i

CHAPTER 7. ENERGY USE CHARACTERIZATION

TABLE OF CONTENTS

7.1 INTRODUCTION ...............................................................................................................1

7.2 ENERGY USE ANALYSIS FOR ELECTRIC MOTORS .................................................1

7.2.1 Introduction........................................................................................................1

7.2.2 Motor Losses......................................................................................................2

7.2.3 Reactive Power ..................................................................................................4

7.2.4 Motor Applications............................................................................................5

7.2.5 Loading ..............................................................................................................7

7.2.6 Motor Hours of Operation/Duty Factor.............................................................7

7.3 ANNUAL ENERGY USE...................................................................................................9

LIST OF TABLES

Table 7.1.1 Representative Units for Preliminary Analysis........................................................1

Table 7.2.1 Polynomial Equation Coefficients for Losses vs. Loading Relationship ................2

Table 7.2.2 Polynomial Equation Coefficients for Power Factor vs. Loading 

Relationship .............................................................................................................4

Table 7.2.3 Distribution of Motors by Application for NEMA Design A and B Motors 

(in percent)...............................................................................................................6

Table 7.2.4 Distribution of Motors by Application for NEMA Design C Motors (in 

percent) ....................................................................................................................6

Table 7.2.5 Motor Distribution across Sector by Motor Size ....................................................7

Table 7.2.6 Average Motor Loading by Application..................................................................7

Table 7.2.7 Average Motor Operating Hours by Application and Horsepower Range..............9

Table 7.3.1 Average Annual Energy Consumption by Efficiency Level for 

Representative Units..............................................................................................10

LIST OF FIGURES

Figure 7.2.1 Cumulative Distribution for 21-50 Horsepower Motors by Applications in 

Industry Sector.........................................................................................................8
1

CHAPTER 7. ENERGY USE CHARACTERIZATION

7.1 INTRODUCTION

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

described in chapter 8 of the Technical Support Document is the savings in operating costs that 

customers would realize from more energy efficient equipment. Energy costs are the most 

significant component of customer operating costs. The U.S. Department of Energy (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 electric 

motors.

The analysis focuses on eight representative units identified in the engineering analysis 

(chapter 5) and for which engineering analysis outputs were obtained. (Table 7.1.1)

Table 7.1.1 Representative Units for Preliminary Analysis

Representative 

Unit

Equipment class

Group Specifications Horsepower

1

NEMA Designs

A & B

NEMA Design B, T-frame, 

enclosed, 4-pole

5 

2 30 

3 75 

4

NEMA Design C NEMA Design C, T-frame, 

enclosed, 4-pole

5 

5 50 

6

Fire Pump Uses same engineering 

outputs as units 1, 2, and 3

5 

7 30 

8 75 

7.2 ENERGY USE ANALYSIS FOR ELECTRIC MOTORS

7.2.1 Introduction

The energy use by electric motors is derived 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-load 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-load losses are also 

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

losses.
2

7.2.2 Motor Losses

For each representative unit, DOE obtained data on part load motor losses from test data 

developed in the engineering analysis (chapter 5). Based on the test data, DOE modeled the 

motor losses as a function of loading using a third degree polynomial equation2

:

Loss(L) = A + B × L + C × L2 + D × L3

where:

Loss(L ) = the losses of the motor at loading L in watts

L = motor loading as a fraction of rated power in percent

A/B/C/D = polynomial equation coefficients

Table 7.2.1 presents the polynomial equation coefficients for modeling losses as a 

function of loading for the eight representative units at each efficiency level analyzed by DOE. 

These efficiency levels correspond to the candidate standard levels (CSLs) analyzed in the 

engineering analysis (chapter 5). 

