### Harmonics

The electric power distribution system is designed to operate with sinusoidal voltages and currents. But not all waveforms are sine waves. Electronic loads, for example, often draw current only at the peak of the voltage waveform, which always means that the current is distorted, and may distort the voltage as well. One convenient way to describe these waveforms is to make a list of sine waves that, when added together, reproduce the distorted waveform. The sine waves in this list are always multiples, or harmonics, of the fundamental frequency (50 Hz or 60 Hz). A typical input circuit of a single-phase supply. All of the graphs below are automatically produced by the Industrial Power Corruptor’s power flow option. A typical distorted current waveform, drawn by the supply above. It only draws current at the peak of the voltage waveform, because the diodes in BR1 only conduct when the AC voltage is higher than the voltage on C1. This is the same waveform, expressed as a frequency spectrum. Note that the frequency content of the waveform consists of odd multiples (3,5,7,9, etc.) of the fundamental. This is typical for electronic loads. The same waveform, expressed as a frequency spectrum. This time the values are listed. Sometimes, the phase angles of the harmonics can be important, too, but they are not shown here.

THD, or Total Harmonic Distortion, is one measure of the total distortion. It is the RMS sum of the harmonics, divided by one of two values: either the fundamental value, or the RMS value of the total waveform. Both are legitimate definitions of THD. For small values of distortion, they both produce roughly the same number. For the waveform above, using the fundamental as the reference produces a THD value of 93.2%, and using the RMS as the reference produces a THD value of 67.8%. Both values are correct.For this and other reasons, most experts in power system harmonics frown on using THD as a measure of harmonics. Other measures such as TDD (IEEE 519) or volts and amps make more sense. For example, the waveform above consists of 32.4 amps at 60 Hz, plus 25.4 amps at 180 Hz, plus 14.8 amps at 300 Hz, etc.

Many devices on the power system respond poorly to non-sinusoidal waveforms. Transformers, for example, become less efficient. Many revenue meters become less accurate. Protection devices such as circuit breakers may trip too soon, or too late.

Balanced harmonics at multiples-of-3-of-the-fundamental, or triplen harmonics (3rd, 9th, 15th, etc.), fail to rotate on three-phase systems. As a result, neutral conductors may overheat, and transformers and motors become less efficient.

• Harmonic standards and enforcement
• Ways to reduce harmonics
• Effects of harmonics on equipment and grids

Alex McEachern, 1/2004, based in part on work done with Mark McGranaghan

Power Standards Lab
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