# Lightning Surge Analysis for Overhead Lines Considering Corona Effect
## 5 Calculated Results and Discussions
Figure 17: Calculated and field test voltage waveshapes under negative polarity (\(U_{\rm m}\) is the voltage amplitude at the sending end; \(\ldots\) sending end; \(\ldots\) sending end; \(\ldots\) field test; calculated). (**a**) In the presence of minor loops, (**b**) in the absence of minor loops. As can be seen from Figures 16 and 17 and Tables 2 and 3, the distortion and attenuation of the surge voltages in the first oscillation cycle are considerably more severe under positive polarity than under negative polarity. This is due to the fact that the area of the main loop formed by the curve in the first oscillation cycle is much larger under positive polarity than under negative polarity according to the measured \(q\)-\(u\) curves shown in Figure 3. Hence the corona discharge in the first oscillation cycle can cause much higher energy loss under positive polarity than under negative polarity. The attenuation decrement of the first wave crest is 44.0-56.4% under positive polarity, whereas that is only 24.1-26.7% under negative polarity. In addition, the minor loops also have different influences on calculation of the distortion and attenuation of the surge voltages. Under positive polarity, as shown in Figure 16 and Table 2, the calculated errors (relative to the field test results) at the first wave trough and second wave crest are 1.7-6.1% and 1.1-4.7% in the presence of the minor loops and 2.8-6.7% and 1.5-4.5% in the absence of the minor loops, respectively. It is thus clear that the calculated errors in the presence and absence of the minor loops are close to each other. The reason is that the area of the minor loops is relatively small on the \(q\)-\(u\) curves under positive polarity in terms of the measured results given above, and incapable of producing considerable energy loss for the distortion and attenuation after the first oscillation cycle. However, the case under negative polarity is different from that under positive polarity. As shown in Figure 17 and Table 3, the calculated errors at the first wave trough and second crest reach 5.2-10.2% and 5.1-10.6% in the absence of the minor loops, whereas those are only 1.5-4.8% and 0.94-5.4% in the presence of the minor loops, respectively. It follows that there is an appreciable difference in the calculation precision in the presence and absence of the minor loops. Moreover, the calculated results in the presence of the minor loops more closely approximate the field test results. This can be interpreted as the area of minor loops being relatively large on the \(q\)-\(u\) curves under negative polarity in the light of the aforementioned experimental observation and causing considerable energy loss to distort and attenuate the surge voltages in the subsequent oscillation cycles. Therefore, neglect of the minor loops in the transient calculation may give rise to non-negligible error for predicting the distortion and attenuation of negative damped oscillation surges. For a further verification of the proposed method, the calculated voltage waveshapes are also compared with those obtained from the FDTD method [32], as shown in Figure 18. On the whole, the former agrees with the latter and both are close to the field test voltage waveshapes. Figure 18: A comparison with FDTD method (\(U_{\rm m}\) is the voltage amplitude at the sending end; \(\ldots\)\(\ldots\) sending end; \(\ldots\) field test; \(\ldots\