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Space weather and power grids - a vulnerability assessment


Abstract and Figures

Strong geomagnetic disturbances resulting from solar activity can have a major impact on ground-based infrastructures, such as power grids, pipelines and railway systems. The high voltage transmission network is particularly affected as currents induced by geomagnetic storms, so-called GICs, can severely damage network equipment possibly leading to system collapse. Therefore, increasing attention has been devoted to understanding the vulnerability of power grids to space weather conditions. In this study, we aim at analysing the vulnerability of power grids to extreme space weather. By means of complex network theory, we propose an analysis approach to understand how geomagnetically induced currents are driven through the power network based on its structural and physical characteristics. As a test network we used the Finnish power grid for which a study using network centrality measures was carried out to understand which components are the most critical for the system when exposed to an electric field of 1V/km. This information is helpful as the identification and ranking of critical components can help to identify where and how mitigation measures should be implemented to increase the system’s resilience to space weather impact. We have also subjected the grid to varying angles of the electric field. In addition, we have carried out a scoping study adding load flow to the GICs induced in the system. The preliminary results suggest that the benchmark system can resist GICs induced from high intensity electric fields. Moreover, the simplified network seems more prone to collapse if the electric field is oriented northward. Work is underway to further validate and expand our approach with the aim to eventually carry out a risk assessment of space weather impact on the power grid at EU level.
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Roberta Piccinelli, Elisabeth Krausmann
Space Weather and Power Grids –
A Vulnerability Assessment
Report EUR 26914 EN
European Commission
Joint Research Centre
Institute for the Protection and Security of the Citizen
Contact information
Elisabeth Krausmann
Address: Joint Research Centre, Via E. Fermi 2749, 21027 Ispra (VA), Italy
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Image credits: Aurora Australis, as seen from the ISS (©ESA/NASA)
EUR 26914 EN
ISBN 978-92-79-43971-1
ISSN 1831-9424
Luxembourg: Publications Office of the European Union, 2014
© European Union, 2014
Reproduction is authorised provided the source is acknowledged.
Strong geomagnetic disturbances resulting from solar activity can have a major impact on ground-based
infrastructures, such as power grids, pipelines and railway systems. The high voltage transmission network is
particularly affected as currents induced by geomagnetic storms, so-called GICs, can severely damage networ
equipment possibly leading to system collapse. Therefore, increasing attention has been devoted to
understanding the vulnerability of power grids to space weather conditions. In this study, we aim at analysing the
vulnerability of power grids to extreme space weather. By means of complex network theory, we propose an
analysis approach to understand how geomagnetically induced currents are driven through the power networ
based on its structural and physical characteristics. As a test network we used the Finnish power grid for which a
study using network centrality measures was carried out to understand which components are the most critical fo
the system when exposed to an electric field of 1V/km. This information is helpful as the identification and ranking
of critical components can help to identify where and how mitigation measures should be implemented to
increase the system’s resilience to space weather impact. We have also sub
ected the grid to varying angles of the
electric field. In addition, we have carried out a scoping study adding load flow to the GICs induced in the system.
The preliminary results suggest that the benchmark system can resist GICs induced from high intensity electric
fields. Moreover, the simplified network seems more prone to collapse if the electric field is oriented northward.
Work is underway to further validate and expand our approach with the aim to eventually carry out a ris
assessment of space weather impact on the power grid at EU level.
Space Weather and Power Grids -
A Vulnerability Assessment
Roberta Piccinelli and Elisabeth Krausmann
Strong geomagnetic disturbances resulting from solar activity can have a major impact on ground-
based infrastructures, such as power grids, pipelines and railway systems. The high voltage
transmission network is particularly affected as currents induced by geomagnetic storms, so-called
GICs, can severely damage network equipment possibly leading to system collapse. The first accident
of this kind occurred in Canada in 1989 where it took only 90 seconds for the entire Hydro-Quebec
power grid to collapse during a geomagnetic storm. Since then, increasing attention has been
devoted to understanding the vulnerability of power grids to space weather conditions.
In this study, we aim at analysing the vulnerability of power grids to extreme space weather. By
means of complex network theory, we propose an analysis approach to understand how
geomagnetically induced currents are driven through the power network based on its structural and
physical characteristics. As a test network we used the Finnish power grid for which a study using
network centrality measures was carried out to understand which components are the most critical
for the system when exposed to an electric field of 1V/km. This information is helpful as the
identification and ranking of critical components can help to identify where and how mitigation
measures should be implemented to increase the system’s resilience to space weather impact. We
have also subjected the grid to varying angles of the electric field. In addition, we have carried out a
scoping study adding load flow to the GICs induced in the system. The preliminary results suggest
that the benchmark system can resist GICs induced from high intensity electric fields. Moreover, the
simplified network seems more prone to collapse if the electric field is oriented northward.
Work is underway to further validate and expand our approach with the aim to eventually carry out
a risk assessment of space weather impact on the power grid at EU level.
Table of Contents
1. Introduction .......................................................................................................................................... 4
2. Space weather and GICs ........................................................................................................................ 5
2.1 Geomagnetic Storms (GMSs) .......................................................................................................... 5
2.2 Historical overview – Major GMSs of the past ............................................................................... 8
2.3 Simulation of extreme GMSs .......................................................................................................... 9
2.3.1 Ground conductivity structure ................................................................................................. 9
2.3.2 Temporal and spatial scale ..................................................................................................... 10
2.4 Space weather effects on power systems .................................................................................... 11
2.5 Effects on other earthed critical infrastructures .......................................................................... 14
2.5.1 Pipelines ................................................................................................................................. 14
2.5.2 Railways ................................................................................................................................. 15
2.6 Calculation of GICs in power transmission networks ................................................................. 16
3. Network vulnerability framework and risk assessment ..................................................................... 18
3.1 Vulnerability framework ............................................................................................................. 18
3.2 Complex network theory framework .......................................................................................... 20
3.3 Centrality measures ..................................................................................................................... 21
4. Power Grids and Geomagnetically Induced Currents (GICs) ............................................................. 25
4.1 Case-study: benchmark power grid ............................................................................................. 25
4.1.1 Calculation of GICs: uniform electric field ............................................................................... 29
4.1.2 Calculation of GICs: uniform electric field with varying angles .............................................. 33
4.2 Power Flow and GICs .................................................................................................................... 39
4.3 Discussion ..................................................................................................................................... 42
5. Conclusions .......................................................................................................................................... 43
References ................................................................................................................................................. 44
1. Introduction
Geomagnetic disturbances produced by solar activity, also called space weather, can affect ground-
based critical infrastructures, potentially causing damage to systems and resulting in failures and
service disruptions. Among critical infrastructures, the long-distance, high-voltage power grids are
particularly vulnerable to geomagnetic storms: effects may comprise both limited equipment failure
and potential voltage instability resulting in uncontrolled cascading of the bulk power system
(Krausmann et al, 2013; Schrijver and Mitchell, 2013).
The collapse of the Hydro-Québec transmission network during a geomagnetic storm in 1989 was a
warning sign for the vulnerability of power grids to space weather events. The consequences of the
Hydro-Québec blackout on the industrial production in a number of sectors also highlight the
increased likelihood of significant domino effects in case of a power outage (Boteler, 2001).
Several studies have been dedicated to the assessment of the power grid’s vulnerability to extreme
space weather and to the investigation of the potential consequences of prolonged blackouts on
society (NRC, 2008; Kappenman, 2010; JASON 2011; NERC, 2012). These studies focus on a potential
major space weather impact on the North American transmission network and its components, and
especially on high-voltage transformers. An extreme event, such as the 1859 Carrington event, is
believed to be able to cause disruptions in the power grid that subsequently cascade to other critical
infrastructures with a worst-case long-term recovery time for society of 4-10 years (NRC, 2008).
An extreme geomagnetic storm would encompass also a significant part of Europe (Pulkkinen et al,
2012). Various analyses of the vulnerability of the European power grid have considered reliability
failures and intentional attacks (Brancucci et al, 2012; Rosas-Casals, 2007; Bompard, 2009) but
hardly any information exists on the vulnerability of the European power grid to space weather
This study aims at identifying the vulnerability of the European power transmission grid with respect
to extreme space weather by using complex network theory. We try to understand the spatial
distribution and magnitude of GIC loading and the impact on grid operations potentially incurred. In
a later step, this study will continue to estimate the impact of extreme space weather on society in
Europe via the interdependencies of critical infrastructures with the power grid.
Section 2 presents a general overview of the physical phenomenon of geomagnetic storms and their
impact on ground based critical infrastructures. In Section 3 we propose the vulnerability framework
which will guide our analysis, and first results including a discussion are presented in Section 4.
Conclusions and future work are discussed in Section 5.
2. Space weather and GICs
Space weather is a consequence of the interaction of the Sun, the Earth’s magnetic field and the
atmosphere. High-energy particles and radiation ejected from the Sun, once they reach the Earth,
can cause temporary fluctuations of the geomagnetic field: these variations are called geomagnetic
disturbances (GMDs). Transient fluctuations of sufficient severity are termed geomagnetic storms
Coronal mass ejections (CMEs), solar flares and radio bursts are the main phenomena connected
with the formation of GMDs. CMEs are usually associated with large flares. If CMEs are Earth-
directed, they interact with Earth’s magnetosphere and cause geomagnetic storms that are observed
on Earth one to six days after a flare or an eruption occurs on the Sun (FEN, 2013). GMSs, in turn, can
create geomagnetically induced current (GICs) flows that can potentially affect the operation of
power system equipment. Equipment impacted by previous storms include transformers, circuit
breakers, generators and protective devices.
Several factors determine the degree to which a GMS affects the power system and its equipment.
These include (NERC, 2012):
Magnitude and orientation of the magnetic field
Geomagnetic latitude
Geology of the local area, including the electrical conductivity of the soil
Proximity to an ocean or large water bodies
Directional orientation, resistance and length of transmission lines
Design of the power system and its equipment
GMSs can affect the components and the operation of power systems through a wide range of
impacts. Effects with minor severity may be the tripping of electrical equipment or control
malfunctions. Major GMSs may trigger voltage and reactive power fluctuations, local disruption of
service, equipment failure and potential voltage instability that can potentially result in the
uncontrolled cascading of the bulk power system.
2.1 Geomagnetic Storms (GMSs)
The sun continuously emits charged particles in all directions. This stream of mainly protons and
electrons is called solar wind. CMEs are fast-moving bursts of plasma created by high-energy
phenomena on the sun. They can reach the Earth in a matter of days, if oriented in the right
direction, where the CME plasma then interacts with and perturbs the Earth’s magnetosphere, a
region in space where the motion of charged particles is determined by the Earth’s magnetic field
(Figure 1). Of significance for the formation of GMSs is the ionosphere, a part of the atmosphere
where electric currents, or electrojets, periodically travel around the Earth (Püthe and Kuvshinov,
Figure 1. Schematic representation of solar wind particles interacting with Earth’s magnetosphere. Size is not
to scale (NASA, 2014).
Particularly relevant are the auroral electrojets which are large horizontal currents that flow in the
auroral ionosphere following generally circular paths around the geomagnetic poles at altitudes of
about 100 kilometers in an eastward (EEJ) or westward direction (WEJ), as shown in Figure 2 (INGV,
2014). Since the conductivity of the auroral ionosphere and its horizontal electric field are generally
larger than that at lower latitudes, the auroral electrojet currents are particularly relevant for their
strength and continuity.
Figure 2. Representation of the East (EEJ) and West (WEJ) auroral electrojet (INGV, 2014)
When the geomagnetic activity is low, the electrojet would mostly be limited to the auroral oval.
