## PER Instructions/Description

The Pump Energy Rating (PER) is calculated as a weighted average of the input power to the

“pump,” inclusive of the driver and controls, over all load points (i) as shown in the following

equation:

ܲܧܴ ൌ ܨܥܮ ቈ ∑ ߱ ௜ ൫ܲ ௜௡

௜ ൯

௜

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቉

Where:

PER = Pump Energy Rating (hp);

LCF = Load Control Factor (dimensionless);

w i = weight at each load point i;

P in

i = power input to the “pump” at the driver, inclusive of the controls if present, (hp);

Denominator = potential denominators for comparison; and

i = Percentage of flow at the best efficiency point (BEP) of the pump.

Power input to the pump at a specific load point (P in

i ) is calculated as the power input to the

motor (P i ) plus the motor losses at that load point:

ܲ ௜௡

௜ ܲ ൌ ௜ ܮ ൅ ௜

Where:

P in

i = power input to the “pump” at the driver, inclusive of the controls if present (hp);

P i = the shaft input power to the bare shaft pump (hp);

L i = the fractional load motor losses (hp);

η drive = efficiency of the drive, if present; and

i = Percentage of flow at the best efficiency point (BEP) of the pump.

Expanding the PER equation yields the following equation:

ܨܥܮ ൌ ܴܧܲ ቈ ∑ ߱ ௜ ሺ ܲ ௜ ൅ ܮ ௜ ሻ ௜

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቉

The fractional motor losses at each load point i (L i ) are calculated as the rated full load motor losses

(L rated ) as determined in accordance with the motor test procedure at 10 CFR 431 subpart B multiplied

by the part

‐ load loss factor (y i ). The part

‐ load loss factor (y i ) is calculated as a cubic polynomial of the

load fraction on the motor (x i ). A different cubic polynomial (i.e. different a, b, c, and d coefficients) are

assumed based on the rotating speed (2

‐ pole vs. 4

‐ pole) and motor design (ODP vs. TEFC).

ܮ ௜ ൌ ܮ ௔௥௧௘ௗ ∗ ݕ݅ ൌ ܮ ௔௥௧௘ௗ ∗ ሺ ܽ∗ݔ ௜ ଷ ݔ∗ܾ൅ ௜ ଶ ൅ܿ∗ݔ ௜ ൅ ݀ ሻ

ൌ ܮ ௔௥௧௘ௗ ∗ ቆܽ ∗ ൬ ܲ ௜

݁ݖܵ݅ݎ݋ݐ݋ܯ ൰ ଷ

൅ܾ∗ ൬ ܲ ௜

݁ݖܵ݅ݎ݋ݐ݋ܯ ൰ ଶ

൅ܿ∗ ൬ ܲ ௜

݁ݖܵ݅ݎ݋ݐ݋ܯ ൰ ቇ݀ ൅

Where:L i = the fractional load loss of the motor at load point i (hp);

L rated = the rated full load motor losses as determined in accordance with the DOE test procedure

for motors at 10 CFR 431 subpart B (hp);

y i = the part

‐ load loss factor;

x i = the load fraction for the motor at each load point i;

P i = the shaft input power to the bare shaft pump (hp);

MotorSize = the nominal rated output power of the motor (hp); and

i = Percentage of flow at the best efficiency point (BEP) of the pump.

Note, that the shaft power input to the pump can be calculated as a rat io of the hydraulic output

power of the pump (P Hydro,i ) and the efficiency of the pump ( η pump,i ) at each load point i as follows:

ܲ

௜ ൌ ܲ ு௬ௗ௥௢,௜

ߟ ௜,௣௠௨௣

Load Control Factor values evaluated in this spreadsheet include 1 for no controls and 0.78 for a

variable frequency drive. The value of the LCF accounts for the efficiency of the drive (96%) and

reduced power input to the pump due to speed reduction.

ܨܥܮ ൌ ݂ ሺ ߟ ௗ௥௜௩௘ ሻ



### For Bare Shaft Pumps:

 P i values are the tested shaft input power to the pump (speed x torque) at each load

point i

 L rated is the full load losses of an enclosed motor that is minimally compliant with DOE’s

motor regulations (10 CFR 431.25) for general purpose motors (subtype I) for all pumps

except ESCC and general purpose motors (subtype II) for ESCC pumps

 LCF = 1 (no controls)

 Drive efficiency

= 100% (since no drive)

 i = 75%, 100%, and 110% of flow rate at BEP of the pump

 Equal weigh ting

ܨܥܮ ൌ ܴܧܲ ቈ ߱ ଴.଻ହ ൫ܲ ௜௡

଴.଻ହ ൯൅߱

஻ா௉ ൫ܲ ௜௡

஻ா௉ ൯൅߱

ଵ.ଵ ൫ܲ ௜௡

ଵ.ଵ ൯

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቉

ൌ ܨܥܮ ቈ ߱ ଴.଻ହ ሺ ܲ ଴.଻ହ ൅ ܮ ଴.଻ହ ሻ ൅ ߱ ஻ா௉ ሺ ܲ ஻ா௉ ൅ ܮ ஻ா௉ ሻ ൅ ߱ ଵ.ଵ ሺ ܲ ଵ.ଵ ൅ ܮ ଵ.ଵ ሻ

