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Active power control for wind farms is needed to provide ancillary services. One of these services is to track a power reference signal with a wind farm by dynamically de- and uprating the turbines. Due to the stochastic nature of the wind, it is necessary to take this stochastic behavior into account when evaluating control signals. In this paper we present a closed-loop stochastic wind farm controller that evaluates thrust coefficients providing power tracking under uncertain wind speed measurements. The controller is evaluated in a high-fidelity wind farm model simulating a 9-turbine wind farm to demonstrate the stochastic controller under different uncertainty levels on the wind speed measurement and different controller settings. Results illustrate that a stochastic controller provides better tracking performance with respect to its deterministic variant., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Jan-Willem van Wingerden, Team Tamas Keviczky

Electricity consumption is increasing on a global level. In 2017, non-renewable energy sources such as crude oil, natural gas and coal provided 76% of the required energy, while 24% came from renewable sources such as hydro, wind and solar. Non-renewable sources are finite because they do not replenish rapidly enough relative to the rate at which they are being used, and harvesting these resources is environmental costly. Since renewable energy sources replenish naturally in a relatively short period of time and are cleaner, they are suitable for the sustainable production of electricity..., Team Jan-Willem van Wingerden

Active power control for wind farms is needed to provide ancillary services. One of these services is to track a power reference signal with a wind farm by dynamically de- and uprating the turbines. Due to the stochastic nature of the wind, it is necessary to take this stochastic behavior into account when evaluating control signals. In this paper we present a closed-loop stochastic wind farm controller that evaluates thrust coefficients providing power tracking under uncertain wind speed measurements. The controller is evaluated in a high-fidelity wind farm model simulating a 9-turbine wind farm to demonstrate the stochastic controller under different uncertainty levels on the wind speed measurement and different controller settings. Results illustrate that a stochastic controller provides better tracking performance with respect to its deterministic variant., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Jan-Willem van Wingerden, Team Tamas Keviczky

Active power control for wind farms is needed to provide ancillary services. One of these services is to track a power reference signal with a wind farm by dynamically de- and uprating the turbines. In this paper we present a closed-loop wind farm controller that evaluates 1) thrust coefficients on a seconds-scale that provide power tracking and minimize dynamical loading on a farm level and 2) yaw settings on a minutes-scale that maximize the possible power that can be harvested by the farm. The controller is evaluated in a high-fidelity wind farm model. A six-turbine simulation case study is used to demonstrate the time-efficient controller for different controller settings. The results indicate that, with a power reference signal below the maximal possible power that can be harvested by the farm with non-yawed turbines, both tracking and reduction in dynamical loading can be ensured. In a second case study we illustrate that, when a wind farm power reference signal exceeds the maximal possible power that can be harvested with non-yawed turbines for a time period, it can not be tracked sufficiently. However, when solving for and applying optimized yaw settings, tracking can be ensured for the complete simulation horizon., Team Jan-Willem van Wingerden

Electricity consumption is increasing on a global level. In 2017, non-renewable energy sources such as crude oil, natural gas and coal provided 76% of the required energy, while 24% came from renewable sources such as hydro, wind and solar. Non-renewable sources are finite because they do not replenish rapidly enough relative to the rate at which they are being used, and harvesting these resources is environmental costly. Since renewable energy sources replenish naturally in a relatively short period of time and are cleaner, they are suitable for the sustainable production of electricity..., Team Jan-Willem van Wingerden

This work presents the next step in realizing lidar-based closed-loop wake redirection control. Lidar-based closed-loop wake redirection aims at repositioning the wake at a desired position by yawing the wind turbine. The actual wake deflection is derived from lidar measurements and used in a closed-loop control scheme. Compared to an open-loop setting in which temporal changes are not taken into account, lidar-based closed-loop wake redirection can react on temporal disturbances. This yields a more robust control solution due to the employed closed-loop control framework. In this work, for the first time, the concept is implemented in an LES environment namely the PArallelized Large-eddy simulation Model (PALM) code. In PALM lidar measurements are simulated using a lidar model which are processed to estimate the wake position. A controller is synthesized by the usage of a the reduced order wind farm model WindFarmSimulator (WFSim). High-fidelity simulation results illustrate the controller's ability to adapt to a temporal changing crosswind disturbance in a turbulent simulation scenario. Consequently, it increases the power output of the two-turbine scenario compared to the open-loop approach., Team Jan-Willem van Wingerden

