In response to climate change and to promote sustainable development, this study constructs a game model based on evolutionary game theory involving the interactions of platforms, power generation companies, and consumers. The model breaks through the limitations of traditional bilateral game studies and explores the evolutionary mechanism and equilibrium state of the green electricity market. First, the strategies and payoff functions of the three parties are defined, and the replicator dynamic equations and Jacobian matrix are established to analyze the impact of different initial strategies on the evolutionary path. Then, numerical simulations are 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 is 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.