## 4 Discussion  
### Data Decoupling  
According to the measuring principle, a decoupling process is necessary to recover the actual voltage waveforms on a high-voltage conductor from the original measured data, for which the coefficient matrix is the key. Under an ideal condition, the coefficient matrix can be found by static electric field analysis. However, the actual on-site situation brings about unpredictable variations to the matrix. Therefore, determining the matrix from field measured data is more effective and reasonable. In [23], an example for acquiring the coefficient matrix according to the field measured data is presented in which three capacitor voltage dividers for three phases are switched onto the bus bar by disconnectors. Since the switching processes for the three phases are not absolutely synchronized, the changes of transient voltages would appear asynchronously on the conductors. Taking Phase A as an example, if a sharp voltage change happens in Phase A, all the sensors for the three phases will record an electric field change. According to the definition of \(k\), the first column of the coefficient matrix could be determined. Using the same method, the second and third columns could also be found by recording a sharp voltage change on Phase B and Phase C. Moreover, based on the phase difference and amplitude among three-phase power frequency voltage, several equations could also be established to solve the \(k\) coefficient in (5). Above three switching transient measurement results are all decoupled.  
For the 220 kV Yan-Zhuang overhead transmission line, no asynchronous transient process has been recorded by far. Thus, it is unfortunate that no opportunity has been given to solve the decoupling coefficients. Instead, a calibration work has been planned on the next power outage of this line. In the calibration, the impulse voltage will be applied to each phase conductor by turns to obtain the decoupling coefficients. However, since the data recorded is all triggered by induction strokes, the three-phase waveforms of transient voltages are synchronized with the same variation trend.  
Figure 11: Transient voltage during switching off the #3 power transformer on Batang substation.  
Moreover, the coefficients in the matrix of (5) have the same polarity. With linear superposition, in (5), the variation trends of the measured electric field waveform (\(E\)) and the transient voltage waveform (\(U\)) would be the same in the time domain.  
Setting the waveform on Phase A, Phase B, and Phase C are \(U_{\text{A}}(t)\), \(U_{\text{B}}(t)\), and \(U_{\text{C}}(t)\), respectively. Since they have the same variation trend, they can express as:  
\[U_{A}(t) = m_{a}U_{n}(t) \tag{8}\] \[U_{B}(t) = m_{b}U_{n}(t)\] (9) \[U_{C}(t) = m_{c}U_{n}(t) \tag{10}\]  
where \(U_{n}(t)\) is a normalized waveform, and \(m_{a}\), \(m_{b}\), and \(m_{c}\) are the amplitude coefficients for \(U_{\text{A}}(t)\), \(U_{\text{B}}(t)\), and \(U_{\text{C}}(t)\), respectively. Taking \(E_{\text{a-z}}(t)\) in (5) as an example, it can be express as:  
\[E_{A-z}(t) = (k_{aA-z}m_{a}+k_{bA-z}m_{b}+k_{cA-z}m_{c})U_{n}(t) \tag{11}\]  
It is obvious that the composite electric field has the same variation trend with the original transient voltages. In other words, they will have the same value of time parameters, such as the rising time and half wave time. However, the amplitude value needs to implement the decoupling process.