Geomagnetically induced currents in Europe: Characteristics based on a local power grid model

Authors


Abstract

[1] We consider the model of the Finnish high-voltage power grid in 1978–1979, for which the accurate parameters are available for calculating geomagnetically induced currents (GIC). Moving the grid at different locations across Europe gives estimates of GIC levels in this region. For calculating the geoelectric field driving GIC, we use different layered models of the ground conductivity and 1 min geomagnetic data of the year 2003. The results show a clear concentration of large GIC in north Europe, where the peak values are about 3–5 times larger than in Central and South Europe, being up to about 200 A in this specific power grid. There are two factors contributing to this finding. First, geomagnetic variations are generally stronger in the north. Second, there are regions in the north with clearly smaller ground conductivities than typically at other areas. Both of these reasons lead to larger electric fields in the north. A very similar behavior of GIC is found in the case when a single-layered ground conductivity model is assumed everywhere. We also show that the geographic characteristics of GIC are quite insensitive to the details of the power grid model by modifying various parameters of the Finnish grid.

1 Introduction

[2] The European Risk from Geomagnetically Induced Currents (EURISGIC) project has as one main goal to derive the statistical occurrence of the geoelectric field and geomagnetically induced currents (GIC) in Europe [Viljanen, 2011]. In this paper, we consider a local power grid to provide a reference case. The model is valid for the 400 kV grid that was operated in Finland in 1978–1979 and whose precise parameters needed in the GIC modeling are publicly available. By moving this grid across Europe, we can illustrate how GIC levels vary depending on the geographic location.

[3] This is the first evaluation of GIC hazard across whole Europe. Previous studies on power grids have considered single countries including Finland [Pirjola and Lehtinen, 1985; Elovaara, 2007], Russia [Barannik et al., 2012], Spain [Torta et al., 2012], Sweden [Pulkkinen et al., 2005; Wik et al., 2009], and the United Kingdom [Erinmez et al., 2002; Thomson et al., 2005; Beggan et al., 2013]. Additionally, there has been a study on GIC in the oil pipeline in the Czech Republic [Hejda and Bochníček, 2005]. In North America, Kappenman and Radasky [2005] have studied the occurrence of GIC across the United States, and a recent paper by Wei et al. [2013] estimates the geoelectric fields in the United States and South Canada.

[4] Boteler et al. [1998] present a map of the occurrence of hourly ranges and of the maximum time derivative of the magnetic field (dB/dt) based on Canadian observations. Weigel et al. [2003] show similar results based on North European magnetometer data. Boteler [2001] shows a map of Canada giving the probability of the occurrence of an hour with dB/dt exceeding a given threshold. Due to the close relationship of GIC and magnetic variations, such results provide also a proxy for GIC hazard.

[5] Zheng et al. [2013] considered a simple benchmark grid of Horton et al. [2012] with eight substations and placed the grid on a resistive or conductive 1-D ground conductivity model. To calculate GIC, they used geomagnetic data of the Halloween storm on 29–31 October 2003 from seven magnetometer stations at different magnetic latitudes. They found that moving from a high latitude (∼73°) to a low latitude (∼27°) decreases the peak GIC by a factor of ∼50 for the resistive ground model and ∼20 for the conductive model.

[6] Recent studies on the extreme behavior of geomagnetic field variations [Thomson et al., 2011] and of the geoelectric field [Pulkkinen et al., 2012; Ngwira et al., 2013] indicate a prominent increase of activity north of about 50–55°N in geomagnetic latitudes. Our results will give further confirmation to these results too.

2 Methods

[7] Concerning the modeling method, we refer to Viljanen et al. [2012] and only briefly summarize its application to the present problem. We use geomagnetic recordings as 1 min time series from European observatories and other geomagnetic recording sites in 2003. To calculate the electric field, we apply the ground conductivity map by Ádám et al. [2012] with numerical values available at http://real.mtak.hu/2957/. As in Viljanen et al. [2012], we consider two cases: a single 1-D ground model applied everywhere (Table 1) and the full conductivity map with several different blocks (Figure 1). The single ground model emphasizes the effect of variable geomagnetic activity at different latitudes. The full model shows how the changing conductivities cause additional variability in GIC.

