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Automatic power factor compensation is widely employed in industry to improve system performance and avoid penalty imposed by utility in case of poor power factor. Since relay based capacitor bank ...
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Understanding Power Factor Presented by Scott Peele PE
Understanding Power Factor
Definitions kVA, kVAR, kW, Apparent Power vs. True Power Calculations Measurements Power Factor Correction Capacitors System Impacts 2 R losses, Chapter 9 NEC I Equipment sizing Power Factor Charges Problems with adding Caps Harmonic resonance Volt rise Power Power Factor Factor vs Load Load Fact Factor or
What is Power Factor Power Factor is the cosine of the phase angle between current and voltage. Power Factor is the ratio of true power to apparent power.
Understanding Alternating Current AC 200
l e e d v e u L t i n e g g a t a l M o V
150
120 Volts RMS
100
169 volts 50
0
-50
One Cycle .01666 seconds
-100
-150
60 Hertz/second
-200 0
Duration Time
Phase Angle
200
l e e d v e u L t i n e g g a t a l M o V
150
120 Volts RMS
100
o
90 50
180
o
0
-50
One Cycle -100
-150
360 -200
o
o
0
270
Duration Degrees
Three Basic Circuits or Loads
Resistive
Inductive
Capacitive
Or any combination
Resistive Inductive
Inductive Capacitive
Resistive Capacitive
Resistive Inductive Capacitive
Types of Loads
Resist Resistive ive – Incand Incandesc escent ent Lamp Lamp Resistance heat Indu Induct ctiv ive e – Moto Motors rs – Cont Contac acto torr Coi Coils ls – Relays (coils) Capa Capaci citi tive ve – Capa Capaci cito tors rs – Star Startt Capa Capaci cito tors rs – Run Capa apacit citors ors – Powe Powerr Fac Facto tor r Correction Capacitors
Resistive Loads In Phase 200 150
C u r r e n t v o l t a g e
100
e d l 50 u e t i v 0 n e g L -50 a M -100 -150 -200 0
Duration Time
Inductive Loads Lagging
200
150
e d l u e t i v n e g L a M
C u r r e n t
100
50
0
V o lt a g e
-50
-100
-150
-200 0
Duration Time
Capacitive Loads Leading
200
150
e d l u e t i v n e g L a M
V o l t a g e
100
50
0
C u r r e n t
-50
-100
-150
-200 0
Duration Time
What is Power
Power is measured in Watts.
Volts X Amps X Power Factor = Watts
Watts only equals Volts X Amps when the Power Factor is 1 or unity. Most of the time the Power Factor is less than 1.
Power = Watts : True Power
Volts X Amps = VA : Apparent Power
Understanding Understandin g Right Triangles
e s u n e t e o p y H = C θ
B= Side Adjacent
e t i s o p p O e d i S = A
Right Angle 900
Power Triangle True power
Power Factor =
Cos
=
θ
Apparent power
Adjacent side Hypotenuse
e u s n e t e p o y H C = θ
Power Factor = Cos
θ
B= Side Adjacent
e t i s o p p O e d i S = A
True power
Power Factor =
Apparent power
r e w o e s P u t n e e t r o a p y p H A = C θ
B= Side TrueAdjacent Power
r e e t w i s o o P p e p v i O t c e a d i e S R = A
Right Angle 900
Understanding Power Triangle r , e A w V o k P t ), n s p e e r m a p A p – A l t s s = o C ( V V A θ
B= True Power Watts, KW, Power
r e w o P e v i t c a e R = A
e c n a t c a e R R A V k , R A V
Graphical representation of resistance, reactance, and impedance Inductive Motors
n c e a d m p e I m Z
θ
R Resistance
X
e e c v n i a t t c c u a d e n R I
Graphical representation of resistance, reactance, and impedance
Resistance
θ
R Z
I m m p e ed a d n a c n e e
Capacitors
X
e e v c i t i n a c t a c p a a e C R
y r a n i g a m I
Inductive Motors
θ
A V k r A o V r w e o P n t e e r a A p p
Real Real - WATT WATTS S – kW (KWH (KWH over over Time Time))
Cosine of θ POWER FACTOR
Capacitive Capacitors
True Power
kVAR Reactance Imaginary
10 HP 460 Volt 4 Pole Motor Transformer Conductor
Load
Power Factor
VAR
Amps Reactive
Amps Resistive
VA
Amps
Watts
125%
0.82
13203
16.6
10883
7476
9.4
13.7
115%
0.81
12240
15.4
9972
7099
8.9
12.5
100%
0.79
10830
13.6
8592
6593
8.3
10.8
75%
0.73
8771
11.1
6397
6002
7.5
8.0
50%
0.61
7105
8.9
4323
5639
7.1
5.4
25%
0.40
5886
7.4
2331
5405
6.8
2.9
min load
0.17
5399
6.8
911
5322
6.7
1.1
Motor = KW Load (resistive)
= KVAR Load (reactive)
10 HP Energy Flow Transformer Conductor e r w P o t n e 3 0 r e a p 0 8 A p = 1 C = V A
r e w o 3 P 9 5 e 6 v i t = c a R e A R V = A
θ
Power Factor = .79 B= True Power
Measured Amps = 13.6
Watts =8592
Reactive Amps = 8.3 Resistive Amps = 10.8
Motor
= KW Load (resistive)
= KVAR Load (reactive)
10 HP Adding Capacitance Transformer Conductor Measured Amps = 10.8 VA =8595
Watts =8592
1 = R A V
Measured Amps = 8.3
e r w P o t e n e 3 0 r a p 0 8 p 1 A = C = V A
r e w o 3 P 9 5 e 6 v i t = c a R e A R V = A
θ B= True Power
Measured Amps = 13.6
Motor
Watts =8592
= KW Load (resistive)
= KVAR Load (reactive)
10 HP Energy Savings Transformer Conductor 200 Feet of #12 Gauge wire Saving are calculated on I2 R losses. Using a # 12 gauge wire from Table 9 in the NEC the resistance is 2 ohms per 1000 feet.