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቉ ൌ 1቎ 1

3 ∗ ሺ ܲ ଴.଻ହ ൅ ܮ ଴.଻ହ ሻ ൅ 1

3 ∗ ሺ ܲ ஻ா௉ ൅ ܮ ஻ா௉ ሻ ൅ 1

3 ∗ ሺ ܲ ଵ.ଵ ൅ ܮ ଵ.ଵ ሻ

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቏



### For Pumps Sold Paired with a Motor:

 P i values are the tested shaft input power to the pump (speed x torque) at each load

point i L rated is the full load losses of a motor that is paired with the pump

 LCF = 1 (no controls)

 Drive efficiency

= 100% (since no drive)

 i = 75%, 100%, and 110% of flow rate at BEP of the pump

ܨܥܮ ൌ ܴܧܲ ቈ ߱ ଴.଻ହ ൫ܲ ௜௡

଴.଻ହ ൯൅߱

஻ா௉ ൫ܲ ௜௡

஻ா௉ ൯൅߱

ଵ.ଵ ൫ܲ ௜௡

ଵ.ଵ ൯

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቉

ൌ ܨܥܮ ቈ ߱ ଴.଻ହ ሺ ܲ ଴.଻ହ ൅ ܮ ଴.଻ହ ሻ ൅ ߱ ஻ா௉ ሺ ܲ ஻ா௉ ൅ ܮ ஻ா௉ ሻ ൅ ߱ ଵ.ଵ ሺ ܲ ଵ.ଵ ൅ ܮ ଵ.ଵ ሻ

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቉ ൌ 1቎ 1

3 ∗ ሺ ܲ ଴.଻ହ ൅ ܮ ଴.଻ହ ሻ ൅ 1

3 ∗ ሺ ܲ ஻ா௉ ൅ ܮ ஻ா௉ ሻ ൅ 1

3 ∗ ሺ ܲ ଵ.ଵ ൅ ܮ ଵ.ଵ ሻ

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቏



### For Pumps Sold Paired with a Motor & Controls:

 P i values are the tested shaft input power to the pump (speed x torque) at each load

point i

 L rated is the full load losses of a motor that is paired with the pump, and losses are

calculated for the reduced loading with speed reduction

 LCF = 0.56 for VFD control, 0.67 for 2

‐ speed motor, etc.

 Drive efficiency

= 96%

 i = 25%, 50%, 75%, and 100% of flow rate at BEP of the pump

ܴܧܲ ܨܥܮ ൌ ቈ ߱ ଴.ଶହ ൫ܲ ௜௡

଴.ଶହ ൯൅߱

଴.ହ଴ ൫ܲ ௜௡

଴.ହ଴ ൯൅߱

଴.଻ହ ൫ܲ ௜௡

଴.଻ହ ൯൅߱

஻ா௉ ൫ܲ ௜௡

஻ா௉ ൯

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቉

ൌ ܨܥܮ ቈ ߱ ଴.ଶହ ሺ ܲ ଴.ଶହ ൅ ܮ ଴.ଶହ ሻ ൅ ߱ ଴.ହ଴ ሺ ܲ ଴.ହ଴ ൅ ܮ ଴.ହ଴ ሻ ൅ ߱ ଴.଻ହ ሺ ܲ ଴.଻ହ ൅ ܮ ଴.଻ହ ሻ ൅ ߱ ஻ா௉ ሺ ܲ ஻ா௉ ൅ ܮ ஻ா௉ ሻ

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቉

ൌ 0.78 ቈ 0.25 ሺ ܲ ଴.ଶହ ൅ ܮ ଴.ଶହ ሻ ൅ 0.25 ሺ ܲ ଴.ହ଴ ൅ ܮ ଴.ହ଴ ሻ ൅ 0.25 ሺ ܲ ଴.଻ହ ൅ ܮ ଴.଻ହ ሻ ൅ 0.25 ሺ ܲ ஻ா௉ ൅ ܮ ஻ா௉ ሻ

ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ ቉



## Denominator Options

This spreadsheet explores several denominator options, including:

 No Denominator

 Denominator = 1

ܨܥܮ ൌ ܴܧܲ ቈ ∑ ߱ ௜ ሺ ܲ ௜ ൅ ܮ ௜ ሻ ௜

1 ቉

 Units = hp (or kWh if w i take units of hours) Pump Hydraulic Output Power

 Denominator = hydraulic output power at each load point i

 Note, this example also flips the numerator and denominator to make

higher values “better.”

