On the risk of failure to prevent induction motors permanent damage, due to the short available time ‐ to ‐ diagnosis of inter ‐ turn short ‐ circuit faults

As one of the most important assets of the industry, it is crucial to fully characterise all failure modes showing potential to degrade the normal operation of induction motors (IMs). One of the failure modes which lacks detailed knowledge and proper diagnostic tools is the inter ‐ turn short ‐ circuit (SC) fault. Given the severity of such failure mode, it is pivotal to ensure that incipient fault symptoms are correctly identified, thus preventing critical damages to the IM. Unfortunately, the state ‐ of ‐ the ‐ art does not provide enough data to confirm whether the available diagnostic tools act out in due time to avoid permanent damage to the faulty IM. To evaluate the impacts of this failure mode in the temperature of the stator windings of an IM, this paper presents the results obtained from two alternative thermal models of the same IM, resorting to the finite The results

The inter-turn SC fault arises from the wear out of the stator windings' insulation which, in turn, is considered the element with the lowest capability to withstand overheating episodes. Thermal overload is usually the root of such wear out process [9,10].
Overheating is precisely the most concerning consequence of inter-turn SC faults. Overall, the stator temperature is one of the critical variables defining the lifetime of the IM, since a small increment in the temperature of the stator windings has a major negative impact on the lifetime of the windings' insulation [11,12].
As one of the most severe and critical failure modes of IMs, the inter-turn SC fault is also one of the failure modes of IMs with more prominent lack of diagnostic tools capable of detecting such fault in due time. The literature related to this subject focuses efforts on the development of diagnostic tools for the correct identification of inter-turn SCs, mostly resorting to electrical or magnetic variables [13][14][15][16][17][18]. Recently, an invasive thermal monitoring strategy was introduced for the detection of incipient stator SC faults, using fibre-Bragg grating temperature sensors [19]. The procedure adopted for the experimental validation of the 8-and 10-turns SC conditions resorts to a current limiting resistor, placed outside the IM.
Unfortunately, it is not clear whether the fault diagnostic tools available in the literature allow to correctly detect incipient symptoms of the fault, while allotting sufficient time to take actions suitable to prevent permanent damage to the faulty IM. Recent studies point out that many of the stateof-the-art fault diagnostic strategies fail to properly identify very low-severity SC faults [20]. Besides, most studies do not clearly specify the period of time required to diagnose an interturn SC fault. Also, those studies do not provide sufficient and convincing evidences about the ability to ensure the timeto-diagnosis suitable to prevent permanent damage on the IM, particularly because of the risk of overheating, caused by the fault condition. Experimental testbeds used to validate the fault diagnostic tools proposed in the literature impose controlled SC conditions, resorting to a current limiting resistor, placed outside the stator frame of the machine. This resistor 'transfers' a significant share of the heat generated by the SC condition to the external part of the motor. Therefore, the literature adopts means of experimental verification which are far from replicating, with precision and consistence, the interturn SC fault, particularly in what concerns the thermal aspects of this type of fault.
Since local overheating is one of the most prominent consequences of inter-turn SC faults, the evaluation of the thermal behaviour of IMs appears to be the most straightforward mean to evaluate the effects of this failure mode, on the one hand, and to fully access into what extent inter-turn SC faults of a certain severity incur, or not, permanent and irreversible damages to the IM, on the other hand. It is therefore relevant to fully understand how inter-turn SC faults of different severity levels affect the temperature of IMs.
Provided that researchers typically rely on experimental testbeds that dissipate part of the heat produced in the SC branch outside the motor, it is not possible to perform a completely accurate experimental verification of the effective impact of such faults in the increment of the winding's temperature. Therefore, experimental procedures aiming the thermal analysis of IMs subjected to inter-turn SCs are not a feasible option. Moreover, monitoring the winding's temperature would require a fairly high number of temperature sensing devices. Hence, thermal models based on simulation tools are the only non-destructive approach suitable to carry out an accurate thermal analysis of IMs subjected to such faults.
The available literature devoted to the thermal analysis of IMs operating under degraded conditions aims, in general terms, to assess the effects of supply unbalance conditions on the temperature [21][22][23][24][25]. Inter-turn SC fault conditions are not considered in those studies. Other literature presents thermal models of different electrical machine technologies, resorting to lumped parameter thermal network (LPTN) [26,27].
This paper intends to answer to the abovementioned concerns, by realising into what extent does the available inter-turn SC diagnostic tools act out in due time to avoid permanent damage to the faulty IM. The purpose of this paper is not to present an alternative approach for the diagnostic of inter-turn SC faults. Instead, it aims to carry out a careful evaluation of the effectiveness of state-of-the-art inter-turn SC fault diagnostic strategies, by adopting an approach based on the thermal analysis of faulty IMs. To that end, the paper includes a detailed description of the steps taken to develop both LPTN and finite elements method (FEM) thermal models. Results obtained from the two thermal models are presented and critically compared, aiming to validate the results of the thermal analysis. Finally, a careful evaluation is developed, aiming to identify the potential negative effects of such faults on the motor structure. Interturn SC fault scenarios with distinctive severity levels are evaluated.

