Actuators for Large Wind Energy Systems—A Tutorial-Focused Survey

Abstract

Undoubtedly, wind turbines are currently one of the most significant contributors to clean energy. Therefore, it is crucial to enhance the capability of wind turbines, which in turn leads to an increase in their dimensions. Nevertheless, only advanced control systems can guarantee the optimal and secure operation of these huge machines. On the other hand, the precise control of these modern wind turbines is only achievable through the use of highly specialised actuators. Despite their importance, actuators have historically been overlooked and seen as secondary components in control systems. However, in modern machines, actuators are required to manipulate multiple tonnes or manage thousands of volts and amperes within short times. Consequently, greater emphasis must be placed on their handling and operation. This study aims to review actuators for modern large wind energy converters from a control engineering perspective, using a tutorial approach.

1. Introduction

The operation of wind turbines is impossible without control systems, which are linked to the machine by means of sensors and actuators. In the evolution of wind turbines, where the machines have rapidly increased in size, sensors and actuators have become a difficult technological hurdle. On the one hand, sensors must be able to measure powers of several MW, forces of several MN, and moments of several MNm. On the other hand, actuators must be able to handle masses of many tonnes in mechanical subsystems, as well as several kA and kV in electrical subsystems.

Some wind turbine subsystems are frequently ignored or oversimplified in the modelling process. Actuators are one example of such devices. It is often unnecessary to have models with additional complexity. Hence, it is useless to include more equations in the model. Today, control systems are expected to handle more challenging issues, such as huge and slow actuators, requiring the use of more complex dynamic models [1].

This applies, for example, to the pitch actuators, where the pitch control system exerts increasing pressure. Fault-tolerant control can, therefore, be implemented with a more complex pitch actuator model (see [2,3]). Something akin to this might be considered for a yaw actuator. Yaw systems consider solely electric actuation, whereas pitch systems are designed for both hydraulic and electric actuation.

The wind turbine can be decomposed using decomposition and coordination techniques [4] in several subsystems, such as the aerodynamic, rotor, drivetrain, generator, tower, and actuation subsystems. In principle, three actuation subsystems can be mentioned: pitch, yaw, and power electronic subsystems. All subsystems are coordinated by variables. An example of a spatio-temporal decomposition with highlighted actuation subsystems is shown in Figure 1.

This study is addressed to three-bladed, downstream, variable pitch, variable speed, and very large wind turbines, the purpose of which is to review the most important key elements of actuators related to wind energy converters from an automatic control perspective. The formulation is approached from a tutorial viewpoint, with a particular emphasis on modelling considerations. The paper is structured in the following manner: Section 2 is devoted to the pitch systems, followed by the yaw systems in Section 3. Next, in Section 4, power converters as actuators for torque control are described. Section 5 is dedicated to describing briefly the actuator control problem. Section 6 discusses mathematical tools for assessing actuator performance. Actuators for smart blades are shortly introduced in Section 7 for the sake of completeness. Section 8 is focused on drawing conclusions.

2. Pitch Actuating Systems

The pitch actuation entails the rotation of blades around their longitudinal axis to adjust the angle of the attack in accordance with the relative wind speed. Hence, pitch dynamics can be described as a rotational motion around the pitching axis, as depicted in Figure 2.

On the other hand, the pitch dynamics of wind turbines encompass the rotation of all the blades around the azimuth angle, in addition to the turning on the pitch axis. Furthermore, the blades are elastic, which results in a variable second moment of inertia with respect to the pitching axis, and they depend on the angle of deflection, the azimuth angle, and the pitch angle. Consequently, all dynamics are very complex, but a very simple model, including the actuator, is sufficient for the control system design. A model of the pitch dynamics is examined with details in [5].

