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Tham khảo tài liệu 'fundamental and advanced topics in wind power part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | A Complete Control Scheme for Variable Speed Stall Regulated Wind Turbines 319 The same mechanism holds for the propagation of the covariance p of the true state X around its mean X. As can be seen from Eqns. 12-16 the Kalman filter in principle contains a copy of the applied dynamic system the state vector of which xk is corrected at every update step by the correcting term Kk i zk i -Hirfe 1 fe of Eqn. 14. The expression inside the parenthesis is called the Innovation sequence of the Kalman filter rk zk i-Hxk i k 17 which is equal to the estimation error at every time step. When the Kalman filter state estimate is optimum rk is a white noise sequence Chui Chen 1999 . The operation of any Q and R adaptation algorithms that are included in the Kalman filter is based on the statistics of the innovation sequence Bourlis Bleijs 2010a 2010b . Regarding the stability of the Kalman filter algorithm this is always guaranteed providing that the dynamic system of Eqns. 8-9 is stable and that Q and R have been selected appropriately. In the case of the wind turbine the dynamic system is always stable since in Eqns. 8-9 only the dynamics of the drivetrain are included which have to be stable by default. In addition the Q and R are continuously updated appropriately by adaptive algorithms and the stability of the adaptive Kalman filter can be easily assessed through software or hardware simulations. From the above it becomes obvious that the stability of the closed loop control system of Figs. 6-7 is then guaranteed provided that the speed controller stabilizes the system. 5.2 Adaptive Kalman filtering and advantages In order to see the advantage of the adaptive Kalman filter over the simple Kalman filter software simulations of aerodynamic torque estimation for a 3MW wind turbine for different wind conditions are shown in Figs. 8 a-b . From the below figures the advantage of the adaptive Kalman filter compared to the nonadaptive one can be observed. Specifically the torque .
