Influence of shield wires on geomagnetically induced currents in power systems

Electrical Power and Energy Systems 117 (2020) 105653

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Influence of shield wires on geomagnetically induced currents in power systems☆

T

Chunming Liua, , David H. Botelerb, Risto J. Pirjolab,c ⁎

a

North China Electric Power University, 102206 Beijing, China Natural Resources Canada, Ottawa, ON, Canada c Finish Meteorological Institute, Helsinki, Finland b

ARTICLE INFO

ABSTRACT

Keywords: Geomagnetically induced currents (GIC) Shield wire (Overhead ground wire) Transmission line Substation grounding resistance

There is increasing interest in assessing the GIC risk to power systems with GIC disturbing events to power systems observed in many parts of the world. An essential step in GIC risk assessment is modeling of GIC. Many factors have been considered in the GIC network model, but the effect of shield wires is still not clear. In this paper, we investigate multiple ways in which shield wires can influence the GIC in the transmission lines, including: mutual inductance between the shield wire and the transmission line, voltage change in substation grounding resistance due to GIC flowing to/from the shield wire, the geoelectric field distortion due to GIC flowing to/from the shield wire through tower footings and the influence of shield wires on the effective substation grounding resistance. Typical values for each effect are calculated to determine the significance of the shield wire effect on GIC. For the situations considered, the effect of shield wires on the effective substation grounding resistance is the only one that significantly affects GIC in transformers. To include this effect in GIC modeling a simple formula is given for the resistance of a shield wire and tower network.

1. Introduction Geomagnetically induced currents (GIC) in power networks, are ground effects of space weather. GIC may lead to reactive power fluctuations, voltage sag, harmonic generation, protection relay malfunction, damage of transformers and even collapse of the power system [1,2]. With GIC disturbing events to power systems observed in many parts of the world, e.g. [3–5], there is an increasing interest in assessing the GIC risk to power systems. An essential step in GIC risk assessment is modeling of GIC produced by specified geoelectric fields. Many factors have been considered in the GIC network model, including the line resistances, the transformer winding resistances and the substation grounding resistances [6], but the effect of shield wires is still not clear. Although the effect of shield wires on substation ground grid resistance has been documented in [7], the effect of shield wires has been assumed to be negligible in most GIC modeling papers, e.g. [8–10]. The reason is that the resistances of shield wires are always much larger than those of transmission lines. However, Meliopoulos et al. [11] showed that GIC flowing from a shield wire connected to a substation has a significant effect on the GIC in the transformers. Pirjola [10] has shown that GIC flowing to ground

through tower footings create a distortion of the geoelectric field experienced by the power system, but found that the effect on GIC in the transformers is negligible. There are many publications describing the case of DC currents entering the power grid when HVDC works in the mode with the ground as return circuit [12–14]. The shield wire in that case can be simply treated as a shunt path of the DC current. As for the case of GIC, it is different in principle, because the GIC are driven by an induced Electromotive Force in the transmission lines, which will also exist in the shield wires. The phenomenon won't occur with HVDC ground return current. So the contribution of shield wire to the GIC in transmission lines still remains unclear. In this paper we present an examination of multiple ways in which shield wires could influence GIC so that a comparison can be made of their relative importance. The ways in which the shield wire can affect GIC modeling, include mutual inductance between the shield wire and the transmission line, voltage change in substation grounding resistance due to GIC flowing to/from the shield wire, the geoelectric field distortion due to GIC flowing to/from the shield wire through tower footings and the effect of the shield wire in changing the substation grounding resistance. Then we calculate typical numerical values for

This work was supported by National Nature Science Foundation of China (51677068). Corresponding author. E-mail addresses: [email protected] (C. Liu), [email protected] (D.H. Boteler), [email protected] (R.J. Pirjola).

☆ ⁎

https://doi.org/10.1016/j.ijepes.2019.105653 Received 10 July 2019; Received in revised form 27 September 2019; Accepted 24 October 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 2. Test model for analyzing the effect of shield wire on GIC in the transformer. In Scenario B, RW1 = RWn =∞; In Scenario C, RG1 = RG2 = … = RGn1=∞.

