 3.3, it was found that the optimal

heat pump size exceeded the minimum acceptable size (2.0 tons) in four locations

(Chicago, Boston, Madison and Minneapolis). In each location the house modeled

had annual heating requirements (AHR) exceeding 50 million Btu. In addition,

the house in Kansas City with AHR of 43 million might be included if kWh costs

were raised slightly (e.g., to $0.05/kWh). In the other three locations

examined (where the houses modeled all had AHR less than 40 million Btu) , it

is unlikely that the economically optimal heat pump size will ever exceed the

minimum acceptable size needed for air conditioning purposes. Thus it appears

that serious consideration should be given to increasing the size of a heat

pump above the minimum acceptable size if the AHR of the house in which it is

to be installed are greater than approximately 40 million Btu. For AHR between

approximately 40 and 80 million Btu, a one-half ton increase should be con- sidered. Above approximately 80 million Btu, a one-ton increase in heat pump

size should be considered.

In the following subsection, the optimal heat pump size for houses with

increased heating and cooling requirements will be considered in order to provide additional data for such guidelines.

4.6.2 Optimal Size Heat Pump for House with Increased Heating and Cooling

Loads

In subsection 4.1 the optimal size heat pump was shown to increase

significantly with increases in hourly heating and cooling loads, based on the

Chicago TRY climate data. Specifically, doubling the hourly heating loads

and increasing hourly cooling loads by one half raised the optimal size heat

pump from 2.5 to 4.0 tons, while the minimum acceptable size was increased

from 2.0 to 2.5 tons. In this subsection, hourly heating and cooling loads are increased by the same proportions in the seven additional locations shown

in table 4.7. Annual kWh requirements for heating and cooling are calculated

for each of the six heat pump sizes, based on their performance characteristics

37
as listed in table 3.1. Incremental kWh and dollar value savings due to

increasing output capacities are calculated for the five heat pump sizes

greater than 2.0 tons. As in section 3, dollar value savings are based on 10-year savings at $0.04 per kWh, with a 12 percent increase per year in electricity costs and a 15 percent discount rate. Results of these analyses for

the increased heating and cooling loads are shown in tables 4.15 through 4.21,

corresponding to the base house in tables 4.8 through 4.14.

In all seven cases, increasing the heat pump output capacity reduces annual

kWh consumption throughout the range of sizes examined. In addition, the

minimum heat pump size which satisfies the hourly cooling loads in 97 .5 percent

of the hours in which cooling loads occur is larger than the base case in all

locations. The optimal heat pump size, based on the assumptions made in sec- tion 3 (including an incremental cost per one-half ton increase in output

capacity of $100 up to 3.0 tons and $150 above 3.0 tons) exceeds the minimum

size in all cases except for Atlanta. In Atlanta, the optimal size would be

2.0 tons if a minimum sizing constraint did not require a 3.0 ton unit for

cooling purposes. For Seattle and Washington, D.C. the optimal size is 3.0

tons, while the minimum acceptable size is 2.5 tons in both cases. For Kansas

City the optimal heat pump size is 3.5 tons, while the minimum acceptable size

is 3.0 tons. For Boston and Madison it is 4.0 tons, versus a minimum acceptable 2.5 ton size. For Minneapolis the optimal size is 5.0 tons, while the

minimum acceptable size is 3.0 tons. In Kansas City, Boston, and Madison, a small increase in dollar savings would increase the optimal heat pump size one step further. Significantly higher Incremental costs will reduce the optimal

level in many cases. For example, a 15 percent increase in incremental costs

would reduce the optimal heat pump level to the minimum level in Seattle, Washington, D.C., and Kansas City. However, in the coldest locations (Boston,

Madison, and Minneapolis) incremental costs would have to be increased by

three to four hundred percent before the optimal size would coincide with the

size selected for cooling capacity alone.

The results of this analysis correspond quite well with those of the previous

subsection in terms of the correlation between annual heating requirements

and increased capacity needed for optimal heat pump sizing relative to the

minimum acceptable size. Below 40 million Btu, no increase in sizing is

warranted. Between 40 and 80 million Btu, a one-half ton increase should be

considered. Further analysis of the results in this subsection implies that

for AHR between approximately 80 and 100 million Btu, a one ton increase

should be considered, while above 100 million Btu, a one and one-half ton

increase in heat pump capacity may be optimal. In the most extreme case (AHR of 174 million Btu in Minneapolis), a two ton increase was shown to be

optimal

.

While these AHR intervals may provide some preliminary guidelines for the

optimal sizing of heat pump systems, it must be recognized that incremental

capacity costs, kWh prices, and present -value factors should play an important role in the decision-making process for heat pump selection. Higher

unit capacity costs than those used (see table 3.5 and 3.6) would tend to

raise the AHR intervals shown proportionally. Higher kWh prices and higher

present-value factors would tend to lower them in inverse proportion.

38
Table 4.16 Energy and Dollar Savings Data by Heat Pump

Size: Atlanta; Increased Loads^

(1)

Heat Pump

Size (Tons)

(2) (3)

Incremental Savings

(kWh/yr) ($, Life Cycle)^

(A)

Heat Pump Savings^

($ , Life Cycle)

(5)

Hours Cooling

Load Exceeds

Capacity

2.0 _ $1601 224

2.5 208 $72 1739 41

3.0 178 62 1832 1 3.5 86 30 1889 0

4.0 43 15 1922 0

5.0 24 8 1958 0

® See table B.14 in Appendix B for corresponding annual energy

and seasonal performance factors.

utilization

^ Based on $0.04 per kWh price in base year, 10-year life, 12

annual increase in kWh price, 15 percent discount rate.

percent

^ Total heating savings

Table 4.17

relative to electric resistance heating.