However, during periods with high geomagnetic activity, the electrojet expands to higher and lower
latitudes and becomes stronger. This can result in geomagnetic field fluctuations, or GMDs. Severe
transient fluctuations or GMSs are measured in nanoteslas (nT). The Earth’s magnetic field at the
poles is about 70 000 nT. During a severe storm, the fluctuation can be so strong so as to deflect
compass needles.
A common scale used to indicate levels of geomagnetic activity are the K and A
indices (SWPC,
2014). The K-index ranges from 0 to 9 and is related to the maximum fluctuations of the horizontal
magnetic field variation over a three-hour interval. The maximum positive and negative deviations of
the data recorded every minute over a 3-hour period are added to determine the total maximum
fluctuation. These fluctuations may occur at any time during the 3-hour interval. The A
index ranges
from 0 to 400 and is a 24-hour index derived from 8 daily K indices. Values of K from 0 to 4 (and of A
from 0 to 20) represent quiet geomagnetic activity, values from 5 to 6 (and of A
from 30 to 50)
represent a minor storm and a severe storm results in a K ranging from 7 to 9 (and of A
from 100 to
The solar activity approximately follows an 11-year cycle. Since 1755, when recording of the solar
activity began, 24 cycles have been recorded. The current 24
cycle has begun in January 2009. The
previous cycles 22 and 23 lasted from September 1986 to May 1996 and from May 1996 to
December 2008 respectively.
Figure 3. Sunspot cycles and the occurrence and intensity (using the A
index) of geomagnetic storms
(Kappenmann, 2010)
As shown in Figure 3, it appears that the geomagnetic activity is also cyclical, although it has to be
stressed that a severe storm can occur at any time during a cycle, and not only around the peaks of
sunspot activity. It should also be noted that not every solar event produces a GMD on Earth, which
makes forecasting storms based on solar observation only very difficult. New forecasting capability is
based on missions by NASA and European Space Agency, which provides data on the space
environment (NERC, 2012).
For electric utilities, however, it is more important to know the time derivative of the geomagnetic
field over a few minutes because it is this value that is a key factor in calculating GICs (IEEE, 1993):
for example, a rate of variation of 300 nT/min indicates a violent storm. Large values of K or Ak in
general are not directly translatable into large GICs, since they depend on averages over a fixed
period of time, and are thus only an indirect indicator of a GMD that can affect power systems.
2.2 Historical overview – Major GMSs of the past
The Carrington Event of 1859
The largest recorded magnetic storm occurred between August 27 and September 7, 1859 and it is
known as the ‘Carrington Event’, after the British amateur astronomer who was the first to associate
the storm with an intense solar flare 17.1 hours earlier. There were eyewitness accounts of auroras
even at equatorial latitudes (JASON, 2011). The world’s telegraph networks experienced severe
disruptions, in some cases telegraph operators received electric shocks (NRC, 2008), and Victorian
magnetometers were driven off the scale (BGS, 2014).
The 1921 Solar Storm
In May 1921, auroras were observed in Europe, across North America and far south at latitudes of
30-35 degrees (Silverman, 2001). This storm was reported to have “blown out fuses and injured
electrical apparatus”. Telegraph communications were disrupted in cities in the United States and
some cables and telegraph lines to Alaska did not function during the storm (Solarstorms, 2014 and
references of Newspapers herein).
The 1989 Québec Blackout
On 13 March 1989, a severe geomagnetic storm caused the entire Hydro-Québec transmission
system to collapse (Boteler, 2001), resulting in a blackout that affected 6 million people. It took only
90 second for the grid to break down and more than 9 hours to restore power.
The blackout had ripple effects also on North American power system and utilities. One of the
nuclear power plant transformers in Salem, New Jersey, suffered damage and had to be replaced.
The 2003 Halloween Solar Storms
The largest recent storms originate in 17 major solar flares that erupted on the sun between October
19 and November 5, 2003. Extensive effects on technological systems and human activities were
reported. The most affected were spaced-based infrastructures: sensors and electronic devices of
satellites were damaged and airline routes and schedules were significantly affected due to
communication degradation and concerns about increased radiation exposure (NERC, 2012).
The electric power industry in North America experienced some effects, which include high levels of
neutral current, capacitor trips, and some transformer heating.
The impacts were more significant in Northern Europe where an estimated GIC flow of 330 Amperes
in a transformer in Southern Sweden caused a 130 kV line to trip, resulting in a 40 minutes blackout
(NERC, 2012). No transformer issues were reported to be associated with the currents induced by
the geomagnetic storm in Sweden.
2.3 Simulation of extreme GMSs
In order to simulate extreme GMS events, a number of factors that determine the geoelectric field
need to be considered. The main factors are the effect of the ground conductivity structure and
geomagnetic latitudes on the geomagnetic field amplitudes, as well as the temporal and spatial
scales of the extreme geoelectric fields.
2.3.1 Ground conductivity structure
During geomagnetic storms, magnetic field variations produce an electric field that drives large
electric currents through the ground and in conductor networks (Campbell, 1980; Boteler et al.,
1998). Large power systems extend across different geological structures and the effect of
conductivity changes needs to be accounted for when dealing with geomagnetic fields and GICs
Different techniques are available to develop ground conductivity models (Kappenman, 2010). On
the one hand, descriptions of the local geology can be used to infer an average value of conductivity
versus depth for the region of interest (Thomson et al, 2009; Pracser et al, 2012). Methods for
modeling earth conductivity structures can be one- (1D), two- (2D) or three-dimensional (3D). Some
models and methods are advantageous in terms of computation speed while others provide a better
accuracy (Dong et al, 2013). Past experience has suggested that 1D Earth conductivity models are
sufficient for the evaluation of the local electric field (Viljanen et al., 2012; Pracser et al, 2012;
Kappenman, 2010). The general 1D model consists of a half-space, representing the ground, that is
divided into N layers with the n-th layer having a resistivity ρn (or conductivity σn = 1/ ρn) and
thickness z (Figure 4).
Mono-dimensional models only contain the variation of conductivity with depth and ignore any
lateral variations. Discontinuity of the conductivity structure due to ground variations, for example
near oceans, can be accounted for by using adequate boundary conditions.
On the other hand, actual measurements of geomagnetic and electric fields are available for certain
regions of interest (Kappenman, 2010). Modern fluxgate magnetometers allow magnetic measures
of the three-components of the magnetic field. In North America, The United States Geological
Survey (USGS, and the Geological Survey of Canada (GSC,
science) operates the magnetic observatories. In Europe, the British Geological Survey (BGS, is one of the most active. Magnetic data are also available from these institutes
through the InterMagnet international consortium website (
Figure 4. Mono-dimensional N-layered Earth model. Data are taken from Pracser et al (2012).
2.3.2 Temporal and spatial scale
The digital geomagnetic data can also be used to evaluate the rate of change of the magnetic field
dB/dt. Figure 5 reproduces the percentage occurrences of dB/dt > 300nT/minute, derived from
North American magnetic observatories. Since the probability variation with the geomagnetic
latitude is smooth, the results were extrapolated along lines of constant geomagnetic latitude. The
color grading extends from red, where the probability is higher, to yellow in those areas where the
probability diminishes. A low probability for large GMD events is expected in most of North America
and Central Europe (Molinski et al., 2000).
An alternative approach to the calculation of the electric fields is by means of a statistical analysis on
the electric field values. Pulkkinen et al (2012) used 10-second samplings of geomagnetic data
recorded from 1993 to 2006, thus covering a solar cycle period, to determine the electric field
magnitude expected once in a 100 years. The two main results of this analysis are that the
occurrence of large electric fields decreases with increasing amplitude (Fig. 6 left) and the peak
electric fields shows a strong dependence on latitude (Fig. 6 right).
Figure 5. Map representing the probability of a significant geomagnetic storm, with a field change greater than
300nT/min (Rodrigue, 2014).
Figure 6. On the left, the statistical occurrence of the geoelectric field is represented: the different colors
correspond to different IMAGE stations used in the computation. The thick black and grey lines represents the
approximate extrapolation and the upper and lower boundaries, respectively. The maximum 100-year
amplitude is estimated to be between 10-50V/Km. On the right, the geomagnetic latitude distribution of the
maximum computed geoelectric field for the 2003 Halloween GMS is shown (Pulkkinen et al, 2012).
2.4 Space weather effects on power systems
The critical infrastructure that society has become most reliant on is the power grid. Power networks
play a vital role in everyday life either as a standalone critical infrastructure providing electrical
power but also as a service provider to many other critical infrastructures that critically rely on the
power grid.
GICs are quasi-DC currents that can cause numerous problems when entering the power grid.
Transformers are particularly susceptible to GIC impact as they are not designed to handle the DC
current. In fact, almost all power grid equipment and operations problems due to space weather
arise from disturbed transformer performance, which is driven into half-cycle saturation by the GIC.
As a consequence, the normally nearly linear relationship between input and output voltages and
currents is shifted into a non-linear region. A number of secondary effects follow, such as increased
reactive power consumption and the injection of even and odd harmonics into the power system.
These harmonics cause even less compensating reactive power to be available, which can eventually
lead to grid collapse (Molinski, 2002). Boteler (2001) notes that the situation is worse for power grids
with long transmission lines, e.g. in the range of hundreds of kilometers, because longer lines have
higher voltage support requirements.
The following sections briefly describe the main damage and failure modes associated with GIC
loading in power grids.
Transformer saturation
Power transformers are used for stepping up voltage levels for electricity transport in transmission
lines or reducing the voltage for electricity distribution to the customers. They use steel cores and
are designed to be extremely efficient. As shown in Figure 7 (left), transformers usually operate in
the linear range of their magnetic characteristic, which corresponds to an exciting current of only a
few Amperes of AC. If GICs flow in the system, the operating point on the steel core saturation curve
is shifted towards the nonlinear portion of the characteristic (Figure 7 right). Consequently,
saturation occurs during one half of the cycle, causing a very high and asymmetrical exciting current
(10-15% or more of the rated load current) to be drawn by the transformer (Ngnegueu et al, 2012).
Different transformer types are impacted differently by half-cycle saturation (Kappenman, 2010).
Single-phase transformers, in particular, are more at risk than three-phase transformers because the
quasi DC flux induced by the GIC can flow directly in the core. Furthermore, shell-type transformers
are at greater risk than core-type transformers while autotransformers are particularly susceptible
(Kappenman, 2010).
Reactive power losses
Transformers saturated by GIC loading have a higher reactive power consumption, which increases
linearly with GIC magnitude (Albertson, 1973; Walling and Kahn, 1991). Single-phase transformers
consume the largest amount of reactive power. A 90° voltage shift caused by the excitation current
during saturation creates a reactive power demand from the power system. As a consequence there
may be drops in system voltage and the stability margins may decrease significantly because
additional reactive power is being consumed. The situation is exacerbated if voltage support devices
trip during GIC events (Molinski, 2002) because of the injection of harmonics into the system.
Figure 7. Relationship of exciting current and magnetic flux under normal operating conditions (left) and in the
presence of GICs (right) (Molinski, 2002).
When a transformer is driven into half-cycle saturation, the exciting currents contain harmonics of
various orders (fundamental, 2
, 3
, etc.), giving rise to complex current patterns. In case of very
large GIC levels, the contribution of harmonics declines, especially at the higher orders, since the
transformer is operating in a completely linear, although saturated, region of its magnetizing curve
(Molinski, 2002). Power grids are generally designed to cope with odd harmonics (e.g. 3
). However,
they can be overwhelmed by even harmonics (e.g. negative sequence 2
harmonic) because they
are usually not expected during power operations (Molinski, 2002). False neutral overcurrent relay
actuation may be the consequence. Moreover, harmonic currents can also cause additional series
losses in e.g. circuit breakers and filter banks.
