the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A reference opensource controller for fixed and floating offshore wind turbines
Nikhar J. Abbas
Daniel S. Zalkind
Lucy Pao
Alan Wright
This paper describes the development of a new reference controller framework for fixed and floating offshore wind turbines that greatly facilitates controller tuning and represents standard industry practices. The reference wind turbine controllers that are most commonly cited in the literature have been developed to work with specific reference wind turbines. Although these controllers have provided standard control functionalities, they are often not easy to modify for use on other turbines, so it has been challenging for researchers to run representative, fully dynamic simulations of other wind turbine designs. The Reference OpenSource Controller (ROSCO) has been developed to provide a modular reference wind turbine controller that represents industry standards and performs comparably to or better than existing reference controllers. The formulation of the ROSCO controller logic and tuning processes is presented in this paper. Control capabilities such as tip speed ratio tracking generator torque control, minimum pitch saturation, wind speed estimation, and a smoothing algorithm at nearrated operation are included to provide modern controller features. A floating offshore wind turbine feedback module is also included to facilitate growing research in the floating offshore arena. All of the standard controller implementations and control modules are automatically tuned such that a noncontrols engineer or automated optimization routine can easily improve the controller performance. This article provides the framework and theoretical basis for the ROSCO controller modules and generic tuning processes. Simulations of the National Renewable Energy Laboratory (NREL) 5 MW reference wind turbine and International Energy Agency 15 MW reference turbine on the University of Maine semisubmersible platform are analyzed to demonstrate the controller's performance in both fixed and floating configurations, respectively. The simulation results demonstrate ROSCO's peak shaving routine to reduce maximum rotor thrusts by over 10 % compared to the NREL 5 MW reference wind turbine controller on the landbased turbine and to reduce maximum platform pitch angles by nearly 30 % when using the platform feedback routine instead of a more traditional lowbandwidth controller.
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As wind turbine research has evolved during the past few decades, the need for reference wind turbine controllers has also changed. Traditionally, reference wind turbine controllers have been used for two primary purposes. First, the control systems research community has extensively used reference controllers as a baseline to compare and evaluate more modern and advanced control algorithms (Lackner and van Kuik, 2010; Schlipf et al., 2013). Second, researchers interested in aerostructural dynamics have used reference controllers to enable dynamic simulations in studies concerning other aspects of the wind turbine (Wayman et al., 2006; Sathe et al., 2013). In both applications, a reference controller provides a standardized method by which wind energy researchers can compare and contrast their various turbine designs, aerodynamic models, structural analysis tools, and more.
There has been a lack of reference controllers that can be easily adapted to a wide variety of different wind turbines. The National Renewable Energy Laboratory (NREL) and the Technical University of Denmark (DTU) have published perhaps the most ubiquitous of these reference turbines and respective controllers with the NREL 5 MW (Jonkman et al., 2009) and DTU 10 MW (Bak et al., 2013; Hansen and Henriksen, 2013) turbine models. Generally, for new turbine models, the tuning processes for these turbines' respective controllers necessitate a control systems engineer to generate linear models of the turbine at multiple operating points using aeroelastic simulation solvers to schedule controller gains. At the very least, someone familiar with the NREL 5 MW reference controller tuning process must be able to adequately modify the controller accordingly, as shown in Griffith and Ashwill (2011), where the reference controller is scaled for a rotor with a novel blade design.
Additionally, trends in the wind energy industry heavily favor larger and more flexible rotor designs (Veers et al., 2019). As wind turbines have grown and modeling tools have improved and increased in fidelity, design constraints – such as blade tip deflection – have become increasingly important. Without a controller that performs consistently across turbine designs and is representative of the controllers in the field, dynamic simulations cannot be entirely trusted to provide reliable results that can be used for turbine design. The need to run representative dynamic simulations of large flexible turbines necessitates a controller and controller tuning process that can be implemented consistently by the noncontrols engineer in a streamlined fashion.
Finally, completely automated optimization tools for medium to highfidelity wind turbine designs are becoming well established in research and industry. These tools – such as the WindPlant Integrated System Design & Engineering Model (WISDEM^{®}) (Dykes et al., 2014), HawtOpt (Zahle et al., 2015), and Cpmax (Bottasso et al., 2012) – generally include some element of dynamic wind turbine simulation within the optimization loop. Naturally, changes in the wind turbine design often necessitate an update to the controller. An automated controller tuning process and generalized implementation method provide the opportunity for automated control codesign, where the system and controller are designed concurrently (GarciaSanz, 2019; Zalkind et al., 2020).
In addition to the need for a generic controller for landbased and fixedbottom wind turbines, to the authors' knowledge, the availability of a modern, opensource controller with specific logic for floating offshore wind turbines (FOWTs) is not available. Simply reducing the controller bandwidth, as presented by Larsen and Hanson (2007), has been shown to have disadvantages (Fleming et al., 2014). For the same reasons that a generic controller with automated tuning processes is useful for landbased turbines and rotor design, a specific control implementation for FOWTs has its own utility.
There are numerous motivations for the development of the Reference OpenSource Controller (ROSCO) tool chain and the publication of this paper. Continued development, refinement, and expansion of the Delft Research Controller (Mulders and van Wingerden, 2018) provide a wind turbine controller that is consistent with industrystandard control functionalities for use in the research community. Additionally, the implementation of generalized tuning procedures through opensource software provides a means for noncontrols engineers to conveniently implement and modify a standard wind turbine controller for use in their research applications. This paper provides a more theoretically comprehensive collection of how to tune and implement a baseline wind turbine controller for fixed and floating applications than currently exists in the literature. Specifically, the presented methods contribute, in detail, to the growing body of scientific literature in the wind energy field and show how analytical turbine models and power coefficient surfaces can be used to rapidly tune a wind turbine controller in a completely automated fashion. This paper also provides methods for analytical tuning of a feedback term and pitch saturation routines to specifically address challenges presented by floating offshore wind turbines. Finally, these generalized tuning procedures and controller implementations provide a framework by which systems design optimization tools such as WISDEM can include a controller for timedomain simulations in the optimization loop.
The structure of this paper is as follows. In Sect. 2, we give a highlevel overview of the ROSCO tool chain and implementation methods. Here, we also discuss the structure of the ROSCO controller and some requisite theoretical background for the proceeding sections. In Sects. 3 and 4, we discuss the primary generator torque and collective blade pitch controllers, respectively. In Sect. 5, we provide details on the primary individual “modules” of the controller. For each module detailed in this paper, we provide a review of its purpose, how the generic tuning processes are applied, and in some cases a brief timedomain simulation result to showcase its functionality. Then, in Sect. 6, we provide power and loads analysis results for the ROSCO controller on turbines in both landbased and floating configurations. Finally, Sect. 7 discusses some conclusions and future directions of ROSCO.
ROSCO was developed to provide a modular control systems architecture with a Fortranbased software structure similar to that of OpenFAST (NREL, 2019), a complete aeroservohydroelastic wind turbine simulation tool developed at NREL. The initial work and foundation for the ROSCO controller was done by researchers at the Delft University of Technology and presented in Mulders and van Wingerden (2018). The standard controller functionalities are designed to perform comparably with existing reference controllers in the literature, such as the NREL 5 MW and DTU 10 MW controllers. In addition to the standard control functionalities, a number of operational controller features are included to represent more modern wind turbine control functionalities. The primary functions of the controller are still to maximize power in belowrated operation and to regulate rotor speed in aboverated operation. The controller was developed to communicate with wind turbine simulation software (e.g., OpenFAST) using the Bladedstyle control interface (DNVGL, 2018). The controller source code is compiled once and reads a controller input file. The controller input file can be renamed and changed for any horizontalaxis wind turbine, and it is generally referred to as the “DISCON.IN” file.
