In the context of the shift from “dual control” of energy consumption to “dual control” of carbon emissions, existing power system dispatch optimization tends to focus on total carbon emission constraints while neglecting carbon emission intensity constraints. This often leads to higher carbon emission intensity and poorer economic performance in thermal power unit operations. This paper proposes a low-carbon economic dispatch method for heterogeneous energy power systems, considering interval differentiation of thermal power carbon emission intensity. First, the differentiation characteristics of the relationship curve between carbon emission intensity and load rate in thermal power units are analyzed. The operation intervals of thermal power are divided into low-carbon intensity, high-carbon intensity, and transition zones. Then, a low-carbon economic optimal dispatch model for thermal-wind-solar-storage system is established with the objectives of maximizing the duration of thermal power operating in low-carbon intensity, minimizing total system carbon emissions, and minimizing system operating costs. This model integrates both “dual control” of carbon emissions and economic operation, and a hierarchical and progressive solving strategy is designed accordingly. Finally, the effectiveness and adaptability of the model are verified through case studies. Results indicate that the proposed model can effectively constrain the carbon emission intensity of thermal power units, improve the low-carbon performance of the system, and adapt to the system operating scenarios with different renewable energy penetration levels and weather conditions.