3. Examination of possible effects of shield wires on GIC modeling In the calculation of GIC in a power grid, the three phases are usually treated as one, whose resistance is one-third of that of a single phase and which carries a GIC three times larger than that flowing in a single phase [11,15] To analyze the possible effects of the shield wire on GIC in a power system, we use the test model which consists of two substations and one transmission line between them as shown in Fig. 2. In this model, NA and NB are neutral points of two substations, RSA and RSB are the grounding resistances of substations, RTA and RTB are the resistances of transformers at the substations, RL is the resistance of the transmission line between two substations, RW1, RW2, …, RWn are the resistances of the shield wire within each span length, RG1, RG2, …, RGn1 are the footing resistances of the towers, VL is the equivalent voltage source of the geoelectric field between the two substations, V1, V2, …, Vn are the equivalent voltage sources of the geoelectric field within each span length. In Scenario B, the resistance of the end segments RW1 and RWn are infinite; In Scenario C, the resistances of all tower footings RG1, RG2, …, RGn-1 are infinite. Without the shield wire, GIC in the transformers and transmission lines depend on the line impedance, the transformer impedances, the grounding resistances and the equivalent voltage source of the geoelectric field. What will be changed if we take the shield wire into account? The shield wire and its grounding system produce a circuit in which the geoelectric field can drive GIC as well. Firstly, the mutual inductance between the shield wire and the power line may have some effect, because the shield wire is installed parallel to the power line. Secondly, we can also expect that GIC flowing through the shield wire and the towers have some effect on the GIC in the transformers. Thirdly, when the shield wire is connected to the grounds of substations (i.e. Scenario A and Scenario C), it provides an extra path to the ground for the GIC flowing to/from the transmission line through the tower footings. Each possible effect is considered below.

Fig. 1. Different grounding systems of shield wires.

each effect according to which the significance of the shield wire on GIC can be identified. 2. Scenarios There are different types of shield wire installations commonly used in power systems in different parts of the world. Most systems use continuous shield wires but their ground connections can be different, which make their effects vary from one shield wire to another. In this paper we examine the following typical scenarios: Scenario A: as shown in Fig. 1(a), the shield wires are grounded at each tower and connected to the grounds of the substations at the ends of a transmission line. This is the typical practice, for example, in North America and Finland. Scenario B: as shown in Fig. 1(b), the shield wire is also grounded at each tower, but is not directly connected to the grounds of the substations. This is the typical arrangement, for example, in China. Scenario C: as shown in Fig. 1(c), the shield wire is directly connected to the grounds of the substations, but not grounded directly at each tower, which is the practice for example in Sweden. In Scenarios B and C, small insulators are used to keep the shield wire insulated from the substation grounds or towers in the normal condition, and will flash over when stuck by lightning making the shield wire serve as protection for the power transmission line. Sometimes shield wires are segmented to avoid energy loss due to currents induced in the shield wire and the ground. The segmented shield wire is grounded at one tower and insulated at other towers within one segment. There is thus no circuit between the segmented shield wire and the ground, so that the segmented shield wire does not have any effect on GIC modeling, which will not be considered further here.

A. Mutual Inductance between Shield Wire and Power Line Mutual inductance means that GIC flowing in the shield wire will induce a current in the transmission line, altering the GIC flow there, and vice versa. The self impedance of conductor i and mutual impedance between conductors i and k with uniform earth as a return path, as shown in Fig. 3, can be calculated according to Carson’s Formula [16,17]. For GIC frequencies, as considered here (f ≤ 0.1 Hz), the result is accurate enough by using only the first term of the series included on Carson’s formula. Therefore, after rearranging for easier calculation, we get:

Zii = (Ri +

Zik = 2

2f ·10 4)

