Immediate and delayed responses of power lines and transformers in the Czech electric power grid to geomagnetic storms
Michal Švanda, Didier Mourenas, Karla Žertová, Tatiana Výbošťoková
ssubmitted to
Journal of Space Weather and Space Climate c (cid:13) The author(s) under the Creative Commons Attribution 4.0 International License (CC BY 4.0)
Immediate and delayed responses of power linesand transformers in the Czech electric power gridto geomagnetic storms
Michal Švanda , ,(cid:63) , Didier Mourenas , Karla Žertová , and Tatiana Výbošt’oková Astronomical Institute of the Czech Academy of Sciences, CZ-25165 Ondˇrejov, Czech Republic Astronomical Institute, Charles University, CZ-18000 Praha, Czech Republic CEA, DAM, DIF, F-91297, Arpajon, France Gymnázium Jiˇrího Ortena, CZ-284 80 Kutná Hora, Czech Republic Department of Surface and Plasma Science, Charles University, CZ-18000 Praha, CzechRepublic
ABSTRACT
Eruptive events of solar activity often trigger abrupt variations of the geomagnetic field. Throughthe induction of electric currents, human infrastructures are also a ff ected, namely the equipmentof electric power transmission networks. It was shown in past studies that the rate of power-gridanomalies may increase after an exposure to strong geomagnetically induced currents. We searchfor a rapid response of devices in the Czech electric distribution grid to disturbed days of high ge-omagnetic activity. Such disturbed days are described either by the cumulative storm-time Dst or d ( SYM-H ) / dt low-latitude indices mainly influenced by ring current variations, by the cumulative AE high-latitude index measuring substorm-related auroral current variations, or by the cumula-tive ap mid-latitude index measuring both ring and auroral current variations. We use superposedepoch analysis to identify possible increases of anomaly rates during and after such disturbeddays. We show that in the case of abundant series of anomalies on power lines, the anomaly rateincreases significantly immediately (within 1 day) after the onset of geomagnetic storms. In thecase of transformers, the increase of the anomaly rate is generally delayed by 2–3 days. We alsofind that transformers and some electric substations seem to be sensitive to a prolonged exposureto substorms, with a delayed increase of anomalies. Overall, we show that in the 5-day periodfollowing the commencement of geomagnetic activity there is an approximately 5–10% increasein the recorded anomalies in the Czech power grid and thus this fraction of anomalies is probablyrelated to an exposure to GICs. Key words.
Spaceweather – Geomagnetically induced currents – Impacts on technological sys-tems 1 a r X i v : . [ phy s i c s . s p ace - ph ] M a y vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms
1. Introduction
The Sun is a magnetically active star, filling the interplanetary space with a stream of charged par-ticles called the solar wind (see e.g. a recent review by Verscharen et al., 2019). The solar windproperties are far from being homogeneous, with strong variations in temperature, density, or in-terplanetary magnetic field observed in connection with various phenomena of solar activity. Themain drivers of strong disturbances of the solar wind are coronal mass ejections (CMEs), the fast–slow solar wind interaction on the borders of corotating interaction regions, and fast-wind outflowsfrom coronal holes. Solar-wind disturbances may ultimately interact with Earth’s magnetosphere,thereby triggering geomagnetic activity.As first proposed by Dungey (1961), the dynamic pressure exerted by the solar wind on the mag-netosphere can trigger magnetic reconnection, opening dayside dipolar geomagnetic field lines. Thesolar wind then transports this magnetic field to the nightside, forming a long tail behind the Earth.This transfer of magnetic flux and the resulting reconfiguration of the magnetosphere eventuallyleads to nightside magnetic reconnection, returning flux to the dayside in various phenomenologicalresponse modes that depend on the disturbance level (Dungey, 1961; Kepko et al., 2014). However,a common characteristic of all such response modes is the formation of a current wedge system(Kepko et al., 2014; McPherron and Chu, 2017). A fraction of the tail current along geomagneticfield lines is then temporarily diverted through the ionosphere, allowing a closure of the currentwedge and causing perturbations in the auroral zone and at middle latitudes (McPherron and Chu,2017).Both substorms and geomagnetic storms give rise to a current wedge, plasma sheet inward con-vection by inductive electric fields, and energetic particle injections (Ganushkina et al., 2017; Kepkoet al., 2014; McPherron and Chu, 2017; Thomsen, 2004). However, the current wedge has generallya more limited temporal extent during substorms than during storms, which frequently last for days(Ganushkina et al., 2017; Kepko et al., 2014). Substorms are one of the key dynamical processesoccurring during storms, but isolated substorms also occur outside storms (Viljanen et al., 2006;Turnbull et al., 2009). During storms (mainly caused by strong interactions between CMEs and themagnetosphere), a stronger buildup of the inner ring current (a westward current of ions roughly ∼ − quiet days ,whereas days of stronger and irregular variations have been called disturbed days (Chapman andBartels, 1940).Geomagnetically induced currents (GICs) in the ground are due to strong variations dH / dt ofthe horizontal component H of the geomagnetic field over typical time scales of ∼ − (cid:63) Corresponding author: e-mail: [email protected]
Pokhrel et al., 2018; Zhang et al., 2016). Substorms generally produce the largest dH / dt at highand mid-latitudes during periods of fast solar wind and have caused many of the major GIC im-pacts during large storms – e.g., the Quebec voltage collapse on 13 March 1989 was triggered by afirst substorm, while two later substorms tripped out transformers in the UK (Boteler, 2019). dH / dt was found to be twice smaller in general during non-storm substorms than during storm-relatedsubstorms, possibly due to an additional input from ring current variations during storms (Viljanenet al., 2006; Turnbull et al., 2009). Other important sources of dH / dt during geomagnetic stormsinclude sudden commencements (the shock compression of the magnetosphere when a fast CMEimpacts the magnetosphere at the start of a storm, leading to an increase of Chapman-Ferraro cur-rents at the dayside magnetopause; e.g., see Kikuchi et al. 2001) and rapid variations of the ringcurrent, through its role in the generation of Region 2 field-aligned currents (Ganushkina et al.,2017). Sudden commencements have a large dH / dt because of their shock-like nature, while rapidincreases of ring current energy density following large scale injection or inward convection of en-ergetic charged particles coming from the plasma sheet can also produce large dH / dt (Kappenman,2003, 2005; Kataoka and Pulkkinen, 2008).GICs propagate through conducting regions in the ground and water, but also in the groundedconductors. The presence of GICs in the electric power grid can cause various kinds of damage.GICs are quasi-DC currents that can lead to half-cycle saturation and drive a transformer responseinto a non-linear regime. This poses a risk for transformers by producing high pulses of magnetizingcurrent, a local heating (also vibration) within the transformer (Gaunt, 2014), and the generation ofAC harmonics that propagate out into the power network, where they can disrupt the operations ofvarious devices (Kappenman, 2007; Molinski, 2002). In particular, the propagation of harmonicsin the power grid during half-cycle saturation can distort the electrical current waveform, eventu-ally triggering a detrimental reaction of protective relays connecting power lines, or leading to adisruption of other devices attached to these lines.GICs identified by fast variations of the geomagnetic field have been linked with variouspower grid failures (Schrijver and Mitchell, 2013), eventually leading to power grid disruptions(Kappenman, 2007; Pirjola, 2000; Pulkkinen et al., 2017; Schrijver and Mitchell, 2013). Althoughhigh latitude regions are more at risk from GICs, middle and low latitude regions may also be im-pacted by significant GICs (Bailey et al., 2017; Carter et al., 2015; Gaunt and Coetzee, 2007; Lotzand Danskin, 2017; Marshall et al., 2012; Torta et al., 2012; Tozzi et al., 2019; Wang et al., 2015;Watari et al., 2009; Zhang et al., 2016; Zois, 2013).A first study of anomalies in the Czech power grid as a function of geomagnetic activity (de-fined by the K index computed from the measurements of the Earth’s magnetic field at a localmagnetometer station near Budkov – e.g., see Mayaud 1980; McPherron and Chu 2017) has al-ready identified some statistically significant increases of the rate of anomalies around month-longperiods of higher geomagnetic activity than nearby periods of lower activity (Výbošt’oková andŠvanda, 2019). Nevertheless, the relationship between geomagnetic events and anomalies still re-mained somewhat loose.Accordingly, the main goal of the present paper is to better ascertain the existence of a tightrelationship between power grid anomalies and geomagnetic storms, on the basis of the same dataset. We shall discuss the physical mechanisms by which GICs may cause anomalies in power linesand transformers, and show that our statistical results are suggestive of a causal relationship basedon those mechanisms. We shall also address the important and unanswered question of the time delay between moderate to large geomagnetic storms with minimum Dst < −
40 nT (Gonzalezet al., 1994) and the actual occurrences of anomalies. For that purpose, we shall use SuperposedEpoch Analysis to investigate the relative occurrence of GIC e ff ects in the Czech power grid duringdisturbed days as compared with quiet days. Such disturbed days will be categorized using di ff erenttime-integrated parameters of geomagnetic activity, related to the magnitude of temporal variationsof the horizontal component of the geomagnetic field, which can induce detrimental currents inpower lines.
