Review: Factors Affecting the Performance of Ground Electrodes under High Impulse Currents

: Most studies have observed that the impedance values of ground electrodes under high impulse conditions (Z imp ) are lower than the resistance values under steady-state conditions (R DC ). It has been suggested that this is due to the ionisation process in soil, where streamers will propagate away from the electrodes, causing an increase in the ionisation zone, thus reducing the Z imp values. The percentage difference between Z imp and R DC is found to be dependent on several factors. This paper aims to review and present the ﬁndings of previously published work on the percentage difference between Z imp and R DC in relation to various factors.


Introduction
The impulse characteristics of grounding systems are known to be different from those assessed under steady-state conditions.This is caused by the soil ionisation process, which occurs when the electric field (E) is higher than the critical electric field (E c ) inside the soil.These E c values, which determine the onset of ionisation in soil, were summarised using information from 27 publications in [1], with values ranging from 0.13 kV/cm to 41 kV/cm for various soil resistivities and electrode configurations; most of the E c values in these studies were obtained via laboratory tests.It can be seen in a study by Mohamad Nor et al. [2] that Ec was lower in a hemispherical container, which had a non-uniform electric field, in comparison to the uniform electric field of a parallel plate.In [2], E c was found to be independent of the soil's grain size and moisture content.Moreover, a higher E c value was seen under negative impulse polarity than positive impulse polarity because, as expected, air discharge occurred at higher voltage levels under the former.On the contrary, He et al. [3] observed that E c values were affected by the soil's grain size, where the smaller the soil grain size, the higher the E c value.They [3] also found that the E c values decreased with increasing water content, contrary to the findings of Mohamad Nor et al. [4].
He et al. [3] expanded upon existing work on the effects of soil temperature and density, and found that E c decreases with increasing soil temperature and increases with increasing soil density.Although the E c values contribute to knowledge regarding the initiation of the ionisation process, studies pertaining to the E c of various factors affecting soil appear to be limited.Furthermore, in several studies, E c is not established due to unclear observation of the initiation of the ionisation process, as well as a lack of consistency in the measurements used between studies for determining E c .In [4], E c was determined when the second current peak started to occur, and its voltage was applied to an equation in which the configuration of a hemispherical container was known.In [2], in a parallelplate test cell, E c was calculated from the voltage level at which breakdown occurred in a parallel plate filled with soil, instead of via observation of the second current peak, as seen in [4].This was defined as the moment that ionisation began, and was followed instantaneously by breakdown; hence, the study evaluated E c based on the breakdown of soil.Similarly, in Ref. [5], based on the configuration of the test cell, the breakdown voltage was used to calculate the starting gradient.Some studies calculate E c from the breakdown voltage [2,[6][7][8], which may result in E c being higher than when it was measured at the initiation of the second current peak.This, again, leads to inconsistencies in the evaluation of E c .In some studies, namely [2,4,8], the 'up and down method' is used, while in others, no specific test method is mentioned or presented for obtaining E c or E breakdown .Furthermore, E c is not easily established in some studies, which could be caused by non-observable breakdown or a lack of two current peaks; this may occur due to low soil resistivity, low current magnitudes or a large cross-sectional area, which could prevent the electric field from increasing in the soil.Hence, the method of obtaining E c is not as widely discussed as the method of measuring Z imp in relation to the R DC values, whereby the latter of which is more straight forward.
Due to all of these inconsistencies, the unclear determination of E c and the fact that the percentage difference between Z imp and R DC , for various factors affecting the characteristics of soil, can be more widely obtained than E c , in this study, the percentage difference between Z imp and R DC is presented.

Factors Affecting the Soil Characteristics under High Impulse Conditions
Many studies have focused on the factors that contribute to soil characteristics under high impulse currents, and have found that the performance of grounding systems is affected by soil resistivity, ground electrode configuration, current response time, magnitude, the point of impulse current injection and impulse polarity.However, so far, not all of these effects have been reviewed, and the percentage difference between Z imp and R DC has not been compared from one study to another.In this paper, in order to obtain clarification on the percentage difference between Z imp and R DC in relation to these factors, the results from the literature are reviewed and discussed.Equation ( 1) is used to calculate the percentage difference between Z imp and R DC for all of the results obtained in previously published work.Since many studies have presented plots of Z imp versus current magnitudes, the average Z imp is considered in order to establish a single value of Z imp , which is applied in Equation (1).