Table 1. Thicknesses and Resistivities of the Layers in the Ground Model Applied for Whole Europe in a Test Casea
Thickness (km)Resistivity (Ωm)
  1. aThis corresponds to block 01 in Figure 1.
0.440
1.33
140.02000
170.0118
15
Figure 1.

(top) Numbering of the conductivity blocks (modified from Viljanen et al. [2012]). (bottom) Conductances with the integration depth of 80 km. See Ádám et al. [2012] and http://real.mtak.hu/2957/ for the model parameters.

[8] As the power grid model, we use the 400 kV grid that was operated in Finland in 1978–1979 (Figure 2, Table 2). For this case, the precise parameters are available from Pirjola and Lehtinen [1985] and Pirjola [2009]. As an additional test, we modified this model by adding a grounded node at the midpoint of each transmission line thus increasing the number of nodes from 17 to 36. The modified system covers the same area as the original grid. We assumed the earthing resistance of 0.62 ohm for all new nodes, being equal to the mean value in the original model.

Figure 2.

Schematic map of the Finnish 400 kV power grid in 1978–1979 with transmission lines approximated by straight lines in this plot [Viljanen et al., 2012].

Table 2. Parameters of the Finnish Power Grid in 1978–1979 (Figure 2) [Pirjola and Lehtinen, 1985; Pirjola, 2009; Viljanen et al., 2012]a
Transformers   Transformers   
NodeLatLongRe (ohm)NodeLatLongRe (ohm)
  1. aLocations of the stations are approximate. The earthing resistance is denoted by Re. Pirjola and Lehtinen [1985] and Pirjola [2009] assumed a zero Reat the Swedish border stations Letsi and Messaure. We use the value of 0.50 ohm to roughly approximate the effect of the rest of the Swedish power grid on the Finnish side.
Alajärvi63.024.20.98Loviisa60.426.30.36
Alapitkä63.227.51.14Messaure66.720.20.50
Huutokoski62.227.70.57Nurmijärvi60.524.90.66
Hyvinkää60.624.90.47Olkiluoto61.221.50.33
Inkoo60.023.90.43Petäjäskoski66.325.30.47
Kangasala61.524.00.86Pikkarala64.925.80.70
Koria60.826.60.45Pirttikoski66.327.20.95
Letsi66.420.10.50Ulvila61.522.00.64
Lieto60.522.50.60average62.724.40.62
Lines  Lines    
Node 1Node 2R (ohm)Node 1Node 2R (ohm)  
AlajärviHuutokoski1.88InkooLieto0.59  
AlajärviKangasala1.47KoriaLoviisa0.33  
AlajärviPikkarala0.96LetsiPetäjäskoski1.70  
AlajärviUlvila1.98LietoOlkiluoto0.59  
AlapitkäHuutokoski0.98LoviisaNurmijärvi0.58  
AlapitkäPetäjäskoski3.20MessaurePikkarala2.89  
HuutokoskiKoria1.36OlkiluotoUlvila0.27  
HyvinkääInkoo0.65PetäjäskoskiPirttikoski0.71  
HyvinkääKangasala1.04PikkaralaPirttikoski1.46  
HyvinkääNurmijärvi0.076     

[9] In our modeling method of a power grid, we always treat the three-phase conductors as a single conductor. It follows especially that GIC flowing between the ground and the grid at a substation is the sum of the currents in the three phases. Furthermore, if there are several transformers at a substation, then GIC is the sum of currents through all of them. By “earthing resistance,” we refer to the sum of the transformer resistance, including a possible reactor resistance, and of the grounding resistance.

[10] We move the power grid from its true location by modifying its coordinates. We keep the relative locations of the nodes and the lengths of the transmission lines unchanged. In other words, we move the grid as a rigid body on Earth's surface. For westward shifts, we simply add a longitudinal step. For southward shifts, we must modify the longitudes as a function of the latitudes of the nodes to preserve the correct size and shape. Figure 3 shows a schematic illustration of the shifts. In the calculations in this paper, we shifted the grid southward in 2° steps and westward in 3° steps. The total shift to the south was 24° and to the west 30°. The number of different locations was thus 143.

