Introduction
In March 1989 a geomagnetic storm caused a 9 h long blackout in the Québec
Hydro power grid . This outage was the result of large
geomagnetically induced currents (GICs) affecting the power grid and
transformers within the electrical infrastructure. The Québec blackout is
just one extreme example of the dangers of very large GICs, with other direct
consequences being for example the October 2003 transformer collapse near
Malmö in Sweden .
GICs are a consequence of clouds of energetic particles from the Sun
interacting with the Earth's magnetic field causing geomagnetic storms and
rapid geomagnetic variations, which in turn induce geoelectric fields in the
Earth's surface e.g.. This leads to the development
of electric potentials over large distances. With the arrival of extensive
electrical infrastructure, new paths of least resistance for direct current
flow have been created, and currents can flow through the power grid or gas
pipelines . With transformers as the power
grid's earthing points, this leads to quasi-direct currents passing through
the transformers, which in the long and the short term can cause transformer
damage. Direct currents in transformer windings can lead to half-cycle
saturation of the transformer at levels of tens of amperes
. In mild cases, this can lead to reduced AC transmission
capability, transformer heating , and possibly a
shorter transformer life . In the worst case it can lead to
transformer fires and complete transformer failure .
It is therefore important to study, model, and predict the possible GICs that
could affect a conductive network. High-latitude countries (in particular
those in the auroral zone band of 55–70∘ geographic latitude, where
the auroral electrojet dominates) and regions of high ground resistivity are
most susceptible to GICs , and there have been several
studies conducted in these areas . Research into GICs in low-latitude and equatorial countries such
as the Czech Republic , Brazil ,
Spain , Greece , Japan ,
South Africa , Australia
, and New Zealand , which were
previously considered to be at low risk from all but the most extreme
geomagnetic storms, show that considerable GICs (in the range of tens of
amperes) do also appear at lower latitudes. In these regions, large
geomagnetic variations have been shown to result from ring current
intensification, where solar wind is the driving force .
Austria, being a midlatitude country, is not expected to experience
dangerously large GICs; however, due to the presence of the highly resistive
alpine rocks stretching across the country, it is more at risk than areas at
the same latitude. As can be seen in the study of general European GIC risk
in (cf. Fig. 5) based on subsurface conductivity models
from , Austria has a GIC risk comparable to that of areas in
the lower northern auroral zone such as Denmark and Scotland.
In 2014, during the commissioning of a new transformer designed for very low
sound emissions, unexpected noise was noticed by the Austrian Power Grid
(APG), and saturation due to DC currents or very low-frequency currents (below
1 Hz) was assumed to be the reason. The higher levels of noise were
eventually correlated with geomagnetic activity. Soon after, in partnership
with the APG, studies into the presence and nature of GICs in Austria were
started .
In this paper we will describe the usage of a thin-sheet approximation to
model geoelectric fields in Austria. Both surface and subsurface ground
conductivities are taken into account when modelling the induced geoelectric
field from geomagnetic field variations, and these are detailed in
Sect. along with the model. Using the approach originally
described by , we then show in Sect. how
modelled direct currents resulting from the geoelectric potentials flow
through the power grid network. We will present results from the model
compared to direct measurements of GICs at a transformer neutral point. The
accuracy and applicability of the results will be summarised and discussed in
Sect. .
Modelling GICs
The modelling of GICs is achieved through two steps: the first step, often
labelled the geophysical part, is the modelling of the electric field induced
in the resistive, layered ground by geomagnetic variations. The second step,
or engineering part, is the calculation of the flow of currents through a
power grid with grounding points across the Earth's surface. Here, we present
all aspects and principles applied in the modelling of GICs in the Austrian
power grid.
