Sparsity Applications for Gradient-Based Optimization of Wind Farms

Keywords

sparsity, wind farm, optimization, layout optimization, derivatives, gradient-based, Jacobian

Abstract

Optimizing wind farms is essential for designing efficient energy systems, especially as farms grow larger and span multiple sites. However, this optimization becomes increasingly challenging due to the rising computational cost associated with more turbines. Gradient-­ based optimization methods scale better than gradient-­ free approaches for large problems, but the most computationally expensive component remains the calculation of gradients for the objective function and constraint Jacobians. To address this, we propose leveraging sparsity to accelerate gradient evaluations and reduce the size of the constraint Jacobian. Wind farms naturally exhibit sparsity—many turbines do not influence each other under certain wind directions. However, unlike traditional sparse problems with fixed patterns, wind farm sparsity is dynamic, requiring new strategies to handle changing interactions efficiently. This paper presents a study of sparsity in wind farm optimization and introduces several methods to exploit it. These strategies are tested on multiple farms using the analytic Cumulative Curl model, with gradients computed via automatic differentiation (AD). The same sparsity-­ aware techniques are also applicable to finite difference (FD) methods, where they can yield even greater speedups due to the high cost of directional evaluations. Results show that sparse methods achieve up to a 10x speedup with less than ± 5% variance in optimized wake losses compared to traditional methods. These findings suggest that sparsity-­aware optimization not only maintains solution quality but also scales efficiently with farm size, enabling more comprehensive design exploration at reduced computational cost.

Original Publication Citation

Varela, B., and Ning, A., “Sparsity Applications for Gradient-Based Optimization of Wind Farms,” Wind Energy, Vol. 29, No. 7, p. e70132, Jun. 2026. doi:10.1002/we.70132

Document Type

Peer-Reviewed Article

Publication Date

2026-6

Publisher

Wind Energy

Language

English

College

Ira A. Fulton College of Engineering

Department

Mechanical Engineering

University Standing at Time of Publication

Full Professor

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