Transformer overheating
In case of transformer saturation most of the excess magnetic flux flows externally to the core into
the transformer tank, where currents are created and localized tank wall heating with temperatures
reaching 175°C can occur (Kappenman, 1996). If a transformer is repeatedly exposed to heating due
to GIC loading, it can lead to cumulative insulation damage, accelerated ageing and eventually
transformer failure (Koen and Gaunt, 2003). Unfortunately, in such cases it is usually not
straightforward to relate cause and effect, so the real cause of transformer failure could be
attributed to other reasons.
Generator overheating
Although no serious generator damage due to GMSs has been documented so far, there is at least
theoretically some potential for damage (Molinski, 2002). Generators are usually shielded from
direct GIC impact but they can still be affected by harmonics and voltage unbalance caused by
transformer saturation. If harmonic currents enter the generator, excessive heating and mechanical
vibrations can result. Moreover, the energy of the higher harmonic orders is concentrated near the
rotor surface which can also heat up and create a crack initiation site. As is the case for transformer
heating, these phenomena may diminish the useful life of a generator, although the damage might
not be immediately apparent and a potential failure at a later stage not necessarily attributed to GIC
Protection relay tripping
In case of GIC flows, the harmonic content of the power system increases. With modern digital
relays measuring the peak current value to monitor the status of the system, they are sensitive to
tripping by harmonics. These false trips can then indirectly trigger a cascading failure of the power
system. The relays’ set current can be adjusted to accommodate the higher harmonics during GID
impact and reduce the risk of false trips. However, this comes at the cost of lower protection levels
(FEN, 2013).
Power systems increasingly depend on reactive power compensators and shunt capacitor banks for
voltage control. Generally, shunt capacitors are grounded and have protection against unbalanced
operation via neutral overcurrent relays. However, these capacitors banks are vulnerable to false
trips during GMSs because of the capacitor’s low impedance at the associated harmonic frequencies.
Several power grid operators have upgraded or even replaced their neutral overcurrent unbalance
protection to reduce the likelihood of false trips (IEEE, 1993).
Effects on communication systems for power grids
Geomagnetic storms also affect long-haul telephone lines, including undersea connections, and
internet cables. The measurement and communication infrastructure directly used for power
systems operation and control is expected to be relatively unaffected by GMSs, as the high-
bandwidth lines in SCADA networks consist increasingly of optical fibers, which do not suffer the
effects of electromagnetic disturbance (FEN, 2013). A potential system weakness lies in the use of
Global Satellite Navigation System services (e.g. GPS) to obtain time stamps for, e.g. phasor
measurements, as these space-based infrastructures would take the full brunt of the incoming solar
storm and likely suffer a severe temporary service degradation.
2.5 Effects on other earthed critical infrastructures
2.5.1 Pipelines
Although there is controversy on the true impact of space weather on pipelines, there are
indications that buried pipelines may suffer damage from steel corrosion due to GICs (Gummow,
2002; Pulkkinen et al, 2001; Pirjola et al, 2000). Corrosion is an electrochemical process occurring in
pipelines at points where a current flows from the pipe to the soil. For example, a continuous DC
current of 1 A flowing in a conductor for one year may cause a loss of about 10 kg of steel (Pirjola,
2012). To prevent or minimize corrosion, cathodic protection (CP) systems are implemented for
pipelines. They keep the pipeline at a negative voltage of usually slightly below 1 V with respect to
the soil. Pipe-to-soil voltages associated with GICs may exceed the CP voltage, which can render
protection systems ineffective. Pipelines are covered with highly resistive coating which is preferred
from a protection point of view. However, a high resistance also increases pipe-to-soil voltages
implying larger harmful currents where defects are present in the coating (Pirjola, 2012).
Modeling of GICs in pipelines has evolved over the last thirty years. The first studies of Lehtinen and
Pirjola (1985) presented theoretical calculations of GICs for the Finnish natural gas pipeline, with the
assumption that the insulating coating of the pipeline was earthed at the cathodic protection
stations. Viljanen (1989) presented a GIC study about the Finnish natural gas pipeline based on the
simplified assumption that the pipeline is an infinitely long multi-layered cylindrical structure in a
homogeneous medium.
An improvement in theoretical modelling is given by Boteler (1997) by incorporating the distributed-
source transmission line theory (DSTL) into pipeline-GIC calculations. An extension is provided by
Pulkkinen et al. (2001) which considers the branches of a pipeline network. In the DSTL theory, the
pipeline is considered a transmission line containing a series impedance Z (or resistance due to the
DC treatment) determined by the properties of the pipeline steel, and a parallel admittance Y
associated with the resistivity of the coating (Boteler, 1997). The geoelectric field affecting the
pipeline forms the distributed source. An important parameter, called the adjustment distance, is
the inverse of the propagation constant γ defined by
Typical values of the adjustment distance of a real pipeline are tens of kilometers, with the exact
values depending on the radius of the pipeline at a specific section. Usually, the adjustment distance
ranges from about 20 km to about 60 km.
Pipelines are considered electrically long if their length significantly exceeds the adjustment
distance; for electrically short pipelines the opposite is true. From a GIC point of view, electrically
long pipelines exhibit a different behaviour than electrically short ones. For a long pipeline, the
voltage decays exponentially at a distance comparable to the adjustment distance, when moving
from either end of the pipeline towards the center where it is practically zero. Therefore, GIC flows
between the pipe and the soil near the ends of a long pipeline, but the central parts are not critical
regarding corrosion problems due to GIC Pirjola, 2012) On the other hand, for a short pipeline, the
voltage changes linearly along the pipeline, and the current along the pipe is small when the ends
are insulated from the Earth. Studies also show that the largest potential variations occur at
discontinuities, such as at bends, insulating flanges and at the end of the pipeline.
2.5.2 Railways
Only very few studies exist on the potential impact of GICs on railway networks up till now: they
mainly focus on anomalies in the operation of the signaling system. In 1982, a strong GMS affected
the Swedish railway system. Between the nights of 13 and 14 July, apparently without reason, the
traffic lights on the line turned red in a railway section of about 45 km length in South Sweden. The
intense geoelectric field affected the relays connected to the rails inducing them to react as if a train
occupied the rails (Wik et al, 2009).
From 2000 to 2005, 15 severe magnetic storms took place, and each of them had a response in the
operation of the “Signalization, Centralization and Blockage (SCB)” system in the high-latitude parts
of Russian railways. Also in these cases, the response of the network to the GMS caused false signals
on the train occupation status of some parts of the railways (Belov et al., 2007; N. G. Ptitsyna, 2008;
Eroshenko et al., 2010).
2.6 Calculation of GICs in power transmission networks
The calculation of GICs in conductors is usually carried out in two parts (Pirjola, 2002): first, the
geoelectric field associated with the geomagnetic variation needs to be assessed. This part is purely
geophysical and is independent of the technological system. Secondly, GICs due to the given
geoelectric field are determined in the conductor system whose structure and features are known.
In the following, two possible scenarios will be introduced for the simulation of the geoelectric field:
a first scenario in which the electric field is constant in magnitude but may vary in orientation and a
second scenario in which the electric field can vary with time. The latter has been proposed by
(Pulkkinen et al., 2012).
For the computation of GICs we follow the procedure proposed by Lehtinen and Pirjola (1985) which
is explained in the next paragraphs.
A power system is a discrete grounded system with N nodes (earthing points). The GICs can be
computed following the formula:
+= (2.2)
where U is the unit matrix, and Yn and Ze are the network admittance matrix and earthing
impedance matrix, respectively. The network admittance matrix Yn is defined by
ij = 1 (2.3)
ik n
ii R
Y1 (2.4)
where Rijn refers to the conductor line resistance between nodes i and j. The elements of the Nx1
column matrix Jn are defined by:
iJJ (2.5)
ij R
J= (2.6)
V (2.7)
The conductor line from node i to node j is denoted sij and E is the geoelectric field. Thus Vij is the
voltage affecting the line sij. The transmission line current from node i to node j can be solved from
the equation:
()( )
,ZY (2.8)
3. Network vulnerability framework and risk assessment
Risk and vulnerability analysis are essential tools for proactive risk management. The meaning of the
concepts and the interrelationship between them vary considerably between different disciplines. It
is therefore important to define how these concepts are used for network vulnerability analysis. The
sections below are a synthesis taken from Piccinelli (2013), Zio and Sansavini (2011), Zio et al. (2008),
Zio and Piccinelli (2010) and Cadini et al. (2009). They provide an introduction to the vulnerability
and complex network theory framework we applied, as well as the most important centrality
measures used.
3.1 Vulnerability framework
The concept of the vulnerability of critical infrastructures is still evolving and a definition has not yet
been unanimously established. Referring to the growing body of scientific literature on vulnerability,
it emerges that the term vulnerability has different meanings when used in different contexts and by
different authors (Bouchon, 2006). Disasters in the past showed that to understand risks a
perception that is only centered on the concept of hazard is too limited. White (1974) notes that “a
hazard of low intensity could have severe consequences, while a hazard of high intensity could have
negligible consequences. The level of vulnerability makes the difference.”
In the following, we adopt the definition of vulnerability as a susceptibility to disruption or
destruction (inherent characteristic including resilience capacity) in the design, implementation,
operation and/or management of an infrastructure system or its elements when exposed to a
hazard or a threat (Haimes, 2006). This means that vulnerability is a state that exists within a system
before it encounters a particular hazardous event (hazard independent, inherent vulnerability). This
may depend on the structure of the system or on its operative states. Other definitions exist that
view vulnerability as the amount of (potential) damage caused to a system by a particular hazardous
event (hazard dependent).
Power networks are infrastructures that exhibit the characteristics of complex systems that require
them to be analyzed from a holistic point of view which is challenging. The vulnerability analysis of
these systems must take into account the potentially large number of spatially distributed
components but also the diverse hazards and threats, including failures that the system can be
subjected to. This consists of systematically identifying the possible states a system can be put into,
given a specific strain, and estimating the impact associated with them. The two main outputs of
vulnerability assessment are then 1) the identification of critical elements and 2) the quantification
of system vulnerability indicators (Kröger and Zio, 2011).
There are three different analysis approaches, each covering different important aspects of
vulnerability: global vulnerability analysis, critical component analysis and geographical vulnerability
analysis (Johansson et al., 2011). These approaches are described in more detail in the following.
In a global vulnerability analysis a system is exposed to strains of different type and magnitude, and
the negative consequences that result are estimated. As the magnitude of the strain increases, the
performance of the system tends to degrade. Robust systems degrade slowly, whereas vulnerable
systems might degrade quickly. In network analysis strains are represented by the removal of
components whereas the magnitude of a strain corresponds to the number or fraction of
components removed. Different types of strains can be simulated by selecting different ‘removal
strategies’ which can be random or targeted (Johansson et al., 2010).
Critical component analysis identifies the components that are the most critical and estimates the
consequences of failure of single or sets of components to understand which system elements cause
the largest negative consequences. In this analysis, all possible combinations of failures are
evaluated which puts an upper limit to the feasible number of simultaneous failures that can be
studied and hence it focuses on only relatively small magnitudes of strains. This is in contrast with
global vulnerability analysis which aims to achieve a representative picture of the system’s
vulnerability for all magnitudes of strain and as a consequence, only a small sample of the possible
states are evaluated (Johansson et al., 2010).
Geographical vulnerability analysis studies if geographic interdependencies exist that allow an
external event, e.g., a hurricane, tornado, earthquake, explosion, etc., to damage several systems or
components simultaneously. One type of geographical vulnerability analysis is the identification of
critical geographical locations. In our approach, this is achieved by characterizing the strains through
specific ground resistances values (Viljanen, 2012; Patterson and Apostolakis, 2007).
