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DOE OSTI2026

Sparsity Applications for Gradient‐Based Optimization of Wind Farms

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.

17 WIND ENERGY↗

DOE OSTI2022

A model to calculate fatigue damage caused by partial waking during wind farm optimization

Abstract. Wind turbines in wind farms often operate in waked or partially waked conditions, which can greatly increase the fatigue damage. Some fatigue considerations may be included, but currently a full fidelity analysis of the increased damage a turbine experiences in a wind farm is not considered in wind farm layout optimization because existing models are too computationally expensive. In this paper, we present a model to calculate fatigue damage caused by partial waking on a wind turbine that is computationally efficient and can be included in wind farm layout optimization. The model relies on analytic velocity, turbulence, and load models commonly used in farm research and design, and it captures some of the effects of turbulence on the fatigue loading. Compared to high-fidelity simulation data, our model accurately predicts the damage trends of various waking conditions. We also perform example wind farm layout optimizations with our presented model in which we maximize the annual energy production (AEP) of a wind farm while constraining the damage of the turbines in the farm. The results of our optimization show that the turbine damage can be significantly reduced, more than 10 %, with only a small sacrifice of around 0.07 % to the AEP, or the damage can be reduced by 20 % with an AEP sacrifice of 0.6 %.

17 WIND ENERGY↗

DOE OSTI2023

Sparsity for Gradient-Based Optimization of Wind Farm Layouts

Optimizing wind farm layouts is an important step in designing an efficient wind farm. Optimizing wind farm layouts is also a difficult task due to computation times increasing with the number of turbines present in the farm. The most computationally expensive part of gradient-based optimization is calculating the gradient. In order to reduce the expense of gradient calculation, we performed a study on the use of sparsity in wind farm layout optimization. This paper presents the findings of the sparsity study and provides a method to use sparsity in wind farm layout optimization. We tested this sparsity method by optimizing multiple farms with sparse methods and compared the results to optimizations of the same farms using traditional methods. By using the sparse method to optimize multiple farms, we found that the objective results were comparable between sparse and traditional methods and that sparse methods were 4 times faster than traditional methods on average. We expect more speedups with improved methodology and larger wind farms. By using sparse methods, it is possible to solve the wind farm layout optimization problem more efficiently, thus allowing for a more thorough study of the wind farm layout design space without excessive computational costs. Further work is required to refine the method and prepare for testing on real-world wind farm layout applications.

gradient↗

DOE OSTI2026

Control co-design under uncertainty for offshore wind farms: Optimizing grid integration, energy storage, and market participation

Offshore wind farms (OWFs) are set to significantly contribute to global decarbonization efforts. Developers often use a sequential approach to optimize design variables and market participation for grid-integrated offshore wind farms. However, this method can lead to sub-optimal system performance, and uncertainties associated with renewable resources are often overlooked in decision-making. Here, this paper proposes a control co-design approach, optimizing design and control decisions for integrating OWFs into the power grid while considering energy market and primary frequency market participation. Additionally, we introduce optimal sizing solutions for energy storage systems deployed onshore to enhance revenue for OWF developers over time. This framework addresses uncertainties related to wind resources and energy prices. We analyze five U.S. west-coast offshore wind farm locations and potential interconnection points, as identified by the Bureau of Ocean Energy Management (BOEM). Results show that optimized control co-design solutions can increase market revenue by 3.2% and provide flexibility in managing wind resource uncertainties.

