We used 10 s geomagnetic field data from the IMAGE (International Monitor for Auroral Geomagnetic Effects) magnetometer network. At the time of the Halloween storm in October 2003, 26 magnetometers were operational in the Fennoscandian region. The IMAGE magnetometer network has been used to compute the equivalent ionospheric currents, which represent the horizontal ionospheric currents that would be required to produce the observed ground magnetic variations . This approach is used to obtain the magnetic field all over Sweden. Moreover, since ground-based geomagnetic measurements include both external component (Bext) produced by ionospheric and magnetospheric currents, and internal component (Bint) produced by induced telluric currents, the method has been further refined to separate these components, as described by . We refer the reader to and for a more detailed explanation of the ionospheric equivalent current technique and its applications.

The GIC-SMAP model calculates the horizontal geoelectric field EH(ω)=Z(ω)μ0-1BH(ω) in the frequency domain by relating the ground impedance tensor Z(ω) to local magnetic field perturbations BH(ω). An inverse Fourier transform is then applied in order to transform into the time domain. In a new version of the model, where the EH is computed at every point of the grid in Sweden, the magnetic field data is first interpolated using the Spherical Elementary Current System (SECS) method using all available IMAGE stations.

The ground impedance tensor was previously obtained by computing the geoelectric field using a uniform magnetic field variation with unit amplitude, by solving the equations describing the current distribution in the ground in the frequency domain using the commercial software COMSOL Multiphysics for a unit-amplitude (H0=1 A m⁻¹), uniform magnetic source field applied at 100 km altitude for a fixed set of frequencies (1–100 mHz). For further description of the COMSOL technical setup, see the supporting information (S2) in and for additional details about the model.

The main source of uncertainty in the GIC-SMAP model arises from the sparse distribution of active IMAGE magnetometers in Sweden used in the SECS method to interpolate the magnetic field onto the model grid. Additional sources of uncertainty arise from the conductivity model . First, the underlying crustal conductivity map for the Fennoscandian Shield (SMAP) is well constrained by extensive magnetotelluric surveys in northern Sweden, whereas large parts of southern Sweden remain sparsely surveyed and rely more heavily on extrapolated conductivity estimates. Second, the calculation of the surface impedance assumes a uniform magnetic field, whereas in reality, the magnetic field exhibits spatial variability. Third, frequencies below 1 mHz may contribute to the amplitude of the geoelectric field when superimposed on the higher frequencies .

The model has been validated against GIC measurements in both northern and southern Sweden , indicating that the uniform-source-field assumption performs well during geomagnetically quiet periods, while further validation during geomagnetically active intervals remains pending.

The recently developed RAISE model (Rymdvädersmodell för Analys av Inducerade Strömmar och Elektriska fält, Swedish for “Space Weather Model for the Analysis of Induced Currents and Electric Fields”), introduced by , was employed to analyze the voltages in the Swedish power grid lines. The simplified Swedish power grid representation consists of 194 nodes and 335 transmission lines, of which 49 % are 400 kV lines and 51 % are 220 kV lines. This model has previously been applied to investigate GIC activity during the April 2023 and May 2024 geomagnetic storms . RAISE integrates the GIC-SMAP model with a simplified representation of the Swedish high-voltage power grid, assuming constant earthing resistance and fixed line resistances for both 200 and 400 kV transmission lines. Due to this simplification in line resistances, the results presented here focus on calculated voltages without explicitly computing the corresponding GICs.

The RAISE model relies on the following assumptions and simplifications:

Only transmission lines and power stations operated by the Swedish authority responsible for the electrical transmission system, Svenska Kraftnät (SvK), are included. Substations and lines owned by regional or private operators are not part of the dataset.