2f ·10 4

+ j (4 f ·10 4 ·ln

+ j (4 f ·10 4·ln

DE ) dik

DE ) GMRi

(1) (2)

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Fig. 4. Circuit model used for calculating GIC in the shield wire.

resistances RG are infinite. Using the same numerical values as those in Reference [11] (also shown in Appendix A including Table A1 and A2), we calculate the GIC flowing along the shield wire and GIC flowing to ground through the towers using GIC Simulator Software [18] available from Nature Resources Canada. In this model the resistance RW is 0.31 Ω, the geoelectric field is 1 V/mile (0.621 V/km), and tower footing resistance RG equals to 5 Ω, 10 Ω, 20 Ω, 30 Ω or 100 Ω.

Fig. 3. Calculation of mutual Impedance between shield wire and phase conductor.

where Zii is the self impedance of conductor i in Ω/km, Zik is the mutual impedance of conductors i and k in Ω/km, Ri is the resistance of conductor i in Ω/km, f is the frequency in Hz, GMRi is the geometric mean radius of conductor i in m, dik is the distance between conductors i and k in m, and DE = 658.9 ,with ρ = earth resistivity in Ω⋅m.

1) Voltage Change in Substation Grounding Resistance Due to GIC to/ from the Shield Wire If the shield wire is connected to the grounds of the substations (i.e. Scenario A and Scenario C), the GIC to/from the shield wire cause a voltage change when flowing through the substation grounding resistance. This effect reduces the GIC in the transmission line. The GIC flowing in the nearest 50 shield wire segments (span length) to both substations are shown in Fig. 5 with different tower footing resistances. The infinite tower footing resistance is the case in Scenario C. It can be seen from the results that the shield wire GIC near the substations are smaller than that in the middle of the line. The GIC in the middle of the shield wire is independent of the tower footing resistance because the same current flows in and out along the shield wire, that is, there are no GIC flowing to the ground through the towers. In this test case, the voltage change caused by the maximum shield wire GIC (=0.81A) through grounding resistance (=1Ω) is 0.81 × 1 = 0.81 V for one substation, and 1.6 V in total for both substations. The total voltage change is as much as 0.3% of the equivalent voltage source calculated by integrating the geoelectric field along the transmission line (=473 V). Thus this effect on GIC in the transformers is negligible.

f

We use the same test model as that used in reference [11] for a simplified and modified version of the Minnesota Power Company 500 kV typical transmission line between Dorsey and Minneapolis. The numerical values of the test model can also be seen in Appendix A of this paper. Let conductor i stand for the shield wire, and conductor k stand for Phase A which is the nearest to the shield wire. Then assume f = 0.1 Hz, ρ = 100 Ω⋅m, and the relative permeability μr = 200 for steel and μr = 1 for aluminum. The results are the following: Self impedance of the shield wire

Zii = (2.76 + j8.18 E

3) /km,

Self impedance of Phase A

Zkk = (0.0176 + j1.63 E

3) /km,

Mutual impedance between the shield wire and Phase A Zik = (9.87E−5 + j9.63E−4) Ω/km. The current in the shield wire Ii and the current in Phase A Ik can be expressed as:

Ii Zii Zik = Ik Zik Zkk

1

Vi Vk

2) Effect of Geoelectric Field Distortion Due to GIC Flowing through the Tower Footings

(3)

Substituting the numerical values into Eq. (3), we get:

Ii = Ik

0.36 j0.001 0.004 j0.02

0.004 j0.02 56.3 j5. 2

Vi Vk

If the shield wire is grounded at each tower (i.e. Scenario A and Scenario B), the GIC in the shield wire flows to/from ground through

(4)

