Individual pitch control (IPC) is a well-known approach to reduce blade loads on wind turbines. Although very effective, IPC usually requires high levels of actuator activities, which significantly increases the pitch actuator duty cycle (ADC). This will subsequently result in an increase of the wear on the bearings of the blades and a decrease of the wind turbine reliability. An alternative approach to this issue is to reduce the actuator activities by incorporating the output constraints in IPC. In this paper, a fully data-driven IPC approach, which is called constrained subspace predictive repetitive control (cSPRC), is introduced. The output constraints can be explicitly considered in the control problem formulation via a model predictive control (MPC) approach. The cSPRC approach will actively produce the IPC action for the necessary load reduction when the blade loads violate the output constraints. In this way, actuator activities can be significantly reduced. Two kinds of scenarios are simulated to illustrate the unique applications of the proposed method: wake–rotor overlap and turbulent sheared wind conditions. Simulation results show that the developed cSPRC is able to account for the output constraints into the control problem formulation. Since the IPC action from cSPRC is only triggered to prevent violating the output constraints, the actuator activities are significantly reduced. This will help to reduce the pitch ADC, thus leading to an economical viable load control strategy. In addition, this approach allows the wind farm operator to design conservative bounds to guarantee the safety of the wind turbine control system.

Over the past decades, wind energy has expanded by leaps and bounds in the international energy mix

However, one of the main challenges in the development of wind farms is the high operation and maintenance (O & M) cost

The drawback of these approaches is that the pitch actuator duty cycle (ADC) is dramatically increased due to the cyclic fatigue loads on the pitch actuators. Such an effect is worsened when these approaches attempt to control the non-deterministic wind loads at high wind turbulence intensities and the dynamic loading caused by the wake. This will result in an increase of the wear on the bearings of the blades and eventually a shortening of the lifespan of the pitch control system. Moreover, the pitch control system is usually subjected to various constraints due to the physical restrictions of the pitch actuator, safety limitations, environmental regulations and wind farm manufacturer specifications

In order to address this challenge, a constrained IPC was recently developed by

In order to approach the goal of introducing output constraints in wind turbine control, a novel IPC approach is presented in this paper. It is based on a constrained subspace predictive repetitive control (cSPRC). The basic concept of SPRC was initially proposed by

The main contributions of this paper lie in the following two aspects. The first contribution is the data-driven framework. For the first time, the constraints of the control problem, especially the output constraints of the blade loads, are explicitly considered in the repetitive control formulation.
This is achieved by integrating an MPC approach

The second contribution is the unique application of the cSPRC approach to two independent scenarios: one where the wind turbine is impinged and overlapped by the wake shed from the upstream turbine and one where the turbulent sheared wind condition is present, respectively. In particular, in the wind farm wake scenario the wind turbine will experience partial and full wake overlap due to the wind direction change and the yaw misalignment of the upstream turbine

The effectiveness of the cSPRC approach under these two typical scenarios will be demonstrated through high-fidelity simulations. For this, the FLOw Redirection and Induction in Steady-state (FLORIS) model

The remainder of this paper is organized as follows. Section

In this section, the wind turbine model and its simulation environment are introduced. The wind turbine model is based on the DTU 10 MW three-bladed variable speed reference wind turbine. Its specifications are presented in Table

Specification of the DTU 10 MW reference wind turbine model.

Based on the wind turbine model, the implementation of the case study is illustrated in Fig.

