This from Wikipedia mentions Suzuki...
"Electro-hydraulic power steering systems, sometimes abbreviated EHPS, and also sometimes called "hybrid" systems, use the same hydraulic assist technology as standard systems, but the hydraulic pressure is provided by a pump driven by an electric motor instead of being belt-driven by the engine. These systems can be found in some cars by Ford, Volkswagen, Audi, Peugeot, Citroen, SEAT, Skoda, Suzuki, Opel, MINI, Toyota, and Mazda."
So the wire probably carries power to the hydraulic pump the negative return being through the chassis. A relay likely controls power to the pump.
Peccavi, April 2009