Let us assume that the geoelectric field is 1 V/km, i.e. ΔVi = ΔVk = 1 V/km, thus the current caused by the mutual inductance is 0.02A which is 5% of Ii and 0.03% of Ik. So, the mutual coupling effect of the shield wire on GIC in the transmission line is negligible. Additionally, the GIC in the shield wire can be considered approximately to be independent of that in the transmission line. B. Effect of GIC Flowing through the Shield Wire and Towers GIC flowing to/from a shield wire through the substation ground or tower footing will create a voltage change that may affect the GIC in the transformers. To calculate the GIC in the shield wire more easily we use a circuit model as shown in Fig. 4. In this model, NA and NB are neutral points of two substations, RSA and RSB are the grounding resistances of the substations, RW is resistance of the shield wire within each span length, RG is the footing resistance of each tower, VW is the equivalent voltage source of the geoelectric field within each span length of the shield wire. In Scenario B, the two segment resistances at the ends of the shield wire are infinite; while in Scenario C the tower footing

Fig. 5. GIC flowing in the nearest 50 shield wire segments to both substations in Scenario A and Scenario C (i.e. shield wire is connected to the grounds of substations). 3

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the tower footings, so that an additional electric field is produced in the ground. The extra electric field distorts the original geoelectric field, thus reducing the equivalent voltage source which is the integral of the geoelectric field along the transmission line. We have modeled Scenario A and Scenario B using the parameters in Appendix A. This allows us to calculate the GIC flowing to ground through each tower footing. The GIC flowing through the nearest 30 tower footings to both substations are shown in Fig. 6 with different tower footing resistances. It can be seen from the results that being closer to the substation and the lower the tower footing resistance the more GIC flow through that tower. Additionally, more GIC flow through the tower footings in Scenario B because the shield wire is not connected to the substation ground and all the GIC in the shield wire must flow through the towers. The effect of the geoelectric field distortion corresponds to a potential difference between the two substations due to the currents injected into ground through tower footings. The potential drop near a hemispherical electrode with an injected current I can be calculated by using Eq. (B2) in Appendix B. For an electrode of another shape, Eq. (B2) can also be used if the observation point is far enough (i.e. r > a, where a is radius of the hemispherical electrode with the same grounding resistance). It can be seen from Fig. B1 (in Appendix B) that the potential drops to a small value within several tens of meters. Therefore only those towers very near to the substations need to be considered. In this test case, we can see from Fig. 6 (b) that the GIC through the nearest tower is not more than 0.2A in Scenario B. If we assume that the distance from the substation to the first tower is 50 m, then the potential difference calculated from Eq. (B2) is 0.64 V at one substation, and 1.3 V at both substations. It is negligible compared with the equivalent voltage source of the original geoelectric field (=473 V). For Scenario A, the GIC through the nearest tower is even smaller (< 0.1 A), thus the effect is also negligible.

C. Effect of the Shield Wire and Towers as Extra Path for GIC to/from the Transmission Line The existence of the shield wire tends to increase the GIC in the transmission line because the continuous shield wire and the grounded towers produce an extra path for the GIC to/from the transmission line to flow through. 1) Effect of the Shield Wire as Admittance between the Neutral Points of Two Substations The effect of the shield wire as an extra path between the neutral points of two substations with the admittance of 1/RSW is depicted in Fig. 7. The GIC in the transmission line I1 can be calculated for the numerical values given in the test model. We assume that the resistance of the shield wire is 0.77 Ω/km (=1.24 Ω/mile) and the geoelectric field is 0.6214 V/km (=1 V/mile). Then I1 equals 65.72A or 65.66A with the shield wire connected or disconnected, respectively. It can be seen that the difference is very small because the resistance of shield wire is much larger than any other resistance in the circuit, so this effect can be neglected. 2) Effect of the Shield Wire and Towers as Extra Admittance between the Neutral Point and the Ground Grounded towers are connected to the neutral points of substations by the shield wire and thus produce an extra path to the ground for the GIC flowing to/from the transmission line. The ladder circuit model shown in Fig. 8(a) can be used to calculate the equivalent resistance of the shield wire and grounded towers, where RW1, RW2, …, RWn are the resistances of shield wire within each span length, RG1, RG2, …, RGn-1 are the tower footing resistances. The effect of shield wire and grounded towers can be regarded as an equivalent parallel resistance Req which changes the effective grounding resistance of the substation as shown in Fig. 8(b). Let us assume that

