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 (PER CL ) and pump energy index (PEI CL ) 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 PEI CL 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 (y i )” and proposed to define the part load motor losses as a polynomial

function of the load ing of the motor as shown in the following equation:

y i = ( L i

L full )

= (

A × ( P i

Motor HP ) 3

+ B × ( P i

Motor HP ) 2

C × ( P i

MotorSize )

+ D )

Where:

y i = the part load loss factor at load po int i,

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

L full = motor losses at full load (hp),

P i = 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)

.

F or 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 (PER VL and PEI VL ) metrics for pumps sold with motors and controls.

2 In the pumps test procedure NOPR, DOE proposed metrics of PEI CL and PEI VL . 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 (y i ) , which is a ratio of

the part

- load losses to the nomin al 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 sev en

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 ad dressed 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 database 4 and DOE’s Motor Challenge

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

subcommittee. These data are public ly 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 v s. 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

PEI CL 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 Analyz ed

. 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 ta ble 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.pdf3 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 e ach 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 factor s based on the range of

horsepower curves , as shown in Table 2.

Table 2. Maximum and Minimum Part Load Loss Factors (y i ) 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 (y i ) at Each Load Point i

Motor Rotating Speed

and Design Relative Losses 100% 75% 50% 25%

2

- pole O pen 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 O pen 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 w ith 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 PEI CL value, the minimum an d 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

. Over all Maximum and Overall Minimum Part Load Loss Factor (y i ) Polynomial

Equations.

To determine the significance of th ese different part load loss factor values on the resultant PEI CL , DOE

calculated the PEI CL 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 PEI CL resulting

from the different part load loss fraction values

. This example pump has the following characteristics

shown in Table 3.

Table 3. P arameters of Example Pump Used for Sensitivity Analysis

BEP Flow

Rate Pump

Efficiency Shaft Power at 1 10%

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

T able 4 shows t he constant load pump energy rating (PER CL ) 6 and the PEI CL 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 (PER CL ) and Pumps Energy Index (PEI CL ) for

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

Factor Polynomial Equations

Part Load Loss Factor Equation PER CL (hp) PEI CL

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.5

In addition, Table 4 shows the percent difference in PER CL and PEI CL 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 ana lyzed.6



### 5. APPENDIX A : NEMA MOTOR AND DRIVE WORK ING 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 92.87

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