Power Factor
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Power Factor
Power Factor
WLSA/INDIA/GKT/2006
Power Factor Basic electrical circuits
WLSA/INDIA/GKT/2006
Resistive
-
PF : Unity
Inductive
-
PF : Lagging
Capacitive
-
PF : Leading
Power Factor
Resistive circuits
WLSA/INDIA/GKT/2006
Power Factor
Resistive Circuit
When an alternating voltage is applied in an electrical circuit with only resistance, the voltage wave and current wave pass through the Zero at the same instant
120 V 60Hz
R
60 Ω
In this circuit the current is I = V/R = 120/ 60 = 2 Amps The power dissipated in the resistor is P = i² x R = 2² x 60 = 240 Watts (or) VxI = 120 X 2 = 240 Watts
WLSA/INDIA/GKT/2006
Power Factor
Resistive Circuit
If we plot the instantaneous values or use an oscilloscope to capture the wave forms, we will get ,
Then we say that , Voltage & Current are in phase Irrespective of the direction of e & i the power curve given by product of e & i is always positive. WLSA/INDIA/GKT/2006
Power Factor
The inductances and capacitances in AC circuits, cause the point at which the voltage wave passes through zero, to differ from the point at which the current wave passes through zero.
WLSA/INDIA/GKT/2006
Power Factor
Inductive circuits
WLSA/INDIA/GKT/2006
Power Factor
Inductive Circuit
Consider a simple AC circuit with a pure inductive load:
120 V 60Hz
L
160 mH
In this circuit, the inductive reactance is 2*π*f*L = 60.28 Ω Current through the circuit is 120/60.28 =1.99 Amps If we plot the instantaneous values or use an oscilloscope to capture the wave forms, we will get…
WLSA/INDIA/GKT/2006
Power Factor
90
360 degrees
Current wave LAGS behind the Voltage wave by 90 Deg The Power curve within one cycle of current alternates two times between positive & negative, with Zero effective value i.e p= e*I =0 To conclude, in a pure inductive circuit, ► Current Lags behind the voltage by 90 Deg ► Power dissipated in the pure inductance is zero WLSA/INDIA/GKT/2006
Power Factor
Capacitive circuits
WLSA/INDIA/GKT/2006
Power Factor
Capacitive Circuit
Consider a simple AC circuit with a pure capacitive load:
120 V 60Hz
C
100 microfarads
In this circuit, the capacitive reactance is 1/ 2*π*f*c = 26.5 Ω Current through the circuit is 120/26.5 = 4.52 Amps If we plot the instantaneous values or use an oscilloscope to capture the wave forms, we will get…
WLSA/INDIA/GKT/2006
Power Factor
Capacitive Circuit
90
360 degrees
Current wave LEADS the Voltage wave by 90 Deg The Power curve within one cycle of current alternates two times between positive & negative, with Zero effective value i.e p= e*I =0 To conclude, in a pure Capacitive circuit, ► Current Leads the voltage by 90 Deg ► Power dissipated in the pure capacitance is zero WLSA/INDIA/GKT/2006
Power Factor
Combined circuits
WLSA/INDIA/GKT/2006
Power Factor
Combined Circuit
Consider a circuit with resistance, inductance & capacitance connected across an AC source I
V
V=IR
V=I*XL
V=I*XC
We will consider three conditions ,
VL VR=VZ=IR= IZ
Case 1: When XL=XC, the circuit becomes a pure resistive circuit, and the parameters can be shown in a phasor diagram as ,
I
Since XL=XC VC
Z=R
Note that voltage across the resistor and the current through the resistor are in “phase” and angular displacement between them is “zero” WLSA/INDIA/GKT/2006
Power Factor Case 2: When XC>XL, the circuit becomes a capacitive circuit, and the parameters can be shown in a phasor diagram as ,
Combined Circuit VL VR=IR
I
θ VC-VL
V=IZ =I*sqrt(R2+(XL-XC)2
Note that 1. Voltage across the resistor and the current through the resistor are in “phase” and the angular displacement between the is “zero” 2. Combined effect of resistance & resultant reactance is known as Impedance “Z” and is given by Z = Sq.rt (R²+(XL- XC)² 3. Combined effect of resistance & resultant reactance is known as Impedance “Z” and is given by Z = Sq.rt (R²+(XL- XC)² 4. Considering CCW rotation (normal in Elect. Eng), the current vector “Leads” the voltage vector by an angle “θ” WLSA/INDIA/GKT/2006
Power Factor Case 3: When XL>XC, the circuit becomes an inductive circuit, (most of electrical equipments fall in this category) and the parameters can be shown in a phasor diagram as, Note that
Combined Circuit VL V=IZ=I*sqrt(R2+(XL-XC)2
