Researchers at the University of Leicester, Lancaster University and St Petersburg State Universi... more Researchers at the University of Leicester, Lancaster University and St Petersburg State University have developed various models that can be employed in HF radio propagation predictions. Signal coverage predictions make use of numerical ray tracing to estimate the ray paths through a model ionosphere that includes various ionospheric features prevalent at high latitudes (in particular patches, arcs, ionisation tongue, auroral zone irregularities and the mid-latitude trough). Modelling of D-region absorption is also included. GOES satellites provide information on X-ray flux (causing shortwave fadeout during solar flares) and precipitating energetic proton flux which correlates strongly with Polar Cap Absorption (PCA). Solar wind and interplanetary magnetic field measurements from the ACE or DSCOVR spacecraft provide geomagnetic index estimates used to model the location of both auroral absorption and the proton rigidity cutoff boundary that defines the latitudinal extent of PCA dur...
The need for accurate assessment of the geomagnetic hazard to power systems is driving a requirem... more The need for accurate assessment of the geomagnetic hazard to power systems is driving a requirement to model geomagnetically induced currents (GIC) in multiple voltage levels of a power network. The Lehtinen-Pirjola method for modelling GIC is widely used but was developed when the main aim was to model GIC in only the highest voltage level of a power network. Here we present a modification to the Lehtinen-Pirjola (LP) method designed to provide an efficient method for modelling GIC in multiple voltage levels. The LP method calculates the GIC flow to ground from each node. However, with a network involving multiple voltage levels, many of the nodes are ungrounded, i.e. have infinite resistance to ground, which is numerically inconvenient. The new modified Lehtinen-Pirjola (LPm) method replaces the earthing impedance matrix [Z e ] with the corresponding earthing admittance matrix [Y e ] in which the ungrounded nodes have zero admittance to ground. This is combined with the network admittance matrix [Y n ] to give a combined matrix ([Y n ] + [Y e ]), which is a sparse symmetric positive definite matrix allowing efficient techniques, such as Cholesky decomposition, to be used to provide the nodal voltages. The nodal voltages are then used to calculate the GIC in the transformer windings and the transmission lines of the power network. The LPm method with Cholesky decomposition also provides an efficient method for calculating GIC at multiple time steps. Finally, the paper shows how software for the LP method can be easily converted to the LPm method and provides examples of calculations using the LPm method.
Users may download and print one copy of any publication from the public portal for the purpose... more Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
Journal of Geophysical Research: Space Physics, 2019
The rapid changes of magnetic fields associated with large, isolated magnetic perturbations with ... more The rapid changes of magnetic fields associated with large, isolated magnetic perturbations with amplitudes |ΔB| of hundreds of nanotesla and 5-to 10-min periods can induce bursts of geomagnetically induced currents that can harm technological systems. This paper presents statistical summaries of the characteristics of nightside magnetic perturbation events observed in Eastern Arctic Canada from 2014 through 2017 using data from stations that are part of four magnetometer arrays: MACCS, AUTUMNX, CANMOS, and CARISMA, covering a range of magnetic latitudes from 68 to 78°. Most but not all of the magnetic perturbation events were associated with substorms: roughly two thirds occurred between 5 and 30 min after onset. The association of intense nighttime magnetic perturbation events with magnetic storms was significantly reduced at latitudes above 73°, presumably above the nominal auroral oval. A superposed epoch study of 21 strong events at Cape Dorset showed that the largest |dB/dt| values appeared within an~275-km radius that was associated with a region of shear between upward and downward field-aligned currents. The statistical distributions of impulse amplitudes of both |ΔB| and |dB/dt| fit well the log-normal distribution at all stations. The |ΔB| distributions are similar over the magnetic latitude range studied, but the kurtosis and skewness of the |dB/dt| distributions show a slight increase with latitude. Knowledge of the statistical characteristics of these events has enabled us to estimate the occurrence probability of extreme impulsive disturbances using the approximation of a log-normal distribution.
