Space weather manifests in power networks as quasi-DC currents flowing in and out of the power system through the grounded neutrals of high-voltage transformers, referred to as geomagnetically induced currents. This paper presents a comparison of modeled geomagnetically induced currents, determined using geoelectric fields derived from four different impedance models employing different conductivity structures, with geomagnetically induced current measurements from within the power system of the eastern states of Australia. The four different impedance models are a uniform conductivity model (UC), one-dimensional n-layered conductivity models (NU and NW), and a three-dimensional conductivity model of the Australian region (3DM) from which magnetotelluric impedance tensors are calculated. The modeled 3DM tensors show good agreement with measured magnetotelluric tensors obtained from recently released data from the Australian Lithospheric Architecture Magnetotelluric Project. The four different impedance models are applied to a network model for four geomagnetic storms of solar cycle 24 and compared with observations from up to eight different locations within the network. The models are assessed using several statistical performance parameters. For correlation values greater than 0.8 and amplitude scale factors less than 2, the 3DM model performs better than the simpler conductivity models. When considering the model performance parameter, P, the highest individual P value was for the 3DM model. The implications of the results are discussed in terms of the underlying geological structures and the power network electrical parameters.

Key Points

The study aims to understand the influence of Australia's underlying geology when modeling GICs in Australian power networks
The study compares modeled and measured GICs to assess the influence of different conductivity structures

1 Introduction

There has been an increasing awareness internationally of the potential effects of space weather on critical infrastructure and subsequent flow-on economic and societal impacts (Eastwood et al., 2017; Oughton et al., 2017; Schulte in den Bäumen et al., 2014). Recently, the United States released the United States National Space Weather Strategy and Action Plan (2015), and in 2016, a United States Presidential Executive Order (2016) was issued by President Obama to coordinate efforts for space weather events through a cross-agency response. In the UK, socioeconomic and other impact studies (Cannon, 2013) resulted in space weather being entered into the UK Risk Register of Civil Emergencies (Cabinet Office, 2017), with subsequent development of space weather services and related mitigation activities. In 2017, the Canadian Space Agency embarked on a risk assessment into the impacts of space weather on Canada's critical infrastructure. Further, member states of the United Nations Committee on the Peaceful Uses of Outer Space recently approved new guidelines related to space weather, under actions for the long-term sustainability of outer space activities, including recommendations that member states undertake assessments of the risks and socioeconomic impacts of adverse space weather on their technological systems (Mann et al., 2018, and references therein). One of the critical infrastructure elements often considered in such studies is the nation's power networks.

Space weather manifests in power networks as quasi-DC currents flowing in and out of the power system through the grounded neutrals of high-voltage (HV) transformers. These currents are referred to as geomagnetically induced currents (GIC) due to their source being the time varying geomagnetic field associated with geomagnetic storms. One method for investigating the impact of GIC is through measurement devices on the neutral connections of HV transformers. The interconnected power system of the eastern states of Australia, referred to as the National Electricity Market (NEM), contains over 1,000 HV transformers. Installation of monitoring devices on all transformers is unfeasible and uneconomical. Modeling the flow of GIC in the Australian network is therefore required to obtain an understanding of the potential impacts of space weather. Modeling GIC in power systems typically encompasses two main steps:

Calculating the electric field at the Earth's surface (or geoelectric field).
Applying the geoelectric field to a spatial model of the power network that incorporates the relevant electrical parameters.

One of the simplest approaches for calculating the geoelectric field of step 1 is by assuming a vertically downward propagating plane wave magnetic field incident on a uniform conducting Earth. The assumption that the Earth is a uniform half-space gives the equation of magnetotellurics (e.g., Cagniard, 1953; Pirjola, 1982, 2002):

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0001$ (1)

where σ is a scalar conductivity for this case, μ_o is the permeability of free space, ω is the angular frequency of the incident wavefield, E_y is a function of −B_x, E_x is a function of B_y, and x and y are the north and east directions, respectively. Uniform half-space conductivity structures have been employed in the study of GIC in power networks in South Africa (Koen & Gaunt, 2003), Sweden (Pulkkinen et al., 2005), China (Liu et al., 2009), Spain (Torta et al., 2012), Australia (Marshall et al., 2013, 2017), and New Zealand (Marshall et al., 2012).

For the case where the Earth's conductivity is assumed to be horizontally layered, σ is no longer a scalar and a frequency-dependent surface impedance function is typically used to relate the horizontal magnetic and electric field components. Horizontally layered, or one-dimensional (1-D), conductivity structures have been employed in the study of GIC in the power networks of South Africa (Matandirotya et al., 2015; Ngwira et al., 2009), Sweden (Wik et al., 2008), midlatitude United States (Kappenman, 2003), China (Liu et al., 2014), Europe (Viljanen et al., 2013), and North America and Canada (Wei et al., 2013).

Incorporating lateral variations in the conductivity of the Earth's upper lithosphere, such as those associated with cratonic regions and ocean-continent boundaries, into GIC modeling requires a three-dimensional (3-D) approach. Ground electric fields can be intensified substantially for 3-D nonuniform conductivity structures relative to the 1-D case (Bedrosian & Love, 2015; Bonner & Schultz, 2017; Ivannikova et al., 2018; Love et al., 2016; Torta et al., 2017), and the intensification could be up to an order of magnitude for the Australian cratonic regions (Wang et al., 2016). A quasi 3-D approach that has been employed in a number of GIC studies is the thin sheet conductivity model (Vasseur & Weidelt, 1977), whereby conductivity gradients such as the ocean-continent boundaries are included by employing a thin sheet conductance map overlying layered resistivity structures. This method has been used in GIC studies of power systems in the UK (Beamish et al., 2002; Beggan et al., 2013; Kelly et al., 2017; Thomson et al., 2005), France (Kelly et al., 2017), Austria (Bailey et al., 2017, 2018), and New Zealand (Divett et al., 2017, 2018). The thin-sheet model is a period-dependent model that requires satisfaction of a range of conditions, as discussed by Weaver (1982), and is physically viable for periods in a certain range. Ivannikova et al. (2018) compared thin-sheet modeling for plane wave sources with full 3-D modeling of the electromagnetic field in geospace down to the Earth's surface and concluded that the thin-sheet model is a reasonable approximation for periods greater than a few minutes but shorter periods require a full 3-D approach.

Modeling geoelectric fields at the Earth's surface for GIC studies using finite difference time-dependent solutions to Maxwell's equations for nonuniform source fields has been performed for 2-D (Barnett, 2016) and 3-D (Simpson, 2011) conductivity models of the Earth. A common approach employs a magnetotelluric tensor to describe responses of the Earth's conductivity both vertically and horizontally for a plane wave source (Bedrosian & Love, 2015; Kelbert et al., 2017; Love et al., 2016; Torta et al., 2017; Wang et al., 2016). Although the assumption of the plane wave source might not always be realistic, as discussed in Ivannikova et al. (2018), this assumption is reasonable for low-middle latitude regions (Ngwira et al., 2009; Pulkkinen et al., 2005, 2012; Thomson et al., 2005; Viljanen et al., 2006) and is the method used in this paper to incorporate a 3-D conductivity structure into a GIC model for the Australian power network.

The “engineering step” applies the geoelectric field model obtained in step 1 to a spatial representation of the relevant power network electrical parameters such as substation location, transmission line orientation, transformer and transmission line resistances, and substation earthing resistances. The geoelectric fields are incorporated into the analysis as in-line voltages and currents in the Mesh Impedance Matrix and Nodal Admittance Matrix methods, respectively (see Boteler, (2014) and Boteler & Pirjola (2014) for a comprehensive description of these methods and their equivalence). The power network analysis method used in this study is that presented in Lehtinen and Pirjola (1985), which is based on the Nodal Admittance Matrix method. Application of this model to Australian power networks has been described in detail in Marshall et al. (2017).

