Abstract: This research work sets forward a new formulation of Linear Quadratic Regulator problem (LQR) applied to a Wind Energy Conversion System (WECS). A new necessary and sufficient condition of Lyapunov asymptotic stability is also established. The problem is mathematically described in form of Linear Matrix Inequalities (LMIs). The considered WECS is based on a Doubly Fed Induction Generator (DFIG). An appropriate Linear Parameter Varying (LPV) model is designed. This model stands for a realistic representation of the randomly time varying wind velocity. Stability and robustness of the controller over the admissible values of time varying parameter are investigated. The newly lifted Lyapunov condition gives less conservative conditions for LMI approach in case of parameter-dependent Lyapunov functions PDLF. The considered PDLF has the same variation dynamics as the system matrix. The intrinsic objective for our research is to offer more freedom degrees to the control problem and to improve the efficiency of the controller in case of uncertainties or parametric variations. The performances of the proposed theorems are validated to achieve active and reactive powers tracking of the WECS over the admissible range of wind speeds. The interesting features of the proposed solution are the simpler implementation and the larger robustness margin. It also has the advantage of providing a linear control to the considered nonlinear system without resorting to linearization. The LMIs implementation is performed on Yalmip Matlab toolbox. The proposed controller is verified on a Matlab Simulink emulator. This work presents an extension of the LQR control problem to LPV systems.

Sana Salhi and Salah Salhi, “LQR Robust Control for Active and Reactive Power Tracking of a DFIG based WECS” International Journal of Advanced Computer Science and Applications(IJACSA), 10(1), 2019. http://dx.doi.org/10.14569/IJACSA.2019.0100172

@article{Salhi2019,
title = {LQR Robust Control for Active and Reactive Power Tracking of a DFIG based WECS},
journal = {International Journal of Advanced Computer Science and Applications},
doi = {10.14569/IJACSA.2019.0100172},
url = {http://dx.doi.org/10.14569/IJACSA.2019.0100172},
year = {2019},
publisher = {The Science and Information Organization},
volume = {10},
number = {1},
author = {Sana Salhi and Salah Salhi}
}