# Sensor Fusion and State Estimation of IoT Enabled Wind Energy Conversion System
## 2 IoT Enabled Wind Energy Conversion System and State Space Model  
In general, wind farms are situated in remote locations and thus the control centers are typically located several hours away from the wind farms. Remote data communication connectivity through \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Works** & **Type of Wind Turbine** & **Filter Type** & **Sensor Fusion** & **Impat of Wireless Channel** & **Error Correction Technique** \\ \hline [PERSON] et al. [6] & Generic & Linear Kalman & No & No & No \\ [PERSON] et al. [8] & Generic & Linear Kalman & No & No & No \\ [PERSON] et al. [9] & Generic & Extended Kalman & No & No & No \\ [PERSON] et al. [10] & Generic & Adaptive Kalman & No & No & No \\ [PERSON] et al. [11] & Generic & Extended Kalman & No & No & No \\ [PERSON] et al. [12] & Generic & Particle filter & No & No & No \\ [PERSON] et al. [13] & DFIG & Unscented Kalman & No & No & No \\ [PERSON] et al. [14] & DFIG & Unscented Kalman & No & No & No \\ [PERSON] et al. [15] & DFIG & Unscented Kalman & No & No & No \\ [PERSON] et al. [16] & PMSG & Extended Kalman & No & No & No \\ This work & Generic & Linear Kalman & Yes & Yes & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of different works on state estimation of wind turbine. the Internet in the form of an IoT network can help the control centers to monitor the state of a wind turbine and to control a wind turbine's operation. Due to the remote location of wind turbines, the IoT network connectivity requires wireless networks such as cellular or satellite networks. An integrated scenario comprised of wind turbines and a wireless IoT network [25] is depicted in Figure 1.  
A wind turbine system consists of induction generator, rotors, gearbox, and matrix converter [26; 27]. The matrix converter connects the induction generator with the power grid and controls the output power delivered to the grid. In this paper, we track the output current components of an induction generator in a wind turbine. We adopt the state space model reported in [28], where a fixed-speed wind turbine is considered. Authors in [28] utilized the current model to characterize the induction generator and the following assumptions were considered for the sake of simplicity: (1) the stator current is assumed to be negative when it flows toward the machine; (2) a synchronous reference frame was considered to derive the equations; (3) the d-axis is \(90\deg\) behind the q-axis (Direct axis (d-axis) is the axis of the stator/rotor's salient pole and quadrature axis (q-axis) is the axis in quadrature or perpendicular to the stator/rotor's salient pole.). With the above assumptions, we adopt the linearized state space current model of induction generator, which is described by the following equation:  
\[\dot{\mathbf{X}}=\mathbf{A}\mathbf{X}+\mathbf{B}\mathbf{U}+\mathbf{\Gamma}\mathbf{\mathcal{N}}_{p} \tag{1}\]  
where \(\mathbf{X}=[i_{ds}\ i_{qs}\ i_{dr}\ i_{qr}]^{T}\) is the state of the induction generator, \(\mathbf{U}=[v_{ds}\ v_{qs}\ v_{dr}\ v_{qr}]^{T}\) is control input, \(\mathbf{\Gamma}\) is a constant matrix, and \(\mathbf{\mathcal{N}}_{p}\) is process noise. We model the process noise as Gaussian noise with zero-mean and covariance matrix \(\mathbf{Q}\). In \(\mathbf{X}\), \(i_{ds}\) and \(i_{qs}\) are the stator currents in the \(d\) and \(q\) axes, respectively; \(i_{dr}\) and \(i_{qr}\) are the rotor currents in the \(d\) and \(q\) axes, respectively. In \(\mathbf{U}\), \(v_{ds}\) and \(v_{qs}\) are the stator voltages in the \(d\) and \(q\) axes, respectively; \(v_{dr}\) and \(v_{qr}\) are the stator voltages in the \(d\) and \(q\) axes, respectively. With the specifications of a single-case induction generator, \(\mathbf{A}\) and \(\mathbf{B}\) are characterized by [28; 29],  
\[\mathbf{A}=\frac{\omega_{b}}{X_{s}X_{r}\gamma}