BUILDING TECHNOLOGIE

May 29, 2014

ASRAC Pumps Working Group Webinar Meeting

Metric and Test Procedure
2

Overview

• Review general metric architecture

– Metric nomenclature

• Discuss implementation of PERCL and PERVL metrics

– Labeling/marking logistics, including sales and distribution channels

– Additional reported information or label information– Market impacts, especially application to utility programs

• Finalize metric issues that affect Standard

– Load points and weights

– Motor sizing and losses

• Motor and driver part load loss factor

• Submersible motor minimum efficiency standards
3

Pump Energy Rating (PER) and Index (PEI) NomePump Energy Rating (PER) CL and VL: equally weighted average elec

power to the ‘pump’ measured (or calculated) at the driver input or, 

controls input, over a specified load profile, over the weighted avera

input power to the pump for a minimally compliant, uncontrolled pu

Where:

• wi = weight at each load point i

• Pini = power input to the “pump” at the driver, inclusive of the 

present, (hp)

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

• i = 110%, 100%, 75% of Best Efficiency Point (BEP) flow at 

for uncontrolled pumps

• i = 25%, 50%, 75%, and 100% of BEP flow at nominal spee

sold with motors and controls

௫௠௔,௜௡ ௜ ௜ܲ௜ ߱௜௡ ௜ ௜ ∑ ܲ௜ ߱ ∑ ൌ ࡸࢂ/ࡸ࡯ࡾࡱࡼ
4

Pump Energy Rating (PER) and Index (PEI) NomePump Energy Rating (PER) CL and VL: equally weighted average elec

power to the ‘pump’ measured (or calculated) at the driver input or, 

controls input, over a specified load profile:

Where:

• wi = weight at each load point i

• Pini = power input to the “pump” at the driver, inclusive of the 

present, (hp)

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

• i = 110%, 100%, 75% of Best Efficiency Point (BEP) flow at 

for uncontrolled pumps

• i = 25%, 50%, 75%, and 100% of BEP flow at nominal spee

sold with motors and controls

Pump Energy Index (PEI) CL and VL: PER CL and VL, for a given pump 

the PERCL for a minimally compliant pump (PERmax):

௜௡௜ܲ ௜߱෍ ൌ ࡸࢂ/ࡸ࡯ࡾࡱࡼ

௜

ൌ ࡸࢂ/ࡸ࡯ࡵࡱࡼ

௅௏/௅஼ܴܧܲ

௫௠௔ܴܧܲ
5

Determining PEICL for an Uncontrolled Pump

• Pump Performance

– Pi values are the tested shaft input power to the pump (speed x torque) at ea

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

• Equal weighting

• Motor Performance (Losses)

– Lrated is the full load losses of a motor that is paired with the pump for pumps 

– Lrated is the full load losses of an enclosed motor that is minimally compliant w