2. Data sets
In this study, we searched for a causal relation between two types of time series. The first seriesdescribing the daily anomaly rates in the Czech electric power-distribution grid, and the secondserving as a proxy of disturbed days for the estimation of geomagnetically induced currents.
The Czech Republic is a mid-latitude country (around ∼ ◦ geographic latitude and ∼ ◦ cor-rected geomagnetic latitude), where the e ff ects of solar / geomagnetic activity on ground-based in-frastructures is expected to be moderate at most. The modelled amplitudes of GICs during theHalloween storms in late October 2003 reached 1-minute peaks of about 60 A . The country hasa shape prolonged in the east–west direction (about 500 km length), whereas in the south–northdirection it is about 280 km long from border to border. The spine of the electric power networkis operated by the national operator ˇCEPS, a.s., which maintains the very-high-voltage (400 kVand 220 kV) transmission network, and connects the Czech Republic with neighbouring countries.ˇCEPS also maintains the key transformers and electrical substations in the transmission network.The area of the state is then split into three regions, where the electricity distribution is under theresponsibility of the distribution operators. The southern part is maintained by E.ON Distribuce,a.s., the northern part by ˇCEZ Distribuce, a.s., and the capital city of Prague is maintained byPREdistribuce, a.s. All three distributors maintain not only very-high-voltage (110 kV) and high-voltage (22 kV) power lines, but also connect the consumers via the low-voltage (400 V) electricpower transmission network.All four above-mentioned power companies have agreed to provide us their maintenance logs.The datasets used in this study are exactly the same datasets already used in the study byVýbošt’oková and Švanda (2019). Thus, we refer the reader to section 3.2 of this previous paperfor a more detailed description of the datasets. By mutual non-disclosure agreement with the dataproviders, the datasets were anonymised (by removing the information about the power-companyname, and also by changing the calendar date to a day number) and must be presented as such. Thetotal time span is 12 years, but the span of individual maintenance logs provided by the operators isshorter, varying between 6 to 10 years.We only briefly recall that the obtained logs were cleaned from events that were obviously not re-lated to variations of geomagnetic activity. From these logs, we keep only the dates when the events Smiˇcková, A., Geomagnetically Induced Currents in the Czech Power Grid, BSc. thesis (supervisorŠvanda, M.), Faculty of Electrical Engineering, Czech Technical University, 2019, available online http://hdl.handle.net/10467/84988 . 4vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms occurred and did not consider any other details. These inhomogeneous datasets (the log entries wereprovided by di ff erent individuals with varying levels of details and quality of the event description)were split into twelve subsets D1–D12, which were investigated separately. Each sub-dataset wasselected so that it contained only events occurring on devices of a similar type and / or with the samevoltage level and were recorded by the same operating company. The dataset descriptions are brieflysummarised in Table 1. Table 1.
Datasets analysed in this study. This is a reduced version of Table 1 in Výbošt’oková andŠvanda (2019).
Dataset Voltage level Type SpanID
D1 very high voltage equipment: transformers, 9 yearselectrical substationsD2 high voltage equipment 6 yearsD3 very high voltage equipment 6 yearsD4 high and low voltage power lines 7 yearsD5 high and low voltage equipment and power lines 7 yearsD6 high and low voltage equipment 7 yearsD7 very high voltage power lines 10 yearsD8 high voltage transformers 10 yearsD9 very high voltage transformers 10 yearsD10 very high and high voltage electrical substations 10 yearsD11 very high voltage power lines 10 yearsD12 high voltage power lines 10 years
Various parameters have been considered to estimate the e ff ects of geomagnetic activity on powergrids (Schrijver and Mitchell, 2013). GICs are due to strong variations dH / dt over typical timescales of ∼ − dH / dt at low and middle latitudes: (i) sudden impulses (SI), also called sudden commencements (SC)when they are followed by a storm caused by the shock preceding a fast CME, and (ii) the growthand decay of the ring current during a magnetic storm. Substorm-related disturbances are mostlylimited to high and middle latitudes, whereas disturbances caused by ring current changes generallya ff ect mainly middle and low latitudes. Statistically, periods of stronger cumulative e ff ects of GICsin a power grid are therefore expected to correspond to disturbed days of elevated geomagneticactivity (Chapman and Bartels, 1940). In the present study, we shall use various cumulative (time-integrated) parameters based on di ff erent magnetic indices to categorize such disturbed days, andwe shall investigate the relative occurrence of GIC e ff ects during such disturbed days as comparedwith quiet days.An appropriate quantity to estimate GICs at low latitudes is d ( SYM-H ) / dt , which directly pro-vides a (longitudinally averaged) measure of the 1-minute dH / dt due to ring current variations thatdrive GICs there (Carter et al., 2015; Kappenman, 2003; Zhang et al., 2016). Indeed, the SYM-H in-dex is essentially similar to the hourly
Dst storm time index, but measured on 1-minute time scales – that is, it provides the disturbance ∆ H = H − H quiet of the horizontal component of the magneticfield as compared to its quiet-time level, longitudinally averaged based on ground magnetometermeasurements at di ff erent low latitude magnetometer stations (Mayaud, 1980).Several studies have demonstrated the existence of significant correlations between GICs or elec-tric grid failures and times of large d ( SYM-H ) / dt at low to middle latitudes during geomagneticstorms, although d ( SYM-H ) / dt is often inappropriate during strong substorms (Carter et al., 2015;Wang et al., 2015; Zhang et al., 2016). Carter et al. (2015) have further shown that the actual dH / dt at middle latitudes due to SI / SCs can be a factor ∼ − d ( SYM-H ) / dt , po-tentially allowing GIC e ff ects even during geomagnetic events with relatively small d ( SYM-H ) / dt .We checked that dH / dt at the Czech magnetometer station of Budkov can also be sometimes > − d ( SYM-H ) / dt during SI / SCs. Viljanen et al. (2014) have noticed the presence of aEuropean region of low underground conductivity stretching from France through Czech Republicto Hungary that could favor significant GICs at middle latitudes. Gil et al. (2019) have shown thepresence of GICs during a few selected storms in Poland, while Tozzi et al. (2019) have found thatnon-negligible GICs could exist even down to northern Italy. Wang et al. (2015) have further em-phasized that cumulative GICs in a nuclear plant transformer during a long-duration geomagneticevent could sometimes be more harmful than short events, due to the longer cumulated time oftransformer heating.Accordingly, we consider here the
Int ( d ( SYM-H ) / dt ) parameter to categorize disturbed days ofexpected significant GIC impacts on power grids. Int ( d ( SYM-H ) / dt ) is calculated over each day,as the sum of all 1-minute | d ( SYM-H ) / dt | values (in nT / min) obtained during times when SYM-H remains smaller than some threshold. The selected threshold (varying from −
50 nT to −
25 nT)should ensure that only geomagnetic storm periods are considered (Gonzalez et al., 1994). This
Int ( d ( SYM-H ) / dt ) parameter allows, in principle, to take into account the immediate e ff ects onpower grids caused by large individual | dH / dt | due to ring current variations, as well as the more de-layed, cumulative e ff ects potentially caused by prolonged periods of moderate to significant | dH / dt | levels (Carter et al., 2015; Wang et al., 2015; Zhang et al., 2016) – although large individual | dH / dt | during strong substorms will need other indices such as AE or ap to take them into account (seebelow).Other works have suggested that the mean or cumulative Dst during storm main phase should begood indicators of long duration GICs, because larger and steeper decreases of
Dst correspond tostronger disturbances that should generally lead to larger dH / dt at the relevant shorter time scalesof ∼ − ∼ ◦ − ◦ not much lower than in theCzech Republic), Lotz and Danskin (2017) have demonstrated the existence of a linear relationshipbetween the sum of induced electric fields recorded in the ground during geomagnetic storms andthe integral of SYM-H (or
Dst ) values, suggesting that the cumulative
SYM-H or Dst could be usedas good proxies for cumulated induced electric fields at middle corrected geomagnetic latitudes(although ring current e ff ects are likely more important for GICs in South Africa than in the CzechRepublic, where a more balanced mixture of ring current and substorm e ff ects is present). They alsonoted that some e ff ects might be present as long as SYM-H remained below −
20 nT.Therefore, we also consider the
IntDst parameter to categorize disturbed days of expected signif-icant GICs in the Czech Republic (e.g., see Mourenas et al., 2018).
