The size of the ground wire for a 200 amp service depends on several factors, including the distance from the electric-powered unit, the type of wire used, and the NEC code requirements. Here are some key points from the search results:

• According to the NEC code, the grounding electrode to a single or multiple rods shall not be required to be larger than a #6 copper wire.
• For a feeder with a 200A maximum breaker ahead of it, the NEC requires a minimum of a #6 copper wire for equipment grounding conductors.
• Bonding (water and gas) and Ufer grounds require a minimum of a #4 copper wire.
• The minimum size equipment grounding conductor required for a 200-ampere feeder is not less than 6 AWG copper.
• The conduit for wire for the 200 Amp Service should be at least 2 to 2.5 inches as there are three wires running at once.

In summary, the minimum size ground wire for a 200 amp service is #6 copper wire for equipment grounding conductors and #4 copper wire for bonding and Ufer grounds. The conduit for wire should be at least 2 to 2.5 inches. It is important to check the NEC code requirements and consult with a licensed electrician for specific situations.