Wind farm control often relies on computationally inexpensive surrogate models to predict the dynamics inside a farm. However, the reliability of these models over the spectrum of wind farm operation remains questionable due to the many uncertainties in the atmospheric conditions and tough-to-model dynamics at a range of spatial and temporal scales relevant for control. A closed-loop control framework is proposed in which a simplified model is calibrated and used for optimization in real time. This paper presents a joint state-parameter estimation solution with an ensemble Kalman filter at its core, which calibrates the surrogate model to the actual atmospheric conditions. The estimator is tested in high-fidelity simulations of a nine-turbine wind farm. Exclusively using measurements of each turbine's generated power, the adaptability to modeling errors and mismatches in atmospheric conditions is shown. Convergence is reached within 400 s of operation, after which the estimation error in flow fields is negligible. At a low computational cost of 1.2 s on an 8-core CPU, this algorithm shows comparable accuracy to the state of the art from the literature while being approximately 2 orders of magnitude faster., Team Jan-Willem van Wingerden

The objective of active power control in wind farms is to provide ancillary grid services. Improving this is vital for a smooth wind energy penetration in the energy market. One of these services is to track a power reference signal with a wind farm by dynamically de- and uprating the turbines. In this paper we present a computationally efficient model predictive controller (MPC) for computing optimal control signals for each time step. It is applied in the PArallelized Large-eddy simulation Model (PALM), which is considered as the real wind farm in this paper. By taking measurements from the PALM, we show that the closed-loop controller can provide power reference tracking while minimizing variations in the axial forces by solving a constrained optimization problem at each time step. A six turbine simulation case study is presented in which the controller operates with optimised turbine yaw settings. We show that with these optimized yaw settings, it is possible to track a power signal that temporarily exceeds the power harvested when operating under averaged greedy control turbine settings. Additionally, variations in the turbine's force signals are studied under different controller settings., Team Jan-Willem van Wingerden, Team Tamas Keviczky, Delft Center for Systems and Control

In this paper, we present an implementation of a model predictive controller (MPC) for wind farm power tracking problem. The controller is evaluated in the high-fidelity PAral-lelized Large-eddy simulation Model (PALM). By taking measurements from PALM, we show that the closed-loop MPC can provide power reference tracking while reducing force variations on a farm level by solving a constrained optimization problem at each time step. A six turbine wind farm case study is presented in which the controller operates with yawed turbines that increases the potential power that can be harvested with the wind farm, and we show that it is possible to track a reference power signal that temporarily exceeds the power harvested when operating under the so-called greedy control settings., Team Jan-Willem van Wingerden, Team Tamas Keviczky

Wind farm control research typically relies on computationally inexpensive, surrogate models for real-time optimization. However, due to the large time delays involved, changing atmospheric conditions and tough-to-model flow and turbine dynamics, these surrogate models need constant calibration. In this paper, a novel real-time (joint state-parameter) estimation solution for a medium-fidelity dynamical wind farm model is presented. In this work, we demonstrate the estimation of the freestream wind speed, local turbulence, and local wind field in a two-turbine wind farm using exclusively turbine power measurements. The estimator employs an Ensemble Kalman filter with a low computational cost of approximately 1.0 s per timestep on a dual-core notebook CPU. This work presents an essential building block for real-time wind farm control using computationally efficient dynamical wind farm models., Team Jan-Willem van Wingerden