IntDst (in nT · hr) is calculated asa sum of hourly | Dst | values. This summation starts when Dst first becomes smaller than a thresh- old (taken between −
50 nT and −
25 nT as before) chosen to ensure that only storm periods areconsidered, and this summation ends when
Dst reaches its minimum value over the next 24 hours.Each
IntDst value is then assigned to the starting day of a given summation, with all integrationperiods strictly separated by construction. As a result,
IntDst is generally measured during stormmain phase, where the e ff ects on GICs are likely stronger (Balan et al., 2014, 2016), to provide acomplementary metric to the Int ( d ( SYM-H ) / dt ) metric calculated over each whole day without anyconsideration of storm phase.While ring current variations during storms can be quantified by Dst and
SYM-H indices, themagnetic indices that provide a measure of magnetospheric and ionospheric current variations ob-served during strong substorms are AE , AL , K p , or ap (Kamide and Kokobun, 1996; Mayaud, 1980;Mourenas et al., 2020; Thomsen, 2004). The ap index (as its logarithmic equivalent K p ) provides aglobal measure of the range of magnetic field variations at middle latitudes over 3-hour time scales,obtained by averaging measurements from di ff erent mid-latitude magnetometer stations spread inlongitude (Mayaud, 1980; Thomsen, 2004). In contrast, the range indices AE and AL are measuredat higher magnetic latitudes > ◦ inside the auroral region (Mayaud, 1980; Kamide and Rostoker,2004), and AE saturates at high geomagnetic activity am >
150 (with am a mid-latitude indexsimilar to ap ) because the auroral oval then expands equatorward of the magnetometer stationsmeasuring it (Lockwood et al., 2019; Thomsen, 2004). Therefore, ap is probably more appropri-ate than AE for quantifying the strength of time-integrated geomagnetic disturbances at middle(sub-auroral) geomagnetic latitudes than AE (Thomsen, 2004; Mourenas et al., 2020).Although ap cannot provide an accurate ranking or quantification of the maximum dH / dt val-ues reached during the most disturbed events due to its intrinsic saturation at K p = K p ∼ − ap could still be used to simply categorize disturbed / quiet days of expected stronger oc-currence / absence of GIC e ff ects at middle latitudes, during a large series of medium (most frequent)to strong (more rare) time-integrated ap events spread over 6 to 10 years.Accordingly, we shall consider in section 4.3 a third parameter of geomagnetic activity, IntAp ,corresponding to the daily maximum level of the integral of 3-hourly ap values over a continuouslyactive period of ap ≥
15 nT (Mourenas et al., 2019, 2020). This should allow to categorize disturbeddays that include contributions to GICs from both (storm-time) ring current variations and strongsubstorms, usefully complementing the
Int ( d ( SYM-H ) / dt ) and IntDst parameters. Indeed,
IntAp provides a rough estimate of the e ff ects at middle latitudes of significant time-integrated dH / dt disturbances due to substorms, which often do not reach the low latitudes where SYM-H and
Dst are measured.In addition, we shall consider a fourth parameter, called
IntAE , which is based on the high-latitude AE auroral electrojet index Mayaud (1980). IntAE is the daily maximum level of the inte-gral of AE calculated over the same period of continuously high ap ≥
15 nT as
IntAp (generallycorresponding to AE >
200 nT), to ensure that the corresponding substorm-related magnetic distur-bances e ff ectively reach middle latitudes (Mourenas et al., 2019, 2020). IntAE provides a measureof cumulative substorm-related disturbances, corresponding to continuous periods of auroral currentvariations roughly similar to High-Intensity Long-Duration Continuous AE Activity (HILDCAA)events (Tsurutani et al., 2006). AE [ n T ] D s t, ap , SY M - H [ n T ] apAESYM-HDst 0 500 1000 1500 2000 2500 3000 350013-Feb00:00 13-Feb12:00 14-Feb00:00 14-Feb12:00 15-Feb00:00 15-Feb12:00 16-Feb00:00 0 50 100 150 200 250 300 I n t AE [ n T . h r ] I n t D s t, I n t A p [ n T . h r ], I n t ( d ( SY M - H ) / d t ) [ n T ] Day of year 2011 IntApIntAEInt(d(SYM-H)/dt)IntDst
Fig. 1.
Upper panel:
SYM-H , Dst , Ap , and AE indices during the 13-15 February 2011 geomagneticevent. Bottom panel: corresponding Int ( d ( SYM-H ) / dt ) (in nT), and IntDst , IntAp , and
IntAE (innT · hr) cumulative parameters, calculated using thresholds SYM-H ≤ −
30 nT,
Dst ≤ −
30 nT, or ap ≥
15 nT.These four cumulative metrics of disturbed days are displayed in Figure 1 together with 1-min
SYM-H and AE , hourly Dst , and 3-hourly ap , during a moderate geomagnetic storm on 14-15February 2011 that reached a minimum SYM-H = −
49 nT and a minimum
Dst = −
40 nT on 14February, with strong substorms (identified by peaks in AE and ap ) during storm sudden com-mencement and main phase, and with a very weak secondary minimum of Dst reaching −
30 nT on15 February at 17 UT during a burst of AE activity.