VL-Vc
I
θ VR=IR
Vc
1. Voltage across the resistor and the current through the resistor are in “phase” and the angular displacement between them is “zero” 2. The angular displacement between the current and the total applied voltage is “θ” 3. Considering CCW rotation, the current vector “Lags behind” the voltage vector by an angle “θ”
WLSA/INDIA/GKT/2006
Power Factor
Combined Circuit
The wave form of the voltage, current and power will be.. Voltage
Current
time
θ
Power
It is to be observed that …. The power curve is positive wherever the voltage & current are either positive or negative The power curve is negative wherever either the voltage or current is negative The net power is the sum of positive and negative parts in a full cycle The negative part increases with increase of the angle “θ” WLSA/INDIA/GKT/2006
Power Factor
Comparison
Comparing the four wave forms Resistive
Inductive
Capacitive
Combined Voltage
Current
time
θ
WLSA/INDIA/GKT/2006
Power
Power Factor
Definitions
The power dissipating capacity of a circuit is maximum when the angle between the voltage and current ,“θ” is Zero The power dissipating capacity of a circuit is minimum (Zero) when the angle between the voltage and current, “θ” is 90 Deg. The power dissipating capacity of a circuits depends directly on a factor which is the Cosine of the angle “θ” This factor which decides the power dissipating capacity of a circuit is known as the Power Factor of the circuit, and “θ” is known as power factor angle or Impedance phase angle
WLSA/INDIA/GKT/2006
Power Factor
Definitions
The power dissipated in a circuit determined by the power factor is the TRUE or ACTIVE power and is measured in Watts, kW or MW, and is denoted by letter “P” When the current phasor is in phase with voltage phasor, cosine of the PF angle “θ” is maximum - 1, then the circuit is UPF circuit (DC circuit) When the current phasor lags behind the voltage phasor, then the PF is said to be lagging - Motors, transformers etc When the current phasor leads the voltage phasor, then the power factor is said to be leading - Capacitors, Synchronous condensers
WLSA/INDIA/GKT/2006
Power Factor
Definitions
We have so far seen that reactive loads such as inductors & Capacitors dissipate zero power, yet the fact that they drop voltage and draw current gives the deceptive impression that they actually DO dissipate power This “Deceptive Power” is called Reactive Power and is measured in terms of Volt-Ampere, Reactive VAR, KVAR or MVAR, and is denoted by letter “Q” The combination of reactive power and true power is called Apparent power, and it is the product of a circuit's voltage and current, without reference to phase angle. The Apparent power is measured in terms of Volt – Ampere, i.e. VA, KVA or MVA and is denoted by letter “S”
WLSA/INDIA/GKT/2006
Power Factor
Power equations
There are several power equations relating the three types of power to resistance, reactance, and impedance (all using scalar quantities):
WLSA/INDIA/GKT/2006
Power Factor The three types of Power
True, Reactive and Apparent Relates to each other in trigonometric form We call this, the Power Triangle
WLSA/INDIA/GKT/2006
Power Triangle
Power Factor Power Factor - Effects Very low power factor – lagging or leading causes, - high current for a given power and voltage - Increased I²R losses & IZ drop - KVAR load and hence KVA demand increases for a given kW power If the power factor is low on “lag” side, the terminal voltage of source reduces - In the case of Alternators, this calls for increased excitation If the power factor is on “Lead” side, the terminal voltage of the source increases - In alternators, the AVR looses control - Increase in voltage causes further swing of PF to lead side - this vicious effect might cause the machine to trip on over voltage
WLSA/INDIA/GKT/2006
Power Factor Power Factor – How to improve Rated pf of alternators is 0.8 lag and it is safe to operate at this pf since the current will also be rated value at the rated power output. Some times it is necessary to operate the machine at pf more than 0.8 lag PF can be improved by compensating reactive power by adding more capacitive loads
WLSA/INDIA/GKT/2006
Power Factor
Questions ??
