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# Essential Basics of Total Harmonic Distortion (THD)

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## THD definition

For a signal y, the total harmonic distortion (THD) is defined by the equation:

This definition complies with that of standard IEC 61000-2-2.

Note that the resulting value may exceed one. According to the standard, h can generally be limited to 50. This equation produces a single value indicating the distortion of a voltage or a current flowing at a given point in a distribution system. Harmonic distortion is generally expressed as a percentage.

Definition // ￼THD stands for Total Harmonic Distortion. The level of harmonic distortion is often used to define the degree of harmonic content in an alternating signal.

### Current and voltage THD

When dealing with current harmonics, the equation becomes:

The above equation is equivalent to the one below, which is more direct and easier to use when the total rms value is known:

When dealing with voltage harmonics, the equation becomes:

### Total harmonic factor (THF)

In certain countries with different work habits, a different equation is used to determine harmonic distortion. In this equation, the value of the fundamental voltage U1 or the fundamental current I1 is replaced by the rms values Urms and Irms respectively.

To distinguish between the two equations, we will call the second the total harmonic factor (THF). Example of a voltage THF:

The total harmonic factor, whether for voltage or current, is always less than 100%. It makes analogue measurements of signals easier but is used less and less because the result is very close to the THD defined above when a signal is not significantly distorted.

What is more, it not well suited to highly distorted signals because it cannot exceed the value of 100%, contrary to the THD defined at the beginning of this technical article.

### Importance of Mitigating THD

While there is no national standard dictating THD limits on systems, there are recommended values for acceptable harmonic distortion. IEEE Std 519, “RECOMMENDED PRACTICES AND REQUIREMENTS FOR HARMONIC CONTROL IN ELECTRICAL POWER SYSTEMS” provides suggested harmonic values for power systems:

Computers and allied equipment, such as programmable controllers, frequently require AC sources that have no more than 5% harmonic voltage distortion factor [THD], with the largest single harmonic being no more than 3% of the fundamental voltage.

Higher levels of harmonics result in erratic, sometimes subtle, malfunctions of the equipment that can, in some cases, have serious consequences.

The limits on voltage harmonics are thus set at 5% for THD and 3% for any single harmonic. It is important to note that the suggestions and values given in this standard are purely voluntary.

However, keeping low THD values on a system will further ensure proper operation of equipment and a longer equipment life span.

### Harmonics: What are they, why do I care, how do I solve?

Low Voltage drive Senor Application Engineer Jeff Fell discusses what cause harmonics and what kind of problems can they cause? Learn about this important issue and how to solve the problems.

This 36 minute education video will walk you through definitions to solutions.

References //

• Total Harmonic Distortion and Effects in Electrical Power Systems – Associated Power Technologies (APT)

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### Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.

1. Gajendra Kumar Rathor
Aug 01, 2018

what limit value of THD of current for 440v system.

2. OnGuard
Aug 18, 2016

Thank you for a thorough explanation of THD. The video was especially helpful and we will use parts of it to show clients that are worried about their sensitive electronics.

3. Ashok Kumar Sharma
Sep 03, 2015