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

and general purpose motors (subtype II) for ESCC pumps

ܲܫܧ ௅஼ൌ ఠబ.ళఱ ௉೔೙బ.ళఱ ାఠಳಶು ௉೔೙ಳಶು ାఠభ.భ ௉೔೙భ.భ ௉ாோ೘ೌೣ

ൌ

߱଴.଻ହ ܲ௜௡଴.଻ହ ൅ ߱஻ா௉ ܲ௜௡஻ா௉ ൅ ߱ଵ.ଵ ܲ௜௡ଵ.ଵ

߱଴.଻ହ

ܲு௬ௗ௥௢,଴.଻ହ

0.95 ∗ ߟ௣௨௠௣ ൅ ܮ଴.଻ହ ൅ ߱஻ா௉

ܲு௬ௗ௥௢,஻ா௉

ߟ௣௨௠௣ ൅ ܮ஻ா௉ ൅ ߱ଵ.ଵ

ܲு௬ௗ௥௢

0.985 ∗ ߟ

=

భయ

∗ ௉బ.ళఱା௅బ.ళఱ ାభయ∗ ௉ಳಶುା௅ಳಶು ାభయ∗ ௉భ.భା௅భ.భ

భయ

∗

ುಹ೤೏ೝ೚,బ.ళఱ

బ.వఱ∗ആ೛ೠ೘೛ା௅బ.ళఱ ାభయ∗ ುಹ೤೏ೝ೚,ಳಶು ആ೛ೠ೘೛ ା௅ಳಶು ାభయ∗ ುಹ೤೏ೝ೚,భ.భ బ.వఴఱ∗ആ೛ೠ೘೛ା௅భ.భ

• No Controls Performance
6

Determining PEIVL for a Controlled Pump

ൌ௏௅ ܫܧܲ

1

η௖௧௥௟

߱଴.ଶହ ܲ௜௡଴.ଶହ ൅ ߱଴.ହ଴ ܲ௜௡଴.ହ଴ ൅ ߱଴.଻ହ ܲ௜௡଴.଻ହ ൅ ߱஻ா௉ ܲ

߱଴.଻ହ

ܲு௬ௗ௥௢,଴.଻ହ

0.95 ∗ ߟ௣௨௠௣ ൅ ܮ଴.଻ହ ൅ ߱஻ா௉

ܲு௬ௗ௥௢,஻ா௉

ߟ௣௨௠௣ ൅ ܮ஻ா௉ ൅ ߱ଵ.ଵ

ܲ

0.9

=

ଵ

஗೎೟ೝ೗

భర

௉೔೙బ.మఱ ାభర ௉೔೙బ.ఱబ ାభర ௉೔೙బ.ళఱ ାభర ௉೔೙ಳಶು

ఠబ.ళఱ

ುಹ೤೏ೝ೚,బ.ళఱ

బ.వఱ∗ആ೛ೠ೘೛ା௅బ.ళఱ ାఠಳಶು

ುಹ೤೏ೝ೚,ಳಶು

ആ೛ೠ೘೛

ା௅ಳಶು ାఠభ.భ

ುಹ೤೏ೝ೚,భ.భ

బ.వఴఱ∗ആ೛ೠ೘೛

• Pump Performance

– Pi values are the tested shaft input power to the pump (speed x torque) at ea

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

• Equal weighting

• Motor Performance (Losses)

– Lrated is the full load losses of a motor that is paired with the pump for pumps 

• Controls Performance

– Benefit is captured in calculation of bare shaft input power

– Could still account for drive efficiency
7

Minimally Compliant Pump

• PER for a minimally compliant pump

– Based on PER Standard set through Standards analysis

– Assumes a pump curve shape for the minimally compliant pump and always 

controls

– Motor losses are that of a minimally compliant enclosed motor for the appr

– The minimally compliant pump efficiency is calculated for each pump type b

of flow and speed

ܲܧܴ௔௠௫ ൌ ߱଴.଻ହ

ܲு௬ௗ௥௢,଴.଻ହ

0.95 ∗ ߟ௣௨௠௣,௠௜௡ ൅ ܮ଴.଻ହ ൅ ߱஻ா௉

ܲு௬ௗ௥௢,஻ா௉

௣௠௨௣ߟ

൅ ܮ஻ா௉ ൅ ߱ଵ.ଵ

ܲு

0.985 

ߟ௣௨௠௣ ൌ 88.59 ∗ ln ܰݏ ൅ 13.46 ∗ ln ܳ௠௘௧௥௜௖ െ 11.48 ∗ ln ܰݏ ଶ െ 0.85 ∗ ln ܳ 

∗ ln ܳ െܥ

• Where:

– 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 o

– All values are for the pump at 50 Hz
8

Vote on Overall Metric Architecture?• The Working Group recommends that the general m

architecture be as follows:

Where:

– PEI = Pump Energy Index (dimensionless quantity)

– ∑ ߱௜ ܲ௜௡ ௜ ௜ ൌ ܲܧܴ, 	where PER = Pump Energy Rating 

• wi = weight at each load point i

• Pini = power input to the “pump” at the driver, inclusive o

controls if present, (hp)

– ܲܧܴெ௔௫ = PER for minimally compliant pump (also in h

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

pump

• i = 110%, 100%, 75% of Best Efficiency Point (BEP) flow a

speed for uncontrolled pumps

• i = 25%, 50%, 75%, and 100% of BEP flow at nominal spe

sold with motors and controls

ൌ ࡸࢂ/ࡸ࡯ࡵࡱࡼ

௅௏/௅஼ܴܧܲ

௫௠௔ܴܧܲ
9

Metric: Standard vs. Label
10

Metric Applicability: Standard vs. Label

Pump Configuration

Bare Pump* Bare Pump + Motor Bare Pump + Mo

Standard PEICL (w/ std. motor) PEICL PEILabel

PEICL & PEIVL

(w/ std. driver and

controls

PEICL & PEIVL

(w/ std. controls)

