Harmonic Compensation by Limit Cycle Model Predictive Control

This work develops a novel limit cycle model predictive controller aimed at harmonic compensation. The proposed nonlinear controller embeds the dynamics of a circular limit cycle of a supercritical Neimark-Sacker normal form directly into its cost function. This enables the controller to steer the state dynamics into a fundamental harmonic shape in systems where a periodic solution is desired. The proposed cost function structure is analyzed for possible convex formulations that could lead to more effective methods for solving the optimization problem. A simulation study in the field of electric power systems integrated with renewable energy resources is given. The new controller is used to set the reference of the compensation current of an active power filter to address the harmonic distortion in the grid. The results show that the controller can mitigate the harmonic disturbance content in voltages and currents to the required levels while maintaining the correct amplitudes at the desired fundamental frequency.