This is one of my favorite topics and have been involved for many years. The point to remember is that in Beemans, it says that while harmonic currents are theoretically possible, there is no reason to be concerned about them. That book was written sometime around 1950 or earlier. I am not sure. However, the point made is important. A harmonic problem doesn't exist until you have one. At that time we didn't have many power electronic devices.
What this means, is that harmonic currents are always present because of all the non-linear loads we apply to each and every power system, but only when the magnitude of current distortion is adequate to develop voltage distortion do we develop potential problems. However, if the current is adequate in the 5th harmonic, that negative sequence current may result in excessive heating in transformers or generators. Hence the K-factor rated transformers.
Third harmonic current is particularly nasty because it is in phase and will add arithmetically in the neutral of a three phase system. This also includes all 'Triplen' harmonics. We have switch mode power supplies everywhere. Since these all operate on the peak of the voltage waveform with a positive and negative current pulse, they generate a lot of 3rd harmonic current. I have measured many systems where the neutral current magnitude exceeds the current carrying capacity of the neutral conductor and results in significant heating. Hence the need for doubling the neutral in many installations.
Odd harmonics, 5th, 7th, 11th, 13th, etc are all generated where variable frequency or DC drives are present using a 6 pulse rectifier. Hence the design of the clean power drives that use 12 or 18 pulses. The harmonic generated will be the number of pulses + and - 1. The lower the harmonic order, the larger the current unless the system has capacitance that provides system resonance at some specific higher frequency.
The process of mitigating harmonic issues can be very complex. It entire depends upon what the problem is and what the desired result is. For example, I visited a facility that used large current source inverters in their process. The drives were at the 480V side of some 2500Kva transformers. The problem was that the facility used 4160V distribution throughout the entire operation. The harmonic current distortion was large enough to create a voltage distortion at 4160V. This resulted in voltage distortion at loads where no non-linear equipment was applied and this equipment was malfunctioning. The customer chose not to solve this problem due to the likely cost at the time, but we examined filters at 4160V or replacing the drives with 18 pulse units. Both very expensive and the filters are always a concern because applying multiple filter banks rises concerns over de-tuning when system configuration changes. A third alternative is to install an expensive electronic device called an Active Filter. This device injects harmonic current into the system 180 degrees out of phase with the system harmonic loads. Thus, the upstream source sees no distortion at all. Very effective, but becomes very expensive as it increases in size.