The 27km pipeline would run from the transmission network in Staffordshire to a planned 2,000MW combined cycle gas turbine (CCGT) at Willington.
The energy company also has consent to build a 400MW open cycle gas turbine at the site, which previously held two coal-fired power stations, now decommissioned.
The Planning Inspectorate has 12 months to assess the proposal and make a recommendation to the secretary of state.