# Double Dead-Time Signal Injection Strategy for Stator Resistance Estimation of Induction Machines
## 1 Introduction  
Thermal protection is one of the most important aspects in condition monitoring of electrical machines. An overheating will carry the deterioration of fundamental components of the machine, such as the stator winding, insulation, core or bearings [1]. Currently, embedded temperature sensors inside the motor are the most utilized alternative in medium/high power electrical machines. On the other hand, the integration of these sensors normally increases the number of faults, due to the disintegration of the connections, noise interference, and their large time constant. In recent times, several research works have proposed different kind of strategies for the temperature estimation in different points of the machine [2]. These methods can be classified into two main categories: thermal model-based approaches and estimation of the temperature from the resistance [3; 4; 5; 6]. Thermal model-based approaches are based on a thermal circuit to estimate the temperature in the machine [7; 8]. Thermal parameters are calculated from machine dimensions or characterized from offline experiments. However, the thermal parameters are not constant for the different operation points, so they should be fitted for different operation conditions. This kind of method cannot deal with cooling problems or insulation deterioration. Furthermore, initial temperature needs to be known. On the other side, the methods that estimate the temperature from the resistance variation are not dependent on the operation condition and the cooling status. They are based on the relationship between resistance and temperature as it is shown in [9]. These methods can be divided in two main groups: a machine model-based approach and signal injection approach [10; 11]. Apart from the aforementioned main groups, methods based on artificial intelligence and data have emerged too [12]. Machine model-based approaches use the fundamental excitation and the machine model to estimate the resistance. The main drawback to this method is that it is usually too sensitive to unknown machine parameters and their variations. Several models have been proposed in the literature but they are generally limitedto a small range of speed [13; 14]. Thus, as the approach is limited to a range of speed and torque, the machine is not protected in all the operation points. On the other hand, signal injection approaches excite the machine with a signal, which can be DC or AC, to estimate the resistance [15]. This approach provides an accurate estimation of the resistance in the whole speed region. Different strategies based on the DC and AC injection have been published. AC signals are injected for the stator resistance estimation in [16; 17; 18]. The injected voltage value needs to be estimated or measured, so these methods are not desirable. Furthermore, the AC signal injection algorithm is dependent on machine parameters which can change with the temperature. Finally, a DC injection strategy has been proposed in references [9; 10; 19; 20; 21; 22; 23]. In the strategies proposed in [19; 20], additional hardware is needed for the DC offset generation. On the other hand, there is no need of hardware in [9; 10; 21; 22] because the signal is injected through the inverter. On the other hand, in reference [21], a scalar control is considered, but the proposed implementation at not constant loads turns complicated. The injection through the inverter suffers from some undesired effects. The inverter dead-time effects are studied in [9]. It only considers the dead-time effect, and the strategy is difficult to implement at not constant load. The dead-time is introduced in the commutation of power switches to avoid a shortcut in the DC bus. In reference [22] the effect of a closed loop control and the inverter non-idealities are considered in the injection, however, the DC voltage estimation is needed. The hardware requirement for the obtaining of the exact duty cycle for the voltage estimation is very high.