The electric field instruments onboard the Swarm satellites make high-resolution measurements of ... more The electric field instruments onboard the Swarm satellites make high-resolution measurements of the F-region ion drift. This paper presents an initial investigation of preliminary ion drift data made available by the European Space Agency. Based on data taken during polar cap crossings, we identify large offsets in both the along-track and crosstrack components of the measured ion drift. These offsets are removed by zeroing drift values at the low-latitude boundary of the high-latitude convection pattern. This correction is shown to significantly improve agreement between the Swarm ion drift measurements and velocity inferred from a radar-based statistical convection model for periods of quasi-stability in the solar wind and interplanetary magnetic field. Agreement is most pronounced in the cross-track direction (R = 0.60); it improves slightly (R = 0.63) if data are limited to periods with IMF B z < 0. The corrected Swarm data were shown to properly identify the convection reversal boundary for periods of IMF B z < 0, in full agreement with previous radar and satellite measurements, making Swarm ion drift measurements a valuable input for ionospheric modeling.
Disturbances of the geomagnetic field produced by space weather events can have an impact on powe... more Disturbances of the geomagnetic field produced by space weather events can have an impact on power systems and other critical infrastructure. To mitigate these risks it is important to determine the extreme values of geomagnetic activity that can occur. More than 40 years of 1 min magnetic data recorded at 13 Canadian geomagnetic observatories have been analyzed to evaluate extreme levels in geomagnetic and geoelectric activities in different locations of Canada. The hourly ranges of geomagnetic field variations and hourly maximum in rate of change of the magnetic variations have been used as measures of geomagnetic activity. Geoelectric activity is estimated by the hourly peak amplitude of the geoelectric fields calculated with the use of Earth resistivity models specified for different locations in Canada. A generalized extreme value distribution was applied to geomagnetic and geoelectric indices to evaluate extreme geomagnetic and geoelectric disturbances, which could happen once...
Assessing the geomagnetic hazard to power systems requires reliable modelling of the geomagnetica... more Assessing the geomagnetic hazard to power systems requires reliable modelling of the geomagnetically induced currents (GIC) produced in the power network. This paper compares the Nodal Admittance Matrix method with the Lehtinen-Pirjola method and shows them to be mathematically equivalent. GIC calculation using the Nodal Admittance Matrix method involves three steps: (1) using the voltage sources in the lines representing the induced geoelectric field to calculate equivalent current sources and summing these to obtain the nodal current sources, (2) performing the inversion of the admittance matrix and multiplying by the nodal current sources to obtain the nodal voltages, (3) using the nodal voltages to determine the currents in the lines and in the ground connections. In the Lehtinen-Pirjola method, steps 2 and 3 of the Nodal Admittance Matrix calculation are combined into one matrix expression. This involves inversion of a more complicated matrix but yields the currents to ground directly from the nodal current sources. To calculate GIC in multiple voltage levels of a power system, it is necessary to model the connections between voltage levels, not just the transmission lines and ground connections considered in traditional GIC modelling. Where GIC flow to ground through both the high-voltage and low-voltage windings of a transformer, they share a common path through the substation grounding resistance. This has been modelled previously by including non-zero, off-diagonal elements in the earthing impedance matrix of the Lehtinen-Pirjola method. However, this situation is more easily handled in both the Nodal Admittance Matrix method and the Lehtinen-Pirjola method by introducing a node at the neutral point.
Journal of Atmospheric and Solar-Terrestrial Physics, 2000
Forecasting the geomagnetic e ects to technological systems on the ground requires rapid calculat... more Forecasting the geomagnetic e ects to technological systems on the ground requires rapid calculations of the electric and magnetic ÿelds produced by the auroral electrojet. The electrojet is often modelled as a line current at a height of 100 km, but in reality it has a ÿnite width and is typically spread over 5 • or 6 • of latitude. We show that the width of the electrojet can easily be included in electric and magnetic ÿeld calculations by assuming that the ionospheric current density has a Cauchy distribution with a half-width a; j(x)=(I=)a=(x 2 + a 2), at a height h. It is shown that the electric and magnetic ÿelds produced at the surface of a layered earth by such a current are equivalent to the ÿelds produced by a line current I at a height h + a. This equivalence, combined with the complex image method, leads to simple formulas that provide a method for fast calculation of the electric and magnetic ÿelds that can a ect ground-based systems.
