Harmonic Distortion for a CFL. A harmonic analysis of the current drawn by a CFL yields the following data. Find the rms value of current and the total harmonic distortion (THD).

Question

Harmonic Distortion for a CFL. A harmonic analysis of the current drawn by a CFL yields the following data. Find the rms value of current and the total harmonic distortion (THD).

[latex]\begin{matrix} \hline ext{Harmonics} & ext{rms Current (A)} \ \hline 1 & 0.15 \ 3 & 0.12 \ 5 & 0.08 \ 7 & 0.03 \ 9 & 0.02 \ \hline \end{matrix}[/latex]

Accepted Answer

From (2.94) the rms value of current is

[latex]I_{rms} \ = \ \sqrt{ \ 2 \ \left[ \ \frac{{I_{1}}^{2}}{2} \ + \ \frac{{I_{2}}^{2}}{2} \ + \ \frac{{I_{3}}^{2}}{2} \ + \ \cdot \ \cdot \ \cdot \ \right] } \ = \ \sqrt{{I_{1}}^{2} \ + \ {I_{2}}^{2} \ + {I_{3}}^{2}...} [/latex] (2.94)

[latex]I_{rms} \ = \ \left[\left(0.15\right) ^{2} \ + \ \left(0.12\right) ^{2} \ + \ \left(0.08\right) ^{2} \ + \ \left(0.03\right) ^{2} \ + \ \left(0.02\right) ^{2} \right]^{{1}/{2}} \ = \ 0.211 \ A[/latex]

From (2.95) the total harmonic distortion is

[latex]THD \ = \ \frac{\sqrt{{I_{2}}^{2} \ + \ {I_{3}}^{2} \ + \ {I_{4}}^{2} \ + \ \cdot \ \cdot \ \cdot}}{I_{1}}[/latex] (2.95)

[latex]THD \ = \ \frac{\sqrt{\ \left(0.12\right) ^{2} \ + \ \left(0.08\right) ^{2} \ + \ \left(0.03\right) ^{2} \ + \ \left(0.02\right) ^{2}} }{0.15} \ = \ 0.99 \ = \ 99\%[/latex]

so the total rms current in the harmonics is almost exactly the same as the rms current in the fundamental.

Question 2.12: Harmonic Distortion for a CFL. A harmonic analysis of the cu......

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