This invention relates to controlling a load-following solid oxide fuel cell system such that the fuel cells in the system are operating within an acceptable electrochemical reaction efficiency. The system has a controller that is programmed to detect a load change on a fuel cell stack, and when the load decreases, reduces the fuel flow rate to the stack or deactivates one or more fuel cells in the stack such that the stack operates within an acceptable electrochemical reaction efficiency range corresponding to the decreased load; and when the load increases, the controller increases the fuel flow rate to the stack or activates fuel cells in the stack such that the stack operates within the acceptable electrochemical reaction efficiency range.