Explanation:

A 3-phase voltage source inverter (VSI) is a power electronic device used to convert DC power into AC power. It consists of six power electronic switches (usually MOSFETs or IGBTs) connected in a three-phase bridge configuration. The switches are controlled in such a way that the output voltage waveform is a square wave.

Harmonics in VSI output:

When a VSI operates in square-wave mode, the output voltage waveform contains harmonics. Harmonics are sinusoidal components with frequencies that are integer multiples of the fundamental frequency. In the case of a 3-phase system, the fundamental frequency is the frequency of the AC power supply.

Harmonic frequencies in a 3-phase system:

In a 3-phase system, the harmonic frequencies are given by the formula:

f_harmonic = n * f_fundamental

where f_harmonic is the frequency of the harmonic, n is the harmonic number, and f_fundamental is the fundamental frequency.

Harmonic frequencies in a 3-phase VSI:

In a 3-phase VSI operating in square-wave mode, the harmonic frequencies present in the output voltage waveform are given by the formula:

f_harmonic = n * f_switching

where f_harmonic is the frequency of the harmonic, n is the harmonic number, and f_switching is the switching frequency of the VSI.

Analysis of harmonic frequencies:

The switching frequency of a VSI is typically much higher than the fundamental frequency of the AC power supply. Therefore, the harmonic frequencies present in the output voltage waveform are also much higher than the fundamental frequency.

In the given options, the 3rd harmonic corresponds to three times the fundamental frequency, the 7th harmonic corresponds to seven times the fundamental frequency, the 11th harmonic corresponds to eleven times the fundamental frequency, and the 13th harmonic corresponds to thirteen times the fundamental frequency.

Conclusion:

Since the switching frequency of a VSI is typically much higher than the fundamental frequency, the 3rd harmonic is the lowest harmonic frequency that is present in the output voltage waveform. Therefore, the output line voltage of a 3-phase VSI operating in square-wave mode is free from the 7th, 11th, and 13th harmonics. Hence, the correct answer is option 'A' (3rd harmonic).