Assessing the hazard from geomagnetically induced currents to the entire high-voltage power network in Spain
© Torta et al.; licensee Springer. 2014
Received: 28 January 2014
Accepted: 16 July 2014
Published: 4 August 2014
After the good results obtained from an assessment of geomagnetically induced currents (GICs) in a relatively small subset of the Spanish power transmission network, we now present the first attempt to assess vulnerability across the entire Spanish system. At this stage, we have only included the power grid at the voltage level of 400 kV, which contains 173 substations along with their corresponding single or multiple transformers and almost 300 transmission lines; this type of analysis could be extended to include the 220-kV grid, and even the 110-kV lines, if more detailed information becomes available. The geoelectric field that drives the GICs can be derived with the assumption of plane wave geomagnetic variations and a homogeneous or layered conductivity structure. To assess the maximum expected GICs in each transformer as a consequence of extreme geomagnetic storms, a post-event analysis of data from the Ebre Geomagnetic Observatory (EBR) during the 2003 Halloween storm was performed, although other episodes coincident with very abrupt storm onsets, which have proven to be more hazardous at these mid-latitudes, were analyzed as well. Preferred geomagnetic/geoelectric field directions in which the maximum GICs occur are automatically given from the grid model. In addition, EBR digital geomagnetic data were used to infer statistical occurrence probability values and derive the GIC risk at 100-year or 200-year return period scenarios. Comparisons with GIC measurements at one of the transformers allowed us to evaluate the model uncertainties.
Solar-terrestrial physics is a discipline with a long tradition, and many observatories and research groups have been dedicated to this subject for a long time. However, as modern society has become more dependent on technological systems and therefore vulnerable to disturbances in the upper atmosphere and in the interplanetary space near Earth, the focus of this discipline evolved in new and important directions, and it has been renamed as space weather (e.g., Song et al. 2001). Space weather covers the study of the conditions in space that could affect human activity. Phenomena originating in the Sun that can affect human activity include explosive events such as flares and coronal mass ejections. These produce large quantities of energetic particles and solar wind disturbances, which travel through the interplanetary medium and affect the terrestrial environment. This solar activity is cyclical (solar cycle) and reaches a maximum approximately every 11 years.
The event that sparked global interest in this discipline, beyond academia, was the collapse of the power grid in northeastern Canada due to the great geomagnetic storm of 13 March 1989; this event left millions of people without power for 9 h (Bolduc 2002). In October-November 2003, during the declining phase of the next solar cycle, a series of events known as the Halloween storm occurred, and as a result, some new problems in electrical transmission networks were encountered (e.g., there was a blackout in the city of Malmö in southern Sweden (Pulkkinen et al. 2005; Wik et al. 2009)) and several space missions and satellites experienced numerous anomalies (Royal Academy of Engineering 2013). Motivated by the events of 2003, the Committee on Solar and Space Physics (CSSP) of the U.S. National Research Council (NRC) began to consider the need to systematically assess the social and economic impacts of space weather. To establish objectives for this research, the CSSP organized a workshop in Washington, D.C. during May 2008. The conclusions obtained as a result of that meeting can be found in the workshop report (U.S. National Research Council 2008). One of the most obvious conclusions revealed by the historical records is that past space weather events, such as the Carrington event in 1859 (Cliver and Dietrich 2013) and the great geomagnetic storm of May 1921 (Kappenman 2006), have been as much or even more severe than some of the more recent ones; this suggests that such extreme events, although rare, are likely to happen again sometime in the future. As stated in the workshop report, according to a study by the Metatech Corporation, today the occurrence of an event like the 1921 storm would result in large-scale blackouts affecting over 130 million people and would put more than 350 transformers at risk of permanent damage.
Geomagnetic storms caused by disturbances in solar conditions can affect the terrestrial environment including the magnetosphere, ionosphere, and magnetosphere-ionosphere interaction region; such effects are detectable at the surface of the Earth (e.g., Blanch et al. 2013). The highly conductive nature of the ionosphere produces significant current systems in this region, such as the equatorial and auroral electrojets. During disturbed conditions, there is a significant increase in these currents (the auroral electrojet can measure on the order of millions of amps). As these are time-varying, intense induced electric currents appear occasionally in conductors at the Earth's surface. The European Space Agency (ESA) launched the Swarm mission in November 2013 to better understand the magnetic field around Earth. This mission provides opportunities for near real-time in situ monitoring of the ionosphere and upper atmosphere (Stolle et al. 2013).
