In table II, the inception time of upward streamer from ground wire and conductor was approximately 26.2 μs and 35.9 μs when 3208 kV impulse was applied. This result clearly shows that the inception time of upward streamer from ground wire is earlier and it is mainly due to the stronger electric field around the ground wire. For the inception of positive streamer, Gallimberti [18] has provided a criterion as equation (1).
           (1)
where refers to the number of free electrons. and refers to the ionization coefficient and attachment coefficient respectively.  Equation (1) means the number of free electrons must exceed a critical number  for the inception of streamer.
Compared with conductor, the electric field around ground wire is bigger. This condition makes more free electrons existing in the region around the ground wire and equation (1) can be satisfied more easily. This is an advantage for forming electron avalanches. If one of avalanche can self-propagate, a streamer incepts. So, the inception of upward streamer from ground wire is easier.

C. The process of steamer-leader transition

In table II, the inception time of discontinuous leader from ground wire and conductor was approximately   39.7 μs and 106.9 μs. This result clearly shows that the upward streamer can transit to the discontinuous leader easier from the ground wire.
Analyzing the discharge current in figure 8, a single corona pulse can be found before the inception of upward leader from conductor and the peak value is up to 5A (part A). In the ground wire case, more than one corona pulse is observed but the peak value of these pulses is much smaller (part B). For analyzing this difference, studying the process of steamer-leader transition is needed.
In the model proposed by Gallimberti[18], the structure of the transition area is assumed as a cylinder, and the temperature of this area is heated up by the energy due to the current through the area. When the temperature (T) is higher than 1500K, the transition process is completed and the discontinuous leader incepts. The relationship between the current and the temperature can be expressed as
   (2)
where  is the translation energy corresponding to the temperature(T). , ,  are coefficients. is the time constant for vibrational relaxation and varied with the temperature. All these value can be obtained in Ref [18].
For a given corona pulse current, the variation of temperature with time can be calculated as figure 9 and 10. In this calculation, the radius of the transition area is assumed as 0.1 mm.
In figure 9, only the current due to the big corona pulse is enough to make the temperature of transition area exceed 1500K at about 114.1μs and completed the transition process. Therefore, the discontinuous upward leader (the same as the continuous leader in this case) incepted at about 2 μs later. For ground wire case which is shown in figure 10, the temperature of transition area only can reach to about 500K after the injection of the corona pulses at 27 μs, so the discontinuous upward leader does not incept until the subsequent corona pulses heat up the area and make the temperature exceed 1500 K. In the whole process, about 1.01 μC and 3.64 μC space charge was injected totally into the transition area for conductor and ground wire case respectively.
These two discharge modes occupy about 80% of our experiments and this difference is mainly due to the different electric field around the conductor and ground wire. For ground wire case, the bigger surface electric field can make the streamer incept earlier but the streamer is hard to develop as the electric field is much weaker at a distant. Comparatively speaking, the surface electric field of conductor is much smaller but electric field around conductor is more uniform than the condition of ground wire. When the surface is enough for the inception of streamer, the streamer develops easier in this case because the electric is also strong at a distant. Therefore, more charges will be injected into the conductor continuously. Therefore, the big corona pulse is observed instead of a series of small pulses.
Actually, some small pulses and discharge current are observed from the conductor before the appearance of the big corona pulse and these is mainly contributed by some streamers and corona, which is too dark for observing. Therefore, the current amplitude of the pulses mentioned above may be a little bigger than the real value. According to our experiments, the average input charge for the inception of discontinuous leader from ground wire and conductor was approximately 1.13 μC and 4.81 μC respectively.
From the previous research in rod-plane gap, more input charge was needed for the inception of discontinuous leader when an electrode with bigger curvature radius was used in rod-plane gap [21]. This conclusion may verify our experimental result. Bundled-conductor is a technical method for increasing the curvature radius. Hence, considering the radius of our sub-conductor equal to the radius of ground wire, the curvature radius of conductor is bigger than that of ground wire. So, more input charge should be needed for the inception of discontinuous leader from bundled conductor. And this may explain why the discontinuous leader incepted from the ground wire earlier.