| MOTOR UNDER STUDY
The two thermal models adopted in this paper are implemented on a 2.2 kW IM. Table 1 provides information about the technical specifications of the IM considered for this study.

| LPTN MODELLING
Thermal models based on the LPTN method provide a relatively simple yet effective tool to compute the temperature in different points of IMs. Indeed, the low computational effort required to establish thermal models is the main merit of LPTN methods [28]. This merit of LPTN provides an important competitive advantage, in comparison to FEM and computational fluid dynamics methods, for applications where online temperature estimation is required, as it is the case of online condition monitoring of IMs.
In LPTN analysis, the machine structure is discretised into multiple elements. Each element is described by a thermal resistance and/or a thermal capacitance [9]. In fact, it is possible to establish an analogy between electrical variables and thermal variables [29].
Based on the law of conduction heat transfer, presented by Joseph Fourier, the heat flux density is proportional to the temperature gradient. It is expressed as follows: When the inter-turn SC occurs, the most relevant thermal phenomena to be considered are located in the stator. Hence, particular attention should be devoted to the modelling of the stator thermal networks, in order to accurately model all heat exchange processes taking place in the stator. To elaborate the model, three assumptions have been adopted: 1. The rotor is considered isothermal during the stator thermal transient 2. The IM external environment is also considered isothermal during the stator thermal transient 3. Only the radial heat propagation axis is taken into account, since the FEM model used to validate the LPTN model only considers the 2D radial geometry of the IM The heat transfer along the radial axis is described by: where P denotes the total power losses. The solution of the heat equation is expressed by: where c 1 and c 2 are constants. Based on the boundary conditions, the expressions of these two quantities can be easily solved. Figure 1 provides a schematic representation of the adopted LPTN model, focusing the thermal network that defines the thermal behaviour of the stator. The thermal network is composed of resistance and capacitance (RC) cells, displaced in a cascaded configuration. The values assigned to each RC cell are presented in Tables 2 and 3. To compute the different mathematical expressions of the thermal resistances, the heat equation that describes an internal heat source, transferring heat in the radial axis, was solved, taking into account the heat boundary conditions. Each node defined in the model (environment, frame, stator core, insulator, slot windings, and stator teeth) is characterised by specific thermal phenomena. On the other hand, the thermal capacitances depend on the heat density, volume and volumetric mass density of the material. The adopted LPTN model follows a hybrid approach, that is, the inputs introduced into the LPTN model are the Joule losses and the iron losses provided by the FEM.

