1

Determination of Default Motor Loss Curve: 

Sensitivity Analysis

1. SUMMARY

This memo describes the U.S. Department of Energy’s (DOE’s) analysis to support the use of a single

polynomial loss curve that is applicable to all motors addressed by the proposed pumps test procedure 

notice of proposed rulemaking (NOPR), independent of motor type, speed or size. DOE conducted a 

sensitivity analysis based on each of these factors and, in every case, the maximum impact on the rated 

constant load pump energy rating (PERCL) and pump energy index (PEICL) was less than 1 percent.1 As 

such, DOE determined that the additional complexity associated with multiple curves describing small 

variations in a motor’s part load performance is not justified. 

2. BACKGROUND

The pump energy index (PEI)

2

is a metric proposed by DOE in the pumps test procedure notice of 

proposed rulemaking (NOPR) to support DOE’s efforts to set energy conservation standards for 

commercial and industrial pumps. The PEI standardizes the energy use of pumps as a ratio of a specific 

unit’s energy consumption to a standardized minimally compliant pump. The PEICL is applicable to bare 

pumps and pumps sold with motors and requires standardized values for motor efficiency at full and 

partial loadings be determined based on rated full load motor efficiency. To determine the part load 

efficiency, or part load motor losses, DOE proposed to develop a polynomial loss curve that normalizes 

the part load losses as a fraction of the nominal motor losses at full load. DOE called this normalized 

value the “part load loss factor (yi)” and proposed to define the part load motor losses as a polynomial 

function of the loading of the motor as shown in the following equation: 

yi = (

Li

Lfull) = (A × (

Pi

MotorHP)

3

+ B × (

Pi

MotorHP)

2

C × (

Pi

MotorSize) + D)

Where:

yi = the part load loss factor at load point i,

Li = part load motor losses at load point i (hp),

Lfull = motor losses at full load (hp),

Pi = the shaft input power to the bare pump (hp), 

MotorHP = the motor horsepower (hp), and

i = percentage of the motor’s rated full load (hp).

For more discussion of the part load loss factor equation form, see the DOE test procedure NOPR section 

III.D.2. 

 

1

Because DOE used a separate curve for combined motor and control losses, this analysis is not applicable to the 

variable load (PERVL and PEIVL) metrics for pumps sold with motors and controls.

2

In the pumps test procedure NOPR, DOE proposed metrics of PEICL and PEIVL. These are described collectively 

as “PEI” in this document. 
2

3. DATA

DOE determined the cubic polynomial used to describe the part load loss factor (yi), which is a ratio of 

the part-load losses to the nominal full load losses of the motor at load point i, based on part load 

efficiency data provided by the NEMA electric motors subcommittee (included as Appendix A).

3 The 

data represent the measured part load performance of motors from 1–200 horsepower from seven 

manufacturers that are members of the NEMA subgroup. These data were provided at part load values of 

25, 50, 75, and 100 percent of the rated motor load. To determine how motor losses changed as a function 

of motor load over the range of those motors addressed in this rulemaking, the data were normalized 

based on the minimum full load efficiency of the motors. 

DOE also gathered additional data using DOE’s MotorMaster database4and DOE’s Motor Challenge 

Program Fact Sheet,5to corroborate the values and trends observed in the data provided by the NEMA 

subcommittee. These data are publicly available at the links provided below and not included in this 

memo. 

4. ANALYSIS

DOE recognizes that losses may vary as a function of the motor’s rotating speed (2-pole vs. 4-pole), 

motor design (open vs. enclosed), or the motor’s horsepower rating. To determine if such variation was 

significant enough to warrant separate curves as a function of any of these variables, DOE performed a 

sensitivity analysis to quantify the effect of separate curves versus one single curve on the measured 

PEICL of an example pumps, for each of these variables. Specifically, based on the available data, DOE 

developed unique part load loss curves for each unique combination of motor horsepower rating, rotating 

speed, and design, for a total of 76 individual part load loss curves, as indicated in Table 1. 

Table 1. Summary of 76 Unique Combinations of Motor Horsepower, Rotating Speed (2- or 4-Pole), 

and Motor Design (Open or Enclosed) DOE Analyzed.

