Harmonics in the current or voltage are components at a multiple of fundamental frequency of the system. They are generated mainly due to turn on and off (switching) operation of power electronics-based system, for example, variable frequency drives-VFDs, phase-controlled rectifiers, choppers, battery chargers, televisions, printers, laptops, CFLs and so on.
In Fig. 1, the top waveform represents the distorted/harmonic current. Typically, Fast Fourier Transform (FFT) technique is used to decompose the distorted signal in to set of sinusoidal signals of different frequencies. The fundamental frequency (for example, 50Hz (India) or 60Hz (USA)) is the system operating frequency and often it is called as first harmonic. The multiples of fundamental frequency give higher order harmonics. For example, 3rd harmonics is the pure sinusoidal signal with frequency equal to three time the fundamental (that is, 3 X 50 = 150 Hz and so forth. Ideally, the load should draw only the fundamental current.
Often it is desirable to know the level of harmonics in a given current or voltage waveform. A simplified single number quantitative representation of distorted current/voltage waveform is through most commonly used harmonic index called Total Harmonic Distortion (THD). The THD gives an effective value of the total harmonic components present in the distorted current/voltage waveform. Mathematically it is expressed as:
$$THD = {{{ \sqrt{I^2{2}+I^2{3}+I^2{4}+{....}+I^2{50} }} \over I1}} \times{100} $$
Where I1, I2, I3, I4… are fundamental (or first), second, third, fourth and so on, harmonic current components in the distorted waveform.
Some international standards, such as IEEE-519, have defined additional factor, called as, Total Demand Distortion (TDD). The TDD is mathematically represented as:
$$TDD = {{{ \sqrt{I^2{2}+I^2{3}+I^2{4}+{....}+I^2{50} }} \over Irated}} \times{100} $$
In TDD calculation, instead of fundamental current (in denominator), the rated/maximum current is used to measure the distortion level.
What really happens to power consumed if there are harmonics in the current? Let’s consider a simple case of third harmonic current. Assume that the supply voltage is pure sinusoidal, and the load draws only third harmonic current (shown in Fig. 2).
The average power and instantaneous powers are plotted in Fig. 3.
It can be noticed that, there is presence of instantaneous power (red color waveform) in the circuit. However, the average (active) power drawn in zero (green color waveform). That is, the harmonics contribute to harmonic reactive power or simply to reactive power and not to active power. However, their presence increases the line loading and reactive power losses among other listed problems.