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In general power is the capacity to do work. In electrical domain, electrical power is the amount of electrical energy that can be transferred to some other form (heat, light etc.) per unit time. Mathematically it is the product of voltage drop across the element and current flowing through it.
Considering first the DC circuits, having only DC voltage sources, the inductors and capacitors behave as short circuit and open circuit respectively in steady state. Hence the entire circuit behaves as resistive circuit and the entire electrical power is dissipated in the form of heat. Hear the voltage and current are in same phase and total electric power is given by-

Now coming back to AC circuit, hear both capacitor & inductor offer certain amount of impedance given by-

The inductor stores electrical energy in the form of magnetic energy and capacitor stores electrical energy in the form of electrostatic energy. Neither of them dissipates it. Further there is a phase shift between voltage and current. Hence when we consider the entire circuit consisting of resistor, inductor and capacitor, there exists some phase difference between the source voltage and current. The cosine of this phase difference is called electrical power factor.
This factor (-1 < cosφ < 1 ) represents the fraction of total power that is used to do the useful work. The other fraction of electrical power is stored in the form of magnetic energy or electrostatic energy in inductor and capacitor respectively.
The total power in this case is,

This is called apparent power and its unit is VA (Volt Amp) and denoted by ‘S’.
A fraction of this total electrical power which actually does our useful work is called as active power. It is denoted as ‘P’.
P = Active power = Total electrical power.cosφ and its unit is watt.
The other fraction of power is called reactive power. This does no useful work, but it is required for the active work to be done. It is denoted by ‘Q’ and mathematically is given by,
Q = Reactive power = Total electrical power.sinφ and its unit is VAR (Volt Amp Reactive).
This reactive power oscillates between source and load.
To help understand this better all these power are represented in the form of triangle.

Mathematically, S² = P² + Q² and electrical power factor is active power / apparent power.

Methods of Power Factor Improvement

Capacitors:
Improving power factor means reducing the phase difference between voltage and current. Since majority of loads are of inductive nature, they require some amount of reactive power for them to function. This reactive power is provided by the capacitor or bank of capacitors installed parallel to the load. They act as a source of local reactive power and thus less reactive power flows through the line. Basically they reduce the phase difference between the voltage and current.

Synchronous-Condenser:
They are 3 phase synchronous motor with no load attached to its shaft. The synchronous motor has the characteristics of operating under any power factor leading, lagging or unity depending upon the excitation. For inductive loads, synchronous condenser is connected towards load side and is overexcited. This makes it behave like a capacitor. It draws the lagging current from the supply or supplies the reactive power.

Phase-Advancer:
This is an ac exciter mainly used to improve pf of induction motor. They are mounted on shaft of the motor and is connected in the rotor circuit of the motor. It improves the power factor by providing the exciting ampere turns to produce required flux at slip frequency. Further if ampere turns are increased, it can be made to operate at leading power factor.

Power Factor Calculation

In power factor calculation, we measure the source voltage and current drawn using a voltmeter and ammeter respectively. A wattmeter is used to get the active power.
Now, we know
P=V*I*cosφwatt

Hence, we can get the electrical power factor.
Now we can calculate the reactive power                         Q=VIsinφVAR
This reactive power can now be supplied from the capacitor installed in parallel with load in local. Value of capacitor can be calculated as per below mentioned formula:

IMPORTANT: In power factor improvement, the reactive power requirement by the load does not change. It is just supplied by some device in local, thus reducing the burden on source to provide the required reactive power.

Do you ever know how the energy bill is calculated and how to use to reduce the cost of it ??
Let’s know about it.
When we connect an induction motor in the power supply, it takes up a current. Since the motor coils are inductive in nature they draw     a lagging current with respect to voltage. Since the current is lagging, the angle between the current & voltage is greater. Thus the cos(angle) also known as Power factor is reduced. wider the angle between them the lower is the power factor which increases the cost of bill.

 The apparent power is the addition of squares of reactive and real power. 

Mostly the inductive coils have a lagging power factor whereas capacitive elements have leading power factor. The lagging PF devices causes a huge amount of magnetising current to flow through the circuit which causes a high power loss in   the circuit. To compensate this lagging power factor devices of leading power factor        is used in the circuit such as capacitors banks, Static –VAR sources etc. These            devices compensate the lagging power factor and thus the reactive power is reduced. Power factor of value 1 is the most economical as the apparent power will be equal to active power.

Advantages: –

• Improving the power factor on customer side is that they can actually pay for the real power whereas improving the power factor from sending power side is that the KVA     demand is decreased on plant by neutralizing the reactive kVA.
• Efficiency of plant is improved.
• Cost/unit decreases.
• Regulation of lines is improved.

Devices having Low Power factor: –

• Most of ac appliances have motors which operates on low power factors.
• Transformers at substations.
• Industrial heating furnaces.
• Arc lamps.
• Synchronous motor.
• Rotary converter etc.