Hydrogen conversion plants based on reversible solid oxide cells (rSOCs) provide a potential solution for large-scale energy storage to facilitate renewable integration. When operating an rSOC plant, the security and performance should be monitored at all times, including the steady-state periods and the transient processes connecting them. Model predictive control (MPC) is an appropriate method for this problem. This paper presents a comprehensive rSOC plant model to describe the multiscale dynamics (such as temperature and mass flows) under both fuel cell and electrolysis modes. Then, a time-varying MPC strategy based on a linear parameter-varying prediction model is proposed to provide fast control to the nonlinear rSOC plant. A numerical case is simulated to validate the effects of the proposed MPC strategy. The results suggest that the automatic coordination of actuators ensures consistent stack security, improves both short-term tracking and long-term production performance, and ultimately benefits the plant economically in practical operation.