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

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 in which 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 (EnKF) 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 statistically quasi-stationary, conventionally neutral flow with geostrophic forcing and Coriolis effects included. The controller statistically significantly increases power production compared to the baseline, greedy, yaw-aligned control provided that the EnKF estimation is constrained and informed with a physics-based prior belief of the wake model parameters. 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 underperform the baseline yaw-aligned configuration. Overestimating the power reduction due to yaw misalignment leads to increased power over the greedy operation, while underestimating the power reduction leads to decreased power; therefore, in an application where the influence of yaw misalignment on Cp is unknown, a conservative estimate should be taken. The EnKF-augmented wake model predicts the power production in yaw misalignment with a mean absolute error over the turbines in the farm of 0.02P1, with P1 as the power of the leading turbine at the farm. A standard wake model with wake spreading based on an empirical turbulence intensity relationship leads to a mean absolute error of 0.11P1, demonstrating that state estimation improves the predictive capabilities of simplified wake models.

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

10.5194/wes-2020-52 ◽

2020 ◽

Author(s):

Michael F. Howland ◽

Aditya S. Ghate ◽

Sanjiva K. Lele ◽

John O. Dabiri

Keyword(s):

Boundary Layer ◽

Atmospheric Boundary Layer ◽

State Estimation ◽

Wind Farm ◽

Closed Loop ◽

Mean Absolute Error ◽

Absolute Error ◽

Power Production ◽

Power Reduction ◽

Wake Model

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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An active power control approach for wake-induced load alleviation in a fully developed wind farm boundary layer

10.5194/wes-2018-70 ◽

2018 ◽

Author(s):

Mehdi Vali ◽

Vlaho Petrović ◽

Gerald Steinfeld ◽

Lucy Y. Pao ◽

Martin Kühn

Keyword(s):

Boundary Layer ◽

Power Control ◽

Atmospheric Boundary Layer ◽

Wind Turbines ◽

Wind Farm ◽

Closed Loop ◽

Power Production ◽

Active Power ◽

Active Power Control ◽

The Individual

Abstract. This paper studies a closed-loop wind farm control framework for active power control (APC) with a simultaneous reduction of wake-induced structural loads within a fully developed wind farm flow interacting with the atmospheric boundary layer. The main focus is on a classical feedback control, which features a simple control architecture and a practical measurement system that are realizable for real-time control of large wind farms. We demonstrate that the wake-induced structural loadings of the downstream turbines can be alleviated, while the wind farm power production follows a reference signal. A closed-loop APC is designed first to improve the power tracking performance against wake-induced power losses of the downwind turbines. Then, the non-unique solution of APC for the wind farm is exploited for aggregated structural load alleviation. The axial induction factors of the individual wind turbines are considered as control inputs to limit the power production of the wind farm or to switch to greedy control when the demand exceeds the power available in the wind. Furthermore, the APC solution domain is enlarged by an adjustment of the power set-points according to the locally available power at the waked wind turbines. Therefore, the controllability of the wind turbines is improved for rejecting the intensified load fluctuations inside the wake. A large-eddy simulation model is employed for resolving the turbulent flow, the wake structures and its interaction with the atmospheric boundary layer. The applicability and key features of the controller are discussed with a wind farm example consisting of 3 × 4 turbines with different wake interactions at each row. The performance of the proposed APC is evaluated using the accuracy of the wind farm power tracking and the wake-induced damage equivalent fatigue loads of the towers of the individual wind turbines.

