The coordinated and non-coordinated operations of microgrid and conventional generators are studied considering carbon emission constraints and Stackelberg game model with a bi-level optimization of carbon tax and economic benefit is established. With Karush-Kuhn-Tucker(KKT)conditions

Big-M method and strong duality theorem

the bi-level optimization problem is converted to a mixed integer linear program which could be solved by available mixed integer linear program solvers. A modified Shapley method based on risk factors is proposed to allocate the total profit of microgrid and conventional generators in coordinated operation

and compared with the non-coordinated operation. The case study analyzes the effects of carbon emission constraints on the profit in coordinated operation and non-coordinated operations. The results show that the positivity and stability of coordinated operation are assured with a reasonable carbon tax policy and profit allocation. The profits of both microgrid and conventional generators are improved while the carbon emission is reduced

achieving the development of low carbon economy. This work is supported by National Natural Science Foundation of China(No. 51577115).