The induced electric currents generated by geomagnetic storms in ground-based technical networks are called geomagnetically induced currents (GICs). Their frequencies are typically in the millihertz range, and thus, they can be considered quasi-direct currents (quasi-dc). These currents can disrupt and damage our technological systems, e.g., by affecting transformers of high-voltage networks in the case of power transmission systems. Specifically, transformer cores can saturate under the effect of GICs by operating in the saturation region of the magnetization curve (B-H) of the steel core (Molinski 2002; Kappenman 2007). When a large number of transformers experience GIC saturation, the demand for reactive power and the harmonics of the system voltage are significantly increased. Reactive power demands of this magnitude can cause serious changes in the system voltage. At the same time, the change in the size of the ferromagnetic material (magnetostriction) between the saturated and unsaturated states at twice the power frequency produces heat, noise, and mechanical vibration damage (Koen and Gaunt 2002). The transformers may also suffer premature aging due to the effects of GICs. This aging can be detected by measuring the concentration of gas in the transformer oil. The harmful effects of magnetic storms on power grids have been observed both at high latitudes and at low and middle latitudes. Damage has even occurred in electrical networks at latitudes lower than Spain, such as in the case of South Africa during the Halloween storm of 2003 (Gaunt and Coetzee 2007). This event was related to the onset of damage in a 700 MVA transformer and in several smaller power transformers. It has been shown (Torta et al. 2012) that during that event, the amplitude of the variations of the horizontal geomagnetic field and its time derivative (dB H /dt), which is more important for geoelectric field generation, were significantly higher at the Ebre Observatory in Spain than in Hermanus, South Africa. It is therefore prudent that we assess the effects of magnetic storms on the Spanish power network.
Modeling efforts for calculating GICs in ground-based technological systems require a determination of the electric field that occurs in connection with a magnetic storm at the Earth's surface and a calculation of the resulting GIC (see Pirjola 2002). The practical calculation includes both a geophysical and an engineering problem because the surface geoelectric field is determined from geomagnetic recordings or from ionospheric-magnetospheric current data (if available) as the first step, and then the GIC flow is calculated under the given geoelectric field using the known topology and resistances of a conductor system.
For the determination of the geoelectric field, we have different possibilities. Going from the most sophisticated to the simplest one, one can choose exact formulas for the calculation of magnetic and electric fields at the Earth's surface due to an auroral electrojet, which include contributions from field aligned currents (e.g., Pirjola and Häkkinen 1991). However, the resulting formulas are complicated and unsuited to real-time calculations. On the basis of the experience obtained by this study, we attempt to use a practical procedure for the real-time calculation of GICs, which would allow organizations to find the best way of configuring the power system to mitigate their impact as fast as possible.
Here i, ω, and μ0 are the imaginary unit, the angular frequency, and the vacuum permeability, respectively. Both the complex skin depth and the surface impedance are defined in the frequency domain. As a first approximation to the auroral electrojet, Boteler and Pirjola (1998) derived algebraic expressions for the magnetic and electric fields at Earth's surface due to an infinite line current above the Earth using CIM. They considered two different conductivity models representative of Québec and British Columbia, which are resistive and conductive, respectively. It has been demonstrated that CIM gives a very good agreement with the exact methodology. Although it is a convenient tool for theoretical modeling purposes, it is not the most optimal choice for more operational applications because it was simply derived for a line current above the Earth. However, Pirjola and Viljanen (1991) show that the applicability of CIM is not restricted to the line current case as they extended the use of CIM to a more complicated ionospheric-magnetospheric current system. Pirjola et al. (2000) also show the successful use of CIM for a westward-traveling-surge (WTS) event.
Since the true 3-D ionospheric current system cannot be determined by using ground magnetometer data only, the method of Spherical Elementary Current Systems (SECS) (Amm 1997) can be used to introduce a horizontal equivalent current system, which produces the same magnetic and electric field at the Earth's surface. This method is based on the fact that geomagnetic variations at the Earth's surface can be explained by a horizontal divergence-free current system at the ionospheric level. The amplitudes of the elementary current systems are determined by the inversion technique, by fitting the modeled horizontal field to the measured one, and once the currents are determined, obtaining the electric field at the Earth's surface due to one element is straightforward. Inversion is usually resolved by the singular value decomposition technique because the system is typically underdetermined. Data for just three magnetic observatories have even been reported to have been used in the interpolation process to infer the equivalent ionospheric currents (Caraballo et al. 2013).