Energy and Dollar Savings Data by Heat Pump

Size: Washington, D.C.; Increased Loads^

(1) (2) (3) (4) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size (Tons) (kWh/yr) ($, Life Cycle)

($, Life Cycle) Capacity

2.0 $2461 205

2.5 488 $169 2694 34

3.0 333 116 2840 1 3.5 196 68 2934 0

4.0 128 45 2996 0

5.0 156 54 3077 0

^ See table B.15 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

39
Table 4.18 Energy and Dollar Savings Data by Heat Pump

Size: Kansas City; Increased Loads^

(1)

Heat Pump

Size (Tons)

(2)

Incremental

(kWh/yr) ($,

(3)

Savings

Life Cycle)^

(4)

Heat Pump Savings^

($ , Life Cycle)

(5)

Hours Cooling

Load Exceeds

Capacity

2.0 — $2467 423

2.5 701 $243 2811 139

3.0 633 220 3081 33

3.5 498 173 3290 1 4.0 417 145 3459 0

5.0 581 202 3696 0

® See table B.16 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

Table 4.19 Energy and Dollar Savings Data by Heat Pump

Size: Boston; Increased Loads^

(1) (2) (3) (4) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size (Tons) (kWh/yr) ($, Life Cycle)^ ($, Life Cycle) Capacity

2.0 - - $3390 61

2.5 1325 $460 3873 15

3.0 1088 377 4262 0

3.5 851 295 4567 0

4.0 641 222 4796 0

5.0 799 277 5083 0

^ See table B.17 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

40
Table 4.20 Energy and Dollar Savings Data by Heat Pump

Size: Madison; Increased Loads^

(1)

Heat Pump

Size (Tons)

(2)

Incremental

(kWh/yr) ($,

(3)

Savings

Life Cycle)^

(4)

Heat Pump Savings^

($ , Life Cycle)

(5)

Hours Cooling

Load Exceeds

Capacity

2.0 _ $3411 53

2.5 1390 $482 3912 9

3.0 1107 384 4306 1 3.5 852 296 4610 0

4.0 642 223 4839 0

5.0 857 298 5145 0

^ See table: B.18 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

Table 4.21 Energy and Dollar Savings Data by Heat Pump

Size: Minneapolis ; Increased Loads^

(1) (2) (3) (4) (5)

Hours Cooling

Heat Pump Incremental Savings Heat Pump Savings^ Load Exceeds

Size (Tons) (kWh/yr) ($ , Life Cycle)

($ , Life Cycle) Capacity

2.0 * $3097 152

2.5 1301 $452 3591 34

3.0 1143 396 4008 6

3.5 939 326 4352 0

4.0 770 267 4630 0

5.0 1195 415 5062 0

® See table B.19 in Appendix B for corresponding annual energy utilization

and seasonal performance factors.

^ Based on $0.04 per kWh price in base year, 10-year life, 12 percent

annual increase in kWh price, 15 percent discount rate.

^ Total heating savings relative to electric resistance heating.

41
1

These guidelines are preliminary in nature, however, because they do not

address the important relationship between the heating and cooling requirements of the building in which the heat pump is to be installed. The effects

of an oversized cooling capacity on proper dehumidification must also be

addressed. Additional research is needed to provide a more comprehensive

set of guidelines for field usage.

I

i

42
5.0 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FURTHER RESEARCH

The size of a residential heat pump in terms of its output capacity in the

heating and cooling modes is typically selected to match design cooling loads

rather than design heating loads. Supplementary electric resistance strip

heating is generally added to match heating loads in excess of the heat pump

capacity. However, this supplementary heat source is less efficient than the

heat pump Itself at outdoor temperatures above approximately -20° F. As a result, an Increase in the heating capacity of the heat pump (i.e., selecting

a larger size heat pump), by reducing supplementary heating requirements, may

increase the seasonal heating efficiency of the overall heating system in many

cases

.

The purpose of this report is to identify factors which make the use of larger

size heat pumps cost effective in residential applications and to determine

the economically optimal heat pump size as a function of these factors. The

economically optimal heat pump size is defined as that heat pump size available

for which total owning and operating costs on a life-cycle cost basis are minimized while satisfying design cooling loads. As a result, the optimal size

cannot be smaller than the size selected to match design cooling loads using

conventional selection procedures.

This report uses an hourly simulation model of heat pump performance, heating

and cooling load data for two house sizes for an entire calendar year, performance characteristics typical of a commonly available heat pump, and representative cost data to determine the optimal size heat pump in a variety of geographic locations with significant annual heating requirements. In addition,

a number of sensitivity analyses are performed in order to demonstrate the

effects of changes in certain factors on the optimal heat pump size. Over the

range of variation tested, only changes in the size of the space heating and

cooling loads, the geographic location of the house, and the price of electricity had a significant effect on the optimal heat pump size.