Thin-sheet model
For the first step, calculations of the distribution of the geoelectric field
from the geomagnetic variations are done using a thin-sheet model. This model was originally developed by based on concepts
described in to model induction anomalies. The model is
used to solve quasi-3-D induction problems in areas with large lateral
conductivity variations near the surface. In the model, a 2-D thin-sheet of varying lateral conductivity sits atop a 1-D
half-space of conductivity layers going into the Earth, and therefore more
complex surface currents resulting from shallow conductivity variations can
be accounted for without requiring a full 3-D representation. The version
used in this study is based on code which has been used in modelling GICs in
the UK in the past .
The model input variables are the geomagnetic variations and the surface and
subsurface conductivity models. The geomagnetic variations are passed into
the calculations in the form ΔBx/Δt and ΔBy/Δt,
where ΔBi is the change in the i component of the geomagnetic
field over a certain time period Δt. This means that the analysis occurs
primarily in the time domain. The length of the period that can be used is
constrained by requirements that must be fulfilled for the model to be
physically viable. These requirements are touched on by
and summarised by . They primarily describe relations
between the relative skin depths of the thin sheet and the underlying medium.
The skin depth is given by
δ=2ρωμ=ρπfμ.
It is dependent on both the frequency or period and the resistivity of the
given medium. After applying the constraints to all available subsurface
conductivity models in Austria, we find that the available periods to allow
comparison between models must be greater than 40 s and less than
400 s. To save on computation time, we choose a value of Δt=300 s that will be used for all results throughout this paper. The validity
of this period for modelling geomagnetic storm signals is examined in the
discussion.
Measurements of the geomagnetic variations are taken from the Conrad
Observatory and used to calculate the variation in the field per period (here
300 s) in nanotesla per period. These variations are assumed to be the
same across Austria. Although there are other methods available to model the
changing geomagnetic variations across regions (e.g. spherical elementary
current systems as described in ), the south of Austria is
largely unconstrained due to a general lack of geomagnetic stations and
useful data, which is a potential source of inaccuracies. This will hopefully
be expanded on in the future with the set-up of a new geomagnetic station in
the south of Austria. In the meantime, Austria's relatively small size means
that the assumption of equivalent geomagnetic variations across its area is
reasonable and is not expected to significantly affect the results.
The thin-sheet model described above takes geomagnetic variations and models
of the ground conductivity to compute the geoelectric field strength as a
function of position in Austria. To compute the field as it changes over
time, the day is broken down into 288 windows with Δt=300 s,
each of which is computed individually.
For the second step, the flow of GICs in the network as a result of the
geoelectric field is calculated for each window using the
Lehtinen–Pirjola method described in , which
treats the power grid as an electric circuit and uses Ohm's and Kirchoff's
laws to determine the flow of current.
For this to be valid, we must assume that the system is primarily
time-independent; however, the induced fields vary so slowly with time
(usually in the range of millihertz) that they can be considered constant. This
allows us to ignore contributions to the magnetic field caused by a varying
electric field.
The calculation of GICs using the Lehtinen–Pirjola method reduces to the
following equation in matrix form:
I=(1+YnZ)-1J,
where I is the GIC at all grid nodes or transformer earthing
points and 1 is the identity matrix. The value of I
relies on the following variables: the earthing impedance Z, which
is taken to be only the earthing resistance at each node due to the assumed
time independence of the potentials and the fact that no two stations are
close enough to influence each other's potential; the network admittance
matrix Yn; and the “perfect earthing” or grounding currents
J, which are dependent on the potential difference between two
nodes and the resistance of the line connecting them. The resulting current
I at each node can be positive or negative, representing currents
flowing into or out of the Earth, respectively.
Conductivity models of Austria
The thin-sheet approach described above models the geoelectric field induced
by a changing external magnetic field in an earth with resistivity layers
varying with depth. For a full geoelectric field model, we combine two
different types of conductivity models: firstly, lateral conductivity
variations are taken into account with a 2-D model of the ground conductivity
at the surface of Austria, and secondly, varying subsurface resistivity
layers are represented by a 1-D half-space model of the subsurface
resistivity as a function of depth into the Earth.