PEICL (with ra

& PE

Pump Motor

Pump Control Mot

• Pumps are regulated based on the configuration in which they ar

• Both controlled and uncontrolled performance captured on the l

• Uncontrolled pumps ‐> Constant Load Pump Energy Rating (P

• Controlled pumps ‐> Variable Load Pump Energy Rating (PER

*Pumps sold with non‐electric drives could be rated as bare pumps
11

Metric Goals

1. Be objectively measureable

2. Represent the

performance of thecovered equipment

3. Differentiate performance among pump

models and pump configurations

(e.g. pumps sold with controls)

4. Communicate information

about pump performance tothe consumer

– May not be all the information

a consumer uses to make adecision

5. Compare the

efficiency ofa given pump

model to aminimum standard level

Metric

Test

Procedure

Tested

Performance

of Pump A

Tested

Performance

of Pump B

Bare Pump

Efficiency

or Energy

Use

Mot

Efficie

or En

Us

‘Pump’

Efficiency

or Energy

Use

=
12

Application of Standard vs. Label

Metric Goals Standard LabelBe objectively measureableRepresent the

performance of the

covered equipment

PEICL or PEIVL depending

on pump configuration

Represents the per

the equipment in b

(variable load) and 

(constant load) app

Differentiate performance

among pump models and

pump configurations (e.g.pumps sold with controls)

Communicate informationabout pump performance

to the consumer

N/A Consumer can com

performance with c

variable load to a c

application with no 

Compare the efficiency of agiven pump model to a

minimum standard level

PEI is an index to

standard level, socomparison is inherentin metric value

N/A
13

Potential Impacts on Market

• Consumers/Contractors: Providing both the PEICL and 

the label will provide information to consumers regarimproved performance of pumps with controls in varload applications