Each of the vulnerability analysis approaches described above provide only a partial view of the
vulnerability of a system. If combined, they provide a more complete picture, which allows to obtain
a more complete picture of a system’s vulnerability (Johansson et al., 2011). In order to identify
appropriate risk mitigation measures, the identified vulnerabilities must be combined with a hazard
analysis in a comprehensive risk analysis that also includes determining likelihood estimations.
However, the present report will only address the vulnerability part of risk.
Figure 8 shows the approach we used to model the space-weather impact on the power grid. We
distinguish two models: the structural model, which captures the structural properties of the system
by means of complex network theory modeling. This is the input to the functional model, which
accounts for the physical properties and constraints given by the space weather effects on the
system. Strains can be applied to each model: structural strains, which affect the structural
properties of the system in terms of removal of components, and functional strains, which affect the
physical properties of the system, e.g., increased loading or induced currents. In this report, we
considered only functional strains.
Figure 8. Approach used for modelling the space-weather impact on the power grid, with a structural and a
functional part. The structural model represents a network consisting of nodes and edges. The functional
model is represented by a linear equation (adapted from Johansson et al., 2013).
3.2 Complex network theory framework
Critical infrastructures (CIs), such as power grids, are complex systems of interacting components for
which the actual structure of the interconnection is relevant (Albert et al, 2000). CIs can be modeled
as hierarchies of interacting components. In a topological analysis, a CI is represented by a graph
G(N, K), in which its physical components are mapped into N nodes (or vertices) connected by K
edges (or arcs), which represent the links of physical connections among them.
Topological analysis based on classical graph theory can help to identify the relevant properties of
the structures of a network system (Albert et al., 2000; Strogatz, 2001) by 1) highlighting the role
played by its components (nodes and connecting arcs) (Crucitti et al., 2006; Zio et al., 2008), 2)
making preliminary vulnerability assessments based on the simulation of faults (mainly represented
by the removal of nodes and arcs) and the subsequent re-evaluation of the network topological
properties (Rosato et al., 2007; Zio et al., 2008).
In the case of electrical power systems, the existing literature on vulnerability analysis follows a
topological approach to identifying the critical components in the network (Albert et al., 2004;
Crucitti et al., 2006; Zio et al., 2008). These analyses can help to identify the elements of structural
vulnerability, i.e. network edges and nodes whose failure can induce a severe structural damage to
the network through the physical disconnection of its parts. This kind of analysis is fast from a
computational point of view and only requires information on the network topology.
Unfortunately, topological analysis cannot capture all the complex properties observed in a real
infrastructure system. Consequently, the models need to be extended beyond pure structural
topology (Boccaletti et al., 2006; Eusgeld et al., 2009). Through the identification of critical
components, topological can highlight structural vulnerabilities. However, they are limited from the
point of view of the functional vulnerability of the CI. More specifically, in real network systems the
vulnerability characterization needs to be supplemented by modeling the dynamics of flow of the
physical quantities in the network where physical laws and operational rules influence the flow. As a
consequence, the interplay between structural and dynamic characteristics needs to be evaluated to
provide information on the elements that are critical for the flow propagation process and on
prevention and mitigation actions to reduce the risk of undesired effects. However, topological
analysis is useful as a preliminary screening tool that requires minimal information but it is capable
of identifying major vulnerabilities and guiding in-depth functional vulnerability analysis.
In addition to a complex topological structure, many real power networks exhibit significant physical
inhomogeneities in the capacity and intensity of the connections: for example, there are different
impedance and reliability characteristics of overhead lines in electrical transmission networks (Hines
and Blumsack, 2008; Eusgeld et al., 2009). To capture the heterogeneity of real physical systems,
weights can be assigned to each link of a network that measure the “strength” of the connection. In
this way, the functional behavior of the CI is approximated in a generalized, but still simple,
topological analysis framework. Topological, weighted or unweighted, analyses focus on the static
structural properties of network interconnections and focus on the effects on vulnerability indicators
caused by the removal of a certain percentage of nodes or links (Latora and Marchiori, 2005; Zio et
al., 2008) or identifying the elements whose presence is critical with respect to the network
connectedness (Cadini et al., 2009). Functional models exist that capture the basic realistic features
of CI networks within a weighted topological analysis framework. This approach disregards the
representation of the individual dynamics of the power grid’s elements. These models have helped
to shed light on how complex networks react to faults and attacks under load flow.
Finally, complex network theory allows the consideration of dependencies and interdependencies
among different CIs (Zimmermann, 2001; Duenas-Osorio et al., 2007; Johansson and Jonsson, 2009).
In order to characterize how a threat could weaken, and possibly disrupt, the safe operation of an
interconnected system, the relationship established via the connections linking the multiple
components of the involved infrastructures needs to be modelled (Zio and Sansavini, 2011).
3.3 Centrality measures
Vulnerability analysis related to topology allows to address important questions related to the
connectedness of nodes, shortest path lengths, geographical and regional specifics, etc. and to
provide a reliable identification of the most critical connections, nodes or areas on which to focus a
detailed analysis (Zio and Sansavini, 2011). However, caution needs to be exercised when relying on
topological analysis only as its abstraction level is high. We therefore tried to reduce the gap
between the very abstract topological analysis and the highly detailed (and computationally
demanding) simulations of system behavior.
In order to quantify the structural importance of the network components, several so-called
“centrality measures” have been introduced. Commonly, centrality measures provide an indication
of the importance of a network element (arc or node), i.e., of the relevance of its location in the
network with respect to a given network performance. Depending on the specific definition, a
centrality measure describes the way in which a node interacts with the rest of the network. As such,
it provides a measure that helps to rank and prioritise the importance of the nodes for network
interaction. The term ‘importance’ qualifies the role that the presence and location of the element
plays with respect to the average global and local connection properties of the whole network.
Classical topological centrality measures are the degree centrality (Niemen, 1974; Freeman, 1979),
the closeness centrality (Freeman, 1979; Sabidussi, 1966; Wasserman and Faust, 1994), the
betweenness centrality (Freeman, 1979) and the information centrality (Latora and Marchiori, 2007).
They rely only on topological information to determine the importance of a network element. It is
important to note that critical groups of components can include elements that are not critical when
considered individually. Therefore, the ranking of importance in the grid has to capture the most
important component groups.
The group degree centrality (Everett and Borgatti, 1999), CD(g) of a group g in a network of N nodes,
can be defined as the number of first neighbours of the group nodes, normalized over the number of
non-group members:
() ()
gC gi i
where ki is the degree of node i, in group g and dim(g) is the dimension of the group, i.e. the number
of member nodes. A node that is connected with multiple group nodes is counted only once.
The group closeness centrality (Everett and Borgatti, 1999), CC(g) is based on the idea that a node
can quickly interact with all the other nodes if it is easy accessible because close to all the others. If
dij is the topological shortest path length (i.e., the number of connected arcs) between nodes i and j
(also called geodesics), the group closeness of a group g is the sum of such distances from the group
to all vertices outside the group:
() ()
GJgi ij
This measure is normalized by dividing the distance score by the number of non-group members.
Consequently, larger numbers indicate greater centrality. When the group consists of a single node,
the group closeness centrality becomes the individual node closeness centrality (Sabidussi, 1966;
Freeman, 1979; Wasserman and Faust, 1994).
The distance from other nodes is one but not the only important property in a network of
components. Of significance is also which nodes lie on the shortest paths among pairs of other
nodes, because such nodes have control over the current flow in the network. Freeman (1979)
defines the betweenness. In this definition, a node is central if it lies on several shortest paths
among other pairs of nodes. If g is a subset of a graph, sij is the number of geodesics connecting i to j,
and sij(g) is the number of geodesics connecting i to j passing through g then the group betweenness
centrality of g, denoted by CB(g) is given by (Everett and Borgatti, 1999):
gC jiGji ji
,, ,
where the sum is taken over all pair of nodes.
This measure is normalized by dividing it by the theoretical maximum value, which occurs for a
group of a given size when the result of identifying all the group vertices (i.e., shrinking them to a
single vertex) is a star with the group in the center.
The global efficiency of the graph representing the network is defined as (Latora and Marchiori,
jiGji ij
where 1/dij is the efficiency of the connection between nodes i and j in terms of the number of edges
on the shortest path linking the two nodes. It relates the importance of an edge to the impact on the
network transmission performance of losing the edges of a group and is hence a measure of
importance of the group of edges removed (Crucitti et al., 2006). The relative variation of the global
efficiency due to the removal of a group of edges is calculated as the difference between the global
efficiency of the network with all the edges of the group removed and the global efficiency of the
original network, normalized to the latter value.
The previous measure assume that flow is transmitted along geodesic paths in most networks,
however, this is not the case (Stephenson and Zelen, 1989; Freeman et al, 1991), because the flow
from one node of a network to another can take a circuitous route. For example, in network
infrastructures flow is channeled through selected routes, following the specific operative rules and
constraints which apply to the system. For the electric power network the flow obeys Kirchhoff’s
laws. A realistic betweenness measure should include non-geodesic paths in addition to geodesic
ones. To address this issue, a more sophisticated measure which includes the contributions from
non-geodesic paths, has been proposed (Freeman, 1991).
If the generating sources and load nodes are known, the Ford-Fulkerson algorithm (Ford and
Fulkerson, 1962) can be used to determine the maximum flow in the network, i.e., the largest
possible total flow from sources to target nodes in the network, assuming that the flow at a node
can be split among the edges in each node. The amount of flow through a node i when the
maximum flow is transmitted from a source (s) to a target (t), averaged over all s and t is expressed
by the flow betweenness measure (Freeman, 1991):
jk jk
where mjk be the maximum flow from node i to node k and mjk(i) is the maximum flow from node j
to node k that passes through i. Each edge in the network can be envisaged as a transmission line
carrying a current flow.
The flow betweenness is an indicator of the betweenness of nodes in a network in which a maximum
flow is continuously pumped between all sources and targets. Clearly, the maximum flow needs to
“know” the ideal route (or one of the ideal routes) from each source to each target. However,
normally the flow does not follow the ideal path from source to target. This issue was considered in
the random walk betweenness (Newman, 2005):
where Iist is the current flowing through node i on the path from s to t. This measure is appropriate
to a network in which the flow is transmitted more or less randomly until it finds its target, and it
includes contributions from many paths that are not ideal. This measure is more physically detailed
but it requires information on the system network connection pattern, the edges capacities, the
values of the generating sources and loads, and an algorithm to evaluate the random walk of the
flow through the network (Newman, 2005).
When considering the measurement of the connectivity of a node, the definition should consider the
following three factors (Bompard, 2009): (i) the strength of connection in terms of the weights of the
edge, (ii) the number of the edges connected with the nodes and (iii) the distribution of weights
among the edges. The concept of entropy offers itself to define a degree that represents all the
three factors mentioned above. First, pij, the normalized weight of the edge wij between nodes i and
j, is considered, for each edge lij connecting nodes i and j:
ij w
Since 1=
p the entropic degree gi of node i can be defined using entropy as:
jijiji wppg log1 (3.8)
The degree is a traditional concept in graph theory that is widely applied to the analysis of complex
networks. Bompard, (2009) notes that the entropic degree may be a good replacement for weighted
network models used for power grids, gas pipelines, water ducts and transportation. In the case of
power grids, the entropic degree can provide a direct quantitative measurement of the importance
of buses. This gives an indication of where additional resources should be directed to increase
4. Power Grids and Geomagnetically Induced Currents (GICs)
4.1 Case-study: benchmark power grid
Studies on GIC assessment have been proposed in the scientific literature for different power grid
models: (NERC 2012; Horton et al, 2012; Pirjola, 2009)
Following the suggestion of Pirjola (2009) we adopt, as benchmark model, the Finnish 400-kV
transmission power grid, as it was in its configuration from October 1978 to November 1979. The
network, depicted in Figure 9, consists of 17 stations and 19 transmission lines: the numbers of
stations and transmission lines are high enough to allow a meaningful analysis but is not too large to
complicate computation and analysis. Each station is assumed to include a transformer.
