Harmonics are the non-fundamental components of current or voltage injected in to system due to switching or non-linear load connected in system. Due to this current and voltage are distorted and deviate from sinusoidal waveforms.
Fourier Series Representation of Harmonic
Any non-sinusoidal waveform is analyzed by Fourier series. Suppose Is(t) is non-sinusoidal so it can be represented as:
Here, Io = DC component
Im1 sin ωt = Fundamental component or first harmonics
Im2 sin 2ωt= Second harmonics
Im3 sin 3ωt= Third harmonics
Im4 sin 4ωt= Fourth harmonics and so on.
This can be further clarified as
For AC systems only fundamental component is desirable while for DC systems only DC component is desirable.
The root mean square or RMS value of current can be represented as
[For a system consisting of four harmonic terms]
This shows that the Irms increases with increase in the harmonic. Also the copper loss of the system is given by Irms2R. As Irms increases with increase in harmonic, the copper loss also increases with the increase in harmonic. Also the power factor of the system decreases with increase in harmonic as increase in harmonics results in increase of the current.
DC Harmonics Analysis
Here we will consider a rectifier for analysis of dc harmonics. Also, the consideration of rectifier as our example will ease our understating.
The output of a rectifier is DC as it converts AC to DC.
Any non-sinusoidal waveform can be represented by Fourier series.
If the harmonics are absent in the above system then,
- Form Factor =1. This means that Vorms is equal to a0.
- Harmonic Voltage (Voh) = 0.
- Voltage Ripple Factor (VRF) = 0.
If the harmonics are present then,
- Vorms > a
- Harmonic Voltage V0h > 0.
- Voltage Ripple Factor(VRF) > 0.
- Form Factor > 1.
AC Harmonics Analysis
Here we will consider an inverter for analysis of ac harmonics. Also, the consideration of inverter as our example will ease our understating.
Any non-sinusoidal waveform can be represented by Fourier series. Here desirable output of inverter is fundamental AC or Vm1sin(ωt).
If the harmonic are absent in the above system then,
- Voh = 0.
- V01 = V0rms.
- THD = 0.
- g = 1.
If the harmonic are present then,
- Voh > 0.
- Vorms > V01.
- THD > 0.
- g < 1.