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An active power control approach for wake-induced load alleviation in a fully developed wind farm boundary layer

Wind Energy Science ◽

10.5194/wes-4-139-2019 ◽

2019 ◽

Vol 4 (1) ◽

pp. 139-161 ◽

Cited By ~ 4

Author(s):

Mehdi Vali ◽

Vlaho Petrović ◽

Gerald Steinfeld ◽

Lucy Y. Pao ◽

Martin Kühn

Keyword(s):

Boundary Layer ◽

Power Control ◽

Atmospheric Boundary Layer ◽

Wind Turbines ◽

Wind Farm ◽

Closed Loop ◽

Power Production ◽

Active Power ◽

Active Power Control ◽

The Individual

Abstract. This paper studies a closed-loop wind farm control framework for active power control (APC) with a simultaneous reduction of wake-induced structural loads within a fully developed wind farm flow interacting with the atmospheric boundary layer. The main focus is on a classical feedback control, which features a simple control architecture and a practical measurement system that are realizable for real-time control of large wind farms. We demonstrate that the wake-induced structural loading of the downstream turbines can be alleviated, while the wind farm power production follows a reference signal. A closed-loop APC is designed first to improve the power-tracking performance against wake-induced power losses of the downwind turbines. Then, the nonunique solution of APC for the wind farm is exploited for aggregated structural load alleviation. The axial induction factors of the individual wind turbines are considered control inputs to limit the power production of the wind farm or to switch to greedy control when the demand exceeds the power available in the wind. Furthermore, the APC solution domain is enlarged by an adjustment of the power set-points according to the locally available power at the waked wind turbines. Therefore, the controllability of the wind turbines is improved for rejecting the intensified load fluctuations inside the wake. A large-eddy simulation model is employed for resolving the turbulent flow, the wake structures, and its interaction with the atmospheric boundary layer. The applicability and key features of the controller are discussed with a wind farm example consisting of 3×4 turbines with different wake interactions for each row. The performance of the proposed APC is evaluated using the accuracy of the wind farm power tracking and the wake-induced damage equivalent fatigue loads of the towers of the individual wind turbines.

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Influence of Wake Model Superposition and Secondary Steering on Model-Based Wake Steering Control with SCADA Data Assimilation

Energies ◽

10.3390/en14010052 ◽

2020 ◽

Vol 14 (1) ◽

pp. 52

Author(s):

Michael F. Howland ◽

John O. Dabiri

Keyword(s):

Wind Farm ◽

Closed Loop ◽

Power Production ◽

Model Parameters ◽

Closed Loop Control ◽

Steering Control ◽

Loop Control ◽

Large Eddy ◽

Wake Model ◽

The Impact

Methods for wind farm power optimization through the use of wake steering often rely on engineering wake models due to the computational complexity associated with resolving wind farm dynamics numerically. Within the transient, turbulent atmospheric boundary layer, closed-loop control is required to dynamically adjust to evolving wind conditions, wherein the optimal wake model parameters are estimated as a function of time in a hybrid physics- and data-driven approach using supervisory control and data acquisition (SCADA) data. Analytic wake models rely on wake velocity deficit superposition methods to generalize the individual wake deficit to collective wind farm flow. In this study, the impact of the wake model superposition methodologies on closed-loop control are tested in large eddy simulations of the conventionally neutral atmospheric boundary layer with full Coriolis effects. A model for the non-vanishing lateral velocity trailing a yaw misaligned turbine, termed secondary steering, is also presented, validated, and tested in the closed-loop control framework. Modified linear and momentum conserving wake superposition methodologies increase the power production in closed-loop wake steering control statistically significantly more than linear superposition. While the secondary steering model increases the power production and reduces the predictive error associated with the wake model, the impact is not statistically significant. Modified linear and momentum conserving superposition using the proposed secondary steering model increase a six turbine array power production, compared to baseline control, in large eddy simulations by 7.5% and 7.7%, respectively, with wake model predictive mean absolute errors of 0.03P1 and 0.04P1, respectively, where P1 is the baseline power production of the leading turbine in the array. Ensemble Kalman filter parameter estimation significantly reduces the wake model predictive error for all wake deficit superposition and secondary steering cases compared to predefined model parameters.

