The Lehtinen-Pirjola method modified for efficient modelling of geomagnetically induced currents in multiple voltage levels of a power network

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 [Ze] with the corresponding earthing admittance matrix [Ye] in which the ungrounded nodes have zero admittance to ground. This is combined with the network admittance matrix [Yn] to give a combined matrix ([Yn]g+g[Ye]), 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.