Baseline control is based on the collective pitch control (CPC) approach

Conventional IPC is based on the MBC-based IPC. In MBC-based IPC, the pitch angle of each blade is regulated independently with the aid of the so-called Coleman transformation

Block diagram of the wind turbine model and of the control loop. The aero-hydro-structural dynamic part is simulated in the FAST model, while the turbine control part, including a baseline CPC

The baseline control is based on a linear time-invariant (LTI) dynamical system

This section outlines the theoretical framework of the cSPRC approach for wind turbine load control. First of all, a discrete-time LTI system along with an output predictor is established to approximate the wind turbine dynamics. All the parameters of the linear representation are then identified via an online recursive subspace identification. Based on this, the predictive repetitive control law subjected to the different kinds of constraints is then synthesized by solving an MPC optimal problem in receding horizon. Especially, the output constraints of the controller, because of the presence of uncertainty in the identified model, are implemented as soft constraints by introducing slack variables in the MPC. Furthermore, only the control inputs in the MPC are penalized, which ensures that the controller will be only activated for load mitigation when the blade loads violate the output constraints. The overall structure of the cSPRC approach has been illustrated in Fig.

Implementation of cSPRC, which includes online system identification and repetitive control. MPC optimization is used to incorporate the output constraints in repetitive control formulation.

In the cSPRC framework, the wind turbine dynamics are represented by a LTI system affected by unknown periodic disturbances

The following equations can be derived by rewriting Eq. (

Similarly,

It is worth noting that

Based on the LTI system obtained in subspace identification step, the constrained repetitive control law is formulated over

To solve this problem, the rotor azimuth

Compared to Eq. (

Following the philosophy of the MPC algorithm, the control objectives are introduced in the following cost function as

As usual in MPC implementations, only the first element

Equation (

Combining Eq. (

As a result, the output constraints will be relaxed once the slack variables tend to large values during the control problem formulation. The implementation of the slack variables in the objective function is

The implementation of the constrained repetitive control is schematically presented in Fig.

In this section, the effectiveness of cSPRC in dealing with the output constraints is demonstrated on the wind turbine model via a series of case studies. For the sake of comparison, the load reduction and the pitch ADC of the proposed cSPRC approach, baseline CPC and MBC-based IPC are computed for investigation.

The wind turbine model, which has been introduced in Sect.

wake–rotor overlap condition, in which the wind turbine is impinged by a steady-state wind farm wake shed from an upstream turbine, which shows partial and full wake–rotor overlap;

turbulent sheared wind condition, in which the wind turbine is subjected to turbulent sheared wind flows.

The steady-state wind farm wake is simulated by the widely used FLORIS model

TurbSim: a stochastic inflow turbulence tool to simulate realistic turbulent wind fields (

Model configuration and environmental conditions in FAST–Simulink simulations for all LCs.

Then, the time series of the wind fields, which are based on the simulation results of the FLORIS and TurbSim, are fed into the FAST/Simulink model as the input of the wind turbine simulation. In all the LCs, the simulation lasts 1000 s at a fixed discrete time step of 0.01 s. For comparison, three different control strategies, i.e., baseline CPC, MBC-based IPC and cSPRC, are simulated respectively in each LC. This finally leads to a total of

First of all, the wake–rotor interaction is presented in Fig.

Vertical slice of the wind field at the downstream turbine in LC2 (16 m s

It can be seen that MOoP is significantly increased when the wake impinges on the left sector of the rotor at around 350 s, leading to the partial wake–rotor overlap. Due to the increase of MOoP, the proposed cSPRC actively generates the IPC action to reduce the asymmetric blade loads into the safety bounds and avoid violating the output constraints. Thus, significant load reduction can be observed for 350–550 s. As time goes by, the rotor is fully overlapped with the wake, which results in the reduced MOoP. Since the blade loads do not violate the output constraints at 600 s, only the baseline CPC is active to maintain the basic wind turbine performance, which leads to reduced actuator activities. Again, the wake impinged the right sector of the rotor at around 640 s. The increased blade loads enables cSPRC to provide the IPC action for load mitigation. In comparison, MBC-based IPC, which is a conventional IPC approach, actually shows maximum potential of load reduction. However, significant actuator activities are demanded by MPC-based IPC. For example, the corresponding pitch rates are presented in Fig.

MOoP on the blade root in LC2 (16 m s

The cost function of the MPC optimization in cSPRC is illustrated in Fig.