To facilitate usage of ROSCO, a related “ROSCO toolbox” was developed. The ROSCO toolbox is a Pythonbased tool set developed for tuning, implementing, and postprocessing OpenFAST simulations using ROSCO. Both ROSCO and the ROSCO toolbox are available for download and implementation on GitHub (NREL, 2021): https://github.com/NREL/ROSCO (last access: 10 November 2021).
The primary purpose of the ROSCO toolbox is to automatically execute the generalized tuning procedures for a given OpenFAST turbine model and to generate the necessary input file for the controller. A separate .yaml (BenKiki et al., 2009) formatted parameter file is used for these generic tuning procedures. This file includes relevant turbine and controller tuning parameters that are generally available a priori. Only four parameters are necessary for tuning a complete controller, though additional tuning inputs are available for the user to introduce further modifications and finetune the controller performance. In addition to the controller tuning scripts, postprocessing scripts, plotting scripts, and a MATLAB/Simulink version (MATLAB, 2019) of ROSCO are available through the ROSCO toolbox.
The general workflow for using the ROSCO tool chain is shown in Fig. 1. The tuning file provides necessary controller tuning inputs to the ROSCO toolbox. The ROSCO toolbox then reads an OpenFAST model and writes the DISCON.IN file. The DISCON.IN file is used as the input file to the ROSCO controller and can be directly modified to change the controller performance, to turn on and off individual control modules, or to change the desired control logic. OpenFAST communicates with ROSCO using the Bladedstyle control interface.
The work by Mulders and van Wingerden (2018) modularized the controller architecture and established an input file framework for the compiled Fortran code. Since then, numerous modules and controller features have been introduced and the functionalities of the controller have been expanded significantly into what is now ROSCO. In this article, we provide an overview of the primary controller modules that are generically tuned by the ROSCO toolbox or were added specifically for ROSCO.
2.1 Control regions
There are generally two methods of actuation in the standard reference wind turbine controllers, including ROSCO. A variablespeed generator torque controller is used to control the generator power, and a collective blade pitch controller is used to regulate rotor speed. These methods of actuation are commonly separated into four regions of operation, with transition logic between them. The steadystate operating points, as shown in Fig. 2 for the NREL 5 MW and International Energy Agency (IEA) 15 MW wind turbines, are a convenient way to visualize the regions of operation.
In Fig. 2, regions 1 and 4 are considered to be below cutin wind speed and above cutout wind speed, respectively, so they are not of particular interest. Here, we provide a brief overview of each region and compare how they are implemented in the NREL 5 MW reference wind turbine controller versus ROSCO. In the following sections, we provide more indepth descriptions of the logic and tuning processes.
Region 1 is when the wind speed is below the turbine's cutin wind speed. This region is generally uninteresting for standard control purposes, and it is not shown in Fig. 2 for either turbine.
Region 1.5 is when the wind speed is above the turbine's cutin wind speed, but the turbine cannot operate at its optimal tip speed ratio (TSR). In the traditional NREL 5 MW reference controller, a linear transition from no generator torque to the minimum optimal generator torque is used. In ROSCO, a proportionalintegral (PI) controller modifies the generator torque to maintain a defined minimum rotor speed, and the blades are pitched to their minimum allowable blade pitch angle. In turbines designed to operate at a higher TSR in low wind speeds because of a minimum rotor speed constraint, minimum blade pitch angles can be scheduled by a wind speed estimate to improve power output (see Sect. 5.3.2). ROSCO's different Region 1.5 behaviors are shown in Fig. 2, where Region 1.5 does not span a specific range of wind speeds for the NREL 5 MW wind turbine because of the use of a PI controller, and increased blade pitch angles are seen in low wind speeds for the IEA 15 MW turbine.
Region 2 is when the wind speed is large enough that the turbine can operate at its optimal TSR but is still below rated. Here, the torque controller aims to maximize power as much as possible, and the blade pitch angle is fixed. In ROSCO, the generator torque controller either follows a traditional squared law (Bossanyi, 2000) or employs a TSR tracking PI controller (see Sect. 3.1.2) to track a rotor speed reference that is based on a wind speed estimate (see Sect. 5.1) and optimal TSR. The blades are pitched to fine pitch, where they are generally designed to be the most aerodynamically efficient.
Region 2.5 is when the wind speed is larger than the wind speed that corresponds with rated rotor speed, but less than the wind speed that corresponds with rated power. Here, the turbine operates in transition between regions 2 and 3. In the NREL 5 MW reference controller, a linear transition and switching logic are used across this transitional range of wind speeds. In ROSCO, a PI controller is used in both the pitch and torque controllers to regulate the rotor speed to their respective set points. A set point smoother (see Sect. 5.2) is used to ensure that only the pitch or torque controller is active at any point in time and that there is a smooth transition between them.
Region 3 is when the wind speed is above rated. The blade pitch controller regulates the rotor speed, and the generator torque is either constant or maintains constant power output. In ROSCO, a gainscheduled PI collective pitch controller is used to regulate the rotor speed. For floating systems, the NREL 5 MW reference controller reduces the pitch controller bandwidth to prevent platform instability. In ROSCO, an additional feedback term is added to this controller for FOWTs (see Sect. 5.5) to help stabilize the platform using collective pitch, without the need to detune the rotor speed controller. The generator torque is either kept constant at its rated torque value, or the controller adjusts the torque to maintain constant power output.
Region 4 is when the wind speed is greater than the turbine's cutout wind speed. Here, the blades are pitched to reduce rotor thrust to zero. Other than triggering a shutdown maneuver, this region is also generally uninteresting for standard control purposes and is not shown in Fig. 2.
In the case of the generator torque and blade pitch controllers, a generator speed signal is lowpass filtered and fed back to the respective controllers. The lowpass filter can be chosen as a first or secondorder filter, and the ROSCO toolbox tuning process generically tunes the cutoff frequency for the filter to be onequarter of the blade's first edgewise natural frequency, as suggested in Jonkman et al. (2009). This helps prevent the controller from actuating at a frequency that excites the first edgewise mode of the blade.
2.2 Implementation structure
The highlevel block diagram of ROSCO shown in Fig. 3 provides an overview of the control modules that are implemented in ROSCO. The combination of these modules ensures smooth actuation across the range of operation regions, as described in Sect. 2.1. Table 1 provides a brief description of each controller module.
2.3 The power coefficient surface
Many tuning procedures and module implementations in this work are based on the socalled C_{p} surface. The power coefficient, C_{p}, is the ratio of the power extracted from the wind to the power available in the wind (Burton et al., 2011). For any given wind speed, the C_{p} surface can be calculated to represent the aerodynamic efficiency of the turbine as a function of collective blade pitch angle and TSR. The TSR is the ratio of the speed of the tip of the wind turbine blade to the rotoraveraged wind speed:
where ω_{r} is the rotor speed, R is the rotor radius, and v is the wind speed. Similar parameter surfaces can be generated for the thrust and torque coefficients of the turbine, C_{t} and C_{q}, respectively. An example C_{p} surface is shown in Fig. 4 for the IEA 15 MW wind turbine (Gaertner et al., 2020).
