Control of Large Wind Energy Systems Throughout the Shutdown Process

Abstract

This contribution examines the control problem for very large wind energy converters during shutdown operation and analyses the most important control approaches. The control methods make use of the built-in conventional control infrastructure, but control system reconfigurations are undertaken in order to meet the demands of the shutdown control operation. Hence, the torque controller as well as the collective pitch controller (CPC) are redesigned from their regulator functions to reference tracking control systems with constraints. In addition, the CPC is combined with a feedforward controller in order to gain responsiveness. Constraints in magnitude and rate are managed by a modified anti-windup mechanism. Simulations of a 20 MW reference wind turbine verify the performance of the approaches.

1. Introduction

Due to the extreme complexity of large wind energy converters, they demand a very sophisticated control system, which is mainly concerned with making sure the machine runs as efficiently as possible both when operating at a low wind speed (partial load) or when operating at an overrated wind speed (full load). Such efficiency is related to the excellent performance of the machine operation, which is signalled not only by optimal energy conversion, but also the high damping of vibrations and the significant mitigation of loads. The overall control problem of wind turbines can be studied, for instance, in Refs. [1,2,3,4].

Nevertheless, wind turbines do not only run during underrated or overrated wind conditions, but many other operating conditions can occur, as can be seen from the state diagram of the supervisory control system. In these other operational states, energy conversion is not relevant, but vibration attenuation and load reduction are.

One of these other operation states is devoted to the shutdown process, henceforth referred to as the shutdown state, and the corresponding control procedure is carried out by the shutdown control system.

The shutdown process of a wind turbine is significant from multiple perspectives and well-known for many years (as can be seen in Refs. [5,6]), but has not been a relevant research topic over the years and has received little attention. On the other hand, Refs. [3,4,7] provide detailed explanations of the shutdown procedure as an operating condition of the supervisory control system. However, while the control problem through the shutdown phase is discussed in many references (see, e.g., Refs. [2,7,8,9,10,11]), control strategies and their implementations in the overall control system are seldom tackled in the wind turbine control literature.

One of the first works addressing this subject was reported in Ref. [12], where three control approaches for the shutdown procedure are analysed. The first one is an open-loop control procedure based on conventional control. The second one is a standard closed-loop control approach, and finally, a nonlinear model predictive controller (NMPC) is proposed. The NMPC experiences the best performance. Another concept for open-loop as well as closed-loop control that reduces extreme structural loads in the shutdown phase is studied in Ref. [13]. It solves an optimisation problem and is based on a low-order model. On the other hand, it is suggested in Ref. [14] that varying the pitch rate or starting the shutdown procedure at a certain azimuth angle could reduce loads on blades as well as on the tower top.

Later, another approach based on solving a constrained optimisation problem for an open-loop control system is proposed in Ref. [15]. The idea consists of optimising the pitch profile, considering load reduction and rotor overspeed simultaneously. Finally, the shutdown control problem is briefly introduced in Ref. [11], and a basic feedforward–feedback (FF-FB) control scheme is also depicted. The idea is later examined in Ref. [16].

The necessity of a shutdown can arise for several reasons, typically characterised by varied conditions and subjected to many restrictions. Thus, it is essential to assess control system configurations and control strategies according to their specific circumstances in order to identify an efficient resolution. All of these control approaches share a common goal of reducing rotor power to zero as quickly as possible. It is important to note that the emphasis is on the word possible because the shutdown must be accelerated to prevent any potential complications or damages produced by extreme operational conditions, but fast shutdowns increase loads that may rapidly deteriorate the wind turbine structure. As a result, shutdowns are generally slow, but only as long as necessary.

The scope of this research is limited to large three-bladed healthy wind energy converters with variable pitch and variable speed, which experience shutdowns due to exceeding the maximum permissible wind speed. The approach takes advantage of the existing control infrastructure present in the machine but reconfigures the control system and modifies both the control loops and algorithms.

Classic collective pitch control, typically operated as a regulator in Region III, is reconfigured as a reference tracking control scheme and augmented with a feedforward controller to enhance responsiveness. The active tower damping control is reparametrized to the new work conditions. Finally, the optimal torque control is changed to a torque controller law that is inversely proportional to the generator speed, such that the torque can be increased by falling generator speed. The bounded descendent rate maximisation and the amplitude minimisation of signal peaks are used as joint optimisation objectives to obtain the controller parameters.

This study pertains to three-bladed, downstream, variable pitch, variable speed, very large wind turbines. To analyse the approaches to shutdown control, it is necessary to choose one of the available reference wind turbines. The literature offers several options for this. For example, a 5-MW wind turbine is proposed in Ref. [17] and a 10-MW machine in Ref. [18]. Furthermore, a 15-MW machine from Ref. [19] and a very large 20-MW machine from Ref. [20] are also available. For the present work, the 20-MW reference wind turbine is chosen because it is very large and therefore slow, which is an additional challenge to test fast shutdown procedures. On this machine, three experiments are carried out in order to study the behaviour of three described approaches: open-loop control, feedback control, and feedforward–feedback control.

