Currently, wind and light abandonment is an important problem to be solved in China’s power system. In order to encourage coal-containing captive power plant enterprises to participate in new energy consumption and strengthen the interaction with grid demand response, this paper proposes an alternative trading mechanism for captive power plants within a short period of time that takes into account carbon trading and new energy generation rights. First, the alternative trading strategy between coal-fired captive power plants and new energy enterprises is designed with respect to the new energy enterprises’ wind and light abandonment information forecasts and the enterprises’ unit output forecasts. Second, the load characteristics of enterprises and adjustable capacity of captive power plants are analyzed, the unit model considering demand response is established, and the baseline method is used to allocate carbon emission allowances to the system without compensation. A mathematical model targeting the operation cost of captive power plant, carbon trading cost, power purchase cost, load transfer cost and new energy consumption cost is established, and finally the correctness of the model is verified by simulation examples and the influence of carbon trading price on the transaction is discussed. The results show that the power generation right trading model considering carbon trading effectively improves the efficiency of enterprises in consuming new energy, while reducing the comprehensive electricity cost of enterprises with coal-containing captive power plants and increasing the consumption of new energy, which not only ensures the economy of high-energy-consuming enterprises but also realizes the low-carbon development of electric power.