# Harmonics

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 I_{s}(t) is non-sinusoidal so it can be represented as:

Here, I_{o} = DC component

I_{m1} sin ωt = Fundamental component or first harmonics

I_{m2} sin 2ωt= Second harmonics

I_{m3} sin 3ωt= Third harmonics

I_{m4} 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 I_{rms} increases with increase in the harmonic. Also the copper loss of the system is given by I_{rms}^{2}R. As I_{rms} 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.

Here,

If the harmonics are absent in the above system then,

- Form Factor =1. This means that V
_{orms}is equal to a_{0}. - Harmonic Voltage (V
_{oh}) = 0. - Voltage Ripple Factor (VRF) = 0.

If the harmonics are present then,

- V
_{orms}> a - Harmonic Voltage V
_{0h}> 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 V_{m1}sin(ωt).

Here,

If the harmonic are absent in the above system then,

- V
_{oh}= 0. - V
_{01}= V_{0rms}. - THD = 0.
- g = 1.

If the harmonic are present then,

- V
_{oh}> 0. - V
_{orms}> V_{01}. - THD > 0.
- g < 1.

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