In order to develop a detailed conductivity model of Austria, the approach of
was followed, in which electromagnetic data, available
from more than 50 aero-geophysical campaigns carried out between 1980 and 2014
by the Geological Survey of Austria (GBA), were partly reprocessed with
modern techniques. The results are ground conductivity (or resistivity) data
sets of homogeneous half-space inversion results as well as conductivity
multilayer information of the survey areas. In the next step, these data
sets were correlated with a hydrogeological map of Austria on a scale of
1 : 500 000 and average conductivity values were derived for each of the
hydrogeological units. Additionally, information on ground conductivity
values from more than 1000 multi-electrode geoelectric profiles was available
to supplement the subsurface information to complete the entire Austrian
territory. Using available geological maps for outside of Austria, the
conductivity was extrapolated to a rectangular region resulting in a
high-resolution subsurface conductivity map of Austria and its surroundings,
which is shown in Fig. .
High-resolution subsurface conductivity model of Austria and its
surroundings produced by the GBA.
The inversion program EM1DFM (Version 1.0, University of British Columbia,
2000) which was used constructs one-dimensional models of conductivity at
each measurement point. For a layered model it is necessary to predefine the
depth of each interface. For the task required in this work, a homogeneous
half-space is assumed. Interpolating the models of each sounding results in a
conductivity distribution of around 50 to 100 m thick subsurface layers
inside the survey areas. The variation in volume of the captured layer
depends on the conductivity of the subsurface and the height of the
measurement system above the ground. All soundings were conducted from a
height of roughly 50 m with transmitting coils generating an
electromagnetic field with the frequencies 340, 3200, 7190, and 28 850 Hz
and a sampling rate of 10 measurements per second (resulting in a 3 m
measuring point distance). Using these frequencies, the depth of conductivity
values that can be determined from the results depends on the local ground
conductivity. At 3200 Hz, the skin depth in areas with ground conductivity
of 200 to 2 mS m-1 ranges from roughly 14.1 to 140.7 m. At the
highest frequency of 28 850 Hz, the skin depth ranges from 4.7 to 46.8 m.
The hydrogeological map of Austria on the scale of
1 : 500 000 is suitable for the purpose of generalising airborne
electromagnetic data because hydrogeological parameters such as grain size
and water content are determining factors that influence the range of
measured conductivities. This map considers both hydrological and
lithological aspects. For the areas surrounding Austria, the international
hydrogeological map of Europe 1 : 1 500 000; was
used.
The 1-D layer conductivity model was taken from the European RHO Model
(EURHOM) developed by , which was derived from a collection
of magnetotelluric data sets spanning most of Europe. In this model, areas of
certain resistivities are represented by rectangular cells. The area of
Austria and its borders is covered by a total of six different cells as shown
in Fig. . A table showing the four main model resistivities
and associated depths can be found in Table (models 15
and 17 were left out as they were not very relevant to the power grid and
model). As can be seen in the table, each layer is described by the vertical
size of the layer (dm) and a value of resistivity (ρm). These values
range from hardly resistive (5 Ωm) to highly resistive
(10 000 Ωm) and span total depths ranging from 60 to 152 km.
The bottom value for each cell is assumed in EURHOM to remain the same
indefinitely with growing depth. In application we applied the condition of
ρ→0 over depths of many hundreds of kilometres with an exponentially
decaying resistivity beyond a maximum depth of 200 km.
Cells of EURHOM layer resistivity models across Austria.
EURHOM resistivity models from covering most of
Austria.
03
16
39
55
d (km)
ρ (Ωm)
d (km)
ρ (Ωm)
d (km)
ρ (Ωm)
d (km)
ρ (Ωm)
3.00
5.00
20.00
1500.00
55.00
1000.00
0.90
110.00
57.00
1000.00
20.00
500.00
45.00
300.00
1.10
30.00
∞
10
110.00
800.00
∞
1000.00
150.00
10 000.00
∞
10.00
∞
90.00
Depiction of the Austrian power grid provided by the APG. Triangles
represent substations while circles represent network nodes. Red and grey
lines are 380 and 220 kV lines, respectively.
