6-i 

CHAPTER 6. ENERGY USE CHARACTERIZATION 

TABLE OF CONTENTS 

6.1 INTRODUCTION ........................................................................................................... 6-1 

6.2 ENERGY USE ANALYSIS FOR SMALL ELECTRIC MOTORS............................... 6-1 

6.2.1 Introduction.................................................................................................... 6-1 

6.2.2 Motor Losses.................................................................................................. 6-1 

6.2.3 Reactive Power .............................................................................................. 6-2 

6.2.4 Motor Applications........................................................................................ 6-4 

6.2.5 Loading .......................................................................................................... 6-5 

6.2.6 Motor Hours of Operation/Duty Factor......................................................... 6-5 

6.3 ANNUAL ENERGY USE............................................................................................... 6-8

6-7

6-8

6-6

6-7

LIST OF TABLES 

Table 6.2.1 Losses vs. Loading, Polyphase Motors................................................................ 6-2 

Table 6.2.2 Losses vs. Loading, Capacitor-Start Induction Run Motors................................ 6-2 

Table 6.2.3 Losses vs. Loading, Capacitor-Start Capacitor-Run Motors............................... 6-2 

Table 6.2.4 Power Factor vs. Loading, Polyphase Motors..................................................... 6-3 

Table 6.2.5 Power Factor vs. Loading, Capacitor-Start Induction-Run Motors..................... 6-4 

Table 6.2.6 Power Factor vs. Loading, Capacitor-Start Capacitor-Run Motors..................... 6-4 

Table 6.2.7 Application Shares by Equipment Type .............................................................. 6-5 

Table 6.2.8 Motor Loading by Application ............................................................................ 6-5 

Table 6.2.9 Median and Average Hours of Motor Operation by Application........................ 

Table 6.3.1 Average Annual Electricity Use by Efficiency Level for Small Electric 

Motors.................................................................................................................. 

LIST OF FIGURES 

Figure 6.2.1 Comparison of DOE’s Duty Factor Model with Nadel et al. .............................. 

Figure 6.2.2 DOE Estimates of Duty Factor Distributions for Motors in Analyzed 

Applications......................................................................................................... 

EERE-2007-BT-STD-0007 COMMENT 33
6-1 

CHAPTER 6. ENERGY USE CHARACTERIZATION 

6.1 INTRODUCTION 

A key component of the life-cycle cost (LCC) and payback period (PBP) calculations 

described in chapter 8 is the savings in operating cost customers would realize from more energy 

efficient products. Energy costs are the most significant component of customer operating costs, 

with maintenance and repair costs the other contributors. DOE uses annual energy use, along 

with energy prices, to establish energy costs at various energy efficiency levels. This chapter 

describes how DOE determined the annual energy use of small electric motors. 

6.2 ENERGY USE ANALYSIS FOR SMALL ELECTRIC MOTORS 

6.2.1 Introduction 

The energy use by small electric motors derives from three components: energy 

converted to useful mechanical shaft power, motor losses, and reactive power. Motor losses 

consist of I2

R losses (both stator and rotor), core losses, stray losses and friction and windage 

losses.1

 Core losses and friction and windage losses are relatively constant with variations in 

motor loading, while I2R losses increase with the square of the motor loading. Stray losses are 

also dependent upon loading. DOE models the I2R losses and stray losses as load-dependent 

losses. 

6.2.2 Motor Losses 

DOE obtained estimates of motor losses from estimates of the performance of the 

specific motor designs that it developed in the engineering analysis. To determine the annual 

energy use in kilowatt-hours (kWh), DOE adjusts the full-load losses using the estimate of the 

motor duty factor (hours of operation per year) and loading. Tables 6.2.1 through 6.2.3 present 

the losses as a function of loading for each motor type and for each efficiency level analyzed by 

DOE. These efficiency levels correspond with designs analyzed in the Engineering Analysis. 

