Taxing Strategies for Carbon Emissions: A Bilevel Optimization Approach

This paper presents a quantitative and computational method to determine the optimal tax rate among generating units. To strike a balance between the reduction of carbon emission and the profit of energy sectors, the proposed bilevel optimization model can be regarded as a Stackelberg game between the government agency and the generation companies. The upper-level, which represents the government agency, aims to limit total carbon emissions within a certain level by setting optimal tax rates among generators according to their emission performances. The lower-level, which represents decision behaviors of the grid operator, tries to minimize the total production cost under the tax rates set by the government. The bilevel optimization model is finally reformulated into a mixed integer linear program (MILP) which can be solved by off-the-shelf MILP solvers. Case studies on a 10-unit system as well as a provincial power grid in China demonstrate the validity of the proposed method and its capability in practical applications.