RW 1 = RW 2 = …=RWn = RW , and

RG1 = RG2 = …=RGn

1

= RG

When looked into from the substation, the equivalent resistance of the ladder circuit in Fig. 8(a) can be expressed by a recursive equation

Rn = RW + RG // Rn

1

= RW +

Rn 1· RG Rn 1 + RG

(5)

Based on Eq. (5), Fig. 9 presents some values of Rn with increase of the ladder steps n. It can be seen that Rn approaches a fixed value within 30 ladder steps (i.e. 30 span lengths). If each span length is 500 m, the equivalent resistance of shield wire and towers reaches a fixed value for shield wires with length > 15 km which is quite short compared to the length of a transmission line. It means that, in almost every case, we can

Fig. 6. GIC flowing from the shield wire through the nearest 30 tower footings to both substations.

Fig. 7. Effect of the shield wire as an extra admittance between the neutral points of two substations. 4

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shield wires thus change the effective substation grounding resistance from 1 Ω to 0.66 Ω. This change the GIC in the transmission line and transformers from 65.66A to 72.57A.This is an increase of more than 10% which is not negligible. 4. Discussion A. Effect of the Shield Wire on GIC in the Transmission Line The combined effects of shield wires on GIC in the transmission line and to/from substation grounds are calculated for the test model shown in Fig. 2. The calculation is based on numerical values from [11] (also listed in Appendix A) with different shield wire resistances (0.77 Ω/km and 2.76 Ω/km), and with different tower footing resistances. A1though values less than 5Ωor higher than 50Ωare not practical for the tower footing resistance in a high voltage transmission system, the results calculated by applying those values are helpful for us to understand the effect. The results (Fig. 10) show that the shield wire has a substantial effect on the GIC in the power system. On one hand, the shield wire increases the GIC in the transmission line, because it provides an extra path to the ground so that more current can flow to/from the transmission line through the towers. On the other hand, the shield wire decreases the GIC flowing to/from the substation ground, because the GIC is partially diverted to flow through the towers back again to the ground instead of through the substation grounding resistance. The results shown in Fig. 10 (b) are quite similar to the results in [11]. However these results are the GIC flowing to/from the ground of substation. They are not the same as the GIC flowing to/from transmission line and transformers. Our results in Fig. 10(a) show that the GIC through transformers increase with decreasing tower footing resistance, which is contrary to the interpretation of the results in [11]. According to the investigations in Section III, we know that the shield wire has a negligible effect on the GIC in a transmission line except through changing the effective substation grounding resistance. That effect will not happen unless the shield wire is connected both to each tower and to the substation grounds (Scenario A). The network model for calculating GIC in the transmission line with shield wires can be simplified to the model shown in Fig. 8(b), where Req is obtained from Eq. (9). Fig. 11 presents the comparison of GIC in the transmission line calculated by using both the original model and the simplified model shown in Fig. 8(b). It can be seen that the two models give very close values. The difference is slightly increased when RG equals to 1 Ω, because the condition RW ≪ RG is not satisfied any more. This confirms that the simplified model shown in Fig. 8(b) is accurate enough for modeling GIC in a power network with shield wires. Furthermore, if we define the effective grounding resistance of a substation with the shield wire as:

Fig. 8. Effect of the shield wire and towers as an extra path to the ground.

use that fixed value directly no matter how many towers there are. When n is large enough, and Rn reaches a stable value, approximately, we have Rn = Rn-1. Let us assume

Rn = Rn

1

= R eq

and substitute it into Eq. (5), then we get

R eq = RW +

Req ·RG (6)

R eq + RG

This gives the quadratic equation 2 Req

RW · Req

(7)

RW ·RG = 0

which has the solution

R eq =

RW 1 + RW2 + 4RW · RG 2 2

Because RW ≪ RG, mately,

R eq =

RW + 2

RW · RG

RW2 in

(8)

