Harmonics (electrical power)

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Harmonics are electric voltages and currents that appear on the electric power system as a result of non-linear electric loads. Harmonic frequencies in the power grid are a frequent cause of power quality problems. Harmonic components should be reduced as much as possible.

Causes

There are two types of harmonics in electrical power systems, namely current harmonics and voltage harmonics, which are distortions to current and voltage waves respectively.

Current Harmonics

In a normal alternating current power system, the current varies sinusoidally at a specific frequency, usually 50 or 60 hertz. When a linear electrical load is connected to the system, it draws a sinusoidal current at the same frequency as the voltage (though usually not in phase with the voltage).

Current harmonics are caused by non-linear loads. When a non-linear load, such as a rectifier, is connected to the system, it draws a current that is not necessarily sinusoidal. The current waveform can become quite complex, depending on the type of load and its interaction with other components of the system. Regardless of how complex the current waveform becomes, as described through Fourier series analysis, it is possible to decompose it into a series of simple sinusoids, which start at the power system fundamental frequency and occur at integer multiples of the fundamental frequency.

Further examples of non-linear loads include common office equipment such as computers and printers, Fluorescent lighting, battery chargers and also variable speed drives.

Voltage Harmonics

Voltage harmonics are mostly caused by current harmonics. A non-linear load will not directly cause voltage harmonics unless it is injecting power. However, the voltage provided by the voltage source will be distorted by current harmonics due to source impedance. If the source impedance of the voltage source is small, current harmonics will cause only a small voltage harmonics.

Harmonics Fundamentals

Harmonics provides a mathematical analysis of distortions to a current or voltage waveform. Based on Fourier Series, harmonics can describe any periodic wave as summation of simple sinusoidal waves which are integer multiples of the fundamental frequency.

Harmonics are steady-state distortions to current and voltage waves and repeat every 50 hertz or 60 hertz cycle. They are different from transient distortions to power systems such as spikes, dips and impulses.^[1]

Total Harmonic Distortion

Total harmonic distortion, or THD is a common measurement of the level of harmonic distortion present power systems. THD is defined as the ratio of total harmonics to the value at fundamental frequency.

${\mathrm {THD}}={\frac {{\sqrt {V_{2}^{2}+V_{3}^{2}+V_{4}^{2}+\cdots +V_{n}^{2}}}}{V_{1}}}$

where V_n is the RMS voltage of nth harmonic and n = 1 is the fundamental frequency.

Effects

One of the major effects of power system harmonics is to increase the current in the system. This is particularly the case for the third harmonic, which causes a sharp increase in the zero sequence current, and therefore increases the current in the neutral conductor. This effect can require special consideration in the design of an electric system to serve non-linear loads.^[2]

In addition to the increased line current, different pieces of electrical equipment can suffer effects from harmonics on the power system.

Motors

Electric motors experience losses due to hysteresis and losses due to eddy currents set up in the iron core of the motor. These are proportional to the frequency of the current. Since the harmonics are at higher frequencies, they produce higher core losses in a motor than the power frequency would. This results in increased heating of the motor core, which (if excessive) can shorten the life of the motor. The 5th harmonic causes a CEMF (counter electromotive force) in large motors which acts in the opposite direction of rotation. The CEMF is not large enough to counteract the rotation, however it does play a small role in the resulting rotating speed of the motor. This is true for other negative sequence related harmonics including the 8th, 11th, 14th, etc.

Telephones

In the United States, common telephone lines are designed to transmit frequencies between 300 and 3400 Hz. Since electric power in the United States is distributed at 60 Hz, it normally does not interfere with telephone communications because its frequency is too low.

References

↑ "Power System Harmonics". Rockwell Automation. Allen-Bradley.
↑ For example, see the National Electrical Code: "A 3-phase, 4-wire, wye-connected power system used to supply power to nonlinear loads may necessitate that the power system design allow for the possibility of high harmonic neutral currents. (Article 220.61(C), FPN No. 2)"

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