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Explanation Plus Prediction—The Logical Focus of Project Management Research

Project Management Journal ◽

10.1177/8756972821999945 ◽

2021 ◽

pp. 875697282199994

Author(s):

Joseph F. Hair ◽

Marko Sarstedt

Keyword(s):

Project Management ◽

Statistical Models ◽

Predictive Power ◽

Mean Absolute Error ◽

Explanatory Power ◽

Absolute Error ◽

Model Parameters ◽

Mean Square ◽

Management Research ◽

The Mean

Most project management research focuses almost exclusively on explanatory analyses. Evaluation of the explanatory power of statistical models is generally based on F-type statistics and the R 2 metric, followed by an assessment of the model parameters (e.g., beta coefficients) in terms of their significance, size, and direction. However, these measures are not indicative of a model’s predictive power, which is central for deriving managerial recommendations. We recommend that project management researchers routinely use additional metrics, such as the mean absolute error or the root mean square error, to accurately quantify their statistical models’ predictive power.

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A Maximum Entropy Production Evaporation – Transpiration Product for Australia

10.5194/essd-2019-70 ◽

2019 ◽

Author(s):

Olanrewaju Abiodun ◽

Okke Batelaan ◽

Huade Guan ◽

Jingfeng Wang

Keyword(s):

Entropy Production ◽

Maximum Entropy ◽

Mean Absolute Error ◽

Absolute Error ◽

Production Model ◽

Model Parameters ◽

Drought Period ◽

Maximum Entropy Production ◽

Millennium Drought ◽

Mean Square Errors

Abstract. The aim of this research is to develop evaporation and transpiration products for Australia based on the maximum entropy production model (MEP). We introduce a method into the MEP algorithm of estimating the required model parameters over the entire Australia through the use of pedotransfer function, soil properties and remotely sensed soil moisture data. Our algorithm calculates the evaporation and transpiration over Australia on daily timescales at the 5 km2 resolution for 2003–2013. The MEP evapotranspiration (ET) estimates are validated using observed ET data from 20 Eddy Covariance (EC) flux towers across 8 land cover types in Australia. We also compare the MEP ET at the EC flux towers with two other ET products over Australia; MOD16 and AWRA-L products. The MEP model outperforms the MOD16 and AWRA-L across the 20 EC flux sites, with average root mean square errors (RMSE), 8.21, 9.87 and 9.22 mm/8 days respectively. The average mean absolute error (MAE) for the MEP, MOD16 and AWRA-L are 6.21, 7.29 and 6.52 mm/8 days, the average correlations are 0.64, 0.57 and 0.61, respectively. The percentage Bias of the MEP ET was within 20 % of the observed ET at 12 of the 20 EC flux sites while the MOD16 and AWRA-L ET were within 20 % of the observed ET at 4 and 10 sites respectively. Our analysis shows that evaporation and transpiration contribute 38 % and 62 %, respectively, to the total ET across the study period which includes a significant part of the “millennium drought” period (2003–2009) in Australia. The data (Abiodun et al., 2019) is available at https://doi.org/10.25901/5ce795d313db8.

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Assessing the accuracy of microwave radiometers and radio acoustic sounding systems for wind energy applications

10.5194/amt-2016-321 ◽

2016 ◽

Cited By ~ 2

Author(s):

Laura Bianco ◽

Katja Friedrich ◽

James Wilczak ◽

Duane Hazen ◽

Daniel Wolfe ◽

...

Keyword(s):

