2. Wind turbine simulator model

can produce further problems to the design of the control method. In general, commercial codes are not able to adequately describe the wind turbine overall dynamic behaviour; usually, special simulation software solutions are used. On the other hand, control schemes have to manage the most important turbine dynamics, without being too complex and unwieldy. Control methods for wind turbines usually rely on the signals from sensors and actuators, with a system that connects these elements together. Hardware or software modules elaborate these signals to generate the output signals for actuators. The main task of the control law consists of maintaining safe and reliable working conditions of the wind turbine, while achieving prescribed control performances and allowing for optimal energy conversion, as shown e.g. in recent works applied to the same wind turbine model considered in this chapter [2].

Today's wind turbines can implement several control strategies to allow for the required performances. Some turbines use passive control methods, such as in fixed-pitch, stall control machines. In this case, the system is designed so that the power is limited above rated wind speed through the blade stall. Therefore, the control of the blades is not required [1]. In this case, the rotational speed control is proposed, thus avoiding the inaccuracy of measuring the wind speed. Rotors with pitch regulation are usually used for constant-speed plants to provide a power control that works better than the blade stall solution. In these machines, the blade pitching is controlled in order to provide optimal power conversion with respect to modelling errors, wind gusts and disturbance. However, when the system works at constant speed and below rated wind speed, the optimal conversion rate cannot be obtained. Therefore, in order to maximise the power conversion rate, the rotational speed of the turbine must vary with wind speed. Blade pitch control is thus used also above the rated wind speed [1]. A different control method can introduce the yaw regulation to orient the machine into the wind field. A yaw error reference from a nacelle-mounted wind

direction sensor system must be included in order to calculate this reference signal [3].

fault-tolerant control approaches [2].

by the same authors [6].

218 Adaptive Robust Control Systems

Regarding the regulation strategies proposed in this chapter, two control design examples are described and applied to a wind turbine system. The wind turbine model exploited in this chapter is freely available for the Matlab® and Simulink® environments and already proposed as benchmark for an international competition regarding the validation of fault diagnosis and

In particular, a first data-driven method relying on a fuzzy identification approach to the control design is considered. In fact, since the wind turbine mathematical model is nonlinear with uncertain inputs, fuzzy modelling represents an alternative tool for obtaining the mathematical description of the controlled process. In contrast to purely nonlinear identification schemes, see, e.g. [4], fuzzy modelling and identification methods are able to directly provide nonlinear models from the measured input-output signals. Therefore, this chapter suggests to model the wind turbine plant via Takagi-Sugeno (TS) fuzzy prototypes [5], whose parameters are obtained by identification procedures. This approach is also motivated by previous works

Regarding the second model-based strategy presented in this chapter, it relies on an adaptive control scheme [7]. Again, with respect to pure nonlinear control methods [8], it does not require a detailed knowledge about the model structure. Therefore, this chapter suggests the implementation of controllers based on adaptive schemes, used for the recursive derivation of This section outlines the wind turbine model, whose sampled inputs and outputs will be used for the proposed control designs, as shown in Section 3.

The wind turbine system exploited in this chapter uses a nonlinear dynamic model representing the wind acting on the wind turbine blades, thus producing the movement of the low-speed rotor shaft. The higher speed required by the electric converter is produced by means of a gear box. The simulator is described in more detail, e.g. in Odgaard et al. [10]. A block scheme of the wind turbine simulator considered in this chapter is represented in Figure 1.

Both the generator speed and the generator power are controller by means of the two control inputs representing the generator torque τg(t) and the blade pitch angle β(t). Several signals can be acquired from the wind turbine simulator. In particular, the signal ωr(t) represents the rotor speed measurement, whereas ωg(t) represents the converter velocity. Concerning the electric generator, τg(t) refers to its required torque, which is controlled by the converter. Therefore, this signal represents the measurement of the torque setpoint, τr(t). The aerodynamic model defining the aerodynamic torque provides the τaero(t) signal, which is a nonlinear function of the wind speed v(t). This measurement is very difficult to be acquired correctly, as described in Odgaard et al. [10].