where B(ω) is the Fourier transform of the magnetic field (e.g., Viljanen et al. 2006). The integral in Equation 2 can be easily obtained numerically (Viljanen and Pirjola 1989). In evaluating that integral in practice, the lower limit of integration of Equation 2 is set to t-M, where M is the amount of time taken into account before t (for which the electric field is required). If this interval is sufficient, the time-dependent method (valid for a uniform Earth) provides the same results as the spectral method (valid for the layered Earth) provided that all the layers are given the same conductivity.
where 1, Y, and Z are the identity matrix, the n xn network admittance (related with the line resistances) matrix, and the earthing impedance (related with the earthing resistances) matrix, respectively; the n-element vector J contains information on the electric field computed, as described before, from geomagnetic observatory data.
where R i e is the resistance through which the node i is earthed. Pirjola (2008a, b) demonstrated that accounting for the off-diagonal elements of this matrix can be only relevant when the distances between the stations are on the order of hundreds of meters or less. In the Spanish 400-kV network described in the next section, only three node links are separated by less than 500 m (between approximately 350 and 450 m), so all the off-diagonal elements of the earthing impedance matrix were set equal to zero. In any case, neglecting all off-diagonal elements of Z is in general less important for the knowledge of the expected GICs than the uncertainties produced by the different approximations and assumptions adopted because it is not always possible to get precise values for all the circuit elements.
In summary, the external (or geophysical) conditions are contained in (E x , E y ), while the engineering problem is determined by the scalar constants a and b. Unless one evaluates continental regions (Viljanen et al. 2012), the Earth's curvature can be neglected and planar geometry (rather than spherical) can be used to derive these constants. Horton et al. (2012) even consider the fact that the Earth is not exactly a sphere but an ellipsoid (utilized in global positioning system (GPS) applications that power companies also use).
Results and discussion
Data and results
Information relating to the resistances of all the transformers is still incomplete, so that, for simplification, we completely ignored the autotransformers' low-voltage circuits, whereby the winding resistance is the sum of the common and the series resistances. For calculating the total earthing resistance at each substation, we considered the three phases in parallel and added the substation earthing resistance to their equivalent resistance. If the substation is composed of more than one transformer, we assumed that the transformers are connected in parallel and share the same substation earthing resistance. The values of these earthing resistances are in general unknown, but we assumed that they have a typical value of 0.15 Ω (private communication with related power engineers), except for those few substations of the Catalan subset for which we obtained a different value from our previous project. Similarly, in the cases where the resistance of the windings of transformers is unknown, following the criterion of Viljanen et al. (2012), we assumed that R i e takes a typical value of 0.5 Ω, which implies a total resistance for three parallel windings of 0.35 Ω, or 1.05 Ω for one winding. The phase resistances of the power transmission links were calculated according to the values of the resistance per unit length of the conductors at 20°C and the number of conductors per phase supplied by the power company. Then, one must take into account the reduction of three phases into a single conductor.
Clearly, in a real situation, the geomagnetic field varies in any direction and, consequently, so does the geoelectric field. Thus, the generated GICs will be variable but in proportion to the amplitudes shown in Figures 7 and 8. What is unchanged is the realization, as indicated by Boteler (1994) and Pirjola (2008b), that the GICs are maximized when the incident electric field is in the direction of the bisector of the angle formed by two transmission lines arriving at a substation and minimized in the perpendicular direction. Thus, the transformers at intermediate stations along a long line are not particularly vulnerable to GICs, and therefore, in principle, they are not interesting sites to undertake measurements.
The measured maximum and estimated 100-year and 200-year return levels at the Ebre Observatory
100-year return level
200-year return level
dB H /dt
dB D /dt
Errors by the omission of low-voltage circuits
Horton et al. (2012) provide the calculated GIC results in the network for two geoelectric field scenarios: again, a northward and an eastward uniform electric field of 1 V/km. It was found that we could obtain the same results with our programs. To achieve this, in the case of autotransformers, we had to make use of the concept of virtual nodes (Mäkinen 1993; Pirjola 2005) with an infinite resistance to ground and a resistance of a virtual line between the virtual and the real node equal to the series resistance of the actual autotransformer, while the common resistance is the resistance of the real transformer at the neutral point. Similarly, for full-wound transformers with a Y configuration and grounded both at high- and low-voltage sides, we used an equivalent circuit with two virtual nodes, one in each side of the transformer. Here, again, the virtual nodes have infinite resistances to ground and the virtual line resistances have been set between the virtual and real nodes equal to the real resistances of the transformer windings. Meanwhile, the actual transformer winding resistance was set to zero because it was located at the neutral point of the full-wound transformer.