Figure 9. Schematic map of the Finnish 400 kV power grid in 1978 – 1979. Transmission lines are approximated
by straight lines, while stations are represented by nodes. Each node is assumed to represent a transformer
(taken from Viljanen et al., 2012).
Data of the network have initially been proposed by Lehtinen and Pirjola (1985). The coordinates
and earthing resistances of the stations and the resistances of the transmission lines are given for
the sake of completeness s in Tables I and II, respectively. The earthing resistances listed in Table I
include the effects of the station earthings and the transformers. The earthing resistances of stations
16 and 17 are set equal to zero to account for the connection to the Swedish 400-kV network. Thus,
the currents at nodes 16 and 17 include currents that flow between the Finnish and the Swedish
systems and do not account for earthing GICs (Pirjola, 2009).
Station Coordinates [km] Earthing Resistance [Ω]
East North
1 = Inkoo 351.44 58.17 0.43
2 = Loviisa 492.79 97.60 0.36
3 = Nurmijärvi 411.06 106.25 0.66
4 = Lieto 282.69 120.19 0.60
5 = Hyyinkää 404.33 125.00 0.47
6 = Koria 499.52 146.63 0.45
7 = Olkiluoto 227.40 206.73 0.33
8 = Ulvila 258.65 230.29 0.64
9 = Kangasala 361.06 228.85 0.86
10 = Huutokoski 556.25 305.29 0.57
11 = Alajärvi 375.00 394.23 0.98
12 = Alapitkä 543.27 409.13 1.14
13 = Pikkarala 452.88 593.75 0.70
14 = Petäjäskoski 441.83 746.15 0.47
15 = Pirttikoski 520.19 752.40 0.95
16 = Letsi 244.71 755.77 0
17 = Messaure 256.73 789.90 0
Table I. List of the stations (nodes) of the Finnish 400-kV transmission power grid shown in Fig. 9. The east (x)
and north (y) coordinates and the total earthing resistances of each node are also shown (Lehtinen and Pirjola,
Line Number Station A Station B Line Resistance [Ω]
1 1 = Inkoo 4 = Lieto 0.59
2 1 = Inkoo 5 = Hyyinkää 0.65
3 2 = Loviisa 3 = Nurmijärvi 0.58
4 2 = Loviisa 6 = Koria 0.33
5 3 = Nurmijärvi 5 = Hyyinkää 0.076
6 4 = Lieto 7 = Olkiluoto 0.59
7 5 = Hyyinkää 9 = Kangasala 1.04
8 6 = Koria 10 = Huutokoski 1.36
9 7 = Olkiluoto 8 = Ulvila 0.27
10 8 = Ulvila 11 = Alajärvi 1.98
11 9 = Kangasala 11 = Alajärvi 1.47
12 10 = Huutokoski 11 = Alajärvi 1.88
13 10 = Huutokoski 12 = Alapitkä 0.98
14 11 = Alajärvi 13 = Pikkarala 0.96
15 12 = Alapitkä 14 = Petäjäskoski 3.20
16 13 = Pikkarala 15 = Pirttikoski 1.46
17 13 = Pikkarala 17 = Messaure 2.89
18 14 = Petäjäskoski 15 = Pirttikoski 0.71
19 14 = Petäjäskoski 16 = Letsi 1.70
Table II. Transmission lines between stations A and B and resistances of the Finnish 400-kV power grid shown
in Fig. 9 (Lehtinen and Pirjola, 1985).
The first aim of the vulnerability analysis is to understand if and how the structure of the network
influences the diffusion of GICs in the system. Since the voltage in the transmission lines is obtained
by integrating the horizontal geoelectric field along the path defined by the conductor line that
connects two stations, it is noteworthy to look at the line lengths. The Finnish 400-kV transmission
network shows a broad distribution of line lengths (Figure 10): two lines measure less than 50 km
while the longest line measures 352 km. The average length is 147 km.
Figure 10. Line lengths of the network. Lines 5 and 9 are the shortest of the network, Line 15 that connects
nodes 12 and 14, is the longest.
Classical topological analysis aims to identify the most connected nodes in the network. The degree
Centrality, Cd, shows an average value of <Cd> = 0.1397 for the network (Figure 11); this value means
that the majority of nodes is connected to the other nodes with exactly two links. The power grid
comprises few nodes with more than two links; among them, the only node that is most connected
is node 11, with 4 links. The only two nodes with one link, node 16 and 17, are those connecting the
Finnish and the Swedish grids.
The topological Betweenness Centrality (BC), obtained from Eq. (3.3), when g = 1, measures the
importance of a node in terms of presence of the shortest paths connecting every couple of nodes in
the network. One can expect that the more a node is connected, the higher will be the probability
for the node to be passed through by many paths and therefore, also by many shortest paths. Figure
12 shows that node 11 has the highest betweenness centrality, followed by node 10 and node 5, as
The Degree and Betweenness Centrality measures provide a first picture of the network and of its
underpinning structure in terms of nodes and connections. In order to understand the physical
behavior of the system we also need to consider how it functions when traversed by GICs.
Figure 11. Degree Centrality (Cd) for the power network.
Figure 12. Betweenness Centrality (BC) for the power network.
4.1.1 Calculation of GICs: uniform electric field
In order to validate the implementation of the models, a set of baseline GICs calculations were
performed assuming a uniform electric field E = 1V/km oriented northward and eastward and using
the formula proposed by Lehtinen and Pirjola (1985) and introduced in Section 2.6:
+= (2.2)
Tables III and IV show that the obtained results are in agreement with the numerical calculations
proposed in Pirjola (2009). GICs flowing to (from) the Earth are defined as positive (negative). The
following vulnerability analysis is carried out considering an electric field of constant value and
northward direction.
Station GIC [A]
Eastward E=1V/km Northward E=1V/km
1 = Inkoo 4.10 -107.53
2 = Loviisa 58.04 -88.57
3 = Nurmijärvi -1.11 -35.74
4 = Lieto -25.43 -36.78
5 = Hyyinkää 0.69 -16.17
6 = Koria 27.96 -26.41
7 = Olkiluoto -102.48 14.89
8 = Ulvila -20.98 8.19
9 = Kangasala -26.20 -4.04
10 = Huutokoski 79.54 -15.38
11 = Alajärvi -18.63 15.32
12 = Alapitkä 27.81 1.65
13 = Pikkarala 52.50 36.11
14 = Petäjäskoski 36.40 84.85
15 = Pirttikoski 68.84 63.89
16 = Letsi -105.89 29.12
17 = Messaure -55.16 76.62
Table III Results of the baseline calculations, showing GICs at the stations of the Finnish 400-kV transmission grid.
Line Number Station A Station B GIC [A]
1 1 = Inkoo 4 = Lieto -87.68 64.16
2 1 = Inkoo 5 = Hyyinkää 83.58 43.37
3 2 = Loviisa 3 = Nurmijärvi -103.62 0.61
4 2 = Loviisa 6 = Koria 45.58 87.96
5 3 = Nurmijärvi 5 = Hyyinkää -102.51 36.35
6 4 = Lieto 7 = Olkiluoto -62.25 100.94
7 5 = Hyyinkää 9 = Kangasala -19.63 95.89
8 6 = Koria 10 = Huutokoski 17.63 114.37
9 7 = Olkiluoto 8 = Ulvila 40.22 86.05
10 8 = Ulvila 11 = Alajärvi 61.20 77.86
11 9 = Kangasala 11 = Alajärvi 6.57 99.93
12 10 = Huutokoski 11 = Alajärvi -62.58 34.66
13 10 = Huutokoski 12 = Alapitkä 0.67 95.09
14 11 = Alajärvi 13 = Pikkarala 23.83 197.14
15 12 = Alapitkä 14 = Petäjäskoski -27.14 93.44
16 13 = Pikkarala 15 = Pirttikoski 26.48 84.41
17 13 = Pikkarala 17 = Messaure -55.16 76.62
18 14 = Petäjäskoski 15 = Pirttikoski 42.35 -20.52
19 14 = Petäjäskoski 16 = Letsi -105.89 29.12
Table IV GICs flowing between stations A and B (as positive from A to B) in the line of the 400-kV Finnish
transmission grid.
We apply the definition of Entropic Degree (ED) introduced in Chapter 3 to the Finnish transmission
network to investigate how the degree of connection of the network influences the transit of GIC
flow through the system. During geomagnetic disturbances, every line of the network acts as a
source of current for the system: the induced current depends on the length and on the resistance
of the transmission line but also on the magnitude of the electric field and on the orientation of the
field with respect to the transmission line. Different lines converging in a node, convey GICs of
different magnitude. We can consider these GICs as the weight of the contribution of each
transmission line. Using Eq. (3.8), we consider not only the strength of the connections in terms of
the weight of the links but also the number of the connections to each node and the distribution of
the strength of the connections. Figure 13 shows that the highest value of ED is associated with the
most connected node (node 11), as already seen for the Degree Centrality Cd. The difference
between Cd and ED is in the different values of ED for nodes with the same degree centrality Cd. For
example, nodes 3 and 6 show the same Cd but a completely different ED (Figs. 11 and 13). The links
towards node 6 carry a larger amount of current compared to the links conveying to node 3.
Figure 13. Entropic Degree (ED) for the 400-kV Finnish transmission grid computed using Eq. (3.8).
Upon comparing the Entropic Degree and the Degree Centrality measures, we gain more insight into
the role played by the nodes in the spreading of GICs: nodes with the same number of links can give
a different contribution to the diffusion of GICs The ranking of the ED values is listed in the table of
Figure 14 where the three most connected nodes, in terms of ED, are nodes 11, 13 and 10.
Figure 14. Ranking of the nodes of the 400-kV Finnish power grid with respect to the Entropic Degree (ED)
Centrality Measure.
In this study, the current-flow betweenness centrality (CBC) of every node i has been computed as
the amount of current that flows through i averaged over all the possible paths between source and
Rank Node
1 11
2 13
3 10
4 5
5 6
6 9
7 12
8 7
9 8
10 4
11 1
12 14
13 2
14 17
15 3
16 16
17 15
target nodes. The current-flow betweenness centrality values give a ranking of the relevance of the
nodes in current flow transmission in the network (Fig. 15).
Figure 15. Current-flow betweenness centrality for the stations of the 400-kV Finnish power grid based on the
topology, and on the electric behaviour of the grid.
Except for nodes 16 and 17, which are peripheral vertices, the majority of the nodes of the network
appears to give nearly the same contribution to the diffusion of GICs in the network. Nodes with the
highest degree (nodes 5, 10 and 13 with degree k5 = k10 = k13=3 and node 11 with k11=4) are also
nodes with the highest flow betweenness centrality. These elements mainly affect the spreading of
GICs throughout the network and should be carefully monitored when planning prevention actions
of GIC diffusion during solar storms.
We can also rank the nodes with respect to their CBC measure (Figure 16). Nodes 11, 5 and 10 show
the highest contribution to the diffusion of GICs through the network.
Figure 16. Ranking of the nodes of the 400-kV Finnish power grid with respect to Current-flow Betweenness
Centrality (CBC) measure.
