# Intelligent Fault Diagnosis Techniques Applied to an Offshore Wind Turbine System
## 2 Wind Turbine Simulator and Fault Model  
The three-bladed horizontal-axis wind turbine model considered in this work follows the principle that wind power activates the wind turbine blades, which leads to the rotation of the low-speed rotor shaft. In order to increase its rotational speed to that which is generally required by the generator, a gearbox with a drivetrain is included in the system. A more detailed description of this benchmark is given in [7], and its schematic diagram is presented in Figure 1.  
The wind turbine simulator has two controlled outputs, i.e., the generator rotational speed \(\omega_{g}(t)\) and its generated power \(P_{g}(t)\). The wind turbine model is controlled by means of two actuated inputs, i.e., the generator torque \(\tau_{g}(t)\) and the blade pitch angle \(\beta(t)\). The latter signal controls the actuators of the blades, which are implemented by hydraulic drives [7]. Several other measurements are acquired from the wind turbine benchmark: the signal \(\omega_{r}(t)\) represents the rotor speed, and \(\tau_{r}(t)\) is the reference torque. Moreover, the aerodynamic torque signal \(\tau_{aero}(t)\) is computed from the wind speed \(v(t)\), which is usually available with limited accuracy. In fact, the wind field is not uniform around the wind turbine rotor plane, especially for large rotor systems. Moreover, anemometers measuring this variable are mounted behind the rotor on the nacelle. Therefore, the wind speed measurement \(v_{w}(t)\) is affected by the interference between the blades and the nacelle, as well as the turbulence around the rotor plane. The alteration of the wind speed measurement \(v_{w}(t)\) with respect to its nominal value around the rotor plane represents an uncertainty in the wind turbine model and a disturbance term in the control design [7]. Finally, as sketched in Figure 1, the signals generated by the wind turbine system are assumed to be acquired through the measurement block, whose objective is to simulate the real behavior of the sensors and actuators. Therefore, the measured signals are modeled as the sum of their actual values and white Gaussian process terms. Moreover, the wind turbine simulator includes a baseline controller, represented by standard PID regulators that regulate the generated power on the basis of the actual wind speed, as shown in [4; 7]. The wind turbine simulator also includes the generation of three different typical fault cases: sensor, actuator, and system faults [4; 7]. The sensor faults are generated as additive signals on the affected measurements. As an example, the faulty sensor of the pitch angle \(\beta_{m}\) provides the wrong measurement of the blade orientation, and if not handled, the controller cannot fully track the power reference signal. On the other hand, actuator faults lead to the alteration of the input and output descriptions of the pitch angle and the generator torque models by modifying their dynamics. In this way, a pressure drop in the hydraulic circuit of the pitch actuator and an electronic breakdown in the converter device are simulated, respectively. Finally, a system fault affects the drivetrain of the turbine, which is described as a slow variation in the friction coefficient over time. This can be caused by wear and tear of the mechanical parts over time. This scenario is summarized in Table 1, which also reports the measured signals that are affected by these nine faults. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Fault Case** & **Fault Type** & **Affected Measurement** \\ \hline
1 & Sensor & \(\beta_{1,m1}\) \\
2 & Sensor & \(\beta_{2,m2}\) \\
3 & Sensor & \(\beta_{3,m1}\) \\
4 & Sensor & \(\omega_{r,m1}\) \\
5 & Sensor & \(\omega_{r,m2}\) and \(\omega_{g,m2}\) \\ \hline
6 & Actuator & Pitch system of Blade \#2 \\
7 & Actuator & Pitch system of Blade \#3 \\
8 & Actuator & \(\tau_{g,m}\) \\ \hline
9 & System & Drivetrain \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fault scenario of the wind turbine simulator. Figure 1: Scheme of the offshore wind turbine simulator.