This paper presents a comparison of GIC measurements from within the power system of the eastern states of Australia with modeled GIC determined using geoelectric fields derived from four different impedance models employing different conductivity structures. The four different impedance models are a uniform conductivity model (UC), 1-D n-layered conductivity models (NU and NW), and a 3-D conductivity model of the Australian region from which magnetotelluric tensors are calculated (3DM). The modeled 3DM tensors are compared with measured magnetotelluric (MT) tensors obtained from recently released data from the Australian Lithospheric Architecture Magnetotelluric Project (AusLAMP). The four different geoelectric field models are applied to a network model of the east Australian power system over four geomagnetic storms of solar cycle 24, the geomagnetic storms of 2 October 2013 and 23 June 2015 reported in Marshall et al. (2017) with the addition of 17 March 2013 and 8 September 2017 storms, and compared with observations from up to eight different locations within the network. The four different impedance models are assessed using several statistical performance parameters.

GIC measurements were recorded by monitoring equipment on the neutral lines of HV transformers at Bowen North, Middle Ridge, and Murarrie in the state of Queensland; Bayswater and Bannaby in the state of New South Wales; Para in the state of South Australia; and Chapel Street Hobart and George Town in the state of Tasmania (Figure 1). Modeled GIC were determined using data provided by the Transmission Network Service Providers to extend the models presented in Marshall et al. (2017) to include the entire interconnected eastern Australia power system. The next section describes the modeling used in this paper in more detail.

Details are in the caption following the image — **Figure 1**
Open in figure viewer PowerPoint

Map of geology of Australian region with locations of geomagnetic field monitoring sites (red triangles) and GIC monitoring locations (black squares) used in this study.

2 Modeling

As stated in section 1, the two main steps in modeling GIC are (1) calculation of the geoelectric field and (2) subsequent application to a power network model containing the relevant electrical parameters and topology. In this paper, a grid of geoelectric field vectors for the Australian region is applied to a network model of the NEM for each 1-min sample of the geomagnetic storms being analyzed. This process is repeated to build the time series of modeled GIC for all transformer locations in the network (see Marshall et al. (2017) for more details on this process). The modeled time series for the relevant transformers are then extracted to compare with the observed GIC measurements. The geoelectric field grids are determined from the network of geomagnetic field monitors shown in Figure 1 and the methods described below.

2.1 Geoelectric Field

The geoelectric field in step 1 can be determined for a plane wave using the relationship between electric field vector, E; magnetic field vector, H; and the impedance tensor, Z, of the medium through which they propagate with angular frequency, ω, that is,

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0002$ (2)

The impedance tensor is a function of the conductivity of the medium. For the case where conductivity varies horizontally, equation 2 gives the horizontal geoelectric field components as

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0003$ (3)

where x and y usually denote the north and east directions, respectively. For propagation vertically downward into the Earth assuming a horizontally uniform conductivity, the diagonal elements of equation 3 are zero and Z_xy = Z = −Z_yx, where Z is the intrinsic impedance. The horizontal electric and magnetic field components are then given by

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0004$ (4)

Calculation of the electric field at the Earth's surface can be determined from time series measurements of the horizontal components of the magnetic field and estimates of the surface impedance, including the four tensor components of equation 3 for horizontally nonuniform conductivity models. Application of equations 2–4 require Fourier transforming the geomagnetic field time series data into the frequency domain and calculating the impedance function over the bandwidth up to the Nyquist frequency. As mentioned in section 1, this study employs different conductivity models and methods to calculate four different surface impedances. The four methods utilize the following:

A uniform conducting half-space where conductivity is given by a single scalar value (hereafter referred to as UC).
A one-dimensional (1-D) n-layer model with a conductivity profile that varies in the vertical direction and is the same at each geomagnetic field monitoring location over the Australian continent (hereafter referred to as NU). The model is adapted from the layered Earth conductivity model for the north-west region of Canada as described in Trichtchenko and Boteler (2002), and readjusted using the Campbell et al. (1998) model for Australia.
A 1-D n-layer model where conductivity varies in the vertical direction and is different at each geomagnetic field monitoring location over the Australian continent. The conductivity profiles were derived from a conductivity study of the Australian region given in Wang et al. (2014) (hereafter referred to as NW).
A 3-D model with conductivity that varies vertically and horizontally which is an extension of the MT tensor analysis described in Wang et al. (2016) (hereafter referred to as 3DM).

As highlighted in section 1, uniform, 1-D, and 3-D conductivity structures have been utilized in previous GIC studies. For example, Ivannikova et al. (2018) compared results of local 1-D modeling and 3-D modeling to explore the details of coastal effect penetration distance on land in the British Isles for plane wave excitation. The 3DM impedance tensors in equation 3 above are sensitive to conductivity structure varying with depth, given by the penetration depth or skin depth, and are also sensitive to lateral conductivity variations in the horizontal direction, given by the horizontal adjustment length. Any conductivity anomalies (for example, oceans) laterally displaced by 2–3 times the penetration depth may affect the 3DM impedance tensor (Simpson & Bahr, 2005). In the NU model, the electrical conductivity structure varies only with depth and the distance to the lateral conductivity variations is infinite. The NW model considers a more realistic case than the NU model and uses the local 1-D structure of the 3-D conductivity model and individual 1-D solutions. This approach has already been used within the power industry; for example, the Electric Power Research Institute has published a set of regional 1-D conductivity models for the purpose of GIC modeling (Electric Power Research Institute (EPRI), 2012). One of the main aims of this study is to assess the impact of the various conductivity structures and approaches on GIC calculations over the Australian region. Moreover, this is the first time a 3-D approach has been applied to GIC modeling in the Australian region with previous GIC models utilizing the UC and NU approaches. Sections 2.1.1–2.1.3 describe the above methods and derived impedance models in more detail. Section 2.1.4 discusses utilization of the impedance models to obtain the geoelectric field grids to be applied to the power network model.

2.1.1 The UC Model

The impedance function for a uniform conducting Earth can be derived from equation 1 and is given in Marshall et al. (2017) as

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0005$ (5)

The uniform conductivity value for σ used in this study for the Australian region is σ = 0.002 S/m. This value was determined to be a suitable estimate for a uniform conductivity model of the region utilizing existing conductivity models of Australia (Marshall et al., 2013).

Figures 2a and 2b show the amplitude and phase response, respectively, of the four different impedance models (UC, NU, NW, and 3DM) for each of the geomagnetic field monitoring locations of Figure 1 over the bandwidth up to the Nyquist frequency. The plots are arranged from highest to lowest latitude location from top to bottom, left to right. The impedance calculated using the conductivity value above and equation 5 for the uniform conductivity case are shown in Figure 2 in red. As might be anticipated, this model produces the same impedance at all geomagnetic field monitoring sites.

2.1.2 One-Dimensional N-Layer Conductivity Models

For an n-layered Earth conductivity model and plane wave source field, the impedance of any layer, Z_n, is given by the recursive relationship (Trichtchenko & Boteler, 2002; Weaver, 1994):

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0006$ (6)

where r_n is given by

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0007$ (7)

and k_n is the propagation constant in layer n given by

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0008$ (8)

and d_n is the thickness of the nth layer. The bottommost layer, N, is a uniform half-space with impedance given by

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0009$ (9)

The surface impedance, Z₁, is obtained by recursively evaluating equations 6–9 for a given vertical conductivity profile, σ₁ …., σ_N. The next two sections describe the two different conductivity models used in this study to evaluate equations 6–9 and the resulting surface impedance.

2.1.2.1 The NU Model

The first 1-D conductivity model used in this study is given in Table 1 and is described in Marshall et al. (2010). This model assumes that the variation of conductivity with depth is the same at all locations across Australia and is described using seven layers, that is, n = 7. The model is adapted from the layered Earth conductivity model for the north-west region of Canada as described in Trichtchenko and Boteler (2002). The conductivity from the depth of 6 km was readjusted through linearly extrapolating and interpolating the Campbell et al. (1998) conductivity profile for Australia. The impedance calculated using the conductivity model of Table 1 and equations 6–9 are shown in Figure 2 in green. As might be anticipated, this model produces the same impedance at all geomagnetic field monitoring sites; however, these are different to the impedance determined for the UC model.