The overlaid lines on the C_{p} surface shown in Fig. 4 represent the expected steadystate operation point of the wind turbine. The dashed–dotted black line shows the steadystate operating points at low wind speeds, where the TSR is high because of a constraint on the wind turbine's minimum rotor speed. By imposing a blade pitch angle that is greater than fine pitch at low wind speeds, the turbine can operate at a higher point on the C_{p} surface. In belowrated operation, the turbine is expected to operate with a fixed blade pitch angle and a constant TSR (see Fig. 2); this operation point is denoted by the red dot in Fig. 4. In aboverated wind speeds, the blades pitch to regulate the rotor speed, and there is a reduction in TSR (see Fig. 2), as denoted by the dashed blue line in Fig. 4.
In the standard ROSCO toolbox tuning procedure, the steadystate blade element momentum solver CCBlade (Ning, 2013) is used to find the C_{p}, C_{t}, and C_{q} surfaces quickly and efficiently. Similarly, parameter surfaces can be generated and written to a text file using any other blade element momentum or coupled aeroelastic solver. Using more complex solvers will, naturally, provide a more realistic C_{p} surface, though with a significant increase in computation time. Anecdotally, the authors have found the C_{p} surfaces generated using CCBlade to be sufficiently accurate for controller synthesis on numerous wind turbines thus far. Future work includes a more substantive analysis of the controller performance sensitivity to C_{p} surfaces generated using different aerodynamic solvers.
Within the ROSCO toolbox tuning processes, the C_{p} surface is primarily used to facilitate the calculation of the plant parameters, as discussed in Sect. 2.4. These parameters are used for tuning the blade pitch and generator torque controller gains and for accurate implementation of the wind speed estimator. The C_{p} surface is also used to determine the minimum blade pitch schedule in low wind speeds, if needed, and to determine the optimal belowrated TSR to maximize power output. Finally, the C_{p} surface is used within ROSCO itself so that the wind speed estimator can accurately estimate the operational state of the wind turbine. The C_{t} surface is used to determine the minimum blade pitch schedule for the socalled “peak shaving” routine, as described in Sect. 5.3.1.
2.4 Plant model
A number of generic tuning processes have been developed for the ROSCO controller. The first publication on this work (Abbas et al., 2020) provided an initial formulation of the primary tuning processes in ROSCO. By using simplified analytical models of the wind turbine, the need for numerical linearization routines using servoaeroelastic codes such as OpenFAST is avoided. To define the simplified wind turbine for control systems development, a firstorder model of the wind turbine is used (Pao and Johnson, 2011):
where the aerodynamic torque is
In Eq. (2), ω_{g} is the generator speed, J is the rotor inertia, N_{g} is the gearbox ratio, τ_{g} is the generator torque, and η_{gb} is the gearbox efficiency. In Eq. (3), ρ is the air density, and A_{r} is the rotor area. The power coefficient C_{p}(λ,β) is found via lookup table. The firstorder linearization of Eq. (3) at some nominal steadystate operational point is
where ${\mathrm{\Gamma}}_{{\mathit{\omega}}_{\mathrm{g}}}=\partial {\mathit{\tau}}_{\mathrm{a}}/\partial {\mathit{\omega}}_{\mathrm{g}}$, ${\mathrm{\Gamma}}_{\mathit{\beta}}=\partial {\mathit{\tau}}_{\mathrm{a}}/\partial \mathit{\beta}$, and ${\mathrm{\Gamma}}_{v}=\partial {\mathit{\tau}}_{\mathrm{a}}/\partial v$, and “op” denotes the expected steadystate operational ω_{g}, β, and v for any linearization point. Equation (2) can then be rewritten in a linearized form as
where Δ denotes a perturbation from the steadystate value. Equation (5) is the plant model used to define the generator torque and blade pitch controller gains, where
and λ is the tip speed ratio as defined in Eq. (1). The coefficients ${B}_{{\mathit{\tau}}_{\mathrm{g}}}$ and B_{β}(v_{op}) are described in Sects. 3.1.2 and 4, where the blade pitch and generator torque controllers are described, respectively. To calculate the C_{p} surface gradients, a secondorder central differencing approach is used.
This linearized plant model is used to separately tune above and belowrated controllers. Note that B_{v}, the disturbance (Δv) input matrix to the system, is set to 0 for the controller tuning.
2.5 Proportionalintegral reference tracking control
A reference tracking PI controller is used in aboverated and belowrated operation. The PI controller is generically defined as
where u is an input to the controller, y is the output from the controller passed to the wind turbine, and k_{p} and k_{i} are the proportional and integral gains, respectively. For example, the standard PI blade pitch controller has inputs and outputs such that
and the TSR tracking PI generator torque controller has inputs such that
In Eqs. (10) and (11), the generator speed error input, −Δω_{g}, is defined as a perturbation from the reference speed such that
while Δβ and Δτ_{g} are perturbations from their respective nominal steadystate values such that
By combining the PI controller formulation in Eq. (9) with Eq. (10) or Eqs. (11) and (5), a differential equation relating the reference generator speed perturbation Δω_{g,ref} and the actual generator speed perturbation Δω_{g} is obtained. If we take the Laplace transform of this differential equation, the closedloop transfer function from Δω_{g,ref}=0 to Δω_{g} results in
where B is either ${B}_{{\mathit{\tau}}_{\mathrm{g}}}$ or B_{β}(v_{op}), depending on whether the turbine is in below or aboverated operation, respectively. A block diagram to visualize this closedloop system in aboverated operation is shown in Fig. 5. Note that Δω_{g,ref}=0 because we would not like the rotor speed to differ from the reference value, ω_{g,ref}.
This closedloop system is a simple secondorder system, so we define the PI gains as
where the closedloop response is characterized by a desired natural frequency, ω_{des}, and damping ratio, ζ_{des}. For a standard horizontalaxis wind turbine, B is negative in below and aboverated operation, so k_{i} and k_{p} are negative. Therefore, based on this formulation, an increase in rotor speed results in $\mathrm{\Delta}{\mathit{\omega}}_{\mathrm{g}}<\mathrm{0}$ and an increase in generator torque or blade pitch angle. By defining the desired natural frequency and damping ratio of the rotor speed response, the user can modify the dynamic response of the rotor to changes in the wind speed. Increased desired natural frequencies will decrease the response time of the rotor, whereas increased damping ratios will reduce the amount of oscillation in the response. To learn more about secondorder system responses, the authors recommend Franklin et al. (2019) to the curious reader.
If PI controllers are employed for below and aboverated operation, we are left with the need to define four controller tuning inputs. The choice of ω_{des} and ζ_{des} for the below and aboverated operating regions is the only parameter decision that needs to be made by the control designer or optimization routine, though additional tuning of the individual modules discussed in Sect. 5 might further improve controller performance.
2.6 Filters
Four filters are commonly used in the ROSCO controller (see Fig. 3): first and secondorder lowpass filters, a firstorder highpass filter, and a notch filter. Appendix A shows the continuoustime formulations of these filters. The filters are converted to discrete time for implementation using the bilinear transform.
Four total variablespeed generator torque control methods are available in ROSCO (see Table 1). Two methods of optimal power generation are available for belowrated operation, and two methods of maintaining power output near the turbine's rated value are available in aboverated operation.
