Power Factor

“Cosine of the angle between applied voltage and current drawn in any electrical circuit is known as power factor” and it is denoted by “Cos F”.When a purely resistive circuit is connected across the a.c. supply, the current drawn from the main supply will be in phase with applied voltage and hence the power factor will be unity. But in case of purely inductive and capacitive circuit,the current drawn will lag behind and lead the applied voltage, by an angle of 90 0 respectively. Now, to understand the power factor in detail, let us take an example of inductive circuit

When alternating current (a.c.) supply is connected across the purely inductive circuit as shown above in figure (a). The alternating current will flow in the circuit through the inductance coil. The resistance represents the internal resistance of the inductive coil, as resistance is directly proportional to length of coil, which may be very less. The current drawn (I) by the coil will lag behind the applied voltage by an angle F. This lagging current can be resolved into two components i.e. one I Cos F along the X-axis and I Sin F along the Y-axis, as shown in figure (b). If we multiply these values by KV, as given in figure in (c) then we have

KW = KVI Cos F = KVA Cos F = Active Power or True Power

KVA = Apparent Power

KVAR = KVI Sin F = KVA Sin F = Reactive Power or Watt-less Power

So from the triangle OAB (Figure d)

Cos F = OA/AB = KW/KVA = Active Power/Apparent Power

So, we can say the power factor is ratio of active power to the apparent power.

We can also explain the power factor by an impedance triangle OAB

Cos F = OA/AB = R/Z

So, we can also say that power factor is the ratio of resistance to impedance.

Where z 2 = R 2 + Z 2

The inductive reactance (X L ) and capacitive reactance (X C ) of an electric circuit depends upon supply frequency, because X L = 2pfL and X C = 1/2pfc.So, the inductive reactance increases with the increase in supply frequency where as capacitive reactance decreases and vice versa. With the change in the value of X L and X C , the value of Z changes. Because in this case

Z 2 = R2 + (X L2 ± X C 2 )

So, they create a phase difference between applied voltage and current drawn from the main circuit. In other words for same power more current is needed in ordered to overcome the inductive and capacitive effect. Mathematically we can say cosine of the angle of lag or lead of current with applied voltage is known as power factor.

i. Disadvantage of Low Power Factor
The disadvantages of low power factor are given here.

a) We know that P = VI Cos F In case of single-phase supply.

Also P = Ö3 V L I L Cos F In case of three-phase supply.

The current drawn from the supply mains will be

I = P/V Cos F

I = P/Ö3 V L Cos F

In case of single-phase supply. ———— equation no. 1

In case of three-phase supply. ————— equation no. 2

It is evident from equation 1 and 2, that the current drawn is inversely proportional to the power factor. If the values of power factor increase the value of current decreases and vices versa and hence the cost per unit will increase.

b) Due to increase in current drawn from the supply mains due to decrease in power factor, the rating of transformer, alternator, all the transmission and distribution system will be over load. So, all these equipment need to be upgraded and hence increase in cost per unit.

c) The efficiency of transmission lines, alternator and transformer reduces with increase in current drawn due to low power factor because the copper losses (I 2 R).

d) The voltage drop in transmission line increases due to increase in current and hence the voltage regulation will be poor. To improve the regulations either reduces the current drawn from the main supply or increase the diameter of transmission line conductor. The cost per unit will again increased.Thus we can say, due to decrease in power factor, the cost of transformer, alternator, transmission lines and its accessories will increase and hence costs per unit will increases.

ii. Causes of Low Power Factor

The main causes of low power factor are given here.

a) All the induction motors running on lesser load than the full load is responsible for poor power factor. Approximately, the power factor of motor running on full load is 0.85, at half load, 0.5 and at 25 % of full load, is too low as on no load approximately. Arc lamps and arc furnaces are highly responsible for reducing the power factor drastically.

b) Some time due to defective bearings, the rotor may touch the stator. To overcome such problem, some material removed from the outer surface of the rotor by turning on lathe, which leads to increase in air gap between stator and rotor. So the power factor of the motor will increase due to increase in magnetizing current.

iii. Methods of Improving Power Factor

The main methods of improving the power factor are given here.

a) Static Capacitor: The power factor is generally improved by installing static capacitor bank in parallel with the application having poor power factor

When the supply is switched on the capacitor bank, which is permanently connected in parallel with the application responsible for low power factor starts drawing leading current and hence the phase angle of the resultant current is improved  So, the power factor will increase. In case of three- phase supply, the capacitor is connected either in star or delta

b) Synchronous Condenser: - Synchronous motor with over excited can be used to improve the overall power factor of the complete installation by compensating the lagging components of the current drawn due to inductive loading

iv. Advantages of improved power factor

The advantages of improved power factor are as follows.

a) Voltage regulation is improved.

b) More output power can be taken from the same plant and equipment associated with generation, transmission and distribution of energy.

c) Efficiency of alternator, transformer and transmission lines is improved due to reduction in copper losses.