Electrical loads where the current is not proportional to the voltage are called non-linear loads. Linear loads are pure sinusoidal, and either resistive, inductive or capacitive. To verify the difference between linear and non-linear loads, please refer to the picture below.

The loads such as seen in picture 1.2 and 1.3 are pure sinusoidal, at least in this simplified graph. Based on this it is common practice to define the power-factor as the phase relationship between voltage and current, although this is in fact the displacement factor. Therefore literature often refers to the power factor as the “true power factor” in order to avoid misunderstanding. The definition of (true) power factor and displacement factor are: (v1 and i1 are referring to fundamental frequency)

pf and df may have the same value under the condition that all items are purely sinusoidal. In a real application this does not take place which will be explained in more detail later. Continuously wrong usage of pf for df led to so-called power factor correction equipment (PFC). As this PFC only focuses on phase correction it will not solve problems related to other kinds of distortion. Basically there are different distortions of the main supply such as:

This paper focuses on harmonic distortion, especially the distortion caused by variable frequency drives. Measures for harmonic mitigation usually have a positive impact on other kind of distortion as well.

Ideally, all loads and sources have a pure sinusoidal current waveform. However, the true waveform of most equipment is very different. Non-linear loads like the input current of a standard 6-pulse variable frequency drive (as seen in picture 1.4) cause a distortion of the mains voltage. This distortion is typically evaluated by the Total Harmonic Distortion THD. For power equipment this THD usually obtains frequencies from the 2nd up to the 40th harmonic. Mathematically the harmonics are not limited to the 40th and for other subjects, e.g. audio equipment distortion; the THD range definition might be different.

In order to evaluate the harmonic distortion we need to understand harmonics from a mathematical point of view: Harmonics are multiples of the fundamental frequency (nth Harmonic = n • f).

For the most common domestic power supply of 50Hz this means:

The Fourier transformation decomposes a function of time into its individual frequencies. This means that every periodic signal is a function that can be divided into individual harmonics. The following table helps verify the principle.

This means from a mathematical point of view it is possible to create any periodical signal by adding up harmonics of different order, phase and amplitude.

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As seen in picture 1.4 the input-current-shape of a standard DC-choked drive is far away from the sinus, and the input current of drives with AC-choke is largely similar. The input-current-shape of a drive without any inductance is significantly worse. Although there are many different sources of harmonic distortion, a great part is caused by variable frequency drives (VFD). Therefore these pages focusing on solutions for the drives.

When speaking about harmonics in the context of an electrical power supply and electrical equipment, this is related to the harmonic distortion between 2nd and 40th Harmonic (in a 50Hz supply this is equal to 100Hz – 2kHz). This frequency range is subject to different standards and harmonics recommendations, and the standards are likely to be extended to the frequency of 2kHz to 9kHz very soon.

In a completely symmetrical three-phase supply a 6-pulse rectifier, input does not cause any distortion on the harmonics that are multiples of 3, nor any distortion on the even number harmonics. In the area of 2nd – 40th this excludes every harmonic except for the following twelve: 5th, 7th, 11th, 13tth, 17th, 19th, 23rd, 25th, 29th, 31st, 35th, 37th. This is the reason why standards and recommendations pay attention to these individual harmonic orders. Of course, no true power supply is completely symmetrical; therefore harmonics are also caused on other harmonic orders.

The harmonic distortion is evaluated by the Total Harmonic Distortion (THD) or Total Demand Distortion (TDD) which is each separated for current and for voltage distortion.