Motor Horsepower

Motor 

Design

Open Enclosed

Rotating 

Speed

2-pole 4-pole 2-pole 4-pole

1 X X X X

1.5 X X X X

2 X X X X

3 X X X X

5 X X X X

7.5 X X X X

10 X X X X

15 X X X X

20 X X X X

 

3 During the CIP Working Group negotiations, the NEMA motor and drive working group provided DOE 

contractors with a table of representative nominal motor efficiency values, broken out by horsepower and motor 

load, to support development of the part load loss curves. These data are provided as Appendix A. 

4 Department of Energy. September 21, 2010. MotorMaster+. Version 4.01.01. 

www.energy.gov/eere/amo/articles/motormaster

5 Department of Energy. Determining Electrical Motor Load and Efficiency. pp. 13-14. 

www1.eere.energy.gov/manufacturing/tech_assistance/pdfs/10097517.pdf
3

25 X X X X

30 X X X X

40 X X X X

50 X X X X

60 X X X X

75 X X X X

100 X X X X

125 X X X X

150 X X X X

200 X X X X

For each rotating speed and motor design, DOE determined polynomial part load loss curves that 

described the maximum (or highest) and minimum (or lowest) part load loss factors based on the range of 

horsepower curves, as shown in Table 2. 

Table 2. Maximum and Minimum Part Load Loss Factors (yi) at 100, 75, 50, and 25 Percent of Full 

Motor Load for 2-Pole Open, 2-Pole Enclosed, 4-Pole Open, and 4-Pole Enclosed Motors

Part Load Loss Factor (yi) at Each Load Point i

Motor Rotating Speed 

and Design

Relative Losses 100% 75% 50% 25%

2-pole Open

Maximum 1.00 0.81 0.67 0.57

Minimum 1.00 0.66 0.46 0.33

2-pole Enclosed

Maximum 1.00 0.79 0.64 0.54

Minimum 1.00 0.65 0.46 0.34

4-pole Open

Maximum 1.00 0.83 0.68 0.60

Minimum 1.00 0.67 0.47 0.33

4-pole Enclosed

Maximum 1.00 0.81 0.66 0.58

Minimum 1.00 0.69 0.48 0.35

This resulted in eight unique curves that generally describe the overall maximum and minimum motor 

losses and can be used to identify significant motor loss trends with respect to the analyzed variables. 

Then to isolate the greatest or most significant impact any given part load loss curve could have on the 

calculated PEICL value, the minimum and maximum part load loss fraction values at 25%, 50%, 75% and 

100% over the entire data set, including all combinations of motor type, speed and size were determined 

by identifying the minimum and maximum part load loss curves of the eight “bounding” minimum and 

maximum curves described in Table 2. The “overall minimum” and “overall maximum” curves are shown 

in Figure 1.
4

Figure 1. Overall Maximum and Overall Minimum Part Load Loss Factor (yi) Polynomial 

Equations. 

To determine the significance of these different part load loss factor values on the resultant PEICL, DOE 

calculated the PEICL for an example model of bare pump using overall minimum and overall maximum

part load loss factor curves shown in Figure 1 and quantified the percentage change in the PEICL resulting 

from the different part load loss fraction values. This example pump has the following characteristics 

shown in Table 3. 

Table 3. Parameters of Example Pump Used for Sensitivity Analysis

BEP Flow 

Rate

Pump 

Efficiency

Shaft Power at 110% 

BEP flow

Shaft Power at BEP 

flow

Shaft Power at 75% 

BEP flow

900 GPM 81.6% 49.4 hp 46.5 hp 39.4 hp

Table 4 shows the constant load pump energy rating (PERCL)

6

and the PEICL determined using the overall 

maximum and overall minimum part load loss factor curves for the pump described in Table 3.

Table 4. Constant Load Pump Energy Rating (PERCL) and Pumps Energy Index (PEICL) for 

Example Pumps Based on Overall Maximum and Overall Minimum Part Load Loss 

Factor Polynomial Equations

Part Load Loss Factor Equation PERCL

(hp) PEICL

Overall Minimum 49.24 .8924

Overall Maximum 49.73 .8963

Percentage Difference (%) 0.98% 0.43%

 

6

The pump energy rating (PER) is the numerator of the PEI metric, see the pump test procedure NOPR for more 

information. 

y = -0.4508x3 + 1.2399x2- 0.4301x + 0.641

y = 1.0275x3- 1.0686x2 + 0.8818x + 0.1593

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Part Load Loss Factor (yi)