The model used here considers a rigid, non-rotating blade whose motion equations are formulated by:

$$J_{pe}\ddot{\beta }+B_{pe}\dot{\beta }+K_{pe}\beta =n_p{T}_{pa}-T_b-T_f,$$

(1)

where β is the pitch angle, J_pe is the equivalent second moment of inertia with respect to the pitch axis, B_pe is the equivalent torsional damping coefficient, and K_pe is the equivalent torsional stiffness coefficient. The torque applied to the blade by the actuator is n_p T_pa, with the n_p as a gear ratio that considers the toothing of the pinion and blade bearing as well as the pitch actuator gearbox. T_b is a torsional moment resulting from dynamic and aerodynamic forces that act as disturbances on the blades. At last, the frictional moment generated by the bearing is denoted as T_f.

It should be noted that the torsional moment T_b is normally unmeasurable, but it can be estimated using a simulation program. By using the formula

$$T_f=0.5\mu \left(D_b{F}_{AR}+{\alpha }_1{M}_b+{\alpha }_2{D}_{b}F\right)sign(\dot{\beta })$$

(2)

from [6], the bearing frictional moment can be empirically obtained for ball and roller bearings.

The formula has its origins in experimental data obtained from a product series, and as a result, its validity range is highly limited. Nevertheless, the formula can be curve-fitted with the availability of data coming from other bearings. The radial and axial forces working on the bearing are symbolised by F_R and F_A, respectively. The bearing friction μ depends on the bearing type and is often provided by the manufacturer. Fitted coefficients α₁ and α₂ are also specific for a given bearing. M_b denotes the resulting blade root bending moments, while D_b is the bearing diameter.

2.1. Simple Models of Pitch Actuator

2.1.1. Pitch Actuator as First Order System

The electromechanical nature of the wind energy converter typifies that the system has very different time constants. Mechanical components have large inertia with slow reaction times, while electrical devices are very fast. On the other hand, pitch drivers are situated in between, i.e., they are faster than the mechanical subsystem but slower than the electrical one. These considerations about the time constants justify the idea of using a very simple model for the pitch actuators. Hence, first-order models are often used to this end, as reported in, e.g., [7,8,9]. A typical first-order model for a pitch actuator is formulated in [10] as follows:

$$\dot{\beta }(t)=(1/{\tau }_{\beta })[{\beta }_{ref}-\beta (t)]\mathrm{for}{\beta }_{\min }\le \beta \le {\beta }_{max}\mathrm{and}{\dot{\beta }}_{min}\le \dot{\beta }\le {\dot{\beta }}_{max},$$

(3)

whose block diagram is depicted in Figure 3.

Variables β_ref, β_max, and β_min are pitch angle reference, upper bound, and lower bound, respectively. τ_b is the time constant. Pitch actuators are normally constrained in travel and rate. The travel goes from −3 or −4 to 25–30 degrees in normal overspeed operation and up to 90 degrees in shutdown operation. The rate is limited to ±8 or ±10 degree/s in order to avoid large loads on the blades. Sometimes, it is necessary to filter out low pitch rates smaller than ±0.1 degree/s to avoid noise and excessive pitch activity around zero. This is implemented in [11] using a rate limiter with a dead zone.

First-order models have drawbacks, such as the absence of an initial delay and the inability to model oscillating behaviour. These issues are improved by a second-order model.

2.1.2. Pitch Actuator as Second Order System

Following the idea of simple models for the pitch actuators, a second-order model, as suggested in [12], can be used. More advanced second-order models can include constraints and dead time, as proposed in [13,14]. Thus, the corresponding equation is as follows:

$$\ddot{\beta }=-2\zeta {\omega }_n^2\dot{\beta }+{\omega }_n^2[{\beta }_{ref}(t-T_t)-\beta ]{\beta }_{min}\le \beta \le {\beta }_{max}\mathrm{and}{\dot{\beta }}_{min}\le \dot{\beta }\le {\dot{\beta }}_{max},$$

(4)

and the graphical representation is depicted in Figure 4.

Parameters ζ and ω_n are the damping ratio and the eigenfrequency, respectively. T_t is the dead time. Depending on the wind turbine dynamics, the damping ratio can vary between 0.6 and 0.9 and the eigenfrequency between 8.88 and 11.11 rad/s (see, for instance, [15,16,17]). Notice that β_max is the maximum amplitude constraint, which is selected to keep constant the rotor speed for the maximum wind speed. A typical dependence between wind speed and pitch angle is depicted in Figure 5. β_max must be changed to 90 degrees in the shutdown operational state.

