6-i 

6-3

6-5

6-5

6-7

6-5

6-6

6-6

6-7

6-4

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 .............................................................................................. 

6.2.4 Motor Applications........................................................................................ 

6.2.5 Loading .......................................................................................................... 

6.3 ANNUAL ENERGY USE............................................................................................... 

LIST OF TABLES 

Table 6.2.1 Motor Application Market Shares ....................................................................... 

Table 6.2.2 Motor Operation Characteristics by Application................................................. 

Table 6.2.3 Average Operating Characteristics for Small Electric Motors............................ 

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

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

LIST OF FIGURES 

Figure 6.2.1 Average Dependence of Motor Losses on the Square of the Motor 

Loading for Polyphase 1 Horsepower Motor....................................................... 6-2 

Figure 6.2.2 Average Dependence of Reactive Power on Motor Loading for Polyphase 

1 Horsepower Motor............................................................................................ 

EERE-2007-BT-STD-0007 COMMENT 07.2
6-1 

CHAPTER 6. ENERGY USE CHARACTERIZATION 

6.1 INTRODUCTION 

The U.S. Department of Energy (DOE) carried out the life-cycle cost (LCC) and payback 

period (PBP) calculations described in chapter 8 by determining the savings in operating cost 

consumers would realize from more energy efficient products. Energy costs are the most 

significant component of consumer 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 I2

R losses and stray losses as load-dependent 

losses. 

6.2.2 Motor Losses 

DOE’s mathematical description of energy use separates motor losses into a constant 

component and a component that depends on motor loading. In DOE’s analysis, the design 

efficiency of the motor at full load determines the total losses at 100-percent motor loading. DOE 

then estimates the fraction of these losses that is load independent and the fraction that varies as 

the square of the motor loading. 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. All losses are proportional to duty factor, and DOE approximates the loaddependent losses as proportional to both the duty factor and the square of the loading. Annual 

energy use Eann is represented by the following equation: 

Eann = Hop × (PNL + PLL × L2 ) 

Where: 

 Eann = annual energy use; 

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

 PNL = the power of load-independent losses at full load; 

 PLL = the power of load-dependent losses at full load; and 

 L = motor loading as a fraction of rated power. 

EERE-2007-BT-STD-0007 COMMENT 07.2
y = 67.025x + 139.39

R2

 = 0.9874

0

50

100

150

200

250

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Square of Motor Loading

Loss (watts)

Figure 6.2.1 Average Dependence of Motor Losses on the Square of the Motor 

Loading for Polyphase 1 Horsepower Motor. 

 DOE confirmed the functional form of the dependence of motor losses on loading 

through a review of motor efficiency data from catalogue data available on the Internet as 

illustrated in figure 6.2.1 above. 

 For this preliminary analysis, DOE apportioned the losses at full load equally to PNL and 

PLL. For the notice of proposed rulemaking (NOPR), DOE will use a more sophisticated and 

potentially more precise method for apportioning full load losses to PNL and PLL. 

 While motor manufacturers do not explicitly publish motor losses as a function of load, 

many manufacturers do publish efficiency as a function of motor load. This allows the estimate 

of motor losses as a function of motor loading and a motor-by-motor estimate of PNL and PLL. 

The relationship between motor losses, efficiency and capacity is given by the following 

equation: 

Efficiency= (PW * L)/ (PW * L + Losses) 

Solving for the losses, we obtain: 

Losses = (PW * L)*(1/Efficiency – 1) 

Where: 

 Efficiency = motor efficiency; 

6-2 

EERE-2007-BT-STD-0007 COMMENT 07.2
6-3 

 PW = the motor’s rated power in watts; 

 Losses = the power of load-independent losses at full load in watts; 

 L = motor loading as a fraction of rated power. 

 DOE collected from the Internet efficiency vs. loading for several hundred listed motor 

models built in two-digit frame sizes. In some cases, on-line catalogues for at least two 

manufacturers had efficiency ratings for motors at 25, 50, 75 and 100 percent loading levels. 

