# Linear Method for Diagnosis of Inter-Turn Short Circuits in 3-Phase Induction Motors
## 1 Introduction  
Induction motors are widely used in many industries because they have a simple structure and are easily applicable to a system [1]. However, such motors are exposed to stress because they have to rotate periodically for long intervals. The motors are checked in accordance with a maintenance schedule to prevent faults, but sudden faults still cause considerable financial loss in industry. The causes of induction motor faults can largely be classified into electrical and mechanical defects. Electrical defects are the main causes of stator and rotor faults, whereas mechanical defects are major causes of bearing faults. Mechanical defects account for 41% of all faults of induction motors, and electrical defects account for 45% of all faults, including 36% of stator faults and 9% of rotor faults [2; 3]. In particular, stator faults are caused by dielectric breakdown, and the stator winding insulation is degraded by various causes such as coil movement, thermal stress, overburden, and mechanical vibration. This degradation of the winding insulation eventually leads to turn-to-turn short faults [4]. When a turn-to-turn short fault occurs, a large circulating current and high heat are generated in the fault circuit [5; 6]. Most of these faults are caused by various stresses acting on the stator, such as thermal, mechanical, electrical, and environmental stresses [7]. Therefore, early diagnosis is urgently needed because the detection of inter-turn short circuits (ITSCs) can prevent sequential damage of the motor, minimize motor stop time, and the need for additional manpower and repair cost, thus avoiding considerable economic loss [8; 9; 10]. In the past,detection methods using vibration and noise sensors were applied, but the sensors are expensive and additional circuits need to be designed and attached to the equipment. Recently, non-invasive methods have been developed, e.g., acoustic, vibrational, thermal, magnetic methods [11; 12; 13]. Non-invasive methods are capable of diagnosing early faults without disassembly of the induction motor. Each type of signal has advantages and disadvantages. Measurements of acoustic and thermal signals are noninvasive. Acoustic and thermal signals can be measured without touching the motor. The method of selection of amplitudes of frequencies ratio 50 second frequency coefficient (MSAF-RATIO-50-SFC), MSAF-RATIO-50-SFC-EXPANDED, MSAF-RATIO-24-MULTIEXPANDED-FILTER-8, and shortened method of frequencies selection (SMoFS-15) are methods later used for diagnosis with the recent development of non-invasive sensor technology [14; 15]. The disadvantage of the mentioned diagnostic signals is difficult processing. Because of these inconveniences, the motor current signature analysis (MCSA), which is a sensorless method, is a recent focus of research [16; 17; 18; 19; 20; 21; 22; 23]. The diagnosis of turn-to-turn shorts using MCSA has been researched in earnest using current spectra since 1989 [24; 25]. [PERSON]'s vector approach (PVA) was suggested in consideration of the fact that the induction motor must be diagnosed while it is rotating [25; 26; 27]. As PVA was developed in 1929, it became an analysis method that transformed three-phase orthogonal equations to two-phase orthogonal equations. In 1988, the readability of PVA was improved by enabling the diagnosis of faults by circular patterns [25; 28; 29]. However, fault diagnosis was still difficult due to the problems of iron loss and copper loss (of current) and because there was no clear difference between these and the ITSC condition. Consequently, research was conducted to define a distortion factor by extracting the maximum and minimum values during a short interval of operation [30; 31; 32]. However, the ITSC conditions were not much different from those at steady state. Hence, further research was conducted with a focus on the average shift of the distortion factor.