Total annual losses are proportional to duty factor. Annual energy losses Eloss is represented by 

the following equation: 

Eloss = Hop × Loss(L ) 

Where: 

 Eloss = annual energy consumed by motor losses; 

 Hop = the annual operating hours, also known as the duty factor; 

 Loss(L ) = the losses of the motor at loading L; and 

 L = motor loading as a fraction of rated power. 

EERE-2007-BT-STD-0007 COMMENT 33
6-2 

Table 6.2.1 Losses vs. Loading, Polyphase Motors 

Losses (W) vs. Loading (%) – Polyphase, 1 hp

EL Space Constrained Not Space Constrained 

 0% 25% 50% 75% 100% 125% 150% 0% 25% 50% 75% 100% 125% 150% 

0 123.7 132.7 150.8 179.6 221.5 279.7 361.4 123.7 132.7 150.8 179.6 221.5 279.7 361.4 

1 119.5 127.7 143.1 167.3 202.3 249.6 312.3 119.5 127.7 143.1 167.3 202.3 249.6 312.3 

2 107.3 115.4 130.5 153.6 187.2 232.2 291.2 107.3 115.4 130.5 153.6 187.2 232.2 291.2 

3 87.8 95.8 111.1 133.3 168.3 213.9 274.2 87.8 95.8 111.1 133.3 168.3 213.9 274.2 

4 84.1 91.8 106.1 127.2 158.6 199.4 253.1 84.1 91.8 106.1 127.2 158.6 199.4 253.1 

5 50.9 58.7 73.7 95.3 129.5 173.7 231.9 54.9 62.6 77.1 98.0 130.2 171.6 226.3 

6 46.2 53.7 66.7 85.5 114.0 150.1 197.0 51.1 58.5 71.5 91.0 117.8 153.3 199.0 

7 30.4 37.9 51.0 69.5 98.3 134.5 181.4 45.6 52.0 62.3 77.0 96.7 122.7 152.4 

Table 6.2.2 Losses vs. Loading, Capacitor-Start Induction Run Motors 

Losses (W) vs. Loading (%) – Capacitor-Start Induction-Run, 0.5 hp

EL Space Constrained Not Space Constrained 

 0% 25% 50% 75% 100% 125% 150% 0% 25% 50% 75% 100% 125% 150% 

0 227.3 221.3 230.4 247.0 273.4 312.6 369.0 227.3 221.3 230.4 247.0 273.4 312.6 369.0 

1 207.3 201.5 210.8 227.5 253.8 292.3 347.7 207.3 201.5 210.8 227.5 253.8 292.3 347.7 

2 176.2 178.7 187.9 204.0 228.5 264.0 314.1 176.2 178.7 187.9 204.0 228.5 264.0 314.1 

3 157.1 157.3 166.9 183.4 208.9 245.7 299.0 157.1 157.3 166.9 183.4 208.9 245.7 299.0 

4 120.5 119.1 128.9 145.5 171.2 208.6 262.4 124.3 126.6 134.9 150.0 171.6 202.5 245.8 

5 114.8 109.6 117.7 128.7 149.4 177.4 213.9 114.8 109.6 117.7 128.7 149.4 177.4 213.9 

6 92.0 91.8 100.8 115.4 137.1 168.6 214.6 101.3 99.4 107.3 118.8 137.3 161.3 194.8 

7 65.0 63.3 72.7 88.0 110.8 144.1 192.3 75.8 77.8 84.1 94.5 109.5 129.9 156.7 

Table 6.2.3 Losses vs. Loading, Capacitor-Start Capacitor-Run Motors 

Losses (W) vs. Loading (%) – Capacitor-Start Capacitor-Run, 0.75 hp

EL Space Constrained Not Space Constrained 

 0% 25% 50% 75% 100% 125% 150% 0% 25% 50% 75% 100% 125% 150% 

0 157.3 157.9 170.3 193.2 228.6 281.4 358.9 157.3 157.9 170.3 193.2 228.6 281.4 358.9 

