Total Harmonic Distortion (Two Harmonics, Simplified)
Total Harmonic Distortion (Two Harmonics, Simplified)
Real-world AC waveforms are rarely perfectly sinusoidal — nonlinear loads like variable frequency drives and switching power supplies inject harmonic components at multiples of the fundamental frequency. Total harmonic distortion (THD) quantifies how much of the waveform’s energy is in those unwanted harmonics relative to the fundamental.High THD causes extra heating in transformers and motors, interferes with sensitive electronic equipment, and can trip power-quality limits imposed by utilities, so measuring or estimating THD is a standard power-quality check wherever nonlinear loads are present.
The THD is √(V_2² + V_3²)/V_1, the root-sum-square of the harmonic voltages divided by the fundamental voltage. where V_1 is the fundamental voltage component, and V_2 and V_3 are the second and third harmonic voltage components.
Inputs
V_1 := 120 V=120 V
V_2 := 6 V=6 V
V_3 := 4 V=4 V
Combining the harmonic components in root-sum-square fashion and normalizing by the fundamental gives the standard THD ratio used to judge waveform quality.
THD := sqrt(V_2^2 + V_3^2)/V_1=0.06
Results
A THD around 0.06 (6%) is a moderate distortion level — many power quality standards set a limit near 5% at the point of common coupling, so this result would be borderline and worth investigating further. Because THD only considers two harmonics here, a more complete assessment on a real system would include additional harmonic orders, which would only push the true THD value higher.
Assumptions & limitations
- Only the second and third harmonics included; higher-order harmonics ignored.
- Voltage THD, not current THD (they can differ significantly).
- Steady-state periodic waveform assumed.