Comparison of the total GICs flowing in the ground grid of each substation
GIC for northward E field (A)
GIC for eastward E field (A)
GIC for northward E field, HV only (A)
GIC for eastward E field, HV only (A)
GIC for northward E field (% diff.)
GIC for eastward E field (% diff.)
Comparison of the total GICs flowing in the transformer windings
GIC for northward E field (A/phase)
GIC for eastward E field (A/phase)
GIC for northward E field, HV only (A/phase)
GIC for eastward E field, HV only (A/phase)
GIC for northward E field (% diff.)
GIC for eastward E field (% diff.)
Comparisons with GIC measurements
The best way to evaluate the performance of a model such as the one described here is to compare its predictions at a particular transformer neutral point with actual GIC measurements. This, although planned, is still not possible at key sites such as the transformer at the Manzanares substation. The only measurements coincident with relevant geomagnetic storms were those obtained in 2011 to 2012 on behalf of our previous project (Torta et al. 2012). We do compare here the real observations with the predictions of our new model, including the entire 400-kV Spanish network, for the same transformer named TRP1 (which was wrongly named as TR2 in Torta et al. 2012) at the Vandellòs substation (node 132 in Figure 1) on the occasion of the geomagnetic storm which occurred during 24 to 25 October 2011. Fortunately, there are no autotransformers in this substation, so it is not galvanically interconnected with low-voltage systems and thus we do not expect major errors by ignoring the 220- or 110-kV networks at farther 400-kV stations (Pirjola and Viljanen 1991; Viljanen and Pirjola 1994; Pirjola 2005, 2010).
Quantification of the goodness of different model predictions
Since the calculated GIC at one site is slightly sensitive to changes made at distant points of the network (Pirjola 2009), our results can be reasonably compared with those presented in Figure 6 by Torta et al. (2012), when only a subset of the grid was modeled. It is well known that the load and operating procedure of the grid change over time. When we prepared our previous model, we did not have the exact elements of maintenance conditions (switched off) for the occasion of the geomagnetic storm, so we had to resort to the state of the grid that happened on a particular day about 3 months later, in which the lines Ascó (node 13 in Figure 1)-Pierola (node 98), Vandellòs (node 132)-Pierola (node 98), and Vandellòs (node 132)-Rubí (node 107) were switched off. Now, Red Eléctrica de España has provided us with updates regarding the elements of maintenance during 24 to 25 October 2011. The first important realization was that, on that occasion, one of the transformers at Vandellòs was switched off so that the total current produced by the geomagnetic storm could not be shared among the two transformers at that substation; hence, it only flew through the neutral point of the TRP1 transformer. This explains why the predictions of Torta et al. (2012) were underestimated and they had to artificially decrease the ground conductivity to match the amplitudes of measured and modeled GICs. However, although the overall amplitudes of the present study agree with more realistic conductivity values, our present results correlate worse with the measures of Torta et al. (2012). There are two explanations for this. The first one lies in the fact that Torta et al. (2012) used the time-domain integral approach to infer the electric field from the geomagnetic variation data by setting M equal to just 30 min. This converted the data into a surprising result because one would expect that the spectral method or the time-domain method with a sufficiently high M should give a better fit for the GIC data (in this study, we used values of M around 300 min, which yielded results similar to the spectral method). Using M = 30 means that Torta et al. (2012) truncated the impulse response to include only fast variations (i.e., high frequencies). This, in combination with the Earth model that is perhaps not exactly correct, happened to lead to a good fit with measured GIC data (R. Pirjola, D. Boteler, personal communication). A second explanation is related to the topology of the grid in the vicinity of the measuring substation. Besides the second transformer at Vandellòs, the switched off elements in the present model just included the Vandellòs-Rubí transmission line (other switched off elements far apart are not prone to influence the currents at Vandellòs). If we omit again the Vandellòs-Pierola line, the correlation significantly improves (Table 4, last row). We suspect that, although not reported, this transmission line or the Vandellòs-Garraf (node 51 of Figure 1) line, which runs almost parallel, was not operating for at least some time during the storm.
There is no doubt that space weather effects are an emerging natural hazard, which can have incredibly important effects on our lives, which are marked by increasing levels of technological dependence. They are in the category of high-impact, low-frequency event risks. When space weather effects refer to induced currents in technological systems such as power transmission grids, they are called geomagnetically induced currents, or simply, GICs. Modeling efforts require a determination of the electric field occurring in connection with a magnetic storm at the Earth's surface. There are several possible ways to accomplish this task. Once the geoelectric field is obtained, one can calculate the resulting GIC in the conductor system after obtaining a dc model of it. This engineering task requires knowledge of the geometrical configuration of the network stations and their connections, and also the resistance values of the whole system.
