Adjoint-based model predictive control for optimal energy extraction in waked wind farms

Vali, Mehdi; Petrović, Vlaho; Boersma, Sjoerd; Wingerden, Jan‐Willem van; Pao, Lucy Y.; Kühn, Martin

doi:10.1016/j.conengprac.2018.11.005

Cited by 54 publications

(54 citation statements)

References 38 publications

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“…The combined two-dimensional computational fluid dynamics and adjoint-based optimization model WFSim has been utilized (see e.g. Boersma et al, 2016Boersma et al, , 2018Vali et al, 2019) for control applications. Subsequent studies have used the Ensemble Kalman filter (EnKF) to perform model state estimation as a function of time (Doekemeijer et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Optimal closed-loop wake steering, Part 1: Conventionally neutral atmospheric boundary layer conditions

Howland¹,

Ghate²,

Lele³

et al. 2020

Preprint

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Abstract. Strategies for wake loss mitigation through the use of dynamic closed-loop wake steering are investigated using large eddy simulations of conventionally neutral atmospheric boundary layer conditions, where the neutral boundary layer is capped by an inversion and a stable free atmosphere. The closed-loop controller synthesized in this study consists of a physics-based lifting line wake model combined with a data-driven Ensemble Kalman filter state estimation technique to calibrate the wake model as a function of time in a generalized transient atmospheric flow environment. Computationally efficient gradient ascent yaw misalignment selection along with efficient state estimation enables the dynamic yaw calculation for real-time wind farm control. The wake steering controller is tested in a six turbine array embedded in a quasi-stationary conventionally neutral flow with geostrophic forcing and Coriolis effects included. The controller increases power production compared to baseline, greedy, yaw-aligned control although the magnitude of success of the controller depends on the state estimation architecture and the wind farm layout. The influence of the model for the coefficient of power Cp as a function of the yaw misalignment is characterized. Errors in estimation of the power reduction as a function of yaw misalignment are shown to result in yaw steering configurations that under-perform the baseline yaw aligned configuration. Overestimating the power reduction due to yaw misalignment leads to increased power over greedy operation while underestimating the power reduction leads to decreased power, and therefore, in an application where the influence of yaw misalignment on Cp is unknown, a conservative estimate should be taken. Sensitivity analyses on the controller architecture, coefficient of power model, wind farm layout, and atmospheric boundary layer state are performed to assess benefits and trade-offs in the design of a wake steering controller for utility-scale application. The physics-based wake model with data assimilation predicts the power production in yaw misalignment with a mean absolute error over the turbines in the farm of 0.02 P1, with P1 as the power of the leading turbine at the farm, whereas a physics-based wake model with wake spreading based on an empirical turbulence intensity relationship leads to a mean absolute error of 0.11 P1.

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Section: Introductionmentioning

confidence: 99%

Optimal closed-loop wake steering, Part 1: Conventionally neutral atmospheric boundary layer conditions

Howland¹,

Ghate²,

Lele³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Design problems focus on maximizing wind farm power production and reducing the levelized cost of energy by optimizing wind farm layouts [1][2][3][4] and wind turbine set points for yaw, tilt, and thrust [5,6]. Active control attempts to actuate turbines dynamically to reduce farm level power fluctuations [7], track a power output reference signal to provide power grid services [8][9][10][11], or maximize power production [12,13].…”

Section: Introductionmentioning

confidence: 99%

A Wake Modeling Paradigm for Wind Farm Design and Control

et al. 2019

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Wake models play an integral role in wind farm layout optimization and operations where associated design and control decisions are only as good as the underlying wake model upon which they are based. However, the desired model fidelity must be counterbalanced by the need for simplicity and computational efficiency. As a result, efficient engineering models that accurately capture the relevant physics—such as wake expansion and wake interactions for design problems and wake advection and turbulent fluctuations for control problems—are needed to advance the field of wind farm optimization. In this paper, we discuss a computationally-efficient continuous-time one-dimensional dynamic wake model that includes several features derived from fundamental physics, making it less ad-hoc than prevailing approaches. We first apply the steady-state solution of the model to predict the wake expansion coefficients commonly used in design problems. We demonstrate that more realistic results can be attained by linking the wake expansion rate to a top-down model of the atmospheric boundary layer, using a super-Gaussian wake profile that smoothly transitions between a top-hat and Gaussian distribution as well as linearly-superposing wake interactions. We then apply the dynamic model to predict trajectories of wind farm power output during start-up and highlight the improved accuracy of non-linear advection over linear advection. Finally, we apply the dynamic model to the control-oriented application of predicting power output of an irregularly-arranged farm during continuous operation. In this application, model fidelity is improved through state and parameter estimation accounting for spanwise inflow inhomogeneities and turbulent fluctuations. The proposed approach thus provides a modeling paradigm with the flexibility to enable designers to trade-off between accuracy and computational speed for a wide range of wind farm design and control applications.

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“…With the increasing application of LES, hybrid RANS-LES and direct numerical simulation (DNS) methods, the inflow turbulence generation has become the subject of many research works in recent decades. For a review of such methods and their application in wind energy, we refer to Wu (2017) and Stevens and Meneveau (2017). However, due to computational cost, it is still popular in the wind energy industry to use the RANS model with an inflow boundary obtained from either an analytical formula or a one-dimensional (1-D) simulation.…”

Section: Inflow Boundarymentioning

confidence: 99%

Adjoint-based calibration of inlet boundary condition for atmospheric computational fluid dynamics solvers

et al. 2019

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Abstract. A continuous adjoint solver is developed for calibration of the inlet velocity profile boundary condition (BC) for computational fluid dynamics (CFD) simulations of the neutral atmospheric boundary layer (ABL). The adjoint solver uses interior domain wind speed observations to compute the gradient of a calibration function with respect to inlet velocity speed and wind direction. The solver has been implemented in the open-source CFD package OpenFOAM coupled with the local gradient-based “CONMIN-frcg” solver of the DAKOTA optimization package. The feasibility of the optimizer output is continuously monitored during the calibration process. The inlet flow profile is considered acceptable only if it can be fitted to a logarithmic or power law function with a tolerance of 3 %. Otherwise, the optimization takes the last fitted profile and asks for a new gradient evaluation. The newly developed framework has been applied in two cases, namely the Ishihara case and Kassel domain. By using the measurements over the hill in the Ishihara case, the method was able to predict the velocity profiles upstream and downstream of the hill accurately. For the Kassel domain, despite the complexity of the site, the method managed to achieve the targeted profile within a reasonable number of the solver calls.

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Adjoint-based model predictive control for optimal energy extraction in waked wind farms

Cited by 54 publications

References 38 publications

Optimal closed-loop wake steering, Part 1: Conventionally neutral atmospheric boundary layer conditions

Optimal closed-loop wake steering, Part 1: Conventionally neutral atmospheric boundary layer conditions

A Wake Modeling Paradigm for Wind Farm Design and Control

Adjoint-based calibration of inlet boundary condition for atmospheric computational fluid dynamics solvers

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