2.1.3. Pitch Actuator with Pitch Rate Reference

Modern pitch actuators normally contain an internal servo controller whose reference variable is a rate signal instead of an angle signal. For this reason, it is convenient to express the model of the pitch actuator in terms of rates. Hence, the model can be modified in order to accommodate pitch rates. One way to accomplish this is to modify the model of Figure 3, as shown in Figure 6.

2.2. Modelling Pitch Actuators Using Physical Principles

All the above-described models are generic and normally sufficient for control purposes. However, they cannot study and simulate the internal interactions of different actuator components. Hence, the physical representation of the actuators becomes useful.

Pitch actuators for wind turbines typically are based on two different technologies: electromechanical and hydraulic drives. Hydraulic systems are, on the one hand, more robust, stiffer, with less backlash, and offer more torque; on the other hand, they are larger and slower to respond. For this reason, hydraulic solutions are considered in machines subjected to high aerodynamic loads. Contrarily, electromechanical systems are prone to failures and have a lower strength, but their fast reaction time makes them more appropriate for fast control, such as individual pitch control (IPC). Both drivers are analysed in the following.

2.2.1. Hydraulically Driven Hydraulic Pitch Actuators

A hydraulically driven pitch actuator follows the same concept as many other hydraulic devices. It comprises a set-up of a hydraulic pump, a tank, an electrohydraulic-commanded proportional valve, a relief valve, and a hydraulic cylinder. A simple scheme of a hydraulic pitch drive is shown in Figure 7.

Several dynamic models are available for hydraulic pitch actuators, for instance, in [2,18,19]. The main duty of the actuator is to rotate the blade. To this end, it must provide a torque T_pa greater than the bearing friction moment and the aerodynamic pitching torque. Hence, the torque can be expressed by

$$T_{pa}=f_p(\beta )F_p{r}_p,$$

(5)

where f_p(β) is a functional relationship between piston force and the pitching moment defined as follows:

$$f_p(\beta )=(1/r_p){\displaystyle \frac{d{x}_p}{d\beta }}.$$

(6)

F_p is the piston force, r_p is the actuator torque arm, x_p is the piston rod position, and β is the pitch angle. With the help of Figure 7, the relationship between x_p and β can be derived and expressed as follows:

$$x_p=\sqrt{L_p^2+r_p^2-2L_p{r}_p\cos ({\alpha }_0+\beta )}-l_p,$$

(7)

where α₀ is the angle between the pitch axis and the axis of the pitch to centre for x_p = 0, and L_p is the length from pitch to centre. Thus, α₀ can be calculated from

$${\alpha }_0={\cos }^{-1}(r_p/L_p).$$

(8)

Deriving (7) into β follows

$$f_p(\beta )=(1/r_p){\displaystyle \frac{d{x}_p}{d\beta }}={\displaystyle \frac{L_p\sin ({\alpha }_0+\beta )}{\sqrt{L_p^2+r_p^2-2L_p{r}_p\cos ({\alpha }_0+\beta )}}}.$$

(9)

The pitch angle β is also obtained from (7) as

$$\beta ={\cos }^{-1}\left[{\displaystyle \frac{L_p^2+r_p^2-{(l_p+x_p)}^2}{2L_p{r}_p}}\right]-{\alpha }_0.$$

(10)

The resulting force F_p is then given by the sum

$$F_p=A_a{p}_a-A_b{p}_b-c_p{\dot{x}}_p.$$

(11)

The pressures applied on the respective piston areas A_a and A_b are denoted as p_a and p_b. The final term refers to the viscous damping force applied to the moving piston. Equation (9) provides the basis for computing the derivative of x_p as follows:

$${\dot{x}}_p=(\partial x_p/\partial \beta )\dot{\beta },$$

(12)

which leads to

$${\dot{x}}_p={\displaystyle \frac{L_p{r}_p\sin ({\alpha }_0+\beta )}{\sqrt{L_p^2+r_p^2-2L_p{r}_p\cos ({\alpha }_0+\beta )}}}\dot{\beta }.$$