In the cases studied, annual heating requirements must be approximately 50

million Btu before the optimal heat pump size exceeds the minimum acceptable

size for cooling purposes by one-half ton or more. In addition, annual heating

requirements exceed annual cooling requirements by nearly three to one in all

such cases. Higher electricity costs or more efficient heat pumps would tend

to lower the annual heating requirements needed to increase the optimal size

heat pump above the minimum. On the other hand, substantially higher incremental heat pump costs than those used would tend to hold the optimal level closer

to the minimum acceptable size.

For houses with annual heating requirements above 80 million Btu, a one ton

increase in capacity should be considered. Above 100 million Btu, the optimal

heat pump capacity may be one and one-half tons or more greater than the minimum acceptable size for cooling. However, when such large increases in capacity are considered, care must be taken to assure that dehumidification

requirements can be adequately met without significant increases in cooling

energy usage.

43
In milder climates such as in Seattle and Atlanta, increasing the heat pump

size can actually lower seasonal heating efficiency because reductions in partload efficiency (from cycling on and off) due to oversizing at the higher

outdoor temperatures tend to offset increases in efficiency at lower temperatures. Similarly, increasing the heat pump size in all cases tends to reduce

seasonal cooling efficiency because of oversizing relative to the actual cooling requirements.

The scope of this report is limited primarily to the development of a methodology for the economic sizing of residential heat pumps and some parametric analysis to determine the sensitivity of optimal heat pump size to many

of the important assumptions required. This research could be expanded to

address several areas of additional concern:

(1) The results of this report are based on an hour-by-hour analysis of heating and cooling loads and heat pump performance in residential applications in eight locations. Such a detailed analysis would be prohibitively

costly for most new heat pump Installations. Generalized guidelines based

on estimates of annual heating and cooling requirements, readily available

climate parameters, electricity costs and heat pump costs are needed so that the findings in this report can be made more useful for field usage.

(2) This report investigated the economic efficiency of a one-speed heat pump.

A variable-speed heat pump should yield greater energy savings than the one -speed heat pump because it reduces loss of performance at higher

temperatures resulting from equipment cycling. An economic investigation

of the extent to which this potential energy saving will pay for the

greater initial cost of the variable-speed heat pump as well as the optimal sizing of the latter should be conducted.

(3) In installations with small annual cooling requirements, a heating-only

heat pump may be an attractive alternative to a reversible heat pump

since it will have a higher seasonal performance factor. Heating-only

heat pumps are not currently being manufactured because of low demand.

However, an economic analysis of the superior performance of the heatingonly heat pump, including sizing considerations, may provide an increased

incentive for manufacturing such a system.

44
REFERENCES

[1] Characteristics of New One -Family Homes; 1974 , Construction Reports - Series C25 , U.S. Department of Commerce, Bureau of the Census, Washington,

D.C., 1975.

[2] Characteristics of New Housing; 1978 , Construction Reports - Series

C25-78-13, U.S. Department of Commerce, Bureau of the Census, Washington,

D.C., 1978.

[3] Kelly, G. E., and Parken, W. H. Jr., Method of Testing, Rating and

Estimating the Seasonal Performance of Central Air Conditioners and Heat

Pumps Operating in the Cooling Mode , NBSIR 77-1271, U.S. Department of

Commerce, National Bureau of Standards, Washington, D.C., 1978.

[A] Kusuda , T . , NBSLD, the Computer Program for Heating and Cooling Loads in

Buildings , BSS 69, U.S. Department of Commerce, National Bureau of

Standards, Washington, D.C., 1976.

[5] Parken, W. H., Kelly, G. E., and Didion, D. A., Method of Testing, Rating

and Estimating the Heating Seasonal Performance of Heat Pumps , NBSIR 80-

2002, U.S. Department of Commerce, National Bureau of Standards,

Washington, D.C., 1980.

[6] Stamper, E., "Weather Data," ASHRAE Journal, 19, 2:47, February 1977.

45

Appendix A. Listing of Computer Program for Heat Pump Sizing Analysis

This appendix gives a listing of the computer program used to calculate the

electricity needed to meet heating-cooling loads and the present value of

energy saved by a heat pump.

List of Symbols in the Program

Line of

first

Symbol Interpretation Occurrence

Cl Coefficient of degradation due to frosting 4

C2

Coefficient of degradation resulting from

cycling when heating load is less than

heat pump capacity

5

SENER Sum of electric energy used to meet heating load 81

SENEC Sum of electric energy used to meet cooling load 82

SHL Total heating load 83

SXCI Total cooling load 91

JE Number of hours cooling load exceeds capacity 92

T Dry bulb temperature 100

XL Sensible load 101

XLL Latent load 101

TB Temperature below which heat pump is not used 90

SHL Sum of heating load 103

( initialized 83)

SXCI Sum of cooling load 121

( initialized 91)

SPF Seasonal performance factor, heating load 128

SPC Seasonal performance factor, cooling load 129

SENET Total energy used, heating plus cooling 130

SVG Present value of savings on heating load 132

SENRM Marginal energy savings, heating plus cooling 136

SVGM Present value of total marginal savings 137

A-1
Listing of Computer Program

! • 2*

C . • . aHPJLFL «Ma INU. •

.