The magnetic field time series used in Case 1 are presented in Fig.  and visualized in more detail in the animation Case1_BE.mp4 (panels a, b, c), which consists of frames spanning 19:40 to 20:30 UT (50 min) with a 10 s timestep. Figure a shows the interpolated horizontal magnetic field component (BH), based on data from the magnetic stations marked with black dots. The magnetic field components Bx and By time series at the locations indicated by a star in Fig. a are presented in Fig. b, c. Around 19:47 UT, a local substorm onset occurred, marked by the initial drop in Bx, indicating the presence of a WEJ centred over the Fennoscandian region. During this period the WEJ peaked ∼ 19:53:00–19:58:00 and ∼ 20:02:00–20:08:40 UT, which have been suggested to be caused by dipolarization of the nightside inner magnetosphere . This is also observed in the BH time series at the locations indicated by a star in Fig. a, each location representing a different MLAT band in Sweden. Bx peaks around 19:56 in Northern Scandinavia (>60° MLAT), a few minutes later Bx peaks in central and Southern Scandinavia (54–60° MLAT) around 20:04. Finally, a secondary Bx depression appeared at latitudes above 60° MLAT, followed by an abrupt weakening of Bx and a concurrent increase in By between 20:08 and 20:10 UT.

The maximum estimated EH between 19:40 and 20:30 UT is summarized in Fig. a, together with the EH time series at the locations marked by stars in Fig. b, c. The maximum values of the horizontal geoelectric field (Max(EH)) occur along the Norwegian coast due to the well-known coastal effect with values of 10 up to ∼30 V km⁻¹. During this time interval, regions of Sweden distant from the north-west coast experienced EH values around 2 V km⁻¹, with local maxima between 4 and 8 V km⁻¹ in areas with pronounced conductivity gradients, and generally remaining below 1 V km⁻¹ in regions of high conductivity.

The time series in Fig. b, c shows that almost all locations experienced the maximum dBH/dt=dBx/dt2+dBy/dt2 at the moment of the abrupt weakening of the WEJ at 20:08:30 UT, with a maximum near 62° MLAT (violet line). The magnitude gradually decreases at higher latitudes and drops off more sharply toward lower latitudes. The peaks in EH generally occur during periods of elevated dBH/dt. However, the maximum values of EH do not coincide exactly with the peaks in dBH/dt. We notice that the time series around 60° MLAT (red line) presents relatively larger EH values during the whole substorm.

The EH maps during the evolution of the substorm are provided in the animation Case1_BE.mp4 (panel e). In Sweden, large EH values first appear in the north at the times when the WEJ peaks (19:55 UT), then shifts toward central Sweden by 19:58 UT, and reach lower latitudes near 20:04 UT (second WEJ peak), affecting a broad area of southern and central Sweden. Four minutes later, at 20:07:20 UT, the EH maximum moves back to higher latitudes as the substorm evolves. Large geoelectric fields are again observed in central and southern Sweden around 20:08:50 UT, just after the WEJ weakening.

The EH values were scaled to a 1-in-100-year event according to the MLAT bands presented in Table . The scaled EH and the corresponding response in the Swedish power grid are illustrated in more detail in the animation Case1_EGrid.mp4. In northern Sweden, where the scale factor is 1 (i.e., no scaling is applied), maximum EH values reach only about 2 V km⁻¹. In contrast, southern and central Sweden show EH about 2–6 and 6–10 V km⁻¹ respectively. The largest EH values are observed between 55 and 58° MLAT, with values of around 6–10 V km⁻¹ and a peak of approximately 12–15 V km⁻¹ occurring in regions with pronounced conductivity gradients (Midskog, Töreboda, Söderhamn, Vittersjö, Göteborg). The maximum scaled EH is summarized in Fig.  and will be described in Sect. .

In Case 2, we assume that a large-scale ionospheric current covers all Fennoscandia. The ionospheric equivalent current shown in Fig. a confirms that a current system was indeed present, but was limited to northern and central Fennoscandia, with a maximum between Finland and Sweden. The right panel of Fig.  shows BH,ext and its time derivative at the magnetic stations along Finland and Estonia (solid lines) and in Sweden (dashed lines). This highlights the waveform variations across latitudes, showing similarities among the higher-latitude and, separately, among the lower-latitude, though with notable differences in amplitude. The maximum dBH,ext/dt is observed almost simultaneously across all locations at 20:08:30 UT, with a maximum near 60° MLAT (red line). The dBH,ext/dt magnitude gradually decreases at higher latitudes and drops off more sharply toward lower latitudes. Due to the latitudinal differences in the waveforms, we had to determine which one was most representative of the current system to later apply it across the entire region. As a first approach, we selected the waveform from the OUJ station, as it was located near the centre of the ionospheric current and exhibited the largest dBH,ext/dt. We also considered the magnetic field data from the HAN station, which showed a similar evolution but with a lower dBH,ext/dt. Data from these two stations were used to compute the ground geoelectric field, and the waveform that produced the largest geoelectric field was selected.

