PER 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௅஼/ ௅௏ൌ෍߱௜൫ܲ௜௡

௜൯

௜

Where:

PER = Pump Energy Rating (hp);

wi = weight at each load point i;

Pin

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

CL/VL = constant load/variable load; and  

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

The Pump Energy Index (PEI) for constant load (CL) or variable load (VL) applications can then

be calculated as the PER for a given pump over the PER for a minimally compliant pump with no

controls (i.e. the maximum PER possible for a pump of that type, flow, and specific speed):

௅௏/௅஼ܴܧܲ൤ ൌ௏௅ /஼௅ܫܧܲ

௫௠௔ܴܧܲ

൨ ൌ ቈ

∑ ߱௜൫ܲ௜௡

௜ ௜൯

቉ ௫௠௔ܴܧܲ

Where:  

PERmax = PER Standard (i.e. a minimally compliant pump of the same type, flow, and specific

speed as that being rated) and other values as previously defined.  

Power input to the pump at a specific load point (Pin

i) is calculated as the power input to the

pump (Pi) plus the motor losses at that load point:

ܲ௜௡

௜ܮ ൅ ௜ܲ ൌ௜ 

Where:

Pin

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

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

Li = the fractional load motor losses (hp); and

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

Expanding the PER equation yields the following equation:

ܲܧܴ ൌ ቈ

∑ ߱௜ሺܲ௜ ൅ ܮ௜ሻ ௜

቉ ௫௠௔ܴܧܲ
The fractional motor losses at each load point i (Li) are calculated as the rated full load motor losses

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

by the part‐load loss factor (yi).  Determine Lrated from the motor efficiency as follows:

ܮ௔௥௧௘ௗ ൌ ߟ௢௠௧௢௥ሿ݌݄ሾ݁ݖܵ݅ݎ݋ݐ݋ܯ െ ሿ݌݄ሾ݁ݖܵ݅ݎ݋ݐ݋ܯ

Where ηmotor is the full load efficiency of the motor and MotorSize is the full load size of the motor in

horsepower.   

The part‐load loss factor (yi) is calculated as a cubic polynomial of the load fraction on the motor (xi).  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௘ௗ ∗ ሺܽ∗ݔ௜

௜ݔ∗ܾ൅ ଷ

ଶ ൅ܿ∗ݔ ൅ ௜݀ሻ

ൌ ܮ௔௥௧௘ௗ ∗ ቆܽ ∗ ൬ ܲ௜

൰݁ݖܵ݅ݎ݋ݐ݋ܯ

ଷ

൅ܾ∗ ൬ ܲ௜

൰݁ݖܵ݅ݎ݋ݐ݋ܯ

ଶ

൅ܿ∗ ൬ ܲ௜

ቇ݀ ൅ ൰݁ݖܵ݅ݎ݋ݐ݋ܯ

Where:

Li = the fractional load loss of the motor at load point i (hp);

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

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

yi = the part‐load loss factor;  

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

Pi = 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.  

The denominator represents a pump that is minimally compliant with the PER standard for a

given pump type and flow and head condition

 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

ܲܧܴ௔௠௫ ൌ ߱଴.଻ହ ቆ ܲு௬ௗ௥௢,଴.଻ହ

௣௠௨௣ߟ ∗ 0.95

൅ ܮ଴.଻ହቇ൅߱஻ா௉ ቆ

ܲு௬ௗ௥௢,஻ா௉

௣௠௨௣ߟ

൅ ܮ஻ா௉ቇ൅߱ଵ.ଵ ቆ ܲு௬ௗ௥௢,ଵ.ଵ

௣௠௨௣ߟ ∗ 0.985

൅ ܮଵ.ଵቇ

Where

ߟ௣௨௠௣ ൌ 88.59 ∗ lnሺܰݏሻ ൅ 13.46 ∗ lnሺܳ௠௘௧௥௜௖ሻ െ 11.48 ∗ lnሺܰݏሻଶ െ 0.85 ∗ lnሺܳሻଶ

െ 0.38 ∗ lnሺܰݏሻ ∗ lnሺܳሻ െ ܥ

In this equation, Ns is the specific speed of the pump in metric units, Q is the flow rate of

the pump at BEP in m3

/hr, C is the C‐value of the surface, which is set based on the speed

of rotation of the pump, and all values are for the pump at 50 Hz.  The C‐values used for
determining pump efficiency for the minimally compliant pump and market average pump

are contained in the Assumptions tab.  

For Constant Load PER:

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

point i

 For Bare Shaft Pumps Lrated 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

 For Pumps Sold Paired with a Motor Lrated is the full load losses of a motor that is paired