| FINITE ELEMENTS MODEL
The finite elements model of the IM under study was developed resorting to the software tool Flux2D. Figure 2 provides a representation of the cross-sectional plane of the motor, considered in the 2D thermal analysis based on the FEM. The representation includes a label for each element of the motor.
The thermal analysis based on the FEM allows to get a more detailed representation of the temperature distribution inside the IM, provided that the method computes the temperature for each node of a thin mesh. The computation of the temperatures for each node of the mesh requires the implementation of a two-step procedure. At the first step, which consists of the electromagnetic simulation, a detailed representation of the electromagnetic phenomena taking place inside the motor is obtained, allowing to compute the losses for each component of the IM. A distinction among Joule losses, iron losses and additional losses is developed in that procedure. The Bertotti model is adopted for the computation of the iron losses [30]. Then, at the second step of the procedure, the losses computed in the electromagnetic simulation -53 are considered as the heat sources of the thermal model. Apart the losses, the thermal model also incorporates all parameters and properties relevant to accurately simulate the thermal behaviour of the IM. Resorting to these data, the evolution, in the time domain, of the temperature inside the IM is estimated.
To attain improved accuracy in the results obtained by the FEM, both electromagnetic and thermal simulations adopt a transient analysis, by considering the evolution of all variables in the time domain. Figure 3 provides the schematic of the equivalent electric circuit of the IM. For each phase, the equivalent circuit incorporates multiple identical coils, except phase W. The windings of each phase are split into multiple identical coils, with the exception of coils B1, B2 and B3, which represent a smaller number of turns. Coil B1, the coil with the shorted turns, represents six turns. The resistor rf represents the SC resistance and, consequently, defines the severity of the fault. It should be noted that the resistor rf of the equivalent electric circuit is assigned, in the FEM model, to the geometric region of the stator slots where the shorted turns are allocated. Therefore, the FEM model is able to accurately model the Joule losses, induced by the SC condition, taking place inside the stator slots allocating the shorted turns. The accurate computation of the Joule losses, taking place in the distinctive parts of the motor, is pivotal in ensuring an effective evaluation of the thermal behaviour.

| Electromagnetic simulation
The motor power supply and load conditions are identical for all scenarios. The motor operates at half load, with nominal speed (1435 rpm) and 50 % of the nominal load torque (7 Nm). Table 4 summarises the parameters related to the motor supply and load conditions considered in the electromagnetic simulations.

| Thermal simulation
The thermal analysis is developed considering that the motor starts from standstill condition. Accordingly, it is considered that the motor internal structure is cold (25°C) and isothermal at the beginning of the simulation. Table 5 compiles the thermal conductivities of the distinctive components of the motor.
Another important phenomenon to account for in the thermal simulation is the transfer of heat among distinctive regions, but particularly the transfer of heat between the IM and the surrounding environment. Such heat transfer to the surrounding environment of the IM mainly takes place by the mechanism of forced convection. The convection coefficient selected to represent this phenomenon takes into account factors like the constructive features of the IM or the external IM temperature [31]. To express forced convection conditions, the convection coefficient of the air typically assumes values within the [20 300] W·m À 2 ·K À 1 range, as it is the case here [32]. In this study, the convection coefficient of 80 W·m À 2 ·K À 1 provides the best representation of the forced convection phenomenon taking place in the motor under study. To reproduce the phenomenon of heat transfer through radiation, the emissivity and absorption coefficient of the IM stator frame is defined at 0.95. Please note that the simulation model based on the FEM presented in this study was subjected to experimental validation in another study of the same authors [33]. In particular, the effectiveness of the thermal model based on the FEM was confirmed for the operation of the motor under healthy conditions. Hence, a solid framework for the validation of the thermal model based on the FEM is already established.

| Electromagnetic simulation
To establish into what extent does the SC fault increases the losses of the IM, the following operation scenarios have been evaluated: For comparison purposes, the healthy condition is taken as the benchmark scenario. Three additional conditions are established, to evaluate the consequences of the SC fault, under distinctive severity degrees. In all three fault scenarios, the fault takes place in coil B1. Table 6 shows the supply and SC currents, obtained in the four operation scenarios. These results are obtained from the electromagnetic simulation developed resorting to the FEM.
The SC condition induces an unbalance on the three supply currents-I U , I V and I W -as demonstrated in Table 6. Still, it is stated that there is not a strong correlation between the severity of the supply unbalance and the severity of the SC fault, as the degree of unbalance of the motor supply is quite similar for all fault conditions. Conversely, the current in the SC branch-I rf -rises exponentially with the progressive drop on the SC resistance rf. Table 7 compiles the data related to the Joule losses and iron losses.
As confirmed in Table 7, the SC conditions induce a general rise of the Joule losses in all three phases of the motor. Such increment is particularly sharp in the shorted turns and also on the SC branch. Even in the less severe SC scenario, the Joule losses are multiplied by two when compared to the reference condition, in all the three motor phases.

