The third harmonic of any periodic wave is the frequency of that wave multiplied by three. For example, the third harmonic of a 60Hz wave would be 180Hz.
Third harmonics are a special problem in electrical power quality. Unlike residential installations, which use single phase 120/240 power, many commercial buildings use three phase 120/208 power. Each of these three phases, when used in a line to neutral connection, shares the same neutral conductor. On a well designed system that balances the load between the three phases, the electric current on the neutral conductor from these three phases almost completely cancel each other out, leaving very little current traveling through the neutral conductor.
However, when triplen harmonics (that is, all odd multiples of the third harmonic) are present in the electrical system, they do not cancel each other out on the neutral conductor. Their phases match up they add together, producing a large current. This current heats up the neutral conductor and the transformer that is feeding the system, and can damage the installation.
Third harmonics are most often caused by the non-linear load of the bridge rectifier in a computer power supply. Third harmonics become a serious problem when a large office building has many computers, and sometimes in large grocery stores that use modern cash registers (which are basically computers running cash register software).
There are several solutions to the problem:
Filters are passive electric devices that smooth out the electric current by blocking frequencies above or below a certain value. Some filters are tuned to specifically block only the third harmonic, others block every waveform above the fundamental frequency.
Derating the neutral conductor and the transformer is an inefficient, but simple and effective, solution. By using conductors and transformers that are larger than otherwise necessary, the system can handle the extra current and heat caused by the third harmonics without damage.
K-Factor transformers are specially designed transformers that can handle harmonics. The K-rating is a measure of how much harmonic distortion it can handle.