Wind turbines are often sited together in wind farms as it is economically advantageous. Controlling the flow within wind farms to reduce the fatigue loads, maximize energy production and provide ancillary services is a challenging control problem due to the underlying time-varying non-linear wake dynamics. In this paper, we present a control-oriented dynamical wind farm model called the WindFarmSimulator (WFSim) that can be used in closed-loop wind farm control algorithms. The three-dimensional Navier–Stokes equations were the starting point for deriving the control-oriented dynamic wind farm model. Then, in order to reduce computational complexity, terms involving the vertical dimension were either neglected or estimated in order to partially compensate for neglecting the vertical dimension. Sparsity of and structure in the system matrices make this model relatively computationally inexpensive. We showed that by taking the vertical dimension partially into account, the estimation of flow data generated with a high-fidelity wind farm model is improved relative to when the vertical dimension is completely neglected in WFSim. Moreover, we showed that, for the study cases considered in this work, WFSim is potentially fast enough to be used in an online closed-loop control framework including model parameter updates. Finally we showed that the proposed wind farm model is able to estimate flow and power signals generated by two different 3-D high-fidelity wind farm models., Team Jan-Willem van Wingerden

The objective of active power control in wind farms is to provide ancillary grid services. Improving this is vital for a smooth wind energy penetration in the energy market. One of these services is to track a power reference signal with a wind farm by dynamically de- and uprating the turbines. In this paper we present a computationally efficient model predictive controller (MPC) for computing optimal control signals for each time step. It is applied in the PArallelized Large-eddy simulation Model (PALM), which is considered as the real wind farm in this paper. By taking measurements from the PALM, we show that the closed-loop controller can provide power reference tracking while minimizing variations in the axial forces by solving a constrained optimization problem at each time step. A six turbine simulation case study is presented in which the controller operates with optimised turbine yaw settings. We show that with these optimized yaw settings, it is possible to track a power signal that temporarily exceeds the power harvested when operating under averaged greedy control turbine settings. Additionally, variations in the turbine's force signals are studied under different controller settings., Team Jan-Willem van Wingerden, Team Tamas Keviczky, Support Delft Center for Systems and Control

Wind turbines are often sited together in wind farms as it is economically advantageous. Controlling the flow within wind farms to reduce the fatigue loads, maximize energy production and provide ancillary services is a challenging control problem due to the underlying time-varying non-linear wake dynamics. In this paper, we present a control-oriented dynamical wind farm model called the WindFarmSimulator (WFSim) that can be used in closed-loop wind farm control algorithms. The three-dimensional Navier–Stokes equations were the starting point for deriving the control-oriented dynamic wind farm model. Then, in order to reduce computational complexity, terms involving the vertical dimension were either neglected or estimated in order to partially compensate for neglecting the vertical dimension. Sparsity of and structure in the system matrices make this model relatively computationally inexpensive. We showed that by taking the vertical dimension partially into account, the estimation of flow data generated with a high-fidelity wind farm model is improved relative to when the vertical dimension is completely neglected in WFSim. Moreover, we showed that, for the study cases considered in this work, WFSim is potentially fast enough to be used in an online closed-loop control framework including model parameter updates. Finally we showed that the proposed wind farm model is able to estimate flow and power signals generated by two different 3-D high-fidelity wind farm models., Team Jan-Willem van Wingerden

Wind farm control research typically relies on computationally inexpensive, surrogate models for real-time optimization. However, due to the large time delays involved, changing atmospheric conditions and tough-to-model flow and turbine dynamics, these surrogate models need constant calibration. In this paper, a novel real-time (joint state-parameter) estimation solution for a medium-fidelity dynamical wind farm model is presented. In this work, we demonstrate the estimation of the freestream wind speed, local turbulence, and local wind field in a two-turbine wind farm using exclusively turbine power measurements. The estimator employs an Ensemble Kalman filter with a low computational cost of approximately 1.0 s per timestep on a dual-core notebook CPU. This work presents an essential building block for real-time wind farm control using computationally efficient dynamical wind farm models., Team Jan-Willem van Wingerden