Control Co-design↗

DOE OSTI2021

Progress on Optimizing Wind Farms and Rotor Designs Using Adjoints

Modern wind plants are increasingly tasked with multiple performance objectives. In addition to designing plants that maximize power output and minimize the levelized cost of energy (LCOE), the design and operation of wind plants is increasingly influenced by challenges regarding grid integration of variable generation renewables. This places a growing emphasis on making wind plants more controllable and predictable. WindSE is a Reynolds-averaged Navier-Stokes (RANS) model designed around analytical gradient and adjoint methods, with the ability to capture terrain-induced effects, as shown in Figure 1. The recent addition of an unsteady solver with an actuator line method (ALM) and ongoing work to enable massively parallel optimizations gives it a unique niche to explore coupled plant-level controls and design problems. This code is an open source python package built on the FEniCS framework that utilizes fast, parallel PETSc solvers to model fluid flow throughout wind-farm scale domains. Two recent studies performed using WindSE demonstrate the capability to optimize under a wide variety of flow conditions and objective functions. In the first, we present an optimization focused on modifying the layout of a wind farm with a fixed number of turbines for maximum total power output [1]. This study highlights the ability to quickly perform simulations using the steady Navier-Stokes solver combined with rotors represented as actuator disks while also stressing the importance of capturing terrain-induced effects. Gradient-based optimization using the RANS equations is viable due to the inclusion of efficiently computed adjoint derivatives. We interpret the physical results of the optimal layout and also discuss the computational cost of scaling to larger problems. In the second study, we present the capabilities of the unsteady Navier-Stokes solver, where rotor-blade profiles represented by actuator lines are optimized to enhance wake steering effects and overall power production [2]. We quantify the wind plant performance gains obtained from this type of simultaneous control co-design optimization as compared to optimizing the blade design and yaw independently. Figure 2 shows the differences between a baseline two-turbine system and an optimized system where we fine-tune the blade chord profile. Results and challenges from each study are quickly summarized and used to motivate the current development efforts within WindSE. Current and future work is focused on enabling higher-resolution studies with more degrees of freedom through parallelization of both the simulation and optimization algorithms. We present benchmarking results to show that WindSE performs well in both weak- and strong-scaling tests and further demonstrate that the optimizer obtains the same convergence rates in both shared- and distributed-memory environments. Using larger wind farms, we can study deep-array effects within an optimization context, allowing the use of objective functions that have been previously unstudied. As an example, we present ongoing work on a blockage metric which characterizes the loss of available kinetic energy due to wake effects from multiple upstream turbines.

adjoint optimization↗

DOE OSTI2023

A comparison of eight optimization methods applied to a wind farm layout optimization problem

Abstract. Selecting a wind farm layout optimization method is difficult. Comparisons between optimization methods in different papers can be uncertain due to the difficulty of exactly reproducing the objective function. Comparisons by just a few authors in one paper can be uncertain if the authors do not have experience using each algorithm. In this work we provide an algorithm comparison for a wind farm layout optimization case study between eight optimization methods applied, or directed, by researchers who developed those algorithms or who had other experience using them. We provided the objective function to each researcher to avoid ambiguity about relative performance due to a difference in objective function. While these comparisons are not perfect, we try to treat each algorithm more fairly by having researchers with experience using each algorithm apply each algorithm and by having a common objective function provided for analysis. The case study is from the International Energy Association (IEA) Wind Task 37, based on the Borssele III and IV wind farms with 81 turbines. Of particular interest in this case study is the presence of disconnected boundary regions and concave boundary features. The optimization methods studied represent a wide range of approaches, including gradient-free, gradient-based, and hybrid methods; discrete and continuous problem formulations; single-run and multi-start approaches; and mathematical and heuristic algorithms. We provide descriptions and references (where applicable) for each optimization method, as well as lists of pros and cons, to help readers determine an appropriate method for their use case. All the optimization methods perform similarly, with optimized wake loss values between 15.48 % and 15.70 % as compared to 17.28 % for the unoptimized provided layout. Each of the layouts found were different, but all layouts exhibited similar characteristics. Strong similarities across all the layouts include tightly packing wind turbines along the outer borders, loosely spacing turbines in the internal regions, and allocating similar numbers of turbines to each discrete boundary region. The best layout by annual energy production (AEP) was found using a new sequential allocation method, discrete exploration-based optimization (DEBO). Based on the results in this study, it appears that using an optimization algorithm can significantly improve wind farm performance, but there are many optimization methods that can perform well on the wind farm layout optimization problem, given that they are applied correctly.