Soil Resistivity
One of the most important parameters in the design of grounding systems is soil resistivity, where R DC changes with moisture content, soil composition, soil grain size, compression, chemical content and temperature.Much work [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] has been published on the effect of soil resistivity on the percentage difference between Z imp and R DC when ground electrodes are installed under varying soil resistivity and subjected to high impulse currents; however, no conclusive or summarising work can be found based on the published work.This paper summarises the published results, as shown in Figures 1 and 2, from work based on field and laboratory approaches, respectively.

Field Measurements
In studies of grounding systems under high impulse conditions using field measurements, R DC values are mostly obtained using measurements [9][10][11][12], while in Ref. [13], R DC is calculated based on the soil resistivity value obtained using the Wenner Method.Chen and Chowdhuri [9] performed tests on two rod electrodes of different diameters, with R DC ranging from 220 Ω to 327 Ω. Rod (i) had a diameter of 0.95 cm, with a burial depth of 22.86 cm, and rod (ii) had a diameter of 1.59 cm, with a burial depth of 30.48 cm.The tested rod electrodes were installed at two sites, and it was found that the higher the R DC values, the higher the percentage difference between Z imp and R DC for both electrodes (see Figure 1).When Reffin et al. [14] carried out studies on the effect of soil resistivity using 2 m × 2 m mesh electrodes installed at four different sites, giving R DC values ranging from 12.9 Ω to 62.6 Ω, they found that the higher the R DC value, the higher the percentage difference between Z imp and R DC .Abdul Ali et al. [15] observed that the percentage differences between an average Z imp and R DC for six different electrodes, installed at two sites with high soil resistivity, were higher in high-R DC ground electrodes subjected to impulse currents up to 5 kA.Oettle and Geldenhuys [7] found that the percentage difference between Z imp and RDC was approximately 57% for an electrode with an RDC of 834 Ω, while the percentage differences between Z imp and R DC were close (between 32% and 36%) for the other three electrodes, despite large variation in the R DC values of 53.5 Ω, 240 Ω and 635 Ω.He et al. [16] conducted impulse tests on a number of electrodes whose soil resistivity values changed from 100 Ωm to 5103 Ωm.They observed that the higher the soil resistivity, the higher the impulse resistance value.The impulse coefficient, measured as the ratio of Z imp to R DC , was found to decrease with increasing soil resistivity, which was reflected in the percentage difference between Z imp and R DC , calculated using Equation (1); the higher the soil resistivity, the higher the percentage difference between Z imp and R DC .However, this is not included in Figure 1, since only the soil resistivity values were presented, and not in the form of R DC values; hence, the relationship between R DC and the percentage difference between Z imp and R DC could not be plotted in the figure .PEER REVIEW 4 of 14 [8], where they found that, like in [18], almost all ground electrodes produced a percentage difference between Zimp and RDC close to 100%.This could be due to the boundary conditions of the test cell, which enabled full discharge of the current in the soil, unlike in the case of field tests, in which the large area allows a large amount of the current to dissipate into the soil.There are also several published studies [4,5] that show Zimp at various soil resistivities.However, no RDC values are presented in these studies; hence, the percentage difference between Zimp and RDC is not included in Figure 2.