| Thermal simulation
The thermal analysis developed in this study focuses on the period of time required for the IM to meet the thermal steadystate condition, as defined in [34,35].
Another important factor to be considered in the following thermal analysis has to do with the admissible operating temperatures, defined by the properties of the windings' insulation. According to the NEMA and IEC 60085 classifications, the maximum temperature supported by class F insulating materials, that can be reached without the total loss of the material -55 properties, is 155°C [36,37]. This information is critical to establish the period of time taken until a thermal overrun condition is observed, comprised between the imposition of a SC fault and the moment when the critical temperature of the insulation is reached.
The following thermal analysis considers the same four operating scenarios defined for the electromagnetic simulation developed in FEM. Following sub-sections provide the results of the thermal simulations obtained from both LPTN and FEM models. Evaluation of the motor temperature is developed at both point-and geometry-level for FEM, while the LPTN model provides an evaluation of the temperature at the point-level. Figure 4 shows the location of point PT100_2A, a position of the stator where the temperature increases the most as a result of the SC condition.

| Healthy operation
To develop a transient analysis of the IM thermal behaviour, a hybrid LPTN model has been implemented. Figure 5 presents the evolution, over time, of the temperature in point PT100_2A, considering healthy operating condition. The developed LPTN model provides an accurate estimation of the temperature at point PT100_2A, following the trend obtained by the FEM, with minimal deviation between the temperatures obtained by the two models (2.01%).
To get a better picture about the temperature distribution inside the motor, Figure 6 provides the map of temperatures obtained at instant t ¼ 8000 s, when the thermal steady-state condition is reached. Provided that the operation of the motor is not affected by any asymmetry, all the stator is evenly warmed. Since the windings act as the most significant heat source, the stator slots appear as the warmest parts of the stator. On the other hand, the stator smoothly cools down in the radial direction, towards the stator frame. Also, it is noticed that the rotor is the warmest component of the motor. According to the FEM model, the temperature at this position stabilises at 56.44°C, while the hybrid LPTN model predicts that the temperature stabilises at 55.42°C. The difference between the temperatures predicted by the two models is 1.84 %, as expressed in Table 8. Figure 8 illustrates the temperature distribution when the inter-turn SC fault is introduced in phase W. Some remarks can be taken, based on the map of temperatures. The rotor, which is still the warmest component of the IM, remains isothermal. However, the temperature distribution along the stator is no  Abbreviation: SC, short-circuit.

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longer uniform. The windings of phase W become significantly warmer, as additional Joule losses are incurred in the shortcircuited turns. If the temperature along the stator external boundary was measured for this scenario, it would be stated that the temperature distribution remains uniform across the entire stator frame and, consequently, the fault effects would not be noticed from outside. Based on the results illustrated by Figures 7 and 8, it is concluded that the IM is still able to work, even in the presence of the fault. Nonetheless, early ageing of the insulation will take place. The condition of the insulation will deteriorate significantly, extending the number of turns affected by the SC condition, on the one hand, and reducing the SC resistance, on the other hand.

| Faulty operation (inter-turn SC, rf ¼ 0.1 Ω)
The second fault scenario is introduced by adjusting rf to 0.1 Ω. The increment on the severity of the SC introduces a noticeable unbalance on the supply currents, expressed as an increment on current I W . Figure 9 shows the thermal transientand steady-state, in point PT100_2A.
Based on Table 8, the error between the LPTN and the FEM models is 2.69 %. Figure 10 depicts the temperature distribution inside the motor, when the SC resistance is defined at rf ¼ 0.1 Ω. Far more prominent warming takes place next to the shorted turns, in comparison to the previous fault scenario. Also, it is observed that the rotor remains isothermal, but it is no longer the warmest component of the motor. Given the severe warming of the short-circuited turns, the stator slots containing the shorted turns become warmer than the rotor.
In case of rf ¼ 0.1 Ω, the maximum windings' temperature is almost 145°C, at the thermal steady-state. As the windings' temperature is just next to the thermal reserve region, it is expected that the IM does not suffer major damages arising from thermal overrun, since the maximum temperature does not surpass 155°C. Still, the risk of imposition of permanent damage to the IM should not be overlooked.
If a thermal analysis of the stator external boundary was carried out in this scenario, it would be stated that the stator frame is no longer isothermal. Therefore, symptoms of the fault could be also noticed resorting to simple thermal imaging techniques.

