When does harmonic currents appear and why?


I’ve read about this on wikipedia, but I don’t really understand what linear- and non-linear loads is and why it can create harmonic currents. How can there be other frequencies than the supply frequency on 50/60Hz?

I’m studying Technology Management and Marine Engineering, so I have some knowledge in electricity.

In: 7

Linear load is something that will respond with current in the same shape as you apply voltage. For example, resistor: If you put sinusoidal voltage on it’s terminal, current will also be a sinus. Similarly ideal capacitor, if you apply sinus voltage, current will be sinus with the same frequency, just different phase.
On the other hand, when you look at [voltage – current curve](https://learn.sparkfun.com/tutorials/diodes/real-diode-characteristics) of non linear component (diode), it is visible that this response is non linear. If you apply sinus voltage across ideal diode terminals, then for half cycle current will be 0, and for another half it’s going to be the same as for resistor.
Now, how can we represent this new current graph as function? It’s no longer pure sinus. [Fourier transfrom](https://en.wikipedia.org/wiki/Fourier_transform) tells us, that any function can be represented as sum of sinuses. And to do this, we are using sum of base frequency of our voltage (lets say 50Hz), and higher harmonics (multiples of base frequency, so 100Hz, 150Hz, 200Hz… etc).
Basically, to mathematically describe current curve in circuit with non linear component, we need to add bunch of harmonics to our base frequency.

There is a mathematical theorem (Fourier theorem) which says that any waveform can be thought of as a sum of multiple sine waves. When the waveform is periodic (repetitive) than the multiple sine waves that make it up are multiples (or harmonics).

If you recall Ohm’s law for a resistor, then current (I) = V / Resistance. This means that current in a resistive load has the same waveform as the voltage. A 50 Hz voltage will result in a 50 Hz current.

more complicated theory explains that in a capacitative or inductive load, the frequency is still the same as the voltage, but it is shifted in time.

However, if there is a “non-linear” component to the load (in other words, the current is not proportional to voltage, and there is something more complicated than a time shift), then the current wave form becomes a distorted copy of the voltage waveform.

A good example is a half-wave rectifier load (just a diode and a resistor). In this case, the diode conducts for only one half of the cycle and does not for the rest. This leads to a current waveform where the positive half of the current waveform is the same shape as the voltage waveform, but the negative half is cut off and zero.

Fourier theorem states that that distorted current wave will contain harmonic frequencies. In the above example, the rectified current will not just contain 50 Hz – it will contain some 100 Hz and 200 Hz currents, as well as many more.

The above diode example is somewhat unrealistic, as half wave rectification is not generally used in commercial products. However, many electronic devices use a full bridge rectifier and a smoothing capacitor to produce DC power. The capacitor charges up when the rectified mains voltage is higher than the capacitor voltage, and discharges when it is lower. This results in the overall circuit taking pulses of current when the voltage waveform reaches the top of the peak/bottom of the trough, and taking no current for the rest of the waveform. This distorted spiky current waveform contains a ton of odd harmonics (3rd, 5th, 7th, 9th and so on). As this rectifier/capacitor circuit is used in pretty much all electronic devices, many countries have laws and regulations which have effectively banned it for anything that takes a meaningful amount of power. If you want to sell an electronic product which takes more than about 75W, then you have to include some form of circuit to deal with the harmonics at source (this is typically something called active power factor correction, or aPFC)

There are lots of other sources of waveform distortion due to non-linearity. Fluorescent lights are a good example. The tube current rises drastically as the mains voltage waveform rises, giving a spiky waveform, with lots of odd harmonics.