(13)

In order to solve (11), pressures p_a and p_b in the cylinder are necessary. They satisfy the first-order laws given by (see [20])

$${\dot{p}}_a={\displaystyle \frac{B_a}{V_a(x_p)}}[-A_a{\dot{x}}_p+q_a(p_a,u)] \mathrm{and},$$

(14)

$${\dot{p}}_b={\displaystyle \frac{B_b}{V_b(x_p)}}[A_b{\dot{x}}_p+q_b(p_b,u)].$$

(15)

Parameters B_a and B_b denote the effective bulk moduli in chambers a and b and the associated volume flow rates by q_a and q_b. The control signal is denoted by u, and chamber volumes V_a and V_b depend on x_p, namely

$$V_a(x_p)=A_a{x}_p+V_{a0} \mathrm{and},$$

(16)

$$V_b(x_p)=A_b(l_s-x_p)+V_{b0},$$

(17)

with V_a0 and V_b0 being unusable piston volumes. The piston stroke is l_s. Hence,

$$q_a=\left\{\begin{array}{l}sign(p_s-p_a)k_v\sqrt{|p_s-p_a|}u(t)u(t)>0\hfill \\ sign(p_a-p_r)k_v\sqrt{|p_a-p_r|}u(t)u(t)\le 0\hfill \end{array}\right.$$

(18)

$$q_b=\left\{\begin{array}{c}-sign(p_b-p_r)k_v\sqrt{|p_b-p_r|}u(t)u(t)>0\\ -sign(p_s-p_b)k_v\sqrt{|p_s-p_b|}u(t)u(t)\le 0\end{array}\right.,$$

(19)

expresses the flow rates throughout the chambers, where p_r and p_s are the ambient pressure and the pressures provided by the pump [20]. k_v denotes the valve coefficient. The proportional control law

$$u(t)=K_p\{x_p[\beta (t)]-x_p[{\beta }_{ref}]\}$$

(20)

provides the control signal u(t). The piston dynamics is finally modelled by the second-order motion

$$m_p{\ddot{x}}_p+b_p{\dot{x}}_p+k_p{x}_p=F_p-T_b/r_p,$$

(21)

where the stiffness, the damping coefficient, and the piston mass are denoted by k_p, b_p, and m_p, respectively.

2.2.2. Electrically Driven Pitch Actuators

In essence, an electrically driven pitch actuator comprises a gearbox coupled with an electrical motor. It is coupled with the blade root through a pinion that engages with a bearing and a gear rim. A scheme of such an actuator is depicted in Figure 8.

Any type of electric drive can be used to assemble a pitch actuator. However, the most commonly used today are permanent magnet synchronous motors. Mechanical components follow the motion Equation (1) but are expressed in terms of the blade and motor parameters, namely

$$J_{pe}\ddot{\beta }+B_{pe}\dot{\beta }+K_{pe}\beta =n_p{T}_{pa}-T_b-T_f,$$

(22)

with

$$n_p=n_{px}{n}_{gr},J_{pe}=J_{pb}+n_p^2{J}_{pm},B_{pe}=B_{pb}+n_p^2{B}_{pm}\mathrm{and}{K}_{pe}=K_{pb}+n_p^2{K}_{pm},$$

(23)

where the stiffness coefficients, damping coefficients, and mass moments of inertia for the blade and motor are represented by K_pb, K_pm, B_pb, B_pm, J_pb, and J_pm.

