Emissions trading and clean-energy technologies can help the power industry to reduce CO₂ emissions and achieve carbon peak and carbon neutrality. In the context of carbon trading with thermal power enterprises as the main participants in China, this study applied fractional Brownian motion to the energy-switching cost for thermal power enterprises’ strategies and established a stochastic optimization model for a compliance period. We deduced that the carbon-allowance price obeyed the mixed fractional Brownian motion model with the Hurst exponent and volatility coefficient estimated, and the validity of the estimated results verified. Then, we derived the Hamilton-Jacobi-Bellman equation for the optimal total compliance cost by combining the dynamic optimization principle and the fractional Itô’s formula. In this way, we obtained the optimal emission reduction and equilibrium carbon-allowance price. Taking 2021-2030 as the compliance period, we conducted numerical simulations using real data under the premise of ensuring both power supply and economic growth. The simulation results showed the effects of different peak years on the optimal reductions and desired equilibrium prices of annual carbon allowances. Further, sensitivity analyses showed how the Hurst exponent, volatility coefficient, and depreciation rate affect optimal reduction, as well as how initial carbon allowance affect the equilibrium carbon quota trading price and the optimal reduction. Our findings could provide a reference to develop emission-reduction strategies for thermal power companies and carbon pricing in the carbon market.
 

Carbon peak, Mixed fractional Brownian motion, Optimal control, Carbon-allowance price