# Power factor Correction

Power factor correction is improving power factor by connecting capacitors parallel to load. There is generally a phase difference between voltage and current in A.C. circuits.  The cosine of angle between voltage and current in an A.C. circuit is known as power factor. Most probably inductive loads will lag the current by voltage. Capacitive loads will lead the current by voltage. To learn more about Three Phase Electric Power visit our article.

When we are talking about power factor correction, using capacitive loads in parallel opposes the inductive effects in circuits, hence angle between voltage and current will reach zero. After the power factor correction, theoretical value of power factor should be 1. But, practically it is not possible. Real values for power factor lies between 0\le p.f.<1 .

## What is Power Factor?

The cosine of angle between voltage and current in an A.C. circuit is known as power factor. There is generally a phase difference (say ø degrees) between voltage and current in A.C. circuits. The term cos ø is called the power factor of the circuit.

If the circuit is inductive, the current lags behind the voltage and If the circuit is capacitive, the current leads the voltage.

In other words, power factor can be defined as, the ratio of the real power that is used to do work and the apparent power that is supplied to the circuit. The power factor can get values in the range from 0 to 1 as mentioned before. When all the power is reactive power with no real power (usually inductive load – pure inductive) – the power factor is 0. When all the power is real power with no reactive power (resistive load) – the power factor is 1.

Consider an inductive circuit taking a lagging current I from supply voltage V; the angle of lag being Ø. The phasor diagram of the circuit is shown above. The circuit current I can be resolved into two perpendicular components, namely;

1. I cosØ in phase with V
2. I sin(Ø-90) out of phase with V

The component IcosØ is known as active component, whereas component IsinØ is called the reactive component. The reactive component is a measure of the power factor. If the reactive component is small, the phase angle Ø is small and hence power factor cos Ø will be high.

Therefore, a circuit having small reactive current (i.e., IsinØ) will have high power factor and vice-versa. It may be noted that the value of the power factor can never be more than unity.

1. It is a usual practice to attach the word ‘lagging’ or ‘leading’ with the numerical value of the power factor to signify whether the current lags or leads the voltage. Thus if the circuit has a p.f. of 0·5 and the current lags the voltage, we generally write p.f. as 0·5 lagging.
2. Sometimes power factor is expressed as a percentage. Thus 0·8 lagging power factor may be expressed as 80% lagging.

## Power Triangle

The analysis of power factor can also be made in terms of power drawn by the a.c. circuit. If each side of the current triangle oab of above image is multiplied by voltage V, then we get the power triangle OAB shown below.

OA = VI cosØ and represents the active power in watts or kW
AB = VI sinØ and represents the reactive power in VAR or kVAR
OB = VI and represents the apparent power in VA or kVA
The following points may be noted from the power triangle :

1. The apparent power in an a.c. circuit has two components viz., active and reactive power at right angles to each other.
{ OB }^{ 2 }=OA^{ 2 }+{ AB }^{ 2 } or
{ apparent power }^{ 2 }=active power^{ 2 }+{ reactive power }^{ 2 } or
{ kVA }^{ 2 }=kW^{ 2 }+{ kVAR }^{ 2 }
2.  Power factor, \cos { \phi \quad =\frac { OA }{ OB } =\frac { active\quad power }{ apparent\quad power } =\quad \frac { kW }{ kVA }  }
Thus the power factor of a circuit may also be defined as the ratio of active power to the apparent power. This is a perfectly general definition and can be applied to all cases, whatever be the waveform.
3. The lagging* reactive power is responsible for the low power factor. It is clear from the power triangle that smaller the reactive power component, the higher is the power factor of the circuit.
kVAR=kVA\sin { \phi =\frac { kW }{ \cos { \phi } } \sin { \phi } } \\ kVAR=kW\tan { \phi }
4. For leading currents, the power triangle becomes reversed. This fact provides a key to the power factor correction. If a device taking leading reactive power (e.g. capacitor) is connected in parallel with the load, then the lagging reactive power of the load will be partly neutralized, thus improving the power factor of the load.
5. The power factor of a circuit can be defined in one of the following three ways:
1. Power factor = cos Φ = cosine of angle between V and I
2. Power factor =\frac { Resistance }{ Impedance } =\frac { R }{ Z }
3. Power factor =\frac { VI\cos { \phi } }{ VI } =\frac { Active\quad power }{ Apparent\quad power }
6. The reactive power is neither consumed in the circuit nor it does any useful work. It merely flows back and forth in both directions in the circuit. A wattmeter does not measure reactive power.