The 3D geoelectric field response in Sweden, computed using uniform magnetic field waveforms from OUJ and HAN ground-based stations as inputs, is shown in Fig. . Differences in induced EH at fixed positions are primarily driven by variations in the input BH,ext. Although the OUJ and HAN stations exhibit similar BH,ext waveforms (Fig. a, d), the magnitude and perturbations are larger at OUJ; however, the induced geoelectric fields calculated using BH,ext from HAN at the locations marked with stars in Fig. a were greater than those calculated using BH,ext from OUJ. This highlights how the geoelectric field is strongly influenced not only by the local ground conductivity but also by the frequency content of geomagnetic field variations. As shown in Fig. 9, two distinct dH/dt peaks are observed around the time of the transformer trip event, yet the largest peak in the geoelectric field corresponds to the smaller of the two dBH/dt peaks, further illustrating the non-linear and frequency-dependent nature of the relationship between magnetic and geoelectric fields.

For the scenario evaluated in this study, we chose the HAN station waveform, which resulted in the largest EH response. However, we note that this is not a unique, but rather a representative selection for worst-case assessment. In the case of a spatially uniform magnetic field, the geoelectric field differences across the country purely depend on the ground conductivity. The time evolution of BH,ext, dBH,ext/dt and EH is shown in the animation Case2_BE.mp4. The maximum EH is detected around 20:09 UT, just after the dBH,ext/dt peak, however the magnitude is smaller than Case 1 since we are evaluating the EH from the external part of BH. A second relative EH maximum is detected at 20:03:40 UT. As in Case 1, we scaled the EH field values to be a 1-in-100-year event using the scaling factors in Table . The animation for the scaled EH using HAN station waveform as input and the power line voltages are shown in Case2_EGrid.mp4.

A snapshot at the time of the scaled EH peak (20:03:40 UT) for Case 1 and Case 2 are shown in Fig. a, b, and the difference between both cases in Fig. c. Above 62° MLAT, the largest differences are confined to the Norwegian coast, likely due to variations in the B waveform at high latitudes between the two cases. In Fig. a, b, Case 1 shows southward-oriented E on the seaside and landside of the Norwegian coast, while Case 2 exhibits eastward-oriented E at both sides. Between 58 and 62° MLAT, the differences are minimal because the magnetic field input in Case 1 at these latitudes is mainly dominated by the observations in HAN and OUJ, which are very similar to the input used in Case 2. The remaining variations can be mainly attributed to the difference between Btot and Bext.

Below 60° MLAT, the differences become more evident. In the 55–58° MLAT band, both cases present the largest maximum scaled EH, but for Case 1 EH is larger than in Case 2, particularly in the western region due to pronounced conductivity gradients, as well as along the east coast. In southern Sweden (51–55° MLAT band), the scaled EH values in Case 2 exceed those in Case 1 by about 4 V km⁻¹ at the coasts. This difference is mainly related to the larger B magnitude and perturbations obtained in Case 2 compared to those derived from the B interpolation, which is strongly affected by the lack of magnetic field measurements in southern Sweden and relies primarily on interpolation from the TAR magnetic station.

For each line, we computed its orientation by assuming a straight line between its starting and ending geographic positions. This analysis shows that the network is largely north–south oriented, with 63 % of the lines having angles greater than 45°, reflecting the country’s elongated shape. East–west oriented lines (angles less than 45°) are mainly concentrated within the latitude band 58–64° N, which is also where most lines are located, as shown in Fig. a.

The maximum voltage for each line during the two worst-case scenarios, categorized by its orientation, is summarized in Fig. . Voltages are highest for north–south oriented lines, which are typically the longest. However, when normalized by line length, east–west oriented lines exhibit the largest values, ranging between 6–8 V km⁻¹ due to the dominant east-west orientation of the EH (specially for Case 2). In general, the voltage in the line increases with length as shown in Fig. c; however, because line resistance also increases with length, longer lines might not contribute significantly higher induced currents. Lines shorter than 20 km did not reach the level of 100 V in either scenario, and voltages above 10 V begin to appear for lines longer than 2 km. The median length of the 335 transmission lines is 53 km. For lines longer than 50 km, 73 % experience voltages above 100 V at least once in Case 1, and 60 % in Case 2. These fractions decrease to 37 % and 28 %, respectively, when the threshold is raised to 200 V, which still represents a substantial number of affected lines.