This paper is organised in the following manner: Section 2 focusses on the control problem that arises during the shutdown process and presents the control approach to address it. The control system design is described in Section 3. Section 4 is devoted to the numerical study, the reference wind turbine, and the simulation experiments. The results are presented in Section 5. Ultimately, in Section 6, conclusions are derived.

2. Wind Turbine Shutdown Control Problem

2.1. Shutdown as State of the Supervisor

Large, three-bladed, horizontal axis, variable-pitch, variable-speed wind turbines are typically characterised by four operational regions (see, e.g., Refs. [1,3,11]), which are determined by the wind speed, as depicted in Figure 1.

Region I corresponds to a wind speed lower than the cut-in value (v_{w_ci}). In this case, no energy conversion takes place. Over the cut-in value, but under the rated value v_w,rated, the machine is operated in Region II, i.e.; some energy is converted, but the delivered power cannot reach its rated value due to insufficient wind speed. When the wind speed exceeds the rated value, the wind turbine enters Region III and remains in it as long as it stays below the cut-out value v_{w_co}. Once the wind speed goes over the threshold v_{w_co}, the machine moves to Region IV, where it is shut down because of a wind speed beyond the safety limit. In addition, two transitional regions are defined in order to characterise the zones between Region I and II, as well as Regions II and III. They are known as Regions I½ and II½, respectively. Hence, the wind turbine control in Region IV is the subject of the present work.

The advent of shutdown circumstances can be triggered by either an unforeseen incident or a planned procedure. The classic scheduled shutdown takes place, for instance, prior to commencing regular maintenance. Common unexpected occurrences requiring shutdown may include, among others, grid loss, alarms, failures, faults, blade icing, overheating, and high wind speeds [13]. A scenario of intermediate nature occurs when the wind speed repeatedly surpasses the cut-out value (Region IV in Figure 1): while the timing of the event is unexpected, it is a common occurrence that can be programmed to happen in an organised manner. For example, Ref. [21] suggests introducing hysteresis in the control algorithms in order to prevent frequent start-up and shutdown operations produced by wind speed intermittence around the cut-out threshold.

Scheduled and unexpected shutdown operations are treated differently by the supervisory control system. While scheduled shutdown operations are included as part of the operational state Shutdown, unforeseen shutdowns are normally implemented in a separate operational state called Emergency Shutdown. The main difference between both of these states is the available time to complete the shutdown programme. Pre-programmed shutdowns have much more time to complete their required operations, and all restrictive conditions can be freely contemplated during the process. Contrarily, sudden shutdowns are normally associated with dangerous situations, and they therefore have to be carried out as fast as possible to prevent or limit damages [2,13].

A complete shutdown procedure requires multiple operating states, and the order of execution will vary depending on the initial state in which the process begins. For instance, if the machine is now in either the partial load or full load operation, the first step in the shutdown procedure will be to disconnect the generator from the grid. Furthermore, it is central that the shutdown operating states are reachable from all other states [22]. A reduced and splintered scheme of a supervisory control system that includes the emergency shutdown state is presented in Figure 2.

Once the management system verifies that the wind speed consistently runs over the cut-out threshold, the wind turbine enters Region IV of Figure 1, triggering an emergency shutdown event in order to start the sequence of Figure 2. In addition, the transition between Regions III and IV should be considered. In this transition zone, called here Region III^1/2, several operations take place, e.g., disconnection from the grid and the activation of a parking brake. The grid disconnection is necessarily carried out before shutdown, when the shutdown order is initiated with the machine working in one of the production states.

It should be noted that the grid disconnection in the shutdown state is widely indicated in the literature (see, e.g., Refs. [4,7,23]). However, this is not strictly necessary currently if the grid is healthy.

2.2. Conditions and Characteristics for the Shutdown

The most common technique for shutting down the wind turbine involves adjusting the blade angles to the feather position, where the blade chords are parallel to the wind direction. This action typically lasts a few seconds (3−10 s) limited by the speed fixed by the pitch system, usually between 6 and 12 degrees per second. There are several attributes of a wind turbine that impact the shutdown procedure and limit the operational capability of the control system. Some of these attributes are described in the following list.

