# Double Dead-Time Signal Injection Strategy for Stator Resistance Estimation of Induction Machines
## 5 Discussion  
A temperature-monitoring algorithm based on a DC injection and stator resistance estimation is presented in this paper. This strategy permits to eliminate the temperature sensors in the machine, and as consequence, the potential faults of the sensors, increasing the reliability of the system. The main difficulty of DC injection methods resides in the estimation of the DC voltage component of the commutated voltage, as there are not voltage  
Figure 10: Temperature error histogram for all the experiment working points. Figure 9: Stator winding temperature estimation for two operation points being the stator frequency equal to 30 Hz. (**a**) At nominal torque. (**b**) At 120% of nominal torque. sensors. Thus, an injection strategy should be proposed for an accurate and reliable DC voltage value. Furthermore, the different methods previously presented have limitations, as is shown in Table 5. The double dead-time strategy solves these limitations; as it is not dependent on machine parameters, it can be used in the whole region of speeds and it is able to compensate the dead-time voltage drop, which is a key point for an accurate estimation in DC injection methods. Moreover, additional hardware is not needed. A novel strategy based on a double dead-time injection is presented. A symmetric DC current injection is applied to two phases. Furthermore, this original method is capable to compensate the voltage drop caused by the dead-time effect of the inverter. The dead time is introduced in the commutation of the IGBTs to avoid a shortcut in the DC bus. This phenomenon produces a voltage drop in the injected offset, and it depends on the duty cycle. This strategy avoids computing the number of switching cycles for the positive and negative cycles of the fundamental signal. It should be noted that this computation is quite difficult to compute correctly under real working conditions where the current waveform has a high number of ripples, sub-oscillations and frequency oscillations  
Other non-idealities of the inverter such as the voltage drop in the semiconductors are easily compensated for with a simple look-up table. The voltage drop in the cable can also be easily compensated for. The presented method has been implemented in a typical closed loop vector control. The injection is performed introducing a controlled current offset, which simplifies the estimation. An offset is injected in one phase and the same but negative is injected in another phase. In this way, the system can be analyzed as a one-phase system. The presented algorithm needs no extra measurement hardware because it only uses the already existing current sensors. It can be implemented in a variable load system and is suitable for medium/high size machines. The estimation is performed in some seconds avoiding a perturbation in the system. This strategy has been designed for thermal protection of railway traction units where there are some working-point steady-state periods that can be used to make the estimation. However, the strategy could be implemented in any other system that fulfils this requirement. The system has been validated in a real railway test bench. The maximum estimation error is around \(\pm 10\)\({}^{\circ}\)C, so the validation of the system for thermal protection is ensured. In conclusion, a novel signal injection strategy to estimate the stator resistance of induction motors is presented. This strategy allows the online temperature estimation for the protection of motors, and it can be applied to the whole range of speeds. A double dead-time DC signal is injected in the machine, but the method compensates the voltage drops due to dead-time effect, this being a key point for an accurate estimation of the stator resistance. Furthermore, additional hardware is not needed. The strategy has been validated in a real railway test bench. Conceptualization, J.P. and U.L. ; methodology, J.P. and U.L. ; validation, U.L. and I.I. ; formal analysis, J.P., C.A.R. and U.L.