Table 1. The Seven-Layer Earth Model Resistivity Values of Section 2.1.2.1 Used to Evaluate Equation 6 for the NU Impedance Model

Layer Number	Layer Thickness (km)	Resistivity (Ωm)
1	0.025	50
2	6	20
3	15	1000
4	25	250
5	60	125
6	300	25
7	∞	10

The resistivity values were manually scaled from a conductivity study of the Australian region described in Campbell et al. (1998).

2.1.2.2 The NW Model

The second 1-D conductivity model used in this study utilizes the results of a conductivity study and 3-D model of the Australian region detailed in Wang et al. (2014) and shown in Figure 3. The 3-D Australian electrical conductivity model was inverted from vertical magnetic field transfer functions of AWAGS (Australia-Wide Array of Geomagnetic Stations) data using the 3-D code of Siripunvaraporn and Egbert (2009). The vertical magnetic field transfer function approach is favorable to islands or island continents, as the island and surrounding oceans can be represented electrically as a resistive block embedded in a conductive uniform host, for example, the 3-D electrical conductivity model of Japan (Hata et al., 2017).

The Australian geological setting is broadly grouped into western, northern, and southern cratons (Myers et al., 1996) that are largely devoid of electrical conducting mineral phases, thus have lower conductivity (Selway, 2013). The intracratonic basins filled with sedimentary rocks have relatively higher conductivities (Duan et al., 2013; Lilley et al., 2001) due to several potential causes such as interconnected saline fluids in porous sedimentary rocks or metamorphic fluids being released from active dehydration reactions. The nonuniform conductivity of the Australian continent is reflected in the top three layers of the 3-D model to a depth of 2 km. The layers of the 3-D model below 2 km were initially assigned 0.001 S/m to a depth of 250 km, then 0.1 S/m to depth of 648 km. During the inversion process, the 3-D model was iteratively updated by fitting AWAGS magnetic transfer function data (Chamalaun & Barton, 1993) with periods from 388 to 9,480 s until a desired misfit was achieved (Wang et al., 2014). Figure 3 presents 21 depth slices of the final 3-D inverse model obtained using a continent-ocean-sedimentary basin prior model with basins represented as being 2 km deep. There is a tendency for shallow structures (cratons and sedimentary basins) in the prior model to confine significant structures in the final model to shallow depth as shown in the top three layers due to the 388-s short-period data limiting the resolution to the shallow structures. The 4th to 21st layers represent heterogeneous continental electrical conductivity structures to a depth of 648 km. As the AWAGS magnetometer array did not occupy the Island of Tasmania, the conductivity structures under Tasmania used for this study were primarily inverted from the nearby stations in the continent. The final 3-D model has a horizontal grid resolution of 0.5° × 0.5° in latitude and longitude.

To evaluate the impedance using equations 6–9 for the NW case, a 21 layer (n = 21) vertical profile of conductivity with depth was extracted from the 3-D data shown in Figure 3 for each geomagnetic field observing location of Figure 1. The impedance determined for each location using the nearest grid point vertical conductivity profile and equations 6–9 are shown in Figure 2. Figures 2a and 2b show the amplitude and phase response, respectively, of the impedance for this case in orange. This model produces different impedance at the different geomagnetic field monitoring sites due to the different conductivity profiles extracted from the 3-D model for each location.

2.1.3 The 3DM Model

As stated previously, for the case where conductivity varies both vertically and horizontally, equation 2 is evaluated using the form of equation 3. Wang et al. (2016) presents details of using the conductivity model shown in Figure 3 to forward model the tensor components that are required for equation 3. For this study, the process has been performed to produce a 0.5° × 0.5° grid in latitude and longitude of tensor components as a function of frequency, resulting in 2,777 grid points over the Australian continent.

The impedance tensors for the 3-D model were computed using the ModEM-3D algorithm of Egbert and Kelbert (2012) and Kelbert et al. (2014) at the National Computational Infrastructure. For the forward modeling, the ModEM-3D requires a parameterized input model which comprises a grid of 86 × 71 cells, each 55 × 55 km (approximately 0.5°), surrounded on all sides by a border of two 110 × 110 km (approximately 1°) cells, giving a total grid of 90 × 75 cells. Horizontally, the input model is bounded by longitudes 110.0°E and 157.0°E, and latitudes 7.0°S and 46.5°S. Vertically, it consists of 21 horizontal layers to a depth of 648 km (see Figure 3).

Figures 2a and 2b show the amplitude and phase response, respectively, of the four modeled tensor components of the nearest grid point to each of the geomagnetic field monitoring locations of Figure 1 in blue. Four different symbols are used to indicate each of the different tensor components of equation 3 with solid symbols used for the off-diagonal elements and open symbols used for the diagonal elements: Z_xy (●), Z_yx (▲), Z_xx (○), and Z_yy (∆). Figures 2a and 2b show significantly different responses for each of the four modeled tensor components at, and between, each location.

A campaign is currently being conducted within Australia to provide a set of measured magnetotelluric (MT) data on a regional scale. This project is referred to as the Australian Lithospheric Architecture Magnetotelluric Project (AusLAMP). AusLAMP impedance tensors only for the south-east state of Victoria were released in July 2018 by Geoscience Australia (Duan & Kyi, 2018). The impedance tensors are used to assess the modeled 3DM tensors described above. The impedance tensors were derived from measured magnetic field and electrical field data at 96 sites across the state of Victoria with a nominal 0.5° × 0.5° (~55 km) site spacing. These sites are shown in Figure 4 as the magenta dots. Figure 4 shows locations in blue where modeled 3DM impedance tensors used in this study are compared with measured MT impedance tensors from AusLAMP data. The locations are from three regions where AWAGS sites (indicated by green triangles) were occupied (TOO: Toolangi, −37.533°, 145.467°; POL: Portland, −38.313°, 141.467°; BAL: Balranald, −34.624°, 143.573°).

The inland site BAL is approximately 350 km from the coast and located on the Murray Basin and as expected the coast effect on the data is minimal. Figure 5a shows the measured amplitude and phase of impedance tensors for site nos. 78, 79, and 80. For display purpose, only the two off-diagonal elements Z_xy and Z_yx are presented. The modeled tensor components Z_xy and Z_yx are displayed as the blue circles and triangles, respectively. The measured tensor components Z_xy and Z_yx are displayed as the magenta circles and triangles, respectively. Figure 5a shows the phase of the measured impedance tensors are in good agreement with the modeled impedance tensors at sites 78, 79, and 80; however, the amplitudes of modeled and measured impedance tensors are offset on average less than 1 mV/km nT at sites 78 and 80 and more than 1 mV/km nT at site 79. When the impedance tensors for sites 79 and 80 are converted to apparent resistivity and plotted in log-log scale (Figures 6a and 6b, respectively), it clearly shows that the measured apparent resistivity curve for site 79 is shifted by a constant reference to the modeled 3DM apparent resistivity. This is a typical static shift distortion effect in the amplitude of the measured impedance tensor for site 79, manifesting itself in the apparent resistivity, which can vary from site to site due to near surface resistivity inhomogeneities (Bonner & Schultz, 2017). This mismatch in amplitude is primarily contributed to static shift distortion in the measured impedance tensor.

The coastal site POL is a few kilometers from the ocean. Figure 5b (analogous to Figure 5a) shows that the measured and modeled impedance tensors at site nos. 12, 13, and 14 are in good agreement. The amplitude of the measured impedance tensors of Z_xy and Z_yx are significantly different between POL and BAL regions. For example, the amplitude of measured Z_xy and Z_yx are below 2 mV/km nT at POL while up to 6 mV/km nT at BAL in the frequency range of greater than 0.01 Hz. The differences are manifested in apparent resistivity data converted from the impedance tensors. Site 12 (Figure 6c) shows that the underlying conductivity structure in the POL region is much more conductive than the BAL region (site 80; Figure 6b). Despite the significant conductivity contrast in the two regions, the modeled impedance tensors in general matched the measured impedance tensors in both regions.