Eq. (8) can be neglected. Thus approxi-

(9)

This equation can also be seen in reference [19]. In the case of the test model, from Fig. 9, where RW is 0.31 Ω and RG is 10 Ω, Eq. (9) gives the equivalent resistance Req = 1.92 Ω. Adding the

1 1 1 = + Reff RS R eq

(10)

where Req is given by Eq. (9), this gives a simple way of including the significant effect of the shield wire in GIC modeling without the need to include the detail of the shield wires in the model itself. B. Significance of the Shield Wire effect on GIC The influence of Req on Reff can be different because RS varies from one substation to another. Usually RS of a transmission substation is limited to 1 Ω or less for safety reasons. To investigate how significant the influence of the shield wire could be, we calculate typical values for the changing percentage of the effective substation grounding resistance due to the shield wire, i.e.

Reff % =

Fig. 9. Equivalent resistance of the ladder circuit Rn with increase of the ladder steps.

Reff

RS RS

The ΔReff% due to a shield wire (RW = 0.31 Ω) for different RG 5

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Fig. 12. Changing percentage of substation effective grounding resistance with a shield wire (resistance: 0.77 Ω/km) at different tower footing resistance.

same towers, they are only counted as one but with a smaller RW (see Fig. 8(a)). The changing percentage of the effective substation grounding resistance (i.e.ΔReff%) with increasing the number of shield wires is shown in Fig. 13. Each shield wire is assumed to have a resistance of 0.31 Ω within each span length, and to be connected to each tower with 10 Ω footing resistance. From the results we can see that the influence of shield wires on the effective grounding resistance can be quite large. However, it is still hard to say whether the shield wire has a significant effect on GIC in the transmission line and transformers because the grounding resistances of the substations usually are not the dominant part of the overall circuit resistance. The shield wire has little effect in a power system where the resistance of the transmission line is much larger than the substation grounding resistance, see e.g. [20]. Otherwise, the effect of shield wire can be significant in a system where the substation grounding resistances are more important, e.g. [21]. As for the test model in this paper, the substation grounding resistance is about 30% of the total resistance in which the resistances of the transmission line and the transformer windings are also included. Roughly speaking, several shield wires can reduce the effective substation grounding resistance by 60% ~ 80%, so that the total resistance can be reduced by 20% or so, which means that the GIC in the transmission line may increase by that amount. Although this effect is not the largest in comparison with other inaccuracies, it needs to be considered in GIC modeling.

Fig. 10. GIC results calculated from the test model (shown in Fig. 2).

Fig. 11. Comparison of the transmission line GIC results calculated from the original model (shown in Fig. 2) and the simplified model shown in Fig. 9(b).

values is shown in Fig. 12. It can be seen that the substation grounding resistance RS is an important factor for the change. For example, with a tower footing resistance of 10 Ω, the shield wire reduces Reff by 35% when RS is 1.0 Ω,but by only 5% when RS is 0.1 Ω. It should be noted that there are usually more than one shield wire connected to the ground of a substation. Each shield wire has its contribution to decreasing the effective grounding resistance, so that:

1 1 1 1 = + + + Reff RS R eq1 R eq2

+

1 R eqn

Fig. 13. Changing percentage of substation effective grounding resistance with increase of the number of shield wires (Each shield wire has a resistance of 0.31 Ω within each span length, and is connected to each tower with 10 Ω footing resistance).

(11)

where Req1, Req2, …, Reqn is the equivalent parallel resistance corresponding to each shield wire. If two shield wires are connected to the 6

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5. Conclusions

parallel to the substation grounding resistance, and the parallel resistance can be calculated from Eq. (9). Therefore a simple method can be used to calculate the GIC in the transmission line, i.e. just model GIC without considering the shield wire but replace Rs with Reff. The effect of shield wires on effective substation grounding resistance depends on the shield wire resistance within each span length, the footing resistance of each tower, the substation grounding resistances and the number of shield wires. However the effect on GIC also depends on the “weight” of the substation grounding resistance in comparison with the transmission line and transformer winding resistances. It can increase the GIC in the transmission line and transformers by 20%, which should be considered in GIC modeling.

