To address climate change and promote sustainable development, based on evolutionary game theory, a game model was constructed for the interaction between platforms, power generation companies, and consumers, breaking through the limitations of traditional bilateral games and exploring in depth the evolutionary mechanism and equilibrium state of the green electricity market. Firstly, the strategies and payoff functions of the three parties were defined, and the replicator dynamic equations and Jacobian matrix were established to analyze the impact of different initial strategies on the evolutionary path. Then, numerical simulations were conducted to study the effects of changes in green electricity costs, platform incentive strength, and consumer preferences on the system's equilibrium, revealing the dynamic interactions between platform incentives, production strategies of power generation companies, and consumer preferences. Finally, stability analysis was used to discuss the conditions under which the system reaches an ideal equilibrium state. The results show that the promotion of green electricity faces key barriers, including the inertia resistance of consumer behavior changes, the sensitivity of green electricity costs, and the scale paradox of increasing electricity demand. These findings highlight that the sustainable development of the green electricity market requires effective coordination between policy incentives, market mechanisms, and consumer behavior.