3.1 Belowrated torque control
In belowrated operation, the generator torque controller's goal is to maximize power production. If the blades are pitched to fine pitch, maximum aerodynamic efficiency can be achieved and power can be maximized if the torque controller maintains the TSR corresponding to the peak of the C_{p} surface. In ROSCO, this is done in one of two ways.
3.1.1 Kω^{2} law
A study of Eq. (2) in steady state, such that ${\dot{\mathit{\omega}}}_{\mathrm{g}}=\mathrm{0}$, provides the foundation for the socalled “$K{\mathit{\omega}}_{\mathrm{g}}^{\mathrm{2}}$ law” for optimal torque control (Bossanyi, 2000; Johnson et al., 2006). By restructuring Eq. (2), and assuming that the wind turbine is operating at its optimal TSR, λ_{opt}, and corresponding power coefficient, C_{p,max}, one can realize a quadratic relationship between the generator speed and demanded generator torque. This relationship is commonly defined as
3.1.2 Tip speed ratio tracking torque control
Two primary motivations are behind the development of the TSR tracking controller in ROSCO. First, although the $K{\mathit{\omega}}_{\mathrm{g}}^{\mathrm{2}}$ law has historically worked reliably in idealized simulation environments, the calculation of K can be subject to modeling and assumption errors. For example, the assumption that R is a constant value across wind speeds does not hold as strongly in modern, highly flexible rotors as it has in the past. Fortunately, modern rotors are still commonly designed to maximize aerodynamic efficiency at a specific TSR. Second, industry collaborators have indicated that a TSR tracking controller is more representative of the controllers often used in the field.
If the blades are pitched to their most aerodynamically efficient angle and the wind turbine rotor is operating at its optimal TSR, the turbine power is theoretically maximized. This suggests that if the wind speed can be measured or estimated accurately, a generator torque controller can be designed to maintain the rotor's λ_{opt} and maximize power capture. In ROSCO, a standard PI controller is used to track a generator speed reference. For the generator torque controller:
where $\widehat{v}$ is the estimated rotoreffective wind speed provided by the wind speed estimator described in Sect. 5.1. This reference signal is also constrained by
where ω_{g,min} is the minimum allowable generator speed, and the subscript “rated” denotes the value as calculated at rated operation.
A straightforward and automated tuning process has been developed for the PI gains for the TSR tracking torque controller. With the assumption that the blade pitch is held constant at fine pitch in belowrated operation, Δβ=0 in Eq. (5). This means that $B={B}_{{\mathit{\tau}}_{\mathrm{g}}}$ in Eqs. (15) and (16) and is defined as
for the generator torque controller. With this, ω_{des} and ζ_{des} can be chosen to describe the belowrated closedloop rotor speed response, and Eqs. (15) and (16) can be calculated for the generator torque controller. Equation (15) suggests that k_{p}(v) and A(v) are both dependent on v; however, it was found that fixing ${k}_{\text{p,vs}}={k}_{\mathrm{p}}(v={v}_{\text{rated}})$, where the subscript “vs” denotes variablespeed torque control, simplifies the controller implementation without negatively affecting power production or generator loads.
3.2 Aboverated torque control
There are two standard methods of actuating the generator torque in aboverated operation. Defining P as the generator power output, in aboverated operation the generator torque is defined to be
for constant torque or constant power output, respectively.
If the $K{\mathit{\omega}}_{\mathrm{g}}^{\mathrm{2}}$ law is used for belowrated torque control, the torque controller switches to aboverated operation when the blades are pitched beyond an offset, denoted by PC_Switch
in the DISCON.IN file. When the turbine is in aboverated operation, the generator torque is then defined directly by the relationships in Eq. (21). If the TSR tracking control is used for belowrated operation, the aboverated generator torque output is simply constrained such that τ_{g}(t)≤τ_{g,ar}(t). In aboverated operation, the set point smoother (see Sect. 5.2) shifts the reference generator speed such that the generator torque is saturated at its maximum allowable value, resulting in either constant torque or constant power output.
If constant torque control is used, power output changes are directly correlated to the changes in the generator speed in aboverated operation. If constant power control is used, there are still some changes in power output because ω_{g}(t) in Eq. (21) is lowpass filtered, but the power is more consistent than in the constant torque case. As discussed by Jonkman (2010), using a constant generator torque controller in aboverated operating conditions can help improve FOWT platform stability.
In belowrated operation, the generator speed is less than the rated generator speed, so the blade pitch angle, β, saturates at β=β_{min}. This is generally the finepitch angle, unless a pitch saturation schedule is implemented, as described in Sect. 5.3.
In aboverated operation, a PI controller is used to determine the collective blade pitch angle to keep the turbine at a rotor speed reference. The aboverated rotor speed reference ω_{g,ref} for the blade pitch controller is generally defined as
It is well established, and common in reference controllers, to employ a gain schedule to improve blade pitch controller performance (Jonkman et al., 2009; Hansen and Henriksen, 2013; Mulders and van Wingerden, 2018). In the ROSCO toolbox we use the C_{p} surface to prescribe this gain schedule, rather than using aeroservoelastic linearization tools.
When tuning the pitch controller's gain schedule, we cannot directly assume that the generator torque is kept constant because it may change if constant power operation is used. In constant power operation, the firstorder Taylor series expansion of the generator torque in Eq. (21) is
Considering that the generator torque as defined by Eq. (13) can be rewritten as ${\mathit{\tau}}_{\text{g,ar}}\left(t\right)={\mathit{\tau}}_{\text{g,rated}}+\mathrm{\Delta}{\mathit{\tau}}_{\mathrm{g}}$ in aboverated wind speeds, we define
If constant power operation is used, then A(v_{op}) in Eq. (6) is redefined to
For constant torque operation, it can be assumed that Δτ_{g}=0, so no modifications are made to A(v_{op}). In both cases, B in Eqs. (15) and (16) is
For any wind speed v_{op}, the expected steadystate C_{p,op} can be calculated by (Bottasso and Croce, 2009)
Through the relationship in Eq. (27) and the C_{p} surface, we can find the expected blade pitch angles, β_{op}(λ_{op}), for any TSR. In steadystate aboverated operation the generator speed is considered to be constant, so the TSR is only a function of the wind speed, and we can define β_{op}(v). This enables us to change A(v_{op}) and B_{β}(v_{op}) to be A(β_{op}) and B_{β}(β_{op}) for controller tuning purposes. Equations (15) and (16) are then defined for the blade pitch controller to be k_{p,pc}(β_{op}) and k_{i,pc}(β_{op}), and the blade pitch controller gain schedule can be implemented as a function of blade pitch angle rather than an estimated wind speed. In the ROSCO implementation of the blade pitch controller, a lowpassfiltered blade pitch angle, β_{lpf}, is used to interpolate the necessary pitch controller gains, k_{p,pc}(β_{lpf}(t)) and k_{i,pc}(β_{lpf}(t)), for the PI controller at each time step.
Notably, the C_{p} surface gradients used to calculate both A(v_{op}) and B(v_{op}) approach zero near the “peak” of the C_{p} surface. Because B_{β}(v_{op}) is in the denominator of Eqs. (15) and (16), the gains would theoretically approach infinity near rated operation. To avoid unrealistically high gains, A(v_{op}) and B(v_{op}) are each approximated by a linear fit for the blade pitch controller gain calculation in the ROSCO toolbox. With this foundation, the blade pitch controller's gain schedule can be generated using the ROSCO toolbox for any userdefined ω_{des} and ζ_{des}.
