Harmonic currents

The electric currents in the electrical communications are of periodicals type, but not always sinusoidal. However, it is known that a periodic wave can be broken up by decomposition into Fourier series.
It is starting from this concept that the branch of mathematics known under the name of harmonic analysis developed. in a succession of sinusoidal waves whose frequency is a multiple of the fundamental frequency
The user who affixes this stringcourse is invited to state the points to be improved on page of discussion. network of these currents, and the harmonic currents which come to be added with the basic component to give to the current its nonsinusoidal form.
In general, the harmonics do not come from the feeding but from the network customer: the powerplants generating of the sinusoidal tensions parfaitements, the harmonic currents are due to the presence of a nonlinear electric charge in an electrical communication.


Mathematics In linear algebra, the row of a family of vectors is the dimension of the vectorial subspace generated by this family. The theorem of the row binds the row and the dimension of the core of a linear application definite on a vector space of finished size. Toponymes Rang is a commune of the department of Doubs. Row-of-Fliers the east a commune of the harmonics
Within the framework of the decomposition in Fourier series of a signal.
The signals periodical, an electric current is broken up into a sinusoidal signal at the frequency of the network, and summons it sinusoidal signals, of frequency 2, 3, 4, 5. .n time the frequency of the network.
It is this number N which one calls the row of the harmonic component.

Particular case of the harmonic of row 2

In general the network loads are symmetrical. Under these conditions the harmonics of row 2 are judicious being null.

Particular case of the harmonic of row 3

It is the most frequent case. It is generated amongst other things by the computers, the television sets or other electronics components. They are particularly harmful for the three-phase electrical communications because of the important currents of neutral then produced. The same applies to the odd harmonics of the third (9th, 15th, 21e, etc) also known under name "harmonics sequence zero".


The name of interharmonic returns to harmonics of nonwhole row. Such harmonics are frequent in the light-arc furnaces, but can also be generated by systems of electronics of power.

Apparatuses generator of harmonics

It was considered often wrongly that the generators of harmonics were primarily industrial. However of measurements on the French electrical communication, showed that the moment when the network is polluted the most by the harmonics is Sunday evening, that is to say at one moment when industries idle, but where the television sets are massively lit
The television sets or the computers are the principal transmitters of harmonics. Indeed, these apparatuses comprise capacitive filters made up of diodes, reels and capacitors which disturb the tension of the network. The role of these filters is to transform an alternating voltage delivered by the network into a continuous tension. Being given the number of this equipment during each hearth and their long period of use in one day, these home devices emit a current and a harmonic tension which will disturb the sinusoidal tension of the network, even if they do not consume an important power.

In industry

Variable speed transmission for engines
Welding machines

In the domestic uses

Lamp low consumption called to energy saving (electronic feeding)
Fluorescent tubes
All appareils électroménager
feeding with cutting

Instantaneous effects

The effects of the most known harmonics are the destruction of the capacitors and the circuit breakers.
Trading loss per inopportune opening of the circuit breakers.
Vibrations, noises on the revolving machines.
Various electromagnetic interferences.

Long-term effects

Additional heating of the cables and transformers, therefore premature ageing, except if downgrading of the electrical material.
one defines the concept of THD In certain countries, the provider of electrical energy engages on the purity of the power supply provided to his industrial customers, via a level of guaranteed THD
The harmonic tensions can be evaluated: individually, according to their amplitude
broadly that is to say according to the value of the harmonic rate of distortion THD.

limit while running

In certain case, the provider of electrical energy can impose maximum levels of harmonic currents generated by his customers. These levels are expressed as a percentage fundamental level


Passive filtering, the goal is to lower the harmonic impedance of the network using filters granted on the frequencies of the harmonics generated by the process.
The filters are generally installed in HTA. They can take part in the compensation in reactive energy. They are condensing overall compounds - coils whose frequency of resonance is granted on the rows of the generated harmonics.
Generally the harmonics of row 3 are filtered by the network and do not require specific filtering. A filter will be on the other hand often prévoiera
Active filtering, the active filter is a converter which injects into the network of the of the same harmonics amplitude than those generated by the industrial process, but in opposition of phase. The harmonics generated by the active filter and the process are thus cancelled. It is about a solution which is applicable only in low tension.

Modification of the installation

Feeding of the circuits pollutants and sensitive by 2 distinct transformers
Downgrading installation

Rate of distortion

The harmonic rate of distortion represents the variation of a signal compared to a reference.
The rate of harmonic distortion total describes the influence of the harmonic components of a signal:
Qh: effective value of the harmonic to the row H of the current ⁄ the tension
Q1: basic component
QHM: effective value of the harmonic currents ⁄ tensions
H: harmonic row
H: maximum harmonic row, in theory infinite
This definition does not take into account the interharmonic components of the signal. one can then use the >Rapport Total Distortion (TDR), definite like this:
Q1: effective value of the basic component
Q: total effective value of the size (running or tension)


The harmonic Rate of distortion compared to the fundamental one (THD-F) is defined as:

with effective Vh = Value of the harmonics and effective Vf = Value of the fundamental one


The rate of harmonic distortion total (THD-G) is defined as:

Effective value of the harmonics and effective Vg = Value of the total signal

Total harmonic voltage distortion Aftermath
THD < 5% No problems
5% < THD < 7% Equipment malfunction "sensitive"
7% < THD < 9% Equipment malfunction "normal"
THD > 9% Dysfunction of virtually all devices, destruction of certain materials in the short, medium and long term almost certain.

execution time customer :
runtime server : 0.006 seconds