Electrode Configurations
Variation in the configuration of ground electrodes under high impulse conditions is one of the most commonly investigated topics, whether using laboratory or field approaches.Due to the large number of studies using both approaches, this paper is divided into two sub-sections (laboratory and field measurements), and the results from the published work are plotted in Figures 3 and 4, respectively.In Ref. [17], electrodes installed in natural soil, encased in concrete and bentonite, were tested in July and November.Higher R DC values were seen for ground electrodes measured in summer (July) in comparison to those measured in autumn (November).The higher the R DC values (the highest were seen in July), the higher the observed percentage difference between Z imp and R DC .It was also noticed that for ground electrodes tested in November, whose RDC values were 135 Ω and below, the percentage difference between Z imp and R DC was negative, indicating that Z imp was higher than R DC .This shows that the soil resistivity underwent seasonal changes, and significantly affected the percentage difference between Z imp and R DC .

Laboratory Measurements
In order to evaluate the percentage difference between Z imp and R DC at various soil resistivities, the R DC values from the published papers had to be known so that the relationship between soil resistivity (R DC ) and Z imp could be calculated.The results are plotted in Figure 2. It can be seen from the figure that for most of the published work, there is a clear relationship between R DC and the percentage difference between Z imp and R DC , where the higher the R DC value, the higher the percentage difference between Z imp and R DC ; the exception is Ref. [18], where the percentage difference between Z imp and R DC is independent of the R DC values.
Loboda and Scuka [6] used cylindrical test cells filled with soils of three different resistivities, giving R DC values of 38.6 Ω, 195.7 Ω and 782.8 Ω.The percentage differ-ence between Z imp and R DC was found to be close for the electrodes with R DC values of 195.7 Ω and 782.8 Ω, and 50% lower for the electrode with a much lower R DC value (38.6 Ω).This shows that low soil resistivity resulted in a low percentage difference.Similarly, when Berger [11] carried out tests on a hemispherical model, he found that the higher the R DC value, the higher the observed percentage difference between Z imp and R DC .For R DC values ranging between 27 Ω and 150 Ω, the percentage differences between Z imp and R DC were found to be between 54% and 92%.On the other hand, Cabrera et al. [18] found that the percentage difference between Z imp and R DC was close to 100% for soil in a cylindrical test cell, with an R DC value above 2000 Ω.This may be because the measurement of Z imp was based on the Rarc, which was obtained from the voltage and current waveforms about 1µs after breakdown.During breakdown, it can be expected that there will be a large current flow, causing a significant drop in Z imp values.Another recent study on the effect of soil resistivity on the percentage difference between Z imp and R DC was conducted in Ref. [8], where they found that, like in [18], almost all ground electrodes produced a percentage difference between Z imp and R DC close to 100%.This could be due to the boundary conditions of the test cell, which enabled full discharge of the current in the soil, unlike in the case of field tests, in which the large area allows a large amount of the current to dissipate into the soil.There are also several published studies [4,5] that show Z imp at various soil resistivities.However, no R DC values are presented in these studies; hence, the percentage difference between Z imp and R DC is not included in Figure 2.

Electrode Configurations
Variation in the configuration of ground electrodes under high impulse conditions is one of the most commonly investigated topics, whether using laboratory or field approaches.Due to the large number of studies using both approaches, this paper is divided into two sub-sections (laboratory and field measurements), and the results from the published work are plotted in Figures 3 and 4, respectively.