3. Methods
In the present follow-up study to the work by Výbošt’oková and Švanda (2019), we search fora tighter relationship between power grid anomalies and geomagnetic storms, based on the samedatasets of anomalies in the Czech power grid. We also address the important and as yet unansweredquestion of the time delay between geomagnetic events and the occurrences of anomalies.Our working hypothesis is that disturbed days of high geomagnetic activity should cause anincrease in daily rates of anomalies in the power distribution network as compared with quiet days .Accordingly, the daily anomaly rates should sharply peak within a few days (with some delay) aftersuch disturbed days, and then decrease back to normal levels. This corresponds to a rapid response to GICs induced by substorms and storms, as observed for a few selected events – e.g., see Gil et al.(2019); Wang et al. (2015).Unfortunately, in a mid-latitude country such as the Czech Republic, the e ff ects of geomagneticactivity are expected to be weak. Consequently, an investigation of individual, moderate geomag-netic events is not expected to reveal a significant increase of anomalies, because such anoma-lies induced by geomagnetic activity (via GICs) will generally remain hidden among many otheranomalies caused by various other e ff ects. It is therefore imperative in our statistical analysis to finda way to reduce the importance of anomalies caused by other e ff ects. Note that our data series cover6 to 10 years, each subset providing records of anomaly rates occurring during many separated dis-turbed days of high geomagnetic activity. Therefore, a feasible approach is to average over all thesedi ff erent events. The corresponding methodology is the Superposed Epoch Analysis , widely used inastrophysics.A Superposed Epoch Analysis (SEA; Chree, 1913) is a statistical technique used to reveal eitherperiodicities within a time sequence, or to find a correlation between two time series. In the latercase, the method proceeds in several steps.1. In the reference time series, occurrences of the repeated events are defined as key times (orepochs).2. Subsets are extracted from the second time series within some range around each key time.3. Subsets from each time series are superposed, synchronized at the same key time (Day 0), andaveraged, allowing inter-comparisons.This methodology is known to e ffi ciently enhance the “signal” (related variations in both series)with respect to “noise” (unrelated variations in both series), because the noise adds up incoherently,whereas the signal is reinforced by the superposition.Thus, we performed the SEA of geomagnetic activity defined by Int ( d ( SYM-H ) / dt ) or IntDst parameters. A range of event thresholds
SYM-H (or
Dst ) < −
25 nT to −
50 nT was considered, tokeep only periods corresponding to weak to large geomagnetic storms (Gonzalez et al., 1994) andto allow for the determination of the best thresholds on event strength. Other days were assigneda zero level of
Int ( d ( SYM-H ) / dt ) or IntDst . An important further requirement was that the 5-dayperiod immediately preceding the start of a geomagnetic storm (Day 0 in the SEA) contained azero level of the considered geomagnetic activity parameter (that is, all such quiet days must have
IntDst = Int ( d ( SYM-H ) / dt ) = ff ect of geomagnetic storms on the power grid during disturbed days as compared with quietdays , at the expense of a slight reduction of the number of considered events. In a second step, weanalyzed in more details these SEAs to determine as accurately as possible the time delay (after thestart of a storm) that corresponds to the statistically most significant increase of anomalies, for eachtype of power grid equipment.
4. Results of Superposed Epoch Analysis
A Superposed Epoch Analysis was performed based on
IntDst and
Int ( d ( SYM-H ) / dt ) parameters,considering successively thresholds Dst < −
25 nT, −
30 nT, −
40 nT, and −
50 nT, or
SYM-H < Table 2.
The number of epochs considered in SEAs for various reference series.
Reference series Threshold
IntDst −
50 nT 138
IntDst −
40 nT 172
IntDst −
30 nT 221
IntDst −
25 nT 222
Int ( d ( SYM-H ) / dt ) −
50 nT 154
Int ( d ( SYM-H ) / dt ) −
40 nT 191
Int ( d ( SYM-H ) / dt ) −
30 nT 218
Int ( d ( SYM-H ) / dt ) −
25 nT 231 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400-10 -5 0 5 10 A v e r age i n t D S T Days from epoch A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. 2.
Plots of epoch-superposed daily numbers of anomalies in the D12 series, considering
IntDS T (in nT · hr, left) and Int ( d ( SYM-H ) / dt ) (in nT, right) for di ff erent upper thresholds on Dst and
SYM-H . Solid lines indicate the superposed anomaly rates (upper row) or geomagnetic activityin the reference time series (lower row) during Days − + −
25 nT, −
30 nT, −
40 nT, and −
50 nT, to explore the dependence of power grid anomalies on theminimum strength of geomagnetic storms. The number of epochs considered in the SEAs of eachreference series are given in Table 2.The SEAs obtained for
IntDst and
Int ( d ( SYM-H ) / dt ) both show a clear peak of geomagneticactivity at Day 0 and a sharp decrease on Day 1 for IntDst or on Day 2 for
Int ( d ( SYM-H ) / dt ). Thelater decrease for Int ( d ( SYM-H ) / dt ) is due to the presence of significant d ( SYM-H ) / dt variationsduring the recovery phase of many storms stretching over at least 2 consecutive days, whereas IntDst is generally calculated only during storm main phase. Fig. 2 shows the SEAs obtained forthe D12 series (power lines). Similar trends are found for other datasets concerning power lines. All the figures corresponding to the di ff erent series D1 to D12 are available in the online supplement asFigs. A.1-A.12. ff ects: 5-day Periods After / Before Day 0
Next, we compared the period of 5 disturbed days immediately following Day 0 (the day of peakstorm activity) with the 5-day period immediately preceding Day 0 – a preceding period of quietdays especially selected to have zero
IntDst or Int ( d ( SYM-H ) / dt ) levels. This allows to directlycheck the impact of disturbed days of geomagnetic storms on power grid anomalies, as comparedwith quiet days . For the two time intervals, we summed the total number of registered anomaliesin the superposed series for each data subset and computed the statistical significance of the dif-ferences using the standard binomial statistical test. We tested the null hypothesis that the numberof anomalies recorded over quiet days is not di ff erent from the number of anomalies recorded overdisturbed days, that is, the null hypothesis that the probability of recording anomalies is the sameduring quiet and disturbed days. Should the resulting p -value be smaller than the selected statisticalthreshold (usually 0.05 for single-bin tests), we reject the null hypothesis, thereby saying that therecorded di ff erences are indeed statistically significant.The results, summarized in Table 3, reveal a clear increase of anomalies during the period of 5 disturbed days following Day 0 as compared with the period of 5 quiet days preceding Day 0, for thetwo series D11 and D12 corresponding to power lines. The number of anomalies increases by 5%for D12 and by 30% for D11, with corresponding p -values always statistically significant ( < . < −
30 nT or < −
40 nT – except for
Int ( d ( SYM-H ) / dt ) and D11 for a threshold < − IntDst , the < −
25 nT threshold gives a higher statisticalsignificance. This means that moderate events with minimum
Dst or SYM-H near −
40 nT haveoften a statistically detectable impact on anomaly rates, whereas weaker events do not. The samethresholds also lead to the highest peaks of anomalies after Day 0 in many other series. Finally, forD11 and D12, the < −
40 nT thresholds lead to the smallest p -values ( < .
01) for both
IntDst and
Int ( d ( SYM-H ) / dt ), as well as to the smallest p -values < . − . IntDst , and to the smallest or second smallest p -values < . − .
36 for D2 and D9 when considering
Int ( d ( SYM-H ) / dt ). Therefore, the thresholds SYM-H < −
40 nT and
Dst < −
40 nT are probably themost appropriate to detect statistically significant increases of anomalies related to geomagneticstorms.The weaker significance of results for higher thresholds < −
25 nT agrees with previous obser-vations from Lotz and Danskin (2017) that weaker events have little e ff ects on induced electricfields. However, moderate Dst or SYM-H geomagnetic disturbances in the range −
40 nT to −
50 nTare found to still have some impact on power lines. The weaker significance of results for lowerthresholds < −
50 nT is likely due to a combination of two di ff erent e ff ects: (i) storms start slightlylater when using a threshold < −
50 nT than for higher thresholds < −
40 nT or < −
30 nT, meaningthat the 5-day period preceding Day 0 can actually contain significant dH / dt geomagnetic activityleading to some anomalies, and (ii) the < −
50 nT threshold corresponds to a 30% to 40% smallernumber of events than the < −
30 nT threshold, decreasing the sensibility of the SEA to a potentialslight increase of anomalies due to storms.
