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SPACE WEATHER, VOL. 7, S10002, doi:10.1029/2009SW000478, 2009
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Limitations of the modeling of geomagnetically induced currents in the South African power network Chigomezyo M. Ngwira,1,2 Lee-Anne McKinnell,1,2 Pierre J. Cilliers,2 Ari Viljanen,3 and Risto Pirjola3 Received 26 February 2009; revised 28 July 2009; accepted 9 August 2009; published 8 October 2009.
[1] Geomagnetically induced currents (GICs) are known to affect electric power systems in both the midlatitude and high-latitude regions. Monitoring of GICs in the southern African electrical power grid first started in 1998 with the installation of the Electric Power Research Institute Sunburst monitoring system. Recent research efforts in South Africa have shown that the modeling of GICs is effectively improved by the use of a multilayered ground conductivity model and a modified set of network coefficients. This paper reports on an investigation into the reliability of a new GIC model versus the distance between the magnetometer stations and the GIC measuring site using recent developments within this field and the South African context. Results show that the modeling of GICs degrades with increasing distance between the geomagnetic observation station and the GIC site and that the newly developed GIC model is only appropriate for the specific geomagnetic station and GIC site pair. Citation: Ngwira, C. M., L.-A. McKinnell, P. J. Cilliers, A. Viljanen, and R. Pirjola (2009), Limitations of the modeling of geomagnetically induced currents in the South African power network, Space Weather, 7, S10002, doi:10.1029/2009SW000478.
1. Introduction [2] Geomagnetically induced currents (GICs) are the low-frequency currents (0.01 -- 1 Hz) that flow in power networks as a result of space weather activity and the subsequent rapid variations in the geomagnetic field. GICs can cause transformer saturation which may lead to transformer malfunctions and in worst cases power blackouts and permanent damage of transformers [Kappenman, 1996; Molinski, 2002]. These adverse effects of GICs, such as transformer damages have been reported on the South African power network system [Kappenman, 2005; Gaunt and Coetzee, 2007]. [3] Monitoring of GICs in the southern African region is limited by the lack of adequate monitoring equipment (i.e., magnetometers and GIC monitors). This implies that GIC studies have to be based on reliable modeling techniques. Accurate modeling of the geoelectric field at the surface of the Earth is dependent on ionospheric current and ground conductivity models [e.g., Pirjola, 2000; Trichtchenko and Boteler, 2004; Pulkkinen et al., 2007]. Ngwira 1 Department of Physics and Electronics, Rhodes University, Grahamstown, South Africa. 2 Hermanus Magnetic Observatory, Hermanus, South Africa. 3 Finnish Meteorological Institute, Helsinki, Finland.
Copyright 2009 by the American Geophysical Union
et al. [2008] show that the use of a multilayered ground conductivity structure can effectively improve the modeling of GICs. However, the model derived by them was only tested with geomagnetic data from the Hermanus Magnetic Observatory (HMO) together with GIC data from the Grassridge 400 kV substation in South Africa. Thus, they state that their new ground model ought to be used with caution as it may not work well with data from other sites. This is due to the electrical ground conductivity anomalies known to exist in southern Africa [Hamilton et al., 2006; Weckmann et al., 2007]. This fact probably excludes the possibility of using local conductivity models to compute regional geoelectric fields as earlier done in Finland [Pulkkinen, 2003, and references therein]. [4] Further, the distances between the GIC sites and the magnetometer stations are very large in southern Africa. Koen [2002] was able to model GIC for locations of more than about 590 km from the magnetometer station. However, the modeling efficiency of the new GIC model has not been tested beyond this spatial scale. In this paper we use magnetic observatory data and equation (2) which gives GIC at Grassridge, to test the applicability of the conductivity model by Ngwira et al. [2008]. We show that the modeling efficiency of the recently developed GIC model degrades with increasing distance between the geomagnetic observatory and the GIC site and that the model is only valid for a specific geomagnetic observatory
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[6] The GIC data for the first 12 h of 29 October, which were not used in the model derivation process, were utilized for Grassridge power substation (25.6°E, 33.7°S) in South Africa. The 2-s data provided as part of the Sunburst GIC project were binned and then each bin was averaged to a 1-min sampling interval. Figure 1 shows the locations of the two South African geomagnetic observatories at Hermanus and Hartebeesthoek, the Tsumeb observatory in Namibia, the Grassridge GIC site and the 11 sites where the B field is interpolated as discussed later in this paper. [7] GIC studies can effectively be carried out in two independent steps. The first step is the determination of the horizontal geoelectric field at the Earth’s surface and the second step is the computation of the GIC based on the geoelectric field and the network configuration and parameters. The horizontal components of the geoelectric field Ex,y and of the geomagnetic field Bx,y are related through the frequency-dependent surface impedance and can be expressed as Ex;y ðwÞ ¼
Figure 1. Map showing the positions (red squares) of the geomagnetic observatories at Hermanus (HMO), Hartebeesthoek (HBK), and Tsumeb (TSU); the GIC recording site (black circle) at Grassridge power substation (GSS); and the 11 sites (asterisks, S1 --S11) where the B field was determined. The blue diamonds are the two major towns near to our stations at HMO and GSS. and GIC site pair. Magnetic field data from the three regional observatories were then used as input to the spherical elementary current systems method, which gives the interpolated field for selected locations were a field is required but no observatory exists. Then GIC values at Grassridge were calculated as above and the root mean square deviation values were computed for each case. The results suggest that the inefficiency in the modeling may be due to the spatial nonuniformity of the geomagnetic variation field, which was assumed to be uniform across the southern African region in the application by Koen [2002].