ROSCO is modularized such that various control methods can be switched on and off without the need to recompile any code. Here, we present the theoretical foundations for the module implementations and their respective generic tuning processes.
5.1 Wind speed estimator
In this section, we discuss the wind speed estimator used in ROSCO. The wind speed estimate is used in the TSR tracking generator torque controller (see Sect. 3.1.2) and pitch saturation (see Sect. 5.3) routines. The employed wind speed estimator is inspired by Knudsen et al. (2011) and is based on a continuous–discrete extended Kalman filter. The theoretical background of the continuous and discrete time extended Kalman filters used in this work is further detailed in Grewal and Andrews (2014). The Kalman filter uses informed definitions of the covariance matrices based on the expected wind fields to provide a wind speed estimate, $\widehat{v}$. The derivatives are evaluated in continuous time, whereas the measurement updates are evaluated in discrete time. A forward Euler integration method is used to propagate the state and covariance estimates forward in time.
The nonlinear continuoustime statespace model used for the continuous–discrete Kalman filter implemented in the controller is defined as
where the system noise is ξ_{s}=[n_{1} n_{2} n_{3}]^{T}, and n_{i} is considered to be zeromean white noise. The measurement noise, ξ_{m}, is assumed to be white noise with a constant covariance. The system state, inputs, and outputs are defined as
where v_{t} is the turbulent component of the wind speed, and v_{m} is the mean wind speed. The nonlinear state equations are defined as
and the output is
To complete the state equation definitions, we establish
In Eq. (36), L is a turbulence length scale parameter generically defined as L=3D, where D is the rotor diameter.
In the Kalman filter, the covariance matrices are based on the wind model as defined by Knudsen et al. (2011). In the ROSCO implementation of this wind speed estimator, the process noise (Q) and measurement noise (R_{m}) covariances are
where the turbulence intensity is defined as t_{i}=0.18, the upper limit of the turbulence intensity for standard inflow wind conditions as defined by IEC (2019). A continuous–discrete Kalman filter is then implemented through the following formulation:

Prediction update
$$\begin{array}{ll}{\displaystyle}& {\displaystyle}\dot{\widehat{\mathit{x}}}\left(t\right)=f({\widehat{\mathit{x}}}_{k\mathrm{1}k\mathrm{1}},{\mathit{u}}_{\mathit{k}})\\ \text{(39)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{predicted}\phantom{\rule{0.25em}{0ex}}\mathrm{state}\phantom{\rule{0.25em}{0ex}}\mathrm{estimate}\right){\displaystyle}& {\displaystyle}\dot{\mathbf{P}}\left(t\right)=\mathbf{F}\left(t\right){\mathbf{P}}_{kk}+{\mathbf{P}}_{kk}{\mathbf{F}}^{T}\left(t\right)+{\mathbf{Q}}_{k}{\mathbf{K}}_{k\mathrm{1}}{\mathbf{R}}_{\mathrm{m}}{\mathbf{K}}_{k\mathrm{1}}^{T}\\ \text{(40)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{predicted}\phantom{\rule{0.25em}{0ex}}\mathrm{covariance}\phantom{\rule{0.25em}{0ex}}\mathrm{estimate}\right)\end{array}$$ 
Measurement update
$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\stackrel{\mathrm{\u0303}}{y}}_{k}={y}_{k}{h}_{k}\left({\widehat{\mathit{x}}}_{kk\mathrm{1}}\right)\\ \text{(41)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{innovation}\phantom{\rule{0.25em}{0ex}}\mathrm{residual}\right){\displaystyle}& {\displaystyle}{\mathit{S}}_{k}={\mathbf{H}}_{k}{\mathbf{P}}_{kk\mathrm{1}}{\mathbf{H}}_{k}^{T}+{\mathbf{R}}_{\mathrm{m}}\\ \text{(42)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{innovation}\phantom{\rule{0.25em}{0ex}}\mathrm{covariance}\right){\displaystyle}& {\displaystyle}{\mathbf{K}}_{k}={\mathbf{P}}_{kk\mathrm{1}}{\mathbf{H}}_{k}^{T}{\mathbf{S}}_{k}^{\mathrm{1}}\\ \text{(43)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\text{(nearoptimalKalmangain)}{\displaystyle}& {\displaystyle}{\widehat{\mathit{x}}}_{kk}={\widehat{\mathit{x}}}_{kk\mathrm{1}}+{\mathbf{K}}_{k}{\stackrel{\mathrm{\u0303}}{y}}_{k}\\ \text{(44)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{updated}\phantom{\rule{0.25em}{0ex}}\mathrm{state}\phantom{\rule{0.25em}{0ex}}\mathrm{estimate}\right){\displaystyle}& {\displaystyle}{\widehat{v}}_{k}=\left[\mathrm{0}\phantom{\rule{1em}{0ex}}\mathrm{1}\phantom{\rule{1em}{0ex}}\mathrm{1}\right]{\widehat{\mathit{x}}}_{kk}\\ \text{(45)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{wind}\phantom{\rule{0.25em}{0ex}}\mathrm{speed}\phantom{\rule{0.25em}{0ex}}\mathrm{estimate}\right){\displaystyle}& {\displaystyle}{\mathbf{P}}_{kk}=(\mathbf{I}{\mathbf{K}}_{k}{\mathbf{H}}_{k}){\mathbf{P}}_{kk\mathrm{1}}\\ \text{(46)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{updated}\phantom{\rule{0.25em}{0ex}}\mathrm{covariance}\phantom{\rule{0.25em}{0ex}}\mathrm{estimate}\right)\end{array}$$
Here the state transition and output Jacobians are defined as
Wind speed estimator results from a 10 min simulation of the NREL 5 MW turbine are shown in Fig. 6. In the presented simulation, the rootmeansquare error between the rotoraveraged wind speed and the wind speed estimate is 0.48 m s^{−1}.
5.2 Set point smoothing
The generator torque and blade pitch controllers will conflict with each other in nearrated operation if the generator torque and blade pitch reference speeds are defined only by Eqs. (19) and (22). To avoid this, we employ a set point smoother regime that is akin to a Region 2.5 controller (Schlipf, 2019; Zalkind and Pao, 2019). Practically, the socalled “set point smoother” shifts the generator speed reference signal of the saturated controller while the unsaturated controller is active, so the controllers do not have conflicting behaviors. This encourages one controller to stay active while the other is not.
We first define an offset to the rotor speed set point, Δω, as
where k_{vs} and k_{pc} are unitless gain factors that are greater than 0, and β_{max} is the blade pitch angle at cutout wind speed. Equation (48) is defined such that Δβ=0 in belowrated operation and Δτ=0 in aboverated operation. A piecewise logic is then implemented to shift the blade pitch or generator torque reference generator speeds:
Figure 7 shows a block diagram displaying the set point smoother logic.
The shifting term in the set point smoother defined in Eq. (48) includes normalization terms, so no specific tuning is necessary. The ROSCO toolbox tuning processes define k_{vs}=1 and ${k}_{\text{pc}}=\mathrm{1}\times {\mathrm{10}}^{\mathrm{3}}$. These values were chosen because of their utility across turbine models, although specific tuning of these can improve the controller performance near rated operation.