Figure 3.

Examples of different locations of the shifted Finnish power grid. The red color shows the true location.

3 Results

[11] GIC values always depend on the details of the power grid under study. Given a fixed grid model, we need to estimate how much slightly different grids differ from it regarding GIC to assess the more general usefulness of the results of this paper. We will discuss this briefly in section 3.1.

[12] Another crucial point is the effect of the ground conductivity on GIC. Our conductivity model contains tens of different blocks corresponding to different geoelectric fields and GIC even if geomagnetic variations were identical everywhere. In section 3.2, we consider a simple ranking of the ground models based on conductances and GIC.

[13] Section 3.3 presents the main results illustrating the characteristics of GIC across Europe in 2003. We selected this year, because it includes the big Halloween storm on 29–31 October 2003 when there was a blackout in Malmö, Sweden, on 30 October [Pulkkinen et al., 2005; Wik et al., 2009]. GIC statistics of the European power grids covering the full period of 1996–2008 considered within the EURISGIC project will be presented in another paper.

3.1 Dependence on Power Grid Parameters

[14] When considering a power grid as a whole, it is interesting to know how much statistical characteristics depend on the details of grid parameters, especially on the resistances. The basic approach is to consider a spatially uniform electric field pointing to the north or to the east. GIC due to a uniform field into any other direction is then a linear superposition of these two cases. Although a uniform field is a rough approximation, it reveals many features about the flow of GIC in a network that are valid for more realistic fields too. It is especially useful when studying features related to the parameters in grid models: resistances, number of nodes and lines, and topology of the grid. Several previous papers have discussed this topic widely [e.g., Arajärvi et al., 2011; Pirjola, 2008; Viljanen and Pirjola, 1994], so we only show one basic example and briefly list other main results here.

[15] A simple test is to multiply all earthing resistances (Re) by a common factor C (C=0 corresponds to a “perfect earthing”). We leave transmission line resistances unchanged. When Re increases, the sum of (absolute) GIC at all nodes decreases monotonically (Figure 4). This happens for both north and east directions of the electric field. Even the extreme modification to set all earthing resistances equal to zero only approximately doubles the sum of GIC from the unmodified model. Note that the currents cannot become infinite, because the line resistances are nonzero. To decrease the sum down to half of the unmodified case would require increasing the earthing resistances at least five times larger. An example of such an increase could be an installation of highly resisting neutral point reactors [Arajärvi et al., 2011], which is the actual case at most substations in Finland nowadays [Elovaara, 2007].

Figure 4.

Sum of GIC due to a uniform electric field of 1 V/km in the Finnish high-voltage power grid in 1978–1979 (black: northward field, red: eastward field). The earthing resistances of all nodes given in Table 2 are multiplied by the factor C. Both curves are normalized to the value of the unchanged resistances (C=1).

[16] Other general features concerning the sensitivity of GIC to different grid parameters are as follows:

  1. [17] Keeping earthing resistances unchanged but multiplying all transmission line resistances by the same factor has the following effect: If the line resistances are doubled, then the average earthing GIC is approximately halved. If the line resistances are halved, then the average earthing GIC increases a little more than 1.5 times. We found the same behavior also for the maximum earthing GIC. In practice, the line resistances are known quite accurately, so there is not much uncertainty related to them.

  2. [18] Decreasing the average length of a single transmission line decreases GIC [Pirjola, 2000]. For a more complex system, we considered the Finnish grid model and its modification with additional nodes as described in section 2. When assuming a spatially uniform electric field of 1 V/km to the north, the average GIC at the nodes is 38.7 A in the original grid. The corresponding result for an eastward field is 42.5 A. For the modified grid, the values are 20.3 A and 26.0 A, respectively.

  3. [19] Although national grids are typically connected to other countries, it is not necessary to take into account all of them if only one country is of interest. It is generally sufficient to include only the nearest substations of the neighboring countries [Viljanen and Pirjola, 1994; Pirjola, 2000].

[20] Generally, GIC modeling results are not sensitive to small modifications of the grid parameters. It follows that the results based on the old Finnish grid model can provide reasonable indicators for other networks too. The precise behavior of GIC naturally depends on the parameters of individual grids, so similar straightforward computations as shown here should be repeated separately for each case.

