A reduced-order model for a wind turbine wake is sought from large eddy simulation data. Fluctuating velocity fields are combined in the correlation tensor to form the kernel of the proper orthogonal decomposition (POD). Proper orthogonal decomposition modes resulting from the decomposition represent the spatially coherent turbulence structures in the wind turbine wake; eigenvalues delineate the relative amount of turbulent kinetic energy associated with each mode.Back-projecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reduced-order model of the wind turbine wake (wakeROM) is defined through a series of polynomial parameters that quantify mode interaction and the evolution of each POD mode coefficients. The resulting system of ordinary differential equations models the wind turbine wake composed only of the large-scale turbulent dynamics identified by the POD. Tikhonov regularization is used to recalibrate the dynamical system by adding additional constraints to the minimization seeking polynomial parameters, reducing error in the modeled mode coefficients. The wakeROM is periodically reinitialized with new initial conditions found by relating the incoming turbulent velocity to the POD mode coefficients through a series of open-loop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%, quantified through the normalized root-mean-square error. A high-level view of the modeling approach is provided as a platform to discuss promising research directions, alternate processes that could benefit stability and efficiency, and desired extensions of the wakeROM.
KEYWORDSdynamical system, proper orthogonal decomposition, reduced-order model, wind turbine wake
INTRODUCTIONPerformance of wind farms is highly correlated with the wake following a given wind turbine. 1,2 However, for the sake of design efficiency, wakes and wind plants are typically modeled with simplified engineering or empirical relationships. Wind turbine wakes are highly variable, combining effects from the atmospheric boundary layer, interacting with large rotating structures, and often subject to wake-to-wake interaction within a wind plant. 3 Further, wakes evolving from individual turbines are asymmetrical due to the inherent shear in the atmospheric boundary layer and reflect the specific nature of incoming inflow events that vary significantly with diurnal and seasonal cycles and affect the performance of other turbines in a wind plant. 4 Given the complexity of the wind turbine wake, a computationally efficient means of correctly modeling wake dynamics and interaction is crucial to meet the rapid pace at which wind energy is being adopted globally and to address persistent wind plant underperformance.Reduced-order modeling describes a wide range of approaches that approximate complex system dynamics of large or infinite degrees of freedom with a limited, and more manageable, number of degrees of freedom. For applications in turbulence, the goal ...