In this paper, after investigating the possible effect of the shield wire on GIC in the transmission line, we draw the following conclusions: The shield wire, together with grounded towers, reduces the effective substation grounding resistance, and therefore increases the GIC in the transmission line and transformers. This effect cannot be ignored while the other effects of the shield wire are negligible. Furthermore, that effect will not happen unless the shield wire is connected to each tower and the substation ground. The existence of a shield wire increases the GIC in the transmission line and transformers because it produces an extra path to the ground through the tower footings. At the same time, it decreases the GIC flowing through the substation ground, because the GIC from the transmission line now partially flows to ground through the tower footings instead. The effect of a shield wire can be treated as an equivalent resistance

Declaration of Competing Interest The authors declared that there is no conflict of interest.

Appendix A. Numerical values of the test model The test system consists of a 500 kV transmission line, terminated by three phase transformer banks at both ends [11]. It is assumed that no intermediate substations exist. Fig. A1 presents a single line diagram of the test system. Each of the three phase transformer banks consists of three single phase transformers which are connected as DELTA/GROUNDED Y. The grounded Y sides are connected to the 500 kV transmission line. The winding resistance of each single phase transformer is 1.5 Ω. (see Fig. A1) The transmission line data are listed as follows. Line length: 761 km (473 miles) Configuration: 3-conductor bundle per phase Bundle spacing: 0.457 m (18 in.) Tower spacing: 402 m (0.25 miles) (see Table A1–A2) Tower footing resistance: 30 Ω

Fig. A1. Single line diagram of the test system. Table A1 Conductor data. Conductor

Type

O.D (meters)

Resistance (Ω/km)

Shield Wires Phase Conductors

7/16 steel 1192 ACSR

0.0111 0.0331

2.756 0.05

Table A2 Tower configuration data. Conductor

x – coordinate (meter)

y – coordinate (meter)

Phase A Phase B Phase C Shield Wire 1 Shield Wire 2

−9.75 0, 0 9.75 −10.67 10.67

29.72 29.72 29.72 39.47 39.47

Appendix B. Potential drop due to current injected in a uniform earth In a uniform earth with a conductivity σ, the electric field caused by a hemispherical electrode with an injected current I is:

E=

I 2

r2

er

(B1)

where r is the distance from centre of the electrode to the observation point, and êr is a unit vector in that direction. The voltage from r to a remote Earth is obtained by integrating E, and the result is

7

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Table B1 Radius of a hemispherical electrode in a uniform earth with the conductivity of 10−3 Ω−1 m−1 corresponding to a given earthing resistance. Earthing Resistance [Ω]

Radius [m]

0.5 5 10 20 30 100

318.3 31.8 15.9 8.0 5.3 1.6

Fig. B1. Voltage from a point located at the distance r from the hemispherical electrode to a remote earth. The parameters I and σ equal 1A and 10−3 Ω−1 m−1, respectively.

U (r ) =

I 2

(B2)

r

In Eqs. (B1) and (B2) the distance r must be larger than or equal to the radius of the electrode a (i.e. r ≥ a). If r is smaller than a (i.e. r < a), E = 0 and

U (r ) =

I 2

(B3)

a

By definition, the earthing resistance of the electrode equals

Re =

U 1 = I 2 a

(B4) −3

-1

Using Eq. (B4), we can calculate a from a given value of Re, and some results are shown in Table B1 with the assumption that σ = 10 Ω m−1. Based on Eq. (B2), Fig. B1 presents the voltage between a point located at the distance r(r ≥ a) from the center of the hemispherical electrode and a remote Earth. The injected current I and the Earth’s conductivity have the values of 1 A and 10−3 Ω−1 m−1 respectively.

