# Efficient Zero-Sequence Impedance Measurement in Autotransformers Using Low-Voltage Excitation
## 3 YNa0d11 Three-Winding Autotransformer Zero-Sequence Impedance Field Test Method
### Two-Phase Disconnection Test  
The two-phase disconnection test is similar to the same-phase disconnection test. It also requires three tests of disconnection on the high with low-voltage side, the medium with low-voltage side, with the high- and medium-voltage side results being:  
1. Test 4: Positive-sequence excitation is injected on the low-voltage side; the high-voltage side winding is grounded in one phase and disconnected in two phases and the low-voltage side winding is completely disconnected.
2. Test 5: Positive-sequence excitation is injected on the low-voltage side; the medium-voltage side winding is grounded in one phase and disconnected in two phases and the high-voltage side winding is completely disconnected.
3. Test 6: Positive-sequence excitation is injected on the low-voltage side and both high- and medium-voltage windings are single-phase grounded and two-phase disconnected.  
Both Test 4 and Test 5 are wired similarly to measure the zero-sequence impedance to ground on the high-voltage side \(Z_{\text{Hg-0}}\) and the zero-sequence impedance to ground on the medium-voltage side \(Z_{\text{Tg-0}}\), respectively. Test 4 is wired as illustrated in Figure 14. The subscripts \"a, b, c\" in Figure 14 represent the parameters on the low-voltage side of the transformer.  
The zero-sequence impedance of this autotransformer can be derived from the compound sequence network diagram in Figure 15.  
\[Z_{\text{Hg-0}}=\frac{V_{1}+V_{2}-2I_{1}Z_{\text{HL-1}}}{I_{0}} \tag{17}\]  
Figure 14: Test 4 wiring diagram.  
Figure 13: Sequence network for Test 3.  
\[\left\{\begin{array}{l}\dot{i}_{a}=\dot{i}_{1}\angle 30^{\circ}+\dot{i}_{2} \angle-30^{\circ}=\sqrt{3}I_{1}\\ \dot{i}_{b}=a^{2}\dot{I}_{1}\angle 30^{\circ}+a\dot{I}_{2}\angle-30^{\circ}=0\\ \dot{i}_{c}=a\dot{I}_{1}\angle 30^{\circ}+a^{2}\dot{I}_{2}\angle-30^{\circ}=- \sqrt{3}I_{1}\end{array}\right. \tag{18}\]  
\(Z_{\rm Hg-0}\) and \(Z_{\rm Tg-0}\) can be obtained by combining Equations (15) and (18).  
The test wiring for Test 6 is shown in Figure 16 and the corresponding composite sequence network diagram is shown in Figure 17. The subscripts \"a, b, c\" in Figure 16 represent the parameters on the low-voltage side of the transformer.  
The three tests described above lead to three sets of zero-sequence impedances.  
\[\left\{\begin{array}{l}Z_{\rm Hg-0}=\frac{V_{1}+V_{2}-2I_{1}Z_{\rm HI-1}}{ \frac{I_{0}}{I_{0}}}\\ Z_{\rm Tg-0}=\frac{V_{1}+V_{2}-2I_{1}Z_{\rm HI-1}}{I_{0}}\\ Z_{(\rm H\|T)g-0}=\frac{V_{1}+V_{2}-2I_{1}Z_{\rm HI\|T)-1}}{I_{0}}\end{array}\right. \tag{19}\]  
The zero-sequence impedance of each winding of the autotransformer can be found separately by using Equation (18).  
Figure 16: Test 6 wiring diagram.  
Figure 17: Sequence network for Test 6.  
Figure 15: Sequence network for Test 4.  
In this paper, the theoretical analysis of both the one-phase and two-phase disconnection tests on the high-voltage side of YNa0d11-type autotransformers is described.  
The flowchart of the testing method proposed in this article is shown in Figure 18.