中文摘要：

为研究长空间隙放电分散性和放电路径随机性,建立了结合传统流注放电理论和分形生长理论的正极性流注生长概率模型。首先基于经典的流注起始判据,计算了棒-板间隙流注起始电压;选择空间电位和电子崩形成时间作为流注生长控制变量,结合泊松方程、电荷连续性方程和欧姆定律描述流注通道内部的电荷转移,仿真流注的持续发展过程;当流注到达板电极后,选择放电树枝中电位梯度最大的通道作为最后的主放电通道。分析表明,该模型可描述流注区空间电荷随时间的积累过程,棒-板间隙击穿时间的分散性以及放电路径的随机性;由其计算得的棒-板间隙主放电通道分形维数与试验结果相吻合,同时基于该模型对棒-导线-板间隙放电选择概率分布的计算结果也与试验所得规律一致。

英文摘要：

The model of discharge in long air gaps under impulse voltages in the engineering model stage and physical model stage is analyzed. A stochastic model which combines the traditional streamer theory and fractal growth theory is developed to simulate the growth process of positive streamer in a rod-plane gap. The first corona inception voltage is calculated on the basis of the classical streamer theory. The space potential distribution and the streamer formation time are chosen as control variables of the growth process, and the charge transport in the streamer channel is calculated by solving the Poisson＇s equation, continuity equation and Ohm＇s law simultaneously. When the streamer reaches the plate, the bounds which have the maximum inner channel electric field are selected as the primary discharge path in the streamer zone. This model can represent the total charge accumulation of the streamer zone, the distribution of breakdown time and the trajectory of the discharge. The fractal dimensions of the primary discharge calculated by this model are consistent with the experiment results, and the calculation results of strike probability distribution based on this model for a rod-conductor-plate gap are consistent with the experiment ones.