1 155.5 144.6 151.9 167.2 192.4 231.8 291.4 155.5 144.6 151.9 167.2 192.4 231.8 291.4 

2 119.5 108.6 115.7 130.3 154.7 192.9 251.9 107.4 98.1 105.9 124.3 153.2 201.2 276.1 

3 112.6 98.9 103.8 115.4 135.7 171.3 221.1 87.7 79.5 88.4 106.3 135.5 180.3 248.9 

4 119.5 102.8 103.3 109.6 124.0 153.3 195.4 117.3 95.5 97.8 107.2 124.8 152.5 197.0 

5 134.0 98.4 102.1 106.1 115.9 133.0 159.3 118.5 89.4 94.1 101.7 116.2 139.2 173.1 

6 114.6 100.6 97.8 102.5 116.7 144.0 190.2 117.6 90.5 92.3 98.1 111.1 133.5 170.6 

7 113.0 82.2 84.2 88.7 100.0 119.7 150.0 102.0 71.8 75.4 81.4 94.1 115.0 146.3 

8 79.1 50.1 56.3 65.5 81.8 107.3 144.0 88.6 64.9 66.0 71.9 87.5 113.8 158.4 

6.2.3 Reactive Power 

 In an alternating current power system, the reactive power is the root mean square 

(RMS) voltage times the RMS current, multiplied by the sine of the phase difference between the 

voltage and the current. Reactive power occurs when the inductance or capacitance of the load 

EERE-2007-BT-STD-0007 COMMENT 33
6-3 

shifts the phase of the voltage relative to the phase of the current. While reactive power does not 

consume energy directly, it can increase losses and costs for the electricity distribution system. 

Motors tend to create reactive power because the windings in the motor coils have high 

inductance. 

Alternating current power flow has three components: real power (P), measured in watts 

(W); apparent power (S), measured in volt-amperes (VA); and reactive power (Q), measured in 

reactive volt-amperes (VAr). The power factor is defined as P/S. In the case of a perfectly 

sinusoidal waveform, P, Q and S can be expressed as vectors that form a vector triangle such 

that: S2 = P2 + Q2. This implies that the formula for reactive power as a function of real power 

and power factor is as follows: 

Q = P * (1/PF2-1) 

Where: 

 Q = reactive power in reactive volt-amperes; 

 P = real power in watts; 

 PF = the motor’s power factor; 

 DOE obtained motor power factor as a function of motor loading from estimates of the 

performance of the specific motor designs that it developed in the engineering analysis. Tables 

6.2.4 through 6.2.6 present the power factor as a function of loading for each motor type and for 

each efficiency level analyzed by DOE. 

