# Double Dead-Time Signal Injection Strategy for Stator Resistance Estimation of Induction Machines
## 4 Experimental Validation
### Experimental Results  
Once the \(V_{semi}\) values for different working points are calculated, they are stored in a look-up table. To estimate the temperature, the injection is made at the dead times of 10 us and 13 us, and the DC current was fixed in 10 A. It should be taken into consideration that during the estimation, the point has to be maintained constant. If the working point change before the estimation is finished, the sample will be discarded, and a new estimation will be carried out as soon as a working steady state is reached.  
Table 4 summarizes a comparison between the DC voltage measured (\(V_{DC\_out\_mens}\)) and the estimated value \(V_{DC\_out}\) given by Equation (7) for a stator frequency of 30 Hz. In a similar way, the comparison is performed for the stator resistance for both cases. The injected DC current has been equal to 10 A in all the tests. The presented deviations in Rs are low, below an absolute value of 2 m\(\Omega\), which represent deviations up to 5 \({}^{\circ}\)C, which is acceptable for the application. Up to 10 \({}^{\circ}\)C deviation could be accepted.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Torque (Nm)** & \(V_{semi}\) **(V)** \\ \hline
800 & 0.55 \\
1000 & 0.578 \\
1200 & 0.621 \\ \hline \hline \end{tabular}
\end{table}
Table 3: \(V_{semi}\) look-up table.  
Figure 7: \(V_{semi}\) for different working conditions.  
The Figure 8 the stator current during the injection. Figure 9 shows the estimated temperatures compared to the measured temperatures for two different working points. The \(V_{semi}\) values previously presented in the Table 3, are stored in a look-up table for estimation. These values are an average of the \(V_{semi}\) values obtained at these working points at different temperatures.  
The injection algorithm has been tested at different working points. In all cases, the temperature error committed in the estimation was maintained in the range of \(\pm\)10 \({}^{\circ}\)C. Finally, Figure 10 shows the histogram of the errors for the different measures. The distribution of the errors is quite constant around the range \(\pm\)10 \({}^{\circ}\)C.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Torque** & **Temperature** & \(V_{DC\_out\_meas}\) & \(V_{DC\_out}\) & **Measured** & **Estimated** & **Deviation** \\
**(Nm)** & **(\({}^{\circ}\)C)** & **(V)** & **(V)** & **Rs (mf)** & **Rs (mf)** & **Rs (mf)** \\ \hline
800 & 80 & 1.332 & 1.3132 & 133.2 & 131.32 & 1.88 \\
1000 & 80 & 1.332 & 1.3517 & 133.2 & 135.17 & \(-\)1.97 \\
1200 & 80 & 1.332 & 1.3483 & 133.2 & 134.83 & \(-\)1.63 \\
800 & 100 & 1.418 & 1.4164 & 141.8 & 141.64 & 0.16 \\
1000 & 100 & 1.418 & 1.4322 & 141.8 & 143.22 & \(-\)1.42 \\
1200 & 100 & 1.418 & 1.403 & 141.8 & 140.3 & 1.5 \\
800 & 120 & 1.503 & 1.5225 & 150.3 & 152.25 & \(-\)1.95 \\
1000 & 120 & 1.503 & 1.4839 & 150.3 & 148.39 & 1.91 \\
1200 & 120 & 1.503 & 1.4934 & 150.3 & 149.34 & 0.96 \\ \hline \end{tabular}
\end{table}
Table 4: Comparison between measured and estimated DC voltages and deviation in the Rs estimation.  
Figure 8: Stator current signal during the injection.