Power Factor Correction

As stated above, to minimise I²R losses in AC networks, it may be necessary to manipulate the power factor. This can be attained by connecting purely reactive impedance, Z' in parallel with the load impedance as shown in the Figure drawn below.
 

Figure--Power factor correction by introducing a pure reactance in the parallel with load m impedance.

By doing so, the phase angle among line voltage and line current can be adjusted whereas the power consumption remains the same as a pure reactance does not dissipate any power.

A carefully chosen reactance will decrease φ and therefore increases the power factor which in turn reduces line current.

Example

Given that RMS line voltage and line current are  A respectively, determine impedance which will result in the unity power factor. 

Taking voltage as reference phasor, the phase angle among line voltage and line current can be given as-36.9⁰ 

 

To improve the power factor, an impedance is inserted in the parallel with load as in the Figure drawn below resulting in following nodal equation
 

It is clear that for unity power factor, the imaginary component of the line current must be zero. This is accomplished by assigning a current of j 30 A through the pure reactance resulting in following line current
 
Thus I'j 30A and the magnitude of impedance required can be calculated as follows
 

The power consumed by load remains the same that is
 

Thus to achieve unity power factor, a pure reactance of -j 3.33Ω is connected in parallel with the load. The vector diagram of the above example is shown in Figure drawn below.
 

Figure --Vector diagram to illustrate the power factor correction.

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