Figure 8 shows results from a 10 min timedomain simulations of the NREL 5 MW wind turbine near rated operation. The set point smoother employed in ROSCO provides significantly smoother transitions from above to belowrated operation. When the blade pitch is greater than zero (the first 12 s in Fig. 8), the torque controller set point decreases, which biases the generator torque toward its maximum value. When the generator torque is less than its rated value (the last 12 s in Fig. 8), the set point for the pitch controller increases, and it biases the pitch to its minimum value. The smoother shifts the saturated controller's set point linearly depending on how “far” it is from rated operation. By separating the control regions this way, resonances such as those seen in the time history of the NREL 5 MW torque controller's signal between 15 and 25 s can be reduced.
5.3 Minimum pitch saturation
A method for saturating the minimum blade pitch angle for a given wind speed estimate is also included in ROSCO. This has primarily been used for two purposes: to limit the rotor thrust through a peak shaving algorithm and to implement a minimum pitch angle at low wind speeds for power maximization in the presence of a minimum rotor speed constraint. The ROSCO controller simply defines a minimum blade pitch angle for a given wind speed as specified by a lookup table in the DISCON.IN file. Figure 9 provides an example minimum pitch schedule for the IEA 15 MW wind turbine with a minimum rotor speed constraint and peak shaving, along with the corresponding rotor thrust that is expected with and without peak shaving.
The following two subsections describe the two primary aspects of the minimum pitch schedule in more detail.
5.3.1 Peak shaving
Thrust limiting, or peak shaving, is often used to reduce peak tower base loads. Generally, the largest rotor thrusts are seen near rated operation and have a strong effect on tower base loads. It is has also been shown that rotor thrust is correlated to the blade pitch actuation (Bossanyi, 2003; Fischer and Shan, 2013; Petrović and Bottasso, 2017). We impose a minimum blade pitch angle, β_{min}(v), to “shave” the peak of the rotor thrust curve and subsequently reduce tower base loads near rated. The rotor thrust can be defined by
where C_{t} is the rotor thrust coefficient. Given a maximum allowable rotor thrust, ${T}_{\text{r,max}}=amax\left({T}_{\mathrm{r}}\right(v\left)\right)$, where a≤1, the maximum allowable thrust coefficient is defined as
For all operational TSRs, we can find a blade pitch angle, β_{min}(C_{t,max},λ), through a C_{t} surface similar to the C_{p} surface shown in Fig. 4. Notably, C_{t,max}(v) and λ are both parameterized by v, so we can define a minimum blade pitch schedule, β_{min}(v), that is dependent on a wind speed estimate. Figure 10 shows an example 60 s time series for the NREL 5 MW wind turbine in nearrated operation. Based on the wind speed estimate, the blades are pitched to reduce the rotor thrust to stay at or below the maximum allowable thrust limit.
Peak shaving algorithms implemented with minimum pitch saturation can result in power losses because the turbine will no longer be operating at its highest efficiency near rated. Though the default peak shaving algorithm in the ROSCO toolbox reduces the maximum rotor thrust by 25 %, ultimately the tradeoff between power production and load reductions must be made by the control system designer.
5.3.2 Power maximization in low wind
In certain wind turbine configurations, such as the IEA 15 MW wind turbine (Gaertner et al., 2020), minimum or maximum blade tip speed limits might be imposed for reasons such as tower resonance avoidance or noise avoidance. If a minimum tip speed constraint exists, the wind turbine cannot operate at λ_{opt} in low wind speeds. A minimum pitch schedule can be implemented such that the power can be maximized in low wind speeds while the generator torque controller works to satisfy the minimum rotor speed constraints. The black dashed–dotted line in Fig. 4 provides insight into how the power output can be improved through a minimum pitch angle at low wind speeds by moving the turbine's expected operating point to the “top” of the C_{p} surface for high TSRs.
Figure 11 shows an example of how the power can be increased. A 10 min simulation was run in OpenFAST for an inflow wind with normal turbulence and a 5 m s^{−1} average wind speed. With the pitch saturation module turned on, the blade pitch angle is changed based on the wind speed estimate and the pitch saturation lookup table, resulting in a slightly increased power output.
5.4 Shutdown
A simple shutdown routine is included in ROSCO for shutdown during high wind speed events. A firstorder lowpassfiltered blade pitch angle signal triggers turbine shutdown if it exceeds a certain threshold. If the shutdown is initiated, the blades are pitched to feather at their maximum pitch rate to slow down the rotor. If the TSR tracking torque controller is being used, ω_{ref,τ} is set to the minimum rotor speed. This encourages the torque controller to help slow down the rotor initially. Once the blades are pitched such that very little lift is generated and the rotor is nearly stopped, the torque controller will saturate at zero in an unsuccessful attempt to speed up the rotor to the minimum rotor speed.
It is shown in Bottasso et al. (2014) that there are shutdown methods that could reduce possible designdriving loads during shutdown. Future work includes the investigation and inclusion of these methods in the ROSCO controller. Additionally, a number of events can trigger wind turbine shutdowns, such as generator overspeeds and yaw misalignment. Future work also includes the addition of improved shutdown event detection and control methods for such cases.
5.5 Floating offshore wind turbine feedback
An additional control feedback term is included to account for FOWTs in a method referred to as “parallel compensation” (Van Der Veen et al., 2012). The towertop acceleration is filtered, integrated, and multiplied times a proportional gain feedback, ${k}_{{\mathit{\beta}}_{\text{float}}}$. This modifies the blade pitch control signal to become
where x_{t} is the towertop position in the fore–aft direction. The block diagram in Fig. 3 provides a visualization of how this signal is implemented.
Although some research suggests the use of a platform pitch feedback signal for FOWT control (Fleming et al., 2014, 2016), the nacelle fore–aft signal is used in ROSCO so that the overall controller implementation can maintain the structure of the Bladedstyle communication interface (DNVGL, 2018). A firstorder highpass filter combined with a secondorder lowpass filter are used to filter the nacelle fore–aft acceleration signal. The ROSCO toolbox generically places high and lowpass filter cutoff frequencies at 0.01 rad s^{−1} and the platform's first fore–aft natural frequency, respectively. Additionally, a notch filter is used to remove the tower fore–aft frequency component of the feedback signal for the floating controller. A Bode diagram of the final form of this filter is shown in Fig. 12 for the IEA 15 MW wind turbine on the University of Maine (UMaine) semisubmersible platform (Allen et al., 2020). After this nacelle fore–aft acceleration signal is filtered and integrated, it is similar to a platform pitching velocity signal that is often used for FOWT control.
For consistency with the theme of the ROSCO tool set, a generic tuning process has been developed for this floating feedback term. We start by defining the simplified secondorder equation of towertop motion as
where J_{t} is the total system inertia in the platform pitching direction, c_{t} is a damping constant, k_{t} is a restoring constant, and T_{r} is the rotor thrust as defined by Eq. (50). The rotor effective wind speed is modified by tower motion such that
where Δv_{w} is the change in freestream wind speed. Similar to the derivation of Eq. (4), we can linearize Eq. (50) to be
where ${\mathrm{\Pi}}_{{\mathit{\omega}}_{\mathrm{g}}}=\partial {T}_{\mathrm{r}}/\partial {\mathit{\omega}}_{\mathrm{g}}$, ${\mathrm{\Pi}}_{\mathit{\omega}}=\partial {T}_{\mathrm{r}}/\partial \mathit{\beta}$, and ${\mathrm{\Pi}}_{\mathit{\omega}}=\partial {T}_{\mathrm{r}}/\partial v$.
