**Power factor in Relation to Power**

Power is consumed only in resistance since neither pure inductor nor the capacitor consumes any power. The power consumed (True Power) in Inductor (L) and Capacitor (C) is zero. There is a circulating power that moves from the source to the load back and forth and does not do any useful work in the circuit. Current and voltage are in phase in a Resistance while they are 90 Degrees out of phase in (L) and (C). When current is in phase with voltage it produces active or True Power while it produces Reactive Power when 90 Degrees out of phase with voltage.

**Power Triangle**

Note:Due to formating limitations, all squared values shall be indicated by (squared)

OA(squared) + AB(squared) =OB(squared)

(Active Power)(squared)+(Reactive Power)(squared) = Apparent Power)(squared)

The lagging rective power is responsible for low power factor.The smaller the reactive power component, the higher the power factor.

kVAR = kVISinø

kVAR = kVASinø

but Cosø =kW/kVA

therefore kVA = kW/Cosø

kVAR =kW/Cosø*Sinø

kVAR = kWtanø

For Leading currents, the power factor triangle becomes reverse biased and this provides a key factor in power factor improvement.If a device taking leading currents or reactive power, a capacitor is connected with this device in parrarell and the power factor is improved.Capacitors take in a leading power factor and thus are used in power factor correction.

Example:

If a circuit draws a current of 10A at a voltage of 200V and its pf is 0.8 lagging, determine the Active, Reactive and Apparent Power.

For apparent power;

P = IV

P=10*200

2000VA

For active power;

P = IVCosø

P = 10*2000*Cosø (Cosø =Power Factor=0.8)

P = 1600W

For reactive power;

P = IVSinø

P = 10*200*Sinø

P = 1200VAR

From the above calculations we can see that the circuit receives an apparent power of 2000VA and it is capable of converting only 1600W into useful active power. The reactive power is 1200VAR and it does no useful work. In fact it is a liability on the source because it has to supply an additional current of ISinø.

**Disadvantages of Low Power Factor.**

1. Large kVA rating of equipment (switchgear, alternators, transformers)

We know that kVA =kW/Cosø

Therefore Cosø =kW/kVA

When ø is increasing, Cosø is decreasing and when ø is decreasing Cosø is increasing. It is from this simple fact that we can conclude that when the power factor is decreasing the kVA is increasing, the smaller the power factor the larger the kVA rating of the equipment.

2.Greater Conductor Size

To transmit and distribute a fixed amount of power at a constant voltage, the conductor will have to carry a current at low power factor. This will necessitate the use of a greater conductor size.

3.Large Copper Losses.

The Large current at low power factor causes I2R Losses in all the elements of the supply system and this results in poor efficiency.

4.Poor Voltage regulation.

The large current at a low lagging power factor causes greater voltage drop in alternators, transformers, transmission lines and distributors. This result in increased voltage drop at the receiving end, thus imparing the performance of the utilization devices. Extra equipment is required i.e. Voltage regulators.

Reduced handling capacity of a system.

Because of the reactive component of current, this prevents full utilization of the installed capacity.

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