The Austrian power grid
The APG is the transmission system operator in Austria and is also
responsible for the control area of Austria. The APG grid consists of 110,
220, and 380 kV lines and substations. The overall system length of the
transmission grid is over 6700 km, with a total of 60 substations
operating in Austria. For the simulation model, only the 220 and 380 kV
voltage levels are considered and lower levels are ignored due to more
highly resistant lines and different neutral point treatments of transformers
(such as connection to earth via an inductor or being generally isolated),
making them less relevant for GICs. If the distance between two neighbouring
nodes is less than 7 km, they are merged. The power grid used in the model
is a combination of the APG grid in Austria and the nearest stations in the
surrounding countries (Germany, the Czech Republic, Slovakia, Hungary,
Slovenia, Italy, and Switzerland). There are a total of 113 station nodes in
the model network, 43 of which are within Austria and managed by the APG. The
lines are comprised of both 220 and 380 kV lines, and transformer winding
resistances of 0.06 Ω per phase and 0.2 Ω per phase, respectively, are assumed across the grid. These resistance values were taken
as standard values from literature cf.. In addition, it
is assumed that only one transformer on the 380 and 220 kV level per
substation is grounded. The resistance of the grounding is set to
0.2 Ω at all substations. A representation of the grid can be seen in
Fig. 3.
When modelling the DC equivalent of power transformers in the single-phase
network admittance matrix, the different galvanic connections from the
voltage levels to the ground and between the windings have to be considered
. For a step-up transformer, the high-voltage level is
connected through the winding resistor to the grounding resistance of the
substation. In the case of a two-winding transformer, there are windings for
each voltage level connected to the neutral bus. The neutral bus is a node
between the windings and the grounding resistance of the substation. A
two-winding autotransformer DC model differs from those mentioned above. The
series winding connects the high-voltage with the low-voltage level but not
with the neutral bus. With the common winding, a path between the low-voltage
level and the neutral node occurs. The grounding resistance of the substation
connects the neutral bus to earth.
(a) Change in the horizontal geomagnetic field at the Conrad
Observatory (x and y components) per period of 300 s for the days of 14 and
15 October 2014. Change in the x direction is in green; change in the
y direction is in purple. (b) Modelled geoelectric field for the
area near Vienna on the days of 14 and 15 October 2014. The field in the
north–south direction (Ex) is plotted in green; the east–west direction
(Ey) is plotted in purple.
Results
The GIC model parameters described above were applied and the resulting GIC
values have been compared to quasi-DC currents measured directly at a
transformer in the south of Vienna. The Conrad Observatory is also south of
Vienna at a distance of around 50 km from the measurement location, meaning
the input magnetic field is representative of the field at the transformer
site.
Generally, it is quite challenging to monitor low direct currents in the
presence of high alternating currents, and the current measurement device has
gone through iterations for improvement over time. Direct currents at the
transformer neutral point have been measured using a current clamp with Hall
sensor technology. The signal from the current probe is filtered by a passive
second-order low-pass filter with a cut-off frequency of 1 Hz, thus keeping
the very low-frequency components and removing the rest. Afterwards the
signal is recorded by a data logger. Initially there was an upper limit on
the measured values of ±2.3 A (with a sample interval every 60 s), as
the currents were not expected to exceed this value. This figure was exceeded
multiple times during the measurements, and we cannot know what the actual
value would have been. The measurement device has since been updated to
account for greater currents and will allow for more detailed studies in the
future.
The measurements took place in intermittent periods between August 2014 and
August 2015, with a total of 147 days of clean and unbroken 24 h
measurements. Despite the measurements taking place during a relatively weak
solar maximum period, there were few examples of geomagnetic storms and the
associated rapid geomagnetic variations to draw conclusions on the amplitudes
of extreme events. As such, we have chosen one example of a weaker
geomagnetic storm (spanning the days 14 and 15 October 2014) to illustrate
the model and results.