17 WIND ENERGY↗

DOE OSTI2024

Robust wind farm layout optimization

Wake interactions in wind farms cause losses in annual energy production (AEP) on the order of 10%. Wind farm designers optimize the layout of the farm to mitigate wake losses, especially in the dominant site-specific wind directions. As wind turbines and wind farms grow in scale, optimization becomes more complex. Offshore wind farms regularly comprise more than 100 wind turbines and are characterized by complex boundaries due to shipping lanes, neighboring wind farms, and other constraints. Layout optimization methods are broadly split between gradient-based and gradient-free approaches. Gradient-based approaches can converge quickly and perform well for smaller, academic problems but are often sensitive to initial conditions and tuning parameters and require expert knowledge to use. On the other hand, gradient-free approaches can be more robust to problem complexities. We present a robust layout optimization approach based on a random search algorithm. The algorithm is intended for those who are not optimization experts and has few tuning parameters that need specification to achieve satisfactory results. Unlike off-the-shelf methods, which use generally available, non-domain-specific optimization routines that accept as inputs an optimization function and constraint definitions, this approach takes advantage of the relative computational costs of the different evaluations by evaluating cheaper computations first (boundary and minimum distance constraints) and running expensive AEP evaluations only if all other checks pass. Moreover, an outer genetic algorithm allows multiple solutions to evolve in parallel, enabling rapid solution development on high-performance computers. We discuss the relative ease of selecting necessary tuning parameters and demonstrate the efficacy of the genetic random search on a complex layout problem consisting of placing 70 turbines in a nonconvex and unconnected boundary region.

17 WIND ENERGY↗

DOE OSTI2025

Efficient wind farm layout optimization with the FLOWERS AEP model and analytic gradients

Wind farm layout optimization (WFLO) studies often aim to maximize the annual energy production (AEP) of a wind farm by choosing an arrangement of turbines that minimizes wake interactions. One way to reduce the cost of WFLO studies is by using more computationally efficient AEP models. The cost of standard AEP modeling approaches, based on the numerical integration of low-fidelity engineering wake models, scales poorly with the number of simulated discrete wind conditions. A second way to reduce cost when using a gradient-based algorithm is to supply exact gradient information instead of finite-difference estimates. However, analytical functions for the derivatives of AEP with respect to turbine positions are not always available in the conventional modeling approach. FLOWERS is a computationally inexpensive, analytical model for wind farm AEP that is specifically developed for WFLO applications. In this paper, we analyze the performance of the FLOWERS AEP model with analytic gradients in a layout optimization study compared with a reference optimization framework across three wind farm case studies. We find that the FLOWERS-based approach reduces computation time by a factor of 50–4000 and improves optimal AEP by about 0.3% with less than half of the variability in AEP across instances with randomized initial conditions. We also find the optimal layouts to be insensitive to model parameter tuning, making FLOWERS-based layout optimization a streamlined, user-friendly approach.

17 WIND ENERGY↗

DOE OSTI2023

Wind Farm Control and Layout Optimization for U.S. Offshore Wind Farms (Final Report - D5)

This report reviews the results and main conclusions of the NOWRDC project "Wind Farm Control and Layout Optimization for U.S. Offshore Wind Farms." A key finding is that wake steering should be considered a valuable tool for increasing the energy production of wind farms, especially in the event the farms are designed to maximize the energy production of a given boundary area.

