higher order harmonics are mainly induced by converter commutations. they are not harmful like lower order harmonics, as their amplitudes are usually small, and they can be easily eliminated using a passive RL filter. the main problem with these harmonics is the high frequency electromagnetic noise they generate around cables
With modern switching converters distinction between low- and high-frequency harmonics is not so evident any longer. "Old" rectifiers and square-wave inverters caused clear harmonics such as 5th, 6th, 7th. PWM inverters have harmonic groups at the switching frequency, often in the order of 39th and higher (let's say up to about 200th). Then, only for inverters, think of Neutral Point Clamped and other solutions that allow an overall faster formation of thee waveforms, resulting in a higher equivalent switching frequency.
If then we move the attention to DC/DC converters (for connection to a DC grid), the switching frequency may be quite high.
One note: high-order harmonics can hit against network resonances, more easily than low-order ones.
Elimination
First of all, the architecture allows interleaving suppressing the lower order harmonics, moving the distortion to higher orders. There is a significat effort to do this, that implies that high-order harmonics are preferable. Why?
Although heating inside cables and transformers is larger (more skin effect, more iron losses), they can be filtered more easily, and they propagate to shorter distances inside the network.
So, filtering. There is a wide range of filters, usually built around LC elements (correction to Elyazid Amirouche 's typo, not a passive "RL"). The reason: L does not dissipate as R (some winding resistance, yes, remains) and reactance increases with frequency.
Which filter architectures?
1) for inverter output it is traditionally a LC gamma filter (series L, shunt C), where the C are joint in the neutral point, either fictitious or real.
2) what about network resonances and how to interface with variable network impedance?
> "modern" filters for e.g. PV inverters and in general used in microgrids are LCL (L series, C shunt) for a exigency of decoupling from the network. Think in fact that all LC gamma filters look into the network with their shunt C: you increase the chance of resonances and the flow of current between the filters -> put an additional series L for decoupling from network.
The main reason for the existence of higher order harmonics in the output waveform of the inverter is related to the PWM operation. When the Sinusoidal waveform is modulated by a carrier with the arbitrary frequency of fc (usually triangle waveform), the resultant signal has harmonic orders around the fc, 2fc, 3fc,etc. Therefore, to simply filter the harmonics, the switching frequency is chosen higher enough than the sinusoidal waveform.
The detailed mathematical analysis of the harmonic spectrum of a typical modulation scheme can be found through the NET.
The reasons are already mentioned by the previous commenters.
The most effective way of removing harmonics from grid connected inverters is to use active power filters. There are several control methodologies available for active power filters in the literature. I will highly recommend the following paper to understand the fundamental;
Mainly the electronic components of the network generate harmonics in the system such as MOSFET, IGBT, etc. but they are not harmful like lower order harmonics, as their amplitudes are usually small, and they can be easily eliminated using a passive RL filter. The main problem with these harmonics is the high-frequency electromagnetic noise they generate around cables which causes more loss.