Motor Loading as a Percentage of Full Load (i)

Overall Maximum

Overall Minimum
5

In addition, Table 4 shows the percent difference in PERCL and PEICL for the analyzed pump, which are 

0.98 and 0.43 percent, respectively. DOE notes that, since the motor part load loss curves would be 

applied to all pumps equivalently, the results would be identical if a pump model with different 

characteristics were analyzed. 
6

5. APPENDIX A: NEMA MOTOR AND DRIVE WORKING GROUP-SUPPLIED DATA

NEMA MG1 Table 12-12 - OPEN MOTORS (PREMIUM LEVELS)

HP

Average - 2 Pole Open Average - 4 Pole Open

100% 75% 50% 25% 100% 75% 50% 25%

1 77.0 75.6 71.5 59.4 85.5 84.3 81.3 70.9

1.5 84.0 84.6 82.7 74.8 86.5 86.1 83.7 75.0

2 85.5 85.6 83.3 75.4 86.5 86.8 84.7 76.9

3 85.5 85.8 84.0 76.8 89.5 89.7 87.5 80.9

5 86.5 87.6 86.7 81.5 89.5 89.7 88.9 83.7

7.5 88.5 89.4 89.1 84.6 91.0 91.2 90.3 86.5

10 89.5 90.0 89.2 83.9 91.7 92.5 92.1 88.3

15 90.2 91.3 90.6 86.9 93.0 93.5 93.0 90.0

20 91.0 91.5 90.5 85.8 93.0 93.3 92.7 89.1

25 91.7 92.3 91.8 87.8 93.6 93.8 93.2 89.9

30 91.7 92.3 91.8 88.4 94.1 94.3 93.8 90.9

40 92.4 93.0 92.5 89.8 94.1 94.4 93.8 90.8

50 93.0 93.6 93.5 90.9 94.5 94.8 94.5 91.8

60 93.6 94.0 93.6 90.6 95.0 95.2 94.8 92.0

75 93.6 94.2 94.1 91.4 95.0 95.3 95.2 92.9

100 93.6 93.9 93.6 91.4 95.4 95.8 95.4 93.0

125 94.1 94.5 94.1 91.3 95.4 95.9 95.7 94.0

150 94.1 94.6 94.3 91.7 95.8 95.9 95.6 93.5

200 95.0 95.3 95.0 92.8 95.8 96.0 95.8 93.8

NEMA MG1 Table 12-12 - ENCLOSED MOTORS (PREMIUM LEVELS)

HP

Average - 2 Pole Enclosed Average - 4 Pole Enclosed

100% 75% 50% 25% 100% 75% 50% 25%

1 77.0 76.3 73.1 62.3 85.5 84.5 81.6 71.6

1.5 84.0 83.2 80.5 70.7 86.5 86.3 83.7 75.6

2 85.5 86.0 83.9 75.7 86.5 86.9 85.8 78.7

3 86.5 86.6 84.4 77.0 89.5 89.6 88.4 82.5

5 88.5 89.3 88.4 82.9 89.5 90.1 89.7 85.0

7.5 89.5 89.3 87.7 81.7 91.7 91.9 91.2 86.4

10 90.2 91.4 90.9 87.1 91.7 92.3 91.8 88.7

15 91.0 91.4 90.3 85.5 92.4 92.8 92.0 88.0

20 91.0 91.4 90.9 87.3 93.0 93.6 93.3 90.1

25 91.7 92.0 91.3 87.5 93.6 93.8 93.1 89.3

30 91.7 92.2 91.2 86.9 93.6 93.8 93.2 89.4

40 92.4 92.5 91.4 86.7 94.1 94.5 94.2 91.1

50 93.0 93.3 92.7 89.6 94.5 94.8 94.6 92.0

60 93.6 93.7 93.2 90.1 95.0 95.3 95.0 92.8
7

75 93.6 93.9 93.6 90.9 95.4 95.4 95.5 93.0

100 94.1 94.3 93.8 90.8 95.4 95.7 95.4 93.2

125 95.0 95.1 94.6 91.7 95.4 95.6 95.3 92.9

150 95.0 95.1 94.6 91.6 95.8 96.1 95.7 93.5

200 95.4 95.4 94.8 91.9 96.2 96.4 96.2 94.4