The site TOO is located in the Lachlan fold belt where the near-surface sedimentary and igneous rocks were subjected to folding, faulting, and uplift (VandenBerg et al., 2000). The conductivity structure over the region is more complex than the Murray Basin. Figure 5c (analogous to Figures 5a and 5b) shows the measured and modeled impedance tensors at site nos. 51, 52, and 53. As expected, the measured impedance tensors vary significantly between sites. The modeled impedance tensors are in good agreement with the measured impedance tensors at frequencies less than 10 mHz. At frequencies greater than 10 mHz there is quite large discrepancy between the measured and modeled tensors, which reflect the limitations of this broad-scale 3DM model. The Nyquist frequency used in this study is approximately 8.3 mHz. Therefore, the modeled tensors provide a suitable representation of the Australian region for this study.

2.1.4 Geoelectric Field Grids

As mentioned previously, the time series of modeled GIC in each transformer is obtained by applying a grid of geoelectric field vectors to the power network model for every minute of the geomagnetic storm being analyzed. The necessary geoelectric field time series are obtained by inverse Fourier transform of the convolved impedance and geomagnetic field spectrum (Marshall et al., 2017). The geomagnetic spectra are obtained using 24 hrs of time series data sampled at 1-min intervals, resulting in a Nyquist frequency of 8.3 mHz. Prior to application of the Fourier transform, the time series mean is removed and a Hanning window applied. In this study, geoelectric fields are calculated for each of the four different methods used to derive the impedance described in sections 2.1.1–2.1.3 for four different geomagnetic storms of solar cycle 24. The geomagnetic storms considered in this study are the same days as analyzed in Marshall et al. (2017), 2 October 2013 and 23 June 2015, with the addition of two geomagnetic storms of solar cycle 24 for which GIC monitoring data were made available, 17 March 2013 and 8 September 2017.

Figures 7a and 7b show the calculated geoelectric field time series obtained for each of the geomagnetic field monitoring locations of Figure 1 for 2 October 2013 in the geographic north (x component) and east (y component) directions, respectively. The time series for the four different impedance models are represented by the red (UC), green (NU), orange (NW), and blue (3DM) colored lines, respectively. The plots are arranged from highest- to lowest-latitude location from top to bottom, left to right. Figures 7a and 7b show that there are obvious differences in geoelectric field magnitude between the four time series at, and between, the monitoring locations of at least an order of magnitude in some locations.

Impedance tensors for the four different models were calculated at a spacing of 0.5° × 0.5° in latitude and longitude using the conductivity profiles and methods described above. A grid of geomagnetic field time series data was obtained by 2-D interpolation using a commercial software package to produce a 0.5° × 0.5° grid in latitude and longitude over the observing locations of Figure 1 for each minute sample of the time series. This process is repeated for every minute sample of the geomagnetic storms being analyzed to build geomagnetic time series at each grid point. Geoelectric field time series are obtained by inverse Fourier transform of the convolved geomagnetic field spectrum calculated from associated time series at each grid point with the impedance at each grid point for the four different models. Grids of geoelectric field for each minute sample are then obtained directly from the high-resolution grid of geoelectric field time series for each of the four different models. The high-resolution grids are applied to the power network model for GIC calculations.

Figures 8a–8d show examples of the geoelectric field grids for 0157 UT on 2 October 2013 for the four different models. The grid resolution has been decreased to 1° × 1° for display purposes only. The grids in Figure 8 are color coded analogous to Figure 7, that is, red (UC), green (NU), orange (NW), and blue (3DM). As might be anticipated, the geoelectric field grid of Figure 8d shows the highest degree of spatial variability over the Australian continent of all the grids shown in Figure 8.

In comparison with the UC and NU models, the 3-D electrical conductivity features added more complicated distortions to the relatively uniform geoelectric field patterns of Figures 8a and 8b. Figures 8c and 8d show enhancements in the field, and Figure 8d shows distortions in the direction of the geoelectric field vectors by heterogeneous continental electrical conductivity. For example, Archean cratons in western, northern, and central Australia contain blocks of electrically resistive crustal section that tend to intensify ground electric fields. It is seen in Figures 8c and 8d that geoelectric fields are particularly strong on these cratonic areas. On the majority of eastern Australia where the greater Artesian basin is located, there is moderate to low resistivity (depth slices in Figure 3) with smooth variations of electrical structures across these regions. Geoelectric field vectors here tend to be less distorted.

The influence from ocean-land conductivity contrast (coastal effects) are manifested by the distortion of geoelectrical field vectors along the coastal area where directions and amplitudes of geoelectric field vectors are changed with variations of ocean bathymetry and local conductivity structures. Australia is an island continent surrounded by deep Indian Ocean to the west, Southern Ocean to the south, and Coral Sea to the east with shallow seas to the north. It is noted that the Western Craton is adjacent to a linear coastline which drops abruptly to the deep Indian Ocean from the shelf break within only a few hundred meters, whereas the coastline adjacent to east of the continent is much shallower and more varied for hundreds of kilometers to sea, with the adjacent Great Barrier Reef and its associated islands (Milligan, 1988; Whiteway, 2009). The larger block of the resistive Western Craton (less than 0.001 S/m) and the conductive seawater (3.33 S/m) of the deeper Indian Ocean has significant contrast of conductance (product of conductivity and thickness or depth) across the ocean-land boundary, more than anywhere else along the Australian coast lines. AWAGS data (Chamalaun & Barton, 1993) show that the coastal effect is particularly strong along the Western Australian coast areas with the coastal effect detectable up to 500 km inland. Figure 8d shows that the predominant distortion of geoelectric field vectors occurs in the western coast area, and is less distorted in the east coast.

2.2 Network Modeling

The network model used in this study extends the network model detailed in Marshall et al. (2017) to include the entire interconnected power system of the eastern states of Australia. In addition to the lowest- and highest-latitude states of Queensland and Tasmania presented in the previous study, the states of New South Wales, Victoria, and South Australia have been incorporated into this study. Network data have been provided by Transmission Network Service Providers for all states of the NEM with network data additionally provided by the Distribution Network Service Providers for the states of Queensland and Tasmania.

The network model is derived from the network data provided. Connections between substation nodes/buses are obtained using the network nontransformer bus and branch data to find all branches connecting bus nodes. Information location is only available at substation level and each branch is therefore assumed as the straight-line distance between substation bus locations and as having the associated branch resistance. Connections within substations between transformer nodes/buses are incorporated using the network transformer bus and resistance data and transformer models adapted from Mäkinen (1993), Pirjola (2005), and Boteler and Pirjola (2014) for “star” and “auto” configuration transformer windings. Delta windings or ungrounded star connected windings are incorporated into the model by setting the admittance of the relevant transformer winding to zero. For this study, values of earthing resistances are only known for approximately 15% of the transformers with a range of 0.03 to 6.16 Ω. All transformers with unknown earthing resistances are assumed to have the median value of all known earthing resistances within the network, 0.24 Ω.

The straight-line approximation of the NEM network used in this analysis is shown in Figure 9. The substation locations are indicated by the solid black squares with larger open squares indicating those locations with transformer neutral GIC monitors. Transmission line branches are shown as colored lines with different colors representing different operating voltages (yellow = 500 kV, orange = 330 kV, olive green = 275 kV, blue = 220 kV, pink = 132 kV, and red = 110 kV). The method for analyzing the response of the network model of Figure 9 to geoelectric field grids calculated using magnetometer data from locations shown in Figure 1, and the methods described in section 2.1, is detailed in Marshall et al. (2017). This method was applied to the four geomagnetic storms of 17 March 2013, 2 October 2013, 23 June 2015, and 8 September 2017 to compare the modeled GIC calculated using the four different impedance models with the measured GIC at each of the GIC monitoring locations shown in Figures 1 and 9. The results of this analysis are presented in the next section.

3 Results

Figure 10 shows the modeled GIC time series obtained using the four different impedance models described in section 2.1 plotted with the measured GIC for the geomagnetic storm of 2 October 2013. The modeling described in section 2 produces modeled GIC time series for all transformers within the network and the time series data for the relevant transformer locations of Figure 9 are extracted and plotted in Figure 10 as the colored traces. The time series calculated using each of the four different impedance models are color coded analogous to Figure 8: red (UC), green (NU), orange (NW), and blue (3DM) colored lines, respectively. The measured GIC recorded from the monitoring locations are shown as the black traces. The plots are arranged from lowest to highest latitude of the GIC monitoring locations of Figure 9 in order top to bottom, left to right. Analogous plots to Figure 10 for the geomagnetic storms of 23 June 2015 and 8 September 2017 are provided as Figures S1 and S2 in the supporting information. It should be noted that not all GIC monitoring locations were available for all four storms.