Table 7.2.1 Polynomial Equation Coefficients for Losses vs. Loading Relationship

Representative 

Unit CSL A B C D

1

0 234.2 115.8 273.4 168.0

1 169.6 51.2 208.8 103.4

2 158.0 77.8 68.3 133.6

3 150.3 21.8 182.8 50.4

4 143.5 63.0 110.5 51.8

5 135.3 29.2 147.8 25.2

2

0 1059.3 181.4 1052.5 332.3

1 863.1 -14.8 856.3 136.1

2 639.7 102.7 586.8 201.1

3 509.6 17.5 622.2 253.9

4 444.6 228.4 358.3 271.3

5 444.6 228.4 358.3 271.3

3

0 1775.2 267.1 1757.2 411.8

1 1599.4 91.3 1581.4 236.0

2 870.8 280.9 1037.9 508.1

3 809.6 219.7 976.7 446.9

4 653.5 1006.4 -261.5 811.8

5 608.3 961.2 -306.7 766.6

4

0 220.3 62.5 159.7 90.3

1 202.0 85.7 67.8 82.1

2 194.2 74.6 76.2 60.3

3 179.7 36.1 115.0 38.0
3

5

0 1177.8 106.3 1240.8 282.6

1 829.6 970.7 -111.9 650.4

2 781.6 907.0 -140.1 622.2

3 609.3 1019.3 -575.5 910.2

0 169.6 51.2 208.8 103.4

1 158.0 77.8 68.3 133.6

6 2 150.3 21.8 182.8 50.4

3 143.5 63.0 110.5 51.8

4 135.3 29.2 147.8 25.2

0 863.1 -14.8 856.3 136.1

1 639.7 102.7 586.8 201.1

7 2 509.6 17.5 622.2 253.9

3 444.6 228.4 358.3 271.3

4 444.6 228.4 358.3 271.3

0 1599.4 91.3 1581.4 236.0

1 870.8 280.9 1037.9 508.1

8 2 809.6 219.7 976.7 446.9

3 653.5 1006.4 -261.5 811.8

4 608.3 961.2 -306.7 766.6

To determine the annual energy losses Eloss in kilowatt-hours (kWh), DOE converts the 

full-load losses into part-load losses using the estimate of the motor’s loading, and multiplies by 

the annual operating hours. Annual energy losses are represented by the following equation:

Eloss = Hop × Loss(L)

where:

Eloss = annual energy consumed by motor losses in watts per hour

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

L = motor loading as a fraction of rated power in percent

7.2.2.1 Impact of Higher Operating Speeds

DOE is aware that the installation of a more efficient motor could lead to less energy 

savings than anticipated. According to comments from interested parties, a more efficient motor 

typically has less slip than a less efficient motor, which is an attribute that can result in a higher 

operating speed and potentially overloading the motor. 

DOE acknowledges that the cubic relation between speed and power requirement in 

many variable torque applications can affect the benefits gained by efficient motors, which have 

a lower slip. DOE did not obtain sufficient data to incorporate this effect into the LCC analysis. 

Instead, DOE incorporated this effect as a sensitivity analysis in the LCC spreadsheet, allowing 

the user to consider this effect following a scenario which described in Appendix 7-A of the 

technical support document (TSD).
4

7.2.3 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 

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, and

PF = the motor’s power factor.

DOE used data on motor power factor as a function of motor loading from test data 

developed in the engineering analysis (TSD chapter 5) to develop a relationship between power 

factor and motor loading. This relationship is expressed as a third degree polynomial:

PF(L) = A + B × L + C × L2 + D × L3

Table 7.2.2 presents the polynomial equation coefficients developed to estimate power 

factor for all representative units at each efficiency level analyzed by DOE.

Table 7.2.2 Polynomial Equation Coefficients for Power Factor vs. Loading Relationship

