Question

A three phase star connected alternator develops an rms voltage of V₁ per phase at the fundamental frequency. It also generates a third harmonic component whose rms value is V₃ . What is the line voltage of the alternator?
1. \(\sqrt {3(V_1^2 + V_3^2)}\)
2. \(\sqrt {(V_1^2 + V_3^2)}\)
3. \(\dfrac{\sqrt {V_1^2 + V_3^2}}{\sqrt 3}\)
4. \(\sqrt {2(V_1^2 + V_3^2)}\)

Answer 1

Correct Answer - Option 1 : \(\sqrt {3(V_1^2 + V_3^2)}\)

Concept:

The RMS of an alternating quantity having different harmonic components is given by

\({V_{rms}} = \sqrt {V_1^2 + V_2^2 + \ldots + V_n^2} \)

Where Vn­ represents the nth harmonic component.

V₁ = Fundamental component of voltage

Calculation:

Given harmonic component phase voltages of a three phase star connected alternator are fundamental and third.

As three phase star connected alternator can possibly have Line voltage of third harmonics, Hence third harmonic phase voltage is considered in calculation of total Line voltage.

Total phase voltage  \({V_{ph\ rms}} = \sqrt {V_1^2 + V_3^2} \)

Total line voltage V_L = \(\sqrt3\) V_{ph rms}

V_L = \(\sqrt3( \sqrt {V_1^2 + V_3^2}) \)

= \(\sqrt {3(V_1^2 + V_3^2})\)

If the three phase delta connected alternator is present, then there is no existance of third harmonic component of line voltage implies no consideration of third harmonic component of phase voltage is taken for the calculation.