Tasmania could become a "battery for Australia" under a proposal to double the capacity of the country's largest hydro power scheme, Prime Minister Malcolm Turnbull has declared.

Speaking alongside Tasmanian Premier Will Hodgman in Launceston, Mr Turnbull announced an investigation into an expansion of the state's hydro scheme that, if built in full, would cost more than $3 billion and add 2500 megawatts of storage capacity to the national grid.

It follows the Prime Minister's announcement last month of a feasibility study into an expansion of the Snowy Hydro Scheme. The full Hydro Tasmania expansion would be larger.

Mr Turnbull said it could provide enough electricity to run 500,000 homes.