When all obligations incurred by the corporation and all bonds issued by it shall have been paid in full or provision for payment thereof shall have been made by appropriate, segregation and deposit of funds sufficient for such purposes, then and in such event the corporation may be dissolved by resolution adopted by vote of a majority of the board, which resolution shall set out the plan of dissolution and shall designate three directors who shall act as trustees in dissolution of the corporation. A copy of such resolution, duly certified by the secretary of the corporation under its seal, shall be filed with the Secretary of State, and, if it shows compliance with the foregoing requirements, it shall be recorded by the Secretary of State with the certificate of incorporation. Upon such filing and recording the corporation shall thereupon stand dissolved, and the trustees in dissolution named in such resolution shall thereupon proceed to wind up the business and affairs of the corporation, including the carrying out of the plan of dissolution as specified in such resolution and the conveyance or distribution to the municipalities specified in such plan of the properties and assets of the corporation. Such plan shall provide that the local distribution system (not including transmission lines or generating facilities or like facilities) owned by the corporation and located within the corporate limits of a municipality and within the police jurisdiction of any such municipality shall be conveyed to such municipality and shall provide for sale of the assets of the corporation then remaining and the distribution of the proceeds of such sale among the municipalities in the power district in direct proportion to the net operating income of the corporation derived from the unit of any utility located in such municipalities.