###### Abstract  
In this study, a current vector pattern is analyzed for inter-turn fault (ITF) diagnosis of induction machines (IMs), and an ITF diagnosis algorithm is proposed. When an ITF occurs in IMs, a negative-sequence current is generated due to fault resistance, even though a positive-sequence voltage is applied to IMs. Based on the mathematical model of IMs with an ITF, the current vector patterns in the stationary coordinate frame are analyzed. The superposition of positive- and negative-sequence components results in an elliptical current vector trajectory, and its orientation varies depending on the fault conditions. The co-simulation using finite element analysis and circuit simulation is implemented to analyze the current vector pattern of IMs with an ITF. The ITF diagnosis is proposed based on the current vector pattern. A 12 kW, four-pole, three-phase IM and terminal box, which was used to implement an ITF, is manufactured, and an experiment setup is established to verify the ITF algorithm. The effectiveness of the proposed ITF algorithm is validated through experimental verification of the manufactured IM and terminal box. co-simulation; current vector analysis; induction motor; inter-turn fault diagnosis (ITF); negative-sequence current 2025  
22 July 202522 July 20252 July 20252 July 20252 July 20252 July 2025252 July 2025252525252525252525252525252525252525252525252  
simple structure, lack of permanent magnets, and cost-effectiveness make them a favorable choice for many commercial systems [8]. However, the reliability of IMs is becoming an increasingly important concern, especially in failure-prone environments. As electric vehicles become more widespread, ensuring the robust operation of these motors under a variety of conditions is becoming increasingly important [9]. There are various types of motor faults that can occur during operation, and the appropriate diagnostic method depends on the fault type. In general, motor faults are classified into electrical, magnetic, and mechanical categories [10]. Among these, stator-related faults in IMs account for more than 30% of all failures [11]. An inter-turn fault (ITF) in IMs occurs when the insulation between adjacent stator windings deteriorates, leading to a localized short circuit. This fault induces an unbalanced magnetic field, resulting in localized overheating and magnetic flux distortion. If not detected at an early stage, the fault may evolve into more severe conditions such as phase-to-phase or phase-to-ground faults, ultimately causing complete winding burnout and system failure [12; 13; 14; 15]. Several studies have investigated methods to diagnosis ITFs in IMs; these methods include transient-response-based methods [16; 17; 18], motor current signature analysis (MCSA) [19; 20; 21; 22; 23; 24; 25], and machine learning-based methods [24; 25; 26; 27; 28; 29; 30; 31; 32]. In [17; 18; 19], the transient characteristics of IMs with an ITF are analyzed, and fault diagnosis methods are proposed based on measured physical properties such as current or temperature. Fault diagnosis based on MCSA has been widely adopted due to its simplicity and cost-effectiveness, as it only relies on current sensors. MCSA can be conducted based on the time domain (e.g., current envelope analysis) [19; 20], frequency domain (e.g., Fast Fourier transform) [21; 22], and time-frequency domain (e.g., Hilbert transform, Discrete Wavelet transform, and Short-Time Fourier Transform) [23; 24; 25]. Machine learning-based methods, such as Support Vector Machine (SVM), have been employed for ITF detection [24; 25; 26; 27; 28]. These techniques utilize features derived from a mathematical model and frequency-domain characteristics of the IM under ITF. Although these methods demonstrate high diagnostic performance, their reliance on high sampling rates and considerable computational resources may limit their feasibility for implementation in embedded systems.