Cost function of the control objective in the developed cSPRC approach in LC2 (16 m s

Pitch rate of the blade in LC2 (16 m s

MOoP on the blade root and its corresponding pitch angles in LC4 (12 m s

Pitch rate of the blade in LC4 (12 m s

Another scenario considered in the case study is the turbulent sheared wind condition. Figures

Other LCs show similar patterns and hence are omitted for brevity. Based on these comparisons, it can be concluded that the developed cSPRC approach shows good performance in handling the output constraints in both wake overlap and turbulent sheared wind scenarios. By designing safety bounds, it allows the wind farm operator to mitigate the loads into the safety bounds while reducing the actuator activities. However, the conventional approach, such as MBC-based IPC, usually mitigates the blade loads as much as possible. As a consequence, more actuator activities are demanded by the controller, which may lead to the reduced reliability of the control system due to the higher cyclic fatigue loads on the pitch actuators.

In order to quantify the load reduction and pitch activities of these control strategies, two indicators, namely the reduction of MOoP relative to baseline controller and the pitch ADC, are calculated for comparison.
The latter one can be calculated according to the pitch rate

Comparison of the indicators (reduction of MOoP, pitch ADC and ratio

In comparison, MBC-based IPC aims at attaining the maximum load reduction.
However, it causes excessive pitch ADC and thus leads to a lower

In this paper, a fully data-driven individual pitch control (IPC) approach, which is called constrained subspace predictive repetitive control (cSPRC), is developed to explicitly consider the output constraints in the control problem formulation. This approach involves using online recursive subspace identification and model predictive control (MPC) to formulate the repetitive control law subjected to the output constraints. The cSPRC approach aims to produce the IPC action for load mitigation when the blade loads violate the output constraints while the baseline pitch controller is always active to maintain the basic wind turbine performance.

The effectiveness of the developed cSPRC in dealing with the output constraints is illustrated on a DTU 10 MW reference wind turbine model, where the wake–rotor overlap and turbulent sheared wind conditions are considered respectively. It proves that the cSPRC approach is effective at limiting the blade loads into the designed safety bounds, showing effective load mitigation with low pitch activities: the blade loads are reduced by

In this paper, the cSPRC approach is compared to MBC-based IPC. The case study shows that MBC-based IPC attains maximum load reduction, however at the expense of increased pitch ADC. In comparison, the proposed cSPRC framework, by dealing with the output constraints, is capable of achieving more economical load reduction and shows much lower pitch ADC. More importantly, this approach enables the wind farm operator to design conservative bounds for the load control. Since cSPRC only formulates the IPC actions to prevent violating constraints, it will significantly alleviate the pitch ADC and extend the lifespan of the pitch control system. Based on the comparison study, it is worth noting that both cSPRC- and MBC-based IPC show similar but substantially different scopes. MBC-based IPC targets a maximum load reduction at the expense of high-pitch ADC. cSPRC might be a complementary alternative to MBC-based IPC to achieve a trade-off between the load reduction and the pitch ADC. Future work will include, but are not limited to, considering other wake effects such as wake meandering and dynamic propagation of the wake, executing scaled wind tunnel experiments, and full-scale tests on a real wind turbine or wind farm.

The data analyzed in this paper are confidential and cannot be shared publicly.

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YL and JWvW conceived the idea of this research. YL performed the data processing, formal analysis, visualization and wrote the paper. RF and JWvW provided essential suggestions and reviewed the paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors are grateful for support from the European Union via the Marie Skłodowska-Curie Actions (Grant EDOWE, no. 835901) and the Horizon 2020 Research and Innovation Programme (Project HIPERWIND, no. 101006689). The authors also would like to thank the reviewers and the editors for their thoughtful comments and contribution to this research.

This research has been supported by the H2020 Marie Skłodowska-Curie Actions (Grant EDOWE, no. 835901) and the Research and Innovation Programme (Project HIPERWIND, no. 101006689).

This paper was edited by Alessandro Croce and reviewed by Torben Knudsen and one anonymous referee.

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