Figure 10 (and Figures S1 and S2 of the supporting information) show obvious similarities in modeled GIC magnitude and phase with respect to the measured GIC for each location. A linear regression provides two important measures of model performance, a correlation coefficient, ρ, and an amplitude scaling factor, α, between the modeled and measured GIC. Table 2 gives correlation coefficient, ρ, values for the storms of 17 March 2013, 2 October 2013, 23 June 2015, and 8 September 2017 for each of the four different models. It should be noted that the monitor at George Town in Tasmania was measuring small GIC and hence the signal-to-noise level is relatively low, reducing the correlation for the George Town cases. Table 2 shows some negative values for ρ indicating that those time series are anticorrelated or 180° out of phase when ρ ≈ −1. The modeled time series with ρ approaching −1, such as Murarrie and Middle Ridge, have been inverted for display purposes. The presence of negative correlation could be due to a number of factors and is discussed further in section 4.

Table 2. Correlation Coefficients, ρ, for Modeled Versus Observed GIC From Listed Substations Obtained Using the Four Different Impedance Models UC, NU, NW, and 3DM for Geomagnetic Storms of (a) 17 March 2013, (b) 2 October 2013, (c) 23 June 2015, and (d) 8 September 2017, Respectively

(ρ)	Model	Bowen north	Murarrie	Middle ridge	Bayswater	Bannaby	Para	George Town	Chapel street
(a) 17 March 2013	UC	0.94	−0.55	0.91	NA	NA	0.57	NA	NA
	NU	0.92	−0.49	0.88	NA	NA	0.53	NA	NA
	NW	0.76	−0.8	−0.76	NA	NA	0.43	NA	NA
	3DM	0.86	−0.95	−0.89	NA	NA	0.72	NA	NA
(b) 2 October 2013	UC	0.94	−0.86	0.95	−0.12	−0.5	0.81	NA	0.91
	NU	0.89	−0.78	0.93	−0.28	−0.37	0.79	NA	0.88
	NW	0.92	−0.88	−0.83	0.55	0.24	0.74	NA	0.9
	3DM	0.92	−0.96	−0.94	−0.29	0.63	0.82	NA	0.93
(c) 23 June 2015	UC	0.96	−0.73	0.92	−0.28	−0.45	NA	0.66	0.91
	NU	0.93	−0.65	0.92	−0.32	−0.41	NA	0.57	0.81
	NW	0.87	−0.79	−0.82	0.19	−0.12	NA	0.71	0.82
	3DM	0.91	−0.94	−0.95	−0.34	0.15	NA	0.6	0.91
(d) 8 September 2017	UC	0.92	−0.68	0.93	−0.54	−0.1	NA	0.42	0.95
	NU	0.92	−0.66	0.93	−0.49	−0.12	NA	0.42	0.88
	NW	0.82	−0.77	−0.76	0.02	0.25	NA	0.46	0.87
	3DM	0.89	−0.95	−0.93	−0.61	0.41	NA	0.41	0.91

Another convenient way to visualize the relationships between the observed and modeled data is using a scatterplot. Figure 11 shows scatterplots of measured versus modeled data for each monitor location for the storm of 2 October 2013 for each of the four different models using the color scheme of Figure 10. Table 3 gives scaling factor, α, values for the storms of 17 March 2013, 2 October 2013, 23 June 2015, and 8 September 2017 for each of the four different models. The α values of Table 3 for 2 October 2013 are used to plot the solid lines in Figure 11. As might be anticipated, those values in Table 2 with ρ < 0 have corresponding α < 0, indicating that those time series are out of phase.

Table 3. Linear Regression Scaling Coefficients, α, for Modeled Versus Observed GIC From Listed Substations Obtained Using the Four Different Impedance Models UC, NU, NW, and 3DM for Geomagnetic Storms of (a) 17 March 2013, (b) 2 October 2013, (c) 23 June 2015, and (d) 8 September 2017, Respectively

(α)	Model	Bowen north	Murarrie	Middle ridge	Bayswater	Bannaby	Para	George Town	Chapel street
(a) 17 March 2013	UC	0.39	−0.1	0.3	NA	NA	0.11	NA	NA
	NU	0.46	−0.11	0.35	NA	NA	0.13	NA	NA
	NW	0.27	−0.06	−0.35	NA	NA	0.38	NA	NA
	3DM	1.4	−0.44	−0.45	NA	NA	0.15	NA	NA
(b) 2 October 2013	UC	0.41	−0.16	0.34	−0.07	−0.78	0.18	NA	0.53
	NU	0.41	−0.16	0.41	−0.17	−0.64	0.2	NA	0.67
	NW	0.4	−0.09	−0.41	0.37	0.3	0.72	NA	1.35
	3DM	1.51	−0.43	−0.52	−0.12	1.36	0.17	NA	1.28
(c) 23 June 2015	UC	0.4	−0.21	0.34	−0.29	−1.9	NA	0.75	0.46
	NU	0.42	−0.2	0.38	−0.37	−1.96	NA	0.82	0.49
	NW	0.34	−0.1	−0.38	0.22	−0.38	NA	1.48	1.04
	3DM	1.41	−0.52	−0.51	−0.27	0.69	NA	1.98	1.22
(d) 8 September 2017	UC	0.33	−0.13	0.33	−0.43	−0.24	NA	0.56	0.46
	NU	0.36	−0.15	0.34	−0.44	−0.32	NA	0.69	0.49
	NW	0.26	−0.06	−0.27	0.01	0.61	NA	1.03	0.97
	3DM	1.07	−0.46	−0.43	−0.41	1.36	NA	1.61	1.00

A convenient way to visualize the results in Tables 2 and 3 is shown in Figure 12. For the idealized case, the parameters of Tables 2 and 3 should have a correlation coefficient, ρ, and scale factor, α, of 1.0. Plotting |α| as the abscissa using a log scale, where || indicates magnitude, and 1 − ρ (ρ > 0) and − 1 − ρ (ρ < 0) as the ordinate values with the axes origin at (1,0) should highlight the models performing well as those points clustered around the origin. Figure 12a plots the parameters of Tables 2 and 3 obtained using the four different impedance models and the four storm analysis days in this manner. The points are color coded for the four different impedance models analogous to Figure 11: red (UC), green (NU), orange (NW), and blue (3DM). Although there is considerable scatter, Figure 12a shows more blue points closer to the origin than orange, green, and red points, suggesting that the 3DM impedance model performs better than the other models. The range of ρ > 0.8 and 0.5 < α < 0.2 (model underestimating or overestimating the observations by less than a factor of 2) is suggested as a measure of good model performance and is indicated on Figure 12a by the area enclosed within the dashed region. Within this region, the occurrence for the UC:NU:NW:3DM models is of the ratio 3:3:7:12, suggesting that the 3DM impedance model performs better than the NW 1-D layered model which in turn performs better than the models based on more simplistic conductivity models.

Additional information can be included by identifying the transformer locations to which the modeling and observations correspond. Figure 12b incorporates this information using the following symbols for each of the transformer locations of Figure 9: Bowen North (∆), Murarrie (◊), Middle Ridge (o), Bayswater (+), Bannaby (*), Para (x), Chapel Street (□), and George Town (∇). It should be noted that the same symbol, ●, was used in Figure 12a for all locations so the impact of the different conductivity models could be visualized without the added complication of the location information symbols. The majority of the points in and around the dashed region, represented by the open symbols, for example, ◊, ∆, and □, are for transformer locations within the networks that are the most well known in terms of their electrical parameters, having information for both the transmission and distribution networks. With the exception of George Town, which has a reduced signal-to-noise level, there are relatively fewer points from those locations identified by the open symbols moving outward from the origin, suggesting that the modeling performs better with increased knowledge of the network parameters, as might be expected.