17 WIND ENERGY↗

DOE OSTI2024

FLOWERS AEP: An Analytical Model for Wind Farm Layout Optimization

Annual energy production (AEP) is commonly used in objective functions for wind farm layout optimization. AEP is proportional to wind farm power production integrated over an annual distribution of free-stream wind conditions. Physics-based estimates of wind farm power production typically rely on low-fidelity engineering wake models that approximate the steady-state wind farm flow field. AEP estimates are then obtained by performing independent simulations for discrete wind conditions and using rectangular quadrature to account for each condition's expected frequency of occurrence. Depending on the number of simulated discrete wind conditions, this numerical integral could be hampered by poor accuracy or high computational costs. The FLOWERS AEP model instead poses an analytical integral of the engineering wake model over the variable wind conditions, yielding a closed-form, analytical function for wind farm AEP. This paper derives the analytical functions for FLOWERS AEP and its derivatives with respect to turbine position, which are useful for gradient-based wind farm layout optimization, in nondimensional form. We then analyze the benefits of the FLOWERS AEP model over conventional reference models, focusing on its low cost, adequate wake loss predictions, and smooth design space. Although the FLOWERS approach is found to predict the exact value of AEP with some error relative to the reference model (within 14% on average), it dramatically reduces computation time by an order of magnitude, produces a qualitatively similar design space at relatively low resolution, and yields comparable optimal layouts. This significant speed improvement is critical in layout optimization applications, where determining an optimal layout in an efficient manner is more important than precise AEP prediction.

17 WIND ENERGY↗

DOE OSTI2024

Ard [SWR-25-18]

A wind farm optimization suite for wind energy that is built for modular, gradient-enabled multi-disciplinary and multi-fidelity optimizations. Dig into wind farm design. An ard is a type of simple and lightweight plow, used through the single-digit centuries to prepare a farm for planting. The intent of Ard is to be a modular, full-stack multi-disciplinary optimization tool for wind farms. The problem with wind farms is that they are complicated, multi-disciplinary objects. They are aerodynamic machines, with complicated control systems, power electronic devices, social and political objects, and the core value (and cost) of complicated financial instruments. Moreover, the design of one of these aspects affects all the rest! Ard seeks to make plant-level design choices that can incorporate these different aspects and their interactions to make wind energy projects more successful.

Frontin, Cory [National Renewable Energy Laborator↗

DOE OSTI2020

Wind Farm Simulation and Layout Optimization in Complex Terrain: Preprint

This work reports on incorporating complex terrain into wind farm simulations for the purpose of layout optimization. Adding complex terrain boundary conditions to NREL's medium fidelity computational fluid dynamics model, WindSE, produces significant separation, flow curvature, and speedup effects that would otherwise be difficult to capture with lower-fidelity models or a flat-terrain assumption. These flow features, in turn, can significantly impact the optimal turbine array layout. We demonstrate the impact of complex terrain on flow in both an idealized and real-world setting, and discuss modifications to the code that enable gradient-based optimization using terrain-aware adjoint gradients. Through several optimization case studies, we show that the layout optimization process takes advantage of speedup effects on terrain high points, and leverages flow curvature effects that modify wake trajectories. This yields substantial power improvements over gridded layouts, and hints at future research directions in simulation and optimization for wake trajectories in complex terrain.

17 WIND ENERGY↗

DOE OSTI2020

Wind Farm Layout Optimization with Loads Considerations

The objective of this paper is to improve the annual energy production of a wind farm by optimizing the layout of a wind farm, while considering fatigue loads on turbines. In this paper, the loads are estimated using the edgewise bending moment computed using CCBlade, a steady-state blade element momentum code. The edgewise bending moment is then used to calculate fatigue damage using Miner's rule. The fatigue damage is used to constrain the layout optimization problem. We show that our method can predict blade root damage with similar trends to damage calculated with other methods, such as a complex, computationally expensive large-eddy simulation and unsteady aeroelastic code. We also optimize wind farm layouts and show that, for a simple problem with two wind directions and ten turbines, the fatigue damage can be constrained without sacrificing wind farm power production.

