Harmonic Currents

Many nonlinear loads present on an electrical network creates a high level of harmonic currents in the electrical networks.

These harmonic currents:

These distortions, if they are significant, can result in:

These various problems increase the system installation and operating costs. It is therefore necessary to control the energy quality carefully.

A periodic signal is a superimposition of:

The original sinusoidal signal at the fundamental frequency (for example, 50 Hz or 60 Hz)
Sinusoidal signals whose frequencies are multiples of the fundamental frequency called harmonics
Any DC component

This periodic signal is broken down into a sum of terms:

where:

NOTE: The DC component is usually very low (even upstream of rectifier bridges) and can be deemed to be zero.

NOTE: The first harmonic is called the fundamental (original signal).

Example of a current wave distorted by a harmonic component:

1 I_rms: rms value of the total current

2 I1: Fundamental current

3 I3: Third order harmonic current

4 I5: Fifth order harmonic current

MicroLogic E trip units display the rms values of currents and voltages.

The total rms current I_rms is the square root of the sum of the square of the rms currents of each harmonic:
The total rms voltage V_rms is the square root of the sum of the square of the rms voltages of each harmonic:

Various standards and statutory regulations set the acceptable harmonic levels:

Electromagnetic compatibility standard adapted to low voltage public networks: IEC/EN 61000‑2‑2
Electromagnetic compatibility standards:
- For loads below 16 A: IEC/EN 61000-3-2
- For loads higher than 16 A: IEC/EN 61000-3-4
Recommendations from energy distribution companies applicable to the installations

The results of international studies have identified typical harmonic values that should not be exceeded.

The following table lists the typical harmonic values for voltage as a percentage of the fundamental:

Odd harmonics that are not multiples of 3		Odd harmonics that are multiples of 3		Even harmonics
Order (n)	Value as a % of V₁	Order (n)	Value as a % of V₁	Order (n)	Value as a % of V₁
5	6%	3	5%	2	2%
7	5%	9	1.5%	4	1%
11	3.5%	15	0.3%	6	0.5%
13	3%	>15	0.2%	8	0.5%
17	2%	–	–	10	0.5%
>19	1.5%	–	–	>10	0.2%

NOTE: Harmonics of a high order (n > 15) have very low rms values and can therefore be ignored.