jewell powerfactor westar-energy oct2006

PSERC

Power Factorand

Reactive Power

Ward JewellWichita State University

Power Systems Engineering Research Center (pserc.org)

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Energy to lift a 5 pound weight2 feet high:

2 ft x 5 lb = 10 ft-lb= 0.0000038 kWh

= 0.0033 “calories” (which are actually kcal)

Value at 10.3 cents per kWh:(average residential US price, summer 2006)

0.000039 cents

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As dragline bucket lowers, motors generate, return electricity to source

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Induction motor with no load

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018600

400

200

0

200

400

600

800735.249

465.196−

p t( )

0.0170 t

time (seconds)

pow

er (w

atts

)

energyto motor

energyfrom motor

0

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0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018600

400

200

0

200

400

600

800735.249

465.196−

p t( )

0.0170 t

time (seconds)

pow

er (w

atts

) averagepower:

130 watts

Induction motor

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Incandescent lights

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.0180

50

100

150

200

250

300

350306.8

0

p t( )

0.0170 t

0time (seconds)

pow

er (w

atts

)

averagepower:

150 watts

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Incandescent Lights

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Lights and Motor

5.1 A

1.3 A

Current

117.7 V0.13 kWInduction motor with

no load

118.0 V0.15 kWIncandescent lights

VoltagePower

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Why do the Volts and Amps matter?

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Motors and Resistance Heat:100 MW

2.3 MW11.7 kVMotors

1.0 MW12.3 kVResistance Heat

Power lost in wiresCustomer voltage

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Incandescent Lights

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Incandescent lights power:

Power = 118 V x 1.3 A= 153 W

= 0.15 kW= power measured by meter

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Incandescent Lights

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Induction motor power:

117.7 V x 5.1 A= 600 W?= 0.6 kW?

NOT the power measured by meter

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Define some new values:

Apparent power = volts x ampsFor the motor:

117.7 V x 5.1 A= 600 VA= 0.6 kVA

VA: volt-ampere

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Define some new values:

Power Factor =

Average (“real”) (kW) powerApparent (kVA) power

For the motor:pf = 0.13 kW / 0.60 kVA

pf = 0.22

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Define some new values:the power triangle

for the motor:

real power = 0.13 kW

reactive power =

reac

tive

pow

er =

0.5

8 kV

AR

0.60kVA( )2 0.13kW( )2− 0.59kVAR=

VAR: volt-ampere reactive0.58 kVAR

VI2 – average power2

Appa

rent

pow

er =

0.6

0 kV

A

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Lights and Motor

0.22

1.0

Power factor

0.60 kVA

0.15 kVA

Apparent power

0.58 kVAR

0 kVAR

Reactive power

5.1 A

1.3 A

Current

117.7 V0.13 kW

Induction motor with

no load

118.0 V0.15 kW

Incan-descent

lights

VoltageReal Power

Note: the motor’s reactive power will stay near its no-load value of 0.58 kVAR as its load and real

power (and thus apparent power and power factor) vary from no load to full load.

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Power factor and reactive power are indicators of

power losses in wiresvoltage drop between supply and load

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Typical Power Factors

0.5-1.0Variable Speed Motor Drives

0.5-1.0Computers

0.6-1.0Battery Chargers

0.6-1.0Fluorescent lights

1.0Incandescent lights

1.0Resistance heat

0.7-0.8Induction motor

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Power factor:lagging or leading?

Most loads with lower power factorare inductive.

Current lags voltage.Power factor is “lagging.”

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Current lags voltage by about 3.6 milliseconds

3.6 ms

currentvoltage

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Another way to calculate power factor

One 60 Hz cycle = 1/60 seconds = 16.7 ms

3.6 ms

16.7 ms

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Another way to calculate power factor:“displacement” power factor

(3.6 ms / 16.7 ms) x 360 degrees = 77 degreescurrent lags voltage by 77 degrees

cosine (77 degrees) = 0.22power factor is 0.22 lagging

pf = cos θθ = angle between voltage and current

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Incandescent lights

Current and voltage are “in phase.”

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Incandescent lights:

displacement power factor:angle between voltage and current

= 0 degreespf = cos(0 degrees) = 1.0

true power factor:pf = 0.15 kW / 0.15 kVA

pf = 1.0

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If voltage and current are sinusoidaldisplacement pf (DPF) = true pf (PF)

motor lights

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Correcting (increasing)power factor

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Capacitors to improve power factor:capacitors release energy when inductors consume

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

1

0.5

0

0.5

11.2

1.2−

iL t( )

ic t( )

0.0170 t

Inductorcurrent

Capacitorcurrent

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Induction motor with power factor correction capacitor

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118.4 V

1.5 A0.960.18 kVA

0.11 kVAR

0.13 kW

Induction motor with capacitors

117.7 V

5.1 A0.220.60 kVA

0.58 kVAR

0.13 kW

Induction motor

VoltageCurrentPower factor

Apparent power

Reactive power

Real power

Induction motor with power factor correction capacitor

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Wire losses:motors with capacitors

1.0 MW12.3 kVMotors with power factor correction capacitor

2.3 MW11.7 kVMotors


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Incandescent lights with power factor correction capacitor

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Incandescent lights with power factor correction capacitor

118.0 V1.3 A1.00.15 kVA0 kVAR0.15 kW

Incan-descent

lights0.23

leading

Power factor

0.66 kVA

Apparent power

0.64 kVAR

Reactive power

5.5 A

Current

119.9 V0.15 kW

Lights with capacitors

VoltageReal power

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Wire losses:lights with capacitors

2.0 MW13.0 kVResistance heat with power factor

correction capacitors

1.0 MW12.3 kVResistance heat


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Leading power factorCurrent leads voltage in a capacitor.

Too much capacitance causes low leading power factor.

(just as bad as low lagging power factor)

Leading power factor causes high voltage and increased wire losses.

Use the correct amount of capacitance.(more is not better)

Switch capacitors off when motors are off(just put capacitor on same switch as motor)

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If voltage and current are sinusoidaldisplacement pf = true pf

motor lights

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If waveform is not sinusoidal:PC voltage and current

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If waveform is not sinusoidal:PC voltage and current

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Harmonic distortion

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Low power factor caused by harmonic distortion cannot be

corrected by capacitors

Harmonic currents are not accompanied by harmonic voltage, so average (real) power

in harmonics is almost zero.pf = average power / apparent power

decreases

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Common harmonic loadscomputersmotor drivesbattery chargersrectifiersinduction heatersarc furnaces

To correct low power factor caused by distorted current waveforms, the

harmonic currents must be filtered.

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Capacitors can make harmonic distortion worse:

Lights with power factor correction capacitor

This is rare, but should be considered in the presence of harmonic loads

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SummaryInduction motors and other inductive equipment load the electricpower system differently than incandescent lights and resistive heatersPower Factor and Reactive Power are indicators of power lost in wires and reduced customer voltageLow displacement power factor caused by induction motors (and other inductive loads) can be corrected with power factor correction capacitorsPower factor correction capacitors must be sized properlyPower factor correction capacitors cost much less than utility power factor charges and will eliminate those chargesPower factor correction capacitors should be disconnected when motors are disconnectedLow harmonic power factor is corrected with filters, not capacitors. Capacitors may make it worse.

PSERC

Ward Jewell316.978.6340

[email protected]

(slides are posted under “presentations”)

jewell powerfactor westar-energy oct2006

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