This work presents the next step in realizing lidar-based closed-loop wake redirection control. Lidar-based closed-loop wake redirection aims at repositioning the wake at a desired position by yawing the wind turbine. The actual wake deflection is derived from lidar measurements and used in a closed-loop control scheme. Compared to an open-loop setting in which temporal changes are not taken into account, lidar-based closed-loop wake redirection can react on temporal disturbances. This yields a more robust control solution due to the employed closed-loop control framework. In this work, for the first time, the concept is implemented in an LES environment namely the PArallelized Large-eddy simulation Model (PALM) code. In PALM lidar measurements are simulated using a lidar model which are processed to estimate the wake position. A controller is synthesized by the usage of a the reduced order wind farm model WindFarmSimulator (WFSim). High-fidelity simulation results illustrate the controller's ability to adapt to a temporal changing crosswind disturbance in a turbulent simulation scenario. Consequently, it increases the power output of the two-turbine scenario compared to the open-loop approach., Team Jan-Willem van Wingerden

Wind farm control often relies on computationally inexpensive surrogate models to predict the dynamics inside a farm. However, the reliability of these models over the spectrum of wind farm operation remains questionable due to the many uncertainties in the atmospheric conditions and tough-to-model dynamics at a range of spatial and temporal scales relevant for control. A closed-loop control framework is proposed in which a simplified model is calibrated and used for optimization in real time. This paper presents a joint state-parameter estimation solution with an ensemble Kalman filter at its core, which calibrates the surrogate model to the actual atmospheric conditions. The estimator is tested in high-fidelity simulations of a nine-turbine wind farm. Exclusively using measurements of each turbine's generated power, the adaptability to modeling errors and mismatches in atmospheric conditions is shown. Convergence is reached within 400 s of operation, after which the estimation error in flow fields is negligible. At a low computational cost of 1.2 s on an 8-core CPU, this algorithm shows comparable accuracy to the state of the art from the literature while being approximately 2 orders of magnitude faster., Team Jan-Willem van Wingerden

In this paper, we present an implementation of a model predictive controller (MPC) for wind farm power tracking problem. The controller is evaluated in the high-fidelity PAral-lelized Large-eddy simulation Model (PALM). By taking measurements from PALM, we show that the closed-loop MPC can provide power reference tracking while reducing force variations on a farm level by solving a constrained optimization problem at each time step. A six turbine wind farm case study is presented in which the controller operates with yawed turbines that increases the potential power that can be harvested with the wind farm, and we show that it is possible to track a reference power signal that temporarily exceeds the power harvested when operating under the so-called greedy control settings., Team Jan-Willem van Wingerden, Team Tamas Keviczky

For short-term power predictions and estimations of the available power during curtailment of a wind farm, it is necessary to consider the flow dynamics and aerodynamic interactions of the turbines. In this paper, a control-oriented dynamic two-dimensional wind farm model is introduced that aims to incorporate real-time measurements such as flow velocities at turbine locations to estimate the ambient wind farm flow. The model is intended to derive flow predictions for real-time applications. Since fully resolved computational fluid dynamics are too CPU-intensive for such a task, the dynamic model presented in this paper relies on an approximation of the flow equations in a two-dimensional framework. A semi-Lagrangian advection scheme and a step-wise flow solver together offer fast calculation speed, which scales linearly with the number of grid points. In order to emulate effects of realistic three-dimensional wind farm flow, a relaxation of the two-dimensional continuity equation is presented. Furthermore, with little extra computational expense, additional dynamic state variables for various possible applications can be propagated along the wind flow. For instance, a dynamic confidence parameter can provide estimations of the accuracy of flow predictions, while a turbulence parameter adds the possibility to estimate wake induced loads on downstream turbines. In order to demonstrate the performance and validity of the new model it is compared with other models. At first a two turbine reference case is compared with a steady-state model and secondly with results obtained by the dynamic wind farm flow model WFSim. Finally a small wind farm is simulated in order to show the computational scaling of the model., Team Jan-Willem van Wingerden

In this paper, we extend our closed-loop optimal control framework for wind farms to minimize wake-induced power losses. We develop an adjoint-based model predictive controller which employs a medium-fidelity 2D dynamic wind farm model. The wind turbine axial induction factors are considered here as the control inputs to influence the overall performance by taking wake interactions of the wind turbines into account. A constrained optimization problem is formulated to maximize the total power production of a given wind farm. An adjoint approach as an efficient tool is utilized to compute the gradient for such a large-scale system. The computed gradient is then modified to deal with the defined final set and practical constraints on the wind turbine control inputs. The performance of the wind farm controller is examined for a more realistic test case, a layout of a 2 x 3 wind farm with dynamical changes in wind direction. The effectiveness of the proposed approach is studied through simulations., Team Jan-Willem van Wingerden

