Distributed Model Predictive Control of a Wind Farm for Optimal Active Power ControlPart I: Clustering-Based Wind Turbine Model Linearization

This paper presents a dynamic discrete-time piece-wise affine (PWA) model of a wind turbine for the optimal active power control of a wind farm. The control objectives include both the power reference tracking from the system operator and the wind turbine mechanical load minimization. Instead of partial linearization of the wind turbine model at selected operating points, the nonlinearities of the wind turbine model are represented by a piece-wise static function based on the wind turbine system inputs and state variables. The nonlinearity identification is based on the clustering-based algorithm, which combines the clustering, linear identification, and pattern recognition techniques. The developed model, consisting of 47 affine dynamics, is verified by the comparison with a widely used nonlinear wind turbine model. It can be used as a predictive model for the model predictive control (MPC) or other advanced optimal control applications of a wind farm.