OIMfNSION DB ( 24 ) ,0UM ( 24 ) , XL < 24

)

,XLL ( 24 1 3* I NPUT*9

4* ri*,925

5* C2-.250

6* 3 1 nn write ( 6 t 1 5 > Cl iC2

7* DO ISO K=1 tA

a* &n rn (211Q..:2120. 2130^2140. 2150 .2160.2170) .1C 9*

- 10*--

2110 CONTI NUE

CAPi7*1325M

1 1 • CAP47*24000

-i_2 ft- POW 1 7 * 2 * 1 5 7

13* P0Wm7»2.705

1 4 * CAP7‘^«?2A is

15* CAPr5»223 1

3

16* - CA.E9S*-2LAQQ. - - - 17* CAPi5*19138

18* P0W75*2.29 Heat pump

1 9* P0W95=2.70

20* GO TO 2000 design parameters

2 1 • 2170 continue

22* CAPi 7*165A7 (lines 9 through 79)

23* CAP47*30000

24* P0W1 7*2.697

25* P0W47»3 • 38

1

26* CAP75»28269 Table 3.1

27* CAPB5*2709

1

28* CAP95*27000

29* CAP 1 5*23922

30* P0W75*2.87

31* P0W95*3. 30

32* GO TO 2000

33* 2130 continue

i4 f. . CAPl7»1908O

35* CAP47*36000

36* POW 17*3.236

37* P0W47*4 .057

3 0*_. CAP75*33923

39* CAPr5*33469

40* CAP95*32400

4 1 CAP 1 5*20706

42* P0W75*3.43

43* P0W95*4.05

44* GO TO 2000

45* 71‘40 CONTINUE

46* CAP 1 7*23194
M8*

M9«

50*

5 1 • S2*

«53*

55*

56*

57*

58*

59*

60*

6 1 • 62*

63*

69*

65*

_ 6_6*

67*

68 * 69*

70*

7 1 * 72*

73*

79*

7*i*

76*

77*

78*

79*

80*

8 1 * 82*

83*

89*

8

5'*^

86 *

j! 8 7*

I 88*

89*

90*.

91 * 92*

93*

99*

! 95*

I ? 6

*

1 98*

I 99*

IQO*

10 1*

llQ.2±

103*

! 109*

Cip«7*920d0

POW! 7»3«775

POW '4 7*9*733

CAP7^?39577

CAPP5*39097

CAPo5 = 378 00

CAP15-33991

P 0W75*9 *0 1 P0W95*9*73

GO TO 2000

21P0 CONTINUE

CjAPj7»26507

" CAp447*98'000

P0Wl7»9*3I^_

' P0W9y*5V^909

CAP75*95?30

CAPP5*99626

CAP95*93200

CAP 1 5«38275

P0 W75»9 *58

P0W95*5* 90

G.O. TO 2000 _ 2160 continue

CAP 17*33 1 39

C AP97*60000

PJDWJ_7*^113

P0W97*6* 76

1

CAP75*56538

CAP«5®55782

CAP9S-59Q0Q _ CAP 1 5*97899

eatt25?-5AZ-2

P0W95*6 * 75

?170 continue

2000 SENFR*0*

SENrC*0*

'SHL=0.

CAPt5«( *9*CApi 7*»6»CAP97)*C1 Heat ing performance

P0W‘^5*( *9*P0w 17 + *6*P0W97) parameters

A 1 » ( CAP97-CAP I_7 )/30*

b T * » C a P 3 5 - C A P~1 7 ) / I 8 * A2*(P0W9 7-P0Wl7)/ 3 0* Subsection 2.1

82* ( P0W35-P0W1 7 ) /'fe*

T6«17**((3913**P0W17-CAP17)/ (A1 »39 13*»A7 ) 1 SXCl *0*

?JD SC 1 * ( C AP85-C AP 75 ) / I 0 * Cooling performance

SC2* j C AP95-C AP85 ) / I 0» jjarameters

SC3*(CAP15-CAP95)/20*

SP »(P0W 9 5-P0W75)/2Q* 2.

2

DO I 00 I * 1 I 367

R E AQ_ 1. 1 Nf U T • E N P

» 9 9 9 ) O B » 0 U M * 0 U M * D U M . X L » X L L

DO 90 J* 1 » 29

.. HL* f XL ( J ) *XLL I J 1 » IF (HL«LT*0*1 GO TO 290

SHL*SHL*HL

IF (T*LE*TB) GO TO 70

A-3
Energy use heating 'load hour

i OG#

06 • 07*

08 • 09*

in*

1 1 • 'o

12* .3 0

1 3*

1 4* 290

IS*

1 6 • 17*

1 8*

19*

20* 260

2 1 * 22*

23*

24*

2S* PfJ 26* 1 GO

27* PP9

28 * 29*

30*

3 I * 32*

3 3*

34*

3S* 1 <0

36*

37*

38*

39*

40 * 4 1 * 42* - ...... 4 3*

MM*

MS*

M6*

M7*

M 8 * 15’0

M 9 • 7 SO* {

\ S 1 * 1 s S2* 1 7 S3* 1 9

SM * 7 1 SS* 7 3 S6* 3 1 S7* 1 S0*

S9 • 60* . 6 1 *

1 62*

VAL=CAPCTY(T)

X1=‘'L/VAL

X * A M I M 1 I 1 . 0 . X I ) pnw 1 “POWER ( T . y I C?

)

CMFRX“ENrR(VAl. fPOWI H|.,X)

GO TO ao

E:NE'?X“HL/.''‘413.