17 WIND ENERGY↗

DOE OSTI2025

Design, Optimization, and Control of Floating Offshore Wind Farms for Optimal Energy Production (Final report)

The uncertainty and irregularity of ocean waves and the ocean environment is a major factor in the development of commercial scale floating wind turbines as the operation of floating structures in such an environment can lead to irregular and unpredictable loading, fatigue, and ultimately a reduction in the operational life of the turbine system which affects energy production over the lifetime of the turbine. Control solutions that can limit float motions and mitigate stressful events on the structure become essential for extending lifetime and limiting the operational uncertainty of a floating wind turbine. Digital twins are computational replicas of physical systems that operate in parallel with the operation of the physical system. Given advanced knowledge of a systems input, digital twins have the ability to predict the behavior of a system in advance, which can be valuable in the control of that system. In this project, we developed and assessed potential digital twin models developed in house and openly available (OpenFast) for use in the real time control of the six degree of freedom response motions of a floating wind turbine in ocean waves. Coupling these models with near-field real time irregular sea surface (wve) measurement/sensings and prediction models, we used the digital twin to predict how the floating turbine will respond to the incoming waves. Applying this information to a motion control system of the float, one can limit and control float motions to prevent undesirable loading events/large angular motions, thus increasing system life and ultimately contributing to optimizing energy production. Due to the computational intensity of operating a digital twin in real time, we investigated the use of artificial intelligence techniques to speed-up the processes of the digital twin, as well as the wave reconstruction/prediction models. Model tank testing at the University of Rhode Island and University of Maine both validated and demonstrated the developed techniques on simple float geometries and a scale model of the NREL 15 MW reference turbine.

17 WIND ENERGY↗

DOE OSTI2024

Floating Wind Farm Layout Optimization Considering Moorings and Seabed Variations

This paper presents a method for optimizing the layout of floating wind farms that accounts for realistic seabed variations and the consequent adjustments to the mooring systems required for different turbine positions. The mooring lines of floating wind farms create large spatial constraints that are depth-dependent, since mooring designs must adapt to variations in seabed conditions over the array area. We develop a layout optimization methodology that addresses this, adjusting mooring system designs based on the local seabed characteristics as the layout changes and using steady-state models for the wake effects and mooring lines. The approach includes design algorithms that adjust the anchor positions and line length to achieve the desired mooring line profile for different water depths, and a layout optimization framework that implements spatial constraints between the turbines, mooring lines, and lease area boundaries. Demonstrating the method on several cases shows the effect of the seabed and spatial-constraint factors, as well as their interactions, on the optimal array layout. This demonstration paves the way for scaling up the method, using more powerful optimization algorithms to handle larger farm sizes and situations with more intensely varied seabed conditions.

17 WIND ENERGY↗

DOE OSTI2026

FAD-Toolset (Floating Array Design Toolset) [SWR-26-056]

The Floating Array Design (FAD) Toolset is a collection of tools for modeling and designing arrays of floating offshore structures. It was originally designed for floating wind systems but has applicability for many offshore applications. A core part of the FAD Toolset is the floating array model, which serves as a high-level library for efficiently modeling a floating array, such as a floating wind array. It combines site condition information and a description of the floating array design, and contains functions for evaluating the array's behavior considering the site conditions. For example, it combines information about site soil conditions, mooring line loads, and an array's anchor characteristics to estimate the holding capacity of each anchor. The library works in conjunction with the tools RAFT, MoorPy, and FLORIS to model floating platforms, wind turbines, mooring systems, power cables, and array wakes respectively. Layered on top of the floating array model is a set of design tools that can be used for algorithmically adjusting or optimizing parts of the a floating array. Specific tools existing for mooring lines, shared mooring systems, dynamic power cables, static power cable routing, and overall array layout. These capabilities work with the design representation and evaluation functions in the floating array model, and they can be applied by users in various combinations to suit different purposes. In addition to standalone uses of the FAD Toolset, a coupling has been made with Ard, (https://github.com/NLRWindSystems/Ard) a sophisticated and flexible wind farm optimization tool. This coupling allows Ard to use certain mooring system capabilities from FAD to perform layout optimization of floating wind farms with Ard's more advanced layout optimization capabilities. The FAD Toolset works with the IEA Wind Task 49 Ontology (https://github.com/IEAWindTask49/Ontology), which provides a standardized format for describing floating wind farm sites and designs. See example use cases in our examples folder (https://github.com/NLRWindSystems/FAD-Toolset/blob/main/examples/README.md) For working with the library, it is important to understand the floating array model structure, which is described more here: https://github.com/NLRWindSystems/FAD-Toolset/blob/main/fad/README.md.

