The company would not “replace existing energy suppliers or directly set household electricity prices”, it said in a consultation document.
It added that its purpose would be to “help Wales reduce energy costs over time by developing and owning renewable energy assets” and “supporting local and community ownership, investing in smart local energy systems”.
It would also “help more organisations use locally generated energy” and try to attract investment into Welsh energy infrastructure.
The company would be separate from Great British Energy, which the UK government set up in 2024.
TGC is working on a number of projects on land owned by the Welsh government, including proposed wind farms at Carreg Wen near Aberdare and Glyn Cothi in Carmarthenshire.
The consultation asks if TGC should form the basis of the new company and whether it should use its name or call itself Ynni Cymru, external.
It also proposes that the company could take stakes in larger schemes – suggesting this could involve offshore wind, marine energy and nuclear.
The consultation looks at establishing a Welsh Energy Wealth Fund to allow energy projects “to support the most vulnerable in Wales as well as those living in areas where projects are being delivered”.
Speaking to BBC Radio Wales Breakfast, Price said: “Our vision for the future of the energy system in Wales is one in which it’s clean, it’s cheap and it’s owned by us.”
He said the organisation was bringing the different elements together “to create a single company that, if you like, has the range of expertise and the sort of critical mass of resources and knowledge to make a real difference”.
Price said Wales was “an energy giant at the Industrial Revolution with coal, but unfortunately we didn’t see the benefit of that being derived largely by our own people”.
He added: “We don’t want to make the same mistake with the huge potential that Wales has in this new energy revolution with renewable energy.”
The minister said many of the levers for energy are decided at a UK level, but added that energy produced by a public energy company could allow “lower energy prices” through agreements with local large energy users.
