Zero Level Concept of HARMONIC

• What is harmonic?  

"Harmonic is defined as the unwanted signals present along with fundamental signal."

Harmonic will creates the disturbance in system and also due to presence of harmonic losses are increases.

How harmonics are produced in the system?

➝Non linear components likes Diode, Thyristor, Transistor, Diac etc are used in the system for various purposes like AC to DC converter, Variable voltage variable frequency operations (VVVF), Automatic Power factor correction etc. This non linear components will introduce the harmonic in the system due to switching.

• Amplitude and frequency of signal along with harmonic:-

1. Amplitude "Am"(harmonic) = 1/n^2 * Am(fundamental)

Frequency "f"(harmonic) = n*f (fundamental)

Where; 

              n= integer 

Fig(a) Fundamental signal along with 3rd Harmonic

• Why 3rd harmonic component is dangerous in system compare to other harmonic?

➝ Because 3rd harmonic component is "Co-phaser phaser it means amplitude of all three phases (ia, ib, and ic) are maximum at same instant and due to Co-phaser phasor it produces the current which is peaky in nature as shown in fig (a).

☆PROOF:-

➝Assumig three phase balanced system ;

             ia+ib+ic= 0.    ................(1)

We know that in three pase balanced system all three phases are displaced in time by 120°. So that,

ia = im sin wt + im/9 sin 3wt + ..............(2)

ib = im sin wt + im/9 sin (3wt-120) + .......(3)

ic = im sinn wt + im/9 sin (3wt-240) +........(4)

NOTE:

 In equation (2),(3) and (4) we only consider odd harmonic because even harmonic is cancelled out in Fourier series.

And we only writing the equation upto 3rd harmonic because here we only prooved why 3rd harmonic is dangerous in the system

And last point is that Amplitude of current is divided by "n^2" { here, n= 3 so im is divided by 3^2 = 9).

Now only we consider 3rd harmonic component of equation (2),(3)and (4)..........

                ia                    ib                ic 

              3×0°              3×120°        3×240°

                 ↓                    ↓                   ↓

                 0°                  0°                 0°

Please shows and compare above three phases with wave form.

Fig(b) Balanced three phase system

Fig(c) Co-phaser phasor

Here; 

          3×0 = 0°

          3×120 = 360° =0°

          3×240 = 720° =0° please observed in wave form.

From the above three pase wave form we conclude that all three phases containing 3rd harmonic component are maximum and zero at same instant.

     .........................Thank you 🙂....................,