The sustainable development of power construction projects (PCPs) is of great significance in solving the issue of high carbon emissions in the power industry. However, the profit-seeking nature of stakeholders’ strategic choices and other conflicts have seriously hindered this process. This study constructs a tripartite game evolution model for the government, grid companies and the public, and determines the factors and range of values that affect the behavioral and strategic choices of stakeholders based on the literature analysis method and case study method. Numerical simulations are conducted with the help of MATLAB R2021a software to explore the changes in decision-making behavior of stakeholders and system stabilization strategies in different stages of the industry life cycle and the influencing mechanisms. The results show that in the initial stage, the government lays the foundation for the development of PCPs through policy guidance under the government-led mechanism. As PCPs move into the development stage, stakeholders’ benefits increase, creating a collaborative participation situation. As PCPs mature, the role of market guidance comes to the fore, and the interventionist role of government diminishes to a guardian role. In terms of sensitivity analysis of relevant parameters, low government rewards and penalties are not conducive to the adoption of low-carbon sustainable construction programs by power grid companies. The public influences the sustainable behavior of the government and power grid companies through public opinion. In addition, reasonable cost inputs from all stakeholders are critical to effectively promote the steady growth of PCPs. Based on the results, a sustainable development promotion mechanism for PCPs is constructed based on multiple dimensions, with a view to providing decision-making services for stakeholders and thus contributing to the sustainable development of PCPs.