• During regular operation, the wind turbine accumulates energy within its structure. Hence, it is imperative to execute the shutdown process in a manner in which the energy is freed without significant accelerations, oscillations, tower deflections in the fore-and-aft direction, and elevated blade root bending moments. This is critical to preventing additional loads and, ultimately, fatigue;
• The blades could be pushed into negative angles of attack in the case where the blades are pitched at a high speed. Consequently, the rotor experiences significant loads. On the other hand, dynamic stall can occur when the blades are quickly rotated to the feather position [9]. Therefore, the pitching speed is restricted both at the upper and lower bounds because the shutdown operation has to be fast but with low loads;
• If the blades are working at different pitch angles, as would be the case with a control system in IPC configuration (individual pitch control), a periodic force arises that can affect the drivetrain [9]. Thus, the pitch angles should be equalled first, and then only collective pitch control should be used in the shutdown procedure;
• Blade pitching leads to perturbations in the thrust force, which are then transmitted to the tower and become apparent as oscillations. Therefore, it appears beneficial to preserve the operation of the active tower damping controller (ATDC), typically integrated into the control system for Region III. However, its parameters might require retuning, and the natural frequency of the tower fore–aft motion should be filtered out;
• Fluctuations in the wind direction impact the rotational momentum on the yaw axis. The resulting force is perpendicular to the rotation plane and might potentially cause the blades to collide with the tower. Therefore, it is imperative to significantly minimise the yawing activity when carrying out the shutdown procedure.

2.3. Shutdown by Using Open-Loop Control

The control strategy for the shutdown using an open-loop approach requires two phases. The first one is carried out with the generator connected to the grid, then the generator torque is increased to the maximum in order to reduce the rotor speed as much as possible. The generator is then disconnected from the grid, initiating the second phase. With the disconnection, the torque is lost, and the rotor accelerates abruptly until the control system takes over and the speed begins to decrease once more.

The blades are thereafter rotated at a constant speed, which is determined as a balance between ensuring a safe shutdown, accommodating the highest permissible loads, and considering the capabilities of the pitch actuator. The movement starts from the current pitch angle and moves to a 90° angle (feather position). In the end, the wind turbine can be disengaged from the wind by means of the yaw control, if it is needed.

2.4. Shutdown by Using Closed-Loop Control

Open-loop control presents several inevitable drawbacks (see, e.g., Refs. [24,25]). One of the most relevant in the present control case is a stability problem. The machine will become unstable if the generator accelerates while the open-loop control is in progress. Hence, a closed-loop system could enhance the control performance.

The shutdown control, implemented through the closed-loop pitch control architecture, is basically a reference tracking control approach with constraints. The primary constraint is the speed saturation of the pitch actuators. However, the saturation limit is a value imposed by a compromise between shutdown rate and permissible loads rather than the physical limits of the actuators.

Some approaches are available to address tracking control problems with constraints as, for instance, controllers with an anti-windup methodology [26], saturated controllers with awareness of the limitations [27], reference governors [28], and finally, model predictive controllers (MPC) [29].

Both reference governors and model predictive controllers depend on highly complex algorithms. Additionally, a significant change in the control system architecture is required. For these reasons, the approach developed utilises the first concept, i.e., a classic control system with an anti-windup mechanism.

In the open-loop shutdown, the generator torque can be first increased to the maximum in order to reduce the rotor speed to the minimum. In a closed-loop shutdown scenario, this procedure is more complex due to the coupling between generator speed and torque provided by the OTC (Optimal Torque Control). In other words, the OTC cannot be used if the intention is to reduce speed by increasing the torque. An inverse proportional control law would be more appropriate for this purpose.

3. Multi-Loop Control System for the Shutdown Operation

3.1. Feedforward–Feedback Tracking Control Systems

The control system used in Region III is based on the collective pitch controller, which is typically implemented using a PI controller that serves as a regulator. A gain scheduling algorithm is used for parameter adaption. This control scheme is also suitable for shutdown control, but the regulator needs to be reconfigured to follow a monotone declining ramp reference variable. The slope of this reference signal must satisfy the constraints of the pitch actuators. Moreover, the gain scheduling mechanism is not necessary in Region IV. For instance, the pitch travel is limited in Region III to a range from −3 to 24–28 degrees with a rate of 8–12 deg/s. This span must be augmented up to 90 degrees in Region IV to take full advantage of aerodynamic braking.

The main drawback of a PI controller for the current application is its reactive nature, which results in a controller that lacks appropriate tracking properties. It is well-known (see, e.g., Refs. [30,31]) that small settling times and high accelerations are obtained by combining feedforward and feedback controllers in a two-degree-of-freedom control topology, as shown in Figure 3. While the feedback part ensures stability and enhances perturbation rejection, the feedforward part improves tracking behaviour.

Thus, a feedforward controller is added to the CPC, such that its proactive property complements the PI deficiency [32]. The feedforward/feedback control scheme for Region IV is shown in Figure 3.