Wind turbine wake redirection is a promising concept for wind farm control to increase the total power of a wind farm. Further, the concept aims to avoid partial wake overlap on a downwind wind turbine and hence aims to decrease structural loads. Controller for wake redirection need to account for model uncertainties due to the complexity of wake dynamics. Therefore, this work focuses first on modeling a wind farm using an uncertain plant description and second on the design of a robust H∞ controller for closed-loop wake redirection by applying standard robust modeling and control techniques on a wind farm. The wake center position is estimated and fed back to a controller which uses the yaw actuator to redirect the wake. For several inflow conditions, step simulations are conducted and system identifications are performed to obtain multiple plant models. This set of models is used to derive a nominal plant and an uncertainty set. Both the nominal model and the uncertainty set define the uncertain plant model. The robust controller is then designed showing promising results in a medium-fidelity CFD simulation model with time-varying inflow conditions., Team Jan-Willem van Wingerden

Wind turbine wake redirection is a promising concept for wind farm control to increase the total power of a wind farm. Further, the concept aims to avoid partial wake overlap on a downwind wind turbine and hence aims to decrease structural loads. Controller for wake redirection need to account for model uncertainties due to the complexity of wake dynamics. Therefore, this work focuses first on modeling a wind farm using an uncertain plant description and second on the design of a robust H∞ controller for closed-loop wake redirection by applying standard robust modeling and control techniques on a wind farm. The wake center position is estimated and fed back to a controller which uses the yaw actuator to redirect the wake. For several inflow conditions, step simulations are conducted and system identifications are performed to obtain multiple plant models. This set of models is used to derive a nominal plant and an uncertainty set. Both the nominal model and the uncertainty set define the uncertain plant model. The robust controller is then designed showing promising results in a medium-fidelity CFD simulation model with time-varying inflow conditions., Team Jan-Willem van Wingerden

In this paper, we extend our closed-loop optimal control framework for wind farms to minimize wake-induced power losses. We develop an adjoint-based model predictive controller which employs a medium-fidelity 2D dynamic wind farm model. The wind turbine axial induction factors are considered here as the control inputs to influence the overall performance by taking wake interactions of the wind turbines into account. A constrained optimization problem is formulated to maximize the total power production of a given wind farm. An adjoint approach as an efficient tool is utilized to compute the gradient for such a large-scale system. The computed gradient is then modified to deal with the defined final set and practical constraints on the wind turbine control inputs. The performance of the wind farm controller is examined for a more realistic test case, a layout of a 2 x 3 wind farm with dynamical changes in wind direction. The effectiveness of the proposed approach is studied through simulations., Team Jan-Willem van Wingerden

For short-term power predictions and estimations of the available power during curtailment of a wind farm, it is necessary to consider the flow dynamics and aerodynamic interactions of the turbines. In this paper, a control-oriented dynamic two-dimensional wind farm model is introduced that aims to incorporate real-time measurements such as flow velocities at turbine locations to estimate the ambient wind farm flow. The model is intended to derive flow predictions for real-time applications. Since fully resolved computational fluid dynamics are too CPU-intensive for such a task, the dynamic model presented in this paper relies on an approximation of the flow equations in a two-dimensional framework. A semi-Lagrangian advection scheme and a step-wise flow solver together offer fast calculation speed, which scales linearly with the number of grid points. In order to emulate effects of realistic three-dimensional wind farm flow, a relaxation of the two-dimensional continuity equation is presented. Furthermore, with little extra computational expense, additional dynamic state variables for various possible applications can be propagated along the wind flow. For instance, a dynamic confidence parameter can provide estimations of the accuracy of flow predictions, while a turbulence parameter adds the possibility to estimate wake induced loads on downstream turbines. In order to demonstrate the performance and validity of the new model it is compared with other models. At first a two turbine reference case is compared with a steady-state model and secondly with results obtained by the dynamic wind farm flow model WFSim. Finally a small wind farm is simulated in order to show the computational scaling of the model., Team Jan-Willem van Wingerden