Another parameter for comparing model performance is achieved by comparing residuals of both time series and is given in Torta et al. (2017) as

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0010$ (10)

where o_i, μ_o, m_i, and μ_m are the observed and modeled values and means, respectively, of the N point time series and σ_o is the standard deviation of the observed time series. As discussed in Torta et al. (2017) and Ingham et al. (2017), when the observed and modeled time series are a perfect match, the P value will equal 1; however, it is generally lower than around 0.6 and can extend to negative values. When 0 < P < 1, depending on the relative phase of the time series, the modeled values may underestimate or overestimate the observations. Moreover, P is also ambiguous regarding the relative phase of the time series when −1 < P < 0. Only when P < −1 the modeled values predominantly overestimate the observations regardless of their relative phase (see Appendix A). The P values calculated using equation 10 for all the time series of all four storms are given in Table 4.

Table 4. Model Performance, P, Values for Modeled Versus Observed GIC From Listed Substations Obtained Using the Four Different Impedance Models UC, NU, NW, and 3DM for Geomagnetic Storms of (a) 17 March 2013, (b) 2 October 2013, (c) 23 June 2015, and (d) 8 September 2017, Respectively

(P)	Model	Bowen north	Murarrie	Middle ridge	Bayswater	Bannaby	Para	George Town	Chapel street
(a) 17 March 2013	UC	0.37	−0.11	0.29	NA	NA	0.1	NA	NA
	NU	0.43	−0.13	0.32	NA	NA	0.11	NA	NA
	NW	0.23	−0.06	−0.38	NA	NA	−0.01	NA	NA
	3DM	0.06	−0.44	−0.47	NA	NA	0.14	NA	NA
(b) 2 October 2013	UC	0.39	−0.17	0.33	−0.19	−1.22	0.17	NA	0.47
	NU	0.38	−0.17	0.38	−0.32	−1.3	0.19	NA	0.51
	NW	0.38	−0.09	−0.44	0.16	−0.37	0.29	NA	0.25
	3DM	0.2	−0.43	−0.53	−0.2	−0.74	0.17	NA	0.44
(c) 23 June 2015	UC	0.38	−0.22	0.32	−0.61	−3.78	NA	0.11	0.42
	NU	0.39	−0.22	0.36	−0.74	−4.23	NA	−0.19	0.38
	NW	0.31	−0.1	−0.41	−0.39	−2.38	NA	−0.54	0.26
	3DM	0.24	−0.53	−0.52	−0.47	−3.54	NA	−1.82	0.39
(d) 8 September 2017	UC	0.32	−0.14	0.31	−0.59	−1.79	NA	−0.3	0.44
	NU	0.34	−0.16	0.33	−0.63	−2.02	NA	−0.53	0.42
	NW	0.24	−0.06	−0.29	−0.18	−1.39	NA	−0.97	0.44
	3DM	0.45	−0.46	−0.44	−0.51	−2.08	NA	−2.6	0.55

A convenient way to visualize the P values in Table 4 is shown in Figure 13. For the idealized case, ρ and P values should be primarily located toward the top-right corner of Figure 13a. Although the upper rightmost region of Figure 13a is not dominated by any one color, the upper rightmost point corresponds to the blue color indicating that the 3DM model has the best single performance as measured by this metric. Figure 13b includes the location information analogous to Figure 12b. Figure 13b shows the symbols indicating that the best model performance corresponds primarily to those locations within the network segments that are the most completely known in terms of electrical parameters (indicated as open symbols). Figure 13b also shows a cluster of open symbols in the lower left region with P < 0 that are highly anticorrelated. The influence of highly anticorrelated signals on P values is discussed in Appendix A.

4 Discussion

This paper presents a comparison of GIC measurements from within the power system of the eastern states of Australia with modeled GIC determined using geoelectric fields derived from four different impedance models employing different conductivity structures. The four different geoelectric field models are applied to the same power network model which contains the electrical parameters for over 2,000 buses/nodes, 1,500 transmission lines, and 1,000 HV transformers within the east Australian power system. The network is analyzed using the method developed by Lehtinen and Pirjola (1985). The modeling is performed for four geomagnetic storms of solar cycle 24 and compared with observations from up to eight different locations within the network. A summary of the results and model performance parameters is given in Tables 2-4 and Figures 12 and 13.

Although there are obvious similarities between the modeled and observed GIC shown in Figure 10 and the supporting information, the performance parameters suggest that the modeling does not perform well under all circumstances. The averages of all correlation coefficients, ρ, over all storms and locations (including negative values) for the four different models give values of 0.32, 0.31, 0.12, and 0.05 for the UC, NU, NW, and 3DM impedance models, respectively, suggesting that all models are performing poorly when averaged over all locations and storms. The averages of all correlation coefficient magnitudes, |ρ|, over all storms and locations for the four different models give values of 0.70, 0.67, 0.64, and 0.75 for the UC, NU, NW, and 3DM impedance models, respectively. The averages of all scale factor values, α, over all storms and locations (including negative values) for the four different models give values of 0.06, 0.08, 0.31, and 0.47 for the UC, NU, NW, and 3DM impedance models, respectively, suggesting that the 3DM models perform better than the NW 1-D n-layer model which performs better than the simpler conductivity models. The averages of all scale factor magnitudes, |α|, over all storms and locations for the four different models give values of 0.41, 0.45, 0.47, and 0.83 for the UC, NU, NW, and 3DM impedance models, respectively. The averages of all model performance parameters, P, over all storms and locations for the four different models gives values of −0.19, −0.24, −0.22, and −0.53 for the UC, NU, NW, and 3DM impedance models, respectively, suggesting that all models are performing poorly when averaged over all locations and storms with the UC model performing marginally better on average. The model with the single highest P value is the 3DM model.

Figure 12b suggests that the highest correlation coefficient magnitudes, |ρ|, occur for the locations within the networks where the details of the electrical parameters are more completely known. These locations are within the networks of the states of Queensland and Tasmania. Considering only the results of Tables 2-4 for locations within these states gives average |ρ| values of 0.83, 0.79, 0.80, and 0.87 and average α values of 0.29, 0.33, 0.32, and 0.51 for the UC, NU, NW, and 3DM impedance models, respectively, suggesting that the 3DM model performs better in terms of predicting the amplitude. The average model performance, P, values for the same data set are 0.19, 0.17, −0.07, and −0.35 for the UC, NU, NW, and 3DM impedance models, respectively, suggesting that the UC and NU models are comparable and perform better than the NW and 3DM models when the phase of the signal is considered. The contrast in performance between the metrics is suggested to be due to the anticorrelation between modeled and observed values. The impact of anticorrelation on the performance parameter, P, is considered in detail in Appendix A.

The presence of negative correlation, or anticorrelated modeled and measured values, could be due to the polarity of GIC monitoring devices; however, the GIC monitor polarities have been confirmed as consistent with the model conventions used in this study. The scatterplots of Figure 11 show for Murarrie all four models produce anticorrelated values with the observations while for Middle Ridge the UC and NU model values are correlated while the NW and 3DM models produce anticorrelated values with respect to the observations. Detailed investigation of geoelectric field values, the perfect Earth currents (the J matrix elements of the Lehtinen and Pirjola GIC calculation method), and the resultant modeled GIC values for the bus nodes (the I matrix elements of the Lehtinen and Pirjola GIC calculation method) at Murarrie and Middle Ridge, reveal that the modeled GIC flowing through the transformer neutral to/from ground are typically a small fraction of the perfect Earth currents. For example, for Murarrie the perfect Earth currents for the four different models of UC, NU, NW, and 3DM for one specific time sample are approximately 109, 146, 9, and 180 Amps, respectively. These large differences are due to the large range of geoelectric field amplitudes between the four models being 171, 232, 16, and 279 mV/km, respectively. The corresponding orientations are 265°, 259°, 238°, and 266°. The corresponding modeled GIC flows to ground are approximately 7, 9, 3, and 13 Amps and of opposite polarity to the observations. The significantly reduced amplitudes from the modeled perfect Earth currents is due to the reduction and redistribution of the perfect Earth currents within the network via the ground impedance matrix, Z, and network admittance matrix, Y. This differencing process can result in anticorrelated values when electrical parameters within the model differ from actual values or where values are assumed in situations where actual values are unknown. Under this situation, increased geoelectric field magnitudes will result in larger anticorrelated signals. This trend is exhibited by the values above for Murarrie for the selected time sample. The trend is also reflected in the scatterplot of Figure 11 for Murarrie for all time samples of 2 October 2013 where the scale factor, α, becomes more negative with the increasing geoelectric field magnitudes of the four models at that location. Further, this trend is maintained over all storms and geoelectric field magnitudes and orientations.