The electric part is expressed by using the motor convention in the rotating dq reference frame [21]. The mathematical modelling includes the first-order differential equations

$$L_d{\displaystyle \frac{d{i}_d}{dt}}+R_s{i}_d-L_q{\omega }_e{i}_q=v_d,$$

(24)

$$L_q{\displaystyle \frac{d{i}_q}{dt}}+R_s{i}_q+L_d{\omega }_e{i}_d+{\lambda }_m{\omega }_e=v_q,$$

(25)

and the dq-transformation

$$\begin{array}{c}\begin{array}{c}\left[\begin{array}{c}{v}_d\\ v_q\end{array}\right]=\end{array}\\ \end{array}\begin{array}{cc}{\displaystyle \frac{2}{3}}& \left[\begin{array}{ccc}\cos ({\beta }_e)& \cos ({\beta }_e-2\pi /3)& \cos ({\beta }_e-4\pi /3)\\ -\sin ({\beta }_e)& -\sin ({\beta }_e-2\pi /3)& -\sin ({\beta }_e-4\pi /3)\end{array}\right]\\ & \end{array}\left[\begin{array}{c}{v}_a\\ v_b\\ v_c\end{array}\right].$$

(26)

The three-phase input voltages are denoted by [v_a v_b v_c]^T. The electrical speed is ω_e, and the electrical rotational angle is β_e. The electrical parameters are L_q and L_d as the self-inductances, λ_m as the flux linkage between the stator and the rotor, and R_s as the stator resistance. Finally, the electrical torque with p as the number of pole pairs is given by

$$T_{pa}={\displaystyle \frac{3p}{2}}[{\lambda }_m{i}_q+(L_d-L_q)i_d{i}_q].$$

(27)

Figure 9 shows a scheme of the electrical components.

The mechanical pitch angle is related to the electrical rotational angle according to the relationship

$${\beta }_e=p{n}_{px}{n}_{gr}\beta ,$$

(28)

where ratios of gear rim and gearbox are denoted by n_gr and n_px, respectively. Thus, the electrical speed links to the pitch rate by

$${\omega }_e=p{n}_{px}{n}_{gr}\dot{\beta }.$$

(29)

Figure 10 illustrates a schematic diagram of the whole pitch actuator.

In the end, a second-order model is used to represent the electrical subsystem, whereas another second-order model is applied to model the mechanical components. Thus, the entire model becomes fourth-order.

Based on the premise that the electrical subsystem exhibits significantly faster dynamics than the mechanical components, the electric subsystem can be viewed as being in a steady state, and hence, the pitch actuator behaves according to second-order dynamics.

3. Yaw Actuating Systems

The principal objective of the yaw subsystem is the maximisation of the captured energy via maintaining the machine orientated in the direction of the wind by means of accurate direction tracking. Although hydraulic yaw actuators are possible, they are essentially electric. Hence, yaw systems comprise multiple electric motor drives synchronised by a common control signal. In essence, yaw drives use the same concept as electric pitch drives, including an electric motor, gear rim, pinion, and planetary gearbox. Furthermore, the yaw rim and yaw brakes are attached together in order to secure the rotor remains in its 90-degree orientation with respect to the wind direction or during maintenance procedures. The yaw mechanism commonly provides a considerable yaw torque to move the nacelle. A schematic representation of a six-driver yaw system is shown in Figure 11, where three drives are maintained behind the visible ones to improve the legibility of the diagram.

It is assumed, for the sake of simplicity, that the drive assembly comprises m_y identical synchronous motors with the same electrical models as provided by (24)–(26). The applied torque that is required for the nacelle rotation is determined by

$$T_{ya}=m_y{\displaystyle \frac{3p}{2}}[{\lambda }_m{i}_q+(L_d-L_q)i_d{i}_q].$$

(30)

The wind rotor aerodynamics, including factors like wind shear, skewed wake effects, horizontal and vertical wind components, and blade rigidity, have an important contribution to the yaw motion, resulting in quite complex yaw dynamics, which is, in turn, very difficult model. Therefore, a simplified model for control purposes is given by

$$J_{ye}\ddot{\gamma }+B_{ye}\dot{\gamma }+K_{ye}\gamma =n_y{T}_{ya}-T_y-T_{yf}$$

(31)

is considered here. J_ye is the equivalent second moment of inertia around the yaw axis, including the rotor and nacelle; K_ye denotes the torsional stiffness coefficient; and B_ye represents the torsional damping coefficient. The yaw angle is denoted by γ. The torque applied by the yaw actuators multiplied by n_y is denoted by T_ya, where n_y is the gear ratio that considers the gearbox ratio of the yaw actuator and the toothing of the yaw bearing and pinion. In addition, the equation contains two more moments: T_y, which is a torsional moment for all external moments acting in the yaw-axis direction, and T_yf is the yaw-bearing frictional moment.

