Harmonics: Harmonics are the non-fundamental components of current or voltage injected into the system due to switching or non-linear load connected in the system. Due to this current and voltage are distorted and deviate from sinusoidal waveforms.

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## Fourier Series Representation of Harmonic

Any non-sinusoidal waveform is analyzed by the 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 a fundamental component is desirable while for DC systems only a 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 increase with the increase in the harmonic. Also, the copper loss of the system is given by Irms2R. As Irms increases with an increase in harmonic, the copper loss also increases with the increase in harmonic. Also, the power factor of the system decreases with an increase in harmonicas an increase in harmonic results in an increase of the current.

## DC Harmonics Analysis

Here we will consider a rectifier for the 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 the Fourier series.   Here, If the harmonics are absent in the above system then,

1. Form Factor =1. This means that Forms is equal to a0.
2. Harmonic Voltage (Voh) = 0.
3. Voltage Ripple Factor (VRF) = 0.

If the harmonics are present then,

1. Forms > a
2. Harmonic Voltage V0h > 0.
3. Voltage Ripple Factor(VRF) > 0.
4. Form Factor > 1.

## AC Harmonics Analysis

Here we will consider an inverter for analysis of ac harmonic. Also, the consideration of the inverter as our example will ease our understating.

Any non-sinusoidal waveform can be represented by the Fourier series. Here the desirable output of the inverter is fundamental AC or Vm1sin(ωt).  Here, If the harmonic is absent in the above system then,

1. Voh = 0.
2. V01 = V0rms.
3. THD = 0.
4. g = 1.

If the harmonics are present then,

1. Voh > 0.
2. Forms > V01.
3. THD > 0.
4. g < 1.

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