Harmonics are unwanted high frequencies that create a distorted wave pattern superimposed on the basic waveform.

In an AC circuit, a resistance behaves exactly the same as in a DC circuit.In other words, the current passing through the resistance is proportional to the voltage on it.This is because a resistance is a linear device, and if the voltage applied to it is a sinus wave, the current flowing through it is also a sinus wave, so the phase difference between the two sinusoids is zero.

Usually, when dealing with alternating voltages and currents in electrical circuits, it is assumed that they are pure and sinusoidal with a single frequency value called "basic frequency", but this is not always the case.

In an electrical or electronic device or circuit with an electrical or electronic device or circuit with a voltage-current characteristic that is not linear, that is, not proportional to the voltage applied through it, the alternative waveforms associated with the device will differ larger or less than that of an ideal sinusoidal waveform. Such waveforms are often called non-sinusoidal or complex waveforms.

Complex waveforms are produced by common electrical devices such as iron-core inductors, switching transformers, electronic ballasts in fluorescent lamps and other heavy inductive loads, as well as output voltage and current waveforms of AC generators, generators and other such electric machines.The result is that even if the voltage is a waveform, the current waveform may not be sinusoidal.

In addition, most electronic power supply switching circuits, such as rectifiers,silicon-controlled retractions (scrs), power transistors, power converters, and other solid state switches that interrupt the power supply sinusoidal waveform to control engine power, tend to draw current only at peak values of the AC supply, and since the switching current waveform is not sinusoidal, the resulting load current is said to contain Harmonics.

Complex non-sinusoidal waveforms are created by "adding" a series of sinus wave frequencies known as "Harmonics".Harmonics are a generalized term used to describe the distortion of a sinusoidal waveform with waveforms at different frequencies.

Then, regardless of its shape, a complex waveform can be mathematically divided into its own components, called the basic frequency and a series of "harmonic frequencies".

Base Frequency

The Basic WaveForm (or first harmonic) is a sinusoidal waveform with a feeding frequency. The base is the lowest or basic frequency on which the complex waveform is built, and therefore the periodic time will be equal to the periodic time of the resulting complex waveform Τ, the base frequency.

Let's consider the basic or 1st harmonic AC waveform as shown.

Let's consider the basic or 1st harmonic AC waveform as shown.


Where: V max is the peak value in volts and ε is the waveform frequency in Hertz (Hz).

We can see that a sinusoidal waveform is an alternating voltage (or current) that changes to the 2ππ angle as a sinus function.The waveform frequency is determined by the number of cycles per second.In Turkey, this basic frequency is set to 50Hz.

Harmonics are voltages or currents that operate at a frequency that is an integer multiple of the base frequency. Therefore, given a basic waveform of 50hz, this means that the 2nd harmonic frequency will be 100Hz (2 x 50Hz), the 3rd harmonic will be 150Hz (3 x 50Hz) and so on. Similarly, given the 60Hz basic waveform, 2., 3., The 4th and 5th harmonic frequencies will be at 120Hz, 180Hz, 240Hz and 300hz respectively.

So in other words, we can say that "harmonics" are multiples of the basic frequency, and therefore can be expressed as: 2ε , 3ε , 4ε , etc., as shown.

Complex WaveForms From Harmonics


Note that the above red waveforms are actual shapes of waveforms seen by a load due to harmonic content added to the base frequency.

The basic waveform can also be called the 1st harmonic waveform. Therefore, it has a frequency twice that of a second harmonic foundation, three times the frequency of the third harmonic foundation, and the fourth harmonic has a frequency four times the frequency of the foundation, as shown in the graph on the left side.

The graph on the right shows the complex waveform formed as a result of the effect between the addition of the basic waveform and harmonic waveforms at different harmonic frequencies.Note that the shape of the resulting complex waveform will depend not only on the number and amplitude of existing harmonic frequencies, but also on the phase relationship between the basic frequency and individual harmonic frequencies.

We can see that a complex wave consists of a basic waveform plus harmonics, each with its own peak value and phase angle.For example, if the basic frequency is given as follows; E = V max (2πεt), the values of harmonics will be given as follows:

For a second harmonic:

E 2 = V 2(max) (2*2πππt) = V 2(max) (4ππt), = V 2(max) (2ωt)

For a third harmonic:

E 3 = V 3(max) (3*2πππt) = V 3(max) (6πεt), = V 3(max) (3ωt)

For the fourth harmonic:

E 4 = V 4(max) (4*2πππt) = V 4(max) (8ππt), = V 4(max) (4ωt)

And like this.

Then the equation given for the value of a complex waveform will be:


Harmonics are usually classified according to their names and frequencies, for example, the order of the basic frequency at 100 Hz. Harmonic array refers to phaser rotation of harmonic voltages and currents according to the basic waveform in a balanced, 3-phase 4-wire system.

A positive set of harmonics (4., 7., 10.,…) will rotate in the same direction (forward) as the basic frequency. Harmonic here as a negative array (2., 5., 8.,…) reverses (inverse) of the basic frequency.

In general, positive array harmonics are undesirable because they are responsible for overheating conductors, power lines and transformers due to the addition of waveforms.

Negative array harmonics, on the other hand, cause additional problems in the engines by moving between excesses, since the opposite phaser rotation weakens the rotating magnetic field needed by the motors and especially asynchronous motors, causing them to produce less mechanical torque.

Another special set of harmonics called "Triplens" (multiples of three) has a zero rotation sequence. Triplens, the third harmony ( 3rd, 6., 9.,…) etc. They are multiples, hence their names, and therefore replace them with zero degrees. Zero array harmonics circulate between phase and neutral or soil.

Unlike the positive and negative sequence harmonic currents that destroy each other, third-degree or triple harmonics do not destroy each other.Instead, they are arrhythmically collected in the common neutral wire, which is exposed to currents from all three phases.

As a result, due to these triplen harmonics, the current amplitude in the neutral wire can increase up to 3 times the amplitude of the phase current at the basic frequency, making it less efficient and overheating.

Then we can summarize the effects of the array as multiples of the base frequency of 50 Hz as follows:

Harmonic Sorting

Frequency, Hz.50100150200250300350400450

Note that the same harmonic array applies to 60 Hz basic waveforms.

QueueDirectionHarmonic Effect
+ForwardOverheating Effect
ReverseEngine Torque Problems
0NoneAdds Heat-Causing Voltages and/or Currents in Neutral Wire

Harmonic Summary

Harmonics are higher frequency waveforms that are superimposed on the frequency of the basic frequency, that is, the circuit, and are sufficient to disrupt the waveform.The amount of distortion applied to the base wave will depend entirely on the type, quantity and shape of the existing harmonics.

Harmonics in the electrical power distribution system combine with the basic frequency (50Hz or 60Hz) source to create distortion in voltage and/or current waveforms.This distortion creates a complex waveform consisting of a series of harmonic frequencies that can have a negative effect on electrical equipment and power lines.

The current waveform distortion amount, which gives a complex waveform its own unique shape, is directly related to the frequencies and magnitudes of the most dominant harmonic components, whose harmonic frequency is multiples (integers) of the base frequency. The most dominant harmonic components are low-level harmonics from 2nd to 19th degree, and triplens are the worst.