The scatterplots of Figure 11 for Middle Ridge show that the UC and NU model values are correlated with the observations while the NW and 3DM produce anticorrelated model values. Analysis for Middle Ridge analogous to Murarrie for the same selected time sample shows that for the four different models the J matrix element values are all of the same sign or polarity for each of the Middle Ridge bus nodes. On application of the (1 + YZ)⁻¹ network matrix in the Lehtinen and Pirjola GIC calculation method, the modeled perfect Earth currents become increasingly anticorrelated with observations (and the UC and NU models) for the NW and 3DM cases which have successively larger geoelectric field amplitudes. Similar to Murarrie, increased geoelectric fields magnitudes result in larger anticorrelated values. Alternatively, the anticorrelation could be due to significant differences in orientation of the geoelectric field vectors; however, for the Middle Ridge area the range of orientation (between 246° and 265° for the same time sample as Murarrie above) is insufficient to produce a 180° phase difference between the UC and NU models (and observations) and the NW and 3DM models. This trend for Middle Ridge is observed for all time samples of 2 October 2013 as shown in the scale factors, α, in Figure 11. Further, the trend for Middle Ridge is maintained over all storms and geoelectric field magnitudes and orientations.

Zhang (2017) shows GIC measurements for 8 September 2017 storm for both Middle Ridge and Murarrie from conventional transducers and nonconventional instrument transformers on the transformer neutral and high-voltage buses, respectively, as part of Powerlink's GIC monitoring. The transformer neutral GIC measurements are highly anticorrelated with GIC flow on the high-voltage bus at both locations. Application of Kirchoff's current law results in highly anticorrelated currents on the low-voltage bus compared to the transformer neutral with different magnitudes to the high-voltage bus. As might be anticipated, these observations confirm that the GIC flow into/out of the transformer ground is the sum of signed GIC into the high- and low-voltage bus nodes, resulting in highly correlated or anticorrelated time series depending on the relative amplitudes. Although the network model used in this paper contains many known electrical parameters, there are a considerable amount of unknown values, particularly with respect to the Earth impedance matrix, Z. It is suggested that variations in assumed or known electrical parameters from actual are resulting in some poor model performance values, P, due to the anticorrelated values as described above. For example, the 3DM model produces some of the highest |ρ| values of all the models; however, the larger geoelectric fields compound differences in the network model from actual, resulting in larger differences from the observations and poorer performance as specified by P. More detailed analysis that includes modeling the GIC flow in the transmission lines into the bus nodes, as detailed in Boteler (2014), and subsequent comparison with GIC monitoring on the high- and/or low-voltage buses (such as shown in Zhang, 2017), is the intended subject of future studies.

The above discussion suggests that the assessment of the four models using the statistical metrics above requires some caution. Ideally, if all network electrical parameters were known precisely, the performance metrics would give a reliable indication of the performance of the different impedance models. Using the average |ρ| as a measure of the models' ability to predict the relative phase of GIC (with respect to both correlated or anticorrelated observations), ranks the model performance in decreasing order as 3DM, UC, NU, and NW. Torta et al. (2017) similarly reported that their 1-D model performed more poorly than the uniform conductivity and 3-D models. Using the average scale factor, α, as a measure of the models' ability to predict GIC magnitude ranks the model performance in decreasing order as 3DM, NW, NU, and UC. Using the average P value as measure of the models' ability to predict both GIC amplitude and phase ranks the model performance in decreasing order of UC, NW, NU, and 3DM; however, the average P values are poor across the four models. It should be noted that the highest individual P value was for the 3DM model. Further, considering the range of ρ > 0.8 and 0.5 < α < 0.2 as a measure of good model performance, the occurrences for the 3DM:NW:NU:UC models are in the approximate ratio of 4:2:1:1. Under this scenario, the best-performing model is the 3DM model. Although the average, ρ, α, and P values are less than optimum (ideally should all equal 1.0), there are some good individual model performances across all models considering the large number of physical and electrical parameters used.

A possible explanation as to the good individual performances across all models may be obtained by examination of Figure 8. Figures 8c and 8d show considerable variation in the magnitude and direction of the geoelectric field over the Australian region, at least an order of magnitude in some locations. However, examination over the region where the grid is primarily located (Figure 9) shows considerably less variability than other regions, that is, Western Australia. In addition, due to the relatively high conductivity of the coastal regions of the eastern states (Figure 3), the ocean-continent boundary contrast is relatively small, leading to a reduced “coastal effect” and a more uniform geoelectric field along the east coast than may otherwise be anticipated. More specifically, examination of 44 sites of a magnetometer array with averaging spacing of about 100 km in northern East Australia shows that the Gulf of Carpentaria to the north (Figure 1) is relatively shallow (it is everywhere less than 70 m deep), and as such is an insufficient electrical conductor to cause a coastal effect (Chamalaun et al., 1999). For the east Australian continent, the conducting ocean waters of the Coral Sea cause weak coastal effects at a distance of 100 km in the sedimentary basin from the Coral Sea and are undetectable at a distance of 500 km from the Coral Sea. In contrast, Western Australia coastal effects are detectable up to 500 km inland (Chamalaun & Barton, 1993).

Another factor contributing is that the coastal effect may be insufficiently modeled on small spatial scales due to the coarse grids of the 3-D model (55 × 55 km) and the sparse spacing (275 km) of the AWAGS sites used to derive the 3-D model. The 50 × 50 km spacing tends to average out 3-D coastal effects on the cells adjacent to oceans, although analysis presented earlier of recently released measured MT tensors from the AusLAMP with those obtained from the 3DM model suggest that the 3DM model is a good approximation for the Australian region. The aim of this study was to compare GIC estimates derived using a realistic 3-D model that accounts for the influence of coastal effects and heterogeneous continental electrical conductivity structures with GIC estimates obtained using half-space or 1-D models that ignore these effects. The impact of updating the current 3DM model by using AusLAMP data (www.ga.gov.au/about/projects/resources/auslamp) with site spacing of 50 km will be the subject of future work when these data become available.

There are a number of areas within this study that could be improved in future studies:

The results presented in Figures 12b and 13b, and the related discussions, suggest that improved knowledge of the grid electrical parameters is an important factor to improve model predictions.
The network of magnetometers in Figure 1 used as input to the geoelectric field calculations is relatively sparse and a denser network should be used in future work if possible.
Alternative interpolation methods, such as the method of Spherical Elementary Current Systems (Amm, 1997; Amm & Viljanen, 1999; Pulkkinen et al., 2003; Wei et al., 2013), should be considered to interpolate the magnetic field at a given location for use in the models, although Torta et al. (2017) noted that Spherical Elementary Current Systems is not necessarily the most adequate method for magnetic field interpolation purposes at middle latitudes during disturbed periods.
As discussed in section 2, the 3-D conductivity model was derived by fitting AWAGS data to a prior model of the Earth's conductivity structure based on geology and previous studies. The impedance tensors of the 3DM model were derived from this 3-D conductivity model. Although the analysis presented in this paper utilizing recently released data from the AusLAMP confirms that the 3DM model compares well with observed MT impedance tensors, the 3DM model should be updated as additional AusLAMP data become available.

5 Conclusion

This paper presents a comparison of measured GIC from within the power system of the eastern states of Australia with modeled GIC determined using geoelectric fields derived from geomagnetic field measurements and four different impedance models that employ different conductivity structures. The four different models are determined from a uniform conductivity model (UC), 1-D n-layered conductivity models (NU and NW), and a 3-D conductivity model of the Australian region from which magnetotelluric tensors are calculated (3DM). The 3DM model impedance tensors are compared with measured MT tensors obtained from recently released data from the AusLAMP and show good agreement for the sample locations. The four different geoelectric field models are applied to a network model that contains the electrical parameters for over 2,000 buses/nodes, 1,500 transmission lines, and 1,000 HV transformers. The modeling is performed for four geomagnetic storms of solar cycle 24 and compared with observations from up to eight different locations within the network. The models are assessed using several statistical performance parameters.

