In the 19th century, Jean-Baptiste Joseph Fourier presented his theorem, which is known as the Fourier’s theorem. According to this theorem, a periodic function of period T can be represented as the summation of a sinusoid with the identical period T, additional sinusoids with frequency same as integral multiples of the fundamental, and a possible continuous component, provided the function has a non-zero average value in the period. The first two are known as harmonics, while the third is known as the DC component.
Of the three, the first waveform with a frequency matching the period of the original waveform is called the fundamental harmonic, while the second may have more than one component. Those with frequency equal to ‘n’ times of the fundamental are called harmonic components of order ‘n’. A conclusion drawn from the above discussion about Fourier’s theorem is a perfectly sinusoidal waveform can have only the fundamental component, and no other harmonics.
This also means an electrical system with sinusoidal current and voltage waveforms has no harmonics. However, protective devices and malfunctioning equipment in an electrical system can lead to distribution of electrical power with distortions of the voltage and current waveforms, creating harmonics. In other words, harmonics represent the components of a distorted waveform, and their presence allows analysis of any repetitive non-sinusoidal waveform from a study of the different sinusoidal waveform components.
Most non-linear loads generate harmonics. When a sinusoidal voltage encounters a load of this type, it produces a current with a non-sinusoidal waveform. It is possible to deconstruct these non-sinusoidal waveforms into harmonics. Provided the impedances present in the network are low, the distortions of the voltage resulting from the distorted current are also low, and the pollution level in the system from harmonics is below the acceptable level. Therefore, even in the presence of distorted currents, the voltage can remain sinusoidal to some extent.
Typically, the operation of many electronic devices leads to cutting the sinusoidal waveform to change its rms value or to obtain a direct current from the alternate value. In such cases, the current on the line transforms to a non-sinusoidal waveform. Several such equipment produce harmonics—welding equipment, variable speed drives, continuity groups, static converters, fluorescent lamps, personal computers, and so on.
In most cases, waveform distortion results from the bridge rectifiers present within the above equipment. Although these semiconductor devices allow the current to flow for a major duration of the whole period, they stop conducting for the balance part. This creates discontinuous waveforms with the consequent addition of numerous harmonics.
Apart from electronic equipment, transformers can also be the cause of harmonic generation and pollution. Even when a perfectly sinusoidal voltage waveform is applied to a transformer and it generates a sinusoidal magnetizing flux, the magnetic saturation of its iron core may prevent the magnetizing current from remaining sinusoidal.
The distorted magnetizing current waveform from the transformer now contains several harmonics, with the third one being of the greatest amplitude. Fortunately, compared to the rated current of the transformer, its magnetizing current is only a small fraction. As the load on the transformer increases, this percentage becomes increasingly negligible.
