Abstract
In this paper, we present a novel control-oriented model for predicting wake effects in wind plants, called the FLOw Redirection and Induction Dynamics (FLORIDYN) model. The model predicts the wake locations and the effective flow velocities at each turbine, and the resulting turbine electrical energy productions, as a function of the control degrees of freedom of the turbines (the axial induction and the yaw angle of the different rotors). The model is an extension of a previously presented static model (FLORIS). It includes the dynamic wake propagation effects that cause time delays between control setting changes and the response of downstream turbines. These delays are associated with a mass of air in the wake taking some time to travel from one turbine to the next, and the delays are dependent on the spatially- and time-varying state of the wake. The extended model has a state-space structure combined with a nonlinear feedback term. While including the control-relevant dynamics of the wind plant, it still has a relatively small amount of parameters, and the computational complexity of the model is small enough such that it has the potential to be used for dynamic optimization of the control reference signals for improved wind plant control.
Highlights
Each wind turbine has a wake of turbulent flow downstream of its rotor
The topology and amount of the wake interaction depends on time-varying atmospheric conditions, and on the control settings of each turbine: the rotor speed and pitch angles of the blades affect the axial induction and the wake velocity deficit [1], and the rotor yaw angle affects both the velocity deficit and flow direction in the wake [2, 3])
In [4], we developed the FLOw Redirection and Induction in Steady-state (FLORIS) model, a simplified control-oriented model that predicts the steady-state characteristics of wakes in a wind plant as a function of the axial inductions and yaw angles of the rotors
Summary
Each wind turbine has a wake of turbulent flow downstream of its rotor. Because the turbine extracts energy from the flow, the wind velocity in the wake is reduced with respect to the freestream velocity. In [4], we developed the FLOw Redirection and Induction in Steady-state (FLORIS) model, a simplified control-oriented model that predicts the steady-state characteristics of wakes in a wind plant as a function of the axial inductions and yaw angles of the rotors. The complete flow field in a plant does not respond instantaneously to a change in turbine control settings since the flow takes some time to move downstream, resulting in a delay of the response of the downstream turbine. The lengths of these delays are dependent on the spatially- and time-varying flow velocity profile in the wake. Model description The FLORIDyn model is a combination of static nonlinear mappings describing the wake velocity profile, based on an augmented Jensen model [5, 6], and the wake deflection through yaw (based on [3]), extended with a state-space model describing the propagation of control settings changes through the wake
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