Example: Let us illustrate the power relations in an A.C. circuit with an example. Suppose a circuit draws a current of 10 A at a voltage of 200 V and its p.f. is 0·8 lagging. Then,

Apparent power = VI = 200 x 10 = 2000 VA

Active power = VI cosΦ = 200 x 10 x 0·8 = 1600 W

Reactive power = VI sinΦ = 200 x 10 x 0·6 = 1200 VAR

The circuit receives an apparent power of 2000 VA and is able to convert only 1600 watts into active power. The reactive power is 1200 VAR and does no useful work. It merely flows into and out of the circuit periodically. In fact, reactive power is a liability on the source because the source has to supply the additional current (i.e., I sin Φ).

### Importance of Power Factor Correction

The power factor plays an important role in a.c. circuits, since power consumed, depends upon the power factor.

P={ V }_{ L }{ I }_{ L }\cos { \phi }            (For Single Phase Supply)

{ I }_{ L }=\frac { P }{ { V }_{ L }\cos { \phi }}

P={ \sqrt { 3 } V }_{ L }{ I }_{ L }\cos { \phi }      (For Three Phase Supply)

{ I }_{ L }=\frac { P }{ { \sqrt { 3 } V }_{ L }\cos { \phi }}

It is clear from above that for fixed power and voltage, the load current is inversely proportional to the power factor. Lower the power factor, higher is the load current and vice-versa. A power factor less than unity results in the following disadvantages:
1. Large kVA rating of the equipment – The electrical machinery (e.g., alternators, transformers, switchgear) is always rated in *kVA.
Now,          kVA=\frac { kW }{ \cos { \phi } }
It is clear that kVA rating of the equipment is inversely proportional to power factor. The smaller the power factor, the larger is the kVA rating. Therefore, at low power factor, the kVA rating of the equipment has to be made more, making the equipment larger and expensive.
2. Greater conductor size – To transmit or distribute a fixed amount of power at a constant voltage, the conductor will have to carry more current at low power factor. This necessitates large conductor size.
For example, take the case of a single-phase A.C. motor having an input of 10 kW on full load, the terminal voltage being 250 V. At unity p.f., the input full load current would be 10,000/250 = 40 A. At 0·8 p.f; the kVA input would be 10/0·8 = 12·5 and the current input 12,500/250 = 50 A.
If the motor is worked at a low power factor of 0·8, the cross-sectional area of the supply cables and motor conductors would have to be based upon a current of 50 A instead of 40 A which would be required at unity power factor.
3. Large copper losses – The large current at low power factor causes more I2R losses in all the elements of the supply system. This results in poor efficiency.
4. Poor voltage regulation – The large current at low lagging power factor causes greater voltage drops in alternators, transformers, transmission lines and distributors. This results in the decreased voltage available at the supply end, thus impairing the performance of utilization devices. In order to keep the receiving end voltage within permissible limits, extra equipment (i.e., voltage regulators) is required.
5. Reduced handling capacity of system – The lagging power factor reduces the handling capacity of all the elements of the system. It is because the reactive component of current prevents the full utilization of installed capacity.
The above discussion leads to the conclusion that low power factor is an objectionable feature in the supply system. There fore it is clear that power factor correction is needed for the efficient operation.