SENFR = 5ENER + Er4ERX

(jO TO 90

CL = -HL

V AL = CAPC < T ) X 1 =CL/VAL

IF (Xl.LE.1.0) r,n TP 2A0

JE=JE>1 . C L = '/ A 1. X = AMI^'l(l#O.Xl)

SXCl =‘^XCl.+CL

POW 1 =POWC ( T , X .C2

)

E Nj E P X = X • P 0 W 1 5 E NELC = 5 E N F C + E N E P. X C 0 M T I M IJ E COMT I ^'UE

COMT I MUF

SPF = 5HL/ (

1

3*SFNFR ) SPC=SXCL/(3R13.*SFnFC)

Subsection 2.1

Energy use

cooling load hour

Subsection 2.2

5EMFT = SFrJER-^5ENFC

CALI LCCF(FlC)

liV& = FLC*(SHL/3Rl3.-SFNE'’)

IF (K'.GF.?) GO TO 1.30

SENR 1 =5EME T CONT I WtIF

S£M.OM = SENRi-SENET _ S V G M = F L C * S E R M

write (6,7) K wPItF (6,11) SFWFR.SPF

WPI tE ( 6 ,M I ) SENEC ,SPC . write (6,23) SENET

WBl-lE (6il7) SVG „ write (6,19) SE^JRM

write (6,21) svr,M_

write (6,31) JE

5FNPl=SENET

REWINO INPUT

CONTINUE

FORMAT (16HnHFAT P U m

P

5 I 7 F » , I 2

)

format (7H RENER=,F10,1,7H SPF»,F9.M)

format (SHiFcn»,Fin.R,aH plco=,fio.m)

format (19H heat PUMp S A V I M G »

, F 1 0 . I ) format (7H SFNRM=,F9.I)

format (7H GvGM = ^,FR*1J __ _

format (7H GENFT=,F10.1)

format (37H HOURS COOLING LOAD FXCEDFS CAPACITY*,

format (7H SENEC=»F!0.1,7H SPC»,F9.*4)

stop

FUN^TIO^J CAPCTY(T)

IF I T.LEf I7J..,G.C> _TQ lono _ IF IT.GT.MS.) GO TO 1 000

CAPCTY=CAP17>01*(T-17)

I M )

A4

Heating c apac ity
1 63* GO TO i n 1 0

1 6M* \ nno CAPCTY = CAP17-*-Al*(T“l7) Subsection 2.1 (a)

I mm RETII9M

1 6A* F U N r T I 0 N P 0 '.v' t R ( T . X , C 2 )

1 A7* IF ( T . G T • I 7 1 GO TO 1 1 0 0 Heating power

1 6fl* pnwpR = POWl7-*-A7*(T-l7)

1 A9* GO TO 1170

1 70* 1 l no IF (T.GT.4G.) GO TO lllO

17 1* P0WFR = R0W17 + I^2*(T-17) Subsection 2.1 (c)

177* GO TO 1 1 70

1 7 3» 1110 PLF= I .0-C7* ( 1 .n-x 1

1 7M* pnwrR=(POWl7>A2«(T-l7) ) /PLF

1 75* 1 l 70 RFTliRN

1 7 6 * FUNrTION FNrR(VAL»POWl.HL.X) Heating electricity

\ 77 * IF ( X . G E . 1 .

0

) GO TO 120 0

178* £ M E P * X • P 0 w 1 179* GO TO 1210

1 PO* 1 7no £^JF^= ( HL - V A| 1/3413 + POWl End Subsection 2.1

181* 12 10 R F T

1

! R M

IP?* function CAPC(T)

183* IF (T.GT.P5) GO TO 1010 Cooling capacity

I 8H» CAPC*CAP7G+FG1*(T-7S. )

1 RP.* GO TO loon Subsection 2 .2 (a)

1 0^>* 10 10 IF (T.GT.RS) GO TO 1020

1 P7* CAPr=rApRF+qc7*( T-RF. )

1 80* GO TO 1 n 0 0

109* 1 0 :?n CAPr=CAPlG+FcT*( T-9G. ) 190* 1 OPO R F T R N

1 9 1 FUNCTIOM POv'c ( T , X , C7 ) Cooling power

192* PLF=1 .0-f7*( 1 .0-X)

193* POWr=(POM7G^SP*lT-7F.) )/PLF

Subsection 2.2 (c)

1 94* RFTcRN

I 9S* ENO

A5
Subroutine to Calculate the Present Value

of an Annual Expenditure per kWh of Electricity Over

Ten Years (Subroutine called in main program at line 131.)

12

3

5

6

7

8

9

10

11

1 2

13

1 9

IS

1 6

17

1 8

4 9--

20

?l

22

24

29

C . . . OJHP JLFLf LCCF , . , SUMPOUT IMF LCCF(FlC)

dimension FDl(9).FD2{9).FP3(9).nri9)

P 1 * .09

N P * I _ Fn 1 ( 1 » = . 07

EH2J_L) = * 1 F03 ( 1

) = 1 n

.

FlC=0..