Figure shows the geoelectric field values computed by the
thin-sheet model using geomagnetic variations (dB/dt) at
the Conrad Observatory and the surface and subsurface conductivity models as
input. Here, we can see that the maximum field strength reached is
52 mV km-1 in the Ex component. This corresponds to a
dB/dt value of 23 nT/300 s as also seen in
Fig. .
The GICs that are computed from the modelled geoelectric field using the
Lehtinen–Pirjola method are shown in Fig. . As can be seen from
this example, most modelled GIC behaviour matches the measured DC in both
shape and magnitude reasonably well. The coefficient in the top left, r for
the Pearson's correlation coefficient, shows quantitatively that there is
also a good match in form. The maximum amount of GICs observed here was
2.0 A.
Note that during the measurements shown in Fig. , the measuring
device was saturated at the following times: 14 October 2016 17:00:00 UTC,
14 October 18:23:00, 14 October 2014 22:45:00, and 15 October 2016 01:48:00.
We cannot draw any conclusions on the exact size of the currents flowing
through the transformer during these times other than to say that they were
larger than ±2.3 A (currents in the figure larger than this are due to
a level offset). As there were unknown scales of currents present, this could
mean that the model is underestimating the GICs. One such saturated period
lasted 15 min, suggesting that the currents were much larger during this
time.
Modelled GICs (blue) in comparison to the measurements (red). The raw
measurements are plotted in lighter red and the solid red line are the
measurements that have been filtered to remove noise and reduce to the same
sampling rate of 300 s for comparison to the model. The value in the top
left is the Pearson's correlation coefficient r between the model and
filtered measurements.
A further observation is that there is a long-period (several hours) signal
mid-morning on both days that is only barely accounted for in the model. We
will call this the diurnal signal. As the measurement device was kept at a
roughly constant temperature throughout measurement periods, it is unlikely
that this is a result of daily temperature variations, and it is more likely
a result of the solar-quiet daily variation (Sq) in the horizontal component
geomagnetic field see, e.g.,. This variation is
caused by the influence of the Sun on the sunlit part of the ionosphere and
the resulting current systems and is greatest during the daytime hours.
The diurnal signal can be quantified independently of other variations by
averaging the daily variations in both the measured DC and modelled GICs over
a span of days. The longest available unbroken period of measurements was the
whole of the month of October in 2014 with a few additional days for a total
of 34 averaged days. It is important in this case to restrict the analysis to
one time of year due to the seasonal variation in the Sq variation in the
geomagnetic field. Plotted in Fig. is the result of
measurements and model outcomes being averaged over all 34 days as well as
the residuals. Plotted alongside the averages for comparison is the
mean-subtracted geomagnetic field variation in the horizontal component H
for the same period. The DC measurements have been filtered to remove a
prevalent and regularly recurring 15 min signal, which originates from the
power system itself. As can be seen clearly in the figure, both the modelled
and measured GIC variations contain a long-period signal between the times
05:00 and 14:00 UTC, but they appear to be phase-shifted. Other
shorter-period signals that appear later in the day (later than 14:00) are
not phase-shifted.
Panel (a) displays the averaged daily variations in
measured DC currents (red) and the model results (blue) with 95 %
confidence intervals, while (b) shows the averaged residuals between
the measurements and models, revealing signals that are not covered by the
model. (c, d) The cross-correlation between model and measurements
within the diurnal signal (c) and outside (d), with the
maxima highlighted in red.
We can quantify the amount of phase shift by looking at the cross-correlation
between the model and measurements, shown on the right side of
Fig. . The upper plot shows the cross-correlation between
averaged measurements and model results during the diurnal variation time,
which should be 0 but is offset by 10 data points (maximum shown in red). In
our case of Δt=300 s, this equates to a time lag of the model
behind the measurements of τ=3000 s or 50 min. A sine fit to both
signals in the restricted time period results in fitted periods of
PDC=2.96×104 s and Pmodel=2.82×104 s (8 h). The equivalent phase shift between the two using
PDC is φ=36.4∘, which is considerable and
unexpected.
