Load Reduction for Wind Turbines: an Output Constrained, Subspace Predictive Repetitive Control Approach

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 make the current IPC design not economical viable. 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 5 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 wind conditions. Simulation results show that the developed cSPRC is able to account for the output constraints into the control 10 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.

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 van Wingerden et al. (van Wingerden et al., 2011). It is essentially a fully data-driven approach comprised of subspace identification and repetitive control. The subspace identification step, based on an online solution, is used to recursively derive a linear approximation of the wind turbine dynamics (van der Veen et al., 2013). Based on it, a predictive repetitive control law is then formulated to reduce only specific deterministic loads, such as 1P loads, under varying operating 65 conditions. The SPRC approach has shown promising results in numerical simulations Liu et al., 2020) and in wind tunnel experiments (Navalkar et al., 2015;Frederik et al., 2018).
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 (Qin and Badgwell, 2003) 70 into SPRC, so that the repetitive control law subjected to specified output constraints can be formulated. Since the accuracy of the control output prediction is affected by the model uncertainty of the identified model, the output constraints may cause instability of the closed-loop system and severe deterioration of the control performance (Wang, 2009). Therefore, the output constraints are implemented as soft constraints by introducing so-called slack variables in the control problem formulation. The output constraints will be relaxed if the slack variables become large enough. In case there are no constraint violations, only 75 the widely-used baseline pitch controller is active to maintain basic wind turbine performance. Once the blade loads induced by the wind turbulence and wind farm wake increase and violate the output constraints, cSPRC will actively produce the IPC action for the necessary load mitigation. This is achieved by penalising the control inputs only in the control objectives, which ensures that the controller will be inactive if the blade loads are lower than the safety bounds. Moreover, the safety bounds, corresponding to the values of the output constraints in cSPRC, can be designed according to the design regulations of wind 80 farms, such as IEC 61400-1 (IEC, 2005). Since cSPRC is only enabled for necessary load reduction, the pitch activities would be significantly reduced while the safety of the wind turbine can be still guaranteed.
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 turbulent wind flow is present, respectively. In particular, in the wind farm wake scenario the wind turbine will experience partial and full wake overlap due to 85 the wind direction change and the yaw misalignment of the upstream turbine (Fleming et al., 2015). The partial wake overlap, together with the velocity deficit within the wake, will induce asymmetric loading of the rotor plane of the wind turbine. This will vividly illustrate the capability of dealing with output constraints in the cSPRC approach.
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 (Gebraad et al., 2016), which is a 90 parametric model for predicting a steady-state wake in a wind farm, is utilized to simulate the wind farm wake. It actually provides the wind speed input for the wind turbine simulations. Then, the wind turbine simulations are executed using the U.S. National Renewable Energy Laboratory (NREL)'s Fatigue, Aerodynamics, Structures, and Turbulence (FAST) tool (Jonkman and Buhl, 2005). In this respect, a 10MW wind turbine model is used, which is developed by the Technical University of Den-against baseline and conventional IPC approaches is made to evaluate the performance of the proposed cSPRC.
The remainder of this paper is organized as follows. Section 2 introduces the wind turbine model and the simulation environment. In Section 3, the methodology of the cSPRC with the inclusion of output constraints is elaborated. Then, the potential of cSPRC for load mitigation in wake-rotor overlap and turbulent wind scenarios is illustrated through high-fidelity simulations in Section 4. Conclusions are drawn and future work is discussed in Section 5. In this section, the wind turbine model and its simulation environment are introduced. The wind turbine model is based on the DTU 10MW three-bladed variable speed reference wind turbine. Its specifications are presented in Table 1. More details can be found in the reports (Bak et al., 2013;Lemmer et al., 2016). Based on the wind turbine model, the implementation of the case study is illustrated in Figure 1. The aero-structural dynamic 105 part of the wind turbine is simulated in the FAST model (Jonkman and Buhl, 2005) while the turbine control part is implemented in Simulink (Mulders et al., 2019). The developed the cSPRC approach, which is encompassed by a light grey block, will be described in Section 3. Other two pitch control strategies are implemented for comparisons. They are: 1) Baseline control based on the Collective Pitch Control (CPC) approach (Jonkman and Buhl, 2005). In CPC, the classical gain-scheduled Proportional Integral (PI) control (Boukhezzar et al., 2007) is utilized to regulate the pitch angles of all blades synchronously. It is denoted 110 by a white block in Figure 1. 2) Conventional IPC, which is based on the Multi-Blade Coordinate (MBC)-based IPC. In MBCbased IPC, the pitch angle of each blade is regulated independently with the aid of the so-called Coleman transformation (Bir, 2008). Note that the constraints are usually not considered in such an MBC-based IPC approach (Selvam et al., 2009). It is indicated by a dark grey block in Figure 1.  the MPC are penalised, 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 Figure 2.

