# POWER FACTOR :

We have already seen that electric power generated, transmitted and distributed in the form of alternating current is generated.

## what is power factor?

In case of alternating current, inductance and capacitance play a major role with resistance whereas; in direct current only resistance is available. In D.C inductor act as a short circuit and capacitor act as a open circuit.

Inductor stores electrical energy as magnetic energy and capacitor stores as electrostatic energy.

So, circuit with resistor, inductor and capacitor should have a phase difference between voltage and current.

When phase difference occurs, the useful power depends upon a factor, known as power factor.

#### It is nothing but the cosine of angle between voltage and current of an a.c circuit.

The value of p.f depends upon the phase difference between voltage and current and its range is -1 to +1.

So, we have come to know, that all power in a.c circuit is not useful power. The total power generated is Volt X ampere or VI is known as **apparent power**. (VA)

The useful power is Volt X Ampere X Cos ø or, VICos ø is known as **active power**. (Watt)

And useless power Volt X Ampere X Sin ø or vISinø is known as **reactive power**. (VAR)

It will be easily understood by power triangle.

So, we can easily write **(KVA) ^{2}= (KW)^{2}+ (KVAR)^{2}.**

And,

**p.f,(cosø) = KW/KVA.**

If one a.c circuit has resistance, R and impedance, Z, then, p.f = R/Z.

## Lagging and leading power factor.

In case of inductive circuit, the current lags behind the voltage and referred as power factor lagging.

In case of capacitive circuit, the current leads the voltage and referred as power factor leading.

So, **power factor lagging or leading means current lag or lead with respect to voltage.**

## Problems for low power factor:

As we know that, in single phase system power, P = VI cosø and in 3 phase system, power =√3VICosø, so, in case of power consumption in both cases power factor (cosø) plays an important role. From the above equation we can see that, current, I is inversely proportional to the power factor. So, low power factor causes increasing current and hence the problems are,

1) **Large KVA rating of Transformer, switchgear, alternator:** As these a.c machines are always rated in KVA and we know that KVA= KW/Cos ø, decreasing power factor (Cos ø) increases the KVA rating as well machine size and cost.

2) **Greater conductor size:** We have already seen that, low power factor causes increasing current. For fixed amount power transmission or distribution at constant voltage, the greater size conductor is needed to carry this increasing current at low power factor.

3) **Cost**: With increasing equipment cost, overall cost is increased.

4) **Increased copper loss**: As copper loss directly depends on the square of the current, (I^{2}R), increasing current also increases copper loss in low power factor.

5) **Poor voltage regulation:** At low lagging power factor, the current increases, which increase the voltage drop at alternator, transformer, and transmission – distribution system. So, receiving end voltage becomes low and voltage regulation become poor.

6) **Efficiency**: Due to higher copper loss and poor voltage regulation, the equipments as well as system frequency become low at low p.f.

7) **Reduced handling Capacity**: As the reactive component of the current prevents the full utilization of installed capacity of all elements of the system, the handling capacity has been reduced due to low lagging p.f.

8) **Maximum demand of consumer increases:** In case of low power factor, current consumption becomes high which not only increases the rate per unit consumption, maximum demand also increases.

## **Causes of low power factor:**

Due to presence of inductive reactance in the circuit, the value of power factor decreases, as in case of inductance, the current lags behind the voltage.

Now the question is **why so much inductive reactance present in a.c circuit?**

a) Most of connected motors are induction type which may 1phase or 3 phase.

b) In case of low or light load induction motor works at very low 0.2 to 0.3 power factor.

c) Transformers also have high inductive reactance.

d) Arc lamp, discharge lamp operates at very low power factor.

e) Industrial heating furnaces also work at low power factor.

f) Varying load during peak time and other time also a cause of low power factor.