Field Study
Chen and Chowdhuri [9] installed two electrodes at two sites with different soil resistivities, where RDC ranged from 220 Ω to 320 Ω, and they were subjected to high impulse conditions.The authors observed that the higher the RDC value, the higher the observed percentage difference between Z imp and RDC.Stojkovic et al. [19] performed tests on three large electrodes, and there was a clear trend whereby the percentage difference between Z imp and R DC was higher in the grid electrodes with high R DC values.Due to the presence of inductive components in the large grid electrodes, it was noticed that the percentage difference between Z imp and RDC was negative for all of the electrodes [19], indicating that Z imp was higher than R DC .A clear relationship between R DC and the percentage difference between Z imp and R DC was also seen in Ref. [10], in which rod and wire electrodes were subjected to high impulse conditions.The rod electrode with a higher R DC was found to produce a higher percentage difference between Z imp and R DC than the wire electrode.A similar observation was made in a study by Vainer [20], where the percentage difference between Z imp and R DC was higher in a ground electrode with a high R DC value.For the ground electrode with a low R DC value of 1.7 Ω, Z imp was found to be higher than R DC , thus producing a negative percentage difference between Z imp and R DC .Ametani et al. [12] also obtained a negative percentage difference between Z imp and R DC for ground electrodes with R DC values of 12 Ω and 6 Ω, but Z imp was lower than R DC for the ground electrode with an R DC of 16 Ω.In Ref. [21], the percentage difference between Z imp and R DC was also found to be negative for ground electrodes with a low R DC value of 3.2 Ω.A concrete pole was used in their study [21]; however, it did not follow the same trend, with a very low percentage difference observed between Z imp and R DC at an R DC of 39 Ω.He et al. [16], Towne [22], Hizamul-Din et al. [23], Harid et al. [24] and Elmghairbi et al. [25] found the same relationship, whereby the higher the R DC value, the higher the percentage difference between Z imp and R DC .In Ref. [24], for a ground electrode consisting of a circular ring 60 m in diameter with eight vertical rods, with an R DC of 18 Ω, Z imp was found to be higher than R DC .A negative percentage difference between Z imp and R DC was also seen in Ref. [25] for electrodes with much lower R DC values of 5 Ω and 4 Ω.Mohamad Nor et al. [26] found that the percentage difference between Z imp and R DC was −2200% at an R DC of 0.3 Ω, which was due to the inductance components of the large grid of the gas insulated sub-station (GIS); meanwhile, for a smaller test grid with a larger R DC value of 7 Ω, the percentage difference was found to be −12%.
x FOR PEER REVIEW 6 of 14

Field Study
Chen and Chowdhuri [9] installed two electrodes at two sites with different soil resistivities, where RDC ranged from 220 Ω to 320 Ω, and they were subjected to high impulse conditions.The authors observed that the higher the RDC value, the higher the observed percentage difference between Zimp and RDC.Stojkovic et al. [19] performed tests on three large electrodes, and there was a clear trend whereby the percentage difference between Zimp and RDC was higher in the grid electrodes with high RDC values.Due to the presence of inductive components in the large grid electrodes, it was noticed that the percentage difference between Zimp and RDC was negative for all of the electrodes [19], indicating that Zimp was higher than RDC.A clear relationship between RDC and the percentage difference between Zimp and RDC was also seen in Ref. [10], in which rod and wire electrodes were subjected to high impulse conditions.The rod electrode with a higher RDC was found to produce a higher percentage difference between Zimp and RDC than the wire electrode.A similar observation was made in a study by Vainer [20], where the percentage difference between Zimp and RDC was higher in a ground electrode with a high RDC value.For the ground electrode with a low RDC value of 1.7 Ω, Zimp was found to be higher than RDC, thus producing a negative percentage difference between Zimp and RDC.Ametani et al. [12] also obtained a negative percentage difference between Zimp and RDC for ground electrodes with RDC values of 12 Ω and 6 Ω, but Zimp was lower than RDC for the ground electrode with an RDC of 16 Ω.In Ref. [21], the percentage difference between Zimp and RDC was also found to be negative for ground electrodes with a low RDC value of 3.2 Ω.A concrete pole was used in their study [21]; however, it did not follow the same trend, with a very low percentage difference observed between Zimp and RDC at an RDC of 39 Ω.He et al. [16], Towne [22], Hizamul-Din et al. [23], Harid et al. [24] and Elmghairbi et al. [25] found the same relationship, whereby the higher the RDC value, the higher the percentage difference between Zimp and RDC.In Ref. [24], for a ground electrode consisting of a circular ring 60 m in diameter with eight vertical rods, with an RDC of 18 Ω, Zimp was found to be higher In some studies, namely [7,15,[27][28][29][30][31][32][33], the percentage difference between Z imp and R DC was not influenced by the R DC values.In Ref. [33], close percentage differences between −22% and 7% were seen for all of the electrodes, with R DC values ranging from 36 Ω to 183 Ω, when tested using a low-impulse-voltage generator with a magnitude of up to 400 V. On the other hand, when these electrodes were tested at much higher current magnitudes, up to 7 kA, two current peaks were observed.When Z imp was measured from the second current peak, referred to as post-ionisation resistance, it was found that the higher the R DC value, the higher the percentage difference between Z imp and R DC .