The relation between the seafloor electric field and the surface magnetic field is studied. It is... more The relation between the seafloor electric field and the surface magnetic field is studied. It is assumed that the fields are created by a 2-D ionospheric current distribution resulting in the E-polarization. The layered earth below the sea water is characterized by a surface impedance. The electric field at the seafloor can be expressed either as an inverse Fourier transform integral over the wavenumber or as a spatial convolution integral. In both integrals the surface magnetic field is multiplied by a function that depends on the depth and conductivity of the sea water and on the properties of the basement. The fact that surface magnetic data are usually available on land, not at the sea surface, is also considered. Test computations demonstrate that the numerical inaccuracies involved in the convolution method are negligible. The theoretical equations are applied to calculate the seafloor electric fields due to an ionospheric line current or associated with real magnetic data collected by the IMAGE magnetometer array in northern Europe. Two different sea depths are considered: 100 m (the continental shelf) and 5 km (the deep ocean). It is seen that the dependence of the electric field on the oscillation period is weaker in the 5 km case than for 100 m.
For studying the auroral electrojet and for examining the effects it can produce in power systems... more For studying the auroral electrojet and for examining the effects it can produce in power systems on the ground, it is useful to be able to calculate the magnetic and electric fields that the electrojet produces at the surface of the Earth. Including the effects of currents induced in the Earth leads to a set of integral expressions, the numerical computation of which is complicated and demanding of computer resources. An approximate solution can be achieved by representing the induced currents by an image current at a complex depth. We present a simple derivation of the compleximage expressions and use them to calculate the fields produced by the auroral electrojet at the surface of an earth represented by layered conductivity models. Comparison of these results with ones obtained using the exact integral solution show that the errors introduced are insignificant compared to the uncertainties in the parameters used. The complex-image method thus provides a simple, fast and accurate means of calculating the magnetic and electric fields.
Active geomagnetic conditions on 12-13, 15-16, and 22-23 September 1999 resulted in geomagnetical... more Active geomagnetic conditions on 12-13, 15-16, and 22-23 September 1999 resulted in geomagnetically induced currents (GIC) measurable in power systems in Canada and the United States. Different solar origins for these three events gave rise to dissimilar interplanetary signatures. We used these events to present three case studies, each tracing an entire space weather episode from its inception on the Sun, propagation through the interplanetary medium, manifestation on the ground as intense magnetic and electric fluctuations, and its eventual impact on technological systems. Key words. Geomagnetism and paleomagnetism (rapid time variations)-Interplanetary physics (interplanetary magnetic fields)-Solar physics, astrophysics, and astronomy (flares and mass ejections)
Geomagnetic field variations induce telluric currents in pipelines, which modify the electrochemi... more Geomagnetic field variations induce telluric currents in pipelines, which modify the electrochemical conditions at the pipe/soil interface, possibly contributing to corrosion of the pipeline steel. Modelling of geomagnetic induction in pipelines can be accomplished by combining several techniques. Starting with geomagnetic field data, the geoelectric fields in the absence of the pipeline were calculated using the surface impedance derived from a layered-Earth conductivity model. The influence of the pipeline on the electric fields was then examined using an infinitely long cylinder (ILC) model. Pipe-to-soil potentials produced by the electric field induced in the pipeline were calculated using a distributed source transmission line (DSTL) model. The geomagnetic induction process is frequency dependent; therefore, the calculations are best performed in the frequency domain, using a Fourier transform to go from the original time domain magnetic data, and an inverse Fourier transform at the end of the process, to obtain the pipe-tosoil potential variation in the time domain. Examples of the model calculations are presented and compared to observations made on a long pipeline in the auroral zone.
Geomagnetically induced currents in power systems are due to space weather events which create ge... more Geomagnetically induced currents in power systems are due to space weather events which create geomagnetic disturbances accompanied by electric fields at the surface of the Earth. The purpose of this paper is to evaluate the use of the finite element method (FEM) to calculate the magnetic and electric fields to which long transmission lines of power systems on the Earth are exposed. The well-known technique of FEM is used for the first time to simulate magnetic and electric fields applicable to power systems. Several test cases are modelled and compared with known solutions. It is shown that FEM is an effective modelling technique that can be applied to determine the electric fields which affect power systems. FEM enables an increased capability beyond the traditional methods for modelling electric and magnetic fields with layered earth conductivity structures, as spatially more complex structures can be considered using FEM. As an example results are presented for induction, due to a line current source, in adjacent regions with different layered conductivity structures. The results show the electric field away from the interface is the same as calculated for a single region; however near the interface the electric field is influenced by both regions.