For the controller, we have suggested that a proportional feedback term should be added to the standard blade pitch PI controller, such that the control input should be defined by Eq. (52). We also define the generator position as θ such that
After substituting Eqs. (52) and (54)–(56) in Eqs. (53) and (5), we arrive at the equations of motion for the closedloop towertop (Eq. 57) and rotor (Eq. 58) dynamics:
If we then convert Eqs. (57) and (58) into the statespace form $\dot{\mathit{x}}=\mathbf{A}\mathit{x}+\mathbf{B}\mathit{u}$, where
we can define
Note that A(4,2) is the state transition term from $\mathrm{\Delta}{\dot{x}}_{\mathrm{t}}$ to $\mathrm{\Delta}\ddot{\mathit{\theta}}$. This suggests that if ${\mathrm{\Gamma}}_{\mathit{\beta}}{k}_{{\mathit{\beta}}_{\text{float}}}{\mathrm{\Gamma}}_{v}=\mathrm{0}$, then the towertop pitching velocity will have no direct effect on the rotor acceleration. To attempt to achieve this, we define
Including the additional parallel compensation term β_{float} reduces the need to detune the standard blade pitch PI controller because of the infamous negativedamping problem (Larsen and Hanson, 2007). If tuned appropriately, the parallel compensation term can help negate the effect of towertop motion and subsequent changes to the relative wind speed at the rotor. Additionally, combining the use of this β_{float} feedback term with a peak shaving routine from Sect. 5.3.1 can reduce the towertop pitching transients and further stabilize the system. Though the peak shaving does, theoretically, reduce power output near rated operation, the towertop stabilization benefits generally outweigh the power losses because less fore–aft tower motion can lead to increased power output.
In this section, we use ROSCO v2.3.0 and present results from both landbased and floating wind turbine simulations. First, the ROSCO controller, as tuned by the ROSCO toolbox, is compared to the NREL 5 MW wind turbine controller using the landbased NREL 5 MW wind turbine. Then, results from the IEA 15 MW atop the UMaine semisubmersible floating wind turbine configuration are shown to illustrate the effect of the FOWT β_{float} control feedback loop. The subset of the International Electrotechnical Commission (IEC) design load cases (DLCs) (IEC, 2019) shown in Table 2 were run for both turbines to offer a comparison of controller performance.
6.1 NREL 5 MW landbased wind turbine results
The landbased NREL 5 MW turbine with the NREL 5 MW wind turbine controller is compared to ROSCO with the ROSCO toolbox generic tuning values and ROSCO with minimal manual tuning and peak shaving implemented. As previously stated, there are only four necessary tuning parameters when tuning ROSCO using the generic ROSCO toolbox tuning functionalities. For the NREL 5 MW configuration, the choices for ζ_{des} and ω_{des} are shown in Table 3. The controller tuning parameters used for ROSCO's pitch controller in the results presented in this section were chosen to be the same as those used for scheduling the gains of the NREL 5 MW reference controller. ROSCO's TSR tracking torque controller was tuned manually so that belowrated simulations resulted in consistent TSR tracking.
The collective blade pitch controller gain schedules from the ROSCO tuning process are similar to those from the NREL 5 MW reference controller's tuning process, but they are not the same. The NREL 5 MW reference controller's gain schedule is based on the turbine's sensitivity of aerodynamic power to the collective blade pitch angle, a value that has generally been found using more computationally expensive aeroelastic solvers, whereas the ROSCO tuning process depends directly on the C_{p} surface.
Highlevel comparison results of the ROSCO controller compared to the NREL 5 MW reference controller are shown in Fig. 13. Results are shown from both the generic ROSCO controller and a ROSCO controller with peak shaving. For the ROSCO controller with peak shaving, all controller tuning input parameters were kept the same as for the generic ROSCO controller with the exception of implementing the standard peak shaving routine. The results from the generic ROSCO controller are consistent with the expected steadystate operating points shown in Fig. 2. In the results from the generic ROSCO controller, there is a noticeable increase in rotor thrust compared to the NREL 5 MW reference controller. This is attributed to the difference in pitch controller gains, and it can be mitigated with slightly different controller tuning parameters. Also, note that the NREL 5 MW reference controller exhibits significantly higher TSRs because of the torque controller's linear transition between regions 1 and 2 (Jonkman et al., 2009) rather than the PI controllerbased transition that is used in ROSCO. The ROSCO controller tracks the optimal TSR of 7.5 well during belowrated operation.
The power output and subsequent annual energy production from the ROSCO controller without peak shaving is 0.1 % greater than that of the NREL 5 MW reference controller. This is consistent with observations by Holley et al. (1999) and Bossanyi (2000), who note that minor energy production gains are possible to be achieved through an optimal TSRtracking controller, though at the cost of more generator power fluctuations. In fact, the maximum standard deviation of the power output during DLC 1.1 decreased by 1.5 % when using ROSCO instead off the NREL 5 MW reference controller, so no significant power increases are expected. The annual energy production from the ROSCO controller is 1.7 % less than that of the NREL 5 MW reference controller when the peak shaving routine is implemented in ROSCO. This is expected because rotor thrust reductions reduce the wind turbine's power output as well. Notably, the maximum rotor thrust seen is slightly higher than the expected maximum rotor thrust (see Fig. 10). This is attributed to the imperfect nature of a peak shaving routine based on a wind speed estimate, and it could likely be improved through an observerbased rotor thrust shaving algorithm or similar. The peak shaving also helps to both mitigate rotor thrusts introduced by the initial ROSCO tuning and reduce them further than those from the simulations using the NREL 5 MW reference controller.
6.2 IEA 15 MW on the UMaine semisubmersible FOWT results
We compare results from the IEA 15 MW wind turbine on a semisubmersible floating turbine platform for the ROSCO controller with and without the floating feedback and peak shaving modules enabled (see Fig. 3). Larsen and Hanson (2007) suggest that the tuned bandwidth of a rotor speedregulating collective blade pitch controller should not be higher than the platform's first fore–aft eigenfrequency. This method of “derating” the blade pitch controller has traditionally been employed in baseline FOWT controllers, such as the NREL 5 MW OC3 and OC4Hywind FOWT models (Jonkman, 2010; Robertson et al., 2014). Though derating the turbine can provide stable platform dynamics, generator overspeeds can generally be very high with this method of control. The standard distribution of the IEA 15 MW wind turbine on the UMaine semisubmersible platform (IEA Wind Task 37, 2021) employs ROSCO, and the pitch controller bandwidth is 0.2 rad s^{−1}, which is already less than the UMaine semisubmersible's first platform eigenfrequency of ∼0.21 rad s^{−1}. Also, the IEA 15 MW wind turbine uses constant generator torque control in aboverated operation. For this comparison, the floating feedback and peak shaving modules are either enabled or disabled, and the rest of the controller is not changed at all.
