Stochastic modeling and performance monitoring of wind farm power production

Abstract

We present a new stochastic approach to describe and remodel the conversion process of a wind farm at a sampling frequency of 1 Hz. The method is trained on data measured on one onshore wind farm for an equivalent time period of 55 days. Three global variables are defined for the wind farm: the 1-Hz wind speed u(t) and 10-min average direction ϕ¯ both averaged over all wind turbines, as well as the cumulative 1-Hz power output P(t). When conditioning on various wind direction sectors, the dynamics of the conversion process u(t) → P(t) appear as a fluctuating trajectory around an average IEC-like power curve. Our approach is to consider the wind farm as a dynamical system that can be described as a stochastic drift/diffusion model, where a drift coefficient describes the attraction towards the power curve and a diffusion coefficient quantifies additional turbulent fluctuations. These stochastic coefficients are inserted into a Langevin equation that, once properly adapted to our particular system, models a synthetic signal of power output for any given wind speed/direction signals. When combined with a pre-model for turbulent wind fluctuations, the stochastic approach models the power output of the wind farm at a sampling frequency of 1 Hz using only 10-min average values of wind speed and directions. The stochastic signals generated are compared to the measured signal, and show a good statistical agreement, including a proper reproduction of the intermittent, gusty features measured. In parallel, a second application for performance monitoring is introduced. The drift coefficient can be used as a sensitive measure of the global wind farm performance. When monitoring the wind farm as a whole, the drift coefficient registers some significant deviation from normal operation if one of twelve wind turbines is shut down during less than 4% of the time. Also, intermittent anomalies can be detected more rapidly than when using 10-min averaging methods. Finally, a probabilistic description of the conversion process is proposed and modeled, which can in turn be used to further improve the estimation of the stochastic coefficients.