**6. Conclusions**

The corona characteristics have been measured experimentally in a corona cage under damped oscillation and double exponential surges. The measured results shows that a basic difference between the *q*–*<sup>u</sup>* curves under the two types of surge voltage appears after their respective maximum charges. In these curve parts, the *q*–*<sup>u</sup>* curves under double exponential surges descend monotonically, whereas those under damped oscillation surges behave as the minor loops. The area of the minor loops is significantly larger under negative polarity than under positive polarity. In order to characterize the complicated trajectory feature of the minor loops, an extended approach has been presented by considerably improving the traditional approach. The extended approach is adaptable not only to double exponential surges but also to damped oscillation surges. Based on the extended approach, an efficient method has been proposed for calculating the distortion and attenuation of damped oscillation surges on the overhead lines with corona. A better agreemen<sup>t</sup> between the calculated and field test results confirms the validity of the proposed method. Furthermore, special emphasis is put on the fact that the influence of the minor loops on the distortion and attenuation of damped oscillation surges is obviously stronger under negative polarity than under positive polarity in the subsequent oscillation cycles. The calculated results under negative polarity indicate that the calculated errors due to neglecting the minor loops may reach 10.2~10.6% at the first wave trough and second crest, respectively. Since most lightning surges have the negative polarity, it is of practical significance to take into account the influence of the minor loops in the transient calculation. In future work, a further improvement will be made to the proposed method in the lightning transient calculation of multiphase overhead lines with bundle conductors.

**Author Contributions:** Conceptualization, X.Z.; methodology, X.Z. and K.H.; software, K.H.; validation, K.H.; formal analysis, X.Z.; investigation, K.H.; resources, K.H.; data curation, K.H.; writing— original draft preparation, X.Z.; writing—review and editing, X.Z.; visualization, K.H.; supervision, X.Z.; project administration, X.Z. Both authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, gran<sup>t</sup> number 51777007.

**Institutional Review Board Statement:** No applicable.

**Informed Consent Statement:** No applicable.

**Data Availability Statement:** The data present in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.