4.1.2 Calculation of GICs: uniform electric field with varying angles
The uniform field scenarios are now assumed to vary their direction. The uniform electric field E =
1V/km is considered at different orientation angles, starting with the direction from south to north
(where north is at zero degree), increments of 15 degrees are progressively added up to 165 degree.
Electric fields of equal magnitude separated by 180 degrees give rise to the same GICs intensity,
except that the sign is reversed. For each station (Figure 17) and for each line (Figure 18), GICs at
different angles are represented with different colors, starting from 0 degree (in blue) passing
through 90 degree (east direction, in green) to 165 degree (in red). The sign of the currents refers to
the direction of the flow at the stations (Figure 17): GICs entering a node have negative values while
GICs exiting a node have positive values.
Rank Node
1 11
2 5
3 10
4 13
5 6
6 1
7 3
8 2
9 14
10 9
11 8
12 7
13 4
14 12
15 15
16 16
17 17
Figure 17. Representation of GICs computed for the stations of the 400 kV Finnish power grid. For each station,
the different colors represent a different orientation angle of the geoelectric field E.
Figure 18 shows the magnitude of GICs flowing through the transmission lines. As before, each color
represents a different angle between the orientations of the electric field. The sign refers to the
orientation of the flow: positive values suggest that GICs flow from station A towards station B (as
listed in Table II), negative values indicate that GICs flow the opposite way, from station B to station
Figure 18. Representation of GICs computed for each transmission line of the 400 kV Finnish power grid. For
each line, the different colors represent a different orientation angle of the geoelectric field E.
The ED and the CBC measures have been investigated for each different angle (Figs. 19 and 20). The
Entropic Degree centrality measure represents the behavior of each node along with the variation of
the orientation between the electric field and the orientation of the lines. In Fig. 19, every box
represents the entropic degree value of the system computed for a specific angle, starting from the
first box in which the electric field is directed northward, (0 degree, in blue) and increasing, in each
box, the orientation angle by 15 degrees until 165 degrees (dark red).
Figure 19. The Entropic Degree (ED) centrality measure is represented for each angle, starting from 0° (bar
graph in the first box from the top) and continuing with an increase of 15° for each successive bar graph.
Figure 19 shows that, despite the variation of the angle between the electric field and the
transmission lines, the ranking of the nodes given by the ED centrality measure does not change
drastically: on average, nodes 11 and 13 maintain the highest values of ED, as shown in Table V.
ED Orientation Angle (degree)
0 15 30 45 60 75 90 105 120 135 150 165
Ranking Order
1 11 11 11 11 11 11 5 5 11 11 11 11
2 13 13 13 13 5 5 3 14 14 13 13 13
3 10 10 6 5 13 3 14 11 5 14 10 10
4 5 6 5 10 10 13 11 3 4 10 14 14
5 6 9 10 6 2 2 1 4 13 5 4 5
6 9 8 8 8 8 1 4 1 3 4 5 4
7 12 12 9 2 3 10 2 10 10 3 12 9
8 7 5 12 14 6 8 13 13 1 12 9 12
9 8 7 7 9 14 14 7 2 12 9 7 7
0 4 4 2 3 1 6 8 7 9 7 6 6
11 14 2 14 12 15 4 10 12 7 1 3 8
12 1 1 1 7 9 7 15 16 2 2 2 15
13 15 15 3 1 12 15 16 9 16 6 15 2
14 2 14 15 15 7 16 6 8 15 15 8 1
15 17 17 4 4 16 9 17 17 17 16 1 3
16 3 3 17 16 4 12 9 15 6 17 17 17
17 16 16 16 17 17 17 12 6 8 8 16 16
Table V. Ranking of the nodes of the system according to the importance given by the entropic degree
centrality measure (ED).
However, the entropic degree values decrease in magnitude with the increase of the orientation
angle (Fig. 20). For example, we can fix the attention on node 11 and follow the trend of the colored
bar along the field orientation angle direction. Starting from the dark blue bar and following the
shades of blue along node 11, we can see a decrease in the ED measure until the green bar, where
ED for node 11 is at its minimum. Then, continuing with increasing angles, the ED value increases
again (following shades from yellow to dark red).
The ranking of the nodes with respect to the ED centrality measure reproduced in Table V shows
that, in general, the importance (ranking) of the nodes does not change with the variation of the
orientation angle. However, there is a change when the orientation angle is 90 and 105°, which
corresponds to the electric field being oriented eastward. In our definition, ED measures the
connectivity of the network in term of GICs that traverse it. A major contribution to the spreading of
GICs is given when the electric field is “aligned” with the orientation of the transmission lines. Nodes
11 and 13 in the 400-kV transmission power grid connect lines whose principal components are
directed mainly northward. Their contribution is possible when the electric field is oriented
eastward: in this latter case, lines that have a major eastward component give the highest
contribution to the spreading of GICs and are connected by nodes 5 and 14, which, in this case,
become critical with respect to GICs.
Figure 20. Three-dimensional representation of the Entropic Degree (ED). The centrality measure is shown for
all the stations for each angle, starting from 0 degrees (blue bar on the left) and continuing with an increase of
15° for each successive bar to 165° (last red bar on the right).
Similarly, the Current-flow Betweenness computed for the different angle orientations considered, is
represented in Fig. 21, and the ranking of nodes with respect to CBC is listed in Table VI. For CBC, the
different orientations of the electric field do not affect the ranking for node 11. In this case, those
nodes which are traversed more by the flow are more important. These are the nodes with the
highest connection degree: nodes 11, with 4 connections and nodes 5, 13 and 10, with three
connections each.
Figure 21. Bar-Plots of the Current-flow Betweenness Centrality (CBC). Each color represent an angle, starting
from 0° (top plot, blue), and continuing with 15° increments until 165° (dark red, bottom plot).
CBC Orientation Angle (degrees)
0 15 0 45 60 75 90 105 120 135 150 165
Ranking order
1 11 11 11 11 11 11 11 11 11 11 11 11
2 5 5 5 5 13 13 10 10 10 10 10 5
3 10 10 10 13 10 10 13 13 5 5 5 10
4 13 13 13 10 14 14 14 5 13 13 13 13
5 6 1 1 14 5 5 12 14 14 6 6 6
6 1 6 14 1 8 8 15 12 6 14 2 3
7 3 3 8 8 15 15 8 8 8 2 3 2
8 2 2 7 7 7 12 5 6 12 3 14 1
9 14 14 4 15 12 7 6 15 2 8 1 14
10 9 9 3 4 1 1 7 2 3 12 8 8
11 8 4 9 12 4 4 2 3 15 1 12 9
12 4 8 6 9 9 6 3 7 1 7 9 7
13 7 7 2 3 3 9 1 1 7 9 7 4
14 12 15 15 2 6 2 4 9 9 15 4 12
15 15 12 12 6 2 3 9 4 4 4 15 15
16 17 17 17 17 17 17 16 16 17 16 17 17
17 16 16 16 16 16 16 17 17 16 17 16 16
Table VI. Ranking of the nodes of the system according to the importance given by the current-flow
betweenness centrality measure (CBC).
4.2 Power Flow and GICs
Work is in progress on adding GICs in a power grid system under load flow. A scoping study was
carried out, the results of which are described in the following section.
No data on bus loads or generators capacity are publicly available for the model of the 400kV-
transmission power grid proposed as a benchmark case. As a consequence, we inferred the values
for the requested and supplied power from statistics available at the websites of the Finnish Energy
Authority (2014), the Finnish transmission power grid operator (Fingrid Oyj, 2014) and the European
Network of Transmission System Operators for Electricity (ENTSOE, 2014). This data are summarized
in Tables VII e VIII.
The percentage of system load was assigned to every single node on the basis of the statistics on the
power consumption of each area served by the stations listed in the first column of Table VII.
Following the example proposed in Grigg (1999), the reactive part of the loads (forth column) was
interpolated from the reliability test system RTS96.
Station Bus load Load
% of System Load [MW] [MVAr]*
1 = Inkoo 10.8 458 93
2 = Loviisa 5.4 229 47
3 = Nurmijärvi 9.5 403 82
4 = Lieto 5.6 237 49
5 = Hyyinkää 4.5 191 39
6 = Koria 3.7 157 32
8 = Ulvila 8.2 348 71
9 = Kangasala 6.1 259 53
10 = Huutokoski 4.2 178 36
11 = Alajärvi 6.3 267 55
12 = Alapitkä 3.5 148 30
13 = Pikkarala 5.7 242 49
14 = Petäjäskoski 11 466 95
15 = Pirttikoski 11.1 471 96
16 = Letsi 2.1 89 18
17 = Messaure 2.3 97 20
Total 100 4240 865
Table VII. Table of real power and reactive power demand for the system loads (* MVAr is the unit for reactive
Data on generating units (Table VIII) show that more than half of the supplied power is produced by
the nuclear power plants located at Loviisa and Olkiluoto. This latter is also assumed as the slack
node of the transmission grid.
Station Unit Size Unit type
1 = Inkoo 690 Coal
2 = Loviisa 1032 Nuclear/Fossil fuel
4 = Lieto 330 Coal
6 = Koria 160.5 Fossil fuel/Biomass
7 = Olkiluoto 1860.5 Nuclear/Fossil
8 = Ulvila 285 Biomass/Coal
9 = Kangasala 333 Fossil fuel/Coal
10 = Huutokoski 180 Fossil fuel/Biomass
13 = Pikkarala 195 Fossil fuel/Biomass
Total 5066
Table VIII. Table of the generating unit type and capacity for the system.
Once GICs have been calculated for every node, their effect needs to be inserted into the
transmission power grid model. As introduced in Section 2.4, GICs can induce saturation in
transformers and, as a main consequence, cause reactive power losses (Kappenman, 2010; Overbye
et al., 2012). If the system cannot supply the increase in reactive power demand, it can eventually
Following the observations of Albertson et al. (1973) and Walling and Kahn (1991), we adopt the
assumption that each transformer’s reactive power losses Qloss vary linearly with GICs and with the
voltage of the bus:
Qloss = VkVkIgic (4.1)
In Equation (4.1) V
is the station voltage, expressed in kV, I
is the current induced in the
transformer, expressed in Ampère, and k is a transformer specific constant. In principle, the value k
for each transformer should be known. In this study, we consider the constant k to have, for all the
transformers, a value equal to 2.8, as suggested in the literature (Albertson et al., 1981).
GICs computed for different scenarios have been included in the AC power flow for the 400kv
Finnish transmission power grid, as shown in Fig. 22.
Figure 22. Outline of the method employed to evaluate the load flow in the 400kV transmission grid in the
presence of GICs.
For our scoping study we considered four scenarios. In each of them we increased the magnitude of
the electric field, which assumes the peak values computed by Pulkkinnen (2012): |E|=1V, 2V, 5V
and 20V. For each of these electric field magnitudes and for each orientation angle, the resulting AC
power flow has been calculated using MATPOWER (2011). The collapse of the system was signaled
by the non-convergence of the power flow calculation. Results are summarized in Table IX.
0 15 30 45 60 75 90 105 120 135 150 165
Table IX. Schematic representation of the convergence of the power flow algorithm for the 400-kV power
transmission power grid. Convergence is represented by green boxes; red boxes represent collapse of the
The first results of this study seem to indicate that the system can resist GICs induced from high
intensity electric fields. Moreover, the network seems more prone to collapse when the electric field
has a northward direction, as shown by the red boxes in Table IX.
