The supercritical carbon dioxide Brayton cycle has become the choice of a wide range of users because of its higher efficiency and smaller turbine size, and is often used in space vehicles, sodium cooled fast reactors, Marine power equipment and other energy storage and power generation applications. However, in the process of use, the detachment of the load is a common problem, if not well handled often cause the system to crash. In this paper, based on the software Simulink in MATLAB, the moment of inertia of turbine and generator is regarded as fixed value, the key parameter differential equations of Brayton cycle are derived, and the dynamic recompression and intercooling Brayton cycle models are established. The response parameters of the system after load disconnection and different time tie-back are studied. The responses of key parameters of the system after load detachment were obtained. It was found that the recompression model had higher stability under load detachment and tie-back conditions than the intercooling model, and the length of parameter variation after load detachment was linear. The earlier the tie-back was, the faster the system could restore stability.