Last Updated 6/19/2014 by Sarah Widder

PEI Constant Load Description

Pumps sold as bare shaft pumps or with a constant speed motor are to tested in accordance

with HI 40.6 and their energy use is to be described based on the Constant Load Pump Energy

Index (PEICL).  The procedure for determining the PEICL and using the associated PEICL Calculator

(issued 6/19/2014) is as follows:

The Pump Energy Rating for Constant Load (PERCL) for 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 = constant load; and  

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

The Pump Energy Index (PEI) for constant load (CL) applications can then be calculated as the

PERCL for a given pump over the PER for a pump that is minimally compliant with DOE’s pump

standards (PERSTD) with no controls (i.e. the maximum PER possible for a pump of that type,

flow, and specific speed):

௅஼ܴܧܲ ൤ ൌ஼௅ ܫܧܲ

஽்ௌܴܧܲ

൨ ൌ ቈ

∑ ߱௜൫ܲ௜௡

௜ ௜൯

቉ ஽்ௌܴܧܲ

Where:  

PERSTD = 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.  

The power input to the pump at a specific load point (Pin

i) can be tested using a wire‐to‐water

test and input directly on the _Test tabs in the PEICL Calculator or can be calculated.   

PEICL 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.  
Last Updated 6/19/2014 by Sarah Widder

Expanding the PEICL equation yields the following equation:

ܲܫܧ ௅஼ൌ ቈ

∑ ߱௜ሺܲ௜ ൅ ܮ௜ሻ ௜

቉ ஽்ௌܴ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
Last Updated 6/19/2014 by Sarah Widder

ηBEP,60    = a’ (lnQ60)

2 + b’ (lnQ60 ∙ lnNs60) + c’ (lnNs60)2 + d’ lnQ60 + e’ lnNs60 + f ’

In this equation, Ns60 is the specific speed of the pump in IP units and Q60 is the flow rate

of the pump at BEP in GPM, both at 60 Hz, and the coefficients are defined as follows:  

Coefficents a’ b’ c’ d’ e’ f ’

US units (60 Hz) ‐0.85 ‐0.38 ‐11.48 17.80 179.80 C – 555.6

C is the C‐value of the surface, which is set based on the speed of rotation of the pump.  

The C‐values used for determining pump efficiency for the minimally compliant pump and

market average pump are contained in the Assumptions tab and are based on the

combined HI and DOE data set.  

Calculating Constant Load PEI:

 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

቉ ஽்ௌܴܧܲ

ൌ ቈ

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

቉ ஽்ௌܴ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

Pass/Fail Determination in the Calculator:

 For pumps sold as bare pumps or pumps sold with constant speed motors:

o If PEIେ୐ > 1 , FAIL

o If PEIେ୐	 ≤ 1 , PASS

PEI Instructions

How to Calculate the PEICL from Pump Data:
Last Updated 6/19/2014 by Sarah Widder

 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.

 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, 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.   

 For bare shaft pumps sold with motors and tested using the wire‐to‐water method,

enter the input power to the motor at 75%, 100%, and 110% of BEP flow.   

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.