# What You Need to Know About Third Harmonic

## Definition, causes, and effects!

Harmonics are an important concept in power systems, which significantly impacts power quality. In this post, we will address only third harmonics and for a general case, check this article.

Let’s get into the details!

## What is 3rd harmonic and what is its frequency?

In AC three-phase systems, each phase has a periodic current/voltage wave with a specific fundamental frequency with 120 degrees phase angle difference between phases. There are two common fundamental frequencies in power systems, including 50Hz and 60Hz. For simplification, 50Hz frequency is considered as the fundamental frequency, but all subjects can be extended to other frequencies.

So what is 3rd harmonic frequency? As the harmonics are the integral multiple of the fundamental frequency, the third harmonic frequency is three times greater than the fundamental frequency which means that the third harmonic frequency would be 150Hz (3×50 Hz), check the above illustration. It is worth noting that the frequency of the third harmonic in the 60 Hz system is 180 Hz.

## What causes 3rd harmonics?

In symmetrical three-phase systems, there are no harmonics, and all waves are purely sinusoidal with the fundamental frequency. However, some types of electric loads create disturbances in electric systems, and waves with non-fundamental frequencies are added to the original one. Therefore, the system is no longer pure sinusoidal.

In fact, non-linear loads are the main cause of distortion and produce harmful third harmonics in energy systems. A wide range of non-linear loads is available in each system due to advances in power electronics. Nowadays, there are many power electronics devices such as:

• power converters,
• switching power supplies,
• inverters, and transistors in the systems,

Apart from power electronic devices, electric motors and non-ideal transformers can be the main sources of the third harmonics.

In distribution systems, having a balanced power system is challenging because there are many consumers who use different types of single-phase electric loads. Therefore, the distribution may be unbalanced, and, in this situation, the third harmonics are shown up in voltages and currents.

Asymmetrical short-circuit faults like phase to ground faults act as a huge non-linear load and make the system unbalanced. Thus, third harmonics would also be available in fault conditions.

## Why 3rd harmonic is dangerous?

In power systems, the presence of odd harmonics is more probable than even ones. Moreover, higher-order harmonic magnitudes are relatively low in general, and in most cases, they are filtered in the system. It means that low-order odd harmonics can be more harmful because their magnitudes are considerable.

Generally, as the harmonic magnitudes decrease in higher-order harmonics, the third harmonic in the system would be the dominant harmonic component, which distorts the voltage or current waveform.

In the third harmonic, all phases have the same phase angle, and the instantaneous sum of the currents in the three phases taken at any moment will not be zero (phases cannot cancel out each other).

The current harmonics can flow in the entire system and devices, which may reduce their efficiencies and performance significantly.

Moreover, the third harmonic currents in the three-phase system are not eliminated in the neutral conductor, and in this situation, the neutral conductor will draw a cumulative third harmonic current which is too dangerous because it may lead to maloperation of electric apparatus and protection systems.

The problem gets more concerning once the neutral conductor/cable size is lower than phase one because when it becomes overloaded by third-order harmonic, substantial losses (heat) are produced in the neutral. As the overheating results from overloading losses, the neutral cable insulation can deteriorate, or its conductor may be deformed due to the high temperature.

Moreover, the neutral point can be loosened if its connection is not well. All these consequences are probable when a neutral path is available, and designers must be aware of the mentioned issues when designing neutral conductors.

However, the third harmonic can be a problem when the system does not have a ground path for the current third harmonic. If the current third harmonic cannot find a way to the ground, the current will be sinusoidal, but the peak voltage will go up significantly, which is undesirable and may lead to damage.

## Effect of 3rd harmonics (power system, transformer, generator, induction motor)

To be more specific, the third harmonic has detrimental effects on generators, transformers, and induction motors which are available in each electric system. These effects can be somehow similar. For instance;

• The third harmonic in a grounded generator with a resistor may create continuous heating (without fault) of the earthing resistor and malfunction the protection system.
• About induction motors, the winding connection configuration is important because, in delta connection, the current third harmonic circulates in the delta and does not reflect at the source side. This harmonic increases the current RMS value, and more copper and core losses will be generated. Owing to an increase in losses, the motor output de-rating should be considered to prevent any damages. It means that the output will be decreased to follow the allowable temperature rise, and efficiency will be reduced due to losses.
• These impacts are also in transformers as third harmonic can increase core and copper losses, and core saturation may decrease the transformer efficiency and reduce the transformer operating power. In star-star connection, the third harmonic current is either towards the neutral point or away from it, and this harmonic will flow through the line. However, in the star-delta connection, the third harmonic will be trapped in the delta, and there is no path for flowing the harmonic.

In most cases, the third harmonic is dominant among Triplen harmonics (third, ninth, etc.), and other harmonics can be neglected. Thus, as mentioned before, the current third harmonic is accumulated in the neutral conductor, and it can be measured easily. The measured neutral current would be three times greater than the phase third harmonic currents and I3N=3×I3p.

## Conclusion

To sum up this article, it is worth noting that the solution for the third harmonic in the power system is using a delta connection in the transformer. In this way, the current third harmonic will be rotated in the delta connection, and it never shows up in line currents.

Apart from that, to reduce the risk of the third harmonic in grounded star connection, the neutral conductor size should be three times one phase conductor’s size to decrease the risk of overloading and overheating.