The outer radiation belt injection, transport, acceleration and loss satellite (ORBITALS) is a sm... more The outer radiation belt injection, transport, acceleration and loss satellite (ORBITALS) is a small satellite mission proposed as a Canadian contribution to the satellite infrastructure for the International Living With a Star (ILWS) program. The ORBITALS will monitor the energetic electron and ion populations in the inner magnetosphere across a wide range of energies (keV to tens of MeV) as
Geomagnetic field variations produce geoelectric fields that can affect the operation of technolo... more Geomagnetic field variations produce geoelectric fields that can affect the operation of technological networks at the Earth's surface, including power systems, pipelines, phone cables and railway circuits. To assess the geomagnetic hazard to this technology, it is necessary to model the geomagnetically induced currents (GIC) produced in these systems during geomagnetic disturbances. This requires use of geomagnetic data with appropriate Earth conductivity models to calculate the geoelectric fields that drive GIC. To provide a way of testing geoelectric field calculation software, we provide a benchmark test case by defining a synthetic geomagnetic field variation and deriving exact analytic expressions for the Earth response based on both uniform and layered Earth conductivity models. These are then used to provide exact analytic expressions for the geoelectric fields that would be produced by the synthetic geomagnetic field variation. The synthetic geomagnetic data can be used as input to numerical geoelectric field calculation software, the output of which can be tested by comparison with the analytically-generated geoelectric fields. INDEX TERMS Geoelectric fields, geomagnetic disturbances, power systems.
Space weather storms involve intense and rapidly varying electric currents in the ionosphere, whi... more Space weather storms involve intense and rapidly varying electric currents in the ionosphere, which create electric and magnetic fields at the Earth's surface. The electric fields drive geomagnetically induced currents (GIC) in technological networks and may have serious impacts. For assessing the hazards it is necessary to estimate GIC magnitudes, and this requires calculations of the electric and magnetic fields produced at the Earth's surface by the ionospheric currents. The surface fields are also affected by currents induced within the ground and influenced by the conductivity of the Earth. This also has to be taken into account. The calculation methods should be fast enough that they can be applied to forecasting the fields and GIC, for example, by using satellite observations of the solar wind. In this paper, we consider an infinitely long horizontal line current, which is the basic model of an auroral electrojet and simple enough to give insight into the physics and ...
2007 7th International Symposium on Electromagnetic Compatibility and Electromagnetic Ecology, 2007
Page 1. EFFECTS OF RECENT GEOM AGNETIC STORM S ON POW ER SYSTEM S ... Fig. 1a is representing the... more Page 1. EFFECTS OF RECENT GEOM AGNETIC STORM S ON POW ER SYSTEM S ... Fig. 1a is representing the image of the major solar source of the ground magnetic storms, a full halo coronal mass ejection (CME) which occurred on October 28. ...
2013 IEEE Power & Energy Society General Meeting, 2013
ABSTRACT Geomagnetically induced currents (GIC) can pose a problem for power system operation. To... more ABSTRACT Geomagnetically induced currents (GIC) can pose a problem for power system operation. To assess the geomagnetic threat requires modelling of the GIC in the power system. However, as well as the characteristics of the system itself, GIC are affected by connections to neighbouring systems. This paper considers three choices of equivalent circuit for a neighbouring system. Model calculations are made for the Ontario system with equivalent circuits for the neighbouring Manitoba system, and vice versa. Values from these calculations are compared with the exact values determined from model calculations for the combined Ontario and Manitoba systems. The calculations with equivalent circuits produce errors in the GIC at substations that diminish with increasing distance of the substation from the connection to the neighbour. Comparison of the results showed that the best choice for an equivalent circuit comprises the induced voltage and resistance for the first transmission line into the neighbouring system.
