*Article* **Design and Simulation of an LQR-PI Control Algorithm for Medium Wind Turbine**

**Kwansu Kim 1, Hyun-Gyu Kim 1, Yuan Song 1 and Insu Paek 2,\***


Received: 31 March 2019; Accepted: 11 June 2019; Published: 12 June 2019

**Abstract:** In this paper, a new linear quadratic regulator (LQR) and proportional integral (PI) hybrid control algorithm for a permanent-magnet synchronous-generator (PMSG) horizontal-axis wind turbine was developed and simulated. The new algorithm incorporates LQR control into existing PI control structures as a feed-forward term to improve the performance of a conventional PI control. A numerical model based on MATLAB/Simulink and a commercial aero-elastic code were constructed for the target wind turbine, and the new control technique was applied to the numerical model to verify the effect through simulation. For the simulation, the performance data were compared after applying the PI, LQR, and LQR-PI control algorithms to the same wind speed conditions with and without noise in the generator speed. Also, the simulations were performed in both the transition region and the rated power region. The LQR-PI algorithm was found to reduce the standard deviation of the generator speed by more than 20% in all cases regardless of the noise compared with the PI algorithm. As a result, the proposed LQR-PI control increased the stability of the wind turbine in comparison with the conventional PI control.

**Keywords:** horizontal-axis wind turbine (HAWT); permanent-magnet synchronous-generator (PMSG); linear quadratic regulator (LQR); PI control algorithm; LQR-PI control
