## 3 Experimental Setup  
### Extraction of D-Axis Current Component  
Three-phase current can be represented in both the D-Q stationary reference frame (\(\alpha\), \(\beta\)) and the D-Q synchronous reference frame (d, q) via D-Q transformation, as illustrated in Figure 1.  
These three components have a 120\({}^{\circ}\) phase difference and form a rotating current vector over time. By projecting this vector onto a two-dimensional stationary frame, the analysis can be simplified. This process is known as the Clarke transformation and is defined by Equation (1):\[ \begin{bmatrix}\text{i}_{\alpha}\\ \text{i}_{\beta}\end{bmatrix} =\frac{2}{3} \begin{bmatrix}1&-\frac{1}{2}&\frac{1}{2} \\ 0&\frac{\sqrt{3}}{2}&-\frac{\sqrt{3}}{2}\end{bmatrix}\begin{bmatrix}\text{i}_{ \alpha}\\ \text{i}_{b}\\ \text{i}_{c}\end{bmatrix}  \tag{1}\]  
Here, \(\text{i}_{\alpha}\) represents the component in the fixed a-axis direction, and \(\text{i}_{\beta}\) is the orthogonal component in the b-axis direction. The output of the Clarke transformation is useful for visualizing the rotational trajectory of the current vector in a stationary 2D plane. In the event of an unbalanced condition or fault, characteristic asymmetries or distortions in this trajectory often appear. The \((\text{i}_{\alpha},\text{i}_{\beta})\) components obtained through the Clarke transformation are still AC signals that rotate over time. By converting them into a synchronously rotating reference frame aligned with a reference angle \(\theta\), these components can be expressed as rectified DC signals under normal operating conditions. This process is called the Park transformation and is defined by Equation (2):  
\[ \begin{bmatrix}\text{i}_{\alpha}\\ \text{i}_{\text{d}}\end{bmatrix} = \begin{bmatrix}\cos\theta&\sin\theta\\ -\sin\theta&\cos\theta\end{bmatrix}\begin{bmatrix}\text{i}_{\alpha}\\ \text{i}_{\beta}\end{bmatrix}  \tag{2}\]  
Figure 2 visually illustrates the frequency-domain characteristics of current components under D-Q transformation in a three-phase current source. Figure 2a shows the original three-phase current waveform during the motor's operation. Figure 2b displays the current distribution in the stationary reference frame based on  
Figure 1: D-Q stationary and synchronous reference frames for three-phase current signals. Figure 2: Frequency variation according to D-Q transformation: (**a**) Three-phase current source, (**b**) D-Q stationary frame, and (**c**) D-Q synchronous frame. Equation (1). Figure 2c presents the frequency characteristics of the current components in the D-Q synchronous reference frame, derived using Equation (2). Under ideal conditions, the Id component in the D-Q frame is expressed as a constant magnitude value without time-domain oscillation, since the frequency components of the three-phase current are rectified with respect to the rotating reference axis. However, in practical motors, various factors such as internal inductance, copper losses, and iron losses introduce ripple components into the Id signal. These fluctuations become more pronounced under abnormal conditions such as winding short circuits or asymmetric faults. The Id component derived through the D-Q transformation represents the projection of the three-phase current onto the rotor flux axis. It compresses and integrates physical characteristics such as current magnitude, phase, and spatial distribution into a single reference axis-aligned signal. Thus, i\({}_{\text{d}}\) serves as a representative component that preserves the overall vector behavior of the three-phase current in a rectified format, acting as a compact information index for the current distribution along a specific axis. Figure 3 shows the time-domain waveform of the D-axis current (i\({}_{\text{d}}\)), obtained from actual measured data, under three conditions: Normal, ITSC, and 4 Turn faults. As the number of shorted turns increases, the Id waveform becomes increasingly distorted and exhibits larger amplitude fluctuations.