Representative 

Unit CSL A B C D

1

0 0.036 2.055 -1.856 0.595

1 0.034 2.053 -1.858 0.592

2 0.066 1.664 -1.314 0.374

3 0.071 2.140 -2.034 0.663

4 0.074 2.140 -2.025 0.661

5 0.071 2.140 -2.034 0.663

2

0 0.076 2.143 -2.023 0.664

1 0.034 2.053 -1.858 0.592

2 0.034 2.053 -1.858 0.592

3 0.075 1.977 -1.817 0.575
5

4 0.047 2.332 -2.387 0.794

5 0.047 2.332 -2.387 0.794

3

0 0.036 2.055 -1.856 0.595

1 0.034 2.053 -1.858 0.592

2 0.074 2.140 -2.025 0.661

3 0.036 2.055 -1.856 0.595

4 0.043 2.492 -2.625 0.900

5 0.038 2.487 -2.630 0.895

4

0 0.033 1.612 -1.276 0.381

1 0.040 0.860 -0.269 -0.012

2 0.059 1.324 -0.831 0.177

3 0.077 1.746 -1.453 0.420

5

0 0.074 2.140 -2.025 0.661

1 0.044 1.925 -1.704 0.515

2 0.044 1.925 -1.704 0.515

3 0.050 2.401 -2.506 0.849

6

0 0.034 2.053 -1.858 0.592

1 0.066 1.664 -1.314 0.374

2 0.071 2.140 -2.034 0.663

3 0.074 2.140 -2.025 0.661

4 0.071 2.140 -2.034 0.663

7

0 0.034 2.053 -1.858 0.592

1 0.034 2.053 -1.858 0.592

2 0.075 1.977 -1.817 0.575

3 0.047 2.332 -2.387 0.794

4 0.047 2.332 -2.387 0.794

8

0 0.034 2.053 -1.858 0.592

1 0.074 2.140 -2.025 0.661

2 0.036 2.055 -1.856 0.595

3 0.043 2.492 -2.625 0.900

4 0.038 2.487 -2.630 0.895

7.2.4 Motor Applications

The annual operating hours and loading of motors depend on the sector (i.e., industry, 

agriculture, and commercial), motor size (in horsepower), and end-use application (e.g., pump). 

DOE estimated the share of motors in each type of application depending on the National 

Electrical Manufacturers Association (NEMA) design and size of the motor, and used a 

distribution of motors across sectors by motor size. DOE drew upon several data sources to 

develop a model of the applications for which motors covered in this analysis are used. 

Six motor applications (air compressors, fans, pumps, material handling and processing, 

fire pumps, and others) were selected as representative applications based on a previous DOE 

study (DOE-ITP study)3 and a database of motor nameplate and field measurement data 

compiled by the Washington State University (WSU) Extension Energy Program, Applied 
6

Proactive Technologies (APT), and New York State Energy Research and Development 

Authority (NYSERDA)4 (“WSU/NYSERDA database”)a. The tables below summarize the 

distribution of NEMA Design A and B motors (Table 7.2.3), and NEMA Design C motors 

(Table 7.2.4) across applications by horsepower range in the industrial sector. No sufficient data 

were available to develop similar estimates in the commercial or agricultural sector and, instead, 

the estimates in the industrial sector were used as an approximation.

Table 7.2.3 Distribution of Motors by Application for NEMA Design A and B Motors (in 

percent)

Horsepower (hp) range 

Application 1-5 6-20 21-50 51-100 101-200 201-500

all 

hp

Air Compressor 1.8 1.3 2.2 5.6 5.4 8.3 2.2

Fans 22.5 24.9 26.6 25.7 18.9 21.7 24.0

Pumps 22.3 31.6 33.0 34.2 36.0 25.5 28.5

Material Handling and Processing 12.0 9.4 6.8 10.6 7.8 7.6 10.0

Other 41.4 32.8 31.4 23.9 31.9 36.9 35.3

Fire Pumps 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Table 7.2.4 Distribution of Motors by Application for NEMA Design C Motors (in 

percent)

Horsepower (hp) range 

Application 1-5 6-20 21-50 51-100 101-200 all hp

Air Compressor 0.0 0.0 0.0 0.0 0.0 0.0

Fans 25.0 11.1 0.0 11.1 10.3 10.3

Pumps 0.0 0.0 28.6 0.0 6.9 6.9

Material Handling and Processing 25.0 11.1 14.3 11.1 13.8 13.8

Other 50.0 77.8 57.1 77.8 69.0 69.0

Fire Pumps 0.0 0.0 0.0 0.0 0.0 0.0

The distribution of motors across sectors by motor size was extracted from an Easton 

Consultants report5 which provides the distribution of alternating-current integral-horsepower 

motors by horsepower across various sectors. DOE adjusted the distribution across sectors to 

only account for three-digit NEMA frame size motors assuming that two-digit NEMA frame size 

 a The motors database comprised of information gathered by WSU and APT during 123 industrial motor surveys or 

assessments: 11 motor assessments were conducted between 2005 and 2011 and occurred in industrial plants; 112

industrial motor surveys were conducted between 2005 and 2011 and were funded by NYSERDA and conducted in 

New York State.
7

motors account for 30 percent of total integral motors below 5 hp and are primarily used in the 

commercial sector. (Table 7.2.5) 

Table 7.2.5 Motor Distribution across Sector by Motor Size

Horsepower 

range 

Industry 

%

Agriculture 

%

Commercial

%

1-5 37 0 63

6-20 26 0 74

21-50 26 0 74

51-100 63 7 30

101-200 76 3 21

201-500 69 3 28

7.2.5 Loading

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

used the losses versus load curves from the engineering analysis (Table 7.2.1), along with 

estimates of motor operating hours and average loading. 