CDF=

I

. DO 15Q__L» l.iNR .. _ . 0F(I) = (l.-*-F01(I))/(l.+Fn2(I))

I F___ ( D£jL1 ) .-N Ft J .4. Q 0 _T 0 , J n 0

FLC = FLC-tCDF*Fn3 ( I ) -X50

inn Yl»FxP(FD7(I)*AL00(nF(I))I

BPVF = DF I 11* I 1 .-Y 11/ I 1 .-DF ( I ) ) _ .. PVF=CDF*BPVF

- VF

C0F*CDF«Yt

IPO cn^^T-iNUF

FLC»P 1 •Fl.r

RFTURW -- END

A6
Appendix B. Annual Heating and Cooling Energy Utilization by Heat

Pump Size: Sensitivity Analysis

B-1
Table B.l Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Chicago; Increased Loads;

Cp=0.925, Cp=0.25^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 20771 1389 22160 1.44 2.48

2.5 19539 1469 21008 1.53 2.39

3.0 18612 1510 20122 1.61 2.34

3.5 17937 1545 19482 1.67 2.29

4.0 17444 1568 19012 1.72 2.25

5.0 16796 1602 18398 1.78 2.20

^ Annual heating requirements = 102.2 million Btu; electric

equivalent = 29944 kWh. Annual cooling requirements = 12

resistance

.0 million Btu

Table B.2 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Chicago; Base Loads;

Cp=0.925, Cp=0.15^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 8683 952 9635 1.72 2.47

2.5 8358 971 9329 1.79 2.43

3.0 8153 979 9131 1.84 2.41

3.5 8024 988 9013 1.87 2.38

4.0 7944 994 8937 1.88 2.37

5.0 7858 1002 8860 1.91 2.35

^ Annual heating requirements = 51.1 million Btu; electric resistance

equivalent = 14972 kWh. Annual cooling requirements =8.0 million Btu.

B-2
Table B.3 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Chicago; Base Loads;

Cp=0.850, Cp=0.25^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 9140 1008 10148 1.64 2.33

2.5 8790 1040 9830 1.70 2.26

3.0 8577 1057 9634 1.75 2.23

3.5 8444 1074 9519 1.77 2.19

4.0 8362 1085 9448 1.79 2.17

5.0 8278 1102 9380 1.81 2.14

^ Annual heating requirements = 51.1 million Btu; electric

equivalent = 14972 kWh. Annual cooling requirements = 8

resistance

.0 million Btu

Table B.4 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Chicago; Base Loads;

Cp=0.850, Cp= 0.15^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 9101 952 10054 1.65 2.47

2.5 8749 971 9720 1.71 2.43

3.0 8533 979 9512 1.75 2.41

3.5 8400 988 9388 1.78 2.38

4.0 8317 994 9310 1.80 2.37

5.0 8231 1002 9233 1.82 2.35

^ Annual heating requirements = 51.1 million Btu; electric resistance

equivalent = 14972 kWh. Annual cooling requirements =8.0 million Btu.

B-3
Table B.5 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Chicago; Base Loads;

Power Input Reduced by 10 Percent^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 8112 907 9019 1.85 2.59

2.5 7746 936 8682 1.93 2.52

3.0 7512 952 8464 1.99 2.47

3.5 7364 967 8331 2.03 2.44

4.0 7268 977 8245 2.06 2.41

5.0 7164 991 8155 2.09 2.38

^ Annual heating requirements = 51.1 million Btu; electric resistance

equivalent = 14972 kWh. Annual cooling requirements =8.0 million Btu.

Cp = 0.925, Cj) = 0.25.

Table B.6 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Seattle; Base Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 5097 285 5381 2.16 2.29

2.5 5082 293 5375 2.16 2.22

3.0 5088 298 5386 2.16 2.19

3.5 5096 302 5398 2.16 2.16

4.0 5102 305 5407 2.15 2.13

5.0 5111 310 5420 2.15 2.11

^ Annual heating requirements = 37.5 million Btu; electric resistance

equivalent = 10990 kWh. Annual cooling requirements =2.2 million Btu.

Cp = 0.925, Cj) = 0.25.

B-4
Table B.7 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Atlanta; Base Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 2633 2108 4741 2 .05 2.42

•

CM 2581 2181 4762 2.09 2.34

3.0 2564 2222 4785 2.11 2.30

3.5 2558 2261 4819 2.11 2.26

4.0 2556 2286 4843 2.11 2.23

5.0 2557 2325 4881 2.11 2.19

^ Annual heating requirements = 18.4 million Btu; electric resistance

equivalent = 5403 kWh. Annual cooling requirements = 17.4 million Btu.

Cp ~ 0.925, Cp — 0.25.

Table B.8 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Washington, D.C.; Base Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 4468 2112 6579 1.97 2.33

2.5 4351 2181 6533 2.02 2.26

3.0 4287 2221 6508 2.05 2.21

3.5 4251 2258 6509 2.07 2.18

4.0 4231 2283 6514 2.08 2.15

5.0 4214 2320 6534 2.08 2.12

^ Annual heating requirements = 30.0 million Btu; electric resistance

equivalent = 8786 kWh. Annual cooling requirements = 16.8 million Btu.

Cp = 0.925, % = 0.25.

B-5
Table B.9 Annual Heating and Cooling Energy Utilization

by Heat Pump Size; Kansas City; Base Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 7720 2527 10247 1.65 2 .37

2.5 7379 2624 10002 1.72 2.28

3.0 7171 2678 9849 1.77 2.24

3.5 7035 2728 9764 1.81 2.20

4.0 6949 2761 9710 1.83 2.17

5.0 6855 2812 9666 1.85 2.13

^ Annual heating requirements = 43.4 million Btu; electric resistance

equivalent = 12706 kWh. Annual cooling requirements = 20.5 million Btu.

Cp = 0.925, Cjj ~ 0.25.

