## 6 Model Validation  
An experimental test is performed on a three-phase DFIG of 3 kW, 230/400 V, and 11.5 A to validate the proposed model. The PWM converters used were standard 4.5 kW with a maximum switching frequency of 5 kHz. The schematic and block diagram of the experimental rig are exhibited in Figures 8 and 9, respectively. Figure 8: Experimental setup of the tested DFIG. Figure 7: Interconnection diagram of the DFIG with the electrical grid. The detailed parameters of the experimental setup are listed in Table 2. The DFIG parameters are provided in Appendix A. This system contains an induction motor, a single helical gearbox, an adjustable frequency drive (AFD), a three-phase DFIG wind turbine, and a three-phase B2B power converter. This system involves a 10 HP squirrel-cage induction motor with its rotor coupled directly to a single helical gearbox, where the 3 kW-DFIG is also connected. The speed of the induction motor is controlled by an AFD to simulate different wind speeds. The rotor winding of the DFIG is connected to the rotor-side converter of the B2B, while the stator winding of the DFIG is connected directly to the electrical grid by means of the three-winding transformer. The grid-side converter controls the DC-link voltage at 160 V. The sampling and switching frequencies for both converters are 5 and 2.5 kHz, respectively. The results of the model proposed in steady-state are compared with real lab measurements. The machine's steady-state operating point results from the load flow analysis are presented in Table 3, assuming wind speeds \(P\) and \(Q\) as input data. Different wind speeds are considered as input data assuming a unit power factor, which means that the grid-side converter transmits active power in both directions (positive and negative), so that the B2B power converter operates with a unit power factor; the reactive power should be zero. If the power factor is positive, the electrical grid consumes the active power from the B2B power converter. The power factor is a unit because the reactive power is zero. In this mode of operation, the current and voltage must be in phase with the electrical grid. \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Equipment** & **Characteristics** \\ \hline
1 & Power supply & 450 V, 18 A. \\ \hline
2 & Adjustable Frequency Drive & 480 V, 35.5 A, Motor: 20 HP. \\ \hline
3 & Squirrel cage motor & 10 HP, 460 V, 17.3 A. \\ \hline
4 & Gearbox & Ratio 4.5:1, 12.5 kW \\ \hline
5 & DFIG & 3 kW, 230/400 V \(\Delta\)/Y, 4.5 A. \\ \hline
6 & Rotor side converter & IGBT Type: 1 MBH30D, 4.5 kW, 5 kHz. \\ \hline
7 & Grid side converter & IGBT Type: 1 MBH30D, 4.5 kW, 2.5 kHz. \\ \hline
8 & Three-phase transformer & 480 V Y-Y \\ \hline
9 & Power quality analyzer & PowerPad, Mod. 3945-B. \\ \hline
10 & Computer & Software MATLAB/Simulink® \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of the experimental setup. Figure 9: Block diagram of the experimental setup. Alternatively, if the power factor is negative, the electrical grid provides active power to the B2B power converter. From the electrical grid, the active power is negative, indicating that active power is generated and consumed by the B2B power converter. Again, in this operating mode, the unit power factor is suitable because the reactive power is zero. Concerning the voltage and current of the electrical grid, a phase shift of 180\({}^{\circ}\) exists. Finally, another operation mode of the B2B power converter is analyzed, when the exchange of active power with the electrical grid is minimal such that the B2B power converter is considered to operate with a power factor of zero. In this situation, only the reactive power exchange takes place, without considering the voltage drop in the resistance. Additionally, the current is delayed by 90\({}^{\circ}\) relative to the voltage of the electrical grid, indicating the availability of inductive reactive power. The operating condition that enables increasing the available power because of a rise in the wind is considered.