# Lightning Surge Analysis for Overhead Lines Considering Corona Effect
## 2 Experimental Investigation on Corona Characteristics  
An experimental arrangement was built in a high voltage laboratory for measuring the corona \(q\)-\(u\) curves, as shown in Figure 1. Its schematic diagram is illustrated in Figure 2. Double exponential and damped oscillation surge voltages can be generated by putting the wavefront resistor \(R_{\mathrm{W}}\) and inductor \(L_{\mathrm{W}}\) into operation in the impulse generator IG, respectively. The corona cage consists of an inner electrode and three sections of outer electrodes. These electrodes are coaxially assembled with the longer outer electrode \(\mathrm{E_{L}}\) (1 m) in the middle and the two shorter outer electrodes \(\mathrm{E_{S}}\) (0.52 m) at both sides to shield the end effect of the electric field. When a surge voltage is applied to the inner electrode \(\mathrm{E_{i}}\), corona discharge is produced in the corona cage. The charge signal \(q\) and voltage signal \(u\) are taken from the integral capacitor \(C_{\mathrm{e}}\) and voltage divider VD, respectively. The two signals are recorded by a digital oscilloscope DS, so that the \(q\)-\(u\) curves can be obtained from the data processing for the signals \(q\) and \(u\). For the sake of comparison, the wavefront time and amplitude are held to be approximately equal for double exponential and damped oscillation surges. Figure 3 shows a group of measured \(q\)-\(u\) curves under negative and positive polarities. It can be noticed that the \(q\)-\(u\) curves under damped oscillation surges roughly coincide with those under double exponential surges until their respective charges reach the maximum values. The difference appears between the curve parts subsequent to the maximum charge points. In these parts, the \(q\)-\(u\) curves under double exponential surges descend monotonically; however, those under damped oscillation surges follow a hysteresis-like trajectory. The possible forming mechanism of the hysteresis-like trajectory might be attributed to the occurrence of the opposite polar corona [21] and is illustrated by Figure 4. With the voltage \(u\) decreasing to the first wave trough, the slope of the section FG becomes larger than the geometrical capacitance \(C_{0}\), which causes the section FG to deviate from the section EF. In fact, as the voltage \(u\) decreases to a certain extent, the electric field near the surface of the inner electrode could be reversed. Once the reversed field strength exceeds a critical value, the opposite polar corona discharge may occur, which produces the opposite polar space charge near the inner electrode. Thence a reduction in the net space charge leads the total charge \(q\) on the section FG to decrease more rapidly than that on the section EF. A similar interpretation can be reached for the section HP as the voltage \(u\) decreases to the second wave trough. For this reason, the minor loops is formed after the first oscillation cycle. The minor loops enclosed by the hysteresis-like trajectory are significantly larger under negative polarity than under positive polarity. The area of the minor loops represents the energy loss and can distort and attenuate damped oscillation surges in the subsequent oscillation cycles.  
Figure 1: Experimental arrangement in high voltage laboratory.  
Figure 2: Diagram of experimental system (E\({}_{\text{i}}\)—inner electrode; E\({}_{\text{L}}\)—longer outer electrode; E\({}_{\text{S}}\)—shorter-outer electrode; DS—digital oscilloscope; VD—voltage divider; IG—impulse generator).  
Figure 3: Measured \(q\)–\(u\) curves. (**a**) Under negative polarity, (**b**) under positive polarity.