Table B.IO Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Boston; Base Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 8316 822 9138 1.83 2.35

2.5 7903 848 8752 1.93 2.27

3.0 7682 863 8544 1.98 2.24

3.5 7570 877 8447 2.01 2.20

4.0 7519 886 8405 2.03 2.18

5.0 7485 900 8385 2.03 2.14

^ Annual heating requirements = 52.0 million Btu; electric resistance

equivalent = 15229 kWh. Annual cooling requirements =6.6 million Btu.

Cp = 0.925, Cj) = 0.25.

B-6

i
Table B.ll Annual Heating and Cooling Energy Utilizatiqn

by Heat Pump Size: Madison; Base Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 12542 755 13298 1.56 2.33

2.5 12103 778 12881 1 .61 2.26

3.0 11829 790 12620 1.65 2.22

3.5 11645 803 12448 1.68 2.19

4.0 11514 810 12324 1.70 2.17

5.0 11336 822 12158 1.72 2.14

* Annual heating requirements = 66.6 million Btu; electric resistance

equivalent = 19518 kWh. Annual cooling requirements =6.0 million Btu.

Cj. = 0.925, Cq = 0.25.

Table B.12 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Minneapolis; Base Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 18851 1367 20219 1.35 2.34

2.5 18231 1414 19645 1.40 2.26

3.0 17785 1440 19225 1.44 2.22

3.5 17459 1465 18923 1.46 2.19

4.0 17228 1481 18709 1.48 2.16

5.0 16944 1505 18449 1.51 2.13

^ Annual heating requirements = 87.1 million Btu; electric resistance

equivalent = 25527 kWh. Annual cooling requirements = 10.9 million Btu.

Cp = 0.925, Cq = 0.25.

B-7
Table B.13 Annual Heating and Cooling Energy Utiliz^ition

by Heat Pump Size: Seattle ; Increased Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 11426 394 11819 1 .92 2.43

2.5 10771 415 11187 2.04 2.34

3.0 10429 427 10856 2 .11 2.29

3.5 10259 436 10695 2.14 2.24

4.0 10192 442 10634 2.16 2.21

5.0 10163 451 10614 2.16 2.17

^ Annual heating requirements = 75.0 million Btu; electric resistance

equivalent = 21980 kWh. Annual cooling requirements = 3.3 million Btu.

Cp = 0.925, Cj) = 0.25.

Table B.14 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Atlanta; Increased Loads^

Heat Pump Annual Energy Seasonal Performance

Size (Tons) Utilization (kWh) Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 6189 2880 9070 1.75 2.58

2.5 5793 3070 8863 1.87 2.49

3.0 5525 3160 8685 1.96 2.42

3.5 5362 3237 8598 2.02 2.36

4.0 5265 3290 8556 2.05 2.32

5.0 5161 3371 8532 2.09 2.27

^ Annual heating requirements = 36.9 million Btu; electric resistance

equivalent = 10806 kWh. Annual cooling requirements = 26.1 million Btu.

Cp = 0.925, % = 0.25.

B-8
Table B.15 Annual Heating and Cooling Energy Utilization by

Heat Pump Size: Washington, D.C.; Increased Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 10477 2894 13371 1.68 2.49

2.5 9807 3076 12883 1.79 2.39

3.0 9384 3165 12549 1.87 2.33

3.5 9115 3239 12354 1.93 2.28

4.0 8935 3290 12225 1.97 2.24

5.0 8701 3368 12069 2.02 2.19

* Annual heating requirements = 60.0 million Btu; electric resistance

equivalent = 17572 kWh. Annual cooling requirements = 25.2 million Btu

Cp = 0.925, Cd = 0.25.

Table B.16 Annual Heating and Cooling Energy Utilization by

Heat Pump Size; Kansas City; Increased Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 18300 3351 21651 1.39 2.52

2.5 17309 3641 20951 1.47 2.43

3.0 16530 3788 20318 1.54 2.37

3.5 15927 3893 19820 1.60 2.31

4.0 15441 3962 19403 1.65 2.27

5.0 14755 4066 18822 1.72 2.21

^ Annual heating requirements = 86.7 million Btu; electric resistance

equivalent = 25412 kWh. Annual cooling requirements = 30.8 million Btu

Cp = 0.925, % = 0.25.

B-9
Table B.17 Annual Heating and Cooling Energy Util i nation

by Heat Pump Size; Boston; Increased Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 20684 1133 21817 1.47 2.50

2.5 19293 1199 20492 1.58 2.41

3.0 18172 1232 19404 1.68 2.35

3.5 17293 1260 18553 1.76 2.30

4.0 16633 1279 17912 1.83 2.26

5.0 15805 1308 17113 1.93 2.21

^ Annual heating requirements = 104.0 million Btu; electric resistance

equivalent = 30458 kWh. Annual cooling requirements =9.9 million Btu.

Cp = 0.925, Cj) = 0.25.

Table B.18 Annual Heating and Cooling Energy Utilization

by Heat Pump Size: Madison; Increased Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 29204 1046 30250 1.34 2.47

2.5 27757 1103 28860 1.41 2.38

3.0 26621 1132 27753 1.47 2.33

3.5 25745 1156 26901 1.52 2.28

4.0 25086 1173 26259 1.56 2.25

5.0 24204 1197 25402 1.61 2.20

^ Annual heating requirements = 133.2 million Btu; electric resistance

equivalent = 39036 kWh. Annual cooling requirements =9.0 million Btu.

Cp = 0.925, Cj) = 0.25.