The control system design is carried out by assuming a plant from the collective pitch angle as fictive input and the generator speed as output, i.e.,

$${\omega }_g(s)={\displaystyle \frac{B(s)}{A(s)}}\beta (s)$$

(1)

The denominator A(s) is normally approximated by a polynomial of the second degree

$$A(s)=s^2+a_1\hspace{0.17em}s+a_2$$

(2)

and polynomial B(s) has the form B(s) = b₁ s with b₁ < 0 (see the example given by (23)). Moreover, the control laws are represented by the transfer functions denoted as

$$G_{fb}(s)={\displaystyle \frac{Q(s)}{P(s)}}\mathrm{and}{G}_{ff}(s)={\displaystyle \frac{T(s)}{S(s)}}$$

(3)

correspondingly. In turn, the closed-loop transfer functions for Ω_g,rated(s) to Ω_g(s) and E(s) are

$${\Omega }_g(s)={\displaystyle \frac{B(s)}{S(s)}}{\displaystyle \frac{P(s)T(s)+Q(s)S(s)}{A(s)P(s)+B(s)Q(s)}}{\Omega }_{g,rated}(s) \mathrm{and}$$

(4)

$$E(s)={\displaystyle \frac{P(s)}{S(s)}}{\displaystyle \frac{A(s)S(s)-B(s)T(s)}{A(s)P(s)+B(s)Q(s)}}{\Omega }_{g,rated}(s)$$

(5)

It follows immediately from (5) that the ideal feedforward controller is given by the plant inverse, i.e., G_ff(s) = A(s)/B(s). However, this controller is noncausal for the considered application, and therefore, another concept has to be used for the control system design. The closed-loop control system will be stable if the feedforward controller is.

A PI controller given by

$$G_{fb}(s)={\displaystyle \frac{Q(s)}{P(s)}}=K_p+{\displaystyle \frac{K_i}{s}}={\displaystyle \frac{K_{p}s+K_i}{s}}$$

(6)

is chosen as feedback control component. For the feedforward controller, two simple polynomials are chosen, namely

$$T(s)=t_1\hspace{0.17em}s+t_2\mathrm{and}S(s)=s^2+s_1\hspace{0.17em}s+s_2$$

(7)

3.2. Active Tower Damping Control

Blade pitching causes perturbations in the aerodynamic thrust force, resulting in vibrations in the tower’s fore–aft direction because of a poorly damped first oscillating mode [33]. Due to the structural coupling between the tower and blades, vibrations occurring in the tower are also transmitted to the blades. This topic is not part of the present work, but it can be studied in Refs. [34,35,36,37,38,39,40,41].

The interest here is to modify the pitch control system to attenuate tower oscillations. The concept is not new and has its roots in the damping injection methodology developed first for the vibration control of robotic manipulators (see, e.g., Refs. [42,43,44]). It consists of superimposing an additional derivative control loop so that the damping coefficient of the system results increase. The control law as proposed in Ref. [33] is then expressed by

$$\Delta {\beta }_{atdc}(t)=-{\displaystyle \frac{D_t}{{(\partial F_t/\partial \beta )}_{{\beta }_0}}}{\dot{x}}_t(t)=K_{tdc}\hspace{0.17em}{\dot{x}}_t(t)$$

(8)

where ∂F_t/∂β is the aerodynamic sensitivity function of the thrust force regarding the pitch angle at the operating point β₀ and acts as a scheduling parameter, D_t is the proportional constant that represents the additional damping, $\dot{x_t}$ is the tower top speed in the fore–aft direction, and Δβ_atdc is the contribution of the ATDC to the whole pitch angle.

From Figure 4, it is also observable that CPC and ATDC are coupled, as highlighted in Ref. [45] as well. On one hand, the CPC generates significant pitch activity in the presence of turbulent wind, which leads to tower vibrations. On the other hand, the ATDC reduces these oscillations by readjusting the pitch angles, namely by counteracting the actions of the CPC. Hence, controller design entails attempting to strike a balance between the two controllers.

The joint parameter tuning of both controllers can be performed as in Ref. [46] by solving a parametric multi-objective optimisation problem and a Pareto method [47,48,49,50].

3.3. Anti-Windup Mechanism for Collective Pitch Control

Controllers with integral action followed by saturable actuators are susceptible to integrator windup. The integrator windup problem in PI and PID has been thoroughly examined in numerous studies (see, for instance, Refs. [51,52,53]). However, the most research has been limited to saturated actuator magnitudes. For such a case, an effective approach has been suggested in Ref. [54], which is currently referred to as back calculation.

Nonetheless, pitch actuators are limited in magnitude and rate. Hence, a modified anti-windup mechanism for saturated magnitudes and rates is presented in Ref. [55] by using the PI controllers in the automatic reset configuration [56]. See the scheme in Figure 5.

