Optimal endogenous carbon taxes for electric power supply chains with power plants

In this paper, we develop a modeling and computational framework that allows for the determination of optimal carbon taxes applied to electric power plants in the context of electric power supply chain (generation/distribution/consumption) networks. The adoption of carbon/pollution taxes both internationally and regionally has been fueled by global climate change and fuel security risks, with a significant portion of such policy interventions directed at the electric power industry. The general framework that we develop allows for three distinct types of carbon taxation environmental policies, beginning with a completely decentralized scheme in which taxes can be applied to each individual power generator/power plant in order to guarantee that each assigned emission bound is not exceeded, to two versions of a centralized scheme, one which assumes a fixed bound over the entire electric power supply chain in terms of total carbon emissions and the other which allows the bound to be a function of the tax. The behavior of the various decision-makers in the electric power supply chain network is described, along with the three taxation schemes, and the governing equilibrium conditions, which are formulated as finite-dimensional variational inequality problems. Twelve numerical examples are presented in which the optimal carbon taxes, as well as the equilibrium electric power flows and demands, are computed. The numerical results demonstrate, as the theory predicts, that the carbon taxes achieve the desired goal, in that the imposed bounds on the carbon emissions are not exceeded. Moreover, they illustrate the spectrum of scenarios that can be explored in terms of changes in the bounds on the carbon emissions; changes in emission factors; changes in the demand price functions, etc.