B-10
Table B.19 Annual Heating and Cooling Energy Utilization by

Heat Pump Size; Minneapolis; Increased Loads^

Heat Pump

Size (Tons)

Annual Energy

Utilization (kWh)

Seasonal Performance

Factors (SPF)

Heating Cooling Total Heating Cooling

2.0 42127 1865 43991 1.21 2.49

2.5 40702 1989 42690 1.25 2.40

3.0 39498 2049 41548 1.29 2.34

3.5 38509 2100 40609 1.33 2.29

4.0 37705 2133 39838 1.35 2.25

4.5 36460 2184 38643 1.40 2.20

* Annual heating requirements = 174.2 million Btu; electric resistance

equivalent = 51054 kWh. Annual cooling requirements = 16.4 million Btu.

Cp = 0.925, Cj) = 0.25.

B-11
FEDERAL INFORMATION PROCESSING STANDARD SOFTWARE SUMMARY

01. Summary date

Yr. Mo. Day

8 0 1 1 2 6

04. Software date

Yr. Mo. Day

8 0 1 1 2 6

02. Summary prepared by (Name and Phone)

Joel Levy (301) 921 x2607

05. Software title Program for Heat Pump Sizing Analysis

06. Short title

03. Summary action New Replacement Deletion 0

Previous Internal Software ID

07. Internal Software ID MAINU

08. Software type 09. Processing mode 10. General

Application area

Specific Automated Data

[~~| System

pC] Computer Program

r~| Subroutine/Module

r~| Interactive 0 Batch

r~| Combination

11. Submitting organization and address Applied Economics Group

Computer Systems

Support/Utility

Scientific/Engineering

Bibliographic/Textual E

Management/

Business

Process Control Other

Life-cycle cost of

different heat pump

sizes.

12. Technical oontact(s) and phone

Building Economics and Regulatory Technology Div.

Center for Building Technology, NEL

National Bureau of Stcindards

Washington, D.C. 20234

13. Narrative

Joel Levy x2607 (301) 921-2607

Stephen R. Petersen x3701

(301) 921-3701

From data on hour by hour heating and cooling loads and weather conditions the

program calculates electricity saved by use of given size heat pump. On the basis

of electricity price data and the discount rate these life—cycle savings on electricity are converted to their present value. Comparison with heat pump costs

then allows selection of heat pump size maximizing net savings.

14.

Keywords

Benefit -cost analysis; energy conservation; equipment selection; equipment sizing;

heat pump; life-cycle costs.

15.

Computer manufr and model

16.

Computer operating system 17. Programing language(s) 18. Number of source program state- ments UNIVAC 1108 EXEC 8

19. Computer memory requirements

Max. 32K

23. Other operational requirements

20. Tape drives

1

FORTRAN IV

21. Disk/Drum units 195 MAIN22. Terminals

None NA

24 Sub

None

24. Software availability

Available Limited 0

Applied Economics Group

Bldg. 226, Rm. A319

National Bureau of Standards

Washington, D.C. 20234

26. FOR SUBMITTING ORGANIZATION USE

25. Documentation avaiiabiiity

In-house only Available Inadequate In-house only

Q

Applied Economics Group

Bldg. 226, Rm. A319

National Bureau of Standards

Washington, D.C. 20234

standard Form 185

1974 July

U.S. Dept, of Commerce—NBS

(FIPS. Pub. 30)

185-101
NBS-114A (REV. 0-76)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR BO -2176 • i.-;

tle.i 9. Ac:ce$$:l9i}No.

4. TITLE AND SUBTITLE

ECONOMIC EFFICIENCY IN THE SIZING OF

RESIDENTIAL HEAT PUMPS

5. Publication Date

7. AUTHOR(S) 8. Performing Organ. Report No. Joel Levy and Stephen R. Petersen

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS fSfreer, City, state, zip)

Office of Buildings and Conmiunity Systems

Department of Energy

Washington, D.C. 20545

13. Type of Report & Period Covered Final

15. SUPPLEMENTARY NOTES

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

II. ABSTRACT (A 200-word or teas {actual aummary of moat aignificant information. H document includes a signiiicant bibliography or

literature survey, mention it here.) This report provides a methodology for determining the optimal heat pump size,

in terms of heating output capacity, for residential installations having annual

heating requirements significantly greater than annual cooling requirements. The

optimal size heat pump is defined as the size for which total present value,

life-cycle heating and cooling costs (including equipment costs) are minimized.

Incremental energy savings from increasing the output capacity of the heat pump

are calculated using hourly simulation models of heat pump and building performance

developed at NBS. The dollar value of the incremental savings, in present -value,

life-cycle terms, is then calculated and compared with incremental costs to

determine the optimal heat pump size. A base case analysis of an 1800 square-foot

house in the Chicago climate shows that a slightly larger heat pump size than would

typically be selected for air conditioning purposes alone is optimal for the

assumptions specified. A number of sensitivity analyses are performed to show the

effects of changes in load size, degradation coefficients, power utilization

efficiency, economic assumptions and geographic location on the optimal heat

pump size

.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unleaa a proper name;

separated by semicolons)

Benefit-cost analysis; energy conservation; equipment selection; equipment

sizing; heat pump; life-cycle costs.

18. AVAILABILITY ^Unlimited

I I For Official Distribution. Do Not Release to NTIS

I I Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003-

I I Order From National Technical Information Service (NTIS), Springfield,

VA. 22161

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF

PRINTED PAGES

74

22. Price

$ 8.00

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