Power Factor
and
Reactive Power
Ward Jewell
Wichita State University
Power Systems Engineering Research Center
(pserc.org)
PSERC
Energy to lift a 5 pound weight
2 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
800
energy
to motor
735.249
power (watts)
600
400
200
p ( t)
0 energy
from
motor
0
200
400
− 465.196
600
0
0
0.002
0.004
0.006
0.008
0.01
0.012
t
0.014
time (seconds)
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0.016
0.018
0.017
Induction motor
800
735.249
power (watts)
600
average
power:
130 watts
400
200
p ( t)
0
200
400
− 465.196
600
0
0.002
0
0.004
0.006
0.008
0.01
0.012
0.014
0.016
t
0.018
0.017
time (seconds)
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Incandescent lights
350
306.8
power (watts)
300
250
average
power:
150 watts
200
p ( t)
150
100
50
0
0
0
0
0.002
0.004
0.006
0.008
0.01
0.012
t
0.014
time (seconds)
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0.016
0.018
0.017
0
Incandescent Lights
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Induction motor with no load
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Lights and Motor
Power
Current
Voltage
Incandescent
lights
0.15 kW
1.3 A
118.0 V
Induction
motor with
no load
0.13 kW
5.1 A
117.7 V
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Why do the Volts and Amps matter?
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Page 5
Motors and Resistance Heat:
100 MW
Customer voltage
Power lost in wires
Resistance Heat
12.3 kV
1.0 MW
Motors
11.7 kV
2.3 MW
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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 with no load
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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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Induction motor with no load
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Define some new values:
Apparent power = volts x amps
For 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) power
Apparent (kVA) power
For the motor:
pf = 0.13 kW / 0.60 kVA
pf = 0.22
VI2 – average power2
2
2
( 0.60kVA) − ( 0.13kW) = 0.59 kVAR
0.58 kVAR
reactive power = 0.58 kVAR
reactive power =
Appa
rent p
ower
=
Define some new values:
the power triangle
for the motor:
0.60
kVA
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VAR: volt-ampere reactive
real power = 0.13 kW
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Induction motor with no load
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Lights and Motor
Real Reactive Apparent Power Current Voltage
power
factor
power
Power
Incandescent
lights
0.15
kW
0 kVAR
0.15 kVA
1.0
1.3 A
118.0 V
Induction
motor with
no load
0.13
kW
0.58
kVAR
0.60 kVA
0.22
5.1 A
117.7 V
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 wires
voltage drop between supply and load
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Typical Power Factors
Induction motor
0.7-0.8
Resistance heat
1.0
Incandescent lights
1.0
Fluorescent lights
0.6-1.0
Battery Chargers
0.6-1.0
Computers
0.5-1.0
Variable Speed Motor Drives
0.5-1.0
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Power factor:
lagging or leading?
Most loads with lower power factor
are inductive.
Current lags voltage.
Power factor is “lagging.”
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Induction motor with no load
voltage
current
3.6 ms
Current lags voltage by about 3.6 milliseconds
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Another way to calculate power factor
16.7 ms
3.6 ms
One 60 Hz cycle = 1/60 seconds = 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 degrees
current lags voltage by 77 degrees
cosine (77 degrees) = 0.22
power factor is 0.22 lagging
pf = cos θ
θ = angle between voltage and current
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Incandescent lights
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Current and voltage are “in phase.”
Incandescent lights:
displacement power factor:
angle between voltage and current
= 0 degrees
pf = cos(0 degrees) = 1.0
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true power factor:
pf = 0.15 kW / 0.15 kVA
pf = 1.0
Page 15
If voltage and current are sinusoidal
displacement pf (DPF) = true pf (PF)
lights
motor
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Correcting (increasing)
power factor
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Page 16
Capacitors to improve power factor:
capacitors release energy
when inductors consume
1.2
1
Capacitor
current
0.5
iL( t)
0
ic ( t)
Inductor
current
0.5
1
− 1.2
0
0.002
0.004
0.006
0.008
0
0.01
t
0.012
0.014
0.016
0.018
0.017
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Induction motor with
power factor correction capacitor
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Page 17
Induction motor with
power factor correction capacitor
Real Reactive Apparent
power power
power
Power
factor
Current Voltage
Induction
motor
0.13
kW
0.58
kVAR
0.60
kVA
0.22
5.1 A
117.7
V
Induction
motor with
capacitors
0.13
kW
0.11
kVAR
0.18
kVA
0.96
1.5 A
118.4
V
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Wire losses:
motors with capacitors
Customer voltage
Power lost in wires
Motors
11.7 kV
2.3 MW
Motors with power
factor correction
capacitor
12.3 kV
1.0 MW
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Page 18
Incandescent lights with
power factor correction capacitor
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Incandescent lights with
power factor correction capacitor
Incandescent
lights
Lights with
capacitors
Real Reactive Apparent
power power
power
0.15
0 kVAR 0.15 kVA
kW
0.15
kW
0.64
kVAR
0.66 kVA
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Power
factor
1.0
0.23
leading
Current Voltage
1.3 A
118.0 V
5.5 A
119.9 V
Wire losses:
lights with capacitors
Customer voltage
Power lost in wires
Resistance heat
12.3 kV
1.0 MW
Resistance heat
with power factor
correction
capacitors
13.0 kV
2.0 MW
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Leading power factor
Current 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 sinusoidal
displacement pf = true pf
lights
motor
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If waveform is not sinusoidal:
PC voltage and current
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Page 21
If waveform is not sinusoidal:
PC voltage and current
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Harmonic distortion
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Page 22
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 loads
„
„
„
„
„
„
computers
motor drives
battery chargers
rectifiers
induction heaters
arc 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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Summary
„
„
„
„
„
„
„
Induction motors and other inductive equipment load the electric
power system differently than incandescent lights and resistive
heaters
Power Factor and Reactive Power are indicators of power lost in
wires and reduced customer voltage
Low displacement power factor caused by induction motors (and
other inductive loads) can be corrected with power factor
correction capacitors
Power factor correction capacitors must be sized properly
Power factor correction capacitors cost much less than utility
power factor charges and will eliminate those charges
Power factor correction capacitors should be disconnected when
motors are disconnected
Low harmonic power factor is corrected with filters, not capacitors.
Capacitors may make it worse.
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Ward Jewell
316.978.6340
ward.jewell@wichita.edu
pserc.org
(slides are posted under “presentations”)
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