Table 3.
Comparison of the number of power grid anomalies in the 5-day period prior to Day 0 N − and in the 5-day period after Day 0 N + , together with p -values of the statistical significance ofthe di ff erences. These values are given for di ff erent reference series involved in SEAs with varyingthresholds. IntDst ID < −
25 nT < −
30 nT < −
40 nT < −
50 nT N − N + p N − N + p N − N + p N − N + p D1 60 59 1.0 54 52 0.92 35 33 0.90 29.0 36.0 0.46D2 100 115 0.34 109 137 0.08 94 112 0.24 82 94 0.41D3 17 17 1.0 20 23 0.76 16 22 0.42 18 12 0.36D4 58 38 0.05 52 43 0.41 45 46 1.0 38 40 0.91D5 86 75 0.43 91 84 0.65 83 82 1.0 71 68 0.87D6 30 36 0.54 40 39 1.0 38 37 1.0 34 31 0.80D7 134 132 0.95 143 137 0.77 115 120 0.79 98 105 0.67D8 968 955 0.78 892 922 0.50 710 760 0.20 562 586 0.50D9 105 102 0.89 95 112 0.27 70 67 0.86 44 53 0.42D10 14292 14338 0.79 13245 13477 0.16 10791 11047 0.08 8601 8764 0.22D11 415 494 0.01 403 476 0.02 302 387 < .
01 247 297 0.04D12 11366 12118 < .
01 10787 11748 < .
01 8965 9421 < .
01 7242 7606 < . Int ( d ( SYM-H ) / dt ) ID < −
25 nT < −
30 nT < −
40 nT < −
50 nT N − N + p N − N + p N − N + p N − N + p D1 59 56 0.85 59 58 1.0 43 47 0.75 32 37 0.63D2 98 98 1.0 104 110 0.73 101 121 0.20 93 107 0.36D3 20 15 0.50 20 16 0.62 15 20 0.50 17 18 1.0D4 53 36 0.09 51 37 0.17 43 45 0.92 46 49 0.84D5 79 66 0.32 83 70 0.33 80 78 0.94 83 77 0.69D6 29 28 1.0 35 31 0.71 38 33 0.64 38 29 0.33D7 115 118 0.90 137 127 0.58 116 122 0.75 119 118 1.0D8 964 936 0.54 1005 964 0.37 784 790 0.90 635 667 0.39D9 98 101 0.89 107 102 0.78 80 93 0.36 58 74 0.19D10 14220 14061 0.35 14594 14518 0.66 11951 11877 0.64 9702 9854 0.28D11 408 450 0.16 420 473 0.08 334 415 < .
01 300 323 0.38D12 11273 11798 < .
01 11675 12305 < .
01 9669 10162 < .
01 8385 8714 0.01
A detailed inspection of the SEAs of D12 lends further credence to the impact of geomagneticstorms on power lines. Indeed, for both
IntDst and
Int ( d ( SYM-H ) / dt ), the peaks of anomalies inthe few days following Day 0 reach the highest daily levels of anomalies of the whole 21-day SEAsfor < −
30 nT to < −
50 nT thresholds, the main increases of anomalies occurring from Day + +
3. For D11 and thresholds < −
30 nT to < −
40 nT, the 4-day period following Day 0 has alsothe highest number of anomalies of the whole 21-day SEA, while the 5-day interval preceding Day0 has the lowest average number of anomalies of the whole SEA. D a y s f r o m e p o c h Relative increase 0.940.960.981.001.021.041.06 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 3.53.02.52.01.51.00.5 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.920.940.960.981.001.021.041.061.08 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 4321 l o g ( p - v a l u e ) Fig. 3. (left) Maps for D12 of increases (or decreases) of the number of anomalies as a function ofthe middle day of the first (abscissa) and second (ordinate) considered 3-day periods. (right) Maps ofthe corresponding p -values. The upper row is computed for the IntDS T reference series, whereasthe lower row corresponds to the
Int ( d ( SYM-H ) / dt ) reference series. The p -values are evaluatedonly if there is an increase of anomaly rates in the second 3-day period as compared to the first3-day period. Note the logarithmic scale of the plotted p -values: p = . p = − .
26. Statistically significantbins are indicated by white dots. Blank bins are indicated by the white colour. ff ects: 3-day Periods Before / After Day 0 with Time Lags
Next, we examined in more details the SEAs performed based on
IntDst and
Int ( d ( SYM-H ) / dt )parameters for thresholds Dst < −
40 nT and
SYM-H < −
40 nT. We considered two shorter 3-day periods, located before and after Day 0. We varied the time lag between them and calculated(as before for 5-day periods) the statistical significance of the di ff erence in anomaly rates betweenthese two periods. Considering shorter 3-day periods should help to determine more precisely the(statistically most significant) time delay between the start of a geomagnetic storm and the relatedincrease of the number of anomalies. D a y s f r o m e p o c h Relative increase 0.800.850.900.951.001.051.101.151.20 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 2.01.51.00.5 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.850.900.951.001.051.101.15 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 1.41.21.00.80.60.40.20.0 l o g ( p - v a l u e ) Fig. 4. (left) Maps for D8 of increases (or decreases) of the number of anomalies as a function of themiddle day of the first (abscissa) and second (ordinate) considered 3-day periods. (right) Maps ofthe corresponding p -values. The upper row is computed for the IntDS T reference series, whereasthe lower row corresponds to the
Int ( d ( SYM-H ) / dt ) reference series. The p -values are evaluatedonly if there is an increase of anomaly rates in the second 3-day period as compared to the first3-day period. Note the logarithmic scale of the plotted p -values: p = . p = − .
26. Statistically significantbins are highlighted by white dots. Blank bins are indicated by the white colour.Fig. 3 for D12, Fig. 4 for D8, and Figs. A.13–A.24 in the online supplement for all other datasets,show two-dimensional maps of the increases (or decreases) of the number of anomalies as a functionof the middle day of the first and second 3-day periods, together with maps of the corresponding p -values computed only for increases.Let us examine these maps of p -values. For consistency with the procedure of estimation ofthe statistical significance adopted in Section 4.1, we need to compare the number of anomaliesover the same 5-day periods after and before Day 0. Accordingly, we must only consider the bins(representing 3-day periods) comprised between Days − − − − + + Days + +
5) for the period following Day 0. There are 3 × = p -value ∼ .