WLSA/INDIA/GKT/2006
Power Factor
WLSA/INDIA/GKT/2006
Power Factor
WLSA/INDIA/GKT/2006
Power Factor Basic electrical circuits
WLSA/INDIA/GKT/2006
Resistive
-
PF : Unity
Inductive
-
PF : Lagging
Capacitive
-
PF : Leading
Power Factor
Resistive circuits
WLSA/INDIA/GKT/2006
Power Factor
Resistive Circuit
When an alternating voltage is applied in an electrical circuit with only resistance, the voltage wave and current wave pass through the Zero at the same instant
120 V 60Hz
R
60 Ω
In this circuit the current is I = V/R = 120/ 60 = 2 Amps The power dissipated in the resistor is P = i² x R = 2² x 60 = 240 Watts (or) VxI = 120 X 2 = 240 Watts
WLSA/INDIA/GKT/2006
Power Factor
Resistive Circuit
If we plot the instantaneous values or use an oscilloscope to capture the wave forms, we will get ,
Then we say that , Voltage & Current are in phase Irrespective of the direction of e & i the power curve given by product of e & i is always positive. WLSA/INDIA/GKT/2006
Power Factor
The inductances and capacitances in AC circuits, cause the point at which the voltage wave passes through zero, to differ from the point at which the current wave passes through zero.
WLSA/INDIA/GKT/2006
Power Factor
Inductive circuits
WLSA/INDIA/GKT/2006
Power Factor
Inductive Circuit
Consider a simple AC circuit with a pure inductive load:
120 V 60Hz
L
160 mH
In this circuit, the inductive reactance is 2*π*f*L = 60.28 Ω Current through the circuit is 120/60.28 =1.99 Amps If we plot the instantaneous values or use an oscilloscope to capture the wave forms, we will get…
WLSA/INDIA/GKT/2006
Power Factor
90
360 degrees
Current wave LAGS behind the Voltage wave by 90 Deg The Power curve within one cycle of current alternates two times between positive & negative, with Zero effective value i.e p= e*I =0 To conclude, in a pure inductive circuit, ► Current Lags behind the voltage by 90 Deg ► Power dissipated in the pure inductance is zero WLSA/INDIA/GKT/2006
Power Factor
Capacitive circuits
WLSA/INDIA/GKT/2006
Power Factor
Capacitive Circuit
Consider a simple AC circuit with a pure capacitive load:
120 V 60Hz
C
100 microfarads
In this circuit, the capacitive reactance is 1/ 2*π*f*c = 26.5 Ω Current through the circuit is 120/26.5 = 4.52 Amps If we plot the instantaneous values or use an oscilloscope to capture the wave forms, we will get…
WLSA/INDIA/GKT/2006
Power Factor
Capacitive Circuit
90
360 degrees
Current wave LEADS the Voltage wave by 90 Deg The Power curve within one cycle of current alternates two times between positive & negative, with Zero effective value i.e p= e*I =0 To conclude, in a pure Capacitive circuit, ► Current Leads the voltage by 90 Deg ► Power dissipated in the pure capacitance is zero WLSA/INDIA/GKT/2006
Power Factor
Combined circuits
WLSA/INDIA/GKT/2006
Power Factor
Combined Circuit
Consider a circuit with resistance, inductance & capacitance connected across an AC source I
V
V=IR
V=I*XL
V=I*XC
We will consider three conditions ,
VL VR=VZ=IR= IZ
Case 1: When XL=XC, the circuit becomes a pure resistive circuit, and the parameters can be shown in a phasor diagram as ,
I
Since XL=XC VC
Z=R
Note that voltage across the resistor and the current through the resistor are in “phase” and angular displacement between them is “zero” WLSA/INDIA/GKT/2006
Power Factor Case 2: When XC>XL, the circuit becomes a capacitive circuit, and the parameters can be shown in a phasor diagram as ,
Combined Circuit VL VR=IR
I
θ VC-VL
V=IZ =I*sqrt(R2+(XL-XC)2
Note that 1. Voltage across the resistor and the current through the resistor are in “phase” and the angular displacement between the is “zero” 2. Combined effect of resistance & resultant reactance is known as Impedance “Z” and is given by Z = Sq.rt (R²+(XL- XC)² 3. Combined effect of resistance & resultant reactance is known as Impedance “Z” and is given by Z = Sq.rt (R²+(XL- XC)² 4. Considering CCW rotation (normal in Elect. Eng), the current vector “Leads” the voltage vector by an angle “θ” WLSA/INDIA/GKT/2006
Power Factor Case 3: When XL>XC, the circuit becomes an inductive circuit, (most of electrical equipments fall in this category) and the parameters can be shown in a phasor diagram as, Note that
Combined Circuit VL V=IZ=I*sqrt(R2+(XL-XC)2
VL-Vc
I
θ VR=IR
Vc