The anti-windup for a CPC has an additional complexity since a unique controller feeds three actuators that can saturate. Thus, there are three errors that have to be fused to go to one back calculation scheme. Let β _cpc be the pitch angle from CPC, and β_ai, for i = 1…3 be the actuator output. Variable Δu in Figure 5 is now called Δβ. As a fusion procedure, the minimum negative difference is used for the back calculation, namely

$$\Delta {\beta }_{cpc}=\underset{1\le i\le 3}{\min }({\beta }_{ai} -({\beta }_{cpc}+{\beta }_{atdc}))\mathrm{with}\hspace{0.33em}{\beta }_{ai}-({\beta }_{cpc}+{\beta }_{atdc}) \hspace{0.33em}\le 0\hspace{0.17em}\hspace{0.33em}\forall \hspace{0.17em}i$$

(9)

The diagram is depicted in Figure 6.

3.4. Generator Torque Control

The OTC given by

$$T_g(t)=K_{opt}{\omega }_g^2(t)$$

(10)

is the standard torque controller in Region II. In Region III, the torque control law can be either

$$T_g(t)=P_{rated}/{\omega }_{g,rated}\mathrm{or}{T}_g(t)=P_{rated}/{\omega }_g(t)$$

(11)

Under the assumption of perfect pitch control, i.e., ω_g(t) = ω_g,_rated, and defining

$$K_{opt}=P_{rated}/{\omega }_{g,rated}^3$$

(12)

both control laws (11) can be implemented by using Equation (10). In that case, the torque exhibits a tendency to diminish when the generator speed falls, whereas it remains consistent while the speed stays the same. However, in Region IV, the objective is to decrease speed while raising torque. This can be achieved by uncoupling the torque and speed control loops and then using, for example, an open-loop linear law of type

$$T_g(t)={\displaystyle \frac{T_{gmax}-T_{g,rated}}{{\tau }_{max}-{\tau }_{sd}}}(t-{\tau }_{sd})+T_{g,rated}$$

(13)

for torque, where T_gmax is the torque to be reached after τ_max and τ_sd is the time at which the shutdown started. Another way is preserving the coupling between the control loops and applying an inversely proportional control law (InPC) like the second equation in (11), but with modifications in order to comply with the requirements of Region IV, i.e.,

$$T_g(t)={\displaystyle \frac{K_{IV}}{{\omega }_g(t)}}$$

(14)

The gain K_IV is computed in the following section.

4. Design of the Control System

The control system topology employed for designing the control system is shown in Figure 7.

As already mentioned, the reference variable to be tracked can be modelled as a descending ramp that begins at the set-point of Region III ω_g,rated, and approaches zero after a duration of τ_st seconds, i.e.,

$$r(t)={\omega }_{g,rated}(1-(1/{\tau }_{st})\hspace{0.17em}t)$$

(15)

In Laplace domain, it corresponds to

$$R(s)={\omega }_{g,rated}\left[{\displaystyle \frac{1}{s}}-{\displaystyle \frac{1}{{\tau }_{st}\hspace{0.33em}{s}^2}}\right]={\omega }_{g,rated}\left[{\displaystyle \frac{s-1/{\tau }_{st}}{s^2}}\right]$$

(16)

By substituting (16) and B(s) = −b₁ s into (5), the closed loop control error is expressed by

$$E(s)={\displaystyle \frac{P(s)}{S(s)}}{\displaystyle \frac{A(s)S(s)-b_1\hspace{0.17em}s\hspace{0.17em}T(s)}{A(s)P(s)+b_1\hspace{0.17em}Q(s)}}{\displaystyle \frac{{\omega }_{g,rated}(s-1/{\tau }_{st})}{s^2}}$$

(17)

On the other hand, the steady-state error follows the final value theorem [25], namely

$$e_{ss}=\underset{t\to \infty }{\lim }e(t)=\underset{s\to 0}{\lim }s\hspace{0.17em}E(s)$$

(18)

In the case of a classic PI controller, P(s) = s (with reference to Equation (6)), and the steady-state error given by

$$e_{ss}=\underset{s\to 0}{\lim }{\displaystyle \frac{1}{S(s)}}{\displaystyle \frac{A(s)S(s)-b_1\hspace{0.17em}s\hspace{0.17em}T(s)}{A(s)+b_1\hspace{0.17em}Q(s)}}{\displaystyle \frac{{\omega }_{g,rated}(s-1/{\tau }_{st})}{s}}$$

(19)

diverges to infinite. Thus, it is necessary to set at least P(s) = s² in order to obtain a bounded steady-state error, namely

$$e_{ss}=\underset{s\to 0}{\lim }{\displaystyle \frac{s}{S(s)}}{\displaystyle \frac{A(s)S(s)-b_1\hspace{0.17em}s\hspace{0.17em}T(s)}{sA(s)+b_1\hspace{0.17em}(K_{p}s+K_i)}}{\displaystyle \frac{{\omega }_{g,rated}(s-1/{\tau }_{st})}{s}}={\displaystyle \frac{1}{S(0)}}{\displaystyle \frac{A(0)S(0)}{b_1\hspace{0.17em}{K}_i}}{\displaystyle \frac{(-{\omega }_{g,rated})}{{\tau }_{st}}}, \mathrm{and}$$