| Faulty operation (inter-turn SC, rf ¼ 0.001 Ω)
For the third fault scenario, the SC resistance rf is adjusted to 0.001 Ω. According to the results provided in Figure 11, this TA B L E 7 Distribution of the Joule losses and iron losses among the distinctive components of the motor The motor internal temperature distribution is illustrated in Figure 12. A non-uniform temperature distribution is clearly observed. A sharp and extreme warming is observed in a pretty focused area, namely the stator slots hosting the faulty turns. This overheating phenomenon ends up spreading to all the motor structure and to the surrounding environment, thus extending the negative influence of high operation temperatures to the entire motor. The rotor is now much cooler than the faulty windings.
Considering that the motor is subjected to exceptionally high temperatures, it is conceivable that the IM will suffer F I G U R E 6 Temperature distribution over a 2D cross-section of the induction motor (IM), at t ¼ 8000 s, observed when the motor is operating under healthy condition F I G U R E 7 Temperature evolution on the phase W stator windings, assessed for a 6-turns short-circuit (SC) condition, predicted by the lumped parameter thermal network (LPTN) and the finite elements method (FEM) models. The SC resistance rf is set to 1 permanent damages, due to thermal overrun, in a very short period of time (less than 3 min). Since the inter-turn SC condition is imposed when the motor is cold (25°C), the thermal overrun condition should probably be met in a fairly shorter period in case that the fault takes place when the motor was already warm, at the moment of imposition of the fault. If a thermal analysis of the stator frame was carried out, the abnormal and non-uniform warming of the stator frame could be taken for granted.

| CONCLUSIONS
This paper presents a careful assessment of the consequences of inter-turn SC faults in the integrity of IMs, resorting to an approach based on thermal analysis. The results obtained from the two models presented in this paper (LPTN and FEM) show a reasonable degree of agreement.
Globally, it is observed that this type of fault has an extremely negative impact on the operating temperature of IMs. Furthermore, such condition also promotes a non-uniform distribution of the temperature inside the motor. Based on the results of the FEM thermal model, such unbalance in the internal motor temperature distribution can spread so much in space, that it can be even noticed by simply measuring the temperature of the motor frame. F I G U R E 8 Temperature distribution over a 2D cross-section of the induction motor (IM), at t ¼ 8000 s, observed when the motor is operating under a 6turns short-circuit (SC). The SC resistance rf is set to 1.35 Ω F I G U R E 9 Temperature evolution on the phase W stator windings, assessed for a 6-turns short-circuit (SC) condition, predicted by the lumped parameter thermal network (LPTN) and the finite elements method (FEM) models. The SC resistance rf is set to 0.1 Ω Provided that the simulated operating scenarios considered the IM operation in derated mode, far more severe consequences should be experienced if the motor is operated close to the nominal load torque. Much faster warming of the stator windings will shorten even more the already very narrow window of chance for the diagnosis of this fault.
Given the multiple factors playing an important role on the determination of the severity of a SC fault (number of shorted turns, SC resistance, motor technical specifications, load level, speed and motor temperature under healthy condition, to name a few), it is difficult to perform a concise judgement about the effectiveness of the fault diagnostic algorithms available on the literature, in what concerns their ability to prevent permanent damage on faulty IMs. Still, the results presented in this paper give strength to the hypothesis formulated in the introduction: some of the diagnostic tools available in the literature show a serious risk of failure to properly diagnose the fault in sufficient time to avoid permanent damage to the IM. This statement is particularly valid for algorithms which are unable to detect very low-severity SC faults [20], as well as for those with high complexity, requiring high processing effort and at least one minute to identify an inter-turn SC fault.
Further insight into the multiple parameters impacting the severity of the fault is vital in establishing a concise evaluation to confirm the effectiveness of the state-of-the-art inter-turn SC fault diagnostic algorithms. F I G U R E 1 0 Temperature distribution over a 2D cross-section of the induction motor (IM), at t ¼ 8000 s, observed when the motor is operating under a 6turns short-circuit (SC). The SC resistance rf is set to 0.1 Ω F I G U R E 1 1 Temperature evolution on the phase W stator windings, assessed for a 6-turns short-circuit (SC) condition, predicted by the lumped parameter thermal network (LPTN) and the finite elements method (FEM) models. The SC resistance rf is set to 0.001 Ω