– may not be all the information a consumer uses to make a d

but is an indicator of the opportunity for savings

• Utilities: Utilities could choose to incentivize a PEIVL o

certain value for variable load applications to encoura

use of VFDs (which will have a different system curve 

other controls) and a PEICL of a certain value for constapplications
14

Other Label or Reporting Options• Energy use/yr

– Establishing weights as operating hours at each weight

• Assume an annual number of operating hours/yr

• Still equally weighted over 3 or 4 load points for uncontrolled 

controlled pumps

ࡸ࡯ࡾࡱࡼ/ࡸࢂ ൌ ෍߱௜ ܲ௜௡௜ ൌ ߱଴.଻ହ ܲ௜௡଴.଻ହ ൅ ߱஻ா௉ ܲ௜௡஻ா௉ ൅ ߱ଵ.ଵ ܲ௜௡ଵ

௜

ൌ

1	ܹ݇

݌݄	1.34

∗ ߱଴.଻ହ ܲ௜௡଴.଻ହ ൅ ߱஻ா௉ ܲ௜௡஻ா௉ ൅ ߱ଵ.ଵ ܲ௜௡ଵ.ଵ

ൌ

1	ܹ݇

݌݄	1.34

∗ 1,000	݄ݏݎ ∗ 	ܲ଴௡௜.଻ହ ൅ 1,000	݄ݏݎ ∗ 	ܲ஻௡௜ா௉ ൅ 1,000	݄ݏݎ ∗ ܲ

ൌ

1	ܹ݇

݌݄	1.34

∗ ݏݎ݄	1,000 ൅ ݌3.40݄ ൅ ݌݄	47.66 ∗ 	ݏݎ݄	1,000 ൅ ݌3.01݄ ൅ ݌݄	40.16 ∗ 	ݏݎ݄	1,000 ∗

࢘࢟/ࢎࢃ࢑	ૠૡૠ , ૚૚૙ൌ ࡸ࡯ࡾࡱࡼ

࢘࢟/ࢎࢃ࢑	૙ૢ૝ ,ૡ ૝ൌ ࡸࢂࡾࡱࡼ
15

Motor Sizing and Motor Losses
16

Motor Selection

• Standardized Motor Performance

– Lrated is representative of enclosed motor that is minimally co

DOE’s motor regulations (10 CFR 431.25) for general purpose 

(subtype I) for all pumps except ESCC and general purpose m

(subtype II) for ESCC pumps

– Motor size will be next HP above maximum of pump shaft inp

horsepower at BEP, 110% of BEP, or 120% of BEP Q

• Pump shaft input horsepower at BEP, 110% of BEP, and 120% of 

determined based on linear regression of tested pump shaft hp 

– Poles will be based on speed at which pump is being rated

• Manufacturer Motor Performance

– Lrated is the full load losses of a motor that is paired with the p

– Motor size will be that sold with the pump

– Poles will be based on speed at which pump is being rated
17

Pump Curve Example – Determining Bare Shaft Input P

25% 50% 75% 100% 110% 120%

Percent of BEP Flow
18

Determining Bare Shaft Pump Input Power

– After determining BEP flow, part load power is determined th

regression of pump shaft input power vs flow rate for all data p

50% of BEP flow

• At very low part load, pump shaft input power vs flow rate curve 

• Using best fit linear regression, obtain pump shaft input power f

(QBEP, Q75%, Q110%)

y = 0.031x + 18.805

R2 = 0.9968

0

102030405060

0 500 1000 1500

Pump shaft input power (hp)

Flow rate (GPM)

Above 50% BEP flowBelow 50% BEP flow

120% of BEP flow

(for motor sizing)

% of BEP

flow

Flow R

(GPM

100 940 

75 705 

110 1034 120 1128 

– Instead could linea

between points to 

input power at part 

– Could also establish 

which interpolation 
19

Accounting for Motor Losses

• The proposed PERCL,PERVL, and PERmax calculations require assum

regarding how motors perform at part load

• Options to address motor efficiency in the PER calculations inclu

*Conservative = will result in a higher PER for calculation

method, as compared to testing

Option Accuracy Simplicity Burden Use only fullload efficiency Low High Low Use full loadlosses and

default losscurves

Medium Medium Medium 

Use measured

part loadefficiencies

High High

High – requires part load motortest procedure (IEEE 112B forpumps with motors and/or CSAC‐838 for pumps with motors

and controls), could consider

AEDM
20

Determining Part Load Motor Losses

The fractional motor losses at each load point i (Li) are calculated as the ra

motor losses (Lrated) multiplied by the part‐load loss factor (yi), which is calcubic polynomial* of the load fraction on the motor (xi):

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

ൌ ܮ௔௥௧௘ௗ ∗ ܽ ∗

ܲ௜

݁ݖܵ݅ݎ݋ݐ݋ܯ

ଷ

൅ܾ∗

ܲ௜

݁ݖܵ݅ݎ݋ݐ݋ܯ

ଶ

൅ܿ∗

ܲ௜

ݎ݋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 accorda

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); 

• i = Percentage of flow at the best efficiency point (BEP) of the pu

*A different cubic polynomial (i.e. different a, b, c, and d coefficients) cou

assumed based on the rotating speed (2‐pole vs. 4‐pole) and motor desig

vs. TEFC) or a single curve should be assumed for all

motors
21

Generating a Motor Loss Curve

• Use part load motor efficiency at 25%, 50%, 75%, and 

rated load

– Used efficiency values from DOE’s Motor Challenge Program1

݁ݓ݋ܲ	݁݀ݐܴܽ	݂݋	100% 75%, 50%, 25%, ൌ ݔ

• Obtain the part load fraction of total motor loss

௅ிߟെ1 ݔ ߟെ1 ∗ ݔ ߟ ௅ிߟ ∗ݔൌ ݔ ݂

1DOE. 2004. “Determining Electric Motor Load and Efficiency.” Available at:

http://www1.eere.energy.gov/manufacturing/tech_assistance/pdfs/10097517.pdf
22

Generating a Conservative Motor Loss Curve

• Find the maximum values of ݂ ݔ for each load fractio

across the entire power range

• Create a polynomial curve from the maximum points

– Scale the curve ݂ ݔ௔௠ ௫ by a scaling factor (ݏ. ݂. (to obtain co

values of ݂ ݔ

0.95 ൌ ݂. .ݏ	݁ݎ݄݁ݓ , ݂. .ݏ െ 1 ൅ ݂. .ݏ ∗ ௫ ௠௔ݔ ݂ ൌ ௦ ௖௢௡ݔ ݂ –

• Plot these conservative values of ݂ ݔ for all four load 

determine coefficients of the best fit cubic polynomial

݀൅ݔ∗ܿ൅ ଶݔ∗ܾ൅ ଷݔ∗ܽൌ ݔ ݂
23

HP Sizes 100% 75% 50% 25%

10 86.3 87.7 86.4 79.2

15 87.9 88 87.3 82.820 89.1 89.5 88.7 85.225 89 89.9 89.1 84.430 89.2 89.3 88.3 84.840 90 90.4 89.9 86.950 90.1 90.3 88.7 85.875 90.7 91 90.1 85.7

