You’ve been with us on a journey from the Sun and its activity, all the way to calculating the electric field across the UK. Along the way, we have explored how charged particles in the solar wind interact with Earth’s magnetic field and how, when combined with the conductivity of the Earth, those interactions induce electric currents.
We are now nearing the end of that journey and arriving at our final challenge: calculating geomagnetically induced currents, or GICs, in the UK power network and assessing the risk they pose to our electrical infrastructure. If you have stayed with us through magnetic field interpolation and electric field calculation, we have some news…those were the easier steps!
Now we must understand exactly what that electric field does to the UK power grid. As you will soon see, it effectively turns our beautifully complex AC power system into one giant, rather messy DC circuit. At this point, we need to think like both engineers and computer scientists. Before we dive in, though, it is worth revisiting why GICs are dangerous in the first place, and why they deserve serious attention.
GIC… just an acronym, or an electrical nightmare?
In power systems, GICs flow along transmission lines and through transformer windings to the ground. When GIC flows through a transformer, it creates an additional magnetic field in the transformer core that interferes with normal operation. This can lead to overheating, the generation of harmonics that cause protective relays to mis-operate, and increased consumption of reactive power that can trigger voltage instability. In extreme cases, these effects result in equipment damage or widespread power outages.
One of the most well-known examples occurred during the extreme solar storm of 1989, often referred to as “the day the Sun brought darkness to Earth”. During this event, a transformer in Quebec suffered damage, shown in Figure 1. Just ninety seconds after Earth’s magnetic field began to fluctuate, the Hydro-Québec power grid collapsed. The result was a nine-hour blackout, leaving thousands of people without electricity or heating.
Figure 1: Damage done to a transformer in Quebec during the 1989 solar storm. Image credit: NASA.
Power systems are becoming increasingly vulnerable to GICs. Modern networks rely on higher-voltage, lower-resistance transmission lines, and they operate under heavier loading, leaving little spare capacity to cope with unusual conditions. GICs are therefore not just a source of temporary inconvenience for customers. They also pose a risk of long-term transformer damage, which is costly and time-consuming to repair or replace.
This is where our work comes in. By modelling GICs in the UK power grid, we can provide engineers with insight into which transformers are likely to be most affected during a geomagnetic storm. With that information, the risk of outages and equipment damage can be reduced. The task is far from simple, however, so we will break it down step by step. First, we need a model of the UK power grid and its voltage connections. Then we can calculate GICs and identify where they are strongest. Time to put our construction hats on and build a simplified UK power grid.
Modelling the UK Power Grid
Step One: Strip the Grid for Parts
The first step is to create a DC model of the system by representing each component using its DC resistance. This requires combining AC power flow models, equipment data, and precise geographical information. To do this, we discard everything that GICs, which are quasi-DC in nature, do not interact with.
What remains is a much shorter list of components we need to model:
- Transformers, specifically those with grounded windings
- Transmission lines
- Substation grounding grids
We explicitly exclude components that block DC, such as generators, which are isolated by step-up transformers, and capacitors. What we are left with is a skeletal version of the UK power grid. From here, we can focus on modelling the components that matter most for GICs.
Step Two: Model the Components that Matter
Transformers: The Unwitting Doormen
Transformers sit at the heart of the GIC problem. They provide the primary path for GIC to flow from high-voltage transmission lines into the Earth. Not all transformers are involved, however. GIC can only flow through grounded windings, as other winding configurations do not provide a conductive path to ground.
For every transformer in the UK power grid with a grounded connection, we model the winding as a simple DC resistance.
Substations: The Exit
Within each substation, all grounded transformers are connected to a common neutral bus. This bus is connected to Earth via the substation ground grid, which provides a stable electrical reference for the entire site. In our model, we represent this ground grid as a single resistance value, Rg.
This grounding resistance is critical. It represents the resistance to remote Earth and must account for all grounding paths, including overhead shield wires. It is the final route through which GIC leaves the power network and returns to the ground.
Transmission Lines: The Real Villains
Here’s the critical part. In our DC model, the transmission lines aren’t just wires. They are the batteries. The geoelectric field, E, which we worked so hard to calculate in earlier posts, is applied along every transmission line in the network. GIC is driven by the geoelectric field integrated along the length of a line, which can be represented as a DC voltage source:
Equation 1: Induced voltage caused by the geoelectric field, E, at the location of the transmission line, and the line segment length, dl, inclusive of direction.