The aerodynamic model reported in Figure 1 is described as follows:

$$\pi\_{aerv}(t) = \mathbb{C}\_p\left(\beta(t), \lambda(t)\right) \frac{\rho A v^3(t)}{2\omega\_r(t)}\tag{1}$$

Figure 1. Scheme of the wind turbine process.

where the variable r represents the air density and A is the effective rotor area. Another important variable is represented by the so-called tip-speed ratio, which is defined as

$$
\lambda(t) = \frac{\omega\_r(t)R}{v(t)}\tag{2}
$$

When the power reference is achieved and the wind speed increases, the controller can be switched to the control region 2 (full load condition). In this zone, the control objective consists of tracking the power reference Pr, obtained by regulating β, such that the Cp is decreased. In a traditional industrial control scheme, usually a PI controller is used to keep ω<sup>r</sup> at the prescribed

The baseline controller considered in this chapter was implemented with a sample frequency at 100 Hz, i.e. Ts = 0.01 s. In full load conditions, i.e. in region 2, the actuated input β is

<sup>β</sup><sup>k</sup> <sup>¼</sup> <sup>β</sup><sup>k</sup>�<sup>1</sup> <sup>þ</sup> kp ek <sup>þ</sup> ki Ts � kp

with the sample index k = 1, 2, …, N. The parameters for this PI speed controller are ki = 0.5 and

To control the further input τ<sup>g</sup> shown in Figure 1, a second PI regulator is used, in the form of

τrk ¼ τrk�<sup>1</sup> þ kp ek þ ki Ts � kp

The parameters for this second PI power controller are ki = 0.014 and kp = 447 � <sup>10</sup>�<sup>6</sup> [10].

Finally, note that in region 1 (partial load, below the rated wind speed), the wind turbine is regulated only by means of the torque input τg(t). In this situation, the blade pitching system is not exploited to achieve the optimal power conversion. On the other hand, in region 2 (full load, above the rated wind speed), the wind turbine control regulates both the blade pitch angle β(t) and the control torque τg(t). The wind turbine Simulink® simulator considered in this work includes also saturation blocks limiting the values of these control signals and their rates.

This section describes the two approaches considered in this chapter for obtaining the control laws by using data-driven and model-based methodologies. Once a suitable mathematical description of the monitored process is provided, the derivation of the controller structure is sketched in Section 3.1 for the fuzzy approach, whereas Section 3.2 proposes a different

The first method proposed in this chapter for the derivation of the wind turbine controller is based on a fuzzy clustering technique to partition the available data into subsets characterised by linear behaviours. The integration between clusters and linear regression is exploited, thus allowing for the combination of fuzzy logic techniques with system identification methodologies. These tools are already available and implemented in the Matlab® Fuzzy Modelling and

ek <sup>¼</sup> <sup>ω</sup>gk � <sup>ω</sup>nom (

ek ¼ Pgk � Pr

� �ek�<sup>1</sup>

Robust Control Applications to a Wind Turbine-Simulated System

http://dx.doi.org/10.5772/intechopen.71526

� �ek�<sup>1</sup>

(6)

221

(7)

value by changing β; the second input of the controlled is τg.

kp = 3, with sampling time Ts = 0.01 s, as reported in [10].

(

3. Data-driven and model-based designs

method relying on an adaptive technique.

controlled via the relations of Eq. 6 [10]:

Eq. (7):

with R the rotor radius. Cp(�) represents the power coefficient that is normally represented via a two-dimensional map [10]. The expression of Eq. (1) allows the computation of the signal τaero(t), by means of the estimated wind speed v(t), and the measured β(t) and ωr(t). Due to the uncertainty of the wind speed, the estimate of τaero(t) is considered affected by an unknown measurement error, which justifies the robust approaches described in Section 3. Moreover, the nonlinearity represented by the expressions of Eqs. (1) and (2) motivates the required reliable and robust control approaches suggested in this chapter.

