The store uses hydro-electricity sourced from the nearby river Goyt to meet more than 50% of its power requirements.
The town, at the foot of the Derbyshire Peaks, has set up an Industrial and Provident Society to run the plant, now known as Torrs Hydro.
Steve Welsh, managing director of Water Power Enterprises, the company which built the plant, hopes that Torrs Hydro will be the first of many. "Setting up and seeing the UK's first community-owned hydro installation generate electricity is absolutely superb and it's wonderful that the electricity is being used to power a store which lies at the heart of the whole community for everyone to use. We now have a model that can be adopted on weirs up and down the country."
Co-operative sustainable development manager Chris Shearlock was delighted that Torrs Hydro was up and running and hoped it would lead to other micro-hydro plants.
"We are very proud to be taking our climate change agenda to new levels by adding micro-hydro power to our strong track record on renewable energy," he said. "We are also planning to extend our support to other schemes across the country."