# Total Harmonic Distortion(THD) & Its Measurement

Total harmonic distortion (THD) shows how much of a voltage or current distortion is due to harmonics in the signal. If the sinusoidal voltage is applied to linear devices like inductors, capacitors, and resistors, the current drawn by these devices varies according to the variation of sinusoidal voltage. In this case, both voltage and current waveforms do not introduce any harmonics in the supply network.

If the sinusoidal voltage is applied to nonlinear semiconductor devices, the current flowing through these devices does not vary as per the applied sinusoidal voltage. The distorted current waveform introduces harmonics in the system. The current distortion further exacerbates if the applied voltage is also distorted.

The distortion in voltage and current waveform caused by harmonics is called harmonic distortion. Thus, the harmonics pollute the supply system and decrease the efficiency of the electrical supply network.

According to the Fourier series, the distorted non-sinusoidal waveform can be resolved into the following components.

1. Fundamental frequency as a sinusoidal component
2. Integral multiples of fundamental frequency components
3. DC components

Suppose the fundamental frequency is 50 C/s, then the harmonic frequency is 100,150,200,250,300… Hz etc. The even multiples of fundamental frequency 100,200,300… Hz etc is known as even harmonics and, the odd multiples of fundamental frequency 150,250,350… Hz etc is known as odd harmonics.

The distorted waveform symmetrical about the x-axis contains only odd harmonics.

The harmonics cause numerous problems in the supply network and are also pernicious for electrical equipment health, therefore measurement of harmonics and their mitigation is a must for maintaining the power system efficiency.

The total harmonic distortion is measured to determine the degree of harmonics present in the power supply system. For a signal m, the total harmonic distortion is defined by the following equation.

The total harmonics distortion of current and voltage is measured in terms of THDv and THDi. The harmonic current drawn by no linear devices causes voltage distortion and again the distorted voltage cause current distortion. Therefore, it is essential to mitigate the harmonic current to avoid electrical pollution.

## Current and Voltage Total Harmonic Distortion(THD)

### Total harmonic distortion of voltage (THDv)

The total harmonic distortion of voltage (THDv) is defined as the ratio of the sum of root means squares of all the harmonic voltages to the RMS voltage of fundamental frequency. The equation of total harmonic distortion of voltage in percentage is given below.

The generalized equation of total harmonic distortion of voltage is;

If the total RMS value of the distorted voltage waveform is known, the total harmonic distortion of voltage can be calculated by the following equation.

### Total harmonic distortion of current (THDi)

The total harmonic distortion of current (THDi) is defined as the ratio of the sum of root means squares of all the harmonic currents to the RMS current of the fundamental frequency. The equation of total harmonic distortion of current in percentage is given below.

The generalized equation of total harmonic distortion of current is;

If the total RMS value of the distorted current waveform is known, the total harmonic distortion of the current can be calculated by the following equation.