This paper provides much useful information about the expected GIC values in the entire Spanish 400-kV power transmission network, which enables us to conduct an assessment of the vulnerability from that hazard. The network contains 165 substations, to which we added 8 substations from France, Portugal, and Morocco across the respective borders. This represents a complex circuit with 375 transformers and 300 transmission lines. After obtaining the electrical network model to evaluate the maximum expected GIC in each transformer as a result of extreme geomagnetic storms, we developed a post-event analysis from the geomagnetic data obtained at the Ebre Observatory during certain storms, such as the Halloween storm in 2003. We also analyzed other episodes coincident with very abrupt sudden storm commencements, as they have proven to be even more dangerous in mid-latitudes. We found, as expected, that the most susceptible substations to GICs are those in corners or edges of the network. A typical case is that of the Manzanares station which, by having a single transformer, makes it particularly vulnerable. Had the storm of 24 March 1991 occurred with the current network configuration and with all the elements operative, GICs would exceed 100 A in the neutral point of the transformer. However, this extreme value will surely be significantly reduced when transmission lines that are under construction join Manzanares with another station to the east and become operational.
Assessing the vulnerability of a system to GIC hazards usually does not require knowledge of the precise values of expected GICs, instead rough magnitude estimates are sufficient (Pirjola 2008a). However, substantial improvements in our enterprise could be attained with further insights. A clear source of uncertainty in the obtained results arises from the fact of having completely ignored the low-voltage circuits that are galvanically connected to the 400-kV system through autotransformers. This was done because we had neither information on the 220 kV network nor the separate value of the common and series winding resistances of these autotransformers. The 110-kV grid obviously does not have a very big effect on the GIC in the 400-kV system since the lower the voltage, the higher the transmission line resistances, which makes the GICs smaller. The importance of the omission of the low-voltage network has been demonstrated through a test under a GIC benchmark network that has been recently developed by Horton et al. (2012).
To test the model performance on a substation close to the location of Ebre Observatory, where the geomagnetic data came from, a homogenous Earth and a couple of 1-D Earth conductivity models have been employed based on the sparse results of magnetotelluric surveys published in the geophysical literature. This could give rise to calculated geoelectric field amplitudes that may be scaled to incorrect values due to the lack of precise ground conductivity data. In the few sites in which GICs have been or will be effectively measured, the two geoelectric components should be given the correct relative weight when the calculated values are fitted to the measured GIC data (Pirjola 2009; Torta et al. 2012), but because the source field is not exactly a plane wave and the real Earth is not homogeneous, we must consider the specific value of proportionality between the GIC and the electric field only as an ‘effective conductivity’ (Viljanen 1998). Therefore, another improvement would be expected after realistically modeling the induced electric field on the surface of the Earth by using a 3-D model of Earth's conductivity, and this can be done in the manner of recent works such as those by Beggan et al. (2013), Dong et al. (2013), and Püthe and Kuvshinov (2013). In particular, Spain is located on a peninsula, so a precise estimation of the geoelectric field would benefit from modeling the effects of non-uniform conductivities produced by the coast (Gilbert 2005; Thomson et al. 2005; Bürstinghaus et al. 2013; Pirjola 2013).
A critical fact, nevertheless, is the difficulty of obtaining detailed network parameters in the precise instant of a geomagnetic storm and determining the topology of the network for a given amplitude of the incident field. The switching off of a key transmission line or transformer can be essential to boost significant currents through the remaining elements.
This research is part of the project ‘Geomagnetically induced currents in the power transmission network,’ which is funded by Red Eléctrica de España, S.A.U. The GIC measurement data at the Vandellòs substation were obtained by a previous project funded by ENDESA Distribución Eléctrica, S.L. We wish to thank Lluís Serrano, formerly at Ebre Observatory, for preparing most of the software used in this paper, and Ewan Dawson of the Geomagnetism Team, British Geological Survey, Edinburgh, for computing the values provided in Table 1. Some discussions with Risto Pirjola, David Boteler, and Ari Viljanen and their suggestions helped to improve our work. Finally, we wish to acknowledge Risto Pirjola and an anonymous reviewer for their valuable comments and constructive criticisms that greatly enhanced the quality of the manuscript.
