Control

Laboratory in Hydrodynamics, Energetics & Atmospheric Environment, Nantes, France (LHEEA) in 2014 with the DeepCwind semi-submersible as part of the project INNWIND.EU5_, see [158, 159]. The other one focused on active blade pitch control on the TripleSpar semi- submersible concept designed as part of this research and described in Section 2.10 with a scaled 10 MW turbine, see [160]. This test was performed in a joint eort with DTU and Na- tional Renewable Energy Centre of Spain (CENER). The experience from both tests was fed back into the development of the reduced-order model of this thesis and a rst validation study was done by Wei Yu in her thesis, see [161]. The hydrodynamic drag model of the simplied simulation model of Chapter 3 will be validated through these tests and the drag coecients of the TripleSpar platform will be identied in Chapter 4.

2.9 Control

This section provides the basics of modern wind turbine control and a review of challenges and state-of-the-art control design methods for FOWTs.

2.9.1 Variable speed blade-pitch-to-feather-controlled turbines

The control system of modern wind turbines includes supervisory control for special events like start-up and shut-down. The safety system regulates emergency shut-down events when failures are detected to prevent damage to the turbine. Feedback control is mainly responsible for capturing the maximum amount of energy from the wind through controlling the rotor speed, depending on the wind conditions. In this work, the focus is on the feedback control of the rotor speed. Feedforward control is benecial when information of the incoming disturbance is known, such as wind and waves for wind turbines, see [162]. Feedforward control is not considered in the present work.

The feedback control of wind turbines depends on the operating point with three regions and the switchings in between. Region 1 covers wind speeds not relevant for energy production. In region 2, the rotor speed is controlled by actuating the generator torque in a way that the optimal TSR is maintained in order to capture the maximum amount of energy. Region 3 is the above-rated region, where the blade pitch angle is actuated to control the rotor speed at its rated speed and consequently maintaining the rated power. Earlier control methodologies make use of the stall eect to reduce the lift force. This method avoids the blade pitch actuator but is not present anymore in most modern wind turbines. An introduction to wind turbine control can be found in [44] and [163].

2.9.2 Floating wind turbines

Whereas below-rated control does usually not imply challenges for the design of FOWT con- trollers, the coupled dynamics of the oating system pose diculties together with the blade- pitch controller for above-rated wind speeds. A standard rotor-speed controller for above- rated wind will pitch the blades when the rotor speed exceeds its rated value. In the case of FOWTs, this feedback loop can imply, as a side-eect, that the tower or the platform ex- periences large excursions. This is due to the aerodynamic properties of the rotor: When the relative wind speed (the one seen by the rotor) increases, the controller will pitch the blades to- wards feather (increasing blade pitch angle) and thereby reduce the aerodynamic rotor torque. As a consequence, the thrust also decreases. This means, on the other hand, that an oscilla- tion of the platform in pitch (about y, Figure 3.1) will become unstable if the controller reacts suciently fast to the sinusoidally oscillating relative wind speed.

The contradicting goals of stabilizing power for above-rated wind speeds and minimizing platform motion are a key challenge for FOWTs and of general importance for the fatigue life, see [164]. A too aggressively tuned blade-pitch controller results in unstable platform behavior. This is due to a Non-Minimum Phase Zero or Right Half-Plane Zero (RHPZ) of oating platforms. This leads to a bandwidth reduction of the blade pitch controller. A good explanation of this negative damping problem is given in [165]. A simple pole-placement method to adjust the Proportional-Integral (PI)-controller to mitigate this negative damping problem was proposed by [10]: The de-coupled rotor (including drivetrain) is considered as rigid body in the closed loop (with active blade pitch control). Then the rotor closed-loop eigenfrequency has to be selected lower than the critical support structure eigenfrequency, which is usually the platform pitch frequency. This is roughly aligned with the general control rule of thumb to limit the bandwidth for systems with RHPZs to half the frequency of the RHPZ according to [166, p. 187]. The advantage of this procedure is that no linearized model of the complete FOWT system is necessary but only the isolated rotor model and a quick denition of reasonable control gains for conceptual design is rather straightforward. The disadvantage is that rst, the isolated rotor eigenfrequency might deviate from the coupled rotor eigenfrequency and therefore also the desired pole will deviate from the real pole of the coupled system. Second, the overall system stability is not ensured with this method and therefore, instabilities might still exist for certain operating points. The method was applied in [15] and compared with an additional tower-feedback controller in [11] for a barge-type platform. An evaluation of this method, also called de-tuning of gains was carried out by [167] and [168]. The comparison in [169] includes also controllers with more than one feedback loop, in order to further improve the control performance.

More advanced strategies are, among others, Multi-Input-Multi-Output (MIMO) controllers: Here, the feedback of additional signals, the addition of more loops to the control architecture,

2.9 Control 41 can help to reduce the coupling eects in the system. The feedback of, e.g. the tower-top acceleration is possible such that the blade pitch angle reacts not only to the rotor-speed deviation but also to the tower-top acceleration. A sequential, manual tuning of feedback loops and their respective gains, comparable to decentralized control, has been called multi-SISO control, see [3, Appendix]. Real MIMO control looks at the FOWT system as a dynamic system with multiple inputs (actuators like generator torque and blade pitch angle) and outputs (rotor speed, tower-top displacement, etc.). As several standard linear control design methods do not hold anymore for MIMO systems, the design process is more complex, see [170] for a study on onshore turbines. Therefore, the authors of [12] published a parallel path modication approach to mitigate the constraints from the RHPZ through the feedback of the tower-top acceleration on the generator torque  an approach published in the early stages of MIMO control research, see [171].