05 (corresponding to a 5% probability to obtain an increase of anomalies bychance) among 9 bins is not anymore as statistically significant as before. Therefore, an individualbin (representing 3-day periods) is hereafter required to have a smaller p -value ≤ . / = . p -values < . IntDst and
Int ( d ( SYM-H ) / dt ) in the considered square of 3 × − , +
3) in Fig. 3,corresponding to a statistically significant increase of anomalies. A significant increase of anomaliesis already observed over final 3-day periods centered on Day +
1, as compared with initial 3-dayperiods centered on Days − −
2, indicating an immediate e ff ect of geomagnetic storms onpower lines.In the case of D8 (transformers), however, the three bins corresponding to increases of anomalieswith the smallest p -values are found in Fig. 4 for final 3-day periods centered on Days + + − ∼ − IntDst or Int ( d ( SYM-H ) / dt ) and the correspondingvariation of the number of anomalies in the D8 dataset. In such a situation, it is more appropriateto consider for D8 the square of 3 × = − , +
3) in Fig. 3. Inside this domain,one bin has a p -value = . < . IntDst in Fig. 4, indicating a statistically significant delayed increase of anomalies for D8.Overall, the results displayed in Figs. 3-4 and in Figs. A.13–A.24 therefore confirm the precedingresults obtained for 5-day periods, but they further allow to determine the optimal time delays beforea statistically significant increase of anomalies in di ff erent power grid equipment.Most strikingly, a statistically highly significant increase of anomalies is found for D11–D12(power lines) for both IntDst and
Int ( d ( SYM-H ) / dt ) only ∼ − IntDst = Int ( d ( SYM-H ) / dt ) = IntDst . Such results imply an immediate e ff ect of geomagnetic storms on power lines,already on Days 0 to +
1. This looks quite realistic, because any e ff ect of GICs on power lines (dueto harmonics-related current waveform distortion leading to a detrimental reaction of protectiverelays or other devices connected to these lines) is likely to occur almost immediately.Furthermore, Fig. 4 reveals the presence of a statistically significant delayed increase of anoma-lies for D8 (high voltage transformers) following geomagnetic storms when considering IntDst (anincrease is also present for
Int ( d ( SYM-H ) / dt ) but somewhat less significant), with a delay of ∼ ff ects of storm-time geo-magnetic activity on transformers (note also that the lowest rates of anomalies are observed hereon Days − ff ect of the previous days of zero stormactivity). Transformers may indeed be a ff ected by GICs but still continue to operate for a while –typically for a few days – before actual problems ultimately show up and are registered in logs (e.g.,Wang et al., 2015). ff ects: IntAp parameter Since both ring current variations during storms and other (mainly auroral) current variations dur-ing strong substorms may produce significant GICs, we further performed similar SEAs for the
IntAp parameter, which (despite its own limitations, see section 2.2 and Kappenman (2005)) is ex-pected to roughly take into account the e ff ects of both kinds of disturbances – whereas IntDst and
Int ( d ( SYM-H ) / dt ) only correspond to storm periods. However, due to the relatively low threshold ap ≥
15 (equivalent to
K p ≥
3) of integration used to calculate daily
IntAp levels, this new data se-ries contained many more events (notably, many isolated substorms, sometimes outside of storms)than the previous
IntDst (storm) data set. As a result, requiring as before a 5-day period prior toevents with
IntAp = IntAp maximum on Day 0, with a preceding
IntAp peakon Days −
10 to − IntAp > · hr and such that no similar event was present inthe preceding 5 days.The resulting SEAs displayed in Fig. 5 show that this new selection procedure produces a largepeak IntAp ∼ · hr on Day 0 in the SEAs, with much lower levels on all 10 previous days,especially between Days − −
2. The daily number of anomalies is found to increase by a statis-tically very significant amount during the 5-day period following Day 0 as compared to the 5-dayperiod preceding Day 0, for series D11 and D12 in Fig. 5, with corresponding p -values 0.03 and0.007, respectively. There is a remarkable simultaneity between the peak of IntAp and the peak ofanomalies in the two SEAs with at most one day of delay. Moreover, such peaks of daily anomalieson Days 0 or + ff ects of both storm-relatedand substorm-related geomagnetic disturbances on GICs and power lines (D11–D12) in the Czechpower network. This is certainly due to the major impact of strong substorms on GICs, both duringand outside geomagnetic storms.There are also detectable increases of daily anomalies between 5-day periods before / after Day 0for D8 (transformers, with a delay of ∼ p -values (cid:39) .
25 (see SEAs for all D1 to D12 series provided inFigs. A.25–A.36 in the online supplement).Besides, there is a statistically significant increase of anomalies for D10 (high and very highvoltage electrical substations) with a p -value of 0.006, with a first peak of anomalies at Day + + +
5. While power lines react immediately to GICs, highand very high voltage electrical substations, which comprise busbars, capacitors, or transformers,may indeed be a ff ected but still continue to operate without registered problems until the cumulativedamage reaches a su ffi cient level. A time lag of 3–5 days does not seem wholly unrealistic in thisrespect (Kappenman, 2007; Wang et al., 2015).It is worth noting that our previous analysis based on IntDst did not show a statistically significantimpact of storms for D10 (although the smallest p -value reached 0.08 in Table 3), contrary to thepresent analysis based on IntAp . This suggests that prolonged 2-3 day periods of repeated non-storm-time substorms or solar wind sudden impulses (SIs), taken into account by
IntAp but not by
IntDst , could have a noticeable e ff ect on some electrical substations. ff ects: IntAE parameter Next, we performed similar SEAs for the
IntAE parameter that provides a measure of cumulatedhigh-latitude auroral current variations. An increased hourly auroral electrojet index AE > − AE to
10 20 30 40 50 60 70-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
650 700 750 800 850 900 950 1000 1050-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. 5.
Plots of epoch-superposed subsets D11 (left) and D12 (right) of variations of the daily num-ber of anomalies as a function of time, considering the
IntAp parameter. Solid lines indicate meansuperposed daily rates of anomalies (upper row) or geomagnetic activity
IntAp (in nT · hr) in thereference time series (bottom row) during Days − + AE is not a specific measure of substorms (Kamideand Kokobun, 1996; Tsurutani et al., 2004). We compared the period of 5 disturbed days (withdaily IntAE >
150 nT · hr) immediately following Day 0 (the day of peak IntAE ) with the 5-dayperiod immediately preceding Day 0 – a preceding period of nearly quiet days (with daily
IntAE <
30 nT · hr) especially selected to have such nearly zero IntAE levels. This way, we can check theimpact of disturbed days of strong AE activity (often corresponding to substorms, occurring bothduring and outside storms) on power grid anomalies, as compared with quiet days . We also tried asbefore to consider shorter 3-day periods to help determine the best time lags between increases ofanomalies and Day 0.All the corresponding plots are given in Figs. A.37–A.48 in the Online attachment. In general,these results mostly agree with the IntAp results. However, they are somewhat less statistically sig-nificant than the results obtained with all the preceding metrics, except for the D11-D12 (powerlines) series. For D11, we find a statistically significant 15% increase in the total number of anoma-lies after / before Day 0, with a p -value of 0.034 (see Fig. 6), while for D12 (power lines) the increaseof anomalies is only 2.6%, with a barely significant p = . IntAE confirm the impact on power lines ofauroral electrojet disturbances, often related to substorms. Nevertheless, these results also suggestthat the
IntDst , IntAp , or
Int ( d ( SYM-H ) / dt ) metrics may be slightly more appropriate than IntAE for categorizing disturbed days leading to GIC e ff ects at middle latitudes in the Czech power grid.This could stem from the higher latitudes of stations measuring AE than for the mid-latitude ap
50 60 70 80 90 100 110 120 130-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. 6.
Epoch-superposed daily numbers of anomalies in the D11 series, considering the
IntAE parameter. Solid lines indicate superposed anomaly rates (upper panel) or
IntAE (in nT · hr) in thereference time series (lower panel) during Days − + IntAE may either take into account weak substorms that actually do not strongly a ff ectmiddle latitudes, or it may under-estimate mid-latitude disturbances produced by large substorms(Lockwood et al., 2019; Thomsen, 2004). Alternatively, there could be some significant impacts ofring current variations on GICs at mid-latitudes, not taken into account in IntAE .