The primary contributing factor to T_y is the resulting blade root bending moment translated to the yaw axis. It is estimated in [22] by using

$$T_{bm}=\sqrt{M_x^2+M_y^2}$$

(32)

with

$$M_x=\left(2/9\right)R{F}_{t,max}\mathrm{and}{M}_y=m_{b}g{r}_{cg}+1/3,$$

(33)

where F_t,max is the maximum thrust force in the wind direction, R is the rotor radius, r_cg is the location of the gravity centre, m_b is the blade mass, and g is the gravitational acceleration. For the frictional moment T_yf, the estimative formula is provided in [6], i.e.,

$$T_{yf}=0.5\mu \left(D_b{F}_A+{\alpha }_1{D}_b{F}_R+{\alpha }_2{M}_t\right)sign(\dot{\gamma }).$$

(34)

The tilting moment working on the bearing is denoted in (34) by M_t.

4. Power Converters as Actuators

When the wind speed is sufficiently fast to convert energy but not high enough to reach the nominal operation, the primary control goal is to maximise power extraction. Nevertheless, this goal can only be achieved with variable-speed wind turbines, as their operation relies on the separation between the generator and the power network facilitated by power converters.

To this end, the sole relevant input variable is the electromagnetic generator torque. By manipulating this variable with a power converter, it is possible to follow the generator characteristic curve, obtaining the maximum possible power capture. The control system configuration comprises three stages. The initial stage involves implementing the control law, which generates the control signal for the subsequent phases. In the second stage, a reference signal is generated to govern the power converter. Lastly, the third stage involves the low-level control device responsible for managing the power electronics. The approach is illustrated in Figure 12.

Hence, the power converter serves as an interface between the control system (MPPT, maximum power point tracking) and the generator, fulfilling the role of an actuator. There are several types of power converters, depending on the generator type. Modern wind turbines have attached either a permanent magnet synchronous generator (PMSG) or a double-fed induction generator (DFIG). In both cases, bidirectional back-to-back power converters are used, although connected differently. A schematic back-to-back power converter is shown in Figure 13.

Back-to-back power converters are built using two voltage source converters (VSC) connected by a DC link, where the VSCs are normally controlled using the pulse-wide modulation (PWM) technique with variable modulation index. Power converters, their operation, and control are part of a wide discipline within electronics, whose details exceed the scope of the present contribution. To delve further, interested readers may refer to [23,24,25,26,27].

The active power, P_G, and reactive power, Q_G, transferred from the generator to the power converter are calculated by (see, e.g., [28])

$$P_G={\displaystyle \frac{v_G{v}_C}{X_G}}\sin \delta \mathrm{and}{Q}_G={\displaystyle \frac{v_G^2}{X_G}}-{\displaystyle \frac{v_G{v}_C}{X_G}}\cos \delta ,$$

(35)

where v_G and v_C are the magnitude of the generated voltage and the magnitude of the converter output voltage, respectively. The electric phase angle between the voltages is represented by δ, whereas the equivalent generator reactance is denoted by X_G.

To regulate the magnitude of the v_C output voltage, one can adjust the amplitude modulation index. Similarly, the phase angle can be controlled by adjusting the phase angle of a reference voltage V_ref in relation to the generated voltage.

5. Actuator Control

Pitch and yaw actuators are mechanisms designed to precisely move blades or the nacelle to a specified position, necessitating a certain level of accuracy. In order to accomplish this, actuators rely on an internal low-level controller that is interconnected in a cascade configuration inside the entire control system. The internal controller is typically pre-configured and unreachable from the outside. An example of this topology for one blade of the pitch system is depicted in Figure 14. A similar scheme is also found in yaw actuator systems. Low-level controllers for power converters are often implemented as PWM devices and can be studied in [24] or [27].