The maximum cross-correlation for the rest of the day
(Fig. , lower right), in contrast, behaves as expected and
shows no lag, as do all analyses of individual days; therefore, we can exclude
the possibility of this effect being caused by an artefact in the model. We
will investigate the cause of this localised phase shift in the discussion.
Susceptibility of grid to field orientation
Following the approach used in , , and
most recently , a uniform horizontal geoelectric field of
1 V km-1 in all possible field orientations is applied to the grid
to evaluate the susceptibility of particular substations and sections in the
grid to varying field directions. A field strength of 1 V km-1 would
only arise as a result of particularly strong geomagnetic variations, and the
results are also a useful indication of the GICs that can be expected during
extreme geomagnetic storms.
The results of this analysis are plotted in Fig. . Each
circle represents a node, with the size of the circle the magnitude of the
GICs experienced at that node. At each station, the maximum GICs resulting from
an electric field of 1 V km-1 in all possible directions has been
plotted and thereby reveals which stations are at risk of particularly
large currents. The red arrows show the direction of the electric field
leading to the maximum levels of GICs (0∘ = N–S,
90∘ = E–W, etc.). Only the maxima are plotted here, although a
reversed field (rotated by 180∘) would result in the same amount of
current flowing in the opposite direction. The largest resulting current in
the stations controlled by the APG is 49.13 A in southern Vienna for a N–S-oriented electric field. In contrast, the maximum GICs seen with an applied
E–W-oriented electric field is only 82 % of this value at 40.21 A.
The largest value in the whole network (including surrounding countries) was
49.38 A in western Slovakia for an electric field in the NW–SE direction.
In summary, we see that the Austrian power grid is more susceptible to
northerly geoelectric fields or strong east–west geomagnetic field
variations, such as can be seen during substorm periods in geomagnetic
storms.
Maximum GICs at the various stations in the Austrian and nearby
network for all orientations of a geoelectric field with magnitude
1 V km-1. Each circle represents a node, and the line connections
between nodes are shown in grey. The size of the circle represents the
magnitude of GICs, while the arrows depict the geoelectric field orientation
that leads to a maximum at that node. The position of the Conrad Observatory
(WIC) is marked by the black triangle.
Spatial distribution of GICs in Austria
As can be seen in Fig. , the largest currents are seen
primarily in the east and west of Austria (near Vienna and Innsbruck) with
some central spots also seeing larger GICs. As the Austrian power grid is
connected to those of its neighbours, there are no edge affects as seen in
countries with, e.g., coastlines where the grid has a defined edge, but
considerable GICs can still arise. Generally, nodes sitting on
north-/northwest-running lines experience the largest amounts of GICs, roughly twice as much as nodes
sitting only on east-running lines.
Discussion
Analyses of geomagnetically active days in the data such as the period in
October presented in the figures show very good correlation (r>0.8)
between the model and measurements, which is what we would hope for in order
to correctly model large and potentially dangerous currents that would only
appear during geomagnetically active storm times. This good correlation does
not, however, carry over to geomagnetically quiet days, where the model fit
is not optimal (r∼0.5–0.7). The reason for this is partly due to
non-geomagnetically induced current signals prevailing at lower-magnitude DC but is also largely a result of the dominance of the “diurnal signal” noted
above, and it becomes clear that the model does not accurately represent the
long-period signal seen in the measurements. Therefore, we wish to evaluate
the source of this signal in order to discover areas in which the model is
lacking and to better model all types of signals.
Impedance phase shift
We can first approach this as a quasi-static system in which the source of
the phase shift is the components of the power grid itself. The circuit
formed by the ground potential between two nodes and the lines that join them
can be treated as an RLC circuit or resonant circuit. Here, we review the
concept of impedance phase, which is the phase shift by which an alternating
current lags the voltage. We will treat the diurnal signal as a very
slowly varying AC current and the circuit as one in which the ground
potential is the applied voltage and the transformer earthing resistances and
the line resistances in series make up the circuit. The phase shift between
the voltage and current in a circuit with resistors, capacitors, and inductors
can be calculated using the following equation:
θ=atanXL-XCR,
where the variables in the numerator are the inductive and capacitive
reactances, respectively, calculated using the formulae XL=2πfL and
XC=1/(2πfC). In a purely resistive circuit with XL-XC=0,
the phase shift would be θ=0∘.
