Numerical analysis of effect of avalanche space charges on corona onset voltage

Based on the Townsend collision theory, the number and field strength of the space charges have great effect on the onset voltage of partial discharge in gaseous insulated apparatus. The facts have not only been proved by many researchers´ work, but also been demonstrated by mathematical analysis. In fact, the effects of space charge field created by both the positive ions and the electrons are largely different. The electrons of the head avalanche cause the avalanche to further grow because the electron field strengthens the electric field between the bead avalanche and the anode. And positive ion field also reinforces the electric field between the tail avalanche and the cathode, and the middle areas of the electron avalanche are full of the equivalent ions and electrons, which are called the zone plasma. With growing of the zone plasma in great speed, the gap of electrodes quickly breakdown. Computer programs are developed to calculate the onset voltage. The space charge fields of both the positive ions and the electrons are considered in the calculations. The calculation procedures are represented in detail. Meanwhile, results are gained for the air and the SF₆ for a wide range geometrical parameters and gas pressures. The results show that the electrons promote the growth of the avalanche while the positive ions retard the growth of the avalanche.