2. Data and Methods [5] The geomagnetic data used in this study were taken from three southern African geomagnetic observatories at Hermanus (19.2°E, 34.4°S), Hartebeesthoek (27.7°E, 25.9°S) and Tsumeb (17.4°E, 19.2°S) for the storm period of 29 -- 31 October 2003, with the locations given in geographic coordinates. The 1-min mean values of the horizontal components X and Y were recorded using three-axis suspended FGE fluxgate magnetometers manufactured by the Danish Meteorological Institute.
ZðwÞ By;x ðwÞ; m0
ð1Þ
where Z(w) is the surface impedance, w is the angular frequency and m0 is the permeability of free space [e.g., Dmitriev and Berdichevsky, 1979]. To simplify the modeling, it is usually assumed that the Earth’s conductivity (s) varies only in the vertical (z) direction. [8] In principle, equation (1) presumes that the electric and magnetic fields have no spatial dependence in the area considered; that is, we have the ‘‘plane wave’’ case. This is usually an acceptable assumption at midlatitudes in the absence of conductivity anomalies. However, Viljanen et al. [2004] have shown that equation (1) can be applied to infer the GIC at a specific site from local values of the electric field, magnetic field and the site-specific surface impedance, even when the fields and impedance may vary from one site to another. [9] For a spatially constant geoelectric field, GICs can be modeled by the equation GIC ðtÞ ¼ a Ex ðt Þ þ b Ey ðt Þ;
ð2Þ
where the GIC and electric field are local (site specific) and the coefficients a and b are specific to each transformer and power line. The coefficients a and b depend only on the resistances and configuration of the power system [Viljanen and Pirjola, 1994]. This study uses the network coefficients a = 80 A km/V and b = 1 A km/V for Grassridge [Ngwira et al., 2008].
3. Results [10] The plane wave method is applied to the computation of the geoelectric field first by using Hermanus geomagnetic data and the layered ground conductivity 2 of 5
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Figure 2. Comparison of measured GIC and modeled GIC for the Halloween storm of 29 October 2003. (top) GIC modeled using Hermanus geomagnetic field data. (middle) GIC modeled using Hartebeesthoek geomagnetic field data. (bottom) GIC modeled using Tsumeb geomagnetic field data. The interval shown here was not used in the derivation of the ground conductivity model.
model. Then the applicability of the same model to other geomagnetic observatory data is tested by separately computing the geoelectric field using Hartebeesthoek and Tsumeb geomagnetic data. We then compare the computed and the measured GIC for the Halloween storm event of 29 October 2003 and the results are shown in Figure 2. The October 2003 storm is the only storm for which GIC measurements are available to the authors. [11] The distances of the three geomagnetic stations from the Grassridge GIC site are about 590, 892 and 1759 km for Hermanus, Hartebeesthoek and Tsumeb, respectively. Figure 2 shows that the performance of the data sets for Hartebeesthoek and Tsumeb is not as good as for Hermanus, so the results degrade with an increasing distance of the magnetometer from the GIC site. Particularly notable in Figure 2 is the failure of the data from Hartebeesthoek and Tsumeb to efficiently represent the
amplitude of the GIC peaks seen between the hours 0600 to 0700 and 0700 to 0800 UT. [12] We then make use of the median error and root mean square Pndeviation (RMSD). The RMSD is defined as RMSD = ( i¼1 (GICmeasured,i GICmodeled,i)2/n)1/2. We
consider 152 data points for values corresponding to jGICmeasuredj > 1 A. The median errors for Hermanus, Hartebeesthoek and Tsumeb distributions are 48%, 64% and 74% with RMSD values of 1.56, 2.21 and 2.73 A, respectively, which agree with the observations in Figure 2. These results emphasize the importance of proximity for an efficient modeling of GICs.