Laboratory Study
There have been numerous studies on the effects of electrode configuration on Z imp values.However, since this paper aims to evaluate the relationship between R DC and the percentage difference between Z imp and R DC , the values of R DC and Z imp in the test cell had to be known, and were found to be limited.In Ref. [5], although several ground electrodes were used with the Z imp values, only hemispherical test cells with inner electrodes 3 cm and 5 cm in diameter provided information on R DC .The percentage differences between Z imp and R DC were found to be 63% and 38%, respectively, at R DC values of 1360 Ω and 770 Ω, indicating that the higher the R DC value, the higher the percentage difference between Z imp and R DC .When Reffin et al. [8] investigated four types of soil in hemispherical containers, containing varying amounts of water, with two types of active electrode used, hemispherical and strip electrodes, they found that the higher the R DC value, the higher the percentage difference between Z imp and R DC .

Impulse Polarity 2.3.1. Field Study
The effect of impulse polarity can be limited by the manufacturer's design of the impulse generator, which is designed to produce only positive impulse polarity.This paper aims to list and review the results obtained from previous investigations on the percentage difference between Z imp and R DC when subjected to both impulse polarities.Figure 5 presents selected results from the literature on field measurements of different impulse polarities.It can be seen that the higher the R DC value, the higher the percentage difference between Z imp and R DC for all electrodes.Androvitsaneas et al. [17] found that for ground rods installed in natural soil and encased with concrete and bentonite, higher Z imp values were found under negative than positive impulse polarity.When the average Z imp value was considered, it was noticed that the percentage difference between Z imp under positive and negative impulse polarity was largest for the ground rod installed in natural soil (with the highest R DC of 486 Ω, which represents an approximately 12% difference), while the Z imp values between the positive and negative impulse polarities were found to be close for the ground rod encased with concrete and bentonite during summer, with RDC values of 135 Ω and 170 Ω, respectively.No impulse polarity effect on the Z imp values was seen for any of the three electrodes during autumn, when the electrodes had lower R DC values.A similar trend was seen in Ref. [34], when high current tests were carried out on a mesh ground electrode with an R DC value of 3.6 Ω under both positive and negative impulse polarities.The Z imp values were found to be close for both impulse polarities.
x FOR PEER REVIEW 9 of 14 In another study, Bellaschi [27] carried out impulse tests on practical ground electrodes under both impulse polarities; however, the ground electrodes subjected to positive impulse polarity had different configurations than those subjected to negative impulse polarity.Therefore, in this study, no direct comparison could be made of the performance of the ground electrodes subjected to positive and negative impulse polarities [27].In Ref. [14], Zimp was found to be 10% higher under negative impulse polarity than positive impulse polarity for a ground electrode with a high RDC value of 62.6 Ω.The difference in the average Zimp between positive and negative impulse polarities was found to be approxi- In another study, Bellaschi [27] carried out impulse tests on practical ground electrodes under both impulse polarities; however, the ground electrodes subjected to positive impulse polarity had different configurations than those subjected to negative impulse polarity.Therefore, in this study, no direct comparison could be made of the performance of the ground electrodes subjected to positive and negative impulse polarities [27].In Ref. [14], Z imp was found to be 10% higher under negative impulse polarity than positive impulse polarity for a ground electrode with a high R DC value of 62.6 Ω.The difference in the average Z imp between positive and negative impulse polarities was found to be approximately 10%, and the difference was more significant with lower current magnitudes.On the contrary, at a slightly lower R DC value of 61.6 Ω, Z imp under positive impulse polarity was found to be 20% higher than under negative impulse polarity for all current magnitudes.
In Ref. [35], a similar observation, whereby Z imp was higher under negative impulse polarity than under positive impulse polarity, was clearly seen in a ground electrode with a high R DC .In a separate study by the same authors [36], the same configurations as those presented in [35] were used, but the ground electrodes were installed in high-resistivity soil of 1464.4Ωm and 443.4 Ωm, at heights of 8.14 m and infinity for the upper and lower layers, respectively.It was noticed that despite having high R DC values for six electrodes, ranging from 253 Ω to 833.78 Ω, no impulse polarity effect was seen on Z imp .This is thought to be due to the high Z imp , which was measured before the occurrence of breakdown in the soil, where low current magnitudes below 2 kA were noted.In terms of breakdown voltage, the authors found that the breakdown voltage under negative impulse polarity was higher than that under positive impulse polarity.Nevertheless, Ref. [37] found that for a rod electrode with an R DC value of 67.8 Ω, the Z imp value obtained under negative impulse polarity was 11% higher than that obtained under positive impulse polarity.An impulse polarity effect was only noticed in two studies [14,17], and this effect was not influenced by the R DC values; in Ref. [17], an impulse polarity effect was seen under high R DC , while in Ref. [14], an impulse polarity effect was seen under low R DC .