- Albertson VD: Modeling and analysis of GIC. Proceedings of EPRI conference on geomagnetically induced currents, Burlingame, California, USA, 8–10 November 1989 1989.Google Scholar
- Amm O: Ionospheric elementary current systems in spherical coordinates and their application. J Geomag Geoelectr 1997, 49: 947–955. 10.5636/jgg.49.947View ArticleGoogle Scholar
- Beggan CD, Beamish D, Richards A, Kelly GS, Thomson AWP: Prediction of extreme geomagnetically induced currents in the UK high-voltage network. Space Weather 2013, 11: 407–419. doi:10.1002/swe.20065View ArticleGoogle Scholar
- Bernabeu EE: Modeling geomagnetically induced currents in Dominion Virginia Power using extreme 100-year geoelectric field scenarios–part 1. IEEE Trans Power Deliv 2013, 28: 516–523.View ArticleGoogle Scholar
- Blanch E, Marsal S, Segarra A, Torta JM, Altadill D, Curto JJ: Space weather effects on Earth's environment associated to the 24–25 October 2011 geomagnetic storm. Space Weather 2013, 11: 153–168. doi:10.1002/swe.20035View ArticleGoogle Scholar
- Bolduc L: GIC observations and studies in the Hydro-Québec power system. J Atmos Sol-Terr Phy 2002, 64: 1793–1802. 10.1016/S1364-6826(02)00128-1View ArticleGoogle Scholar
- Boteler DH: Geomagnetically induced currents: present knowledge and future research. IEEE T Power Deliver 1994, 9: 50–58. 10.1109/61.277679View ArticleGoogle Scholar
- Boteler DH, Pirjola RJ: The complex-image method for calculating the magnetic and electric fields at the surface of the Earth by the auroral electrojet. Geophys J Int 1998, 132: 31–40.View ArticleGoogle Scholar
- Boteler DH, Lackey AJC, Marti L, Shelemy S: Equivalent circuits for modelling geomagnetically induced currents from a neighbouring network. Proceedings of the 2013 IEEE power and energy society general meeting (PES), Vancouver, BC, 21–25 July 2013 2013. doi:10.1109/PESMG.2013.6672982Google Scholar
- Bürstinghaus EJ, Saha TK, Marshall RA, Yumoto K, Waters CL: The importance of non-uniform geoelectric fields in calculating GIC distributions. Proceedings of IEEE power and energy society general meeting 2013, 21–25 July 2013 2013. doi:10.1109/PESMG.2013.6672289Google Scholar
- Caraballo R, Sánchez Bettucci L, Tancredi G: Geomagnetically induced currents in the Uruguayan high-voltage power grid. Geophys J Int 2013, 195: 844–853. 10.1093/gji/ggt293View ArticleGoogle Scholar
- Cliver EW, Dietrich WF: The 1859 space weather event revisited: limits of extreme activity. J Space Weather Space Clim 2013, 3: A31. doi:10.1051/swsc/2013053View ArticleGoogle Scholar
- Dong B, Danskin DW, Pirjola RJ, Boteler DH, Wang ZZ: Evaluating the applicability of the finite element method for modelling of geoelectric fields. Ann Geophys 2013, 31: 1689–1698. 10.5194/angeo-31-1689-2013View ArticleGoogle Scholar
- Gaunt CT, Coetzee G: Transformer failure in regions incorrectly considered to have low GIC-risk. Paper presented at Power Tech 2007. Lausanne, Switzerland: Inst of Electr and Electron Eng; 2007.Google Scholar
- Gilbert JL Space Weather 3:S04A03. Modeling the effect of the ocean-land interface on induced electric fields during geomagnetic storms 2005. doi:10.1029/2004SW000120Google Scholar
- Horton R, Boteler D, Overbye TJ, Pirjola R, Dugan RC: A test case for the calculation of geomagnetically induced currents. IEEE Trans Power Deliv 2012, 27: 2368–2373. doi:10.1109/TPWRD.2012.2206407View ArticleGoogle Scholar
- Kappenman JG: Great geomagnetic storms and extreme impulsive geomagnetic field disturbance events – an analysis of observational evidence including the great storm of May 1921. Adv Space Res 2006, 38: 188–199. 10.1016/j.asr.2005.08.055View ArticleGoogle Scholar
- Kappenman JG: Geomagnetic disturbances and impacts upon power system operation. In The Electric Power Engineering Handbook. 2nd edition. Edited by: Grigsby LL. Auburn, Alabama: CRC Press/IEEE Press; 2007.Google Scholar
- Koen J, Gaunt CT: Geomagnetically induced currents at mid-latitudes. Proc URSI 27th Gral Ass, Maastrich, Netherlands, 17–24 August 2002 2002, 177.Google Scholar
