POWER FACTOR AND POWER TRIANGLE

 INTRODUCTION:

The electrical energy is exclusively generated, transmitted and distributed in the form of alternating current.Therefore the question of power factor immediately comes into picture.Mot of the loads are inductive in nature and have Low Lagging power factor. Low power factor is highly undesirable as it causes an increase in current.

POWER FACTOR:

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

In AC circuits there is a phase difference ɸ between the voltage and current. The term Cosɸ is called the the power factor of the circuit. circuit is inductive, the current lags behind the voltage and the power factor is referred as lagging power factor. However in capacitive circuits, the current leads the voltage and is called as the leading power factor.

                                                                       (Figure 1.1)

Consider an inductive load taking a lagging current I from the source. We can resolve that lagging current into two components as shown in the Figure 1.1. Icosɸ is the active component or wattful component and Isinɸ is the wattless or reactive component of the current. 

We can conclude from the figure that greater the angle ɸ , greater will be the watless component and lesser the angle ɸ less will be the watless component and power factor cosɸ will be high.

THE POWER TRIANGLE:

The analysis of power factor can also be made in terms of power drawn by the ac circuit.

                                                                   (Figure 1.2)

If we see figure 1.1 and multiply each side of the triangle by voltage V i.e. 

VxIcosɸ = P .......... ( i ) 

VxIsinɸ = Q .......... ( ii )

VxI     = S     .......... ( iii )

So we can get three different powers and the triangle we get is called as power triangle shown in figure 1.2.

P  represents the actual or active power in the circuit and its unit is Watt or kilowatt.

Q represents the reactive power in the circuit and its unit is VAR or KVAR

S represents the active power of the circuit and its unit is VA or KVA.

Now we can conclude very important results from the figure 1.2 of power triangle and it is also very helpful in different power factor problem solving.

• Apparent power in ac circuits has two components, active and reactive power at right angles to each others.

            OB² = OA²+AB²

    or (Apparent power)² = (Active Power) ²+ (Reactive Power)²

    or  (KVA)² = (KW)² + (KVAR)² 

• Power Factor Cosɸ = OA/OB

                = Active Power / Apparent Power

                = kW / kVA

    Thus the power factor of the circuit may also be defined as Ratio of active power to the apparent             power

• The lagging reactive power factor is responsible for the low power factor. It is clear from the power triangle that smaller the reactive power component the higher is the power factor of the circuit.

         kVAR = kVA sinɸ = kW(sinɸ)/cosɸ

         kVAR = kWtanɸ

• For leading currents the power triangle becomes reversed. This fact provides a key to the power factor improvement. If a device taking leading power factor(e.g capacitor) is connected in parallel with the load, then the lagging reactive power of the load will be partly neutralized, thus improving the power factor of the load.
• The power factor of the circuit can be defined in one of three ways.

1. Power factor = cosɸ = cosine of the angle between voltage and current. 
2. Power factor = R/Z = Resistance/Impedence.
3. Power factor = VIcosɸ / VI = Active Power / Apparent Power.

• Reactive power is neither consumed in the circuit nor it does any useful work. It merely flows back and forth in both directions in the circuit. A wattmeter doesn't measure reactive power .