How is the heating from harmonic currents related to the harmonic order?

The correct answer is that heating from harmonic currents is proportional to the square of the harmonic order. This relationship arises from the fact that when harmonic currents flow in electrical conductors, they produce heat due to the resistance of the conductor.

Each harmonic current has a different frequency, which is a multiple (the harmonic order) of the fundamental frequency. When considering the effects of these currents, the heating effect, represented by the power, is calculated using the formula ( P = I^2 R ), where ( I ) is the effective current flowing through the conductor and ( R ) is the resistance. As the harmonic order increases, the current can become significantly larger due to the higher frequencies and their interactions within the system, especially in non-linear loads. This leads to a squared relationship: as the frequency or harmonic order increases, the corresponding heating effect increases with the square of that order. Thus, the higher the harmonic order, the greater the heating effect due to the square of the current associated with that harmonic.

Understanding this relationship is essential for engineers and technicians to mitigate the effects of harmonics in electrical systems, as excessive heating can lead to inefficiencies and potential damage to equipment.