Wind turbines are often grouped together for financial reasons, but due to wake development this usually results in decreased turbine lifetimes and power capture, and thereby an increased levelized cost of energy (LCOE). Wind farm control aims to minimize this cost by operating turbines at their optimal control settings. Most state-of-the-art control algorithms are open-loop and rely on low fidelity, static flow models. Closed-loop control relying on a dynamic model and state observer has real potential to further decrease wind's LCOE, but is often too computationally expensive for practical use. In this paper two time-efficient Kalman filter (KF) variants are outlined incorporating the medium fidelity, dynamic flow model "WindFarmSimulator" (WFSim). This model relies on a discretized set of Navier-Stokes equations in two dimensions to predict the flow in wind farms at low computational cost. The filters implemented are an Ensemble KF and an Approximate KF. Simulations in which a high fidelity simulation model represents the true wind farm show that these filters are 101 - 102 times faster than a regular KF with comparable or better performance, correcting for wake dynamics that are not modeled in WFSim (noticeably, wake meandering and turbine hub effects). This is a first big step towards real-time closed-loop control for wind farms., Team Raf Van de Plas

In this paper, we present and extend the dynamic medium fidelity control-oriented Wind Farm Simulator (WFSim) model. WFSim resolves flow fields in wind farms in a horizontal, two dimensional plane. It is based on the spatially and temporally discretised two dimensional Navier-Stokes equations and the continuity equation and solves for a predefined grid and wind farm topology. The force on the flow field generated by turbines is modelled using actuator disk theory. Sparsity in system matrices is exploited in WFSim, which enables a relatively fast flow field computation. The extensions to WFSim we present in this paper are the inclusion of a wake redirection model, a turbulence model and a linearisation of the nonlinear WFSim model equations. The first is important because it allows us to carry out wake redirection control and simulate situations with an inflow that is misaligned with the rotor plane. The wake redirection model is validated against a theoretical wake centreline known from literature. The second extension makes WFSim more realistic because it accounts for wake recovery. The amount of recovery is validated using a high fidelity simulation model Simulator fOr Wind Farm Applications (SOWFA) for a two turbine test case. Finally, a linearisation is important since it allows the application of more standard analysis, observer and control techniques., Team Raf Van de Plas

This paper proposes an adjoint-based model predictive control for optimal energy extraction of wind farms. It employs the axial induction factor of wind turbines to influence their aerodynamic interactions through the wake. The performance index is defined here as the total power production of the wind farm over a finite prediction horizon. A medium-fidelity wind farm model is utilized to predict the inflow propagation in advance. The adjoint method is employed to solve the formulated optimization problem in a cost effective way and the first part of the optimal solution is implemented over the control horizon. This procedure is repeated at the next controller sample time providing the feedback into the optimization. The effectiveness and some key features of the proposed approach are studied for a two turbine test case through simulations., Team Raf Van de Plas

Wind turbines are often grouped together for financial reasons, but due to wake development this usually results in decreased turbine lifetimes and power capture, and thereby an increased levelized cost of energy (LCOE). Wind farm control aims to minimize this cost by operating turbines at their optimal control settings. Most state-of-the-art control algorithms are open-loop and rely on low fidelity, static flow models. Closed-loop control relying on a dynamic model and state observer has real potential to further decrease wind's LCOE, but is often too computationally expensive for practical use. In this paper two time-efficient Kalman filter (KF) variants are outlined incorporating the medium fidelity, dynamic flow model "WindFarmSimulator" (WFSim). This model relies on a discretized set of Navier-Stokes equations in two dimensions to predict the flow in wind farms at low computational cost. The filters implemented are an Ensemble KF and an Approximate KF. Simulations in which a high fidelity simulation model represents the true wind farm show that these filters are 101 - 102 times faster than a regular KF with comparable or better performance, correcting for wake dynamics that are not modeled in WFSim (noticeably, wake meandering and turbine hub effects). This is a first big step towards real-time closed-loop control for wind farms., Team Raf Van de Plas