Figure 14 presents results from the DLC 1.1 and 1.3 simulations. With the peak shaving enabled, slight decreases in power production are seen at nearrated wind speeds. This does, however, correlate to significant reductions of tower fore–aft bending moments and related loads near rated. The presented reduction in platform pitching motion of about 15 % resulting from the floatingspecific feedback term has a clear effect on the tower base bending moment as well. The aboverated maximum rotor speed is not expected to change significantly with and without the peak shaving and floating controller because the standard pitch controller for rotor speed regulation is the same. Similarly, the average power output is expected to drop when peak shaving is introduced, as shown in the bottom right plot of Fig. 14.
Figure 15 shows a comparison of the three presented iterations of the ROSCO controller for the IEA 15 MW wind turbine on the UMaine semisubmersible platform. In Fig. 15, ROSCO with FOWT tuning, low windspeed pitch saturation, and peak shaving is used as the baseline. For a number of metrics of interest, the percent difference when using ROSCO without any pitch saturation and without the FOWT feedback term is shown. As expected, by removing the pitch saturation term, the annual energy production (AEP) increases by 1.6 %. This is directly related to the reduced power output in low wind speeds because there is not powermaximizing pitch saturation and in nearrated wind speeds where the thrust is being reduced. When the pitch saturation module is kept on and the floating feedback term is removed, the AEP decreases by 1.4 %. This suggests that the increased platform damping that results from the floating feedback term also helps increase AEP. Overall, maximum platform deflections and tower damage equivalent loads are also seen to decrease somewhat significantly throughout the turbine, with both peak shaving and the floating feedback term enabled, while AEP is not detrimentally affected. In this work, no specific tuning of the floating feedback term or blade pitch controller gains was done outside of the methods presented in Sects. 5.5 and 2.5, so overall controller performance could certainly be tuned and improved.
We have provided the research community with a reference opensource controller (ROSCO) for fixed and floating offshore wind turbines. Generic tuning methods have been developed for the ROSCO controller and made available through the Pythonbased ROSCO toolbox. The tuning methods can be implemented easily by the interested noncontrols engineer or in a completely automated fashion for use in optimization routines.
On the NREL 5 MW landbased wind turbine, we have shown that the generically tuned ROSCO controller performs comparably to the NREL 5 MW reference controller. We have also shown that, through a small amount of additional controller tuning, ROSCO's performance can be further improved to reduce rotor thrusts without significant reductions in power generation. We have also provided the foundations of more modern, industry standard control methods, such as peak shaving and wind speed estimation. A TSR tracking controller is shown to generate belowrated turbine power outputs that are consistent with the expectation based on the literature without significant power fluctuation or increased towerbase loads. No significant differences have been made to the implementation of the aboverated collective blade pitch controller, but automated tuning methods have been developed to easily generate pitchdependent gain schedules for the blade pitch controller based on the C_{p} surface. A set point smoother has been implemented to improve the transition between the primary blade pitch and generator torque controller regions. A Kalman filterbased wind speed estimator is implemented in ROSCO to enable the TSR tracking and blade pitch saturation capabilities. Pitch saturation routines have been implemented to improve power output in low wind speeds and reduce rotor thrust rated wind speeds. A simple shutdown logic has also been implemented to facilitate more realistic wind turbine testing for the IEC DLCs.
Additionally, a FOWTspecific feedback loop is included in ROSCO and has shown improvements over previously published opensource FOWT control methods. The combination of a FOWTspecific feedback loop and a peak shaving routine has been shown to significantly reduce platform pitch motions and maximum rotor speeds compared to a simple pitch controller with a bandwidth below the first fore–aft natural frequency of the platform. Notably, all the results shown for the IEA 15 MW on the UMaine semisubmersible are shown for the generalized ROSCO tuning values, and there is potential to further improve controller performance through additional finetuning of the input parameters to the ROSCO toolbox.
Several other capabilities are also being incorporated in ROSCO and the ROSCO toolbox generic tuning logic. These capabilities and tuning methods are currently being developed, some of which include individual pitch control, distributed aerodynamic control, and improved FOWT feedback term tuning methods. A number of specific improvements for the control methods discussed in this paper will also be implemented. These include additional functionalities for the blade pitch and torque controller, such as powerreference tracking control and tower resonance avoidance methods. Improved shutdown and yaw methods are also being actively investigated.
Finally, the authors would like to reiterate that ROSCO and the ROSCO toolbox are opensource tools. We invite the research community to download, use, and contribute to these codes in whichever ways they see fit.
Four filters are used in the ROSCO controller. For the filters presented, ω_{f} is a cornering frequency in rad s^{−1}, and ζ_{f} is a unitless damping ratio.
Firstorder lowpass filter
Secondorder lowpass filter
Firstorder highpass filter
Notch filter
The ROSCO controller and toolbox are available for download at https://github.com/NREL/ROSCO (NREL, 2021; https://doi.org/10.5281/zenodo.5748043, nikharabbas et al., 2021).
The data presented in work can be made available upon request.
NA developed the generic tuning processes, formalized the control concepts, and collected the theoretical foundations discussed in this article. He also contributed the majority of the code found in ROSCO and the ROSCO toolbox and established them as the tools that they are today. NA was also the primary contributor to the writing of the article. DZ contributed to much of the testing and verification of the ROSCO toolchain. He has also served in an advisory role during the development of many of ROSCO's modules and reviewed this article multiple times before its submittal. AW contributed the original theoretical idea behind the tuning of the floating feedback term, served in an advisory role, and reviewed this article multiple times. LP served in a supervisory role, guided the theoretical foundations discussed in this article, and reviewed this article extensively.
The contact author has declared that neither they nor their coauthors have any competing interests.
This work was authored in part by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the US Department of Energy (DOE) under contract no. DEAC3608GO28308. Funding was provided by the US Department of Energy Office of Energy Efficiency and Wind Energy Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or the US Government. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paidup, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for US Government purposes.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors specifically thank JanWillem van Wingerden and Sebastiaan Mulders from the Delft University of Technology for their contributions to the Delft Research Controller, which provided much of the foundations upon which the ROSCO controller has been built.
Additionally, we thank the many researchers at the National Renewable Energy Laboratory, who have put the entire ROSCO toolchain through its paces in numerous applications. In particular, the authors thank Pietro Bortolotti and Evan Gaertner (now at Siemens Gamesa), who helped ROSCO through perhaps the most challenging software bugs. A special thanks to Paul Fleming as well for his initial inspiration on the structure of the ROSCO toolbox.
This research has been supported by the US Department of Energy, Office of Energy Efficiency and Renewable Energy (grant no. DEAC3608GO28308) and the US Department of Energy, Advanced Research Projects Agency – Energy (grant no. DEAR0000ABC).
This paper was edited by Michael Muskulus and reviewed by Turaj Ashuri and two anonymous referees.
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 Abstract
 Introduction
 Foundations of the Reference OpenSource Controller
 The generator torque controller
 The blade pitch controller
 Additional control modules
 Example results and analysis
 Conclusions and future work
 Appendix A: Filters
 Code availability
 Data availability
 Author contributions
 Competing interests
 Disclaimer
 Acknowledgements
 Financial support
 Review statement
 References
 Abstract
 Introduction
 Foundations of the Reference OpenSource Controller
 The generator torque controller
 The blade pitch controller
 Additional control modules
 Example results and analysis
 Conclusions and future work
 Appendix A: Filters
 Code availability
 Data availability
 Author contributions
 Competing interests
 Disclaimer
 Acknowledgements
 Financial support
 Review statement
 References