Laboratory Study
Many laboratory studies did not include the R DC values in their measurements; however, the differences in Z imp values between positive and negative impulse polarities were noted for various soil resistivities.A number of investigations on the characteristics of soil under two impulse current polarities were carried out [5,18,35,[38][39][40].In [18], various types of soil were used, with the soil resistivity values ranging between 2.4 kΩm and 8.5 GΩm.The results of soil characteristics under positive impulse polarity are presented in Figure 2. Despite an obvious difference in the effects of impulse polarity on breakdown voltage and breakdown electric field, in high-resistivity soil, the arc resistance (R arc ) values were found to be close for all soil types, regardless of impulse polarity.This may be due to the high current in the test samples; the current magnitudes were measured at the second peak of the current, which occurred about 1 µs after breakdown in the peak current, and were used for R arc .Hence, much lower Z imp values were seen in comparison to R DC ; this caused the percentage difference between Z imp and R DC to be close to 100% in most test samples, making the impulse polarity effect insignificant.Due to their closeness, the results between positive and negative impulse polarity are not presented in this section.Similarly, Petropoulos [5] found that there was an impulse polarity effect on the starting gradient (E o ), where higher E o was seen under negative than positive impulse polarity, while no impulse polarity effect was seen on Z imp values, except at the tail of the Z imp traces (plotted as the ratio of instantaneous voltage to current), where Z imp was found to be higher under negative than positive impulse polarity.
In Ref. [38], impulse resistance values were based on pre-ionisation resistance (R 1 ) and post-ionisation (R 2 ), due to two current peak observations.It was noticed that in medium-grain-size sand with 3% water content in a hemispherical container, the average R 1 value under negative impulse polarity was 46% higher than under positive impulse polarity.On the other hand, for the same test sample, the average R 2 value under negative impulse polarity was 60% higher than under positive impulse polarity.They [38] also found that the breakdown voltage was higher under negative impulse polarity than under positive impulse polarity for sand with 1% and 5% water content.However, these results were not included in this study since there was no R DC value available.
Similarly, the results from Ref. [39] could not be presented in this work due to the lack of data on soil resistivity and R DC values; hence, the relationship between Z imp and R DC could not be determined.However, it was noticed in Ref. [39] that the Z imp values were close for both positive and negative impulse polarities.Furthermore, a higher breakdown voltage was seen under negative impulse polarity than under positive impulse polarity.Different observations were made when impulse tests were carried out by the same authors [40] on the same test cell, but were instead filled with dry soil; Z imp values were noted in the mega-ohm range, and Z imp under negative impulse polarity was found to be higher than Z imp under positive impulse polarity.The difference was approximately 16%, and was found to be more significant at higher current magnitudes, which is a result similar to that found in Ref. [35].Since no soil resistivity or RDC data are available in this work [40], the relationship between Z imp and R DC is not presented in the present paper.