4.3 Discussion
In this study, complex network theory has been used to investigate the vulnerability of the power
network to space weather impact. The ranking of nodes with respect to ED and CBC centrality
measures identifies the most important nodes of the network with respect to GICs: nodes with the
highest number of links contribute the most in the diffusion of GICs through the network. Since we
want to avoid GICs to flow throughout the system, these are the critical nodes to monitor when
considering mitigation measures, in order to avoid effects leading to possible blackouts.
The analysis of the behavior of the system affected by an electric field with different orientation
shows little variation of the importance of nodes with varying angles. However, there are changes in
the ranking of the nodes, as shown in Tables VII and VIII. The electric field integrated along the
transmission lines acts as a voltage generator (Eq. (2.7)) for the network and, since the geoelectric
field is rotational, the integral depends on the path between nodes. In particular, since the
geovoltage is the result of an inner product, it depends on the electric field and on the projection of
the length of the transmission line alongside the direction of the electric field. We kept the
geoelectric field magnitude uniform so the varying contribution to the geovoltage is given by the
projection of the “global length” of the network. If one focuses on the two principal directions,
north and east, one realizes that the network expands more in the northward than the eastward
direction, thus a strong geoelectric field directed northward will have a more pronounced impact on
the network.
Table IX confirms this finding. It represents the risk for the power grid in AC load-flow regime to
collapse due to extreme space weather. Non-convergence for the system occurs when the
magnitude of the geoelectric field is high and directed northward. In our study, the dependence of
the orientations of power lines with respect to the geoelectric field results more pronounced than in
the study of Pirjola (2002).
Further work is underway to analyze the vulnerability of power grids to space weather impact in
more detail, including the refinement of assumptions and models to arrive at a unified assessment
of the associated risk at EU level.
5. Conclusions
During geomagnetic storms, high voltage transmission grids are particularly exposed to damage:
induced geomagnetic currents (GICs) can damage transformer equipment and cause voltage
instability, possibly causing power systems to collapse.
Power systems are large-networked engineered systems, whose complexity and vulnerability to
hazards and failures can be investigated by means of complex network theory. By representing
stations with nodes and transmission lines with links between nodes, complex systems can be
described by models that are abstract enough for handling the computational burden and that are
nevertheless representative of the physical behavior of the system.
In the proposed study, we investigated the vulnerability of power grids to space weather. The
assessment was performed by means of vulnerability indicators applied to a benchmark case study.
The aim of the study was to understand how the structural and physical characteristics of the
network influence and drive the spreading of GICs during a geomagnetic storm, and to identify
which components in the network are more involved. This is the basis for understanding the
behavior of the system under a “geomagnetic” stress and eventually, identifying where and how to
best implement mitigation strategies.
Work is in progress to further validate and expand our approach with the aim to eventually carry out
a risk assessment of the power grid at EU level. This requires an assessment of the likelihood for a
system to experience a strong geomagnetic storm and of the potential consequences. A part of this
study has already been implemented into the Joint Research Centre’s Global Resilience and Risk
Assessment Platform (GRRASP) which we will at a later stage use to model ripple effects due to
space weather induced power grid failure via interdependencies with other critical infrastructures.
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EUR 26914 EN – Joint Research Centre – Institute for the Protection and Security of the Citizen
Title: Space Weather and Power Grids – A Vulnerability Assessment
Authors: Roberta Piccinelli, Elisabeth Krausmann
Luxembourg: Publications Office of the European Union
2014 – 53 pp. – 21.0 x 29.7 cm
EUR – Scientific and Technical Research series – ISSN 1831-9424
ISBN 978-92-79-43971-1
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... In some countries, the transmission grids were less prone to these events (Krausmann et al. 2013). There were significant effects like transformer saturation, reactive power losses, harmonics, transformer heating, generator overheating and protection relay tripping due to space weather events in power systems (Piccinelli and Krausmann 2014). These events also could affect the economic value of power grids (Eastwood et al. 2018). ...
Full-text available
Space weather is a phenomenon in which radioactivity and atomic particles is caused by emission from the Sun and stars. It is one of the extreme climate events that could potentially has short-term and long-term impacts on infrastructure. The effects of this phenomenon are a multi-fold process that include electronic system, equipment and component failures, short-term and long-term hazards and consequences to astronauts and aircraft crews, electrostatic charge variation of satellites, disruptions in telecommunications systems, navigational systems, power transmission failures and disturbances to the rail traffic and power grids. The critical infrastructures are becoming interdependent to each other and these infrastructures are vulnerable if one of them is affected due to space weather. Railway infrastructure could be affected by the extreme space weather events and long-term evolution due to direct and indirect effects on system components, such as track circuits, electronic components in-built in signalling systems or indirectly via interdependencies on power, communications, etc. While several space weather-related studies focus on power grids, Global Navigation Satellite System (GNSS) and aviation sectors, a little attention has focused towards probability of railway infrastructure disruptions. Nevertheless, disruptions due to space weather on signalling and train control systems has documented but other systems that railway infrastructure dependent upon are not very well studied. Due to the advancements in digitalization, cloud storage, Internet of Things (IoT), etc., that are embedded with electronic equipment are also possible to prone to these effects and it is even become more susceptible to the extreme space weather events. This paper gives a review of space weather effects on railways and other transportation systems and provide some of the mitigation measures to the infrastructure and societal point of view.
... Here, they ionize nuclei and the recombination radiation is visible as polar lights. The high particle flux of these low-energy cosmic rays can affect the functionality of satellites in the low Earth orbit and the international space station (Anderson et al., 2018) and extreme geomagnetic storms might cause disturbances of the power grid in the circumpolar regions (Piccinelli and Krausmann, 2014). ...
Das IceCube Neutrinoteleskop hat im Jahr 2013 erstmals einen isotropen, quasi-diffusen astrophysikalischen Neutrinoflusses detektiert. Dieser Fluss kann jedoch bisher keiner astrophysikalischen Quellklasse zugeordnet werden. Um nach kurzlebigen Neutrinoquellen zu suchen, wurde 2008 das optische und Röntgen-Nachfolgebeobachtungsprogramm des IceCube Detektors eingerichtet. Es sucht nach zwei oder mehr Neutrinoereignissen, die von einer Punkquelle stammen könnten und innerhalb von 100s detektiert werden. Ein solches Signal wird unter anderem von langen oder kurzen Gammastrahlungsblitzen (GRBs) erwartet oder von verwandten Objekten wie leuchtschwachen GRBs oder Supernovae mit relativistischen Jets. Die Alarmraten des Nachfolgebeobachtungsprogramms sind jedoch niedrig und bieten bisher keine Hinweise für die Existenz von kurzlebigen Neutrinoquellen. Das Nachfolgebeobachungsprogramm hat bisher nur ein einziges Neutrinotriplet detektiert, das der Auslöser für eine umfassende Beobachtungskampagne war. In den optischen, Röntgen- und Gammastrahlungsbeobachtungen wurde keine wahrscheinliche Neutrinoquelle identifiziert und eine Supernova oder ein heller GRB können ausgeschlossen werden. Das Neutrinotriplet kann entweder eine zufällige Koinzidenz von Untergrundereignissen sein (alle 13.7 Jahre erwartet) oder es kann von einer leuchtschwachen oder besonders schnell verblassenden Quelle stammen. Die niedrige Rate von Neutrinomultipletts stellt außerdem eine obere Schranke auf die Helligkeit von kurzlebigen Neutrinoquellen dar. Seltene Quellen mit lokalen Raten von < 3e-8 – 10e-5 Mpc^-3 Jahr^-1 können nicht den gesammten Fluss erzeugen, ohne die detektierte Anzahl Multipletts zu überschreiten. Der Fluss von GRBs ist dadurch auf 5-30% des astrophysikalischen Flusses beschränkt. Falls 1% aller Kernkollaps-Supernovae einen Jet besitzen, der auf die Erde zeigt, so können sie 40-100% des Flusses erzeugen und ihre durchschnittliche Neutrinohelligkeit ist <3e51erg.
... Geoelectric fields in the solid Earth are induced by external geomagnetic field variations, often associated with geomagnetic storms, passing through a complex Earth filter that is determined by the conductivity structure of Earth's interior. These induced geoelectric fields give rise to anomalous quasi-static voltages across transmission lines that lead to so-called geomagnetically induced currents (GICs) within power transmission networks, which can cause operational interference and damage to critical infrastructure (e.g., Molinski, 2002;Piccinelli & Krausmann, 2014). One of the strongest geomagnetic storms to impact modern power transmission networks occurred in March 1989 when GICs caused the collapse of the Hydro-Québec power grid in Canada (e.g., Bolduc, 2002). ...
Full-text available
A once‐per‐century geoelectric hazard map is created for the U.S. high‐voltage power grid. A statistical extrapolation from 31 years of magnetic field measurements is made by identifying 84 geomagnetic storms with the Kp and Dst indices. Data from 24 geomagnetic observatories, 1,079 magnetotelluric survey sites, and 17,258 transmission lines are utilized to perform a geoelectric hazard analysis with the most comprehensive data publicly available. With these data, we estimate once‐per‐century geoelectric fields at the magnetotelluric survey sites and calculate the theoretical voltages within transmission lines in the U.S. power grid. Once‐per‐century geoelectric field strengths span more than 3 orders of magnitude from a minimum of 0.02 V/km at a site in Idaho to a maximum of 27.2 V/km at a site in Maine, with nearly 30% of the surveyed land area exceeding 1 V/km. We show the influence that geoelectric field polarization has on geoelectric hazards when viewed on a power transmission network. The calculated transmission line voltages can approach 1,000 V in some transmission lines. Four regions in the United States with particularly notable geoelectric hazards are identified and discussed: the East Coast, Pacific Northwest, Upper Midwest, and the Denver metropolitan area.
... At the end of this space weather chain, processes that lead to induction of currents in the ground can potentially impact infrastructure that are critical to society. These geomagnetically induced currents (GIC) flow along long conductor systems such as power grids and can affect or damage the power system (Albertson & Van Baelen, 1973;Boteler, 2013;Bolduc, 2002;Molinski, 2002;Piccinelli & Krausmann, 2014;Samuelsson, 2013;Wik et al., 2009). The strength of the currents that arise in the power lines are determined by the strength of the fluctuating geoelectric field and depends on three main factors: ...
Full-text available
Geomagnetically induced currents (GICs) flowing in long conductors can pose a threat to critical infrastructure such as the power grid in cases of extreme geomagnetic activity. Geomagnetic activity is more pronounced at high latitudes; thus, Nordic countries, such as Sweden, can potentially be vulnerable to GIC. Previous studies have identified the southern region of Sweden as the most vulnerable to extreme space weather, but these studies have relied on 1-D models of the ground conductivity. Sweden, however, has large lateral variations in the underlying ground conductivity structure across the country. Thus, the understanding of the ground response to space weather events cannot be captured by 1-D models. In this paper, we utilize a 3-D crustal conductivity map with surrounding oceans to model the geoelectric ground response due to a uniform magnetic field. We show that southern Sweden is exposed to stronger electric fields due to a combined effect of a low crustal conductivity and the influence of the coast-land interface from both the east and the west coast. The model can further be used to calculate GICs in the Swedish power grid and has been validated by GIC measurements from a site in northern Sweden. The measured and predicted GIC amplitudes are in excellent agreement. The model can be used to quantitatively asses the hazard from space weather in Sweden. Upon further validation at additional sites it can be used as a powerful predictive tool of the response to extreme space weather events in the Swedish power network.
... Geomagnetic storms and the geoelectric fields that they induce in the Earth's conducting interior are hazards for high-voltage electric power grid systems (e.g., Molinski, 2002;Piccinelli & Krausmann, 2014;Samuelsson, 2013). A dramatic realization of these hazards came during the magnetic storm of 13 March 1989 (e.g., Allen et al., 1989) when induced geoelectric fields caused the collapse of the entire Hydro-Québec power grid system in Canada (Béland & Small, 2005;Bolduc, 2002) and caused operational stress in power grids in the United States (North American Electric Reliability Corporation, 1990[NERC], 1990. ...