(20)

$$e_{ss}=-{\displaystyle \frac{a_2\hspace{0.17em}{\omega }_{g,rated}}{b_1\hspace{0.17em}{\tau }_{st}{K}_i}}$$

(21)

Given that a₂, b₁ and ω_g,ref are constant, the tracking error e_ss is inversely proportional to K_i and τ_sp. Hence, reducing the settling time results in a higher tracking error. Notice that e_ss is independent of the feedforward controller.

From (14), (15), and the assumption that the maximum torque T_gmax has to be reached in a time t = α τ_st (with 0 < α < 1), gain K_IV in (14) can be calculated by

$$K_{IV}=(1-\alpha )T_{gmax}{\omega }_{g,rated}$$

(22)

5. Parametrisation and Simulation Study

5.1. Reference Wind Turbine and Configuration of the Simulation Environment

The numerical study of the shutdown control system has been conducted on a 20 MW reference wind turbine. Originally presented in Ref. [20], it was subsequently analysed from the perspective of control in Ref. [57]. Later, it was parametrically modified and adjusted to ensure better behaviour and full compatibility with OpenFAST V3.5.2 (formerly known as FAST [58]). The control system is implemented in MATLAB/Simulink. A concise overview of relevant characteristics is given in

Table 1. Main parameters of the 20 MW reference wind turbine.

Characteristic	Values
Rated mechanical power	21.191 MW
Rated electrical power	20.000 MW
Rated rotor speed	7.1567 rpm
Rated generator speed	1173.7 rpm
Cut-in, cut-out and rated wind speed	4.48, 25.0, 10.92 m/s
Rated aerodynamic torque	28,434.70 kNm
Rated generator torque	169.76 kNm
Maximum generator torque	249.81 kNm
Peak power coefficient, optimal TSR	0.4812, 10.115
Gearbox and generator efficiencies	97.8, 96.1%
Sensibility function ∂Ft/∂β |vw = 25m/s	−4.328 × 103 kN/rad

.

The relationship between important variables and the effective wind speed is illustrated in Figure 8.

5.2. Dynamic Model and Control System Design

A dynamic model is calculated by averaging the models obtained by multiple linearisation around a complete rotation. This model represents the relationship between the collective pitch angle β and the generator rotational speed ω_g at the working point defined by a wind speed of 25 m/s, a pitch angle of 19.5025 degrees, and a rated generator speed of 1173.7 rpm. The corresponding transfer function is

$$G(s)={\displaystyle \frac{B(s)}{A(s)}}={\displaystyle \frac{-6.39092\hspace{0.33em}s}{s^2+0.1040\hspace{0.33em}s+0.00005}}$$

(23)

and the steady-state error is obtained from (21) for T_st = 80 s, considering a settling time of 2% as

$$e_{ss}=-{\displaystyle \frac{1173.7\times 0.00005}{6.39092\times 0.0047\times 80}}=-0.0244\approx 0$$

(24)

5.3. Parameter Tuning for All Controllers

For the torque controller, the gain is calculated from (22). The maximum generator torque is T_gmax = 249.81 × 10³ N, which has to be reached after 25 s, which means α = 0.25. The rated generator speed is ω_g,rated = 1173.7 rpm. Hence, the gain results are

$$K_{IV}=(1-\alpha )T_{gmax}{\omega }_{g,rated}=(1-0.25)\hspace{0.33em}248.81\times {10}^3\hspace{0.33em}1173.7=219.02\times {10}^6$$

(25)

The parameters for all the controllers in the pitch control system are determined via multi-objective optimisation (see, e.g., Ref. [59]) to achieve a rotating generator speed equal to zero in the minimum time under the compromise given by the joint reduction in the maximum amplitudes of the root bending moments, as well as the tower top displacement. The used objective functions are described in the next section, and the controller parameters are condensed in

Table 2. Optimal parameters for all controllers.

Parameters	Open-Loop Control	FB Control	FF-FB Control
Tst [s]	51.22	54.12	51.37
Ktdc	--	0.0011	0.0037
Kp	--	0.1038	0.0956
Ki	--	0.0519	0.0341
Ka	--	2.0021	2.1603
t1	--	--	0.0063
t2	--	--	0.0010
s1	--	--	3.6206
s2	--	--	0.1185

.