Table 6.2.4 Power Factor vs. Loading, Polyphase Motors 

Power Factor (kW/kVAr) vs. Loading (%) – Polyphase, 1 hp

EL Space Constrained Not Space Constrained 

 0% 25% 50% 75% 100% 125% 150% 0% 25% 50% 75% 100% 125% 150% 

0 0.14 0.33 0.50 0.63 0.72 0.78 0.82 0.14 0.33 0.50 0.63 0.72 0.78 0.82 

1 0.13 0.33 0.50 0.63 0.71 0.77 0.81 0.13 0.33 0.50 0.63 0.71 0.77 0.81 

2 0.12 0.33 0.50 0.63 0.72 0.77 0.81 0.12 0.33 0.50 0.63 0.72 0.77 0.81 

3 0.12 0.35 0.54 0.67 0.74 0.79 0.82 0.12 0.35 0.54 0.67 0.74 0.79 0.82 

4 0.12 0.35 0.53 0.66 0.74 0.79 0.82 0.12 0.35 0.53 0.66 0.74 0.79 0.82 

5 0.07 0.30 0.49 0.64 0.72 0.77 0.81 0.08 0.33 0.53 0.67 0.74 0.79 0.82 

6 0.06 0.30 0.50 0.64 0.72 0.78 0.81 0.07 0.33 0.53 0.66 0.74 0.79 0.82 

7 0.04 0.28 0.49 0.63 0.72 0.77 0.80 0.06 0.31 0.51 0.64 0.73 0.78 0.82 

EERE-2007-BT-STD-0007 COMMENT 33
6-4 

Table 6.2.5 Power Factor vs. Loading, Capacitor-Start Induction-Run Motors 

Power Factor (kW/kVAr) vs. Loading (%) – Capacitor-Start Induction-Run, 0.5 hp

EL Space Constrained Not Space Constrained 

 0% 25% 50% 75% 100% 125% 150% 0% 25% 50% 75% 100% 125% 150% 

0 0.24 0.33 0.43 0.52 0.59 0.66 0.71 0.24 0.33 0.43 0.52 0.59 0.66 0.71 

1 0.23 0.32 0.42 0.51 0.59 0.66 0.71 0.23 0.32 0.42 0.51 0.59 0.66 0.71 

2 0.21 0.32 0.42 0.51 0.59 0.66 0.71 0.21 0.32 0.42 0.51 0.59 0.66 0.71 

3 0.21 0.33 0.44 0.54 0.62 0.68 0.73 0.21 0.33 0.44 0.54 0.62 0.68 0.73 

4 0.17 0.30 0.42 0.53 0.61 0.68 0.73 0.21 0.35 0.49 0.59 0.67 0.73 0.77 

5 0.16 0.28 0.41 0.52 0.60 0.66 0.71 0.16 0.28 0.41 0.52 0.60 0.66 0.71 

6 0.16 0.29 0.41 0.52 0.61 0.68 0.73 0.16 0.30 0.43 0.54 0.62 0.69 0.73 

7 0.13 0.30 0.45 0.58 0.67 0.73 0.77 0.14 0.31 0.46 0.57 0.66 0.71 0.75 

Table 6.2.6 Power Factor vs. Loading, Capacitor-Start Capacitor-Run Motors 

Power Factor (kW/kVAr) vs. Loading (%) – Capacitor-Start Capacitor-Run, 0.75 hp

EL Space Constrained Not Space Constrained 

 0% 25% 50% 75% 100% 125% 150% 0% 25% 50% 75% 100% 125% 150% 

0 0.19 0.35 0.49 0.60 0.68 0.74 0.78 0.19 0.35 0.49 0.60 0.68 0.74 0.78 

1 0.26 0.44 0.60 0.70 0.77 0.81 0.84 0.26 0.44 0.60 0.70 0.77 0.81 0.84 

2 0.20 0.39 0.55 0.67 0.75 0.80 0.83 0.27 0.52 0.70 0.79 0.84 0.86 0.87 

3 0.23 0.45 0.62 0.74 0.80 0.84 0.86 0.22 0.49 0.68 0.78 0.83 0.86 0.86 

4 0.43 0.69 0.82 0.88 0.91 0.92 0.92 0.78 0.92 0.95 0.96 0.96 0.95 0.94 

5 0.53 0.79 0.85 0.90 0.92 0.93 0.93 0.76 0.92 0.94 0.96 0.96 0.95 0.94 

6 0.99 1.00 1.00 1.00 0.99 0.99 0.97 0.97 1.00 1.00 1.00 0.99 0.98 0.97 

7 0.98 0.99 0.99 0.99 0.99 0.98 0.97 0.86 0.97 0.97 0.98 0.97 0.97 0.96 

8 0.32 0.69 0.79 0.87 0.90 0.92 0.92 0.77 0.96 0.99 1.00 1.00 0.99 0.97 

6.2.4 Motor Applications 

 The annual operating hours and loading of small electric motors depends on the 

application. For different types of motors, the market shares of different motor applications can 

vary. 