If the geoelectric field is assumed uniform in the geographical area of the transmission line, then only the coordinates of the end points of the line are important, regardless of routing twists and turns. The resulting incremental length vector dl, becomes L. Both E and L can be resolved into their x and y coordinates, and Equation 1 becomes:
Equation 2: The induced voltage assuming an unchanging geoelectric field in the northward and eastward directions, Ex and Ey, in V/km, and the distance of the induced voltage travel, Lx and Ly, in km.
If the geoelectric field is non-uniform, then we have to use Equation 1.
Accurately calculating line lengths is not as simple as drawing straight lines on a flat map. Transmission lines follow the curvature of the Earth. For example, consider a line connecting a substation near Norwich with one in south London, as shown in Figure 2.
Figure 2: Substation location coordinates projected onto a spherical surface.
The north-south distance can be calculated from the difference in latitude. East-west distance is more complicated, as lines of longitude converge towards the poles. To remain consistent with GPS-based substation coordinates, we must account for the fact that the Earth is an oblate ellipsoid, not a perfect sphere. We use the WGS84 Earth model, which underpins modern GPS systems.
In the DC model, each transmission line is represented as a DC voltage source in series with its DC resistance, R.
The Core Theory: Nodal Admittance Analysis
To solve a network as complex as a national power grid, we use the nodal admittance matrix method, also known as the Lehtinen-Pirjola method (Lehtinen-Pirjola et. al 1985). This approach treats the grid as a collection of nodes, representing substations, connected by admittances, which are simply the inverse of resistances.
The governing equation for the entire system is:
Equation 3: Industry-standard “LP” method for calculating GICs.
Let’s break Equation 3 down into its three parts:
- [V] is the Nodal Voltage Vector: A list of the unknown DC voltages at every node (substation) in the model. This is what we must solve.
- [J] is the Nodal Current Vector: A list of the equivalent DC currents being injected into each node. These are the “drivers” of the GIC, which we calculate from the geoelectric field.
- [Y] is the Nodal Admittance Matrix: This is the blueprint of the grid itself. It’s a large, sparse matrix describing all the DC connections (admittances) between the nodes and to ground.
The process is to systematically build the [J] and [Y] matrices from the physical components of the grid. Once they are built, we can solve for the unknown voltages using Equation 4:
Equation 4: Solution to the “LP” method for the final induced voltage.
Once we have the DC voltage at every node, we can use Ohm’s Law to calculate the GIC flowing through any specific component, most importantly, the transformers.
Now we build the matrices.
- Build [Y] (Admittance Matrix): All the DC resistances (R) of the lines, transformer windings, and ground grids are converted to their equivalent admittances (y = 1/R). These values populate the [Y] matrix, defining the grid’s topology.
- Build [J] (Current Vector): The induced DC voltages (V) on each transmission line are converted to equivalent current sources (j = V / R). These values are placed in the [J] vector, representing the “injections” at each node.
- Solve: With [J] and [Y] complete, the system (equation 4) is solved to find the DC voltage at every substation node.
- Calculate GIC: Using these node voltages, we apply Ohm’s Law to find the current flowing through any component. For a transformer, the GIC is the voltage difference across its winding resistance, and most importantly, the current flowing from its neutral through the ground grid resistance (Rg).
GICs in the UK Power Network Model
GICs in the UK high-voltage power grid are calculated using a network topology derived from the Electricity Ten Year Statement (ETYS) 2024. After removing components that are irrelevant to GIC flow, the resulting model contains over 550 substations and approximately 1,500 connections across the 400, 275, and 132 kV networks spanning the UK.
By applying the modelled geoelectric field to this network, we can estimate the magnitude of GIC flowing through each substation during a geomagnetic storm.
At this point, we have stripped the UK power grid down to the components we need and established a method for calculating GICs. The final ingredient is the electric field itself. In our previous blog post, we calculated the geoelectric field using solar wind data and one-dimensional Earth resistivity models across the UK. During the May 2024 “Gannon” storm, the electric field spiked dramatically, marking a one-in-one-hundred-year event with values approaching 1,000 mV/km.
The obvious question is: what level of risk did this pose to the UK power grid?
Our journey does not quite end here. In our fourth and final blog post, we have a surprise in store. We will validate our GIC calculations, illustrate the spatial risk of GICs across the UK, and show how it is possible to forecast GICs in the UK power network using an interactive application that you can control yourself… stay tuned!