To assess the performance of the above-described controllers, several metrics are constructed. During the shutdown process, significant variables include the rotational speed of the generator going from rated to zero, the fore–aft tower top displacement, whose oscillation amplitude should be reduced as much as possible, and the flapwise root bending moments of blades, whose amplitudes should also be maintained to be as small as possible. Moreover, it is important to consider the duration of the shutdown process as well as the maximum peak-to-peak amplitude of the indicated variables. The appropriate performance indices are formulated as follows:

$$J_{\omega g}=(1/t_f-t_i){\displaystyle {\int }_{t_i}^{t_f}t\hspace{0.17em}{[{\omega }_{g,ref}(t)-{\omega }_g(t)]}^2}dt$$

(26)

$$J_{xt}=(1/t_f-t_i){\displaystyle {\int }_{t_i}^{t_f}t\hspace{0.17em}{[{\overline{x}}_{t,ss}-x_t(t)]}^2}dt$$

(27)

$$J_{My}=(1/t_f-t_i){\displaystyle {\int }_{t_i}^{t_f}t\sqrt{M_{Myb1}^2(t)+M_{Myb2}^2(t)+M_{Myb3}^2(t)}\hspace{0.17em}}dt$$

(28)

where τ_st = t_f − t_i is the shutdown time. $\overline{x}$_t,ss represents the average value of x_t for the steady state. All variables are scaled. In addition, peak-to-peak values are also used as metrics, i.e.,

$$\begin{gathered} p{p}_{\omega }=\left|\max ({\omega }_g(t))-\min ({\omega }_g(t))\right|,p{p}_x=\left|\max (x_t(t))-\min (x_t(t))\right|,\mathrm{and} \\ p{p}_{M,i}=\left|\max (M_{yb,i}(t))-\min (M_{yb,i}(t))\right|,\hspace{1em}\mathrm{for}i=1,2,3 \end{gathered}$$

(29)

All metrics consistently show superior performance when the numerical value is lower. The first three indices are an average of the surface under the squared signal weighted by time. Thus, reduced amplitudes with shorter duration result in a lower numerical value. Peak-to-peak amplitudes refer to the maximum magnitude of change in a jumping signal, measured in one instant. Smaller jump amplitudes are indicative of better performance.

5.4. Simulation Experiments

The simulation time for each experiment has been set at 600 s. The machine is first set for working in Region III with the wind speed close to the cut-out value of 25 m/s, a rotating speed of 10.716 m/s, and an average power output of around 20 MW. The stochastic wind speed profile includes 12% turbulence and has been generated following the Kaimal spectra. The wind speed exceeds continuously 25 m/s just after 50 s, i.e., τ_st = 50 s, and therefore the shutdown procedure is triggered. The first stage, characterised by the torque increasing, takes 25 s, such that the second stage begins at t = 75 s. The initial condition for the simulation includes data for the stationary operation at the operating point that corresponds to a wind speed of 25 m/s: the generator speed is set to 1173.7 rpm for a pitch angle of 19.4 degrees, and for a generator torque of 1.71 × 10⁵ Nm, the simulator should output an electrical power of 20 MW. Moreover, all degrees of freedom foreseen in the simulator are activated.

The first experiment studies the shutdown operation under open-loop control. Three cases are considered: without change in the generator torque T_g, with an increase of T_g followed by the pitch increase (sequential control), and with a simultaneous control of T_g and pitch angle.

In the second experiment, the shutdown operation is carried out by using the feedback control, and it is compared with the best result of experiment one. The third experiment considers the FF-FB control approach, and it is compared with the best result of experiment one and with the result of experiment two.

6. Simulation Results and Analysis

6.1. Simulation Results for the First Experiment

The first experiment considers open-loop control, including three strategies: the generator torque remains at the nominal value; the generator torque is increased alongside the pitch control to the maximum allowed value (simultaneous strategy); the generator torque is increased, followed by the start of pitch control (sequential strategy). Simulation curves are shown in Figure 9.

From Figure 9a, it can be inferred that maintaining constant torque at the rated values does not lead to a rotational speed of zero in an acceptable time. Thus, it is no longer subjected to analysis. It also shows the decrease in speed caused by the intentional augmentation of the generator moment (black curve). It is also clear that the torque loss occurs 40 s after the start of the shutdown. Moreover, both other studied strategies are very close in the numeric values of

Table 3. Values of the performance indices for the different strategies in experiment 1.

Strategies	Jω	Jx	JM	ppω [rpm]	ppx [m]	ppM,1 [kNm]
1	0.3308	0.4760	0.3626	1112.8	1.5062	134044.0
2	0.5712	0.4612	0.5654	1170.4	1.1692	122,245.1
3	0.5735	0.3870	0.4898	1140.1	1.1141	115,415.4

, but the third strategy is slightly better. Of particular importance is that large peaks in both tower top displacement and blade root bending moments have to be avoided. Therefore, Strategy 3 is also implemented for the closed-loop experiments.