- Lehtinen M, Pirjola R: Currents produced in earthed conductor networks by geomagnetically-induced electric fields. Ann Geophys 1985, 3: 479–484.Google Scholar
- Mäkinen M: Geomagnetically induced currents in the Finnish power transmission system. Helsinki, Finland: Geophysical publication n° 32, Finnish Meteorological Institute; 1993.Google Scholar
- Molinski TS: Why utilities respect geomagnetically induced currents. J Atmos Sol Terr Phys 2002, 64: 1765–1778. 10.1016/S1364-6826(02)00126-8View ArticleGoogle Scholar
- Myllys M, Viljanen A, Rui ØA, Ohnstad TM: Geomagnetically induced currents in Norway: the northernmost high-voltage power grid in the world. J Space Weather Space Clim 2014, 4: A10. doi: 10.1051/swsc/2014007View ArticleGoogle Scholar
- Ngwira M, McKinnell LA, Cilliers PJ: Geomagnetic activity indicators for geomagnetically induced current studies in South Africa. Adv Space Res 2011, 48: 529–534. 10.1016/j.asr.2011.03.042View ArticleGoogle Scholar
- Pirjola R: Review on the calculation of surface electric and magnetic fields and of geomagnetically induced currents in ground based technological systems. Surv Geophys 2002, 23: 71–90. doi:10.1023/A:1014816009303View ArticleGoogle Scholar
- Pirjola R: Effects of space weather on high-latitude ground systems. Adv Space Res 2005, 36: 2231–2240. doi:10.1016/j.asr.2003.04.074View ArticleGoogle Scholar
- Pirjola R: Study of effects of changes of earthing resistances on geomagnetically induced currents in an electric power transmission system. Radio Sci 2008., 43: RS1004, doi:10.1029/2007RS003704 RS1004,Google Scholar
- Pirjola R: Effects of interactions between stations on the calculation of geomagnetically induced currents in an electric power transmission system. Earth Planets Space 2008, 60: 743–751.View ArticleGoogle Scholar
- Pirjola R: Properties of matrices included in the calculation of geomagnetically induced currents (GICs) in power systems and introduction of a test model for GIC computation algorithms. Earth Planets Space 2009, 61: 263–272.View ArticleGoogle Scholar
- Pirjola RJ: On the flow of geomagnetically induced currents in an electric power transmission network. Can J Phys 2010, 88: 357–363. doi:10.1139/P10–028View ArticleGoogle Scholar
- Pirjola R: Practical model applicable to investigating the coast effect on the geoelectric field in connection with studies of geomagnetically induced currents. Adv Appl Phys 2013, 1: 9–28.Google Scholar
- Pirjola RJ, Häkkinen LVT: Electromagnetic field caused by an auroral electrojet current system model. In Environmental and space electromagnetics, Chapter 6.5. Edited by: Kikuchi H. Tokyo, Japan: Springer; 1991:288–298.View ArticleGoogle Scholar
- Pirjola RJ, Viljanen AT: Geomagnetic induction in the Finnish 400-kV power system. In Environmental and space electromagnetics, Chapter 6.4. Edited by: Kikuchi H. Tokyo, Japan: Springer; 1991:276–287.View ArticleGoogle Scholar
- Pirjola R, Boteler D, Viljanen A, Amm O: Prediction of geomagnetically induced currents in power transmission systems. Adv Space Res 2000, 26: 5–14. 10.1016/S0273-1177(99)01019-4View ArticleGoogle Scholar
- Pous J, Ledo J, Marcuello A, Daignières M: Electrical resistivity model of the crust and upper mantle from a magnetotelluric survey through the central Pyrenees. Geophys J Int 1995, 121: 750–762. 10.1111/j.1365-246X.1995.tb06436.xView ArticleGoogle Scholar
- Pulkkinen A: Geomagnetic induction during highly disturbed space weather conditions: studies of ground effects. Helsinki, Finland: Finnish Meteorological Institute Contributions, No. 42; 2003.Google Scholar
- Pulkkinen A, Amm O, Viljanen A, and the BEAR Working Group: Ionospheric equivalent current distributions determined with the method of spherical elementary current systems. J Geophys Res 2003, 108: 1053. doi:10.1029/2001JA005085View ArticleGoogle Scholar
