Towards high-fidelity wind farm layout optimization using polynomial chaos expansion and Kriging model

Abstract

This paper presents a wind farm layout optimization framework that integrates polynomial chaos expansion, a Kriging model, and the expected improvement algorithm. The proposed framework addresses the computational challenges associated with high-fidelity wind farm simulations by significantly reducing the number of function evaluations required for accurate annual energy production predictions. The polynomial chaos expansion-based prediction method achieves exceptional accuracy with reduced computational cost for over 96%, significantly lowering the expense of training the ensuing surrogate model. The Kriging model, combined with a genetic algorithm, is used for surrogate-based optimization, achieving comparable performance to direct optimization at a much-reduced computational cost. The integration of the expected improvement algorithm enhances the global optimization capability of the framework, allowing it to escape local optima and achieve results that are either nearly identical to or even outperform those obtained through direct optimization. The feasibility of the polynomial chaos expansion-Kriging framework is demonstrated through four case studies, including the optimization of wind farms with 8, 16, and 32 turbines using low-fidelity wake models, and a high-fidelity case using computational fluid dynamics simulations. The results show that the proposed framework is highly effective in optimizing wind farm layouts, significantly reducing computational costs while maintaining or improving the accuracy of annual energy production predictions.