Researchers at the University of Leicester, Lancaster University and St Petersburg State Universi... more Researchers at the University of Leicester, Lancaster University and St Petersburg State University have developed various models that can be employed in HF radio propagation predictions. Signal coverage predictions make use of numerical ray tracing to estimate the ray paths through a model ionosphere that includes various ionospheric features prevalent at high latitudes (in particular patches, arcs, ionisation tongue, auroral zone irregularities and the mid-latitude trough). Modelling of D-region absorption is also included. GOES satellites provide information on X-ray flux (causing shortwave fadeout during solar flares) and precipitating energetic proton flux which correlates strongly with Polar Cap Absorption (PCA). Solar wind and interplanetary magnetic field measurements from the ACE or DSCOVR spacecraft provide geomagnetic index estimates used to model the location of both auroral absorption and the proton rigidity cutoff boundary that defines the latitudinal extent of PCA dur...
The need for accurate assessment of the geomagnetic hazard to power systems is driving a requirem... more The need for accurate assessment of the geomagnetic hazard to power systems is driving a requirement to model geomagnetically induced currents (GIC) in multiple voltage levels of a power network. The Lehtinen-Pirjola method for modelling GIC is widely used but was developed when the main aim was to model GIC in only the highest voltage level of a power network. Here we present a modification to the Lehtinen-Pirjola (LP) method designed to provide an efficient method for modelling GIC in multiple voltage levels. The LP method calculates the GIC flow to ground from each node. However, with a network involving multiple voltage levels, many of the nodes are ungrounded, i.e. have infinite resistance to ground, which is numerically inconvenient. The new modified Lehtinen-Pirjola (LPm) method replaces the earthing impedance matrix [Z e ] with the corresponding earthing admittance matrix [Y e ] in which the ungrounded nodes have zero admittance to ground. This is combined with the network admittance matrix [Y n ] to give a combined matrix ([Y n ] + [Y e ]), which is a sparse symmetric positive definite matrix allowing efficient techniques, such as Cholesky decomposition, to be used to provide the nodal voltages. The nodal voltages are then used to calculate the GIC in the transformer windings and the transmission lines of the power network. The LPm method with Cholesky decomposition also provides an efficient method for calculating GIC at multiple time steps. Finally, the paper shows how software for the LP method can be easily converted to the LPm method and provides examples of calculations using the LPm method.
Users may download and print one copy of any publication from the public portal for the purpose... more Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
Journal of Geophysical Research: Space Physics, 2019
The rapid changes of magnetic fields associated with large, isolated magnetic perturbations with ... more The rapid changes of magnetic fields associated with large, isolated magnetic perturbations with amplitudes |ΔB| of hundreds of nanotesla and 5-to 10-min periods can induce bursts of geomagnetically induced currents that can harm technological systems. This paper presents statistical summaries of the characteristics of nightside magnetic perturbation events observed in Eastern Arctic Canada from 2014 through 2017 using data from stations that are part of four magnetometer arrays: MACCS, AUTUMNX, CANMOS, and CARISMA, covering a range of magnetic latitudes from 68 to 78°. Most but not all of the magnetic perturbation events were associated with substorms: roughly two thirds occurred between 5 and 30 min after onset. The association of intense nighttime magnetic perturbation events with magnetic storms was significantly reduced at latitudes above 73°, presumably above the nominal auroral oval. A superposed epoch study of 21 strong events at Cape Dorset showed that the largest |dB/dt| values appeared within an~275-km radius that was associated with a region of shear between upward and downward field-aligned currents. The statistical distributions of impulse amplitudes of both |ΔB| and |dB/dt| fit well the log-normal distribution at all stations. The |ΔB| distributions are similar over the magnetic latitude range studied, but the kurtosis and skewness of the |dB/dt| distributions show a slight increase with latitude. Knowledge of the statistical characteristics of these events has enabled us to estimate the occurrence probability of extreme impulsive disturbances using the approximation of a log-normal distribution.