In this paper, we present and extend the dynamic medium fidelity control-oriented Wind Farm Simulator (WFSim) model. WFSim resolves flow fields in wind farms in a horizontal, two dimensional plane. It is based on the spatially and temporally discretised two dimensional Navier-Stokes equations and the continuity equation and solves for a predefined grid and wind farm topology. The force on the flow field generated by turbines is modelled using actuator disk theory. Sparsity in system matrices is exploited in WFSim, which enables a relatively fast flow field computation. The extensions to WFSim we present in this paper are the inclusion of a wake redirection model, a turbulence model and a linearisation of the nonlinear WFSim model equations. The first is important because it allows us to carry out wake redirection control and simulate situations with an inflow that is misaligned with the rotor plane. The wake redirection model is validated against a theoretical wake centreline known from literature. The second extension makes WFSim more realistic because it accounts for wake recovery. The amount of recovery is validated using a high fidelity simulation model Simulator fOr Wind Farm Applications (SOWFA) for a two turbine test case. Finally, a linearisation is important since it allows the application of more standard analysis, observer and control techniques., Team Raf Van de Plas

This paper proposes an adjoint-based model predictive control for optimal energy extraction of wind farms. It employs the axial induction factor of wind turbines to influence their aerodynamic interactions through the wake. The performance index is defined here as the total power production of the wind farm over a finite prediction horizon. A medium-fidelity wind farm model is utilized to predict the inflow propagation in advance. The adjoint method is employed to solve the formulated optimization problem in a cost effective way and the first part of the optimal solution is implemented over the control horizon. This procedure is repeated at the next controller sample time providing the feedback into the optimization. The effectiveness and some key features of the proposed approach are studied for a two turbine test case through simulations., Team Raf Van de Plas

Modelling of the behaviour of compliant mechanisms leads to a better understanding and synthesis of designed mechanisms. Static and dynamic responses for compliant mechanisms have been researched extensively. While impact modelling is a well known field in rigid body dynamics, impact modelling in compliant mechanisms research is lacking. By combining the fields of dynamic modelling of compliant mechanisms using the pseudo-rigid-body model and rigid body impact modelling a technique is proposed. The efficiency of the impact is considered as the amount of energy fed back into the first mode shape, for which the compliant mechanism was designed. Energy is expected to be lost higher frequency vibrations of the system. Modelling and experiments were done for a case study to show the effects of impacting in line with and outside of the centre of mass with varying impact angles. Results for an increasing impact angle show less energy returned to the fundamental mode shape. Impacting outside of the centre of mass shows asymmetric results and impacting closer to the base from the centre of mass results in less energy loss than further from the base. Using rigid body impact modelling on the pseudo-rigid-body dynamic model (PRBDM) provides quick simulations including impact. The single degree of freedom of the PRBDM does not capture the effects of higher mode shapes outside of extra energy losses from the first mode. Therefore a two rotation pseudo-rigid-body model (2R-PRBM) is converted into a dynamic model and is applied to the case study including impact equations. This model has multiple degrees of freedom and can therefore contain the higher frequencies in which energy is lost. The dynamic 2R-PRBM provides the same response for an impact in line with the centre of mass and straight path and shows energy moves to higher frequencies at a shifted impact position or angle. The amount of energy loss currently does not match the experiments. Expected cause are assumptions made, Precision and Microsystems Engineering, Mechanical, Maritime and Materials Engineering