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 

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. 

In practice, reactive power may result in only minor increases in energy consumption if 

capacitors in the electrical system compensate (i.e., mitigate) the reactive power. Also in 

previous analyses and standards for both small and medium electric motors, DOE has not 

considered power factor in the estimation of motor losses or efficiency. In this preliminary 

analysis, DOE assumes that, while reactive power may result in extra energy supply costs, actual 

losses before power factor compensation (through distribution system capacitor banks) are small. 

Actual fractional consumptive losses due to reactive power are approximately equal to the 

fractional losses on the electrical distribution system in general. This means that actual 

consumptive losses due to reactive power are likely to be less than 10 percent of total reactive 

power. For the NOPR, DOE will use a more sophisticated and potentially more precise method 

for accounting for the losses and costs due to reactive power. 

 While motor manufacturers do not explicitly report reactive power as a function of load, 

many manufacturers do publish power factor as a function of motor load. Power factor is the 

ratio of the real power divided by the apparent power, where the apparent power is the sum of 

the real power and the reactive power. This allows the estimate of motor reactive power as a 

function of motor loading and a motor-by-motor estimate of reactive power as a function of load. 

The relationship between reactive power (PF), efficiency, and rated power is given by the 

following equations: 

PF=Preal/Papparent

Where: 

Preal = (PW * L)/Efficiency 

and where: 

EERE-2007-BT-STD-0007 COMMENT 07.2
Papparent = Preal + Preactive

Solving for the reactive power, we obtain: 

Preactive = (PW * L)*(1/Efficiency)*(1/PF-1) 

Where: 

 Preal = real power in watts; 

 Papparent = apparent power in watts; 

 Preactive = reactive power in watts; 

 PW = the motor’s rated power in watts; 

 Efficiency = motor efficiency; 

 PF = the motor’s power factor; 

 L = motor loading as a fraction of rated power. 

 DOE collected from the Internet efficiency vs. loading for several hundred listed motor 

models built in two-digit frame sizes. In some cases, on-line catalogues for at least two 

manufacturers had power factor and efficiency ratings for motors at 25, 50, 75 and 100 percent 

loading levels. 

y = 413.73x + 113.35

R2

 = 0.9812

0

100

200

300

400

500

600

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Motor Loading

Reactive Power (watts)

Figure 6.2.2 Average Dependence of Reactive Power on Motor Loading for 

Polyphase 1 Horsepower Motor 

6-4 

EERE-2007-BT-STD-0007 COMMENT 07.2
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. In preparation for the determination analysis, DOE developed a classification of small 

electric motor applications and estimated shipments market shares for such motors in 2001. DOE 

then adjusted these market shares in the determination analysis to account for newly covered 

products and provided adjusted application market shares in the technical support document for 

the small motors determination.2 The estimates from the determination analysis provided 

information on only polyphase and capacitor start motors. For this analysis DOE used equal 

application market shares for capacitor-start induction-run (CSIR) and capacitor-start capacitorrun (CSCR) motors. 

Table 6.2.1 Motor Application Market Shares 

No. Application 

Polyphase 

(%) 

CSIR 

(%) 

CSCR 

(%) 

1 Air and gas compressors 9.2 8.1 8.1 

2 

Commercial and industrial heating, ventilating, 

air-conditioning (HVAC)/refrigeration equipment 4.3 8.4 8.4 

3 Commercial laundry machinery 0.4 1.2 1.2 

4 Conveyors 18.8 11.8 11.8 

5 Farm machinery 3.0 10.9 10.9 

6 Food machinery 8.2 2.1 2.1 

7 General industrial machinery 3.4 2.4 2.4 

8 Industrial and commercial fans and blowers 5.6 5.9 5.9 

9 Machine tools 7.3 1.9 1.9 

10 Packaging machinery 1.0 0.3 0.3 

11 Pumps and pumping equipment 33.0 41.1 41.1 

12 Service industry machinery 1.5 3.0 3.0 

13 Textile machinery 1.2 0.4 0.4 

14 Woodworking machinery 3.1 2.4 2.4 

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 and motor loading from the determination analysis for the applications that use equipment 

containing small electric motors (Table 6.2.2). 

