**1. Introduction**

Nowadays, the insulation requirements of DC equipment are further improved, with the wide application of DC system in high voltage direct current (HVDC) transmission and other aspects. As a reflection of insulation faults in DC system, PD under DC is also concerned in many researches.

Gas partial discharge (PD) under DC voltage is a process closely related to the generation, migration and dissipation of space charges. The main forms of gas PD in DC system are the surface discharge on dielectric materials and the corona discharges under non-uniform electric field [1,2]. Researches on gas corona discharges under DC mainly includes three directions. One is researching on microcosmic discharge theory and discharge mechanism explanation [3–5]. Another one is considering influencing factors of discharge [6–9], such as electrode structure [6,7], air pressure [8] and air flow [9]. The rest one is studying discharge parameters characteristics, and apply them to pattern recognition and stage division of discharges [10–14].

Di fferent from the periodic generation and dissipation of space charges under alternate current (AC), many space charges will be retained in discharge region under DC because the polarity of electric field does not change. Therefore, one of the main points in the gas corona discharge researches under DC is the space charge e ffect and the electric field distortion caused by it. As yet, due to the lack of space charge measurement methods in gas, it is di fficult to describe the space charge and the electric field distributions through testing. Reference [15] studies calibration of field-mill to measure DC electric field with space charges. However, the measurement scope cannot reach the distance of molecular level, so it still cannot precisely describe the distribution of space charge and electric field. Some researches apply simulation methods to describe the discharge mechanism [16,17]. In [17], applying corona discharge fluid model, space charge intensity and electric field variation during a single discharge

process are described. But the simulation starts with none space charge situation and only lasts for the short time of a single discharge, which does not take the retained space charges into account. Space charge distribution are also studied in some experimental methods [18,19]. References [19] describes the corona layer morphology by gray value and thickness on the luminescent image. In this method, only space discharges distribution of ionization region can be obtained. In addition, the space charge behaviors and electric field variation of a single discharge cannot be described. Therefore, proposing new method to reflect the space charge e ffect and the electric field distortion is of significance.

It is obvious that the variation of electric field will affect PD phenomenon, and reflects in PD parameters. In theory, through the deep analysis of discharge parameter characteristics, the space charge and electric field distribution can be reflected. While existing researches on the discharge parameters characteristics are either focused on the differences of characteristics from other discharge stages and patterns [10–12], or focused on the characteristic extraction [13,14]. Few researches relate the statistical rules to the space charge effect and electric field distribution.

So in this paper, it is proposed to apply mathematical statistics methods and microcosmic discharge and space charge theories, to analyze space charge e ffect and electric field distribution on the basis of characteristic parameter rules of PD pulses.

In this paper, the air discharge of needle-plate model under DC is researched. Applying mathematical statistics, the stage characteristics of repetition rate (*n*), amplitude ( *V*) and interval time ( Δ*t*) characteristic parameters are figured out to divide the discharge stages. The variation rule of characteristic parameters of each stage and transition process are explained by the space charge effects and electric field distribution. Furthermore, deduced space charge effects, electric field distributions and discharge characteristics of each stages are summarized to better explain the stage discharge mechanism.
