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௅஼/ ௅௏ൌ ቈ

∑ ߱௜൫ܲ௜௡

௜ ௜൯

቉ ௡௜௠ܴܧܲ

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);

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

speed as that being rated); and  

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

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

 Drive efficiency = 96%  

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

1 ൌ௏௅ ܴܧܲ

ߟ௖௧௥௟ ቈ

߱଴.ଶହ൫ܲ௜௡

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

቉ ௫௠௔ܴܧܲ

ൌ 1

ߟ௖௧௥௟ ቈ

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

቉ ௫௠௔ܴܧܲ

ൌ 1

ۏ ௟௥௧௖ߟ

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

How to Calculate the PERCL or PERVL 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.

 For PERCL, 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.

 For PERVL, based on the tested pump shaft input power at BEP, determine pump shaft

input power at 25%, 50%, 75%, and 100% of BEP flow based on the assumed system

curve: ܪ ൌ 0.8 ∗ ቀுಳಶು

ொಳಶು

మ ቁ ܳଶ ൅ 0.2ܪ஻ா௉.   

 Plug measured or calculated pump shaft input power at each load point into the

equation for PERCL or PERVL.

 For bare shaft pumps sold alone, determine 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), determine Lrated based on the

full load efficiency of the motor sold with the pump.  

 Apply motor losses equation and determine motor losses at each load point and plug

into PER equation.   

 Take a ratio of: (a) the average of the pump shaft input power plus motor losses at each

load point and (b) the average pump shaft input power plus motor losses of a minimally

compliant pump at each load point.  

Pass/Fail Determination in the Calculator:

 For pumps with control type entered as “None”, the numerator of PERCL is compared to

௫௠௔ܴܧܲ

o If PERେ୐ሺnumeratorሻ > ܲܧܴ௔௠௫ , FAIL

o If PERେ୐	ሺnumeratorሻ ≤ ܲܧܴ௔௠௫ , PASS

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

numerator of PERVL is compared to ܲܧܴ௔௠௫

o If PER୚୐ሺnumeratorሻ > ܲܧܴ௔௠௫ , FAIL

o If PER୚୐	ሺnumeratorሻ ≤ ܲܧܴ௔௠௫ , PASS

 The appropriate numerator can be found in column BY of the individual pump type tabs

in the spreadsheet