[13] Our results confirm earlier findings by Bernhardi et al. [2008] who used the method of spherical elementary current systems (SECS) to show that the surface geoelectric field in southern Africa was spatially varying and could not be modeled by only using geomagnetic data
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Figure 3. Calculated horizontal geoelectric field as derived using geomagnetic data from each of the three observatories and the layered Earth model for the 29 December 2003 storm. from a single observatory for the entire network. For more details of the application of the SECS method, see [e.g., Amm, 1997; Pulkkinen et al., 2003a, 2003b; Viljanen et al., 2004]. Figure 3 is a comparison of the calculated horizontal geoelectric fields as derived using geomagnetic data from each of the three observatories and the layered Earth model for the 29 December 2003 storm. The spatial and temporal characteristics of the geoelectric field can clearly be seen in Figure 3. [14] Next, the southern Africa SECS model is used to interpolate the geomagnetic field at each of the 11 different sites separately. We compute the GIC at Grassridge based on the interpolated magnetic field at sites 1 -- 11.
Table 1. GIC Variations for Sites North of Grassridge Using an Interpolated Magnetic Field Site
Distance From Grassridge (km)
Grassridge Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 HBK
0 122 231 314 535 606 880 892
Geographic Coordinate 33.7°S, 32.4°S, 30.4°S, 30.6°S, 28.7°S, 27.8°S, 26.2°S, 27.7°S,
25.6°E 25.7°E 25.7°E 25.6°E 24.8°E 25.5°E 22.8°E 25.9°E
RMSD for GIC > 1 A (A) 1.61 1.60 1.62 1.65 1.74 1.88 1.93 2.21
Then a comparison of the computed with the measured GIC for GIC > 1 A is made using the RMSD. The results are shown for sites north and west of Grassridge in Tables 1 and 2, respectively. These directions represent the approximate configuration of Hartebeesthoek and Hermanus with respect to Grassridge. [15] From Tables 1 and 2, it is noted that the variations in the north direction are much larger than those seen in the western direction. This implies that the changes in the geomagnetic field due to the storm vary more in the north-south direction than in the east-west direction. It is important to note that within a north-south distance of about 314 km, the change in the geomagnetic field is about the same as the east-west change over 722 km and is considered insignificant in terms of GIC variations.
Table 2. GIC Variations for Sites West of Grassridge Using an Interpolated Magnetic Field Site
Distance From Grassridge (km)
Site 7 Site 8 Site 9 Site 10 Site 11 HMO
190 282 395 496 722 590
Geographic Coordinates 33.8°S, 33.7°S, 33.7°S, 33.7°S, 32.8°S, 34.4°S,
23.6°E 22.6°E 21.4°E 20.3°E 17.9°E 19.2°E
RMSD for GIC > 1 A (A) 1.54 1.53 1.52 1.53 1.51 1.56
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However, the geomagnetic field is almost uniform in the east-west direction resulting in almost uniform GIC variations as seen in Table 2.
4. Conclusions [16] It is shown that the reliability of our GIC modeling degrades with increasing north-south distance of the geomagnetic station from the GIC site as shown in Figure 2. The reason for this failure is due to the variation of the geomagnetic field with latitude as shown in Tables 1 and 2. This case study indicates that the geoelectric field can be modeled fairly accurately in the low-latitude to midlatitude region within a spatial scale of about 600 km in the east-west direction but that the field falls off fairly quickly in the north-south direction. Therefore, even though the layered ground model improves the accuracy of GIC modeling, currently it can only be applied for data from a specific geomagnetic and GIC site pair. The peak amplitudes which are important factors in terms of GIC effects are compromised with increasing distance. It is thus important to use geomagnetic observatory data nearer to the GIC site as explained by Pulkkinen [2003] and Viljanen et al. [2004]. This implies that the accuracy of GIC modeling will improve if more magnetometers are deployed in the immediate vicinity or within a north-south distance of 300 km of the GIC sites. [17] In conclusion, it should be stated that to achieve maximum efficiency required for GIC modeling, the layered ground model derived by Ngwira et al. [2008] is well applicable to GIC at the Grassridge 400 kV substation with geomagnetic field data from the Hermanus Magnetic Observatory. [18] Acknowledgments. The authors would like to thank Antti Pulkkinen for his great support in South African GIC research. We would like to extend our gratitude to Edward Bernhardi for his support to this work. Chigomezyo Ngwira would like to acknowledge the National Astrophysics and Space Science Programme for the financial support.