1. Voltage across the resistor and the current through the resistor are in “phase” and the angular displacement between them is “zero” 2. The angular displacement between the current and the total applied voltage is “θ” 3. Considering CCW rotation, the current vector “Lags behind” the voltage vector by an angle “θ”
WLSA/INDIA/GKT/2006
Power Factor
Combined Circuit
The wave form of the voltage, current and power will be.. Voltage
Current
time
θ
Power
It is to be observed that …. The power curve is positive wherever the voltage & current are either positive or negative The power curve is negative wherever either the voltage or current is negative The net power is the sum of positive and negative parts in a full cycle The negative part increases with increase of the angle “θ” WLSA/INDIA/GKT/2006
Power Factor
Comparison
Comparing the four wave forms Resistive
Inductive
Capacitive
Combined Voltage
Current
time
θ
WLSA/INDIA/GKT/2006
Power
Power Factor
Definitions
The power dissipating capacity of a circuit is maximum when the angle between the voltage and current ,“θ” is Zero The power dissipating capacity of a circuit is minimum (Zero) when the angle between the voltage and current, “θ” is 90 Deg. The power dissipating capacity of a circuits depends directly on a factor which is the Cosine of the angle “θ” This factor which decides the power dissipating capacity of a circuit is known as the Power Factor of the circuit, and “θ” is known as power factor angle or Impedance phase angle
WLSA/INDIA/GKT/2006
Power Factor
Definitions
The power dissipated in a circuit determined by the power factor is the TRUE or ACTIVE power and is measured in Watts, kW or MW, and is denoted by letter “P” When the current phasor is in phase with voltage phasor, cosine of the PF angle “θ” is maximum - 1, then the circuit is UPF circuit (DC circuit) When the current phasor lags behind the voltage phasor, then the PF is said to be lagging - Motors, transformers etc When the current phasor leads the voltage phasor, then the power factor is said to be leading - Capacitors, Synchronous condensers
WLSA/INDIA/GKT/2006
Power Factor
Definitions
We have so far seen that reactive loads such as inductors & Capacitors dissipate zero power, yet the fact that they drop voltage and draw current gives the deceptive impression that they actually DO dissipate power This “Deceptive Power” is called Reactive Power and is measured in terms of Volt-Ampere, Reactive VAR, KVAR or MVAR, and is denoted by letter “Q” The combination of reactive power and true power is called Apparent power, and it is the product of a circuit's voltage and current, without reference to phase angle. The Apparent power is measured in terms of Volt – Ampere, i.e. VA, KVA or MVA and is denoted by letter “S”
WLSA/INDIA/GKT/2006
Power Factor
Power equations
There are several power equations relating the three types of power to resistance, reactance, and impedance (all using scalar quantities):
WLSA/INDIA/GKT/2006
Power Factor The three types of Power
True, Reactive and Apparent Relates to each other in trigonometric form We call this, the Power Triangle
WLSA/INDIA/GKT/2006
Power Triangle
Power Factor Power Factor - Effects Very low power factor – lagging or leading causes, - high current for a given power and voltage - Increased I²R losses & IZ drop - KVAR load and hence KVA demand increases for a given kW power If the power factor is low on “lag” side, the terminal voltage of source reduces - In the case of Alternators, this calls for increased excitation If the power factor is on “Lead” side, the terminal voltage of the source increases - In alternators, the AVR looses control - Increase in voltage causes further swing of PF to lead side - this vicious effect might cause the machine to trip on over voltage
WLSA/INDIA/GKT/2006
Power Factor Power Factor – How to improve Rated pf of alternators is 0.8 lag and it is safe to operate at this pf since the current will also be rated value at the rated power output. Some times it is necessary to operate the machine at pf more than 0.8 lag PF can be improved by compensating reactive power by adding more capacitive loads
WLSA/INDIA/GKT/2006
Power Factor
Questions ??
WLSA/INDIA/GKT/2006
Power Factor
WLSA/INDIA/GKT/2006
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