#### Introduction to Power Factor:

The cosine of the angle between voltage and current in an ac circuit is known as power factor.

In an ac circuit, there is generally a phase difference between voltage and current. In an inductive circuit, the current lags behind the applied voltage and the power factor of the circuit is referred to as lagging. In a capacitive circuit the current leads the applied voltage and therefore, the power factor of the circuit is said to be leading.

Consider an inductive circuit, which draws a current I from the supply mains lagging behind the supply voltage V by an angle ɸ, known as phase angle, the phasor diagram is shown in Fig. 15.6.

The current I can be resolved into two components, one along the voltage phasor and the other perpendicular to it. The component along the voltage phasor, I cos ɸ is called the in- phase or active component of current, and the one perpendicular to the voltage phasor, I sin ɸ is called the out of phase or wattless or reactive component of current.

If all these components are multiplied by voltage V, the product of voltage V and in-phase component of current I cos ɸ i.e., VI cos ɸ will represent the true power of the circuit in watts or kW, whereas the product of voltage V and the quadrature component of current I sin ɸ i.e., VI sin ɸ will represent the reactive power in VARs or kVARs and the product of voltage V and current I i.e., VI will represent the apparent power in volt-amperes or kVA. Thus we get a power triangle, as shown in Fig. 15.7.

For leading currents the triangle becomes reversed. This fact provides a key to the power factor improvement. If a device drawing leading reactive power is connected in par­allel with the inductive load, then the lagging reactive power of the load will be partly neutralised, resulting in improve­ment of the power factor of the system.

#### Causes of Low Power Factor:

(i) All ac motors (except overexcited synchronous motors and certain type of commutator motors) and transformers operate at lagging power factor. The power factor falls with the decrease in load. For example an induction motor has a reasonable higher power of 0.85 at full load, 0.8 at 75% of full load, 0.7 at half-full load, 0.5 at 25% of full load and as low as 0.1 on no load.

(ii) Arc lamps and electric discharge lamps operate at low lagging power factor.

(iii) Due to increased supply mains voltage, which usually occurs during low-load periods such as lunch hours, night hours etc., the magnetizing current of inductive reactances increase and power factor of the electrical plant as a whole comes down.

(iv) The power factor at which motors operate falls due to improper maintenance and repairs of motors. In repaired motors, less wire is sometimes used than originally wound motors, therefore, in such motors leakage of magnetic flux increases and power factor of the motor decreases.

In case of heavily worn-out bearings, the rotor may catch at the stator.

Some metal is sometimes removed from the rotor by turning instead of replacing the defective bearings. In doing so, the length of air gap between stator and rotor increase, due to which greater magnetising current is required and, therefore, power factor drops.

(v) Industrial heating furnaces such as arc and induction furnaces operate on very lagging power factor.

#### Disadvantages of Low Power Factor:

The current for a given load supplied at constant voltage will be higher at a lower power factor and lower at higher power factor.

For example if load P is to be supplied at terminal volt­age V and at power factor cos ɸ by a 3-phase balanced system then load current is given by:

If P and V are constant, the load current, IL is inversely proportional to power factor, cos ɸ i.e., lower the power factor, higher the current and vice versa.

The higher current due to poor power factor affects the system and results in following disadvantages:

(i) Rating of generators and transformers are propor­tional to their output current hence inversely pro­portional to power factor, therefore, large generators and transformers are required to deliver same load but at low power factor.

(ii) The cross-sectional area of the bus-bar, and the contact surface of the switchgear is required to be enlarged for the same power to be delivered but at low power factor.

(iii) For the same power to be transmitted but at low power factor, the transmission line or distributor or cable have to carry more current.

The size of the conductor will have to be increased if current den­sity in the line is to be kept constant. Thus more conductor material is required for transmission lines, distributors and cables to deliver the same load but at low power factor.

(iv) Energy losses are proportional to the square of the current hence inversely proportional to the square of the power factor i.e., more energy losses incur at low power factor, which results in poor efficiency.

(v) Low lagging power factor results in large voltage drop in generators, transformers, transmission lines and distributors which results in poor regulation. Hence extra regulating equipment is required to keep the voltage drop within permissible limits.

(vi) Low lagging power factor reduces the handling ca­pacity of all the elements of the system.

Thus we see that the low power factor leads to a high capital cost for the alternators, switchgears, transformers, transmission lines, distributors and cables etc.

Keeping in view the various drawbacks associated with the low power factor, the power suppliers insist on a power factor of 0.8 or above for industrial establishments. The power tariffs are devised to penalize the consumers with low lagging power factor and to encourage them to install power factor correction devices or equipment.