Remote Sensing ◽

Boundary Layer ◽

Relative Humidity ◽

Mean Absolute Error ◽

Microwave Radiometer ◽

Absolute Error ◽

Acoustic Sounding ◽

Energy Applications ◽

Virtual Temperature ◽

Microwave Radiometers

Abstract. To assess current remote-sensing capabilities for wind energy applications, a remote-sensing system evaluation study, called XPIA (eXperimental Planetary boundary layer Instrument Assessment), was held in the spring of 2015 at NOAA’s Boulder Atmospheric Observatory (BAO) facility. Several remote-sensing platforms were evaluated to determine their suitability for the verification and validation processes used to test the accuracy of numerical weather prediction models. The evaluation of these platforms was performed with respect to well-defined reference systems: the BAO’s 300-m tower equipped at 6 levels (50, 100, 150, 200, 250, and 300 m) with 12 sonic anemometers and 6 temperature and relative humidity sensors; and approximately 60 radiosonde launches. In this study we first employ these reference measurements to validate temperature profiles retrieved by two co-located microwave radiometers, as well as virtual temperature measured by co-located wind profiling radars equipped with radio acoustic sounding systems. Results indicate a mean absolute error in the temperature retrieved by the microwave radiometers below 1.5 °C in the lowest 5 km of the atmosphere, and a mean absolute error in the virtual temperature measured by the radio acoustic sounding systems below 0.8 °C in the layer of the atmosphere covered by these measurements (up to approximately 1.6–2 km). We also investigated the benefit of the vertical velocity applied to the speed of sound before computing the virtual temperature by the radio acoustic sounding systems. We find that using this correction frequently increases the RASS error, and that it should not be routinely applied to all data. Water vapor density profiles measured by the MWRs were also compared with similar measurements from the soundings, showing the capability of MWRs to follow the vertical profile measured by the sounding, and finding a mean absolute error below 0.5 g m−3 in the lowest 5 km of the atmosphere. However, the relative humidity profiles measured by the microwave radiometer lack the high-resolution details available from radiosonde profiles. An encouraging and significant finding of this study was that the coefficient of determination between the lapse rate measured by the microwave radiometer and the tower measurements over the tower levels between 50 and 300 m ranged from 0.76 to 0.91, proving that these remote-sensing instruments can provide accurate information on atmospheric stability conditions in the lower boundary layer.

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Comparison of Different Time Series Methods for Short-Term Forecasting of Wind Power Production

ASME 2010 4th International Conference on Energy Sustainability, Volume 2 ◽

10.1115/es2010-90270 ◽

2010 ◽

Cited By ~ 1

Author(s):

Gong Li ◽

Jing Shi

Keyword(s):

Wind Power ◽

Wind Farm ◽

Mean Squared Error ◽

Network Models ◽

Absolute Error ◽

Power Production ◽

Model Parameters ◽

Short Term ◽

Bp Network ◽

Persistence Model

Reliable short-term predictions of the wind power production are critical for both wind farm operations and power system management, where the time scales can vary in the order of several seconds, minutes, hours and days. This comprehensive study mainly aims to quantitatively evaluate and compare the performances of different Box & Jenkins models and backpropagation (BP) neural networks in forecasting the wind power production one-hour ahead. The data employed is the hourly power outputs of an N.E.G. Micon 900-kilowatt wind turbine, which is installed to the east of Valley City, North Dakota. For each type of Box & Jenkins models tested, the model parameters are estimated to determine the corresponding optimal models. For BP network models, different input layer sizes, hidden layer sizes, and learning rates are examined. The evaluation metrics are mean absolute error and root mean squared error. Besides, the persistence model is also employed for purpose of comparison. The results show that in general both best performing Box & Jenkins and BP models can provide better forecasts than the persistence model, while the difference between the Box & Jenkins and BP models is actually insignificant.

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0433 Targeting Light Sensitivity Parameters to Optimize Circadian Phase Predictions

SLEEP ◽

10.1093/sleep/zsaa056.430 ◽

2020 ◽

Vol 43 (Supplement_1) ◽

pp. A166-A166

Author(s):

J E Stone ◽

E M McGlashan ◽

S W Cain ◽

A J Phillips

Keyword(s):

