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Abstract
The calibration of the wake effect in wind turbines is computationally expensive and with high risk due to noise in the data. Wake represents the energy loss in downstream turbines, and characterizing it is essential to design wind farm layout and control turbines for maximum power generation. With big data, calibrating the wake parameters is a derivative-free optimization that can be computationally expensive. But with stochastic optimization combined with variance reduction, we can reach robust solutions by harnessing the uncertainty through two sampling mechanisms: the sample size and the sample choices. We do the former by generating a varying number of samples and the latter using the variance-reduced sampling methods.
Keywords
Wind turbines, stochastic trust-region, derivative-free optimization, stratification, variance reduction
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1.Introduction
The presence of multiple turbines in the wind farm decreases the efficiency of downstream turbines due to the wake effect. Limited availability of land and high set-up and operating costs cause many turbines to be located in the downstream direction. It is necessary to accurately model this wake effect to obtain the best performance out of the wind farm. Modeling the wake effect involves estimating the power deficit at the downstream turbines and deals with accuracy versus computational complexity.
Jensen's wake model is a physics-based engineering model widely used in industry and academia because of its computational simplicity [1]. This model assumes that the wake propagates linearly. In a wind farm, a turbine is likely in the presence of multiple wakes. These multiple wakes can be superimposed. The kinetic energy deficit due to multiple wakes is equated to the sum of kinetic energy deficit due to individual wakes to get the effective wind speed at a turbine. Thus, effective wind speed at a turbine t, Ut is
... (1)
where T (t) is the total number of upstream turbines of the turbine t in the wind farm, Uļ is the wind speed due to wake at the downstream distance x of the t-th turbine, U· is the free-stream wind speed, Ct is the thrust coefficient of the wind turbine, and (1 + 2Ox) formulates the ratio of the downstream wake diameter over the rotor diameter.
Engineering models like Jensen's wake model make certain assumptions that introduce...