Full-text available
Maps of extreme value, horizontal component geoelectric field amplitude are constructed for the Pacific Northwest United States (and parts of neighboring Canada). Multidecade long geoelectric field time series are calculated by convolving Earth surface impedance tensors from 71 discrete magnetotelluric survey sites across the region with historical 1-min (2-min Nyquist) geomagnetic variation time series obtained from two nearby observatories. After fitting statistical models to 1-min geoelectric amplitudes realized during magnetic storms, extrapolations are made to estimate threshold amplitudes that are only exceeded, on average, once per century. One hundred-year geoelectric exceedance amplitudes range from 0.06 V/km at a survey site in western Washington State to 9.47 V/km at a site in southeast British Columbia; 100-year geoelectric exceedance amplitudes equal 7.10 V/km at a site north of Seattle and 2.28 V/km at a site north of Portland. Systematic and random errors are estimated to be less than 20%, much less than site-to-site differences in geoelectric amplitude that arise from site-to-site differences in surface impedance. Maps of 100-year exceedance amplitudes are compared with the peak geoelectric amplitudes realized during the March 1989 magnetic superstorm; it is noted that some storms of relatively modest intensity can generate localized geoelectric fields of relatively high amplitude. The geography of geoelectric hazard across the Pacific Northwest is closely related to known geologic and tectonic structures.
... Geomagnetic storms induce geoelectric fields within the electrically conducting interior of the Earth that produce voltages across grounded transmission lines. These voltages can lead to severe impacts on the transmission of electricity (Boteler, 2001;Molinski, 2002;Piccinelli & Krausmann, 2014;Samuelsson, 2013). A geomagnetic storm on 13 March 1989 caused a widespread blackout in Canada with the collapse of the Hydro-Québec power system (Bolduc, 2002) and caused numerous anomalies and faults within the United States (U.S.) power transmission network (North American Electric Reliability Corporation, 1990). ...
Full-text available
Commonly, one-dimensional (1D) Earth impedances have been used to calculate the voltages induced across electric power transmission lines during geomagnetic storms under the assumption that much of the three-dimensional structure of the Earth gets smoothed when integrating along power transmission lines. We calculate the voltage across power transmission lines in the mid-Atlantic region with both regional 1D impedances and 64 empirical 3D impedances obtained from a magnetotelluric survey. The use of 3D impedances produces substantially more spatial variance in the calculated voltages, with the voltages being more than an order of magnitude different, both higher and lower, than the voltages calculated utilizing regional 1D impedances. During the March 1989 geomagnetic storm 62 transmission lines exceed 100 V when utilizing empirical 3D impedances, whereas 16 transmission lines exceed 100 V when utilizing regional 1D impedances. This demonstrates the importance of using realistic impedances to understand and quantify the impact that a geomagnetic storm has on power grids.
... This induction occurs all the time, during both magnetically calm and stormy conditions. During intense storms, induced geoelectric fields can drive quasi-direct currents in bulk electric-power grids of sufficient strength to interfere with their operation, sometimes even causing blackouts and damaging transformers (e.g., Boteler et al., 1998;Piccinelli and Krausmann, 2014). Notably, the magnetic storm of March 1989 (e.g., Allen et al., 1989) caused the collapse of the Hydro-Québec power-grid system in Canada, leaving 6 million people without electricity (Bolduc, 2002;Béland and Small, 2005). ...
Full-text available
Despite its importance to a range of applied and fundamental studies, and obvious parallels to a robust network of magnetic-field observatories, long-term geoelectric field monitoring is rarely performed. The installation of a new geoelectric monitoring system at the Boulder magnetic observatory of the US Geological Survey is summarized. Data from the system are expected, among other things, to be used for testing and validating algorithms for mapping North American geoelectric fields. An example time series of recorded electric and magnetic fields during a modest magnetic storm is presented. Based on our experience, we additionally present operational aspects of a successful geoelectric field monitoring system.
... Magnetic storms can induce geoelectric fields in the Earth's electrically conducting interior, interfering with the operation of electric power grids and pipelines [e.g., Albertson et al., 1993;Boteler, 2003;Samuelsson, 2013;Piccinelli and Krausmann, 2014]. The potential risks were dramatically demonstrated during the magnetic storm of March 1989 [e.g., Allen et al., 1989], which caused strong geomagnetically induced currents (GICs) to flow along the power lines, collapsing the entire Hydro-Québec electric power grid in Canada [Bolduc, 2002;Béland and Small, 2005], as well as causing severe damage to step-up transformers in Delaware Bay (see North American Electric Reliability Corporation (NERC) [1990], for a compilation of effects). ...
Full-text available
Geoelectric fields at the Earth's surface caused by magnetic storms constitute a hazard to the operation of electric-power grids and related infrastructure. The ability to estimate these geoelectric fields in close to real time and provide local predictions would better equip the industry to mitigate negative impacts on their operations. Here, we report progress towards this goal: development of robust algorithms that convolve a magnetic storm time series with a frequency domain impedance for a realistic three-dimensional (3D) Earth, to estimate the local, storm-time geoelectric field. Both frequency domain and time domain approaches are presented, and validated against storm-time geoelectric field data measured in Japan. The methods are then compared in the context of a real-time application.
Full-text available
Geoelectric field time series can be estimated by convolving estimates of Earth‐surface impedance, such as those obtained from magnetotelluric survey measurements, with historical records of geomagnetic variation obtained at magnetic observatories. This straightforward procedure permits the mapping of geoelectric field variation during magnetic storms. Statistical analysis of the time series allows extrapolation to extreme‐value amplitudes, such as might be realized during an intense magnetic storm in the future. The development of these products is illustrated for the Mid‐Atlantic United States, using impedances obtained from EarthScope survey data and geomagnetic variation records obtained at the Fredericksburg observatory operated by the U.S. Geological Survey. For this region, 100‐year geoelectric exceedance amplitudes have a range of almost three orders of magnitude (from 0.04 V/km at a site in southern Pennsylvania to 24.29 V/km at a site in central Virginia), and they have significant geographic granularity, which is due to site‐to‐site differences in surface impedance (and subsurface electrical conductivity structure). Maps of 100‐year exceedance amplitudes resemble those of geoelectric amplitudes for the March 1989 magnetic storm, and, in that sense, the March 1989 storm resembles what might be loosely called a “100‐year” event.
Full-text available
Maps are presented of extreme-value geoelectric field amplitude and horizontal polarization for the Northeast United States. These maps are derived from geoelectric time series calculated for sites across the Northeast by frequency-domain multiplication (time-domain convolution) of 172 magnetotelluric impedance tensors, acquired during a survey, with decades-long, 1-min resolution time series of geomagnetic variation, acquired at three magnetic observatories. The maps show that, during intense magnetic storms, high geoelectric amplitude hazards are realized across electrically resistive, igneous and metamorphic rock of the Appalachian Mountains and the New England Highlands, while low geoelectric hazards are realized across electrically conductive, sedimentary rock of the Appalachian Plateau and the Mid-Atlantic Coastal Plain. From statistical extrapolation, once-per-century (100-year) geoelectric amplitudes are highest at a site in Virginia at 25.44 V/km (followed by a site in Maine at 21.75 V/km and a site in Connecticut at 19.39 V/km); 100-year geoelectric amplitude exceeds 10 V/km at 12 sites across the northeast; geoelectric amplitude is lowest at a site in Virginia at 0.05 V/km. Average errors for these values are estimated to be about 38%, or much less than the more than 2 orders of magnitude range seen in geoelectric amplitudes from one survey site to another across the northeast. It is noteworthy that geoelectric fields tend to be most (least) polarized at locations with high (low) geoelectric hazard. Furthermore, geoelectric fields over the Appalachians tend to be polarized southeast-to-northwest, or generally in a direction orthogonal to the southwest-to-northeast geological strike. Results reported here inform utility companies in projects for evaluating and managing the response of power grid systems to the deleterious effects of geomagnetic disturbance.
The intuitive background for measures of structural centrality in social networks is reviewed and existing measures are evaluated in terms of their consistency with intuitions and their interpretability.
Power transformers are one of the most strategic equipment in the power system. Though they are generally designed for operation under sinusoidal waves (including the harmonics), in reality, they may be subjected to superimposed DC currents excitation with varying levels which may reach up to few hundreds amps. These DC currents may be of external origin as GIC or HVDC ground return mode stray currents. They may also have an internal origin, being directly linked to the use of power electronic convertors under certain non-ideal conditions (eg. SVC transformers, HVDC transformers). Depending on their magnitude, the DC bias currents may have a detrimental effect on the integrity of the power transformers or their long term performance, meaning to affect the power system reliability. With this respect, users specifications relating to concern with superimposed DC excitations are generally clear enough regarding expected levels and possible durations. On the other side, a good understanding of the behaviour of power transformers or shunt reactors under combined AC and DC excitations as well as comprehensive modelling tools are essential to enable the design of power transformers which fit these requirements. In this paper, further to explaining the half cycle saturation effect resulting from combined AC and DC excitations of magnetic cores, measurements on model transformers are used to illustrate this effect. Then different aspects of numerical modelling of the phenomenon are presented with application to the design and design verification of a 550 MVA autotransformer prone to GIC, with analysis performed for the no load and for the on load conditions, taking into account the load power factor and varying levels of the DC current as appearing in the specifications. Additionally, more specific aspects of behaviours of convertors and HVDC transformers, relating to DC bias current and related numerical models are addressed.
Society depends on services provided by critical infrastructures, and hence it is important that they are reliable and robust. Two main approaches for gaining knowledge required for designing and improving critical infrastructures are reliability analysis and vulnerability analysis. The former analyses the ability of the system to perform its intended function; the latter analyses its inability to withstand strains and the effects of the consequent failures. The two approaches have similarities but also some differences with respect to what type of information they generate about the system. In this view, the main purpose of this paper is to discuss and contrast these approaches. To strengthen the discussion and exemplify its findings, a Monte Carlo-based reliability analysis and a vulnerability analysis are considered in their application to a relatively simple, but representative, system the IEEE RTS96 electric power test system. The exemplification reveals that reliability analysis provides a good picture of the system likely behaviour, but fails to capture a large portion of the high consequence scenarios, which are instead captured in the vulnerability analysis. Although these scenarios might be estimated to have small probabilities of occurrence, they should be identified, considered and treated cautiously, as probabilistic analyses should not be the only input to decision-making for the design and protection of critical infrastructures. The general conclusion that can be drawn from the findings of the example is that vulnerability analysis should be used to complement reliability studies, as well as other forms of probabilistic risk analysis. Measures should be sought for reducing both the vulnerability, i.e. improving the system ability to withstand strains and stresses, and the reliability, i.e. improving the likely behaviour.
Critical infrastructures provide essential services which enable our society to function. Disruptions in infrastructures can have widespread effects, not only for the originating infrastructure but also, through mutual dependencies, for other infrastructures. Identifying vulnerabilities inherent in these system-of-systems is thus highly critical for the proactive management and avoidance of future crises. A modelling approach for interdependent technical infrastructures is proposed and three perspectives for the analysis of vulnerabilities are introduced, addressing the complexities associated with comprehensively analysing technical interdependent infrastructures. An empirical analysis of the railway system in southern Sweden is conducted, a system consisting of seven interdependent supporting systems. It is concluded that the proposed modelling approach and the three perspectives of vulnerability analysis give valuable insights for the proactive risk management of technical infrastructures.