Controllers with integral actions, such as PI or PID controllers, are susceptible to the integrator windup problem, which refers to the blow-up of the integrator as a result of saturated actuator outputs. The problem has been intensely studied in the past for actuators with saturated magnitude (see, e.g., [29,30,31]). Nowadays, the most popular anti-windup procedure is known as back calculation, which was proposed in [32].

However, pitch and yaw actuators experience saturation in both amplitude and rate, which limits the loads generated by the actuation on the wind turbine. This hurdle is addressed in [33], which proposes an anti-windup mechanism based on the automatic reset configuration [34]. The concept is described in Figure 15.

6. Assessment of Performance for Actuator Protection

Actuators supply power and correct the control signals as the interface between the wind turbine and controller. On the other hand, they also add to the control system’s retards, restrictions, and nonlinearities. An indirect evaluation of control signals can be achieved by utilising performance indices [35], which quantify the energy with the control signals. Furthermore, they restrict the magnitudes of the control signals and derivatives to the actuator limits. As previously described, anti-windup methods can overcome or at least mitigate nonlinearities.

All previously discussed factors pertaining to actuators fail to account, especially in the context of wind energy converters, that their operation is uninterrupted because of the unpredictable variations in wind speed and direction. Consequently, the actuators experience continuous and escalating deterioration until they fail or even collide. Therefore, a key goal of the control system should be to balance all factors, including those related to the time for which the actuator operates, without any failures. The present section is devoted to introducing these aspects.

6.1. The Concept of Actuator Travel

Actuator travel refers to the overall distance covered by an actuator during a single cycle, starting with its activation and finishing with its deactivation. In [36], the metric is expressed by

$$J_{AT}={\displaystyle {\int }_{t_{\min }}^{t_{\max }}|{\dot{u}}_a(t)|}dt,$$

(36)

with u_a denoting either the yaw or the pitch angle, while J_AT represents the overall angle traversed.

6.2. The Concept of Actuator Duty Cycle

The duty ratio, which is likewise referred to as the duty cycle, represents the difference, expressed in percentage, between a complete cycle and the working periods. The total cycle considers on-time and off-time periods (see, e.g., [37,38]). It can be mathematically formulated by

$$DC={\left.{\displaystyle \frac{t_{on}}{t_{on}+t_{off}}}\times 100\right|}_{1\mathrm{cycle}}.$$

(37)

Hence, a continually operating actuator has a duty cycle of 100%.

However, there are other definitions. For instance, in [39], the duty cycle is the duration of actuator activity before needing cooling, while in [40], it is the average of actuator travel (36) and is given by

$$J_{ADC}={\displaystyle \frac{1}{t_{\max }-t_{\min }}}{\displaystyle {\int }_{t_{\min }}^{t_{\max }}|{\dot{u}}_a(t)|}dt.$$

(38)

This definition is also applied in [35]. Equation (38) is the classic time-limited integrated absolute derivative index (IADE) but applied to the control variable u_a(t) rather than the control error.

Though the actuator fatigue is not quantified by this metric, it provides a valuable objective function for assessing control strategies in terms of how they affect the actuators. The function can be utilised for evaluation during the procedure by setting t_max as the present time t. In [41], (38) is normalised and afterward employed in [42,43], i.e.,

$$J_{nADC}={\displaystyle \frac{1}{t_{\max }-t_{\min }}}{\displaystyle {\int }_{t_{\min }}^{t_{\max }}\frac{|{\dot{u}}_a(t)|}{{\dot{u}}_{a,\max }}}dt.$$

(39)

Furthermore, the metric has been adjusted to account for actuators having an asymmetric span in [44], resulting in the formula

$$J_{nADC}={\displaystyle \frac{1}{t_{\max }-t_{\min }}}{\displaystyle {\int }_{t_{\min }}^{t_{\max }}\frac{|{\dot{u}}_a(t)|}{0.5[sign({\dot{u}}_a)({\dot{u}}_{a,\max }-{\dot{u}}_{a,\min })+({\dot{u}}_{a,\max }+{\dot{u}}_{a,\min })]}}dt.$$

(40)

To date, the metrics have been established for a single simulation. However, it is possible to conduct successive simulation runs for various average wind speeds ${\overline{v}}_w$, resulting in a collection of actuator duty cycles as a consequence of a collection of simulations. These cycles are then indexed as J_nADC(i), where i varies from 1 to the number of simulations n_s.