wires on GIC modeling. J Atmos Sol Terr Phys 2007;69:1305–11. [11] Meliopoulos APS, Glytsis EN, Cokkinides GJ, Rabinowitz M. Comparison of SS-GIC and MHD-EMP-GIC effects on power systems. IEEE Trans Power Deliv 1994;9(1):194–207. [12] Pesonen AJ. Effects of shield wires on the potential rise of h.v. stations. SAHKOElectricity Finland 1980;53(10):305–8. [13] Unde M, Maske R, Kushare B. Parametric analysis of fault current distribution. Proc. of Int. Conf. on control, communication and power engineering. 2013. [14] Li Y, Dawalibi F. Advanced practical considerations of fault current analysis in power system grounding design. J Int Council Electri Eng 2012;2(4):409–14. [15] Pirjola R. Effects of space weather on high-latitude ground systems. Adv Space Res 2005;36(12):2231–40. [16] Dommel, H. Electro-Magnetics Transient Program (EMTP) Theory Book; 1994: page 4–6. [17] CCITT: Directives concerning the protection of telecommunication lines against harmful effects from electric power and electrified railway lines. vol. 2, page 154; 1989. [18] Boteler DH, Pirjola R, Blais C, Foss A. Development of a GIC Simulator, Paper 14PESGM1889. Proceedings of IEEE PES GENERAL Meeting, Washington, DC. 2014. [19] Pesonen AJ. Effects of shields wires on the potential rise of h.v. stations. Electricity Finland 1980;53(10):305–8. [20] Pirjola R. Study of effects of changes of earthing resistances on geomagnetically induced currents in an electric power transmission system. Radio Sci 2008;43. https://doi.org/10.1029/2007RS003704. [21] Bui U, Overbye TJ, Shetye K, Zhu H, Weber J. Geomagnetically induced current sensitivity to assumed substation grounding resistance. 2013 North American Power Symposium, Manhattan, KS. 2013.

References [1] Kappenman JG. Geomagnetic disturbances and impacts upon power system operation. In: Grigsby LL, editor. The electric power engineering handbook. 2nd ed.CRC Press/IEEE Press; 2007 Chapter 16 pp. 16-1 – 16-22. [2] Molinski TS. Why utilities respect geomagnetically induced currents. J Atmos Sol Terr Phys Nov. 2002;64:1765–78. [3] Kappenman John G. An overview of the impulsive geomagnetic field disturbances and power grid impacts associated with the violent Sun-Earth connection events of 29-31 October 2003 and a comparative evaluation with other contemporary storms: GEOMAGNETIC FIELD DISTURBANCES AND POWER GRID. Space Weather 2005;3(8):n/a–. https://doi.org/10.1029/2004SW000128. [4] Gaunt CT, Coetzee G. Transformer failures in regions incorrectly considered to have low GIC risk. Power Tech 2007 IEEE Lausanne. 2007. p. 807–12. [5] Liu CM, Liu LG, Pirjola R. Geomagnetically induced currents in the high-voltage power grid in China. IEEE Trans Power Deliv Oct. 2009;24:2368–74. [6] Zheng K, Boteler DH, Pirjola R, Liu LG, Becker R, Marti L, et al. Effects of system characteristics on geomagnetically induced currents. IEEE Trans Power Deliv 2014;292:890–8. [7] IEEE Guide for Safety in AC Substation Grounding, IEEE Std. 80-2000. [8] Pirjola R, Lehtinen M. Currents produced in the Finnish 400 kV power transmission grid and in the Finnish natural gas pipeline by geomagnetically induced electric fields. Ann Geophys 1985;3(4):485–91. [9] Prabhakara FS, Hannett LN, Ringlee RJ, Ponder JZ. Geomagnetic effects modeling for the PJM interconnection system Part II – Geomagnetically induced current study results. IEEE Trans Power Syst 1992;7(2):565–71. [10] Pirjola R. Calculation of geomagnetically induced currents (GIC) in a high-voltage electric power transmission system and estimation of effects of overhead shield

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