## 3 Practical Test
The motor model that has been implemented in Simulink is a general model [28] to compromise between simplicity and accuracy of the results since the scope of this research is practical implementation and applications. The following loading scenarios were considered: light load, half load, and full load, which indicate the load percentage of the rated current. Table 3 displays the motor speed and current values in the healthy case and single phasing (faulty) on phase-a for various torque values. These measurements were taken from the real set of the three-phase induction motor shown in Figure 4.  
Table 4 shows closed results of the practical, theoretical, and simulation experiments using Matlab/Simulink for motor currents. In practice, we discovered that the motor speed decreased in a single phasing with the same load values. Figures 5-7 show the Matlab simulation results of the stator currents at healthy and single-phase fault conditions under light loading (30% of the rated value), half load, and full load, respectively. The practical tests show a noticeable change in motor vibration and sound. The recorded result of motor vibration is shown in Figure 8 when it operated under healthy operation [0-4] seconds, and under single-phasing fault [4-10] seconds. Therefore, a fault detection hypothesis can be applied to detect the occurrence of a fault if the vibration signal exceeds the threshold value. A simple form of threshold can be calculated based on the peak value of the vibration signal under fault-free operation, i.e.,  
\[J_{th,peak}\ =\ \frac{sup}{fault-free}\left||v(t)||\right. \tag{14}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Test**} & \multicolumn{2}{c}{**motor current under healthy case [a]**} & \multicolumn{2}{c}{**motor current under single phasing [a]**} \\ \cline{2-4}  & Practical & 2.7 & 4.1 \\ \cline{2-4} Light load torque & Theoretical & 2.68 & 4.25 \\ \cline{2-4}  & Simulation & 2.6 & 4.27 \\ \hline \multirow{4}{*}{Half load torque} & Practical & 3.7 & 7.0 \\ \cline{2-4}  & Theoretical & 3.5 & 6.4 \\ \cline{2-4}  & Simulation & 3.24 & 6.4 \\ \hline \multirow{4}{*}{Full load torque} & Practical & 4.4 & 9.2 \\ \cline{2-4}  & Theoretical & 4.3 & 9.07 \\ \cline{1-1} \cline{2-4}  & Simulation & 4.6 & 9.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Validation of the output results under different load conditions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & \multicolumn{2}{c}{**LIGHT LOAD**} & \multicolumn{2}{c}{**Half Load**} & \multicolumn{2}{c}{**Full Load**} \\ \hline  & **H** & **F** & **H** & **F** & **H** & **F** \\ \hline Speed [rpm] & 1497 & 1497 & 1440 & 1405 & 1410 & 1330 \\ Ia [A] & 2.7 & 0 & 3.7 & 0 & 4.4 & 0 \\ Ib [A] & 2.7 & 4.1 & 3.7 & 7 & 4.4 & 9.2 \\ Ic [A] & 2.7 & 4.1 & 3.7 & 7 & 4.4 & 9.2 \\ \hline H: healthy; F: faulty. & & & & & & \\ \end{tabular}
\end{table} 
Table 3: Healthy and faulty (single phasing) results under different load conditions. Based on the threshold value, the following hypothesis can be used to detect the faults. \[v(t)>\ J_{th,peak}\ \ \ \ \ \ ==>\ alarm,\ fault\ is\ detected\]  
\[v(t)\ \leq\ J_{th,peak}\ \ \ \ \ ==>\ no\ alarm,\ fault-free\]  
where, \(v(t)\) is the vibration measurement signal, and \(J_{th,\ peak}\) is the peak threshold value which is equal to 0.032. Figure 5: Healthy and faulty stator currents at light load. Figure 6: Healthy and faulty stator currents at half load. Figure 7: Healthy and faulty stator currents at full load.