Abstract
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.
Highlights
Wind turbines, having mechanical and electrical components, are known to operate in at least two time-scales: the slow time scale in which mechanical state variables evolve and the fast time scale in which electrical and electronic state variables evolve
This doubly-fed induction generator (DFIG) system model is not expressed in the explicit standard singular perturbation form given in (19), where it can be noticed that e, a small positive singular perturbation parameter, multiplies the derivatives of some states
The output responses of the rotor current in d-axis, idr, and q-axis, iqr, of the original and reduced-order DFIG wind turbine (WT) system are shown in Figures 10 and 11, respectively, which show the robustness of the designed linear quadratic Gaussian (LQG) controller
Summary
Wind turbines, having mechanical and electrical components, are known to operate in at least two time-scales: the slow time scale in which mechanical state variables evolve and the fast time scale in which electrical and electronic state variables evolve. In [9] the linear quadratic regulator (LQR) and LQG controllers were designed for deterministic and stochastic wind energy systems with permanent magnet synchronous generators (PMSG). In comparison to the balanced reduction methods in [13], time scale and singular perturbation analysis provide better results in reducing the order of the DFIG-based WT system. The method of singular perturbation will be used to design LQR, Kalman filter, and LQG optimal controllers in two independent time scales for a fifth-order single-cage DFIG wind turbine. Using this method allows designing linear controllers for the slow and fast subsystems independently, achieving complete separation and parallelism in the design process The advantages of such an approach are alleviating stiffness difficulties and reducing computational complexities and dimensionality burdens resulting from the increased penetration of wind turbines to the power grid.
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