Current Harmonics are caused by non-linear loads even though votage is pure sinusoidal. The voltage harmonics generated due to flow of non-linear current through system impedance and results in corruption of source voltage. Power analyser used to detect current and voltage harmonics.
Current and voltage harmonics both are generated due to nonlinear loads. But the difference is current harmonics are generated in the source side (eg input of rectifier) and the voltage harmonics are generated at output of nonlinear converters which output is AC (eg. Inverter output) or due to uneven generator design. Harmonics Analyzer or Power Analyzer can be used to get current and voltage harmonics. You can also use some standard DSO for measuring harmonics.
Harmonics are generated due to non linearity, periodic switching circuits such as convertors and due to non conformity with ideal machines e.g sinusoidal conductor distributions , slots etc. Regarding voltage and current harmonics please see attached pdf which contains a very simple nonlinear transformer pspice model with a sinusoidal voltage source generating current harmonics from the load side. If the voltage source is replaced with current source you should be able to observe voltage harmonics.
Suggest you use rogowski coil for current m/s and same with high impedance parallel resistor across terminals calibrated to read voltage.