200’ @
2 Ohms/1000’ Ohms/1000’ is .5 ohms. Using this the total total saving will be approx. 11.8 watts. NOTE: This is only if the I2 X R = Watts
capacitor is at the motor.
2.8 2 X .5 = 3.92 3 X 3.92 = 11.76
Motor
= KW Load (resistive)
= KVAR Load (reactive)
10 HP Capacitor Sizing Transformer Conductor
Utility Meter II22 R R Savings Losses
Capacitor Capacitor to large then var var flow in in both directions and one may increase cost.
Motor = KW Load (resistive)
= KVAR Load (reactive)
Power Factor Penalty Based on one month operation at 8 hours a day Example of Power Factor Charge PF Charge Factor NC Charge
$0.40
Max Billing kW
8.592
Power Factor
kW Charge
$10.25
kWh Charge
$0.03854
0.79
Calc
kVA
Calc
kVAR
10.8759 6.6681
kW
8.6
kWh
2064
Less than .85 then a $0.40 charge For For kVar kVar – (kW (kW X.62 X.62))
In this Case $0.54
PF Charge
$0.54
kW Charge
$88.15
kWh Charge
$79.55
Total Charge
$168.23
10 Horse Power Motor VA Watt Watts s VAR VA 14000
Watts
V AR
125% 115%
12000
100% 10000
75%
8000
50%
6000
25%
Min
4000 2000 0 0.82
0.81
0.79
0.73 Power Factor
0.61
0.40
0.17
10 HP Voltage Rise Transformer Conductor 200 Feet of #12 Gauge wire
kVAR * Xsource /kVA/100 = Voltage Rise % Note This does not include the wire inductance that will cause some additional rise in voltage.
Motor = KW Load (resistive)
= KVAR Load (reactive)
System VAR Requirements Power Plant Generator
(Met by Power Plant Generator) T/D Substatio n
Transmission Transmission Circuit
KVAR
MVAR MW
KW
Distribution Circuit
L Industrial Load
L Commercial Load = KW Load (resistive)
Substation Capacitor Bank
L Residential Load = KVAR Load (reactive)
System VAR Requirements Power Plant Generator
(Met by Power T/D Substation)
T/D Substatio n
Transmission Transmission Circuit
KVAR
MW
KW
Distribution Circuit Substation Capacitor Bank
L
L
Industrial Load
Commercial Load = KW Load (resistive)
L Residential Load = KVAR Load (reactive)
System VAR Requirements Power Plant Generator
(Met by T/D Sub and Feeder Capacitors) T/D Substation
Transmission Transmission Circuit
KVAR
MW
KW
Distribution Distribution Circuit Substation Capacitor Bank
L Industrial Load
Feeder Capacitor Bank
L Commercial Load
= KW Load (resistive)
L Residential Load = KVAR Load (reactive)
Things We have Talked About And Other Things to Talk About
Phase Angle
Power Factor
I2R Loss
Power Factor Penalty
Voltage Rise
Harmonic resonance
Load Load Fac Facto torr ----- Powe Powerr Fact Factor or
Harmonic Resonance X Source Equivalent Circuit
XT
3 PHASE AC INPUT
X Source
XT
XC
Harmonic Source
Harmonic Filters L1
XF XC
L2 L3
L1
L2
L3
Power Factor Vs Load Factor
They have no relation
Load Factor is kW at 100% operation
Yielding so many kWh vs. Actual kWh Example Hours in a Month = 30 X 24 = 720 Hours Load is at 8 kW 8 X 720 = 5760 kWh Actual kWh by load is 3240 Load Factor then is 3240/5760 Load Factor = .56
Understanding Power Factor
Definitions kVA, kVAR, kW, Apparent Power vs. True Power Calculations Measurements Power Factor Correction Capacitors System Impacts 2 R losses, Chapter 9 NEC I Equipment sizing Power Factor Charges Problems with adding Caps Harmonic resonance Volt rise Power Power Factor Factor vs Load Load Fact Factor or
