The Trade-Off Between Renewable and Thermal Power in Carbon Trading and Green Certificate–Based Sustainable Electricity Markets

Achieving the dual-carbon goals is a central challenge for global sustainability, requiring electricity systems to expand renewable generation while maintaining market stability. Sustainable electricity markets must integrate low-carbon policies with competitive dynamics, yet the impacts of carbon trading and green certificate (GC) schemes under bounded rationality remain insufficiently explored. This study develops a dynamic duopoly game model of renewable and thermal producers under carbon trading and GC regimes. Firms adjust generation and emission reduction efforts adaptively, and nonlinear dynamic methods—including bifurcation diagrams, Lyapunov exponents, and basins of attraction—are employed to analyze system evolution. The results yield three key findings: (1) cost parameters have counterintuitive effects since very low renewable costs, while increasing market share, destabilize the system by inducing bifurcations and chaos, whereas higher thermal costs encourage emission reduction but can also push renewables into chaotic fluctuations; (2) GC quotas exhibit a dual role, where moderate increases promote renewable penetration and emission reduction, but excessively high quotas accelerate chaotic dynamics and undermine long-term stability; and (3) initial values exert a decisive influence on system evolution, as different starting levels of generation and emission reduction under the same policy parameters may lead the market to converge toward a stable equilibrium or drift into chaotic regimes, indicating pronounced path dependence. Overall, this study uncovers the nonlinear interactions among costs, policy instruments, and initial states in electricity markets, providing theoretical insights for designing coordinated carbon trading and certificate schemes that foster sustainability by balancing renewable transition with system stability.