 As described in more detail in chapter 9 of this TSD, DOE drew upon several data 

sources to develop a model of the applications for which motors covered in this analysis are 

used: data collected by Easton Consultants in the preparation of the Small Motors Determination 

Analysis,2

 DOE’s own analysis in the Determination and Framework stages,3,4 U.S. Census 

reports, comments from interested parties (both written and at the preliminary analysis public 

meeting),5

 and interviews with experts in motor OEM industries.6 

 Table 6.2.7 summarizes the market shares for shipments of small electric motors by 

application based on DOE’s analysis of the available data. 

EERE-2007-BT-STD-0007 COMMENT 33
6-5 

Table 6.2.7 Application Shares by Equipment Category 

Equipment Category 

No. Application Polyphase CSIR CSCR 

1 Air and gas compressors 17.3% 14.9% 14.9% 

2 Conveyors 13.3% 11.9% 11.9% 

3 General industrial machinery 11.3% 12.5% 12.5% 

4 Industrial and commercial fans and 

blowers 7.3% 6.9% 6.9% 

5 Pumps and pumping equipment 50.7% 53.7% 53.7% 

TOTAL 100% 100% 100% 

6.2.5 Loading 

To calculate the annual kWh use at each efficiency level in each equipment class, DOE 

used the efficiencies and losses from the engineering analysis, along with estimates of operating 

hours. Since the losses of a motor depend on the motor loading, DOE estimated average motor 

loading in order to look-up the motor losses from the engineering data. DOE obtained motor 

loading as a function of motor application from the determination analysis for the applications 

that use equipment containing covered small electric motors, as shown in Table 6.2.8. DOE 

assumed that the motor loading distribution took the form of a normal distribution, centered on 

the average value, with a standard deviation equal to one fifth of the average loading. 

Table 6.2.8 Motor Loading by Application 

No. Application Loading 

1 Air and gas compressors 85% 

2 Conveyors 50% 

3 General industrial machinery 70% 

4 Industrial and commercial fans and blowers 80% 

5 Pumps and pumping equipment 65% 

6.2.6 Motor Hours of Operation/Duty Factor 

 DOE developed estimated distributions for the duty factor of motors for each application. 

See chapter 9 for a discussion of the applications that DOE analyzed for covered motors, and the 

fraction of small electric motor shipments for each application. DOE estimated the distribution of 

motor duty factors from data referenced in Nadel et al.

7

 DOE approximated this distribution as a 

decaying exponential curve plus a percentage of motors that operate 8760 hours per year (that is, 

EERE-2007-BT-STD-0007 COMMENT 33
100% of the time). Figure 6.2.1 shows the correspondence between this simple model and the 

data referenced in Nadel et al. 

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Duty Factor (Hours per year)

Cumulative Percentage of Motors

Nadel et al, 1-5 HP data

DOE Model, Small Motors

Figure 6.2.1 Comparison of DOE’s Duty Factor Model with 

Nadel et al. 

 DOE then adapted this model for each of the five application areas analyzed as part of 

this rulemaking: pumps; conveyor, material handling, and packaging systems; air compressors; 

blowers and fans; and general industrial machinery. DOE used estimates for average and median 

hours of operation based on the 2006 Determination Analysis, along with comments from 

interested parties on the Preliminary Analysis, to develop distributions for each application. 

Table 6.2.9 shows DOE’s estimated median and mean hours of operation in each 

application, along with the percentage of motors that operate 100% of the time. Figure 6.2.2 

shows the cumulative form of the discrete distributions DOE used in its Monte Carlo analysis. 

(The Monte Carlo analysis is described in chapter 8.) 