with the pump

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

 Equal weighting

ܲܧܴ ௅஼ൌ ቈ

߱଴.଻ହ൫ܲ௜௡

଴.଻ହ൯൅߱஻ா௉൫ܲ௜௡஻ா௉൯൅߱ଵ.ଵ൫ܲ௜௡ଵ.ଵ൯

቉ ௫௠௔ܴܧܲ

ൌ ቈ

߱଴.଻ହሺܲ଴.଻ହ ൅ ܮ଴.଻ହሻ ൅ ߱஻ா௉ሺܲ஻ா௉ ൅ ܮ஻ா௉ሻ ൅ ߱ଵ.ଵሺܲଵ.ଵ ൅ ܮଵ.ଵሻ

቉ ௫௠௔ܴܧܲ

ൌ

ۏ

ێ

ێ

1 ۍ

3 ∗ ሺܲ଴.଻ହ ൅ ܮ଴.଻ହሻ ൅ 1

3 ∗ ሺܲ஻ா௉ ൅ ܮ஻ா௉ሻ ൅ 13 ∗ ሺܲଵ.ଵ ൅ ܮଵ.ଵሻ

1

3 ∗ ൬ ܲு௬ௗ௥௢,଴.଻ହ

௣௠௨௣ߟ ∗ 0.95

1 ൅ ହ൰଻.଴ܮ ൅

3 ∗ ൬

ܲு௬ௗ௥௢,஻ா௉

௣௠௨௣ߟ

൅ ܮ஻ா௉൰ ൅ 1

3 ∗ ൬ ܲு௬ௗ௥௢,ଵ.ଵ

௣௠௨௣ߟ ∗ 0.985

൅ ܮଵ.ଵ൰

ے

ۑ

ۑ

ې

Variable Load PER (PERVL):

 Pi values are the calculated shaft input power to the pump (speed x torque) at each load

point i, based on the assumed system curve ܪ ൌ 0.8 ∗ ቀுಳಶು

ொಳಶು

మ ቁ ܳଶ ൅ 0.2ܪ஻ா௉.  This

system curve is based on the affinity laws, but is transformed to assume at static head

component that is equivalent to 20% of BEP head.   

 Lrated 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

 Controls efficiency = 96%  

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

ܲܧܴ ௅௏ൌ ቈ

߱଴.ଶହ൫ܲ௜௡

଴.ଶହ൯൅߱଴.ହ଴൫ܲ௜௡଴.ହ଴൯൅߱଴.଻ହ൫ܲ௜௡଴.଻ହ൯൅߱஻ா௉൫ܲ௜௡஻ா௉൯

቉ ௫௠௔ܴܧܲ

ൌ 1

ߟ௡௖௧௥௟௦

ൈ ቈ

߱଴.ଶହሺܲ଴.ଶହ ൅ ܮ଴.ଶହሻ ൅ ߱଴.ହ଴ሺܲ଴.ହ଴ ൅ ܮ଴.ହ଴ሻ ൅ ߱଴.଻ହሺܲ଴.଻ହ ൅ ܮ଴.଻ହሻ ൅ ߱஻ா௉ሺܲ஻ா௉ ൅ ܮ஻ா௉ሻ

቉ ௫௠௔ܴܧܲ
ൌ 1

0.96

ൈ

ۏ

ێ

ێ

ۍ

0.25ሺܲ଴.ଶହ ൅ ܮ଴.ଶହሻ ൅ 0.25ሺܲ଴.ହ଴ ൅ ܮ଴.ହ଴ሻ ൅ 0.25ሺܲ଴.଻ହ ൅ ܮ଴.଻ହሻ ൅ 0.25ሺܲ஻ா௉ ൅ ܮ஻ா௉ሻ

1

3 ∗ ൬ ܲு௬ௗ௥௢,଴.଻ହ

௣௠௨௣ߟ ∗ 0.95

1 ൅ ହ൰଻.଴ܮ ൅

3 ∗ ൬

ܲு௬ௗ௥௢,஻ா௉

௣௠௨௣ߟ

൅ ܮ஻ா௉൰ ൅ 1

3 ∗ ൬ ܲு௬ௗ௥௢,ଵ.ଵ

௣௠௨௣ߟ ∗ 0.985

൅ ܮଵ.ଵ൰

ے

ۑ

ۑ

ې

Pass/Fail Determination in the Calculator:

 For pumps with control type entered as “None”:

o If PEIେ୐ > 1 , FAIL

o If PEIେ୐	 ≤ 1 , PASS

 For pumps with control type entered as “VFD,”“2‐speed motor,” or “ECM”:

o If PEI୚୐ > 1 , FAIL

o If PEI୚୐	 ≤ 1 , PASS

PER Instructions

How to Calculate the PEICL and PEIVL from Pump Data:

 Measure the flow rate (gpm), head (ft), rotational speed (rpm), and torque (in‐lbf) at 7

points from minimum stable flow to maximum flow rate and determine the pump

efficiency at each point.   

 Determine BEP by finding the maximum of the pump efficiency curve, with respect to

flow rate.

 Determine pump input power (torque x speed) and regress power with respect to flow

to find a linear relationship between the 75% and 110% of BEP flow points.  Use this

regression to determine pump shaft input power at 75%, 100%, and 110% of BEP flow.

o For PERVL, based on the tested pump shaft input power at BEP, the calculator will

automatically calculate pump shaft input power at 25%, 50%, and 75% of BEP

flow based on the assumed system curve: H ൌ 0.8 ∗ ቀୌాుౌ

୕ాుౌ

మ ቁ Qଶ ൅ 0.2H୆୉୔.   

 For bare shaft pumps sold alone, no other information is required.  

o the calculator will determine the default Lrated by consulting the table of

minimum motor efficiencies in the test procedure for the given pump size and

type.   

 For bare shaft pumps sold with motors (and controls, if applicable), enter the motor

size, type (ODP or TEFC), and full‐load nameplate efficiency of the motor sold with the

pump.  

o The calculator will determine Lrated based on the full load efficiency and apply the

motor losses equation to determine motor losses at each load point.   

Based on the above data, the calculator will determine the PER of the rated pump and the PEI

for a controlled and variable load application.