A two-mass model is exploited to describe the drive-train system, while the hydraulic pitch system is modelled as second-order transfer function [10]. Moreover, the generator dynamics are described as a first-order transfer function. More details regarding the considered simulator are in Odgaard et al. [10]. Under these assumptions, the complete state-space description of the wind turbine model has the form of Eq. (3):

$$\begin{cases} \dot{\mathbf{x}}\_{\varepsilon}(t) = f\_{\varepsilon}(\mathbf{x}\_{\varepsilon}(t), \boldsymbol{\mu}(t)) \\ \boldsymbol{y}(t) = \mathbf{x}\_{\varepsilon}(t) \end{cases} \tag{3}$$

where u(t)=[β(t), τg(t)]<sup>T</sup> and y(t) = xc(t)=[Pg(t), ωg(t)]<sup>T</sup> are the control inputs and the monitored output measurements, respectively, as shown in Figure 1. Pg(t) is the generator power measurement, whereas fc(�) represents the continuous-time nonlinear function that will be approximated via discrete-time models from N sampled data uk and yk, with the sample index k = 1, 2, …N, as presented in Section 3. Finally, the model parameters and the map Cp(β, λ) are chosen in order to represent a realistic turbine [10].

As described in Odgaard et al. [10], the baseline controller developed for this wind turbine system works in two normal operating conditions, namely, the region 1 corresponding to the power optimisation (partial load) and the region 2 of constant power production (full load). The partial load working condition (also known as working region 1), the optimal wind-power conversion is achieved without any pitching of the blades, which are fixed to 0�. In this case, λ is constant at its optimal value λopt that is defined by the maximal value of the power coefficient map Cp when β = 0. Therefore, this working condition is completely defined by setting τ<sup>g</sup> = τ<sup>r</sup> (i.e. the generator torque is equal to the reference one) with pitch angle β = 0.

The reference torque τ<sup>r</sup> shown in Figure 1 can be written as

$$
\pi\_r = K\_{opt} \omega\_r^2 \tag{4}
$$

where:

$$K\_{opt} = \frac{1}{2} \,\rho \, AR^3 \, \frac{\mathbb{C}\_{p\_{\text{max}}}}{\lambda\_{opt}^3} \,\tag{5}$$

with Cpmax the maximal value of Cp, related the to λopt, i.e. the optimal tip-speed ratio.

When the power reference is achieved and the wind speed increases, the controller can be switched to the control region 2 (full load condition). In this zone, the control objective consists of tracking the power reference Pr, obtained by regulating β, such that the Cp is decreased. In a traditional industrial control scheme, usually a PI controller is used to keep ω<sup>r</sup> at the prescribed value by changing β; the second input of the controlled is τg.

The baseline controller considered in this chapter was implemented with a sample frequency at 100 Hz, i.e. Ts = 0.01 s. In full load conditions, i.e. in region 2, the actuated input β is controlled via the relations of Eq. 6 [10]:

$$\begin{cases} \beta\_k = \beta\_{k-1} + k\_p \mathbf{e}\_k + \left( k\_i T\_s - k\_p \right) \mathbf{e}\_{k-1} \\ \mathbf{e}\_k = \omega\_{\otimes k} - \omega\_{nom} \end{cases} \tag{6}$$

with the sample index k = 1, 2, …, N. The parameters for this PI speed controller are ki = 0.5 and kp = 3, with sampling time Ts = 0.01 s, as reported in [10].

To control the further input τ<sup>g</sup> shown in Figure 1, a second PI regulator is used, in the form of Eq. (7):

$$\begin{cases} \tau\_{rk} = \tau\_{rk-1} + k\_p \mathbf{e}\_k + \left( k\_i T\_s - k\_p \right) \mathbf{e}\_{k-1} \\ \mathbf{e}\_k = P\_{\mathbb{g}k} - P\_r \end{cases} \tag{7}$$

The parameters for this second PI power controller are ki = 0.014 and kp = 447 � <sup>10</sup>�<sup>6</sup> [10].

Finally, note that in region 1 (partial load, below the rated wind speed), the wind turbine is regulated only by means of the torque input τg(t). In this situation, the blade pitching system is not exploited to achieve the optimal power conversion. On the other hand, in region 2 (full load, above the rated wind speed), the wind turbine control regulates both the blade pitch angle β(t) and the control torque τg(t). The wind turbine Simulink® simulator considered in this work includes also saturation blocks limiting the values of these control signals and their rates.