Modelling of the behaviour of compliant mechanisms leads to a better understanding and synthesis of designed mechanisms. Static and dynamic responses for compliant mechanisms have been researched extensively. While impact modelling is a well known field in rigid body dynamics, impact modelling in compliant mechanisms research is lacking. By combining the fields of dynamic modelling of compliant mechanisms using the pseudo-rigid-body model and rigid body impact modelling a technique is proposed. The efficiency of the impact is considered as the amount of energy fed back into the first mode shape, for which the compliant mechanism was designed. Energy is expected to be lost higher frequency vibrations of the system. Modelling and experiments were done for a case study to show the effects of impacting in line with and outside of the centre of mass with varying impact angles. Results for an increasing impact angle show less energy returned to the fundamental mode shape. Impacting outside of the centre of mass shows asymmetric results and impacting closer to the base from the centre of mass results in less energy loss than further from the base. Using rigid body impact modelling on the pseudo-rigid-body dynamic model (PRBDM) provides quick simulations including impact. The single degree of freedom of the PRBDM does not capture the effects of higher mode shapes outside of extra energy losses from the first mode. Therefore a two rotation pseudo-rigid-body model (2R-PRBM) is converted into a dynamic model and is applied to the case study including impact equations. This model has multiple degrees of freedom and can therefore contain the higher frequencies in which energy is lost. The dynamic 2R-PRBM provides the same response for an impact in line with the centre of mass and straight path and shows energy moves to higher frequencies at a shifted impact position or angle. The amount of energy loss currently does not match the experiments. Expected cause are assumptions made, Precision and Microsystems Engineering, Mechanical, Maritime and Materials Engineering

Materials Science and Engineering, Mechanical, Maritime and Materials Engineering

The microstructure of an object of dual phase steel is modelled with an Oriented Cylinder Model, where the martensite grains in the steel object are modelled as oriented cylinders that are randomly distributed within a big block. By cutting this block parallel to the cylinder axes, rectangular visible profiles of the cut cylinders can be observed from the cut-plane. To translate the two-dimensional information about the rectangles to three-dimensional information about the cylinders, an inverse relationship between the bivariate probability density function of the height and squared half-width of a rectangle and the bivariate density of the height and squared radius of a cylinder is established. The former density is estimated by a bivariate modified Gamma kernel density estimator, and the relationship between the two densities is used to numerically transform this estimator into an estimator for the latter density. For the selection of the bandwidth parameters of the kernel density estimator, both a method based on the Integrated Squared Error of the kernel density estimator and a method based on the Integrated Squared Error of the transformed estimator are considered. The estimator for the height and squared radius of a cylinder is constructed for the underlying density of an example data set as well as for the underlying density of an experimental data set. These bivariate estimators are used to construct an estimator for the marginal density of the squared radius of a cylinder and the density of the volume of a cylinder., Statistics, Applied mathematics, Electrical Engineering, Mathematics and Computer Science

Materials Science and Engineering, Mechanical, Maritime and Materials Engineering

The microstructure of an object of dual phase steel is modelled with an Oriented Cylinder Model, where the martensite grains in the steel object are modelled as oriented cylinders that are randomly distributed within a big block. By cutting this block parallel to the cylinder axes, rectangular visible profiles of the cut cylinders can be observed from the cut-plane. To translate the two-dimensional information about the rectangles to three-dimensional information about the cylinders, an inverse relationship between the bivariate probability density function of the height and squared half-width of a rectangle and the bivariate density of the height and squared radius of a cylinder is established. The former density is estimated by a bivariate modified Gamma kernel density estimator, and the relationship between the two densities is used to numerically transform this estimator into an estimator for the latter density. For the selection of the bandwidth parameters of the kernel density estimator, both a method based on the Integrated Squared Error of the kernel density estimator and a method based on the Integrated Squared Error of the transformed estimator are considered. The estimator for the height and squared radius of a cylinder is constructed for the underlying density of an example data set as well as for the underlying density of an experimental data set. These bivariate estimators are used to construct an estimator for the marginal density of the squared radius of a cylinder and the density of the volume of a cylinder., Statistics, Applied mathematics, Electrical Engineering, Mathematics and Computer Science

De Taut String methode wordt toegepast binnen een Current Status model, om zo binnen dat model een verdelingsfunctie te schatten., Applied mathematics, Electrical Engineering, Mathematics and Computer Science

De Taut String methode wordt toegepast binnen een Current Status model, om zo binnen dat model een verdelingsfunctie te schatten., Applied mathematics, Electrical Engineering, Mathematics and Computer Science