At larger industrial facilities, at least here in Illinois, we are required to install large capacitor banks in order to compensate for the large motor loads we have. This is simply so the power factor is correct for the usage meters, so we get billed correctly.
It's not about 'the power factor being correct for the meters', it's about lowering the current drawn in order that electricity bills are lower.
For larger supplies, billing is usually done differently than for smaller (like domestic) supplies. CT metered supplies simply measure the current and volts to calculate kVAh. 'Whole Current' metering measures 'True Power' only so a domestic customer is usually billed purely in kWh so any reactive loads aren't paid for.
An industrial customer will pay for reactive power and so correcting the power factor as close to unity as possible will result in cheaper bills.
As far as CT's go, remember that they are designed differently to a voltage transformer. CT's are designed to deliver the rated current into a specific load impedance range. I.e a 200/5 CT will try and output 5A secondary current for 200A in the primary, or a direct ratio of any current up to that 200A. It will try to do this regardless of the load impedance. This means that it's the voltage that changes to try and drive the current through a particular load. If the load is a very high impedance then the voltage across the CT terminals will be correspondingly large. This can exceed the minimal insulation and cause damage, arcing and fire. If the output terminals are open circuit, with a primary current flowing, then you effectively have infinite load impedance and extremely high voltages can be generated. This is why it is always important to short out CT's when not in use.
Be very careful with CT's, they can be extremely dangerous if you just expect them to act like a voltage transformer, as they are not the same.
As far as this project goes, you need to understand that a CT outputs current in ratio to the primary NOT voltage. The Arduino pins will measure voltage so you need to translate that somehow. If you had a fixed resistance in the CT secondary then you'll know how much secondary current will flow for a given primary so you could then calculate/measure the resultant voltage across that resistance at different current levels. The voltage and power developed will be purely a factor of that impedance so it would need to be very low. If you consider a short then you'd see a 5A current in the short for 200A primary but the voltage across the short would be very low, based purely on the impedance of the short itself and the CT impedance.
EDIT: The first link to CT's isn't working for me. The site shows additional CT's or CT's plus an MTU. I can't see any specs for this 3V RMS output either. Can the OP add a working link to what has actually been bought. I can only assume that this 3V output is from the MTU and NOT the CT's, as they would simply have a ratio of say 200/5A or 200/1A. CT's also have a Class, usually 0.5 for metering CT's which would mean a standard 5% error tolerance.