The operation flexibility of the power system suffers great challenges due to the vigorously developing of renewable energy resources under the promotion of the carbon neutralization goal. To this end, this paper proposes an economical and flexible energy scheduling method for power system integrated with multiple generation resources while considering the operation of low-carbon. Specifically, flexibility evaluation indexes are constructed to describe the characteristics of the flexible generation units. Then they are connected with the flexibility of the power system in an economic and low-carbon flexible energy scheduling model. To coordinate the operation economy, flexibility, and carbon emission reduction, the model incorporates demand response, operational characteristics, and flexibility requirements. Further, the model is fully validated through the simulation on the modified IEEE 30-bus system. Results demonstrate that: the proposed method can reduce the system’s carbon emission and total operating costs and promote photovoltaic consumption.