6-5 

EERE-2007-BT-STD-0007 COMMENT 07.2
6-6 

Table 6.2.2 Motor Operation Characteristics by Application 

No. Application Hours/Year 

Motor Loading 

(Percent of Rated) 

1 Air and gas compressors 800 85 

2 

Commercial and industrial heating, ventilating, airconditioning (HVAC)/refrigeration equipment 

2,500 60 

3 Commercial laundry machinery 2,000 60 

4 Conveyors 3,000 50 

5 Farm machinery 1,000 70 

6 Food machinery 3,000 60 

7 General industrial machinery 2,000 70 

8 Industrial and commercial fans and blowers 5,000 80 

9 Machine tools 2,000 60 

10 Packaging machinery 3,000 60 

11 Pumps and pumping equipment 3,000 65 

12 Service industry machinery 1,500 60 

13 Textile machinery 3,000 70 

14 Woodworking machinery 2,000 35 

 DOE derived the distribution of values for operating hours and motor loading from the 

shares of the applications in the motor stock for each equipment class, as estimated in the 

determination analysis (Table 6.2.1). For this preliminary analysis, DOE used point values for 

hours of operation and loading for each application. For the NOPR, DOE may use a more 

sophisticated characterization of motor operating conditions by replacing these point values by 

distributions that have mean values that approximate the point values. This more precise 

characterization of motor operating conditions is likely to have a small effect on the mean result 

of DOE’s analyses, but may result in greater variability in the distribution of consumer economic 

impacts estimated by the life-cycle cost analysis. 

Table 6.2.3 shows the average values of operating hours and motor loading for each 

equipment class, weighted by the shares of each application. 

Table 6.2.3 Average Operating Characteristics for Small Electric Motors 

Equipment Class Annual Operating Hours 

Motor Loading 

(% of rated) 

Polyphase 2,665 63.2 

CSIR 2,557 64.8 

CSCR 2,557 64.8 

EERE-2007-BT-STD-0007 COMMENT 07.2
6-7 

6.3 ANNUAL ENERGY USE 

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

application) and depending on 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 product 

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

parentheses in each column header. In each case, the motors at the highest efficiency levels have 

losses that are approximately three times lower than the losses for the baseline designs. 

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

Motors 

Candidate Polyphase (1 Horsepower) CSIR (0.5 Horsepower) CSCR (0.75 Horsepower) 

Standard 

Level 

Efficiency 

(%) 

kWh Efficiency

(%) 

kWh Efficiency

(%) 

kWh 

Baseline 75.8 444 62.3 410 68.6 465 

CSL 1 84.0 265 70.9 278 80.2 250 

CSL 2 85.5 236 73.6 243 82.1 222 

CSL 3 86.5 217 75.4 220 83.3 203 

CSL 4 88.0 190 78.2 189 85.2 177 

CSL 5 90.0 154 81.8 151 87.6 143 

 

 

EERE-2007-BT-STD-0007 COMMENT 07.2
6-8 

 

REFERENCES 

1

 National Electrical Manufacturers Association Standards Publication Condensed MG1-2002: 

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, 

2002. Also see http://www.nema.org.. 

2

 U.S. Department of Energy-Office of Building Technologies. Technical Support Document: 

Analysis of Energy Conservation Standards for Small Electric Motors, June 2006, U.S. 

Department of Energy, Washington, DC. Also see 

http://www1.eere.energy.gov/buildings/appliance_standards/commercial/small_electric_motors.

html. 

EERE-2007-BT-STD-0007 COMMENT 07.2