Finally, for both worst-case scenarios, the number of power lines experiencing voltages exceeding 10 V easily exceeds 100 lines on more than 9 occasions during the analyzed period, while about 100 lines exceed 50 V at different stages of the substorm, as illustrated in Fig. . Among these 100 lines, 16, 7, and 1 lines are connected near the main Swedish cities of Stockholm, Göteborg, and Malmö, respectively. At the moment of the WEJ weakening around 100 lines experienced voltages larger than 100 V. Of these, 6 lines were located near Stockholm and 7 near Göteborg, while no lines around Malmö exceeded the 100 V threshold.

In this study, the induced EH for the Halloween event was scaled to represent a 1-in-100-year scenario. In particular, a scaling factor of three was used within the 55–58° MLAT band, representing a conservative lower bound. Based on the 95th percentile confidence interval of , the scaling could be as high as a factor of five. This implies our modeled scenario likely underestimates the potential severity, providing a lower limit benchmark for extreme conditions. Nonetheless, even under this conservative scaling, maximum EH values reached approximately 10–12 V km⁻¹ between 55 and 58° MLAT.

These values are consistent with estimates for the May 1921 storm, which exceeded the 1-in-100-year return level and caused catastrophic damage to the telegraph and telephone station at Karlstad, where geoelectric fields likely reached ∼10 V km⁻¹, as discussed by and references therein. also reports other impacts in Sweden: Östersund and Söderhamn experienced very large earth currents; Telephone lines between Göteborg and Stockholm were unstable and GIC measurements of about 1.1 A; a minor fire at the telegraph and phone station of Ånge. The suggested EH=10 V km⁻¹ in Karlstad discussed in is close to the range of 10–12 V km⁻¹ of the scaled EH of both worst-case scenarios.

In the case of the 13–14 July 1982 storm, which was weaker than the Halloween event (Dst minimum of -325 nT), the voltage peak value in telecommunication cables between Södertälje-Stockholm and Bro-Stockholm was roughly 80 V, implying an estimated east–west-oriented geoelectric fields of approximately 4–5 V km⁻¹ . In Figs. e and e, a power line in Södertälje appears in the lines exceeding Voltages per km >3 V km⁻¹. However, during the 1982 event, highly localized geoelectric fields of up to 9.1 V km⁻¹ were inferred from observations along a short 921 m segment of the 100 km railway communication line between Stockholm and Töreboda . Notably, Töreboda lies within the 55–58° MLAT band, crosses a region with pronounced conductivity gradients, and the EH values in both cases exceeds 10 V km⁻¹.

In the reference study by , maximum EH values of 20 V km⁻¹ were assumed for resistive ground structures above the MLAT threshold (i.e., the magnetic latitude where maximum geomagnetic disturbances and geoelectric fields typically occur) and 5 V km⁻¹ below it, while for conductive ground structures the corresponding values were 2 and 0.5 V km⁻¹. In our analysis, we find scaled EH values exceeding 20 V km⁻¹ in highly localized regions near the west coast. However, the choice of 2 V km⁻¹ for conductive ground areas above the MLAT threshold in appears somewhat higher than our estimates, which range between 0.5 and 1 V km⁻¹. Below the MLAT threshold, their maximum values for resistive ground (5 V km⁻¹) are consistent with our results, where we obtain maximums of 4 to 6 V km⁻¹. For the 0.5 V km⁻¹ limit in conductive areas below the MLAT threshold, no direct comparison with our analysis is possible.

