A Data-Driven Observer for Wind Farm Power Gain Potential: A Sparse Koopman Operator Approach

Maximizing the power output of wind farms is critical for improving the economic viability and grid integration of renewable energy. Active wake control (AWC) strategies, such as yaw-based wake steering, offer significant potential for power generation increase but require predictive models that are both accurate and computationally efficient for real-time implementation. This paper proposes a data-driven observer to rapidly estimate the potential power gain achievable through AWC as a function of the ambient wind direction. The approach is rooted in Koopman operator theory, which allows a linear representation of nonlinear dynamics. Specifically, a model is developed using an Input–Output Extended Dynamic Mode Decomposition framework combined with Sparse Identification (IOEDMDSINDy). This method lifts the low-dimensional wind direction input into a high-dimensional space of observable functions and then employs iterative sparse regression to identify a minimal, interpretable linear model in this lifted space. By training on offline simulation data, the resulting observer serves as an ultra-fast surrogate model, capable of providing instantaneous predictions to inform online control decisions. The methodology is demonstrated and its performance is validated using two case studies: a 9-turbine and a 20-turbine wind farm. The results show that the observer accurately captures the complex, nonlinear relationship between wind direction and power gain, significantly outperforming simpler models. This work provides a key enabling technology for advanced, real-time wind farm control systems.