In the simple case of a homogeneous electric field, V∝E∝dB/dt and we can use the geomagnetic variations as proxy
for the voltage to calculate the phase shift. A cross-correlation analysis
between the diurnal signal in the measurements and dB/dt
shows that the current leads the voltage by around 50 min
(θmea=35.8∘) and the model leads by around
100 min (θmod=71.6∘). There is a residual phase
shift of 35.8∘, with the measurements lagging the model prediction.
If we assume that the grid causes the residual phase shift, then from
Eq. () we know that it is an inductive circuit. However, in
application, a circuit leading to the observed phase shift (with a total
resistance of 8 Ω from the transformers and line) would have an
inductance of L=27 710 H, a highly unrealistic inductance for a
circuit. For comparison, a rectangular coil the size of Austria (∼600×300 km) with a wire diameter of 1 m and a core of iron does not
even reach the above value with an inductance of only ∼23 100 H.
Although there is likely to be a small phase shift in GICs through a power
grid caused by inductive and capacitive components, it would not be to the
extent seen here. We can exclude the quasi-static approach and move on to a
geophysical interpretation.
Phase shift between model and measurements
It is known in the field of magnetotellurics that there is a phase shift in a
geoelectric field induced in a medium that depends on the conductivity of the
medium and the analysed frequencies , with some showing a
decrease with decreasing frequency e.g.. Different
signal frequencies travel preferentially inside different layers within their
penetration depth, and a phase shift between the measurements and the model
could be a result of modelling with an inaccurate subsurface conductivity
model or of not reaching an adequate depth while modelling.
As we are only analysing windows of 300 s in sequence, it is likely that
signals with greater periods are not accurately modelled. However, an
analysis of the same data in greater windows (900 s) results in the same
shift. Here, we include a power spectrum analysis of the GIC measurements for
clarification. Analyses of GICs during geomagnetically active and stormy
times, which are our primary interest, show that the dominant signal periods
are around 1700 s or 6×10-4 Hz, which is well below the
Nyquist frequency of the window used (νn=1.6×10-3 Hz) and
will be covered by the modelling approach. A power spectrum of the DC
measurements in Fig. shows that signals with frequencies
greater than 6×10-3 Hz (<170 s) are swallowed by white
noise.
Power spectrum of DC measurements. The window used in our analysis
as well as the associated Nyquist frequency of that window (νn) are
displayed as red and black lines, respectively. The two defined spikes in the
spectrum around 10-3 Hz result from periodic 15 and 7.5 min signals
related to the power system.
The only clue as to the actual cause comes from a comparison between a model
using the geoelectric field derived from one subsurface layer model and a
model using multiple subsurface models. In the simplest case, the GICs will be
calculated from an Austria-wide geoelectric field modelled from geomagnetic
variations on a single subsurface resistivity layer model (e.g. EURHOM 39). In a more complex and geophysically realistic case, the code extracts
geoelectric fields from multiple EURHOMs (four in total; see again
Fig. ) depending on the area of network being modelled. The
results from the more complex model using multiple EURHOM cells prove to be
better fits to the measurements (an improvement in r averaging 0.05). When
put through the same procedure as above in determining the averaged daily
variations, the phase shift between the more complex model and measurements
is 35 min instead of the original 50 min. A further test on data from
April 2015 with a shorter period of 11 averaged consecutive days, which also
shows a phase shift between model and data of 50 min, results in a similar
improvement of 50 to 40 min in time lag. While only a small improvement,
this highlights the importance of the lateral geoelectric field variations
input parameter in the model, which can be developed further in future model
iterations.