Wind Power Extraction Optimization by Dynamic Gain Scheduling Approximation Based on Non-Linear Functions for a WECS Based on a PMSG

Mathematical models and algorithms for maximizing power extraction have become an essential topic in renewable energies in the last years, especially in wind energy conversion systems. This study proposes maximum power point tracking using gain scheduling approximations for an emulated wind system in a direct-drive connection. Power extraction is obtained by controlling the duty cycle of a Multilevel Boost Converter, which directly varies the rotational speed of a permanent magnet synchronous generator directly coupled to a three-phase induction motor that emulates the wind turbine. The system’s complexity is linked to the inherent non-linearities associated with the diverse electrical, mechanical, and power electronic elements. In order to present a synthesized model without losing the system dynamic richness, several physical tests were made to obtain parameters for building several mathematical approaches, resulting in non-linear dynamic equations for the controller gains, which are dependant on wind speed. Thirty real operational wind speeds considering typical variations were used in several tests to demonstrate the mathematical models’ performance. Results among these gain scheduling approaches and a typical controller constant gains mathematical model were compared based on standard deviations, absolute error, and the time for reaching the optimum generator angular speed related to every wind speed.