Semi-Empirical Calculation Method of the Positive First Corona Space Charge Under Different Impulse Rising Rates in Long Air Gaps

In this paper, the variation of the development of positive first corona space charge in long air gaps is investigated. A 1-m rod-plane air gap under different rising rates
$dU/dt$
of impulse voltages is reported. The current signals and still photographs are recorded during the first corona development. The relationship between the first corona charge
$Q_{{\rm i}}$
and the inception voltage
$U_{{\rm i}}$
is presented. The physical mechanism of the influence of the first corona is provided. With the experiments and the single branch propagation model, a semi-empirical calcultion method for positive first corona charge under impulse in long air gaps is obtained through the calculation of the number of branches
$N_{{\rm b}}$
. Using this method, the variations between
$Q_{{\rm i}}$
and
$U_{{\rm i}}$
for different
$dU/dt$
and electric field distributions are calculated and compared with the reported experimental results. Reasonable agreement between the calculated and experimental results is obtained. It shows that this calculation method is suitable for predicting the positive first corona charge
$Q_{{\rm i}}$
and the discharge current at a given
$dU/dt$
and
$U_{{\rm i}}$
.