6-6 

EERE-2007-BT-STD-0007 COMMENT 33
Table 6.2.9 Median and Average Hours of Motor Operation by Application 

Application 

Median Annual 

Hours of Operation 

Average Annual 

Hours of Operation 

100% Run Time 

Motors (%) 

Compressors 375 600 0 

Conveyors 2000 3000 8 

General Industry 1200 2000 4 

Fans and Blowers 2825 4500 40 

Pumps 1850 3000 12 

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Duty Factor (Hours per Year)

Cumulative % of Motors

Compressors

Conveyors

Pumps

Fans & Blowers

General Industry

Figure 6.2.2 DOE Estimates of Duty Factor Distributions for 

Motors in Analyzed Applications 

6-7 

EERE-2007-BT-STD-0007 COMMENT 33
6-8 

6.3 ANNUAL ENERGY USE 

 Depending on the hours of operation and the loading (which are functions of the 

application) and the efficiency of the motor (which varies with the standard level), the annual 

energy use varies both by efficiency level and from motor to motor. Table 6.3.1 shows the 

average annual energy use as a function of efficiency level for the three representative product 

classes. In the table, the rated capacity of the representative motor from the product class is in 

parentheses. The average energy use estimates are from a calculation for a nationally 

representative distribution of motor applications, include both motor losses and the shaft power 

provided by the motor as described in chapter 8 of this TSD. 

Table 6.3.1 Average Annual Electricity Use by Efficiency Level for Small Electric 

Motors 

Polyphase (1 hp) CSIR (0.5 hp) CSCR (0.75 hp) Efficiency 

Level Efficiency 

(%) 

Energy Use 

(kWh/yr) 

Efficiency

(%) 

Energy Use 

(kWh/yr) 

Efficiency

(%) 

Energy Use 

(kWh/yr) 

Baseline 77.2 1763 57.7 1277 71.0 1451 

1 78.7 1734 59.5 1226 74.3 1389 

2 80.0 1698 62.0 1164 78.3 1278 

3 81.6 1645 64.2 1110 80.3 1233 

4 82.5 1629 68.5 1020 81.6 1239 

5 85.2 1549 71.2 971 82.7 1226 

6 86.7 1529 73.0 942 83.7 1219 

7 88.3 1494 77.0 877 85.4 1175 

8 NA NA NA NA 87.3 1144 

 

 

EERE-2007-BT-STD-0007 COMMENT 33
6-9 

 

REFERENCES 

1

 National Electrical Manufacturers Association, NEMA Standards Publication: 

Information Guide for General Purpose Industrial AC Small and Medium Squirrel-Cage 

Inducation Motor Standards, NEMA, 1300 North 17th Street, Suite 1847, Rosslyn, VA 

22209, 2002. 

2

 The work by Easton Consultants is summarized in Appendix B of Determination 

Analysis Technical Support Document: Analysis of Energy Conservation Standards for 

Small Electric Motors, June 2006 

<http://www1.eere.energy.gov/buildings/appliance_standards/commercial/pdfs/small_mo

tors_tsd.pdf> 

3

 Determination Analysis Technical Support Document: Analysis of Energy Conservation 

Standards for Small Electric Motors, June 2006 

<http://www1.eere.energy.gov/buildings/appliance_standards/commercial/pdfs/small_mo

tors_tsd.pdf> 

4

 Energy Conservation Standards Rulemaking Framework Document for Small Electric 

Motors 

<http://www1.eere.energy.gov/buildings/appliance_standards/commercial/pdfs/small_mo

tors_framework_073007.pdf> 

5

 Transcript of Public Meeting on Energy Conservation Standards for Small Electric 

Motors, January 30, 2009, 

<http://www1.eere.energy.gov/buildings/appliance_standards/commercial/pdfs/transcript

_small_motors_standards_meeting.pdf> 

6

 Joe Evans. PentAir Water Pumps, personal communication, March 5, 2009. 

7

 Nadel, S. ; Elliott, R.N. ; Shepard, M. ; Greenberg, S. ; Katz, G. ; Almeida, A. de, 

Energy-efficient motor systems: A handbook on technology, programs, and policy 

opportunities, 2nd edition. 2000. American Council for an Energy-Efficient Economy, 

Washington, DC (US). 

EERE-2007-BT-STD-0007 COMMENT 33