Online recursive subspace identification
In the cSPRC framework, the wind turbine dynamics are represented by an LTI system affected by unknown periodic disturbances (Houtzager et al., 2013) as where x k ∈ R n , u k ∈ R r and y k ∈ R l denote the state, control input and output vectors. In the wind turbine model, r = l = 3.
u k and y k represent the blades pitch angles and the blade loads, i.e. Out-of-Plane bending moment (MOoP), respectively at discrete time index k. Moreover, d k ∈ R m is the periodic disturbance component of the loads at the blade root, while e k ∈ R l is the zero-mean white innovation process or the aperiodic component of the blade loads. Other matrices A ∈ R n×n , B ∈ R n×r , C ∈ R l×n , L ∈ R n×l , E ∈ R n×m and F ∈ R l×m denote the state transition, input, output, observer, periodic noise input and periodic noise direct feed-through matrices, respectively.
The following equations can be derived by rewriting (1) of the disturbance, equalling to the blade rotation period. Then the effect of the periodic blade loads d k on the input-output system can be eliminated as it holds Similarly, δu, δu and δe can be defined as well. Applying the δ-notation to (2), this equation can be rewritten as follows, where the periodic blade load term disappears.
Then, a stacked vector δU k for a past time window with the length of p is defined as Similarly, the vector δY (p) k is defined. Next, the future state vector δx k+p is introduced based on δU y are: It is worth noting that p need to be selected large enough, which guaranteesÃ j ≈ 0 ∀j ≥ p (Chiuso, 2007). With this in mind, δx k+p can be simplified as By substituting this equation into (3), the approximation of δy k+p is derived as From (7), it can be seen that the matrix of coefficients CK , which is the so-called Markov matrix Ξ, includes all the necessary information on the behaviour of the wind turbine system. It is determined by the input vector u (r) and output 160 vector y (l) . In essence, the subspace identification aims to find an online solution of the following Recursive Least-Squares (RLS) optimization problem (van der Veen et al., 2013) In (8), λ is a forgetting factor (0 λ ≤ 1) to alleviate the effect of past data, and adapt to the updated system dynamics online.
In this paper, a value close to 1, i.e. λ = 0.9999, is chosen to guarantee the robustness of the optimization process. According

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to the definition of Ξ in (7),Ξ k at time index k includes estimates of the following matrices, To obtain a unique solution to this RLS optimization problem, a persistent exciting signals is superimposed on the top of the control input. Subsequently, this RLS optimization (8) is implemented with a QR algorithm (Sayed and Kailath, 1998) in an online recursive manner to obtainΞ k . The estimates ofΞ k are then used in an MPC framework to formulate a repetitive control 170 law subjected to the output constraints. The implementation of the repetitive control problem formulation in MPC, namely the receding horizon repetitive control, will be elaborated in the next subsection.

