# Double Dead-Time Signal Injection Strategy for Stator Resistance Estimation of Induction Machines
## 4 Experimental Validation
### Characterization of the on-Line Injection  
In order to use the Equation (7), it is necessary to know the parameters \(V_{semi}\) and \(V_{cable}\). Different tests demonstrated that the temperature of the resistance of the cable did not practically change, so in the experiment \(V_{cable}\) will be constant with a value of 0.045 V. In this sense, only the voltage drops at semiconductors (\(V_{semi}\)) need to be tuned. This is carried out using Equation (8).  
The \(V_{semi}\) value will be different for different working points. As it has been mentioned, with the designed strategy the voltage drop will be only dependent of the stator current. From the measured temperature, the resistance of the stator can be estimated. Multiplying the stator resistance and the current offset, \(V_{DC\_out}\) is obtained.  
In order to tune the semiconductor voltage drop, the machine has been run at different working points and the double dead-time injection algorithm has been applied.  
In Figure 5, the injection at a fixed working point is shown. The double dead-time injection strategy has been applied and the injection values \(V_{inj1}\) and \(V_{inj2}\) have been monitored. First, the injection voltage value for a dead time of 10 us is plotted. At a time equal to 26 s, the dead-time is changed. From this point, after a transitory state of 1 s, the injection voltage value for the dead-time of 13 us is plotted.  
To obtain the mean value, a running mean value calculator has been used. Applying the same strategy at different working points, \(V_{semi}\) is computed and stored.  
The specific temperature of the semiconductor could vary the \(V_{semi}\) value. Several tests have been performed with a constant torque at different semiconductors temperature obtaining a very similar \(V_{semi}\) value. Then, it is deduced that for the inverter of the experimental test bench, the effect of the semiconductor temperature can be considered negligible.  
Some analyses have been carried out at steady state with constant torque in a higher stator temperature. Both the machine and the converter have correctly dissipated the losses. Analyzing the total increment of \(V_{semi}\), it can be considered constant independently of the stator temperature. In this experiment, it is considered that the parameter \(V_{semi}\) is barely affected by the semiconductor's temperature.  
In Figure 6, the DC currents of the phases \"a\" and \"b\" are shown; the \"a\" phase offset is 10 A and the \"b\" phase offset is \(-10\) A.  
The machine has been run at different working points of torque and speed, and the different \(V_{semi}\) values have been computed. Adapting the commutation frequency in the function of the stator frequency, the voltage drop in semiconductors in the function of the speed can be immunized. In Figure 7, the calculated \(V_{semi}\) values for different working conditions are represented. The shown values are an average of the \(V_{semi}\) value obtained at different temperatures.  
Figure 5: Vainj value at the two different dead-time values.  
Figure 6: DC current during the injection. (**a**) “a” phase. (**b**) “b” phase.  
The calculated \(V_{semi}\) values changed for different torque values as expected. The increase in the torque produces an increase in the stator RMS current value, producing a different voltage drop in the semiconductors. On the other side, the change in the stator frequency barely changes the stator RMS current, producing a similar voltage drop in the semiconductors for different stator frequencies. Thus, a mean value for each torque is stored in a look-up table as shown in Table 3.