To prevent permanent transformer damage from GICs, the Swedish power grid requires that new transformers withstand a direct current of 200 A for 10 min while operating at full load (private communication with Johan Setréus, Svenska Kraftnät). Since the actual line resistances are considered sensitive information, we adopted a constant ground resistance of RGR=0.5 Ω and line resistances of rL,220=0.022 Ω km⁻¹ and rL,400=0.008 Ω km⁻¹, following the values used by . Based on these assumptions, we find that GICs of 200 A can be reached even in short (<20 km) 220 and 400 kV lines under a E∼10 V km⁻¹ oriented parallel to the line. However, such large E values, and consequently large currents, typically occur only in very short bursts rather than being sustained. The 10 min requirement is also ambiguous: it is unclear whether it refers to continuous or cumulative current exposure. Moreover, this specification applies only to the newest transformers, and no information is available for the tolerances of different units. These results are important since they show that the 200 A limit can be reached, however a future study will be required to determine the impact on Swedish transformers.

We have shown that during intervals of very active ionospheric current variations, particularly during substorm activity, large dB/dt and EH values were estimated at latitudes below 60° MLAT. As a consequence, several power lines exceeded high voltage thresholds (e.g., approximately 100 power lines experienced induced voltages exceeding 50 V at several times during the substorm period). For comparison, reported that 62 transmission lines exceeded 100 V during the March 1989 geomagnetic storm, which triggered a major blackout in the Hydro-Québec power system. Although power-grid disturbances do not always coincide with the time of peak voltage or geoelectric field , or with peak GICs , intervals of high induced voltages still imply larger voltage variations.

The large number of power lines subjected to high induced voltages in our scenario could lead to elevated GICs, which in turn may affect protection relays. Relay misoperations are often linked to harmonics, inappropriate relay types or settings, or faulty relay systems, rather than to the voltage magnitude itself. Collapse can be initiated by one or several coincident relay misoperations, each removing a transformer or line from service while its integrity is verified. Based on this, relay actions may occur during intervals of high or rapidly changing rates of change voltage rather than strictly at maximum voltage.

Understanding which combinations of geoelectric field, induced voltage, network configuration, and system state lead to real incidents remains an open problem and requires further investigation. Such studies will soon be possible with the recently installed GIC monitoring device in Karlshamn, connected to the transformer neutral-to-earth point and deployed by the Swedish transmission system operator, Svenska Kraftnät.

This study builds on a series of investigations in Sweden that have significantly advanced understanding of induced geoelectric fields and the power grid’s response to geomagnetic activity e.g.,. Expanding on this foundation, we provide the first detailed and comprehensive assessment of the potential impacts of a 1-in-100-year ground geoelectric field on the Swedish power grid. Importantly, our analysis is based on total voltage, representing the geoelectric field integrated along each line’s path. Because information on individual line resistances is not available, we could not convert voltages into GICs. Future versions of the RAISE model may incorporate this capability.

The main goal of this study is to benchmark an extreme geoelectric field event and understand how it could affect the power grid, given the known layout. This has provided meaningful insights into regions that may be at risk. We also assessed the number of lines that could be subjected to hazardous GICs during a 1–100 year event. An added benefit of this work is that Svenska Kraftnät can use this knowledge for their own investigations using realistic grid configurations. We view this work as a significant advancement for Sweden in understanding the effects of rare, high-impact events.

A particularly important finding concerns the behaviour of substations in southern Sweden. Substations such as Malmö and Karlshamn, show weaker EH responses than expected despite their documented vulnerability to GICs. This behaviour is likely influenced by the limited magnetometer coverage in southern Sweden (MLAT < 55°) and by uncertainties in the regional conductivity model, both of which may lead to underestimated impacts in this region. In addition, both substations lie along the southern edge of the Swedish transmission grid, where GICs are often amplified due to network topology effects. Together, these factors highlight the need for extending the magnetometer array into southern Sweden, updating the regional conductivity model, and improving the representation of the power grid topology in this area.

Moreover, there are still many unanswered questions to address, such as the following: (1) How do small-scale ionospheric currents (<1000 km) during major geomagnetic storms influence the spatial variability of geoelectric fields and GICs? (2) Is the current number of magnetometers sufficient to adequately capture space weather impacts in low MLAT regions, particularly in areas of large conductivity gradients? (3) Are power grid operators equipped and prepared to manage simultaneously high induced voltages occurring on multiple power lines during extreme geomagnetic storms? (4) What defines an extreme event from the perspective of the electricity-system owner and operator? Our aim is to continue to address these key questions in future studies.