Tube‐based robust economic model predictive control with practical and relaxed stability guarantees and its application to smart grid

Summary This article deals with an improved scheme of tube‐based robust economic model predictive control (TEMPC). The controller is robust to unknown but bounded disturbances where guarantees recursive feasibility, robust stability, and convergence to the economically optimal operating point. Time‐varying economic criteria are considered in the stage cost function of the control design. Initial states of the nominal—nondisturbed—system are considered as decision variables. It lets the controller know more information about the real—disturbance affected—system to take advantage of the recursive horizon approach. It also increases the control degree of freedom and enlarges the region of attraction. Making the closed‐loop system work at the economically optimal operating point contradicts with the economic behavior. A convex optimization problem is represented to keep the economic performance from degradation as much as possible. It modifies the control optimization problem to economic optimally guarantee the closed‐loop robust stability, which is called practical stability. It is shown that more economic behavior could be achieved under some conditions by relaxing the stability but maintaining the recursive feasibility guarantee, which is called relaxed stability. To show the efficiency of the proposed method, it is applied to the building energy management of smart grid. A commercial microgrid with battery energy storage dynamics and refrigeration dynamics of a supermarket are considered as a smart building system where the time‐varying electricity price of the main grid is considered in the objective function. The results show valuable achievements in the TEMPC economic performance.