# Distinction Between Interturn Short-Circuit Faults and Unbalanced Load in Transformers
## 4 Results
### Time-Domain Analysis of the ISP and Current Signal  
The time-domain measurements of the current signals for the healthy transformer, where the taps of the single-phase transformer remained open, are shown in Figure 4. The three-phase current had an average amplitude of 3.57 A, and the mean value of the obtained ISP appeared almost as a straight line at the same current level. Both signals were displayed in the time domain. The mean value of the ISP, shown in blue, remained nearly linear, which is characteristic of a healthy transformer, with minimal deviations due to the inherent imbalance of the real machine. This initial condition served as a reference for comparison with subsequent conditions.  
Figure 5 shows the three-phase current signal and the obtained mean value of the ISP, both in the time domain, corresponding to the transformer with an imbalance due to the removal of four turns from the winding connected to the load. In the three-phase signal, phases A and B decreased to 2.97 A, while phase C maintained the same magnitude at 3.57 A. The mean value of the ISP, shown in blue, lost the characteristic straight-line trend of a healthy transformer and took on a sinusoidal shape with an amplitude of 0.47 A at a frequency of 120 Hz.  
Figure 4: Measurements of healthy ISP and three-phase signal.  
The three-phase current signals and the mean value of the ISP corresponding to a two-turn short circuit in the transformer's secondary winding are shown in Figure 6. In this case, phases A and B slightly increased to an amplitude of 4.01 A, while phase C remained unchanged at 3.57 A, as in the healthy state. Although the three-phase current signal changed, the mean value of the ISP remained similar to the signal resulting from the four-turn load imbalance, with an amplitude of 0.425 A and a frequency of 120 Hz.  
The time-domain analysis of the mean value of the ISP shows that a short circuit involving only two turns produces the same effect on the signal as a four-turn load imbalance. The mean ISP value for the two-turn short circuit was 45 mA lower than that of the four-turn imbalance, representing a difference of 9.5%. Therefore, it can be concluded that incipient interturn short-circuit faults cannot be simulated by simply removing turns from the winding.  
Figure 7 shows the three-phase current signals and the mean value of the ISP corresponding to a four-turn short circuit in the transformer's secondary winding. It can be observed that the amplitudes of phases A and B increased to 5.13 A, while phase C remained at 3.57 A. These changes are reflected in the increase in the amplitude of the mean ISP value, which reaches 1.1 A.  
When comparing the three-phase current signal and the mean ISP value for the four-turn short circuit in Figure 7 with the four-turn imbalance in Figure 5, an increase of 234% is observed. Additionally, when compared to the two-turn short circuit in Figure 6, the increase is 258%. These percentages highlight the difference between an incipient short circuit and an imbalance. However, this distinction is only evident when the cause is known; otherwise, it is not possible to determine whether the waveform change is due to an imbalance or an incipient short-circuit fault.  
Figure 5: Measurements of unbalanced ISP and three-phase signal.  
Figure 6: Measurements of 2-turn short-circuited ISP and three-phase signal.  
The results presented in this subsection were derived from observations performed on the three-phase current signal and the mean value of the ISP, both analyzed in the time domain.