**6. Conclusions**

In this paper, a 15-mm needle-plate model is adopted to study the air corona discharge under positive and negative polarity DC voltage. The statistical rules of characteristic parameters of each stage and transition process are explained by the space charge effects and electric field distributions. Furthermore, the discharge characteristics, the reflected space charge effects of each stage are summarized and compared. Discharge mechanisms are explained in microcosmic angle. Microcosmic process of PD under DC voltage can be described based on statistical methods, and several conclusions can be drawn.

Space charges obviously distort electric fields, and the most effective influence to PD development is decreasing *E* down to *E*0 somewhere. For positive corona discharge, the space charge effects are most obvious at the glow-like discharge stage, where cations play a main role. The internal electric field of cation group is weakened but its distribution is relatively flat. The cation group inhibits the development of streamer, but inhibition effect is weakened later. At the breakdown flow stage, the influence of the action group is almost not reflected. For negative corona discharge, at Trichel discharge stage, cations work obviously, producing an electric field distribution with high and flat *E* inside. Then anions take part in and plasma layer forms in peripheral regions of cation layer, and further weakens the periphery electric field. At the glow discharge stage, *E* inside is high enough to sustain stable glow discharges inside. While *E* outside plasma layer is low, until in the breakdown streamer stage, *E* in outer edge of plasma layer reaches *E*0 and streamers 'restart'.

Space charge effects are connected with PD parameter by electric field, and some electrical field distributions contribute to obviously PD parameter rules. When discharge regions are tiny and *E* is relatively weak, it may cause unchanged *V*, and Δ*t*–*V* points distribute horizontally, which are shown at initial discharge stages of both polarities and transition stages of negative-glow discharge. When the electric field is high and relatively flat, Δ*t*–*V* may have an approximate proportional relationship, and Δ*t*–*V* points distribute inclined, which is shown at Trichel discharge stage of negative polarity.

Different forms of discharges may happen under a certain voltage, especially at transition stages, and different forms of discharges can be distinguished on PD parameters. For example, the *V* proportion distribution at glow-like stage of positive polarity, and Δ*t* proportion distribution at Trichel discharge stage of negative polarity. The phenomenon arises in that *E* varies significantly in different discharge regions, which, to a large extent, are caused by the existence of cations and plasmas.

**Author Contributions:** Conceptualization, D.W. and L.D.; Methodology, D.W.; Software, D.W.; Validation, D.W.; Formal Analysis, D.W.; Investigation, D.W.; Resources, L.D. and C.Y.; Writing-Original Draft Preparation, D.W.; Writing-Review & Editing, L.D. and C.Y.; Visualization, D.W.; Project Administration, L.D.; Funding Acquisition, L.D.

**Funding:** This research was funded by "the National Key R&D Program" gran<sup>t</sup> number "2017YFB0902400".

**Acknowledgments:** Many thanks to Deming Zhan and Han Yan for their contributions in experiments and investigations.

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