Modelling geomagnetically induced currents produced by realistic and uniform electric fields

The methods used to model geomagnetically induced currents (GIC) depend on the nature of the electric field used as input. A uniform electric field, often used to simplify the modelling, is shown to have different properties from realistic non-uniform fields. Realistic fields which go to zero at infinity can be uniquely represented by the sum of the gradient of a scalar potential and the curl of a vector function. The scalar potential term is conservative and irrotational, while the vector term is non-conservative and solenoidal. In contrast, a uniform electric field can be represented simply by the gradient of a scalar potential. These different mathematical properties mean that modelling techniques derived for uniform fields may not work for realistic fields. This is examined using, as an example, the modelling of GIC produced in a conducting network at the surface of the Earth. It is shown that uniform electric fields can be represented by voltage sources in the transmission lines or at system ground points. However, realistic electric fields, such as those produced by the auroral electrojet, cannot be represented by voltage sources at ground points and have to be represented by a voltage source in the transmission lines.