The effects of harmonics in electrical installations

Sources of harmonic currents

Within an electrical installation there are generally two types of loads used while connected to an AC supply:

• Linear loads - such as resistive heating, transformers and electric motors,
• Non-linear loads - such as variable frequency drives (VFD), some discharge lighting, LED drivers, UPS and switched mode power supplies.

The non-linear loads are responsible for creating distortion of the supply AC waveform.

Fig 1 shows an example of a typical arrangement of linear and non-linear loads connected within a large installation.


The summation of all the harmonic currents appearing on the network via the common bus bar (see Fig 1) can lead to a number of unwanted effects causing interference both on the supply and within the installation, including:

• overheating of windings in motors, transformers and chokes due to increased iron losses,
• additional current causing overloading of the neutral conductor in three-phase circuits due to triplen harmonics (to be considered in a future article),
• unexpected operation of circuit­breakers and RCDs,
• premature failure of power factor correction capacitors due to increased stressing,
• rectifier type instruments failing to indicate true rms values, and
• the increased risk of damage and interference with communication circuits and equipment.

What are harmonics?

To understand the causes of harmonics we first need to consider the current flowing in AC systems.

If we connect a resistive (linear) load to a supply having a sinusoidal voltage waveform then the resultant current will be a sine wave in phase with the voltage (see Fig 2(b)).


However, even though a load is connected to a sinusoidal voltage, the resultant current sine wave is not necessarily sinusoidal. In practice many of the commonly used loads, as previously mentioned, generally include electronics and have a non-linear current/voltage relationship and therefore take a non­sinusoidal current from the supply.

An example of this is a 230 V AC source used to supply a large current load via a bridge rectifier and a large inductive filter connected in series with the load (see Fig 3(a)). The bridge rectifier would typically invert the negative half cycles of the input voltage. While the inductive filter will offer a high resistance to the AC component after rectification and will therefore oppose any of the remaining AC ripple in the load current to produce a smooth DC current¹. If the ratio of inductance to resistance (L/R) on the DC side of the rectifier is very large, the current taken from the supply forms a rectangular wave and is in phase with the supply voltage, as shown in Fig 3(b).

Although the example shown in Fig 3 is somewhat exaggerated, it is convenient to use this rectangular current waveform methodology as a basis for discussion. Harmonic currents may be considered as sinusoidal currents operating at different frequencies and subsequently with a reduction in magnitude. When combined they construct a distorted non-sinusoidal and complex waveform such as that representing for example a rectangular, triangle or saw-tooth. Such complex waveforms consist of whole multiples of the fundamental frequency at which the supply system is designed to operate.

For example, for a typical fundamental frequency of 50 Hz, then the 3rd harmonic will be at 150 Hz, the 5th will be at 250 Hz, and so on.

Note: This article only considers odd numbered harmonics, as even numbered harmonics such as the 2nd at 100 Hz, the 4th at 200 Hz and so on, are generally rare in AC circuits. However, where they do exist there is a minimum effect as the harmonics 'swing' equally in both the positive and negative cycles and in effect cancel out.

Fig 4 shows the effect the presence of harmonics has on the fundamental sine wave. The complex distorted wave shown is the sum of all the sine waves from the fundamental up to the 9th harmonic.
The resultant complex waveform may be considered as electromagnetic interference (EMI) created by such non-linear loads. Section 444 of BS 7671 provides the requirements and recommendations to enable the avoidance and reduction of such electromagnetic disturbances that may otherwise lead to disturbances in communication and information technology systems, or cause damage to sensitive electronic equipment.

Effects of harmonic currents

Whenever non-linear loads are connected, circulating harmonic currents are produced increasing the overall rms value.

The resultant circuit rms current, as shown in Fig 4, can be found using:


Where:

I_hn is the rms value of current at the various harmonic frequencies

A mathematical technique known as Fourier analysis, although outside the scope of this article, can be applied to an electrical network which allows a regular repetitive waveform to be broken down into its constituent harmonics. However, for convenience and accurate measurement of neutral currents, power quality analysing equipment may be used to determine the impact of harmonic content within an installation.

It can be shown using such analysis that a rectangular wave (see Fig 3(b)) is made up of a sine wave at the fundamental frequency plus a series of odd harmonics, consisting of the 3rd, 5th, 7th, 9th, and so on, and conversely, with a reduction in amplitudes of ½ times that of the fundamental for the 3rd harmonic, and 1/s times for the 5th harmonic, and so on.

Fig 5 shows the situation where the resultant green waveform is derived from a 3rd harmonic (yellow) with an amplitude of ½ of the fundamental added to the fundamental waveform (grey).

Adding further harmonics, the red waveform is derived from the 5th (purple), 7th (orange) and 9th (light blue) waveforms (see Fig 6). It can be seen that the red complex wave is approaching the shape of a rectangular waveform, as shown previously in Fig 3(b). Adding an increased number of odd harmonics in accordance with the above series strategy would produce an infinitely closer approximation to that of the rectangular wave as seen in Fig 3(b).

Note, the higher the order of a harmonic the smaller its influence. Once we approach the 25th harmonic the subsequent effects become insignificant.

Summary

This article discussed harmonic currents, what they are, and the types of electrical loads that create them. Also considered was the summation of harmonics, the effect on the current rms value and the consequences upon the electrical system within an installation.

A subsequent article will focus on the effects of harmonics in a three-phase system when supplying both single-phase and three-phase non-linear loads, and in particular, the impact of triplen harmonics.

Footnotes

¹ Resistors are often used in place of inductors for low current applications and similarly, capacitors may also be used to further smooth a rectified voltage.
² Harmonics other than those detailed in Fig 4 may also be present.