Upon receipt of such petition it shall be the duty of the Nebraska Power Review Board at once to make an investigation of the proposed district and of its proposed plants, systems, or irrigation works, and, if deemed by the Nebraska Power Review Board feasible and conforming to public convenience and welfare, the Nebraska Power Review Board, or its successor, by its executive head, shall thereupon and within thirty days from the receipt of such petition, execute a certificate in duplicate, setting forth a true copy of the petition and declaring that the petition has been approved.