Here is a fine Wire Size Calculator. Scroll down to related links and look at "Wire Size Calculator".
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Ground / earth protection will not impact cable sizing.
Copper xlpe armoured cable
Cable sizing is based on amperage of the load. The rating of the capacitor bank and the voltage at which it operated need to be stated to give an answer.
The main purpose is to reduce cross-talk between the cable pairs. It also has the happy side effect of keeping the cable pairs neatly together while making connections..
Wire sizing is based on the motors full load amperage. The amperage can be calculated but a voltage has to be stated. I = W/E. Amps = Watts/Volts. Restate the question with a voltage and an answer can be given.