5. Discussion
In the SEAs, roughly ≈ −
10% increases of the number of anomalies were often observed duringthe 5 most disturbed days as compared with the preceding 5 consecutive quiet days. However, it isimportant to note that such increases of anomalies were present during only the 5 most disturbeddays among the 21-day total duration of each SEA. It is also unclear if there was any statisticallysignificant increase of anomalies caused by the much weaker geomagnetic activity present duringother days that did not fulfill the criteria for our SEA analysis. It is thus di ffi cult to obtain a credibleestimate of the total fraction of anomalies that could be directly related to geomagnetic e ff ects. Inour previous study (Výbošt’oková and Švanda, 2019), the corresponding total number of anomaliesattributable to variations of geomagnetic activity was also estimated as 1–4%. Such values areconsistent with results from a previous study of the impact of solar activity on the US electric powertransmission network in 1992–2010, which showed that ∼
4% of the corresponding anomalies werelikely attributable to strong geomagnetic activity and GICs (Schrijver and Mitchell, 2013).We also considered di ff erent parameter series, namely cumulative IntDst , IntAp , and
IntAE pa-rameters integrated over the preceding 5 or 10 days, to evaluate the e ff ects of a longer exposure to GICs on power-grid devices. The corresponding superposed epoch analysis did not yield sta-tistically significant results. Without a proper event selection procedure and no integration limit,the SEAs were dominated by weak events, during which the e ff ects were probably weak and didnot emerge from the average rates of anomalies due to causes other than geomagnetic activity.SEAs were further performed separately for weak, moderate, and strong events, but this did notsignificantly improve the results. The most promising results in terms of magnitude of increase ofanomalies during stronger activity were for D8, D10, and D12 for IntDst (with lags of 1–3 days),and D8 and D11 for
IntAE .Based on our analysis, it turns out that geomagnetic disturbances a ff ected mostly the datasetsregistering anomalies on power lines. It is interesting to note that most of the power lines in D7,D11, and D12 are the power lines with distances between grounding points of the order of tens ofkilometers. We also found significant delayed e ff ects in the D8 dataset of high-voltage transformers.Although significant e ff ects were observed in D4 during strong storms (see Fig. S40), the distancesbetween grounding points are of the order of hundreds of meters in this case, that is, much shorterthan for the other power-line datasets. The topology of the network in D4 is also far more complexthan in the other power-line datasets. It is unlikely that GICs induced in the D4 network couldbe responsible for the observed increase of anomaly rate after Day 0 in the corresponding SEA.Nevertheless, some detrimental currents could have entered the D4 network from nearby connectednetworks of other power companies and caused operational anomalies during strong events.
6. Conclusions
As noted by Schrijver and Mitchell (2013), the selection of an appropriate geomagnetic parameteris very important when searching for correlations between anomalies recorded in human infrastruc-tures and variations of geomagnetic activity. Here, we have presented results obtained by consid-ering four di ff erent and complementary parameters of cumulative geomagnetic activity, namely thedi ff erent storm-time Int ( d ( SYM-H ) / dt ) and IntDst low-latitude metrics tracking mainly ring cur-rent variations, the high-latitude
IntAE metric mainly tracking auroral current variations, and themid-latitude
IntAp metric tracking both ring and auroral current variations – all of which were inte-grated over geomagnetically disturbed periods. This allowed us to compare the cumulated numberof anomalies observed in the Czech power grid during the corresponding disturbed days of highgeomagnetic activity with the number of anomalies recorded during quiet days.At the considered middle geomagnetic latitudes, our statistical analysis of ∼
10 years of data hasshown that space weather-related events a ff ected mostly long power lines (D11, D12), probably dueto a distortion of the electrical current waveform that eventually triggered a detrimental reactionof protective relays or disrupted other connected devices. However, significant and slightly moredelayed (by ∼ − ff ects were also observed in high-voltage transformers.Both substorm-related disturbances and magnetic storms were found to have statistically signif-icant impacts on the power grid network, since the four considered measures of disturbed days( IntDst , Int ( d ( SYM-H ) / dt ), IntAp , and
IntAE ) led to more or less similar results – although
IntAE was slightly less e ffi cient. In addition, we found that considering moderate thresholds(neither too large nor too small) on time-integrated geomagnetic activity quantified by IntDst , Int ( d ( SYM-H ) / dt ), or IntAp , produced the most statistically significant increases in anomaly rates,suggesting a non-negligible impact of moderate disturbances. These results are therefore consistent with a major impact of substorms, either inside or outside storms, on GICs at middle latitudes,together with a possible additional impact of ring current variations during storms.It is worth noting that our study showed that in the 5-day period following the commencement ofgeomagnetic activity there is an approximately 5–10% increase in the recorded power line andtransformers anomalies in the Czech power grid, probably related to geomagnetic activity andGICs. Such values are consistent with previous results concerning the US power grid (Schrijverand Mitchell, 2013). Schrijver et al. (2014) further found that for the US network, the 5% stormiestdays were apparently the most dangerous, with a 20% increase of grid-related anomalies as com-pared to quiet periods. We similarly found that the days with a minimum
Dst < −
50 nT (roughlyrepresenting the ≈
8% stormiest days, see Gonzalez et al. 1994) had probably the strongest impactin the Czech power grid, leading to immediate or slightly delayed ∼ −
20% increases of anomaliesas compared to quiet periods.
Acknowledgements.
M.Š was supported by the institute research project RVO:67985815. We are gratefulto power grid data providers for giving us an opportunity to exploit their logs of anomalies, namely toP. Spurný ( ˇCEPS), J. Brož and J. Buˇriˇc ( ˇCEZ Distribuce), R. Hanuš (PREdistribuce), and D. Mezera andR. Bílý (E.ON Distribuce). The maintenance logs are considered strictly private by the power companies andare provided under non-disclosure agreements. We gratefully acknowledge the World Data Center in Kyotoand the Space Physics Data Facility (SPDF) at NASA Goddard Space Flight Center for the OMNI dataat http://omniweb.gsfc.nasa.gov of Dst and
SYM-H geomagnetic indices used in this paper.
Authorcontributions:
DM designed the study and provided processed geomagnetic data, KŽ and TV wrote the pro-cessing code as parts of their student projects under the supervision of MŠ. MŠ performed the analysis. DMand MŠ interpreted the data and wrote the manuscript. All authors contributed to the final version of paper.
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Appendix A: Complete set of figures for all distributors A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400-10 -5 0 5 10 A v e r age i n t D S T Days from epoch A no m a li e s pe r da y Days from epoch 0 20 40 60 80 100 120 140 160 180 200-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.1.
Plot of epoch-superposed D1 series considering intDS T with di ff erent thresholds (left)and int ( d ( S Y M − H ) / dt ) (right). The solid lines indicate the superposed anomaly rates (upper row)or reference time series (lower row) in the Days − + vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 2 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400 450-10 -5 0 5 10 A v e r age i n t D S T Days from epoch A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.2.
Same as Fig. A.1 only for series D2. A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400 450-10 -5 0 5 10 A v e r age i n t D S T Days from epoch A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.3.
Same as Fig. A.1 only for series D3. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 3 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400 450-10 -5 0 5 10 A v e r age i n t D S T Days from epoch A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.4.
Same as Fig. A.1 only for series D4. A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400 450-10 -5 0 5 10 A v e r age i n t D S T Days from epoch A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.5.
Same as Fig. A.1 only for series D5. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 4 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400 450-10 -5 0 5 10 A v e r age i n t D S T Days from epoch A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.6.
Same as Fig. A.1 only for series D6.
10 15 20 25 30 35 40 45-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400-10 -5 0 5 10 A v e r age i n t D S T Days from epoch
10 15 20 25 30 35 40 45-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.7.
Same as Fig. A.1 only for series D7. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 5
80 100 120 140 160 180 200 220 240-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400-10 -5 0 5 10 A v e r age i n t D S T Days from epoch
80 100 120 140 160 180 200 220 240-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.8.
Same as Fig. A.1 only for series D8. A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400-10 -5 0 5 10 A v e r age i n t D S T Days from epoch A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.9.
Same as Fig. A.1 only for series D9. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 6 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400-10 -5 0 5 10 A v e r age i n t D S T Days from epoch A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.10.