Output constrained repetitive control
Based on the LTI system obtained in subspace identification step, the constrained repetitive control law is formulated over a period P . Considering that P ≥ p and usually P is much larger than p, the output equation can be lifted over the period P as H (P ) is the Toeplitz matrix, which is defined as By replacing B with L,G (P ) can be derived as well. In addition, the extended observability matrixΓ (P ) is defined as 180 Substituting (10) with (6), it yields, In (13), it is worth noting that the first (P − p) · r columns of K 185 with the definitions of Γ (P ) andĤ (P ) as follows, In order to take into account output Y (P ) k in the optimization problem, (14) can be expanded as 190 In order to incorporate the output constraints into the control problem formulation, an MPC controller is subsequently implemented to synthesize the repetitive control law. With this in mind, (15) is reformulated into a state space representation where the synthesized final input can be penalised as well, which is The state transition and input matrices are updated at each discrete time instance k. Next, a basis function projection (van 195 Wingerden et al., 2011) is employed to limit the spectral content of the pitch control input within the frequency range of interest. More importantly, it will reduce the dimension of (16) that must be solved in the MPC framework, thus leading to a reduced computational cost. In this paper, the 1P frequency load on the rotor blades, which are mainly induced by the wind shear, wind turbulence, changes in the inflow wind speed and tower shadow, are taken into account. The transformation matrix of the basis function projection can thus be defined as sin(2π/P ) cos(2π/P ) sin(4π/P ) cos(4π/P ) . . . . . .
where U f is the so-called basis function. The mathematical symbol ⊗ represents the Kronecker product. Note that the rotor azimuth ψ, equal to 2πk/P at each time step k, is used in the implementation, instead of the fixed U f . This makes it possible to take into consideration the rotor speed variations caused by wind turbulence, or by changes of the inflow wind speed. Based on the basis function, the control inputs at specific frequencies can be synthesized by taking a linear combination of the sinusoids 205 of the transformation matrix as where j = 0, 1, 2, · · · represents the rotation count, while θ ∈ R 4r , which determines the amplitudes and phase of the sinusoids, is computed based on (16) at each P . Similarly, the output can be transformed onto the subspace that defined by the basis function, as in which the symbol + denotes the Moore-Penrose pseudo-inverse. Based on the basis function projection, (16) is reduced into a lower dimensional form as Compared to (16), the dimension of the projected matrix, i.e.,Ā ∈ R 12l×12l , is much lower than the original matrixÂ ∈ 215 R ((2l+r)·P )×((2l+r)·P ) . Considering P 2r, the order of the state-space representation as well as the following MPC optimization problem can be substantially reduced. On the other hand, such a basis function transformation guarantees that the input U (P ) k is a smooth signal at the specific frequencies. Then, the following output constraints, considering the transformation in (19), are imposed on (20) for all j ≥ 0 as

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whereȲ is the constraints of the future output Y (P ) k+P , which corresponds to the designed safety bounds of the blade loads. If the blade loads do not exceed the desired bounds, then the safety of the rotor is guaranteed. The value of the bounds can be determined by the wind farm operator or according to the safety factors of the loads in the design regulation such as IEC 61400-1 (IEC, 2005), or other safety limitations and environmental conditions. In this paper,T is calculated according to the IEC regulation (IEC, 2005). Since the future outputỸ j+i|j corresponds to the first element in (20), such output constraints can 225 be converted into input constraints. Substituting (20) into (21), the output constraints are reformulated as where C = diag(I l·P , 0 r·P , 0 l·P , 0 r·P ). Following the philosophy of the MPC algorithm, the control objectives are introduced in the following cost function as

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with the MPC optimization problem as where Q and R denote the positive-definite weighting matrices, while N p and N u are the prediction and control horizons, 235 respectively. Since the controller is only active when the blade loads violate the output constraints, Q is set to an all-zeros weight matrix. This will make θ j+i|j the only penalization term in the cost function. U [θ T j+1 , · · · , θ T j+Nu ] ∈ R 4r·Nu is a sequence of a series of future control actions. They are computed by the MPC optimization over the prediction horizon at each rotation count j. This will optimize the future behavior of the wind turbine while respecting the output constraints in (21).
As usual in MPC implementations, only the first element θ T j+1 in the vector of the optimal input sequence U is used while 240 the remaining elements are discarded. The entire optimization procedure is repeated at the end of each rotation of the rotor. At the next rotation period j + 1, the updated stateK j+1 is used as an initial condition, while the cost function time limits in (23) roll ahead one step according to the receding horizon principle (Qin and Badgwell, 2003).
Equation (24) can be solved as a standard Quadratic Programming (QP) problem, by converting the control objectives in (23) to the following form where X = [K j ,K j+1 , · · · ,K j+Np ] T corresponds to the vector of state predictions. Q and R are the weight matrices, which are Q = diag(Q, · · · , Q) R = diag(R, · · · , R) , By introducing the following prediction matrices, equation (20) is rewritten as Combining (29) with (23), the MPC optimization can be solved in a simplified QP problem with only penalization of the control input, where H = 2R. In addition, G and W are defined according to (25), in a similar manner as in the paper (Bemporad et al., 2002).

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Remark 1. The output constraints should be introduced in the control system cautiously as it could cause instability of the predictive control system due to the non-linearity appearing in the control law and the model-plant mismatch (Wang, 2009).
To avoid this issue, we will introduce an output constraints relaxation, such that it allows the output constraints to be violated, but incurring a heavy penalty cost. This is achieved by introducing the so-called slack variables ρ.
As a result, the output constraints will be relaxed once the slack variables tend to large values during the control problem 265 formulation. The implementation of the slack variables in the objective function is subjected to where F is the weight matrix for the slack variables. With the penalization of the slack variables, the output constraints are 270 softened to increase the control stability.
The implementation of the constrained repetitive control is schematically presented in Figure 2. As the Markov matrixΞ k is derived from the online recursive subspace identification (8), the MPC optimization is implemented in (32)-(33). When the blade loads of the wind turbine violate the output constraints, this cSPRC algorithm will formulate the repetitive control law for load mitigation, as shown in (18). Otherwise, only the baseline controller is active to maintain the basic control performance, 275 thus leading to the reduced actuator activities.