3.2 Dependence on Conductivity Models

[21] The geoelectric field and GIC have a pronounced dependence on the ground conductivity. The 1-D block models used in the EURISGIC project (Figure 1) contain a large variation of structures from low to high conductivities. So it is necessary to find out how much variability the conductivity models cause to GIC values.

[22] First, we calculated the conductances (S) of each different 1-D model of Figure 1 according to the definition

display math(1)

where σ is the conductivity as a function of depth (z, positive downward). As an example, we show the result for h=80 km in Figure 1 (bottom). We produced a ranking list of the block models according to the descending value of the conductance (Figure 5). The reason for showing the models in this order is that a large conductance is related to small electric fields and GIC. The conductances vary at a wide range over a few decades (note the logarithmic vertical scale in Figure 5).

Figure 5.

Ranking of conductivity models according to the conductance (depth range 0–80 km). Numbers over the bars refer to the models in Figure 1. The vertical scale is logarithmic (10 base).

[23] In a related test, we ranked the conductivity models using the modeled GIC in a given power grid. As the basic case, we applied the Finnish grid model and geomagnetic data of the highly active month of October 2003. The grid is kept at its true location, and we assume a single-block model of the ground conductivity at a time. The sum of GIC of the whole month at all nodes serves as the activity indicator (Figure 6). We note that the order of the ground models is not exactly the same as in Figure 5. This means that the conductance only provides a qualitative indicator for the electric field and GIC. The integration depth naturally affects the conductance, and details of layers affect the electric field.

Figure 6.

Ranking of conductivity models according to the sum of GIC of all nodes of the Finnish power grid using geomagnetic data of October 2003. Numbers over the bars refer to the different conductivity models in Figure 1.

[24] The most important result is that quite a large subset of the block models gives nearly equal GIC sums. The variability of GIC between different ground models is relatively much smaller than the range of conductances (note the linear vertical scale in Figure 6). We also performed ranking in the same way by using the much larger South and Central European power grid model of Viljanen et al. [2012]. The result is consistent with the Finnish grid.

[25] Based on Figures 56, we can identify three representative block models:

  1. [26] Block 12 in North Germany represents a good conductor (small GIC).

  2. [27] Block 01 in Lithuania represents an “average” conductor in the sense that several blocks give very similar results.

  3. [28] Block 24 in several regions in north Europe represents a poor conductor (large GIC).

[29] Based on these results, we use the parameters of block 01 when assuming a single-conductivity model across Europe (Table 1). We also apply this model on regions for which we have not defined a specific model in Figure 1, especially on sea areas.

[30] In a recent study, Wei et al. [2013] calculated the electric field using 25 different layered ground conductivity models of North America. They performed this calculation for several magnetometer stations during two strong geomagnetic storms. They normalized the peak electric field for each conductivity model to the peak value from the Interior Plains region in the United States. They finally ranked the conductivity models by the normalized peak electric field values. The range of these values varied between 0.38 and 2.41 except for one very small value of 0.07. Such a range is quite similar to what we obtained for the European conductivity models when ranked according to the modeled GIC (Figure 6).

[31] We remark that the local 1-D assumption is still a necessary practical simplification to perform computations with long data sets within a reasonable time. Close to the boundaries of conductivity blocks, the 1-D method obviously leads to inaccurate electric fields, and advanced 3-D modeling techniques should be applied as by Beggan et al. [2013] or Püthe and Kuvshinov [2013], for example.

3.3 GIC Levels Across Europe

[32] We placed the Finnish grid at different locations in Europe and calculated GIC at all nodes as 1 min time series in 2003. We quantified the GIC level by the total sum of GIC at all nodes within the year and by the maximum of the instantaneous 1 min sums. Calculations were performed with two ground models: the single model of Table 1 everywhere and the full model of Figure 1. We show normalized values in the plots. To give a quantitative reference, Table 3 lists the mean and maximum 1 min GIC at the substations, when the grid is at its true location.

