Abstract
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]+[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.
Highlights
Geomagnetic disturbances produce geoelectric fields that drive geomagnetically induced currents (GIC) in power networks
We show how software for GIC calculations using the LP method can be converted to the Lehtinen-Pirjola modified (LPm) method and provide example calculations for the benchmark model introduced by Horton et al (2012), including tables of values at intermediate steps, to help people transitioning their modelling from the LP method to the LPm method
Specific inversion times and memory usage will vary with the programming language used, but it is expected that the general results presented here will apply regardless of the programming language used. 305 7 Conclusions We have presented a new version of the LP method, modified for efficient modelling of GIC in multiple voltage levels of a power system
Summary
Geomagnetic disturbances produce geoelectric fields that drive geomagnetically induced currents (GIC) in power networks. The LP method was designed at a time when mostly only the highest voltage levels of a power network were considered in GIC calculations This was because the transmission lines at the lower voltage levels have higher resistance so will experience smaller GIC values. The main focus of the LP method was the GIC flow to ground through the transformer primary windings, which was the desired output when modelling a single voltage level of a power network. Models for 45 multiple voltage levels require calculation of the nodal voltages which are used to calculate the GIC in the transformer windings (Boteler and Pirjola, 2014). In this paper we show how the LP method can be modified to efficiently model GIC in multiple voltage levels of a power network by converting the LP method to calculate the nodal voltages directly. We show how software for GIC calculations using the LP method can be converted to the LPm method and provide example calculations for the benchmark model introduced by Horton et al (2012), including tables of values at intermediate steps, to help people transitioning their modelling from the LP method to the LPm method
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