In general, the modeled GIC show reasonably good correlation with observed GIC with the average of all correlation coefficient magnitudes, |ρ|, over all storms and locations for the four different models of 0.70, 0.67, 0.64, and 0.75 for the UC, NU, NW, and 3DM impedance models, respectively, and correlation coefficients >0.9 in some cases. However, the models tend to underestimate the GIC magnitudes as suggested by the averages of all scale factor values, α, over all storms and locations for the four different models having values of 0.06, 0.08, 0.31, and 0.47 for the UC, NU, NW, and 3DM impedance models, respectively, suggesting that the 3DM model performs better than the NW 1-D n-layer model which performs better than the simpler conductivity models. When considering the range of ρ > 0.8 and 0.5 < α < 0.2 as a measure of good model performance, the occurrences within this range for the 3DM:NW:NU:UC models are in the approximate ratio of 4:2:1:1. Under this scenario, the 3DM models perform better than the NW 1-D n-layer model which performs better than the simpler conductivity models. When considering the model performance parameter, P, the highest individual P value was for the 3DM model.

Although the performance of the models in terms of the statistical metrics when averaged over all observing locations and storms is less than optimal, all models exhibit good individual performances for specific storms and observing locations. The relatively similar performance across the models in this regard is suggested to be due to relatively uniform geoelectric fields resulting from the shallow coastal regions of eastern Australia combined with the network being primarily located above intracratonic basins filled with sedimentary rocks that have relatively higher conductivities. This study also suggests that improved model performance occurs for those segments of the power network that are more completely known in terms of their electrical parameters.

Acknowledgments

The authors would like to thank the journal reviewers and editor whose expertise, feedback, and suggestions have helped improve this paper. The authors would like to acknowledge the Australian Energy Market Operator and members of the Power System Security Working Group for supporting this study. The authors would also like to thank Chuanli Zhang of Powerlink and Can Van of Transgrid for providing additional network information and other contributions to this work. The authors would like to acknowledge the national coordinators and co-investigators of the MAGDAS/CPMN project and the Geomagnetism Group of Geoscience Australia for the provision of magnetometer data used in this study. Power network and GIC monitoring data used in this study were provided courtesy of Powerlink, Energex, Ergon Energy, Transgrid, AusNet Services, Electranet, TasNetworks, and AEMO, and are proprietary. Access to this data is at the discretion of the relevant power company and is subject to the relevant company terms and conditions. Requests for this data may be made to the lead author and will be forwarded to the relevant company. Magnetometer data and derived indices used in this study are available from Geoscience Australia's Geomagnetism group (https://www.ga.gov.au/scientific-topics/positioning-navigation/geomagnetism), the International Center for Space Weather Science and Education Kyushu University Japan (https://magdas2.serc.kyushu-u.ac.jp/, Yumoto and the 210MM Magnetic Observation Group, 1996), and the Australian Bureau of Meteorology's World Data Centre (WDC) for Space Weather (https://www.sws.bom.gov.au/World_Data_Centre). Data from the AusLAMP are available at https://dx.doi.org/10.11636/Record.2018.021.

Appendix A

One of the parameters used in this paper for assessing model performance, given in Torta et al. (2017) and equation 10, is

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0011$ (A1)

where o_i, μ_o, m_i, and μ_m are the observed and modeled values and means, respectively, of the N point time series and σ_o is the standard deviation of the observed time series. For the case where (o_i − μ_o) = (m_i – μ_m) for all i, that is, the observed and modeled values are identical, except perhaps for a constant value, equation A1 reduces to P = 1. Note that also when they are identical but out of phase, that is, (o_i − μ_o) = −(m_i – μ_m), equation A1 reduces to P = −1.

Let us assume that the model performs similarly for all observations; that is, it either overestimates or underestimates all observations. Additionally, we also assume that the model is either in phase or out of phase with respect to all observations. Then we may regard it as a rescaled version of the observations, that is, (m_i − μ_m) = α(o_i − μ_o), where α ∈ ℝ is the scale factor, which we consider rather constant across the time series, ∀i ∈ ℕ. Thus, equation A1 can be simplified as follows:

$urn:x-wiley:15427390:media:swe20852:swe20852-math-0012$ (A2)

P(α) is presented in Figure A1.

Considering the phase and the magnitude of the model values with respect to observations, we can distinguish four zones in P(α).

Zone A corresponds to modeled values which are out of phase and overestimate observed values, that is, P(α) < − 1 and α < − 1.
Zone B is where modeled values are out of phase with respect to observations and underestimate them, that is, −1<α < 0, with −1 < P(α) < 0.
Zone C contains modeled values that underestimate observations and which are in phase with them, that is, 0 <α < 1, with 0 < P(α) < 1.
Finally, zone D corresponds to modeled values which overestimate observations and are in phase, that is, α > 1, with P(α) < 1.

Note that, only when P(α) < − 1, it is safe to say that the model overestimates observations, provided |α| > 1. This is due to the fact that equation A1 is ambiguous in regards to the phase between observations and measurements. However, if P < 0, it may correspond to underestimated modeled values out of phase (zone B), or overestimated modeled values (zones A and D). Similarly, when α ∈ (0, 1) ∪ (1, 2), then 1 > P(α) > 0. The only nonambiguous values are P(1) = 1 and P(−1) = − 1, both of which correspond to measurements and observations of the same magnitude mutually in and out of phase, respectively. The above may be generalized to

P(1) = 1, when modeled and observed values are identical and in phase.
P(−1) = − 1, when modeled and observed values are identical and out of phase.
0 < P(α) < 1, when the model is in phase with the observations and the former either underestimates the latter or its values are less than twice the observed values, that is, 0 < α < 1 or 1<α < 2.
−1 < P(α) < 0, when out-of-phase modeled values underestimate the observations, that is, −1 < α < 0, or in-phase modeled values are between 2 to 3 times the values of the observations, that is, 2 < α < 3.
P(α) < − 1, when out-of-phase modeled values overestimate the observations, that is, α < − 1, or in-phase modeled values are larger than 3 times the values of observations, that is, α > 3.

Further, the four generalized zones (A–D) can be identified in Figures 12 and 13. For Figure 12, using the assumption that ±α values correspond to ±ρ correlation values, which holds for all values of Tables 2 and 3, Zone A (α < − 1) is the lower right region, Zone B (−1 < α < 0) is the lower left region, Zone C (0 < α < 1) is the upper left region, and Zone D (α > 1) is the upper right region. For Figure 13, Zone A is the lower left region where P < − 1, Zone B is the lower left region with −1 < P < 0, Zone C is the upper right region, and Zone D is the upper half of Figure 13. Comparison of Figures 12b and 13b illustrates the generalized mapping of these regions and the impact of negative correlation on the P values. Many of the values from the upper half of Figure 12b (Zones C and D) map into the Zone C of Figure 13b. As suggested above this corresponds to modeled values that either overestimate or underestimate the observations and are in phase (positive correlation). Similarly, many of the values from Zone B in Figure 12b map to Zone B of Figure 13b, suggesting that underestimated modeled values that are out of phase will generally result in P < 0. Mapping of Zone A between Figures 12b and 13b suggests that overestimated model values that are out of phase with respect to the observations will exhibit poorer performance as quantified by P < −1. Further comparison of Zones B of Figures 12b and 13b shows that modeled values that are significantly underestimated with respect to the observations and have smaller negative correlation perform better in terms of P than modeled values that are closer in |α| to the observed values and highly anticorrelated. Although the above is somewhat intuitive, it highlights the impact of anticorrelated model values on the performance metric P.

Supporting Information

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Citing Literature

Volume17, Issue5

May 2019

Pages 727-756

Modeling Geomagnetically Induced Currents in Australian Power Networks Using Different Conductivity Models

Abstract

Key Points

1 Introduction