## 5 Conclusions  
In this study, the current vector patterns of IM with the ITF were analyzed based on a mathematical model, co-simulation, and experiment. When an ITF occurs in an IM, a negative-sequence current is generated, even though only a positive-sequence voltage is applied. The superposition of positive- and negative-sequence components results in an elliptical current vector pattern, which is characteristic of ITFs. The co-simulation with the FEA and circuit simulation was established to analyze the current vector pattern for an ITF in an IM. The angle of the maximum current vector depends on the fault phase and parameters. Based on this relationship, a fault diagnosis algorithm was proposed, which identifies the faulted phase by detecting the angle of the major axis in the stationary coordinate frame. An experimental setup was established using a 12 kW, four-pole, three-phase IM from a RENAULT Twizy and a terminal box for implementing the winding connections to verify the ITF diagnosis algorithm. The current in the stationary coordinate frame was computed in the DSP based on the measured current from current sensor. The current vector pattern was observed using the DAC and ACD of DSP and oscilloscope. The ITF conditions were implemented through the terminal box, and the current vector pattern was analyzed for the fault phase. As a result, the fault diagnosis algorithm was verified by the co-simulation and experimental results. This approach provides an ITF diagnosis during the operation of the IM, and the position sensor, such as encoder and resolver, is not needed because the stationary coordinate transformation is used. Although current vector pattern analysis has been employed for the diagnosis of ITFs in IMs, the detection of other types of faults also requires further investigation. Therefore, future research will focus on extending current pattern analysis methodologies to encompass various fault conditions in IMs, with consideration of the high-frequency IM model and constraints of motor drive systems. In addition, machine learning-based methods will be explored to improve fault classification accuracy, particularly for distinguishing between ITFs, broken rotor bars, and turn-to-turn faults, by utilizing features extracted from current vector patterns.  
Conceptualization, I.Y. and H.K.; methodology, H.K.; software, I.Y., S.-G.L. and H.K.; validation, I.Y., S.-G.L. and H.K.; formal analysis, S.-G.L. and H.K.; investigation, I.Y.; resources, I.Y. and J.L.; data curation, I.Y. and H.K.; writing--original draft preparation, I.Y. and H.K.; writing--review and editing, S.-G.L., J.L. and H.K.; visualization, I.Y.; supervision, J.L. and H.K.; project administration, J.L. and H.K.; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (No. RS-2023-00237024: Development and Demonstration of Medium-Sized Variable Speed High-Power Motor).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.