The average motor loading mainly depends on the motor’s end-use application (e.g., fan, 

pump) and sector (e.g., industrial). In the industrial sector, the DOE-ITP study shows that, for a 

specific application, loading does not vary significantly across horsepower ranges. DOE 

estimated application-specific average loading based on approximately 15,000 field 

measurements provided by the WSU/NYSERDA database. A statistical distribution to 

characterize variability in the field was also extracted from the WSU/NYSERDA database. Table 

7.2.6 presents the average motor loading by applications in the industrial sector. Because 

sufficient data were not available, the same average loading values and statistical distribution 

were used in the commercial and agricultural sectors.

Table 7.2.6 Average Motor Loading by Application

Application Loading %

Air compressors 0.70

Fans 0.60

Pumps 0.68

Material Handling and Processing 0.48

Other 0.71

Fire Pumps 0.62

7.2.6 Motor Hours of Operation/Duty Factor

DOE estimated average annual operating hours by sector, application, and horsepower 

ranges and developed statistical distributions to use in its Monte Carlo analysis (the Monte Carlo 

analysis is described in TSD chapter 8).
8

For the industrial sector, DOE used the WSU/NYSERDA database to determine average 

annual operating hours by application and horsepower ranges and statistical distributions. For 

example, Figure 7.2.1 shows the cumulative form of the discrete distributions for motors 

between 21 and 50 horsepower in various applications. 

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

0 2000 4000 6000 8000

Cumulative Distribution

Operating Hours (Hours)

Air compressors

Fans

Pumps

Material Handling 

and Processing

Others

Fire Pump

Figure 7.2.1 Cumulative Distribution for 21-50 Horsepower Motors by Applications in 

Industry Sector.

For the commercial and agricultural sectors, DOE derived estimates of average operating 

hours by application and horsepower range from various sources: a presentation by Richard A. 

Peterson6

, an article by Michael Gallaher et al.

7

, the Regional Technical Forum8, DOE’s own 

analysis on classification and evaluation of electric motors and pump9

, an Electric Power 

Research Institute (EPRI) report10, and a DOE report by Arthur D. Little

11. For fire pumps, DOE 

assumed a uniform distribution between 0.5 hours (based on comments from interested parties) 

to 6 hours.

Table 7.2.7 displays the average hours of motor operation by application and motor sizes 

for the industrial, commercial, and agricultural sectors. 
9

Table 7.2.7 Average Motor Operating Hours by Application and Horsepower Range

Horsepower (hp) range 

1-5 6-20 21-50 51-100 101-200 201-500

Industry

Air Compressors 4,647 5,033 4,578 5,337 6,226 6,349 

Fans 6,193 6,490 5,849 6,975 7,163 8,015 

Pumps 6,028 6,773 6,972 6,869 6,985 6,934 

Material Handling 6,486 6,284 6,518 6,315 7,172 6,116 

Other 6,571 6,274 6,814 7,128 7,337 7,528 

Fire Pump 13 366 366 3,848 4,411 4,411 

Commercial

Air Compressors 1,000 1,200 1,500 1,500 1,500 1,500 

Fans 3,000 3,300 3,600 3,900 4,200 4,500 

Pumps 1,500 1,650 1,800 1,950 2,100 2,250 

Material Handling 1,959 2,165 2,380 2,567 2,753 2,939 

Other 1,959 2,165 2,380 2,567 2,753 2,939 

Fire Pump 0.5-6 0.5-6 0.5-6 0.5-6 0.5-6 0.5-6 

Agriculture

Air Compressors 1,901 1,901 1,901 1,901 1,901 1,901 

Fans 4,800 4,800 4,800 4,800 4,800 4,800 

Pumps 1,800 1,800 1,800 1,900 2,000 2,000 

Material Handling 1,500 1,500 1,500 1,500 1,500 1,500 

Other 1,901 1,901 1,901 1,901 1,901 1,901 

Fire Pump 0.5-6 0.5-6 0.5-6 0.5-6 0.5-6 0.5-6 

7.3 ANNUAL ENERGY USE

Depending on the hours of operation, the loading, 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. The annual energy use is calculated using the following expression:

Hop

HP L E ×× = η

where:

E = energy use,

HP = horsepower of the motor, or motor capacity,

L = motor loading as a fraction of rated power in percent

η = operating efficiency, and

Hop = motor operating hours.
10

Table 7.3.1 shows the results of the energy use analysis for the eight representative units

at each considered energy efficiency level. Results are given for baseline units (CSL 0) and the 

three candidate standard levels (CSLs) being considered for motors. 

Table 7.3.1 Average Annual Energy Consumption by Efficiency Level for Representative 

Units 

Rep.

Unit Description kilowatt-hours per yearCSL 0 CSL 1 CSL 2 CSL 3 CSL 4 CSL 5

1 Design B, T-frame, 5 

hp*, 4 poles, enclosed 10,448 9,869 9,691 9,616 9,567 9,487 

2 Design B, T-frame, 30 

hp, 4 poles, enclosed 57,642 55,912 55,021 54,492 54,326 54,326 

3 Design B, T-frame, 75 

hp, 4 poles, enclosed 204,834 202,540 198,496 197,697 197,194 196,604 

4 Design C, T-frame, 5 

hp, 4 poles, enclosed 9,987 9,808 9,738 9,630 - -

5 Design C, T-frame, 50 

hp, 4 poles, enclosed 89,523 88,507 88,119 87,444 - -

6 Fire pump, 5 hp, 4 

poles, enclosed 19.6 19.2 19.1 19.0 18.8 -

7 Fire pump, 30 hp, 4 

poles, enclosed 1,601 1,577 1,562 1,558 1,558 -

8 Fire pump, 75 hp, 4 

poles, enclosed 97,791 95,934 95,554 95,313 95,033 -

* hp = horsepower.
11

REFERENCES

 1 National Electrical Manufacturers Association (2002), NEMA Standards Publication: 

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

Induction Motor Standards, NEMA, 1300 North 17th Street, Suite 1847, Rosslyn, VA 22209.

2 Fernando J. T. E. Ferreira, Aníbal T. De Almeida (September 2011), Technical and 

Economical Considerations of Line-Start PM Motors Including the Applicability of the 

IEC600-34-2-1 Standard, Energy Efficiency in Motor Driven Systems, Alexandria, VA.

3 U.S Department of Energy (December 2002), United States Industrial Electric Motor System 

Market Opportunities Assessment. Retrieved February 9, 2011, from 

http://www1.eere.energy.gov/industry/bestpractices/pdfs/mtrmkt.pdf 

4 Database of motor nameplate and field measurement data compiled by the Washington State 

University Extension Energy Program (WSU) and Applied Proactive Technologies (APT) 

under contract with the New York State Energy Research and Development Authority 

(NYSERDA). 2011.

5 Easton Consultants, I. (2000), Variable Frequency Drive. Retrieved February 9, 2011, from 

http://neea.org/research/reports/E00-054.pdf 

6 Peterson, R. A. (n.d.). General Energy Management for Agricultural Facilities. Retrieved 

March 31, 2011, from http://www.mainerural.org/energy/fieldguide/generalfacilities.pdf

7 Gallaher, M., Delhotal, K., & Petrusa, J. (2009), Estimating the potential CO2 mitigation 

from agricultural energy efficiency in the United States, Energy Efficiency (2), 207-220.

8 Regional Technical Forum. Retrieved March 31, 2011, from Regional Technical Forum: 

http://www.nwcouncil.org/energy/rtf/measures/ag/IrrgAg_PremiumMotorsFY10v1_2.xls

9 U.S. Department of Energy (1980), Classification and Evaluation of Electric Motors and 

Pumps, Washington, D.C.

10 EPRI (1992), Electric Motors Markets, Trends, and Applications, EPRI.

11 Arthur D. Little, I. (1999), Opportunities for Energy Savings in the Residential and 

Commerical Sectors with High-Efficiency Electric Motors. Washington, DC: Department of 

Energy.