Optimal Control of Wind Turbine Systems via Time-Scale Decomposition

In this paper, we design an optimal controller for a wind turbine (WT) with doubly-fed induction generator (DFIG) by decomposing the algebraic Riccati equation (ARE) of the singularly perturbed wind turbine system into two reduced-order AREs that correspond to the slow and fast time scales. In addition, we derive a mathematical expression to obtain the optimal regulator gains with respect to the optimal pure-slow and pure-fast, reduced-order Kalman filters and linear quadratic Gaussian (LQG) controllers. Using this method allows the design of the linear controllers for slow and fast subsystems independently, thus, achieving complete separation and parallelism in the design process. This solves the corresponding ill-conditioned problem and reduces the complexity that arises when the number of wind turbines integrated to the power system increases. The reduced-order systems are compared to the original full-order system to validate the performance of the proposed method when a wind turbulence and a large-signal disturbance are applied to the system. In addition, we show that the similarity transformation does not preserve the performance index value in case of Kalman filter and the corresponding LQG controller.