Building a new-type power system is the key core of the green and low-carbon development of energy, the restructuring of the power system will inevitably have a linked impact on the coordinated development of the economy-energy-environment (3E) system. This paper constructs a "Dual-Triangle" theoretical framework consisting of the “Energy Trilemma” and the "Sustainable Development Triangle", by combining historical statistical analysis with scenario predictive analysis, analyzes the historical characteristics of the "Dual Triangle" and future development trends under different scenarios, and studies the coupled interaction relationship of the "Dual-Triangle" to explore the optimal transformation path of the power system that is most beneficial to the coordinated development of the 3E system. The conclusions are as follows: (1) The energy system gradually inclined towards economy and cleanliness from 2010 to 2022, the level of coordinated development of the 3E system fluctuated upwards, and the operation status of the "Dual Triangle" was stable. (2) Positive coupling relationship between "Dual Triangle" of scenario S1 is close, which can be regarded as the preferred path for the reconstruction of the power system. Due to phased development has clear development priorities, scenario S2 will artificially break the balance of the “Energy Trilemma”, which is a development model that dynamically mitigates the challenges of the “Energy Trilemma”.(3)The contradiction between economy and cleanliness is continuously weakened, and security has become the core contradiction of the "Impossible Triangle". The combination of renewable energy and energy storage is the key to resolving this contradiction. This paper conducts an integrated and innovative application of the "Dual-Triangle" theory, and the results provide a case basis for how to achieve the coupled interaction of the "Dual-Triangle", promote high-quality energy development, and support the sustainable development of the economy and society.