100 91.9 92.1 91.5 89125 91.6 91.8 91.1 88.8150 92 92.3 92 89.2

200 93 93 92.1 87.9250 92.7 93.1 92.4 87.1

300 93.9 94.3 93.8 90.4

Raw Efficiency Data from DOE Motor Challenge

100% 75% 

1 0.663 01 0.743 01 0.719 01 0.682 01 0.742 01 0.717 01 0.733 01 0.723 01 0.730 01 0.731 01 0.720 01 0.750 01 0.706 01 0.698 01 0.750 0

Max ݂ሺݔሻ of 

MAX

Motor Loss Curve – Example (ODP Motor 3600 
24

y = 0.2022x3 + 0.1828x2 + 0.2126x + 0.4

R2 = 1

y = 0.1921x3 + 0.1736x2 + 0.202x + 0.4323

R2 = 1

0.20.30.40.50.60.70.80.9

1

20% 30% 40% 50% 60% 70% 80% 90% 

Fractional load loss

Percent of motor load

Motor Loss Curve – Example (ODP Motor 3600 

X MAX ࢌሺ࢞ሻ X ‐ 1 MAX ࢌሺ࢞ሻ ‐ 1 Contraction 

0.25 0.470 ‐0.750 ‐0.530 ‐0.503 

0.50 0.580 ‐0.500 ‐0.420 ‐0.399 

0.75 0.750 ‐0.250 ‐0.250 ‐0.238 

11000
25

Cubic Polynomial Coefficient ݂(ݔ (Conserv

a 0.2022 0.1

b 0.1828 0.1

c 0.2126 0.2

d 0.4024 0.4

Motor Loss Curve – Example (ODP Motor 3600 

y = 0.1921x3 + 0.1735x2 + 0.202x + 0.4323

R2 = 1

0.30.40.50.60.70.80.9

1

0.2 0.4 0.6 0.8 1

fractional load loss

fractional load power

maximum 
26

Calculating Motor Losses

• Use part load loss curve developed for ODP motor, 180

determine part load loss factor (yi):

• Calculate the fractional input power as follows: ܲ௜௡௜ ൌ 

– Where Pi is the bare shaft input power in hp and the fractiona

each flow point, Lfull,rated is the full load losses determined in a

with 10 CFR 431.25 (subpart B)

% BEP flow

Bare pump

shaft input

power (hp)

Load

fraction

(xi)

Part load

loss factor

(yi)

Fractional

load loss (hp)

Fra

110 50.89 0.85 0.86 3.51 100 47.98 0.80 0.81 3.33 

75 40.69 0.68 0.71 2.92 

0.37

൅ ௜ݔ ∗ 0.1554 ൅ ଶ௜ݔ ∗ 5629 ൅ ଷ௜ݔ ∗ 0.0962െ ൌ௜ ݕ
27

Motor Efficiency for Non‐Covered Motors• PERmax requires a minimally compliant pump/motor

– Minimum motor efficiency needs to be determined and list

procedure for determination of PEI

– This is applicable for:

• Submersible pumps

• Other pumps?

• To generate non‐covered motor efficiency tables:

– Survey industry literature to determine available motor eff

each hp bin

– Select lowest efficiency available in each hp bin as minimum 

to be used as default motor efficiency

• Could also apply a scaling factor to ensure value is a minimum
28

Other Test Procedure Items to be Addressed in • Controls

– Accounting for savings from controls

– What types of controls to give credit to

• Testing vs. Calculation Methods

– Whether both calculation and testing methods are accepta

equipment class

– What to do about pumps sold with motors sized differently 

is specified in the test procedure

• What to do about issues with specific pumps

– i.e. where 120% BEP flow exceeds runout

• Others?
29

TP Process Slides
30

Test Procedure

• The scope of this working group does not include

development of the test procedure.