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Power Tech, pp. 807 -- 812, Inst. of Electr. and Electr. Eng., New York. Hamilton, M. P., A. G. Jones, R. L. Evans, S. Evans, C. J. S. Fourie, X. Garcia, A. Mountford, and J. E. Spratt (2006), Electrical anisotropy of South Africa lithosphere compared with seismic anisotropy from shear-wave splitting analyses, Phys. Earth Planet. Inter., 158, 226 -- 239. Kappenman, J. G. (1996), Geomagnetic storms and their impact on power systems, IEEE Power Eng. Rev., 16, 5 -- 8. Kappenman, J. G. (2005), 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, Space Weather, 3, S08C01, doi:10.1029/2004SW000128. Koen, J. (2002), Geomagnetically induced currents in the southern African electricity transmission network, Ph.D. thesis, Univ. of Cape Town, Cape Town, South Africa. Molinski, T. S. (2002), Why utilities respect geomagnetically induced currents, J. Atmos. Sol. Terr. Phys., 64, 1765 -- 1778. Ngwira, C. M., A. Pulkkinen, L.-A. McKinnell, and P. J. Cilliers (2008), Improved modeling of geomagnetically induced currents in the South African power network, Space Weather, 6, S11004, doi:10.1029/2008SW000408. Pirjola, R. (2000), Geomagnetically induced currents during magnetic storms, IEEE Trans. Plasma Sci., 28(6), 1867 -- 1873. Pulkkinen, A. (2003), Geomagnetic induction during highly disturbed space weather conditions: Study of ground effects, Ph.D. thesis, Univ. of Helsinki, Helsinki. Pulkkinen, A., O. Amm, and A. Viljanen (2003a), Ionospheric equivalent current distributions determined with the method of spherical elementary current systems, J. Geophys. Res., 108(A2), 1053, doi:10.1029/2001JA005085. Pulkkinen, A., O. Amm, A. Viljanen, and T. Korja (2003b), Separation of the geomagnetic variation field on the ground into external and internal parts using the spherical elementary current system method, Earth Planets Space, 55, 117 -- 129. Pulkkinen, A., R. Pirjola, and A. Viljanen (2007), Determination of the ground conductivity and system parameters for optimal modeling of geomagnetically induced current flow in technological systems, Earth Planets Space, 59, 999 -- 1006. Trichtchenko, L., and D. H. Boteler (2004), Modeling geomagnetically induced currents using geomagnetic indices and data, IEEE Trans. Plasma Sci., 32(4), 1459 -- 1469. Viljanen, A., and R. Pirjola (1994), Geomagnetically induced currents in the Finnish high-voltage power system, Surv. Geophys., 15, 383 -- 408. Viljanen, A., A. Pulkkinen, O. Amm, R. Pirjola, T. Korja, and BEAR Working Group (2004), Fast computation of the geoelectric field using the method of elementary current systems and planar Earth models, Ann. Geophys., 22(1), 101 -- 113. Weckmann, U., O. Ritter, A. Jung, T. Branch, and M. de Wit (2007), Magnetotelluric measurements across the Beattie magnetic anomaly and the Southern Cape Conductive Belt, South Africa, J. Geophys. Res., 112, B05416, doi:10.1029/2005JB003975.
P. J. Cilliers, Hermanus Magnetic Observatory, Box 32, Hermanus 7200, South Africa. (
[email protected]) L.-A. McKinnell and C. M. Ngwira, Department of Physics and Electronics, Rhodes University, Box 94, Grahamstown 6139, South Africa. (
[email protected];
[email protected]) R. Pirjola and A. Viljanen, Finnish Meteorological Institute, FIN-00101 Helsinki, Finland. (
[email protected])
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