Modeling the energy produced in wind farms is extremely challenging due to the lack of a set of physics-based governing equations. The reduced order modeling (ROM) methods have received a significant attention in the last decades, when we deal with discrete or so called non-intrusive data.

In this work, we address this family of methods that solely access datasets and identify the system dynamics. Our main target in this study is to obtain a reduced order surrogate model that faithfully imitates the behaviour of the energy produced in a wind farm. Among several model order reduction techniques that perform well with non-intrusive data, Dynamic Mode Decomposition (DMD) is widely applied. Dynamic Mode Decomposition (DMD) is an equation-free, data-driven matrix decomposition that can provide accurate reconstruction of spatio-temporal coherent structures arising in nonlinear dynamical systems.

In the present work, we propose the application of randomized dynamic mode decomposition to a problem originating from renewable energy domain, where the main difficulty consists in obtaining a surrogate model of wind farm output energy. Using an adaptive DMD algorithm we obtain an accurate reduced order model (DMD-ROM) based on offline energy data set. The rank of the DMD-ROM model represents the unique solution to a constrained optimization problem. A major improvement introduced in this work consists in a better calibration of the ROM-DMD by orthonormalization of DMD modes. We demonstrate the effectiveness of this algorithm on high complexity data sets. The key innovation consists in prediction of energy variation during a relative short period of time, using a forecasting sliding window technique. The paper demonstrates that short-medium term prediction of the wind farm energy dynamics is possible by using the DMD-ROM model in association with autoregressive integrated moving average (ARIMA) models.

We illustrate the excellent behavior of the proposed method by performing a qualitative analysis and a rigorous error analysis for the reconstruction of data. We emphasize also additional advantages of the proposed algorithm.