Sensitivity Analysis ◽

Circadian Clock ◽

Mean Absolute Error ◽

Light Response ◽

Absolute Error ◽

Light Sensitivity ◽

Model Parameters ◽

Circadian Period ◽

Individual Level ◽

Circadian Phase

Abstract Introduction Existing models of the human circadian clock accurately predict phase at group-level but not at individual-level. Interindividual variability in light sensitivity is not currently accounted for in these models and may be a practical approach to improving individual-level predictions. Using the gold-standard predictive model, we (i) identified whether varying light sensitivity parameters produces meaningful changes in predicted phase in field conditions; and (ii) tested whether optimizing parameters can significantly improve accuracy of circadian phase prediction. Methods Healthy participants (n=12, 7 women, aged 18-26) underwent continuous light and activity monitoring for 3 weeks (Actiwatch Spectrum). Salivary dim light melatonin onset (DLMO) was measured each week. A model of the human circadian clock and its response to light was used to predict the three weekly DLMO times using the individual’s light data. A sensitivity analysis was performed varying three model parameters within physiological ranges: (i) amplitude of the light response [p]; (ii) advance vs. delay bias of the light response [K]; and (iii) intrinsic circadian period [tau]. These parameters were then fitted using least squares estimation to obtain optimal predictions of DLMO for each individual. Accuracy was compared between optimized parameters and default parameters. Results The default model predicted DLMO with mean absolute error of 1.02h. Sensitivity analysis showed the average range of variation in predicted DLMOs across participants was 0.65h for p, 4.28h for K and 3.26h for tau. Fitting parameters independently, we found mean absolute error of 0.85h for p, 0.71h for K and 0.75h for tau. Fitting p and K together reduced mean absolute error to 0.57h. Conclusion Light sensitivity parameters capture similar or greater variability in phase as intrinsic circadian period, indicating they are a viable option for individualising circadian phase predictions. Future prospective work is needed using measures of light sensitivity to validate this approach. Support N/A

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Parameterization dependence of the hydrological cycle in a general circulation model of intermediate complexity

10.5194/egusphere-egu21-1328 ◽

2021 ◽

Author(s):

Oliver Mehling ◽

Elisa Ziegler ◽

Heather Andres ◽

Martin Werner ◽

Kira Rehfeld

Keyword(s):

General Circulation Model ◽

General Circulation ◽

Hydrological Cycle ◽

Mean Absolute Error ◽

Circulation Model ◽

Absolute Error ◽

Bayesian Optimization ◽

Model Parameters ◽

Climate Projections ◽

Intermediate Complexity

The global hydrological cycle is of crucial importance for life on Earth. Hence, it is a focus of both future climate projections and paleoclimate modeling. The latter typically requires long integrations or large ensembles of simulations, and therefore models of reduced complexity are needed to reduce the computational cost. Here, we study the hydrological cycle of the the Planet Simulator (PlaSim) [1], a general circulation model (GCM) of intermediate complexity, which includes evaporation, precipitation, soil hydrology, and river advection.Using published parameter configurations for T21 resolution [2, 3], PlaSim strongly underestimates precipitation in the mid-latitudes as well as global atmospheric water compared to ERA5 reanalysis data [4]. However, the tuning of PlaSim has been limited to optimizing atmospheric temperatures and net radiative fluxes so far [3].Here, we present a different approach by tuning the model&#8217;s atmospheric energy balance and water budget simultaneously. We argue for the use of the globally averaged mean absolute error (MAE) for 2 m temperature, net radiation, and evaporation in the objective function. To select relevant model parameters, especially with respect to radiation and the hydrological cycle, we perform a sensitivity analysis and evaluate the feature importance using a Random Forest regressor. An optimal set of parameters is obtained via Bayesian optimization.Using the optimized set of parameters, the mean absolute error of temperature and cloud cover is reduced on most model levels, and mid-latitude precipitation patterns are improved. In addition to annual zonal-mean patterns, we examine the agreement with the seasonal cycle and discuss regions in which the bias remains considerable, such as the monsoon region over the Pacific.We discuss the robustness of this tuning with regards to resolution (T21, T31, and T42), and compare the atmosphere-only results to simulations with a mixed-layer ocean. Finally, we provide an outlook on the applicability of our parametrization to climate states other than present-day conditions.[1] K. Fraedrich et al., Meteorol. Z. 14, 299&#8211;304 (2005) [2] F. Lunkeit et al., Planet Simulator User&#8217;s Guide Version 16.0 (University of Hamburg, 2016) [3] G. Lyu et al., J. Adv. Model. Earth Syst. 10, 207&#8211;222 (2018) [4] H. Hersbach et al., Q. J. R. Meteorol. Soc. 146, 1999&#8211;2049 (2020)

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