- Pulkkinen A, Lindahl S, Viljanen A, Pirjola R Space Weather 3:S08C03. Geomagnetic storm of 29–31 October 2003: geomagnetically induced currents and their relation to problems in the Swedish high-voltage power transmission system 2005. doi:10.1029/2004SW000123Google Scholar
- Püthe C, Kuvshinov A: Towards quantitative assessment of the hazard from space weather. Global 3-D modellings of the electric field induced by a realistic geomagnetic storm. Earth Planets Space 2013, 65: 1017–1025. doi:10.5047/eps.2013.03.003View ArticleGoogle Scholar
- Royal Academy of Engineering: Extreme space weather: impacts on engineered systems and infrastructure. 2013. . Accessed 8 April 2014 http://www.raeng.org.uk/news/publications/list/reports/space_weather_full_report_final.pdf . Accessed 8 April 2014Google Scholar
- Song P, Singer HJ, Siscoe GL: Space weather. AGU Geophysical Monograph 125. Washington, D.C: American Geophysical Union; 2001.Google Scholar
- Stolle C, Floberghagen R, Luhr H, Maus S, Knudsen DJ, Alken P, Doornbos E, Hamilton B, Thomson AWP, Visser PN: Space weather opportunities from the Swarm mission including near real time applications. Earth Planets Space 2013, 65: 1375–1383. doi:10.5047/eps.2013.10.002View ArticleGoogle Scholar
- Thomson AWP, McKay AJ, Clarke E, Reay S: Surface electric fields and geomagnetically induced currents in the Scottish Power grid during the 30 October 2003 geomagnetic storm. Space Weather 2005., 3: S11002, doi:10.1029/2005SW000156 S11002,Google Scholar
- Thomson A, Reay S, Dawson E: Quantifying extreme behaviour in geomagnetic activity. Space Weather 2011., 9: S10001, doi:10.1029/2011SW000696 S10001,Google Scholar
- Torta JM, Serrano L, Regué JR, Sánchez AM, Roldán E: Geomagnetically induced currents in a power grid of northeastern Spain. Space Weather 2012., 10: S06002, doi:10.1029/2012SW000793Google Scholar
- Trichtchenko L, Boteler DH: Modelling of geomagnetic induction in pipelines. Ann Geophys 2002, 20: 1063–1072. 10.5194/angeo-20-1063-2002View ArticleGoogle Scholar
- U.S. National Research Council: Severe space weather events–understanding societal and economic impacts. Committee on the Societal and Economic Impacts of Severe Space Weather Events: A Workshop. Space Studies Board. Washington, D.C: National Research Council. National Academies Press; 2008.Google Scholar
- Viljanen A: Relation of geomagnetically induced currents and local geomagnetic variations. IEEE Trans Power Deliv 1998, 13: 1285–1290. 10.1109/61.714497View ArticleGoogle Scholar
- Viljanen A, Pirjola R: Statistics on geomagnetically-induced currents in the Finnish 400 kV power system based on recordings of geomagnetic variations. J Geomag Geoelectr 1989, 41: 411–420. 10.5636/jgg.41.411View ArticleGoogle Scholar
- Viljanen A, Pirjola R: Geomagnetically induced currents in the Finnish high-voltage power system. Surv Geophys 1994, 15: 383–408. 10.1007/BF00665999View ArticleGoogle Scholar
- Viljanen A, Pulkkinen A, Pirjola R, Pajunpää K, Posio P, Koistinen A: Recordings of geomagnetically induced currents and a nowcasting service of the Finnish natural gas pipeline system. Space Weather 2006., 4: S10004, doi:10.1029/2006SW000234 S10004,Google Scholar
- Viljanen A, Pirjola R, Wik M, Ádám A, Prácser E, Sakharov Y, Katkalov J: Continental scale modelling of geomagnetically induced currents. J Space Weather Space Clim 2012, 2: A17. doi:10.1051/swsc/2012017View ArticleGoogle Scholar
- Wait JR: Wave Propagation Theory. Tarrytown, New York: Pergamon; 1981.Google Scholar
- Wik M, Viljanen A, Pirjola R, Pulkkinen A, Wintoft P, Lundstedt H: Calculation of geomagnetically induced currents in the 400 kV power grid in southern Sweden. Space Weather 2008., 6: S07005, doi:10.1029/2007SW000343 S07005,Google Scholar
- Wik M, Pirjola R, Lundstedt H, Viljanen A, Wintoft P, Pulkkinen A: Space weather events in July 1982 and October 2003 and the effects of geomagnetically induced currents on Swedish technical systems. Ann Geophys 2009, 27: 1775–1787. 10.5194/angeo-27-1775-2009View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.