Current Rise Times
In many studies, it can be seen that the voltage probe is parallel to the ground electrode whether the tests are carried out in the laboratory or using field measurements.In Refs.[41,42], this arrangement was shown to cause an inductive effect, which resulted in changes in the voltage amplitude, and in the rise and tail times of the ground electrode under study.The voltage traces that are now applied to ground electrodes would be expected to change the current response times of the ground electrode being tested, and thus, the impulse impedance values.Though several proposed methods of measurement have been adopted to reduce these inductive effects-particularly in investigations of non-linear test load, such as in a surge arrester [41,42]-so far, no specific measurements have been proposed for the arrangement of impulse tests on ground electrodes to reduce these self-and mutually inductive effects.However, a few studies [6,13,43] have been conducted on the effect of current rise times on the behaviour of ground electrodes.Loboda and Scuka [6] performed tests with three current rise times (2-3 µs, 6-7 µs and 8-12 µs) on six test samples in cylindrical test cells.They [6] found that the current rise times had no influence on the Z imp values.Liew and Darveniza [13] used an ionisation model to explain their experimental results obtained using field measurements, and they found that higher Z imp values were observed under short current rise times.This is explained by the ionisation model, which showed that less time was available for full ionisation under shorter current rise times, while under slower current rise times, there was more time for the ionisation process to take place in soil; hence, it produced low Z imp .A similar observation was made by Yang et al. [43], where a shorter current rise time of 2.6 µs produced higher Z imp than a longer time of 8 µs due to the higher frequency under the shorter time response; hence, a higher inductive effect, and therefore, higher Z imp , was expected in 2.6 µs than in 8 µs.

Point of Injection
As is generally known, under high impulse conditions, the inductive effect in a ground electrode is significant due to its fast, steep responses with high frequency.Due to the high inductive effect in ground electrodes, which can delay the current response and increase the Z imp value, the point of injection can affect the characteristics of the ground electrode.However, studies on the effect of point of injection can only be conducted using field measurements, and such studies are found to be limited.Stojkovic et al. [19] injected two grids of 10 m × 10 m, with no mesh and with four meshes, where each mesh measured 5 m × 5 m and was placed in one of two locations: at the corner or at the midpoint of an edge.The authors noticed that there was no influence of point of injection on the impulse impedance and voltage/current shapes.It was noticed that Z imp was higher than R DC , with a percentage difference of −18% to −85%.On the contrary, Ametani et al. [12] found that the point of injection affected the impulse impedance and voltage/current shapes of grid electrodes.They injected five ground electrodes: (i) a single counterpoise measuring 30 m in length, (ii) a cross-shaped counterpoise measuring 30 m in length and crossed with a 20 m long electrode, (iii) Mesh I measuring 10 m × 10 m with 4 meshes, (iv) Mesh II measuring 10 m × 20 m with 8 meshes and (v) Mesh III measuring 24.8 m × 34.1 m with 16 meshes.Different Z imp and voltage/current amplitudes were seen when these electrodes were injected in various nodes.For (i) single and (ii) cross-shaped counterpoises, when the injected point was at the node closest to the source, the voltage amplitude and impulse impedance were at their highest in comparison to those at the other nodes.The electrode (v) with Mesh III showed a more obvious effect when impulse voltage was applied in various nodes due to its large grid size.It was observed that the highest voltage and impedance values occurred when impulse voltage was injected in the centre of Mesh III, while injection at the midpoint of the edge of Mesh III produced the smallest voltage and impulse impedance values.Similarly, in Ref. [20], when three grids measuring 20 m × 20 m, 40 m × 40 m and 60 m × 60 m were subjected to impulse currents at their corners and their centres, significant differences in the effect of point of injection on large ground grids were observed.Another major contribution of their work was that the effect of point of injection was more significant for the grid measuring 40 m × 40 m installed in lower-resistivity soil (100 Ωm) than that installed at 1500 Ωm, with higher Z imp produced at the corner injection point of the grid installed at 100 Ωm.These results are similar to those found in Ref. [29], where higher Z imp values were obtained for both grid electrodes (10 m × 10 m and 20 m × 20 m) when they were injected in the corners than when they were injected in the centre.It was also clear [29] that the peak voltage applied in the corners was higher than the peak voltage applied in the centre of the ground electrodes.Yang et al. [43] observed a similar trend in Z imp , where higher Z imp values were seen when the ground grid was injected at the edge of the grid (corner) than when the grid electrode was injected in the centre.This can be explained by greater dissipation over a larger effective area when the ground electrode was injected in the centre, thus producing lower Z imp than when it was injected at the edge (corner).All of these studies show that there is a need to consider the point of injection in the design of grounding systems, so that the current can be effectively discharged to the ground without creating high potentials in the ground electrodes.

