Question: I'm a student of Politecnico di Milano and today my prof during the lesson told me that it's important to limit current harmonics into the grid and not voltage harmonics because these last do not create problems. I asked the reason to prof but he didn't answer me. He just told me the problems that current harmonics bring, that is current harmonics are critical because they create torque harmonics in motors but also increase ohmic losses. But what problems voltage harmonics in the grid may cause and why is not important to not decrease them? And should voltage harmonics generate also current harmonics?

Answer: 
Harmonic current in the grid is caused by nonlinear loads. Harmonic current is like reactive current. It does not result in useful power delivered to the load, but it causes losses in the generation, transmission and distribution system. Harmonic current can not easily be mitigated by adding capacitors, the remedies are a bit more complex.

Harmonic voltage in the grid is caused by harmonic voltage drops in the transmission components due to the flow of harmonic current. Since Harmonic voltage is caused by harmonic current flowing through impedance, percentage harmonic voltage is the highest near the source of the harmonic current, where the harmonic current is the highest percentage of the total current. The extent to which an entire grid experiences harmonic voltage distortion is determined by the extent to which users with harmonic loads are distributed throughout the grid.

Look at IEEE 519-2014 - IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems.

Also look at questions tagged [harmonics] such as [what causes voltage harmonics](https://electronics.stackexchange.com/questions/360144/what-causes-voltage-harmonics) and [Harmonics are bad... But how bad?](https://electronics.stackexchange.com/questions/97375/harmonics-are-bad-but-how-bad)
In a Power Transmission Grid voltage and current should be always pure sine waves without harmonics.

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Voltage is delivered to homes, firms, and offices in this mathematical form:

V = A \* sin (2 \* π \* **f** \* t)

**f** = 50 Hz in Europe and 60 Hz in USA

Voltage V is measure between LINE (black or gray wire) and NEUTRAL (blue wire).

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Appliances contain non linear components like diodes, diode bridges, and transistors that introduce locally (inside homes, inside offices, ..) non linearities in the **current** sinked.

**Current** non linearities are estimated and valued by measuring how much power is wasted in the harmonics of **f** by special instruments.

In Europe and in the US there are regulations that manufacturers must follow in order not to waste power in harmonics.

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**Voltage** measured across devices is almost always quite linear because it is imposed/stated by the Power Grid Transmission system which is the SOURCE.

Appliances, which are considered LOAD, can't easily modify the shape of the voltage imposed/stated by the SOURCE unless the current sinked is huge.