Case study
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 comparisons, the load reduction and pitch ADC of the proposed cSPRC approach, baseline CPC and MBC-based IPC are computed for investigations.

Model configuration
The wind turbine model, which has been introduced in Section 2, is simulated by the FAST v8.16 simulation package (Jonkman and Buhl, 2005). It is coupled with Simulink where the wind turbine torque and pitch control systems are implemented. Two typical scenarios are considered in this paper, which are: (1) Wake-rotor overlap condition: 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.
(2) Turbulent 285 wind condition: the wind turbine is subjected to turbulent wind conditions.
The steady-state wind farm wake is simulated by the widely-used FLORIS model (Gebraad et al., 2016). In the parameterization of the FLORIS wake model, the Turbulence Intensity (TI) of 6.0% and the center-to-center distance between the wake center and the downstream turbine rotor center (5 rotor diameters (5D)) are specified to characterize the wind farm wake. It implies that the simulated wind turbine in the FAST tool is situated 5D behind the upstream turbine. Other effects such as wake 290 meandering, logarithmic wind profile and turbulence are not included in this scenarios. For the turbulent wind flow, a series of turbulent varying wind fields is simulated by using the TurbSim model 1 , where the TI is set to be 3.75% while the inflow wind speeds are specified as 12m/s, 16m/s and 20m/s. These two scenarios result in a total of 6 Load Cases (LCs) in the case study.
All of them are summarized in Table 2.
Then, the time series of the wind fields, which are based on the simulation results of the FLORIS and TurbSim, are fed 295 into the FAST/Simulink model as the input of the wind turbine simulation. In all the LCs, the simulation lasts 1000s at a fixed discrete time step of 0.01s. Furthermore, the safety bounds for the blade loads, corresponding to the output constraints in cSPRC, are determined according to IEC 61400-1 regulation (IEC, 2005), which leads tō where ξ is the safety factor and Y denotes the characteristic value for the loads, e.g. standard deviation of the loads. For the 300 normal operating condition of the wind turbine, ξ can be selected as 1.35 (IEC, 2005). For comparison, three different control strategies, namely the baseline CPC, MBC-based IPC and cSPRC, are simulated respectively in each LC. This finally leads to a total of 6 · 3 = 18 simulation runs. First of all, the propagation of the FLORIS wake to the downstream wind turbine is presented in Figure 3. As visible, the wind farm wake generated by the FLORIS model shows an in-wake velocity deficit, which is indicated by the blue regions in Figure 3. It will cause significant asymmetric loading on the rotor blades when the downstream turbine experiences the partial wake overlap (such as in 300s-500s and 700s-800s). The load control for such partial overlap induced asymmetric loads is demonstrated through a series of comparison studies. Figure 4 shows the time series of MOoP and corresponding pitch angles 310 on one blade. In order to clearly demonstrate the performance of different IPC strategies, the steady values of MOoP, which are closely related to the pitch angles from the baseline CPC, have been removed in this figure.
It can be seen that MOoP is significantly increased when the wake impinges on the left sector of the rotor at around 350s, 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 315 reduction can be observed during 350s-550s. 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 600s, 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 640s. The increased blade loads enables cSPRC to provide the IPC action for load mitigation. In comparisons, MBC-based IPC, which is a conventional IPC approach, actually shows maximum potential of load reduction.

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However, significant actuator activities are demanded by MPC-based IPC. For example, the corresponding pitch rates are presented in Figure 6. MBC-based IPC shows highest pitch rates, which lead to large cyclic fatigue loads on the actuators.
The developed cSPRC, however, is only active in load mitigation when the blade loads violate the output constraints, thus significantly reducing the actuator activities.
The cost function of the MPC optimization in cSPRC is illustrated in Figure 5. It essentially implies the desired actuator 325 activities for load mitigation in cSPRC. The value of the cost function increases when the wind turbine experiences the partial wake overlap. In the case where the blade loads satisfy the output constraints, the value of the cost function is reduced to zero.
Note that as the slack variables are included in cSPRC, the output constraints are not always respected. Some violations can be still observed in 300s-400s in Figure 4. This will avoid the instability of the closed-loop control system due to the non-linearity occurring in the control law and the model-plant mismatch.

