Unlike case A, in case B the flashovers across the insulator strings are considered, thereby presenting a more realistic situation. Tower insulators are installed between the overhead earthwire and phase conductors on all towers. The voltage across the insulators equals to the voltage difference between the tower top node and phase conductor node. For example, the voltage across the insulators installed between nodes 2 and 5 on tower 1 equals to (V2- V5). This voltage compares with the volt-time characteristic of the tower insulators. If it is greater than the sparkover voltage of the insulators, a flashover is deemed to have occurred. Following the flashover across the tower insulators, the flashed-over path is bridged by the short-circuit arc with zero arc voltage. Then the voltages on tower top node and phase conductor node, connected by the short-circuit arc, become the same. For example, if a flashover occurs across the insulators installed between nodes 2 and 5, then V2 and V5 become the same after the flashover.
For case B the voltage waveforms of nodes involved in the flashovers are shown in Fig.
4.4. The voltage waveforms of nodes on tower 1 are shown in Fig. 4.5. Because of the bilateral symmetry, voltage on nodes of tower 3 are exactly as same as those on tower 2.
Thus only the voltage waveforms of nodes on tower 2 are shown in Fig. 4.6. To observe and analyze the transient behavior clearly and accurately, the time period considered in Figs. 4.5 and 4.6 is 10às, instead of 50às in Fig. 4.4. The current waveform on phase conductor C is shown in Fig. 4.7. The calculated flashover data for this case, showing time, location and path of the flashover as well as the insulation voltage before flashover, are summarized in Table 4.1.
Fig 4.4. Voltages on nodes involved in the flashovers for case B— Line with flashovers across the insulators considered.
Fig 4.5 Voltages on nodes of tower 1 for case B— Line with flashovers across the insulators considered.
Fig 4.6 Voltages on nodes of tower 2 for case B— Line with flashovers across the insulators considered.
Fig 4.7 Current waveform for case B— Line with flashovers across the insulators considered.
Chapter 4 Case study
Table 4.1 Flashovers in Case B--Line with flashovers across the insulators considered.
Time (às)
Flashover node
Flashover patha
Insulation voltage before flashover (kV)
4.1 2,11 p-t 1361.47
5.4 1,12 p-t 1406
5.4 3,10 p-t 1406
ap-t=phase to tower flashover.
In all, three flashovers occurred. The first occurred across the insulator string mounted between tower 1 and phase conductor C, and the second across the insulator string between tower 2 and phase conductor C. The third occurred across the insulator string between tower 3 and phase conductor C at the same time as the second. Because the voltage waveforms of nodes on tower 3 are not shown, thus only two flashovers can be observed from above figures.
Before flashover, the voltages on phase conductors are induced by nearby conductors.
Phase conductor C is the furthest from the overhead earthwire. Larger separation of phase conductor from the overhead earthwire reduces the electromagnetic coupling and hence creates a higher voltage difference across the corresponding tower insulators. Therefore, the voltage across tower insulators of phase conductor C is the largest compared to that across other insulators on other phase conductors. Consequently flashover occurs first across insulators between nodes 2 and 11 on phase conductor C. After the flashover, the flashed-over paths are bridged by the short-circuit arcs with zero arc voltage. Therefore, the voltages of nodes on overhead earthwire and phase conductor C connected by the
flashed-over arcs become the same. As seen from Figs. 4.4 and 4.5, the voltages of nodes 2 and 11 become the same at 4.1às, the moment that the flashover occurs.
The second flashover occurs across the insulators between nodes 1 and 12 at 5.4às, which is the time of arrival of the diverted surge following the first flashover on phase conductor C of tower 1. After the first flashover, phase conductor C forms additional wire in parallel with the overhead earthwire. Then part of the lightning surge is diverted to it. The voltages on phase conductor C are elevated by the diverted surge flowing on it. After 1.2às it reaches node 12, leading to the rise in voltage on it. From Fig. 4.6, a sudden voltage rise on node 12 at 5.4às is observed. Meanwhile, the voltage on node 1 is decreased because a large portion of lightning surge on overhead earthwire flows to ground through tower 2.
Consequently, a great voltage difference appears across the insulator strings mounted between nodes 1 and 12 which leads to the flashover to occur immediately. After the flashover across the insulators between nodes 1 and 12, the flashed-over paths, bridged by the short-circuit arcs, have zero arc voltage. Therefore, the voltages of nodes 1 and 12 become the same. As seen from Fig. 4.6, voltages on nodes 1 and 12 become the same after the second flashover. The third flashover occurs across the insulators between nodes 3 and 10 on tower 3 at exactly the same time as the second.
Following the voltage rise on phase conductor C after the second flashover, the voltages on phases A and B also increased due to the effect of the electromagnetic coupling.
Consequently, the voltage differences between the tower top nodes and phases A and B decreased. Thus, the voltages stressing insulators of phases A and B did not reach their
Chapter 4 Case study
flashover voltage and no flashover occurred across them. It is seen from Figs. 4.5 and 4.6 that there were no flashovers on phases A and B.