Same as Fig. A.1 only for series D10.
20 40 60 80 100 120 140-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400-10 -5 0 5 10 A v e r age i n t D S T Days from epoch
30 40 50 60 70 80 90 100 110 120 130 140-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.11.
Same as Fig. A.1 only for series D11. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 7 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350 400-10 -5 0 5 10 A v e r age i n t D S T Days from epoch A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250-10 -5 0 5 10 A v e r age i n t d ( SY M - H ) / d t Days from epoch-25 nT-30 nT-40 nT-50 nT
Fig. A.12.
Same as Fig. A.1 only for series D12. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 8 D a y s f r o m e p o c h Relative increase 0.60.81.01.21.4 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.40.30.20.10.0 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.70.80.91.01.11.21.3 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.40.30.20.10.0 l o g ( p - v a l u e ) Fig. A.13.
The map for D1 of increases (or decreases) of the number of anomalies as a functionof the middle day of the first and second 3-day periods, together with maps of the corresponding p -values. The upper row is computed for IntDS T as the reference series, whereas the lower row isfor int ( d ( S Y M − H ) / dt ) series. The p -values in the right column are evaluated only if there is anincrease of the grid anomaly rates in the second 3-day period as compared to the first 3-day period.Note the logarithmic scale of the plotted p -values: p = . p = − .
26. Statistically significant bins areindicated by white dots. Blank bins are indicated by the white colour. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 9 D a y s f r o m e p o c h Relative increase 0.70.80.91.01.11.21.3 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.90.80.70.60.50.40.30.20.1 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.60.81.01.21.4 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 1.61.41.21.00.80.60.40.20.0 l o g ( p - v a l u e ) Fig. A.14.
Same as Fig. A.13 only for series D2. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 10 D a y s f r o m e p o c h Relative increase 0.000.250.500.751.001.251.501.752.00 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.80.70.60.50.40.30.20.10.0 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.00.51.01.52.0 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.80.60.40.20.0 l o g ( p - v a l u e ) Fig. A.15.
Same as Fig. A.13 only for series D3. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 11 D a y s f r o m e p o c h Relative increase 0.000.250.500.751.001.251.501.752.00 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 1.61.41.21.00.80.60.40.20.0 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.40.60.81.01.21.41.6 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 1.00.80.60.40.20.0 l o g ( p - v a l u e ) Fig. A.16.
Same as Fig. A.13 only for series D4. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 12 D a y s f r o m e p o c h Relative increase 0.80.91.01.11.2 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.50.40.30.20.10.0 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.70.80.91.01.11.21.3 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.80.70.60.50.40.30.20.10.0 l o g ( p - v a l u e ) Fig. A.17.
Same as Fig. A.13 only for series D5. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 13 D a y s f r o m e p o c h Relative increase 0.60.70.80.91.01.11.21.31.4 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.50.40.30.20.10.0 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.60.70.80.91.01.11.21.31.4 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.50.40.30.20.10.0 l o g ( p - v a l u e ) Fig. A.18.
Same as Fig. A.13 only for series D6. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 14 D a y s f r o m e p o c h Relative increase 0.80.91.01.11.2 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.70.60.50.40.30.20.1 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.80.91.01.11.2 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.60.50.40.30.20.10.0 l o g ( p - v a l u e ) Fig. A.19.
Same as Fig. A.13 only for series D7. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 15 D a y s f r o m e p o c h Relative increase 0.800.850.900.951.001.051.101.151.20 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 2.01.51.00.5 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.850.900.951.001.051.101.15 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 1.41.21.00.80.60.40.20.0 l o g ( p - v a l u e ) Fig. A.20.
Same as Fig. A.13 only for series D8. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 16 D a y s f r o m e p o c h Relative increase 0.20.40.60.81.01.21.41.61.8 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 2.001.751.501.251.000.750.500.25 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.40.60.81.01.21.41.6 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 1.61.41.21.00.80.60.40.20.0 l o g ( p - v a l u e ) Fig. A.21.
Same as Fig. A.13 only for series D9. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 17 D a y s f r o m e p o c h Relative increase 0.970.980.991.001.011.021.03 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 1.41.21.00.80.60.40.2 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.9900.9951.0001.0051.010 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 0.300.250.200.150.10 l o g ( p - v a l u e ) Fig. A.22.
Same as Fig. A.13 only for series D10. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 18 D a y s f r o m e p o c h Relative increase 0.60.81.01.21.4 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 3.53.02.52.01.51.00.5 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.70.80.91.01.11.21.3 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 2.01.51.00.5 l o g ( p - v a l u e ) Fig. A.23.
Same as Fig. A.13 only for series D11. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 19 D a y s f r o m e p o c h Relative increase 0.940.960.981.001.021.041.06 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 3.53.02.52.01.51.00.5 l o g ( p - v a l u e ) D a y s f r o m e p o c h Relative increase 0.920.940.960.981.001.021.041.061.08 R e l a t i v e i n c r e a s e D a y s f r o m e p o c h Increase p-value 4321 l o g ( p - v a l u e ) Fig. A.24.
Same as Fig. A.13 only for series D12. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 20 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.25.
Plot of epoch-superposed D1 of increases (or decreases) of the daily number of anomaliesas a function of time, considering the
IntAp parameter. Solid lines indicate superposed daily ratesof anomalies (upper row) or geomagnetic activity
IntAp in the reference time series (bottom row)during Days − + A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.26.
Same as Fig. A.25 only for series D2. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 21 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.27.
Same as Fig. A.25 only for series D3. A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.28.
Same as Fig. A.25 only for series D4. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 22 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.29.
Same as Fig. A.25 only for series D5. A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.30.
Same as Fig. A.25 only for series D6. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 23 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.31.
Same as Fig. A.25 only for series D7.
30 40 50 60 70 80 90-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.32.
Same as Fig. A.25 only for series D8. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 24 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.33.
Same as Fig. A.25 only for series D9.
750 800 850 900 950 1000 1050 1100-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.34.
Same as Fig. A.25 only for series D10. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 25
10 20 30 40 50 60 70-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.35.
Same as Fig. A.25 only for series D11.
650 700 750 800 850 900 950 1000 1050-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 200 400 600 800 1000 1200 1400-10 -5 0 5 10 A v e r age i n t AP Days from epoch
Fig. A.36.
Same as Fig. A.25 only for series D12. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 26 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.37.
Plot of epoch-superposed D1 of increases (or decreases) of the daily number of anomaliesas a function of time, considering the
IntAE parameter. Solid lines indicate superposed daily ratesof anomalies (upper row) or geomagnetic activity
IntAE in the reference time series (bottom row)during Days − + A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.38.
Same as Fig. A.37 only for series D2. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 27 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.39.
Same as Fig. A.37 only for series D3. A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.40.
Same as Fig. A.37 only for series D4. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 28 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.41.
Same as Fig. A.37 only for series D5. A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300 350-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.42.
Same as Fig. A.37 only for series D6. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 29
10 15 20 25 30 35-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.43.
Same as Fig. A.37 only for series D7.
150 160 170 180 190 200 210 220 230 240-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.44.
Same as Fig. A.37 only for series D8. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 30 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.45.
Same as Fig. A.37 only for series D9. A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.46.
Same as Fig. A.37 only for series D10. vanda et al.: Responses of Czech electric power grid equipment to geomagnetic storms , Online Material p 31
50 60 70 80 90 100 110 120 130-10 -5 0 5 10 A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300-10 -5 0 5 10 A v e r age i n t AE Days from epoch
Fig. A.47.
Same as Fig. A.37 only for series D11. A no m a li e s pe r da y Days from epoch 0 50 100 150 200 250 300-10 -5 0 5 10 A v e r age i n t AE Days from epoch