Grid voltage swell and sag, what happens to harmonics

First of all you should look up the Fourier Transformation/Series.

But you can do some Assumptions based on the time function:

First off ask yourself does the Signal have a DC Offset. In our case yes. So we would have a frequency part at f=0 in the frequency domain of A/2.

Now we look at the fundamental frequency of the Signal. As the period is 20ms it would be 50 Hz. This is our fundamental frequency.

Now we can look up if our time function is point symmetric or axis symmetric. To get information if the resulting frequencies are even or odd.

Just add a current-to-voltage-translator (somethimes called "resistor") in series with the non-linear load and you will see also voltage harmonics across the load (and also across the resistor).

By definition the voltage across a (ideal) voltage source cannot be changed (as also noted in another answer). So if the voltage source provides pure sinusoidal voltage (i.e. no harmonics) no matter what load you have (linear or non-linear) the voltage will be pure sinusoidal. This changes as soon as the voltage source has a series resistance.

^{simulate this circuit – Schematic created using CircuitLab}

Left circuit: current throuh non-linear element (diode) will have harmonics. Voltage across non-linear element will not (cannot) have harmonics because V1 is an ideal voltage source.

Right circuit: current throuh non-linear element (diode) will have harmonics. Voltage across resistor will be proportional to non-linear current through resistor, i.e. will have harmonics. Also voltage across non-linear element (diode) will be pure sinusoidal minus voltage with harmonics, i.e. will also have harmonics.