Furthermore, optimal control design approaches have been presented, where optimization al- gorithms are applied to nd the best feedback law, mostly using a linearized system description. Such optimal controllers are a Linear Quadratic Regulator (LQR), as presented in [172], with a state-feedback law. The LQR problem was extended to include nonlinearities of the FOWT system in [173]. The optimal control problem in the frequency-domain can be solved with H2 or H∞ controllers, see [166]. Here, a target response (sensitivity function) is dened in the frequency-domain with a given set of available sensors. This has been applied to onshore wind turbines in [174, 175] and to FOWTs in [14] and [176]. Other multivariable controllers were developed by [177], mostly using all or the most relevant system states as controller input. A model development and Linear Model-Predictive Control (MPC) design can be found in [106] and, especially aiming at wave disturbance preview in [178]. A comparison of dierent ap- proaches for model predictive control for wind turbines can be found in [179]. An advanced controller addressing specically the purpose of reducing disturbances is Disturbance Accomo- dating Controller (DAC): A waveform of the disturbance is assumed and augmented to the system as a feedforward term to cancel out the disturbance forcing. This was applied by [180] and [181] to onshore wind turbines and to FOWTs in the thesis [182], among others.

Additional actuators to stabilize the tower were implemented in [105]. As was noted by [183], the standard actuators of a turbine (generator torque and blade pitch angle) might not be strong enough to mitigate rst-order wave loads. Here, additional actuators can help to improve the motion response of a FOWT. For onshore turbines, passive systems like TMDs or tuned liquid column dampers have been investigated. Also active systems are possible, see e.g. [105] and the Master's thesis [184]. An additional actuator on the nacelle of a FOWT was proposed by [185], an active vane to damp tower-top vibrations. A semi-active liquid column damper with an optimal control approach was presented in [186]. In the project MARINA-platform, the combination of a FOWT and a wave-energy converter was investigated and the potential to produce energy from the waves. Possible approaches for such multipurpose oshore structures

are compiled in [187]. For xed-bottom foundations structural damping devices have been analyzed to reduce structural loads for large oshore wind turbines in [188], especially focusing on the adaptation of the control to the actual structural properties. A general report on methods for the mitigation of tower loads can be found in [189]. For oshore wind turbines, various control approaches including tower feedback control were compared and assessed in the thesis by Fischer [190]. Within the project INNWIND.EU dierent members and cross-braces with specic dynamic properties are placed inside the tower or foundation to optimize the load response  something which is in general also feasible for FOWTs. Especially for damping the blade response and smoothen the electrical power, smart blades, e.g. with aps, are subject to research, see e.g. [191]. Many of these studies show that additional actuators oer the prospect of damping the structural response with more or less use of actuator power. Some of these systems are already being applied, i.e. TMDs in civil engineering, whereas others, like vanes are still being analyzed in research projects.

With Individual Pitch Control (IPC), the blade pitch angles are not controlled simultane- ously, as in the case of Collective Pitch Control (CPC), but individually. Thus, azimuth- dependent forcing is possible, especially for reducing the 1p blade loads and the Three-Times- Per-Revolution (3p) tower loads due to the vertical wind prole, see Section 2.7.1. A basic IPC controller for wind turbines was proposed by Bossanyi in [192]. For FOWTs an extensive study on IPC for FOWTs can be found in the thesis by Namik [182]. A FOWT controller for all operational regions combining the prospects of DAC and Nonlinear Model-Predictive Control (NMPC) with IPC is presented in [193] with a good improvement in terms of load reduction compared to a standard controller but only short description of the modeling assumptions is given.

Special approaches to improve the control performance for FOWTs were presented: In [194] a set point change of the rotor speed as function of the platform pitch velocity was proposed. This might be comparable to feedforward control such that the knowledge of the change in relative wind speed at the rotor is used to determine the feedforward gain. Another proposed approach is to use an estimator in real-time to distinguish the origin of the rotor speed deviation: Whether it results from a forcing of waves on the support structure or from a change in the wind eld. With an estimator it is possible to have the controller react primarily on the eects from the wind eld uctuation and not the platform oscillation and thereby overcome the RHPZ limitations. Additional sensors, mainly for disturbance preview for FOWTs, have been studied with promising results: A feedforward controller using wind preview information on a FOWT was shown in [108] and [195]. Light Detection And Ranging (LiDAR) signal data, used for an advanced NMPC is presented in [106] and extended for IPC in [196].

First scaled experimental tests of FOWTs including active control were performed in [197] in order to validate simulation models and assess the robustness of the control. Experimental testing of FOWTs including control will be topic of Chapter 4 of this thesis.

2.10 Reference Design 43