# Linear Method for Diagnosis of Inter-Turn Short Circuits in 3-Phase Induction Motors
## 6 Proposed Method  
It is difficult to diagnose ITSC using the PVA method because the maximum and minimum values based on the vector scalar sum of the \(d\)-axis and \(q\)-axis are expressed as ratios. This depends on the current pulsation and is based on the magnetic flux linkage quantity analysis described above. This study indicates that the change of the short circuit current amount can be generated by linear diagnosis of ITSC, and a method using the D-Q synchronous reference frame over time was proposed to apply this procedure to experiments. Figure 11 shows the monitoring results of a steady state and ITSC state using the proposed D-Q synchronous reference frame. It can be seen from this figure that the rotating induction motor in steady state contains an irregular AC component that pulsates due to loss. The pulsation in the ITSC state is not much different from the steady state; however, the overall current value decreases and the above-mentioned definition holds. Figure 11: Inter-turn short circuit (ITSC) monitoring using a D-Q synchronous reference frame. Figure 10: Stator fault diagnosis method using the distortion rate. Figure 12 shows the results of measuring each turn-to-turn short for 30 s in the D-Q synchronous reference frame. Only the measured \(I_{d}\)-axis was monitored as the turn-to-turn short increased from steady state (black line), to ITSC (red line), to a 4-turn short (green line), and then to a 6-turn short (blue line). As can be seen in this figure, the ITSC current decreases, but the pulsation becomes severe from the 4-turn short. The maximum size of the \(I_{d}\) current is similar to the steady-state current, but its minimum size is similar to that of the ITSC. When the turn-to-turn short increased further, the current became larger than the steady-state current range and severe pulsation was generated. Figure 13 visually shows the changes by narrowing the range to 1 s for Figure 12. Table 3 shows the average values per second of the maximum, minimum, peak-to-peak, and average values measured in steady state and short circuit state from steady state to a 12-turn short. As can be seen from peak to peak in Table 3, the peak to peak is 0.1439 A in steady state and 0.1647 A in ITSC. The ITSC is not much different from the steady state: the difference between the steady state and ITSC is approximately 0.02 A. However, in the results of the 4-turn short, the peak to peak is 0.2418 A, showing a difference of 0.1 A, and the amount of current increases by approximately 4.7 times relative to that of the ITSC. The peak to peak represents the difference between the maximum and minimum per second. The existing method using the DR of PVA made it difficult to diagnose ITSC because it is based on this gap. Figure 14 shows a graphic representation of the results in Table 3 for comparison. The maximum current in Figure 14 shows a slightly decreasing trend in the ITSC, but increases sharply when the turn-to-turn short increases. However, the minimum value of the pulsating current increases very little even if the turn-to-turn short increases. Based on these results, the two-dimensional coordinates with pulsating maximum and minimum values as feature points are illustrated in Figure 15.  
In Figure 15, the small circles indicate a steady state, the small squares indicate ITSC, the x marks indicate a 4-turn short, and the + marks indicate a 6-turn short. The maximum and minimum current values of the ITSC generally become smaller with similar pulsation sizes. Figure 14: Changes in the maximum, minimum, and average current by short-circuit type. Figure 13: Comparison of the turn-to-turn short sizes using the D-Q synchronous reference frame (change rate per second).