**2. Wind Turbine Benchmark Systems**

A wind turbine is a complex electro-mechanical system that converts wind energy to electrical energy. Most wind turbines are horizontal three–bladed unites, which are composed of blades, low-speed and high-speed shafts, gearbox, generator, yaw, tower, brake, and controller, and so forth. A typical structure of the wind turbine is depicted by Figure 1. The wind flow in the nature drives the blades and rotor to rotate, converting wind energy to mechanical energy. The rotor drives the generator via the high-speed shaft so that the mechanical energy is converted into electric energy. The pitch angle is controlled to adapt to the varying wind speed to achieve the desired output power. The functionality of the yaw system contributes to align the turbine with the direction of the wind detected by the anemometer.

**Figure 1.** A schematic diagram of the wind turbine system.

A benchmark model of a 4.8 MW wind turbine system was developed in [43,44], which has been widely used for the algorithm validation in control and fault diagnosis. The definitions of the parameters of the benchmark model are shown in Table 1.


**Table 1.** Parameters of the 4.8 MW wind turbine benchmark system [43,44].

The diagram of the 4.8 MW wind turbine benchmark system is shown by Figure 2, which is composed of the blade and pitch subsystem, drive train subsystem, generator and convertor subsystem, and controller, respectively.

**Figure 2.** Block diagram of the 4.8 MW benchmark wind turbine model.

The wind turbine benchmark system has an external input (e.g., varying wind speed), two control reference inputs composed of the reference pitch angle (β*r*) and generator torque reference (τ*g*,*r*).

The wind speed is shown in Figure 3, from which one can see the wind speed ranges from 5 to 20 m/s, with the peak spike over 25 m/s, showing a good coverage of the operation conditions under a healthy situation.

**Figure 3.** Wind speed sequence used in the benchmark wind turbine under fault-free condition.

In this study, we focus on the actuator faults and sensor faults of the wind turbines. Suppose that *u*(*t*) is the control input, *fA*(*t*) is the actuator fault, and *uR*(*t*) is the actuation signal applied to the system; *y*(*t*) is the measured output, *fS*(*t*) is the sensor fault, and *yR*(*t*) is the output from the system. It is clear that *uR*(*t*) = *u*(*t*) + *fA*(*t*), and *y*(*t*) = *yR*(*t*) + *fS*(*t*). As a result, the faults *fA*(*t*) and *fS*(*t*) will divert the performance of the system states and outputs from the normal. The topologies of the actuator faults and sensor faults are depicted by Figure 4.

**Figure 4.** Topologies of the faults in the 4.8 MW wind turbine benchmark system: (**a**). Actuator faults, and (**b**). Sensor faults, respectively.
