Inverter Distortion Factor Formula

The Distortion Factor (DF), often used interchangeably with Total Harmonic Distortion (THD) for voltage, quantifies the level of harmonic distortion present in the output waveform of an inverter relative to the fundamental frequency component.

Distortion Factor Definition

DF is defined as the ratio of the root-mean-square (RMS) value of all harmonic components (starting from the second harmonic) to the RMS value of the fundamental frequency component.

Mathematical Expression

The mathematical expression for the Distortion Factor (DF) in inverters is given by:

Where:

• $V_1$ represents the RMS value of the fundamental frequency component.
• $V_n$ represents the RMS value of the n-th harmonic component (where $n = 2, 3, 4, ...$).
• The summation $\sum_{n=2, 3, 4, 5, ...}^{\infty}$ includes all harmonic components starting from the second harmonic up to infinity.

Formula Comparison

Comparing the standard definition with the provided options:

• Option 1 & 4: $\frac{\sqrt{\sum_{n=2, 3, 4, 5, ...}^{\infty} (V_n/n)^2}}{V_1}$ - Incorrect.
• Option 2: $\frac{\sqrt{\sum_{n=2, 3, 4, 5, ...}^{\infty} (V_n/n^2)^2}}{V_1}$ - Incorrect.
• Option 3: $\frac{\sqrt{\sum_{n=2, 3, 4, 5, ...}^{\infty} V_n^2}}{V_1}$ - Correct. This matches the definition of DF (or THD).

Therefore, the correct expression for the distortion factor in inverters is $\frac{\sqrt{\sum_{n=2, 3, 4, 5, ...}^{\infty} V_n^2}}{V_1}$.