Table 3. Modeled Values of the Mean and Maximum 1 Min GIC in 2003 at the Substations of the Finnish Grid at Its True Location and Using the Full Ground Conductivity Model of Figure 1
StationMean (A)Max (A)
Alajärvi0.1526.7
Alapitkä0.2954.7
Huutokoski0.5090.3
Hyvinkää0.069.9
Inkoo0.2247.3
Kangasala0.1034.5
Koria0.1628.7
Letsi1.80201.9
Lieto0.1138.0
Loviisa0.2338.0
Messaure0.8589.5
Nurmijärvi0.0717.1
Olkiluoto0.25110.5
Petäjäskoski0.93167.2
Pikkarala0.5563.2
Pirttikoski1.46230.0
Ulvila0.0825.8

[33] Figure 7 shows the results for the two ground conductivity models. When a single-conductivity model is assumed everywhere, we find a smooth decrease of GIC when going southward. This is related to the decreasing geomagnetic activity at lower latitudes.

Figure 7.

Sum of GIC in 2003 at all nodes of the shifted Finnish power grid using 1 min geomagnetic data. The values are assigned to the midpoint of the power grid close to station 11 in Figure 2. The values are scaled with respect to the value at the true location of the grid. (left) Single ground conductivity model of Table 1. (right) Full conductivity model of Figure 1.

[34] The situation becomes more complicated when the full conductivity map is used. There is still a clear decrease of GIC when going to the south. Generally, the peak values in north Europe are about 3–5 times larger than in central and south Europe. Different from the case of the single ground model, there is also a notable variation in the east-west direction depending on whether the grid is mostly located in highly or poorly conducting regions. We note that the values can be a little coincidental depending on which region the shifted grid is located. Additionally, the grid is sometimes at least partly on sea areas where the conductivity model is somewhat arbitrarily selected.

[35] When considering the maximum GIC (Figure 8), the result is still quite similar to the average case of Figure 7 in that the largest values dominantly occur in the north. The most prominent change happens with the full ground conductivity model, when the largest GIC peak occurs in southern Norway and southern Sweden. This is due to the small ground conductivities in this region enhancing the electric field. In most cases, the maximum value occurred in the evening of 30 October 2003, but in a few cases in the morning of the previous day when the Halloween storm began. So the values shown in Figure 8 do not correspond to a single time step. A more detailed analysis of the temporal and spatial features of GIC during the largest magnetic storms in Europe will be presented in a subsequent paper.

Figure 8.

Same as Figure 7, but for the maximum 1 min value of the sum of GIC at all nodes.

[36] There is quite a sharp decrease of GIC especially south of Sweden and Denmark below the boundary of about 55°N in geomagnetic latitudes. A similar boundary of a rapid decrease in the time derivative of the ground magnetic field and in the modeled geoelectric field was reported by Thomson et al. [2011], Pulkkinen et al. [2012], and Ngwira et al. [2013]. Ngwira et al. [2013] attribute the boundary location to the movement of the auroral oval. They also state that the maximum equatorward expansion of this boundary could be associated with the auroral electrojet current system, and therefore, it is determined by the saturation of the polar cap potential drop.

[37] Figure 8 shows that the maximum GIC in south and central Europe are mostly less than about one third of the values in Finland. Consequently, based on Table 3, the same Finnish grid would have experienced currents up to a few tens of amperes when located in south and central Europe. GIC in the western parts of the continent (especially France) are larger than at more eastern regions at the same latitudes. This is related to the increasing conductivities when going to the east (Figure 1). The largest GIC occur in South Norway and Sweden, which is due to the location of relatively high latitudes and small ground conductivities. These findings are in a good agreement with the results obtained when using the grid model of whole Europe and a larger data set of 1996–2008, to be discussed in detail in another paper.

[38] We also calculated the corresponding results for the modified grid with additional grounded nodes as described in section 3.1. As Figure 9 shows when compared to Figures  78, the pattern of the geographic variation is nearly identical to the results for the original grid model. Amplitudes of GIC are naturally different from the original case and on average smaller, as shown in Table 4. However, it is noteworthy that there are some stations where GIC becomes larger in the modified grid. The largest changes occur at the very nearby stations Hyvinkää and Nurmijärvi (sites 3 and 5 in Figure 2), so this part of the grid happens to be sensitive to changes in its configuration. At the new nodes not listed in Table 4, maximum GIC vary between 8 and 129 A.