Scenario II: Turbulent wind flow
Another scenario considered in the case study is the turbulent wind flow, where TI of 3.75% is specified in this paper. Figs. 7-8 show the time series of MOoP, corresponding pitch angles and pitch rate in LC5. Similarly, the cSPRC formulates the IPC action for load reduction when the turbulence induced loads violate the output constraints. By using a tight safety bound of 500KN·m, we can see that significant load reduction is achieved by cSPRC while the output constraints are generally respected.

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Since the slack variables are used to relax the ouput constraints, some constraints violations are observed from Figure 7. On the other hand, MBC-based IPC shows maximum load reduction in the turbulent wind flow, however, it will induce more actuator activities, as indicated by the pitch rate in Figure 8. This approach, considering the blade loads are minimized into the safety bounds, is an effective way to reduce the actuator activities and deal with the output constraints.
Other LCs show similar patterns and hence are omitted for brevity. Based on these comparisons, it can be concluded that 340 the developed cSPRC approach shows good performance in handling the output constraints in both wake overlap and turbulent wind flow scenarios. By designing safety bounds, it allows the wind farm operator to mitigate the loads into the safety bounds while reduce 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.

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In order to quantify the load reduction and pitch activities of these control strategies, two indicators, namely the the reduction of MOoP relative to baseline controller and the pitch ADC are calculated for comparisons. The latter one can be calculated according to the pitch rate (Bottasso et al., 2013), which is defined as whereβ denotes the pitch rate while β max is its maximum allowable value which is determined according to the specification 350 of the wind turbine. t is the time. For the 10MW wind turbine model, the value of β max is Pitch ADC, which actually implies the cyclic fatigue loads on the pitch actuators, is a widely-used criterion to estimate the lifespan of pitch actuators. In addition, the ratio r between the reduction of MOoP and pitch ADC is computed to comprehensively evaluate the control strategy. If r is larger, the control strategy is more effective in load reduction with the same amount 355 of pitch ADC, and vice versa. All these results are summarized in Table 3. In general, the proposed cSPRC shows similar or higher values of r compared to MBC-based IPC, while its pitch ADC is significantly reduced in considered cases. For instance, cSPRC shows ∼ 1.7 % of pitch ADC in LC2, whereas MBC-based IPC shows ∼ 5.5 % of pitch ADC in this case. Averaging over all the cases, the proposed control strategy shows pitch ADC of ∼ 4 %, thus leading to a higher r of 8.5 %. Considering the significant reduction of pitch ADC and higher r, it indicates that cSPRC is effective at reducing the actuator activities and 360 maintain the same level of load mitigation. By incorporating the output constraints, this approach is able to minimize the loads into the designed safety bounds with low actuator activities.
In comparison, MBC-based IPC, aims at attaining the maximum load reduction. However, it causes excessive pitch ADC and thus leading to a lower r. According to Table 3, MBC-based IPC shows amount of pitch ADC with an average of 10.80 %, which makes this approach not economical anymore. Therefore, it can be concluded that MBC-based IPC is not an economical 365 way to deal with the blade loads due to the high actuator activities. Since cSPRC is able to take into account the output constraints, it would be only activated to provide the IPC actions for the necessary load reduction when the blade loads exceed the designed safety bounds. In this way, the proposed method is able to alleviate the pitch ADC, achieve more economical load mitigation and guarantee the safety of the wind turbine system in all considered cases.

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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 375 wind turbine performance.  thus leading to a ratio r of ∼ 9 %. Moreover, it is interesting to note that cSPRC only produces the IPC action for load mitigation when the blade loads violate the output constraints. This, to some extent, reduces the actuator activities.
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. This may increase the wear on the bearings of the blades and reduce the reliability of the control system, which makes the conventional IPC approach not economical viable 385 anymore. In comparison, the proposed cSPRC, 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 the proposed cSPRC approach 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. Future work will include, without being limited to, considering other wake effects such as wake meandering and dynamic propagation 390 of the wake, executing scaled wind tunnel experiments, and full scale tests on a real wind turbine or wind farm.
Video supplement. This video shows the comparisons of load reduction between baseline control, MBC-based IPC and the proposed cSPRC strategies, where the wind turbine is impinged and overlapped by the wake shed from the upstream turbine. The ambient wind speed is 16m/s.
The wind farm wake flow is simulated by the steady-state FLORIS model. The designed safety bounds in cSPRC are 1200kN· m.