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

TL;DR

The paper tackles the high computational cost of high-fidelity wind-farm layout optimization (WFLO) by integrating polynomial chaos expansion (PCE) for efficient AEP prediction with a Kriging surrogate-based optimization (SBO) framework and an acquisition strategy based on expected improvement (EI). It develops a PCE-aided SBO workflow that iteratively builds a Kriging model from limited high-fidelity evaluations, guiding layout exploration with an MSP stage followed by EI-driven refinement, and uses a genetic algorithm for optimization. Four case studies (8, 16, 32 turbines with low-fidelity models and a CFD-based 8-turbine case) demonstrate substantial reductions in function evaluations (to roughly 0.3% of brute-force evaluations) while achieving comparable or improved AEP predictions; the high-fidelity case confirms feasibility, with CFD yielding 108.51 MW versus 106.79 MW from the low-fidelity surrogate. The work highlights significant practical potential for high-fidelity WFLO, while noting challenges at larger scales due to the curse of dimensionality and proposing future work in dimensionality reduction and physics-informed optimization to further enhance efficiency and accuracy.

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.

Figures (10)

• Figure 1: The workflow of the adaptive optimization framework.
• Figure 2: ($a$) The wind direction distribution with the bin width of 5 degree and ($b$) the Weibull distribution for wind speed. The distribution is truncated according to the cut-in speed (3 m/s) and cut-out speed (25 m/s). The bin width of wind speed is 1 m/s.
• Figure 3: Effects of sample size on the accuracy of AEP prediction in PCE. Three random layouts are tested, each with five instances of samples. The respective layouts are plotted in the upper right corner.
• Figure 4: Effects of the initial sample size on ($a$) the optimized AEP and ($b$) number of iterations in the Kriging model. Note that in $(b)$, the number of iterations include the evaluations of initial sample size. The shaded area delineates the initial sample size.
• Figure 5: ($a$) Evolution of the optimized AEP using SBO (with and without EI) and direct optimization for case I, with intermediate optimal layout designs during the SBO (with EI) shown in $(b)-(d)$, and the final design in $(e)$. The shaded area in $(a)$ indicates the initial samples. The optimized AEPs for SBO with and without EI module follow the same path in the initial stage of the optimization. The dashed box in $(b)-(e)$ represents the boundary of wind farms.