Fig. 9. The discharge current (conductor) of part A in figure 8 and the temperature corresponding to the current

Fig. 10. The discharge current (ground wire) of part B in figure 8 and the temperature corresponding to the current

D. The inception time of continuous upward leader

  In table II, the inception time of continuous leader from ground wire and conductor was approximately 68.2 μs and 114.1 μs. This result shows that the continuous leader incepts earlier from ground wire, too. And this result can also be explained by using leader progression model (LPM) with critical radius [11]. In the LPM model, the charge of thundercloud is 8 C. The velocity of downward leader is set as 2×10⁵ m/s and it start at the height of 2000 m. The uniform distribution of charge in downward leader was used. The relationship between charge and current can be expressed as following.
                          (3)
where Q is the total charge of the downward leader and I is the lightning current.
The critical radius of sub conductor and ground wire is 3 cm and 10 cm respectively. The calculation result is shown in figure 11. The red lines and black line represents the height of downward leader tip from ground when the continuous upward leader incepted from ground wire and conductor respectively. As the velocity downward leader has been assumed as 2×10⁵ m/s, the difference of inception time, which has been represented by blue line, can be calculated by equation (4).
                      (4)
where  refers to the height of downward leader tip when the upward leader incepts from ground wire and refers to that from conductor.  is equal to 2×10⁵ m/s. The height of conductor and ground wire is 15.5 m from the ground.

Fig. 11. The height of downward leader tip when the upward leader incepted and the difference of inception time between ground wire and conductor.
  In figure 11, the calculation results shows that the continuous leader incepts from ground wire earlier when the lightning current is from 15 kA to 35 kA. And this comes to the same conclusion as our experiment results.
In our experiment, the electric field on the surface of the conductor and ground wire was calculated to be equal to the electric field of a 30 kA lightning downward leader at approximately 200 - 300 m in height [17]. The difference of inception time from our calculation is about 30 μs, and which is smaller compared with our experimental result (44 μs). As the critical radius was acquired in the typical conductor-plane air gap, whether this criterion is suitable for direct using in LPM should be considered. And this may suggest that the critical radius criterion probably underestimate the influence due to the different structure of ground wire and conductor.

E. The velocity of upward leader

The velocity during the propagation of the upward leader is shown in figure 12.

Fig.12. The velocity of upward leader from ground wire and conductor (Points for measurement results and lines for calculated results).
  In figure 12, red points and black points represent the velocity of upward leader from ground wire and conductor respectively. Both of them increase with the development of upward leader. When the length of upward leader is smaller than 0.4 m, the velocity is about 0.6-1.4 cm/μs. While the length is about 1 m, the velocity can reach about 3 cm/μs. The average velocity can be obtained by averaging the data in figure 12. The average value was approximately 2.06 cm/μs and 1.78 cm/μs for ground wire and conductor respectively. Compared the velocity of upward leader from ground wire with that from conductor, it is bigger from ground wire at the beginning. But they are almost the same when the length of leader channel is longer than 0.6 m.
The velocity can also be obtained by using the model which proposed by Marley and Cooray [15]. In this model, based on the experimental result under rod-plane gap, 1 μC was used as the criterion for the inception of upward leader. Based on our experimental results, 1.13 μC and 4.81 μC were selected as the criterion for leader incepted from ground wire and conductor. The lightning current is equal to 30 kA and the height of ground wire and conductor from ground is equal to 15.5 m. In addition, a simplified procedure was used for calculating the corona charge. This is based on the assumption that the total corona charge  can be determined from the difference between the geometrical potential distribution  and the potential distribution after the corona formation . So, the equation (5) will be obtained.
                    (5)
where  is the geometrical factor and it is equal to C/V·m .
The calculation result is shown in figure 12. It shows that the velocity increase with the development of upward leader and this condition is similar to the experimental result. When the upward leader develops, the distance between downward and upward leader tip becomes shorter and this will make the ionization process of upward leader tip stronger. More charge will be injected into the leader channel and the energy which provided by this charge will accelerate the formation of leader channel.  Compared the calculation result of ground wire with conductor, they are almost the same. And this tendency is similar to the experimental result when the length of leader channel is longer than 0.6 m. When the upward leader just incepts, the velocity of upward leader from ground wire is faster based on our experimental result. But it’s almost the same in the calculation result. This maybe mainly due to the value selection of . In our calculation, this value is constant but it should be change with the development of upward leader. Marley has proposed this value can be calculated by using charge simulation method [15]. Actually, some discharge process should also be considered, such as choking effect due to space charge, the shape of corona zone. All these factors will influence the simulation and make the difference between the experimental and the calculation results.