### Causes of Low Power Factor

Low power factor is undesirable from economic point of view. Normally, the power factor of the whole load on the supply system in lower than 0·8. The following are the causes of low power factor:

1. Most of the a.c. motors are of induction type (Single phase and three phase induction motors) which have low lagging power factor. These motors work at a power factor which is extremely small on light load (0.2 to 0.3) and rises to 0.8 or 0.9 at full load.
2. Arc lamps, electric discharge lamps and industrial heating furnaces operate at low lagging power factor.
3. The load on the power system is varying; being high during morning and evening and low at other times. During low load period, supply voltage is increased which increases the magnetization current. This results in a decreased power factor.

## Power factor correction (power factor Improvement)

The low power factor is mainly due to the fact that most of the power loads are inductive and, there fore, take lagging currents. In order to do power factor correction, some device taking  leading power should be connected in parallel with the load. One of such devices can be a capacitor.

The capacitor draws a leading current and partly or completely neutralizes the lagging reactive component of load current. This raises the power factor of the load.

Example: Consider a single *phase load taking lagging current I at a power factor \cos { { \phi }_{ 1 } } as shown in above figures.

The capacitor C is connected in parallel with the load. The capacitor draws current { I }_{ C } which leads the supply voltage by { 90 }^{ o }

The resulting line current I’ is the phasor sum of I and { I }_{ C } and its angle of lag is { \phi }_{ 2 } as shown in the phasor diagram of Fig. (iii) above. It is clear that { \phi}_{ 2 }  is less than { \phi}_{ 1 }, so that cos{ \phi}_{ 2 } is greater than cos { \phi}_{ 1 }

Hence, the power factor of the load is improved. The following points are worth noting,

1. The circuit current I’ after p.f. correction is less than the original circuit current I.
2. The active component remains the same before and after p.f. correction because only the lagging reactive component is reduced by the capacitor.
I\cos { { \phi }_{ 1 }=I’\cos { { \phi }_{ 2 } } }
3. The lagging reactive component is reduced after p.f. improvement and is equal to the difference between lagging reactive component of load (I sin { \phi}_{ 1 }) and capacitor current ({ I}_{ 2 }) i.e.,
I’\sin { \phi } _{ 2 }=I\sin { \phi _{ 1 } } -{ I }_{ C }
4. Active power (kW) remains unchanged due to power factor correction.
5.              I’\sin { \phi } _{ 2 }=I\sin { \phi _{ 1 } } -{ I }_{ C }
VI’\sin { \phi } _{ 2 }=VI\sin { \phi _{ 1 } } -{ VI }_{ C }
i.e., Net kVAR after p.f. correction = Lagging kVAR before p.f. correction – leading kVAR of equipment

## Methods for Power Factor correction

Normally, the power factor of the whole load on a large generating station is in the region of 0.8 to 0.9. However, sometimes it is lower and in such cases, it is generally desirable to take special steps for power factor correction. This can be achieved with the following equipment:

The following devices and equipment are used for Power Factor Correction.

1. Static Capacitor
2. Synchronous Condenser

### a) Static Capacitor method of Power Factor Correction

This method of power factor correction is widely used in factories. Industrial power system loads (Induction motors, transformers) are probably inductive that take lagging current and it decreases the system power factor.

By connecting static capacitors in parallel with that load will increase the power factor.  These static capacitors provide leading current which neutralize (totally or approximately) the lagging inductive component of load current (i.e. leading component neutralize or eliminate the lagging component of load current) thus power factor correction is employed.

We can observe that load current {I}_{1} lags voltage by {Ø}_{2}, because of inductive component on load. By connecting static capacitor in parallel with load will inject a current through capacitor.

Capacitor current will lead by (ideally) 90 degrees from voltage. Then new resultant current {I}_{2} will lag voltage by {Ø}_{1} where {Ø}_{1}<{Ø}_{2}. Then power factor cos({Ø}_{1})>cos({Ø}_{2}). Therefore, can say load power factor is improved.