– The working group may vote or make recommendation

certain high‐level metric and test procedure items that 

standard:

• General metric architecture (i.e., ratio, denominator, etc.

• Load points and weights

• Motor sizing and losses

– It is not likely that detailed discussion of technical test 

issues will occur at this or future meetings.

• DOE anticipates resolving remaining test procedure detai

methodology through the traditional rulemaking process

with a test procedure NOPR this summer.
31

Additional Detail on Motor Losses and Motor L
32

Standard for submersible motors

Motor size

(hp)

Full 

Min

1.5 7

2 73 75 7

7.5 7

10 715 820 825 830 840 850 860 875 8

100 8125 8150 8175 8200 8250 8

72747678808284868890

1 10 100 1000

Efficiency (%)

Motor size (hp) ‐ logarithmic scale

Minimum motor efficiency

standard(submersible)

Minimum motor efficiencyProposed standard ‐ 98% min.
33

Cubic Polynomial Coefficient ݂(ݔ (Conserv

a ‐0.758 ‐0.1

b 1.6844 0.5

c ‐0.5531 ‐0.0

d 0.6267 0.6

Motor Loss Curve – TEFC Motor 3600 RPM

y = ‐0.1309x3 + 0.5333x2 ‐ 0.0209x + 0.6185

R2 = 1

0

0.20.40.60.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

conservative valuesmaximum values
34

Cubic Polynomial Coefficient ݂(ݔ (Conserv

a ‐0.1013 ‐0.0

b 0.5296 0.5

c 0.1635 0.1

d 0.3452 0.3

Motor Loss Curve – ODP Motor 1800 RPM

y = ‐0.0962x3 + 0.5629x2 + 0.1554x + 0.3779

R2 = 1

0

0.20.40.60.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

fractional load loss

fractional load power

maximum valueconservative va
35

Cubic Polynomial Coefficient ݂(ݔ (Conserv

a ‐1.0019 ‐0.2

b 2.6627 1.1

c ‐1.4745 ‐0.5

d 0.8137 0.7

Motor Loss Curve – TEFC Motor 1800 RPM

y = ‐0.2887x3 + 1.1705x2 ‐ 0.5991x + 0.7174

R2 = 1

0

0.20.40.60.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

fractional load loss

fractional load power

maximum valuesconservative values
36

Cubic Polynomial Coefficient ݂(ݔ (Conserv

a ‐0.8716 ‐0.7

b 2.1142 1.7

c ‐0.793 ‐0.6

d 0.5504 0.6

Motor Loss Curve – ODP Motor 1200 RPM

y = ‐0.7409x3 + 1.7971x2 ‐ 0.6741x + 0.6179

R2 = 1

0

0.20.40.60.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

fractional load loss

fractional load power

maximum valuesconservative values
37

Cubic Polynomial Coefficient ݂(ݔ (Conserv

a ‐1.4198 ‐0.2

b 3.2714 0.

c ‐1.5629 ‐0.0

d 0.7113 0.5

Motor Loss Curve – TEFC Motor 1200 RPM

y = ‐0.2541x3 + 0.809x2 ‐ 0.0811x + 0.5263

R2 = 1

0

0.20.40.60.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

fractional load loss

fractional load power

maximum valuesconservative value
38

Cubic Polynomial Coefficient ݂(ݔ (Conserv

a ‐1.8416 ‐0.5

b 3.7822 1.1

c ‐1.6348 ‐0.1

d 0.6942 0.5

Motor Loss Curve – ODP Motor 900 RPM

y = ‐0.5213x3 + 1.1267x2 ‐ 0.1497x + 0.5443

R2 = 1

0

0.20.40.60.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

fractional load loss

fractional load power

maximum valuesconservative value
39

Cubic Polynomial Coefficient ݂(ݔ (Conserv

a 5.2458 0.0

b ‐9.7958 0.0

c 5.8979 0.1

d ‐.3479 0.7

Motor Loss Curve – TEFC Motor 900 RPM

y = 0.0687x3 + 0.0334x2 + 0.1373x + 0.7606

R2 = 1

0

0.20.40.60.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

fractional load loss

fractional load power

maximum valuesconservative value