Sirkis, Leah [National Laboratory of the Rockies (↗

DOE OSTI2022

Efficient Loads Surrogates for Waked Turbines in an Array

Accurately and efficiently predicting wind turbine structural loading is a crucial step in wind farm design. Without considering structural loading, wind farm optimization could negatively impact turbine fatigue and ultimate loads, especially for waked and partially waked turbines, which could result in higher maintenance costs and reduced turbine lifetime. However, predicting turbine loads throughout an array is a costly step, as these quantities require time-accurate results across long time histories, which is often intractable for large array optimization. Therefore, surrogate models that link array spacing to load outputs are often used, but the surrogates are then unique to the inflow conditions and array configurations in the training library. This work develops surrogate models for many wind turbine load outputs based solely on rotor plane velocity measurements, with no required input about array configuration or freestream inflow parameters. Surrogate models were constructed for many turbine quantities of interest (QoI), considering mean, standard deviation, ultimate, and fatigue loads. In general, most QoI statistics were accurately captured, as measured by predicted vs. actual correlation coefficient, confirming the suitability of the approach. Temporal mean values of the QoI required only temporal mean measurements of the rotor plane inflow velocity. However, accurate prediction of temporal standard deviation, ultimate, and fatigue values of QoI also required temporal standard deviations of the rotor plane velocity field. Poor surrogate performance was observed when too many correlated inputs were used, such as multiple velocity components. If the fewest inflow parameters are used to construct the surrogates, the average correlation coefficient value for all output QoI statistics is 0.89. Surrogates for standard deviations and damage equivalent loads (DELs) of turbine QoIs generally had lower accuracy and tower-base and shaft load channels posed the most difficult to capture accurately. The results suggest that these surrogates could be easily paired with analytic wake models, which are frequently used for pre-construction wind farm array optimization, to account for turbine loading in addition to power production. By including the optimal inflow conditions, the surrogate accuracy can improve to an average correlation coefficient value for all output QoI statistics of 0.92. This work has established the ability to build accurate surrogates for mean, standard deviation, ultimate load, and DEL turbine QoI values based on the rotor plane inflow velocity, and identified which inflow conditions lead to greater surrogate accuracy.

17 WIND ENERGY↗

DOE OSTI2025

Deep Reinforcement Learning Based Control of Wind Turbines for Fast Frequency Response

In order to fulfill vital auxiliary grid services, such as load regulation, spin and non-spin reserve provision, and frequency support during emergencies, there is often a requirement for certain wind farms to operate in de-loaded modes. Leveraging the swift response capabilities of wind farms, this study demonstrates that reserving power in de-loaded modes can significantly enhance power grid stability and reliability during system contingencies. Controlling wind farms optimally for frequency support is intricate due to the nonlinearity of models and controllers and the complexity of wind farm interactions with power systems. Here, to address this challenge, this paper introduces a novel approach that integrates wind turbines into reinforcement learning-based solutions for frequency response. This innovative methodology utilizes the state-of-the-art reinforcement learning algorithm known as the surrogate-gradient-based evolutionary strategy. The proposed learning-based algorithm provides continuous control of wind farm output to rapidly stabilize system frequency and prevent unnecessary trips of under-frequency load shedding relays. To facilitate efficient training, parallel computing techniques are employed. The proposed methodology is evaluated on a modified IEEE-39 bus system, and simulation results reveal its efficacy in reliably supporting power system frequency and preventing the need for unnecessary load shedding.

Gao, Wei [Argonne National Laboratory (ANL), Argon↗