6.2. Simulation Results for the Feedback Control System

The second experiment investigates the pure feedback control strategy and compares its results with the best of the first experiment. The simulation curves are shown in Figure 10.

The major advantage of the closed-loop approach over the open-loop approach, apart from the classical advantages of a closed-loop control system [60], is the fact that by keeping the pitch control active, ATDC can also be kept on, which can be appreciated in Figure 10b. However, one drawback is that the shutdown procedure is slightly slower. All the index values are summarised in

Table 4. Values of the performance indices for Experiment 2 compared with Experiment 1.

	Jω	Jx	JM	ppω [rpm]	ppx [m]	ppM,1 [kNm]
Experiment 1	0.5735	0.3870	0.4898	1140.1	1.1141	115,415.4
Experiment 2	0.5541	0.3744	0.5039	1151.9	0.9625	131,906.1

. The values of the first experiment are repeated to simplify the comparison.

6.3. Simulation Results for the Feedforward–Feedback Control System

The last experiment focusses on the study of the FF-FB closed-loop control approach and compares the results with those of the previous experiments. The curves are depicted in Figure 11. The FF controller is found to restore the inherent delay of the FB controller, and then the shutdown time is comparable to the shutdown time of the open-loop approach while preserving the advantages of the FB control, i.e., the attenuation of the oscillations in the tower top displacement and the overall better values of all the indices.

All the values of the performance indices are condensed into

Table 5. Values of the performance indices for Experiment 3 compared with Experiments 1 and 2.

	Jω	Jx	JM	ppω [rpm]	ppx [m]	ppM,1 [kNm]
Experiment 1	0.5735	0.3870	0.4898	1140.1	1.1141	115,415.4
Experiment 2	0.5541	0.3744	0.5039	1151.9	0.9625	131,906.1
Experiment 3	0.5423	0.3710	0.4657	1144.4	1.0996	116,559.3

. The numbers of previous experiments are also included to facilitate the analysis.

6.4. Closing Analysis of Findings and Remarks

The differences and advantages between the presented approaches are mainly conceptual and are founded on the classical control theory. The approaches have been presented in an increasing sequence of complexity (open-loop (OL), feedback (FB), feedforward–feedback (FF-FB)), which coincides at the same time with an increase in performance. The OP control is most commonly used because of its simplicity, but, on the other hand, there is no possibility to modify the process once started, and its stability is not guaranteed.

FB control improves the performance, making the process safer, but the control system is more complex, where a controller has to be parametrised and tuned. By means of the parametrisation, the shutdown trajectory can be managed. On the other hand, the shutdown process can be slower, and the transient may exhibit some oscillations. Nevertheless, the method is often used from time to time. Moreover, FB control makes possible the use of the ATDC together with the PCP, which leads to a reduction in the amplitudes of the tower oscillation as can be observed in the corresponding figures.

Finally, the FF-FB control configuration speeds up the process without deteriorating the properties of the pure feedback. On the other hand, two controllers must be parametrised and tuned simultaneously, making the control system design the most complicated. All these aspects are confirmed by the experiments.

After observing the results, it is clear that open-loop control should be avoided. The election between FB and FF-FB configurations will depend on their particular application. If the difference in performance is small for the given application, it is preferable to implement FB control. In the case of very large and expensive machines, FF-FB should be recommended in order to increase safety and take advantage of the additional performance, despite its complexity.

Finally, the importance of switching the torque control law from OTC to InPC, which enables speed reduction by increasing the torque, should be noted.

7. Conclusions

The present study investigates three methodologies for a controlled shutdown of large wind turbines. The conventional open-loop control method is contrasted with a traditional feedback control system consisting of a proportional–integral (PI) controller, as well as an enhanced concept that incorporates a feedforward controller together with the PI controller. The constrained tracking control approach includes an anti-windup mechanism specifically developed for the collective pitch control system due to the fact that three actuators are connected with only one controller.

The parameter tuning for the closed-loop control approaches is carried out by using parametric multi-objective optimisation. This is particularly important for the FF-FB control system because it has numerous parameters to be adjusted.

The research was conducted on a 20 MW reference wind turbine implemented in OpenFAST, and the control system runs in MATLAB/Simulink. The encouraging results show that the FF-FB technique strikes the ideal balance between speed and the decreased amplitudes of the root bending moments, and fore–aft tower oscillations. The collective pitch control system enables the use of active tower damping control, which enhances the system’s performance in terms of tower top displacement.

Subsequently, future research will use more complex control algorithms, like fractional order PI controllers (FOPI) and nonlinear PI controllers (NPI) and evaluate them in a real-time setting. Another research direction involves developing a procedure that enables the activation of IPC (individual pitch control, [61]) during shutdown processes, thereby improving the system behaviour with respect to root bending moments.