Also note that after the power factor correction, the circuit current would be less than from the low power factor circuit current.

Also, before and after the power factor correction, the active component of current would be same in that circuit because capacitor eliminates only the re-active component of current. Also, the Active power (in Watts) would be same after and before power factor correction.

• Low losses
• Low maintenance due to less moving parts
• It can work in normal conditions (i.e. ordinary atmospheric conditions)
• Do not require a foundation for installation
• They can be easily installed as they are light and require no foundation.

• They have short service life ranging from 8 to 10 years.
• They are easily damaged if the voltage exceeds the rated value.
• Once the capacitors are damaged, their repair is uneconomical.
• With changing load, we have to ON or OFF the capacitor bank, which causes switching surges on the system

### b) Synchronous Condenser method of Power Factor Correction

A synchronous motor takes a leading current when over-excited and, therefore, behaves as a capacitor. An over-excited synchronous motor running on no load is known as synchronous condenser.

When such a machine is connected in parallel with the supply, it takes a leading current which partly neutralizes the lagging reactive component of the load. Thus the power factor correction is employed.

Figure below shows the power factor correction by synchronous condenser method. The 3Φ load takes current { I }_{ L } at low lagging power factor cos{\phi }_{ L }

The synchronous condenser takes a current { I }_{ M } which leads the voltage by an angle {\phi }_{ m }. The resultant current I is the phasor sum of { I }_{ M } and { I }_{ L } and lags behind the voltage by an angle φ.

It is clear that φ is less than { \phi }_{ L } so that cos φ is greater than cos{\phi }_{ L }. Thus the power factor is increased from cos{\phi }_{ L } to cos φ. Synchronous condensers are generally used at major bulk supply substations for power factor correction.

1. By varying the field excitation, the magnitude of current drawn by the motor can be changed by any amount. This helps in achieving stepless † control of power factor.
2. The motor windings have high thermal stability to short circuit currents.
3. The faults can be removed easily.

1. There are considerable losses in the motor.
2. The maintenance cost is high.
3. It produces noise.
4. Except in sizes above 500 kVA, the cost is greater than that of static capacitors of the same rating.
5. As a synchronous motor has no self-starting torque, therefore, an auxiliary equipment has to be provided for this purpose.

Note. The reactive power taken by a synchronous motor depends upon two factors, the d.c. field excitation and the mechanical load delivered by the motor. Maximum leading power is taken by a synchronous motor with maximum excitation and zero load.

### c) Phase Advancer method of Power Factor Correction

Phase advancers are used for power factor correction of induction motors. The low power factor of an induction motor is due to the fact that its stator winding draws exciting current which lags behind the supply voltage by { 90 }^{ 0 }.

If the exciting ampere turns can be provided from some other a.c. source, then the stator winding will be relieved of exciting current and the power factor of the motor can be improved. This job is accomplished by the phase advancer which is simply an a.c. exciter.

The phase advancer is mounted on the same shaft as the main motor and is connected in the rotor circuit of the motor. It provides exciting ampere turns to the rotor circuit at slip frequency. By providing more ampere-turns than required, the induction motor can be made to operate on leading power factor like an over-excited synchronous motor.

Phase advancers have two principal advantages. Firstly, as the exciting ampere-turns are supplied at slip frequency, therefore, lagging kVAR drawn by the motor is considerably reduced. Secondly, phase advancer can be conveniently used where the use of synchronous motors is inadmissible.

However, the major disadvantage of phase advancers is that they are not economical for motors below 200 H.P.

## Conclusion

We have learnt about power factor correction methods in detail. Power factor can be improved using above three methods. For more inquiries regarding these, write to us here

We are looking forward to provide more articles like this for students and professionals. Share our article with others, so they also can get informed by these science articles. Contact us for any suggestions and improvements in this article.