Moreover, the wind speed of each simulation can be weighted by a Weibull-distributed probability p_w covering the entire lifespan of the machine [41,42,43], such that a weighted actuator duty cycle can be built according to

$${\overline{J}}_{nADC}={\displaystyle \sum _{i=1}^{n_s}{p}_w[({\overline{v}}_w(i)]J_{nADC}(i)}.$$

(41)

Hence, the lifespan of the actuator duty cycle is evaluated using (41). Nevertheless, the computation takes place offline and serves the purpose of comparing the performance of various controllers. However, it is unsuitable for online assessment of control performance or offline control system design.

Finally, the design load cases (DLC 1.2, [45]) can be used to generate a set of simulations according to the description provided in [41,42,43].

7. Actuators for Smart Blades

Very large rotor blades are flexible and affected by the spanwise variability of the wind. Therefore, the capacity of standard load control strategies to mitigate loads is reaching its limits. In the search for novel solutions, active flow control seems to be a way to overcome the problem. The idea is to provide the blades with additional devices in order to treat the load locally. They are called smart or intelligent blades.

Currently, smart blades remain in the research phase, and actuators associated with this technology are not yet commercially accessible for wind energy converters. Therefore, they are briefly discussed here only for the sake of completeness.

Thus, smart blades might be categorised into two distinct types: active and passive smart blades. Passive blades mitigate variations in wind speed by adjusting the aero-elastic behaviour of the blades, which is facilitated by the physical properties of the materials involved, such as bend-twist coupling, tension-torsion coupling, and sweep-twist coupling (see, for instance, [41,46,47], for further details). As a passive blade system, they do not need special or additional actuators; therefore, they are not interesting for the present work.

On the other hand, active, intelligent blades are designed to mitigate loads by manipulating the aerodynamic characteristics of the blades. This can be achieved by incorporating elements that enable partial adjustment of the angle of attack or lift coefficient. Thus, the flow passing around the aerofoils can be controlled. The mentioned elements are, for instance, trailing edge flaps, morphing trailing edge flaps, Gurney flaps, and microtabs, among others (see Figure 16 for examples).

Individual flap control (IFC) is the approach that makes use of trailing edge flaps to reduce blade loads. In particular, IFC is combined with IPC (individual pitch control) to obtain the best result (see, e.g., [48,49,50] for hybrid approaches). Details about the needed actuators and their specifications for flap control are given in [51].

The traditional actuation for the flaps is electrical servo motors, but in the last few years, plasma actuators, in particular for morphing trailing edges, have gained attention in order to get controlled deformations of the flaps. Thus, plasma actuators are combined with Gurney flaps in [52] and for morphing trailing edges in [53]. See [54] for a review of plasma actuators in wind energy systems.

The mechanical structure of plasma actuators is one of their main advantages; their compact size and sturdy design make it simple to integrate them into the blades. In addition, their size and maintenance contribute to their low cost. On the other hand, they are vulnerable to a variety of factors, including frequency, supply voltage, and wetness [55,56].

8. Conclusions

Although actuators are essential, they are often characterised primarily from a technical perspective, with little attention given to their control and mathematical modelling aspects. Therefore, there is a scarcity of research that examines wind turbine actuators from a comprehensive viewpoint. Hence, it is the objective of this study.

From a functional perspective, wind turbine actuators can be categorised into three broad groups: blade pitch motion actuators, yaw motion actuators, and generator electrical control actuators. The first two devices are either electromechanical or hydraulic in nature, whereas the third device is exclusively electronic.

The necessary attributes were analysed, mathematical models with different levels of complexity were presented, and an effort was undertaken to offer a presentation with a didactic component.

In addition, the survey examined specific challenges in the control loop, such as anti-windup problems. Furthermore, this study accounted for the assessment of actuator performance for both the analysis and the design of the control system.

Finally, a brief exploration of what are known as intelligent blades was undertaken to address the actuation concerns.