Figure 9.

Characteristics of the sum of GIC at all nodes of the shifted Finnish power grid using 1 min geomagnetic data of 2003. The grid model is now modified from Figure 2 by adding a new grounded node at the midpoint of each transmission line. The full conductivity model of Figure 1 is applied. The values are scaled with respect to the value at the true location of the grid. (left) Sum of 1 min GIC in 2003 at all nodes. (right) Maximum 1 min value of the sum of GIC. Compare to the right-hand-side plots in Figures 78.

Table 4. Same as Table 3, but for the Modified Grid With New Grounded Nodes at the Midpoint of Each Transmission Linea
StationMean (A)Max (A)
  1. aWe show here only the same stations as in Table 3.
Alajärvi0.0922.5
Alapitkä0.1227.4
Huutokoski0.2351.9
Hyvinkää0.0623.6
Inkoo0.1524.9
Kangasala0.0729.1
Koria0.0611.7
Letsi1.70210.9
Lieto0.0618.7
Loviisa0.1527.0
Messaure1.10111.6
Nurmijärvi0.0729.4
Olkiluoto0.1982.0
Petäjäskoski0.53111.0
Pikkarala0.3653.8
Pirttikoski1.10174.1
Ulvila0.0410.7

[39] Our results apparently indicate a slightly smaller difference between northern and southern latitudes than found by Pulkkinen et al. [2012]. Figure 4b in Pulkkinen et al. [2012] shows that the maximum electric field on 29–31 October 2003 is about 10 times larger in the north compared to latitudes south of 50°. Our corresponding result on the left-hand side of Figure 8 gives a relatively smaller latitudinal variation. However, this is expected due to two reasons. First, we have applied a “medium” ground model instead of the very resistive one by Pulkkinen et al. [2012]. It follows that the electric field varies more smoothly in latitude consistently to Zheng et al. [2013]. Second, we consider GIC which depends on the electric field integrated along the transmission lines. Our grid has a north-south extension of 6.7° (about 700 km), so this obviously yields additional latitudinal smoothing.

4 Conclusions

[40] Based on a realistic local power grid model artificially located at different places in Europe, geomagnetic data of an active year 2003, and different 1-D models of the ground conductivity, we have shown that geomagnetically induced currents are on average clearly larger in north Europe than in central and south Europe. This difference is even more pronounced when considering the maximum values in 2003. These results follow from the facts that geomagnetic variations are more intense in the north and that the ground conductivity is smaller at many regions in the north than at more southern regions. We also showed that these results do not depend much on the grid model. We found the same features of GIC when using a grid with a larger number of grounded nodes but covering the same area.

[41] Because the parameters of the model grid are explicitly given, our results are generally applicable when assessing the GIC hazard in Europe. If the parameters of local grids elsewhere in Europe are different from our model case, it is still possible to get reasonable estimates of GIC magnitudes by scaling the results with respect to average resistances of the grid in question.

[42] Finally, we emphasize that the magnitude of GIC as such does not give a direct indicator to the sensitivity of a power grid to adverse effects. In other words, our results show how large GIC can occur in different parts of Europe, but we do not try to analyze their effects on the transformers and power system operation. This should be a topic of a future study. For example, the power grid in the high-latitude country Finland has never experienced serious GIC problems, although large currents up to 200 A have been measured there [Elovaara, 2007]. The same holds for Norway [Brekke et al., 2013], where our results indicate a possibility of even larger currents than in Finland. On the other hand, there were transformer damages in South Africa, located at magnetic midlatitudes, attributed to the strong magnetic storms in the end of 2003 [Gaunt and Coetzee, 2007; Kappenman and Radasky, 2005].

Acknowledgments

[43] The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement 260330.

[44] We greatly acknowledge Fingrid Oyj for a long-term collaboration in GIC studies in Finland. We thank the large number of institutes providing magnetometer data to the World Data Centre for Geomagnetism (Edinburgh) and INTERMAGNET, and to the IMAGE magnetometer network.

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