The electric field instruments onboard the Swarm satellites make high-resolution measurements of ... more The electric field instruments onboard the Swarm satellites make high-resolution measurements of the F-region ion drift. This paper presents an initial investigation of preliminary ion drift data made available by the European Space Agency. Based on data taken during polar cap crossings, we identify large offsets in both the along-track and crosstrack components of the measured ion drift. These offsets are removed by zeroing drift values at the low-latitude boundary of the high-latitude convection pattern. This correction is shown to significantly improve agreement between the Swarm ion drift measurements and velocity inferred from a radar-based statistical convection model for periods of quasi-stability in the solar wind and interplanetary magnetic field. Agreement is most pronounced in the cross-track direction (R = 0.60); it improves slightly (R = 0.63) if data are limited to periods with IMF B z < 0. The corrected Swarm data were shown to properly identify the convection reversal boundary for periods of IMF B z < 0, in full agreement with previous radar and satellite measurements, making Swarm ion drift measurements a valuable input for ionospheric modeling.
Disturbances of the geomagnetic field produced by space weather events can have an impact on powe... more Disturbances of the geomagnetic field produced by space weather events can have an impact on power systems and other critical infrastructure. To mitigate these risks it is important to determine the extreme values of geomagnetic activity that can occur. More than 40 years of 1 min magnetic data recorded at 13 Canadian geomagnetic observatories have been analyzed to evaluate extreme levels in geomagnetic and geoelectric activities in different locations of Canada. The hourly ranges of geomagnetic field variations and hourly maximum in rate of change of the magnetic variations have been used as measures of geomagnetic activity. Geoelectric activity is estimated by the hourly peak amplitude of the geoelectric fields calculated with the use of Earth resistivity models specified for different locations in Canada. A generalized extreme value distribution was applied to geomagnetic and geoelectric indices to evaluate extreme geomagnetic and geoelectric disturbances, which could happen once...
Assessing the geomagnetic hazard to power systems requires reliable modelling of the geomagnetica... more Assessing the geomagnetic hazard to power systems requires reliable modelling of the geomagnetically induced currents (GIC) produced in the power network. This paper compares the Nodal Admittance Matrix method with the Lehtinen-Pirjola method and shows them to be mathematically equivalent. GIC calculation using the Nodal Admittance Matrix method involves three steps: (1) using the voltage sources in the lines representing the induced geoelectric field to calculate equivalent current sources and summing these to obtain the nodal current sources, (2) performing the inversion of the admittance matrix and multiplying by the nodal current sources to obtain the nodal voltages, (3) using the nodal voltages to determine the currents in the lines and in the ground connections. In the Lehtinen-Pirjola method, steps 2 and 3 of the Nodal Admittance Matrix calculation are combined into one matrix expression. This involves inversion of a more complicated matrix but yields the currents to ground directly from the nodal current sources. To calculate GIC in multiple voltage levels of a power system, it is necessary to model the connections between voltage levels, not just the transmission lines and ground connections considered in traditional GIC modelling. Where GIC flow to ground through both the high-voltage and low-voltage windings of a transformer, they share a common path through the substation grounding resistance. This has been modelled previously by including non-zero, off-diagonal elements in the earthing impedance matrix of the Lehtinen-Pirjola method. However, this situation is more easily handled in both the Nodal Admittance Matrix method and the Lehtinen-Pirjola method by introducing a node at the neutral point.
Journal of Atmospheric and Solar-Terrestrial Physics, 2000
Forecasting the geomagnetic e ects to technological systems on the ground requires rapid calculat... more Forecasting the geomagnetic e ects to technological systems on the ground requires rapid calculations of the electric and magnetic ÿelds produced by the auroral electrojet. The electrojet is often modelled as a line current at a height of 100 km, but in reality it has a ÿnite width and is typically spread over 5 • or 6 • of latitude. We show that the width of the electrojet can easily be included in electric and magnetic ÿeld calculations by assuming that the ionospheric current density has a Cauchy distribution with a half-width a; j(x)=(I=)a=(x 2 + a 2), at a height h. It is shown that the electric and magnetic ÿelds produced at the surface of a layered earth by such a current are equivalent to the ÿelds produced by a line current I at a height h + a. This equivalence, combined with the complex image method, leads to simple formulas that provide a method for fast calculation of the electric and magnetic ÿelds that can a ect ground-based systems.