Conclusions
This paper involved a review of published work on the relationship of R DC with the percentage difference between Z imp and R DC .The following can be seen from the reviewed studies: (i) Most of the studies show that, the higher the soil resistivity (and, hence, the R DC values), the higher the percentage difference between Z imp and R DC .This is seen in work conducted using field and laboratory approaches (see Figures 1 and 2).A negative percentage difference is found in several studies indicating that Z imp values are higher than R DC values, particularly for soil mixed with enhancement materials.(ii) Much of the published work investigates the effect of ground electrode configuration on the performance of grounding systems under fast impulses using field measurements.The percentage difference between Z imp and R DC is found to be negative (where Z imp is higher than R DC ) in ground electrodes with R DC values below 10 Ω (see Figure 3).Very few studies present work related to the performance of various ground electrodes under different impulses using a laboratory approach.The results gathered from the literature show that the higher the R DC value, the higher the percentage difference between Z imp and R DC , as shown in Figure 4. (iii) Several published studies have investigated the effect of impulse polarity on ground electrodes using both field and laboratory approaches.It can be seen in Figure 5 that, according to field measurements, the percentage difference between Z imp and R DC increases with increasing R DC for all of the tested electrodes.However, no clear relationship can be seen between the effects of impulse polarity on various R DC values.Several studies using laboratory approaches could not be presented in this paper due to the unavailability of data relating R DC values to the percentage difference between Z imp and R DC values.
(iv) When work on the effect of current rise times on the performance of grounding systems was reviewed, it was observed that, for results obtained using a laboratory approach, there was no current rise time effect.On the other hand, for work conducted using field measurements, a rather consistent result was seen where higher Z imp values were obtained under short current rise times.(v) A very limited number of studies were found that investigated the effect of point of impulse injection on ground electrodes using experimental work.Furthermore, it was found that lower Z imp values occur when ground electrodes are injected in the corner rather than in the centre.In general, the differences in the results for different points of injection are more obvious on large ground grids (with lower R DC values). Funding

Figure 1 .
Figure 1.Percentage differences between Zimp and RDC for electrodes at various soil resistivities based on field measurements.

Figure 1 .
Figure 1.Percentage differences between Z imp and R DC for electrodes at various soil resistivities based on field measurements.

Figure 2 .
Figure 2. Percentage differences between Zimp and RDC for electrodes at various soil resistivities based on laboratory measurements.

Figure 2 .
Figure 2. Percentage differences between Z imp and R DC for electrodes at various soil resistivities based on laboratory measurements.

Figure 3 .
Figure 3. Percentage differences between Zimp and RDC for electrodes with various configurations based on field measurements.

Figure 3 .
Figure 3. Percentage differences between Z imp and R DC for electrodes with various configurations based on field measurements.

Figure 4 .
Figure 4. Percentage differences between Zimp and RDC for electrodes with various configurations based on laboratory measurements.

Figure 4 .
Figure 4. Percentage differences between Z imp and R DC for electrodes with various configurations based on laboratory measurements.

Figure 5 .
Figure 5. Percentage differences between Zimp and RDC for electrodes under different impulse polarities based on field measurements.

Figure 5 .
Figure 5. Percentage differences between Z imp and R DC for electrodes under different impulse polarities based on field measurements.