ܨܥܮ ൌ ܴܧܲ ൥ ߱ ෍

௜ ܲ ு௬ௗ௥௢,௜

ሺ ܲ ௜ ൅ ܮ ௜ ሻ

௜ ൩

 Units = dimensionless

 Minimally Compliant Pump

 Denominator = PER for a minimally compliant pump ( ≈ MEI10)

 Note, this assumes a pump curve shape for the minimally compliant

pump and always assumes no controls

 Motor losses are that of a minimally compliant enclosed motor as

described in the bare pump PER description for the appropriate pump

type

 The minimal ly compliant pump efficiency is calculated for each pump

type based on a function of flow and speed.

ܴܧܲ ௡௜௠

ܨܥܮ ൌ

ۏ ێ ێ ۍ

߱ ଴.଻ହ ൫ܲ ௜௡

଴.଻ହ ൯൅߱

஻ா௉ ൫ܲ ௜௡

஻ா௉ ൯൅߱

ଵ.ଵ ൫ܲ ௜௡

ଵ.ଵ ൯

߱ ଴.଻ହ ൬ ܲ ு௬ௗ௥௢,଴.଻ହ ߟ ∗ 0.95

௣௠௨௣ ൅ ܮ ଴.଻ହ ൰

൅ ߱ ஻ா௉ ൬ ܲ ு௬ௗ௥௢,஻ா௉

ߟ ௣௠௨௣ ൅ ܮ ஻ா௉ ൰

൅ ߱ ଵ.ଵ ൬ ܲ ு௬ௗ௥௢,ଵ.ଵ ߟ ∗ 0.985

௣௠௨௣ ൅ ܮ ଵ.ଵ ൰ ے ۑ ۑ ې

ൌ 1

ۏ ێ ێ ۍ 1

3 ∗ ሺ ܲ ଴.଻ହ ൅ ܮ ଴.଻ହ ሻ ൅ 1

3 ∗ ሺ ܲ ஻ா௉ ൅ ܮ ஻ா௉ ሻ ൅ 1

3 ∗ ሺ ܲ ଵ.ଵ ൅ ܮ ଵ.ଵ ሻ

1

3 ∗ ൬ ܲ ு௬ௗ௥௢,଴.଻ହ ߟ ∗ 0.95

௣௠௨௣ ܮ ൅ ହ଻.଴ ൰

൅ 1

3 ∗ ൬ ܲ ு௬ௗ௥௢,஻ா௉

ߟ ௣௠௨௣ ൅ ܮ ஻ா௉ ൰

൅ 1

3 ∗ ൬ ܲ ு௬ௗ௥௢,ଵ.ଵ ߟ ∗ 0.985

௣௠௨௣ ൅ ܮ ଵ.ଵ ൰ ے ۑ ۑ ې

 Units = dimensionless

 Market Average Pump

 Denominator = PER for a market average pump ( ≈ MEI50)

 Note, this assumes a pump curve shape for the market average pump

and always assumes no controls

 Motor losses are that of a minimally compliant enclosed motor as

described in the bare pump PER description for the appropriate pump

type

 The market average pump efficiency is calculat ed for each pump type

based on a function of flow and speed.ܴܧܲ ௡௜௠

ܨܥܮ ൌ

ۏ ێ ێ ۍ

߱ ଴.଻ହ ൫ܲ ௜௡

଴.଻ହ ൯൅߱

஻ா௉ ൫ܲ ௜௡

஻ா௉ ൯൅߱

ଵ.ଵ ൫ܲ ௜௡

ଵ.ଵ ൯

߱ ଴.଻ହ ൬ ܲ ு௬ௗ௥௢,଴.଻ହ ߟ ∗ 0.95

௣௠௨௣ ൅ ܮ ଴.଻ହ ൰

൅ ߱ ஻ா௉ ൬ ܲ ு௬ௗ௥௢,஻ா௉

ߟ ௣௠௨௣ ൅ ܮ ஻ா௉ ൰

൅ ߱ ଵ.ଵ ൬ ܲ ு௬ௗ௥௢,ଵ.ଵ ߟ ∗ 0.985

௣௠௨௣ ൅ ܮ ଵ.ଵ ൰ ے ۑ ۑ ې

ൌ 1

ۏ ێ ێ ۍ 1

3 ∗ ሺ ܲ ଴.଻ହ ൅ ܮ ଴.଻ହ ሻ ൅ 1

3 ∗ ሺ ܲ ஻ா௉ ൅ ܮ ஻ா௉ ሻ ൅ 1

3 ∗ ሺ ܲ ଵ.ଵ ൅ ܮ ଵ.ଵ ሻ

1

3 ∗ ൬ ܲ ு௬ௗ௥௢,଴.଻ହ ߟ ∗ 0.95

௣௠௨௣ ܮ ൅ ହ଻.଴ ൰

൅ 1

3 ∗ ൬ ܲ ு௬ௗ௥௢,஻ா௉

ߟ ௣௠௨௣ ൅ ܮ ஻ா௉ ൰

൅ 1

3 ∗ ൬ ܲ ு௬ௗ௥௢,ଵ.ଵ ߟ ∗ 0.985

௣௠௨௣ ൅ ܮ ଵ.ଵ ൰ ے ۑ ۑ ې

 Units = dimensionless