The relation between the seafloor electric field and the surface magnetic field is studied. It is... more The relation between the seafloor electric field and the surface magnetic field is studied. It is assumed that the fields are created by a 2-D ionospheric current distribution resulting in the E-polarization. The layered earth below the sea water is characterized by a surface impedance. The electric field at the seafloor can be expressed either as an inverse Fourier transform integral over the wavenumber or as a spatial convolution integral. In both integrals the surface magnetic field is multiplied by a function that depends on the depth and conductivity of the sea water and on the properties of the basement. The fact that surface magnetic data are usually available on land, not at the sea surface, is also considered. Test computations demonstrate that the numerical inaccuracies involved in the convolution method are negligible. The theoretical equations are applied to calculate the seafloor electric fields due to an ionospheric line current or associated with real magnetic data collected by the IMAGE magnetometer array in northern Europe. Two different sea depths are considered: 100 m (the continental shelf) and 5 km (the deep ocean). It is seen that the dependence of the electric field on the oscillation period is weaker in the 5 km case than for 100 m.
For studying the auroral electrojet and for examining the effects it can produce in power systems... more For studying the auroral electrojet and for examining the effects it can produce in power systems on the ground, it is useful to be able to calculate the magnetic and electric fields that the electrojet produces at the surface of the Earth. Including the effects of currents induced in the Earth leads to a set of integral expressions, the numerical computation of which is complicated and demanding of computer resources. An approximate solution can be achieved by representing the induced currents by an image current at a complex depth. We present a simple derivation of the compleximage expressions and use them to calculate the fields produced by the auroral electrojet at the surface of an earth represented by layered conductivity models. Comparison of these results with ones obtained using the exact integral solution show that the errors introduced are insignificant compared to the uncertainties in the parameters used. The complex-image method thus provides a simple, fast and accurate means of calculating the magnetic and electric fields.
Active geomagnetic conditions on 12-13, 15-16, and 22-23 September 1999 resulted in geomagnetical... more Active geomagnetic conditions on 12-13, 15-16, and 22-23 September 1999 resulted in geomagnetically induced currents (GIC) measurable in power systems in Canada and the United States. Different solar origins for these three events gave rise to dissimilar interplanetary signatures. We used these events to present three case studies, each tracing an entire space weather episode from its inception on the Sun, propagation through the interplanetary medium, manifestation on the ground as intense magnetic and electric fluctuations, and its eventual impact on technological systems. Key words. Geomagnetism and paleomagnetism (rapid time variations)-Interplanetary physics (interplanetary magnetic fields)-Solar physics, astrophysics, and astronomy (flares and mass ejections)
Geomagnetic field variations induce telluric currents in pipelines, which modify the electrochemi... more Geomagnetic field variations induce telluric currents in pipelines, which modify the electrochemical conditions at the pipe/soil interface, possibly contributing to corrosion of the pipeline steel. Modelling of geomagnetic induction in pipelines can be accomplished by combining several techniques. Starting with geomagnetic field data, the geoelectric fields in the absence of the pipeline were calculated using the surface impedance derived from a layered-Earth conductivity model. The influence of the pipeline on the electric fields was then examined using an infinitely long cylinder (ILC) model. Pipe-to-soil potentials produced by the electric field induced in the pipeline were calculated using a distributed source transmission line (DSTL) model. The geomagnetic induction process is frequency dependent; therefore, the calculations are best performed in the frequency domain, using a Fourier transform to go from the original time domain magnetic data, and an inverse Fourier transform at the end of the process, to obtain the pipe-tosoil potential variation in the time domain. Examples of the model calculations are presented and compared to observations made on a long pipeline in the auroral zone.
Geomagnetically induced currents in power systems are due to space weather events which create ge... more Geomagnetically induced currents in power systems are due to space weather events which create geomagnetic disturbances accompanied by electric fields at the surface of the Earth. The purpose of this paper is to evaluate the use of the finite element method (FEM) to calculate the magnetic and electric fields to which long transmission lines of power systems on the Earth are exposed. The well-known technique of FEM is used for the first time to simulate magnetic and electric fields applicable to power systems. Several test cases are modelled and compared with known solutions. It is shown that FEM is an effective modelling technique that can be applied to determine the electric fields which affect power systems. FEM enables an increased capability beyond the traditional methods for modelling electric and magnetic fields with layered earth conductivity structures, as spatially more complex structures can be considered using FEM. As an example results are presented for induction, due to a line current source, in adjacent regions with different layered conductivity structures. The results show the electric field away from the interface is the same as calculated for a single region; however near the interface the electric field is influenced by both regions.
