## 4 Practical Model, Experimental Tests and Results
In the first test, a step analysis of \(\hat{P}_{ref}\) and \(\hat{Q}_{ref}\) and the corresponding calculated rotor current references (by using (5) and (6)) is performed, according to Table 2. For this test, two messages were sent, one with \(P_{ref}\) kept constant at 380 W (\(i_{2_{Inf}}\) = 1 A), and the other with \(Q_{ref}\) sweeping from 1 kvar to 1.9 kvar (\(i_{2_{Inf}}\) from 2.3 A to 0 A), according to the pattern shown in Figure 6.  
In this figure, it is possible to observe two and a half messages on the scope screen (the SMS has 8 values, with a duration of 100 ms each). This occurs intentionally, as the microcontroller is programmed to repeat the SMS message until a new one is received. In addition, Figure 7 shows the system behavior during the change on the \(i_{2d}\) (from 2.3 A to 0 A, while the \(i_{2d}\) is kept constant at 1 A). The time response was 8 ms, following \(\hat{Q}_{ref}\) variation. It can be \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Total power & \(S\) & 3 kVA \\ Inertial constant & \(J\) & 0.05 kg\(\cdot\)m\({}^{2}\) \\ Pole pairs & \(PP\) & 2 \\ Stator: [p.p.] & & \\ Voltage & \(V_{1}\) & 220 V \\ Current & \(I_{1}\) & 11.45 A \\ Resistance & \(R_{1}\) & 1 \(\Omega\) \\ Inductance & \(L_{1}\) & 201 mH \\ Rotor: [p.l.] & & \\ Voltage & \(V_{2}\) & 440 V \\ Current & \(I_{2}\) & 4.5 A \\ Resistance & \(R_{2}\) & 3.13 \(\Omega\) \\ Inductance & \(L_{2}\) & 201 mH \\ Mutual inductance & \(L_{M}\) & 191.7 mH \\ \hline \hline \end{tabular}
\end{table} 
Table 1: DFIG nominal parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**References** & **Set-Point Value** & \(i_{2d_{Inf}}\) & \(i_{2d_{Inf}}\) \\ \hline \(P_{ref}\) & 380 W & - & 1 A \\ \(Q_{ref}\) & 1.9 kvar & 0 A & - \\ \(Q_{ref}\) & 1 kvar & 2.3 A & - \\ \(Q_{ref}\) & 1.3 kvar & 1.6 A & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Reference values for the first test. Figure 6: \(Q\) and \(P\) responses for the received references (at \(P\) constant). noted that the stator current changes its phase proportionally, which represents a perfect response of the implemented control system. Observing these graphs, it is possible to notice that there is a noise with random behavior added by the communication system. However, even with the noise, the references are satisfactorily followed by the control system. In the second test, the same procedure as the first one was performed, with the adopted reference values and their respective currents shown in Table 3. This time, \(Q_{ref}\) was kept constant at 1.54 kvar (\(i_{2d_{ref}}=1\) A), while \(P_{ref}\) swept from \(-610\) W to \(-890\) W (\(i_{2q_{ref}}\) from 1.6 A to 2.3 A), according to the pattern shown in Figure 8.  
Figure 8: \(P\) and \(Q\) responses for the received references (at \(Q\) constant). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**References** & **Set-Point Value** & \(i_{2d_{ref}}\) & \(i_{2q_{ref}}\) \\ \hline \(Q_{ref}\) & 1.54 kvar & 1 A & - \\ \(P_{ref}\) & 0 W & - & 0 A \\ \(P_{ref}\) & \(-610\) W & - & 1.6 A \\ \(P_{ref}\) & \(-890\) W & - & 2.3 A \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Reference values for the second test. Figure 7: Stator voltage and current when \(Q\) response changes. To complement the analysis, Figure 9 shows the system behavior during the \(i_{2q}\) variation (from 1.6 A to 2.3 A, while \(i_{2d}\) was kept constant at 1 A). The time response was only 2 ms following \(P\) variation. It is possible to observe that the references are satisfactorily followed by the DFIG control system. From the same figure, it can be verified that the stator current changes its amplitude (from 3.6 A to 3.9 A), according to the expected response of the control system. As in the first test, there is a random noise in the references, which did not compromise the system performance. Although the tests performed have been successful, SMS messages can take seconds to be received and processed properly--which might limit their use, depending on the application.