IV Comparison of the upward leader performance between the ground wire and conductor in transmission lines

  According to the results in section III, the velocity increases with the development of upward leader. And this increasing rate  is about 0.012 μs^-1 from the curve fitting of data in figure 12. Assuming increasing rate keeps a constant and it is the same for the upward leader from ground wire and conductor, the length of upward leader can be calculated by equation (6)
                        (6)
where refers to the time interval for each step.
In our experiment, the upward leader from ground wire incepts earlier (44 μs) when ground wire and conductor is placed at the same height. Combine this result with the equation (6), the minimum difference of striking distance of ground wire and conductor can be estimated. In this calculation, the initial velocity of upward leader (1 cm/μs for ground wire and 0.5 cm/μs for conductor), the initial length of upward leader (5 cm) and the time interval   (0.1 μs) were selected. The length of the upward leader from ground wire and conductor under 30 kA lightning is shown in figure 13.

Fig.13. The length of upward leader from ground wire and conductor when the lightning current is equal to 30kA.
From the observation data in Japan, the length of upward leader before final jump is about 25-125 m for a tower with 140 m height [22]. The length is about 97 to 121 m for a tower with 121 m height in South Dakota [23] and about 10.9 to 113 m for the buildings with 25 to 90 m height in China [24]. According to these results, most of upward leaders from transmission lines are longer than  10 m. Combined these facts and the calculation result, the length of upward leader from ground wire may be at least 7 m longer than that of conductor before the final jump, and this difference increases with a longer upward leader. Actually, the method proposed above probably underestimated the difference. Considering the height of ground is higher than the conductor in transmission lines, the difference of inception time is probably larger than 44 μs. In addition, the space charge due to the upward leader emerging from ground wire will also make the inception of upward leader from conductor more difficult. All these facts will make the difference of upward leader length between ground wire and conductor much bigger.

V Conclusions

In this paper, an experimental system was established to study the characteristics of upward leader from ground wire and conductor. After more than 100 tests, some conclusions can be put forward as following.
1) An experimental system, with 7 m plane/rod to conductor and plane/rod to ground wire long air gap, has been established in order to study the inception criteria and progression characteristics. The equivalence between this system and the natural lightning condition performs well from the height of 15.5 m to 19.83 m.
2) From our experimental result, the upward streamer, discontinuous leader and continuous leader from ground wire incepts earlier than that from conductor. The difference of velocity at the beginning is big, but they are almost the same when the leader channel is longer than 0.6 m. This tendency is similar to the calculation results.
3) Single big corona pulse is observed in the discharge current from conductor and the space charge it injected into the transition area is enough for the inception of discontinuous leader. For the ground wire case, the charge of a small corona pulse is small, so a series of corona pulses are needed to heat up the transition area and make the discontinuous leader incepts.
4) The earlier inception time makes ground wire has a bigger exposed zone. For a 30 kA lightning, the striking distance of ground wire is estimated at least 7 m longer than that of conductor, and this value is probably an underestimated value. Considering the height difference of ground wire and conductor and charge shielding of ground wire, this difference should be bigger.

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