The outer radiation belt injection, transport, acceleration and loss satellite (ORBITALS) is a sm... more The outer radiation belt injection, transport, acceleration and loss satellite (ORBITALS) is a small satellite mission proposed as a Canadian contribution to the satellite infrastructure for the International Living With a Star (ILWS) program. The ORBITALS will monitor the energetic electron and ion populations in the inner magnetosphere across a wide range of energies (keV to tens of MeV) as
Geomagnetic field variations produce geoelectric fields that can affect the operation of technolo... more Geomagnetic field variations produce geoelectric fields that can affect the operation of technological networks at the Earth's surface, including power systems, pipelines, phone cables and railway circuits. To assess the geomagnetic hazard to this technology, it is necessary to model the geomagnetically induced currents (GIC) produced in these systems during geomagnetic disturbances. This requires use of geomagnetic data with appropriate Earth conductivity models to calculate the geoelectric fields that drive GIC. To provide a way of testing geoelectric field calculation software, we provide a benchmark test case by defining a synthetic geomagnetic field variation and deriving exact analytic expressions for the Earth response based on both uniform and layered Earth conductivity models. These are then used to provide exact analytic expressions for the geoelectric fields that would be produced by the synthetic geomagnetic field variation. The synthetic geomagnetic data can be used as input to numerical geoelectric field calculation software, the output of which can be tested by comparison with the analytically-generated geoelectric fields. INDEX TERMS Geoelectric fields, geomagnetic disturbances, power systems.
Space weather storms involve intense and rapidly varying electric currents in the ionosphere, whi... more Space weather storms involve intense and rapidly varying electric currents in the ionosphere, which create electric and magnetic fields at the Earth's surface. The electric fields drive geomagnetically induced currents (GIC) in technological networks and may have serious impacts. For assessing the hazards it is necessary to estimate GIC magnitudes, and this requires calculations of the electric and magnetic fields produced at the Earth's surface by the ionospheric currents. The surface fields are also affected by currents induced within the ground and influenced by the conductivity of the Earth. This also has to be taken into account. The calculation methods should be fast enough that they can be applied to forecasting the fields and GIC, for example, by using satellite observations of the solar wind. In this paper, we consider an infinitely long horizontal line current, which is the basic model of an auroral electrojet and simple enough to give insight into the physics and ...
2007 7th International Symposium on Electromagnetic Compatibility and Electromagnetic Ecology, 2007
Page 1. EFFECTS OF RECENT GEOM AGNETIC STORM S ON POW ER SYSTEM S ... Fig. 1a is representing the... more Page 1. EFFECTS OF RECENT GEOM AGNETIC STORM S ON POW ER SYSTEM S ... Fig. 1a is representing the image of the major solar source of the ground magnetic storms, a full halo coronal mass ejection (CME) which occurred on October 28. ...
2013 IEEE Power & Energy Society General Meeting, 2013
ABSTRACT Geomagnetically induced currents (GIC) can pose a problem for power system operation. To... more ABSTRACT Geomagnetically induced currents (GIC) can pose a problem for power system operation. To assess the geomagnetic threat requires modelling of the GIC in the power system. However, as well as the characteristics of the system itself, GIC are affected by connections to neighbouring systems. This paper considers three choices of equivalent circuit for a neighbouring system. Model calculations are made for the Ontario system with equivalent circuits for the neighbouring Manitoba system, and vice versa. Values from these calculations are compared with the exact values determined from model calculations for the combined Ontario and Manitoba systems. The calculations with equivalent circuits produce errors in the GIC at substations that diminish with increasing distance of the substation from the connection to the neighbour. Comparison of the results showed that the best choice for an equivalent circuit comprises the induced voltage and resistance for the first transmission line into the neighbouring system.
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Papers by David Boteler