# About harmonics in electrical networks

### Risks and Strategies:

All the players working on electrical networks have already heard of harmonics as a beast of worry without necessarily understanding their origin, the risks involved… and how to protect themselves from them or protect themselves from them.

Harmonic currents can cause:

• Heating of neutral conductor,
• Constraints on transformers.

Harmonic voltages can cause:

• Malfunctions and breakage of sensitive equipment,
• Overheating of capacitor banks.

Two strategies exist:

• “Do with” by sizing the installation so that harmonics do not affect operation,
• Reduce harmonics by filtering them.

### Where do harmonics come from ?

They originate in particular from receivers called “loads” supplied with alternating current.

There are 2 types of loads:

• The so-called linear or non-deforming loads: resistance, coil, motor, incandescent lighting, capacitor… the currents which pass through them follow the same forms as the voltages which are applied to them. If the voltage is sinusoidal, the current will be sinusoidal but if the voltage is distorted their current will be too!
• Deforming loads:…. Either all the others! electronic devices, variable speed drive, battery charger, fluorescent or LED lighting…. The forms of the currents which cross them depend on their technologies. In general the currents look like pulses centered on the peak of the voltage sinusoid.

### Harmonic decomposition of distorted currents:

Typically, networks have multiple strain and non-strain loads. The currents flowing through the networks have a periodic shape based on a 50Hz sinusoid (called fundamental) more or less distorted.

Mathematically speaking, all periodic forms – including current forms – can be decomposed into a sum of sinusoids – of varying amplitudes – whose frequencies are integer multiples of the fundamental (Fourier series decomposition).

Practically the currents are therefore to be considered as a fundamental (50Hz), a sine at 2x50Hz (called harmonic 2), a sine at 3x50Hz (called harmonic 3), a sinusoid at 4x50Hz (called harmonic 4), a sine at 5x50Hz (called harmonic 5),…. Under normal operating conditions, the electric currents have almost no even harmonics (zero amplitude of even harmonic currents).

### Voltage wave deformation:

The deformation of the currents results in the deformation of the voltage wave. If we apply the formula Uh = Zh x Ih for each current harmonic order, we can deduce the harmonic voltages of each order and therefore know the shape of the voltage wave.

In this formula, Zh is the impedance of the source at the frequency of the harmonic of order h.

For example, currents in the form of pulses centered on the peak of the voltage sinusoid will tend to flatten the peak of the voltage wave or even widen it if the source impedance is relatively high. The voltage harmonic rates will therefore depend on the source supplying the installation: normal network or backup by generator. In the latter case, the deformations of the voltage wave will be such that they can cause the destruction or the dysfunction of sensitive equipment.