Comparison of methods for modelling geomagnetically induced currents

Abstract

Abstract. Assessing the geomagnetic hazard to power systems requires reliable modelling of the geomagnetically induced currents (GIC) produced in the power network. This paper compares the Nodal Admittance Matrix method with the Lehtinen-Pirjola method and shows them to be mathematically equivalent. GIC calculation using the Nodal Admittance Matrix method involves three steps: (1) using the voltage sources in the lines representing the induced geoelectric field to calculate equivalent current sources and summing these to obtain the nodal current sources, (2) performing the inversion of the admittance matrix and multiplying by the nodal current sources to obtain the nodal voltages, (3) using the nodal voltages to determine the currents in the lines and in the ground connections. In the Lehtinen-Pirjola method, steps 2 and 3 of the Nodal Admittance Matrix calculation are combined into one matrix expression. This involves inversion of a more complicated matrix but yields the currents to ground directly from the nodal current sources. To calculate GIC in multiple voltage levels of a power system, it is necessary to model the connections between voltage levels, not just the transmission lines and ground connections considered in traditional GIC modelling. Where GIC flow to ground through both the high-voltage and low-voltage windings of a transformer, they share a common path through the substation grounding resistance. This has been modelled previously by including non-zero, off-diagonal elements in the earthing impedance matrix of the Lehtinen-Pirjola method. However, this situation is more easily handled in both the Nodal Admittance Matrix method and the Lehtinen-Pirjola method by introducing a node at the neutral point.

Modelling geomagnetically induced currents in midlatitude Central Europe using a thin-sheet approach

“…3. When modelling the DC equivalent of power transformers in the single-phase network admittance matrix, the different galvanic connections from the voltage levels to the ground and between the windings have to be considered (Boteler and Pirjola, 2014). For a step-up transformer, the high-voltage level is connected through the winding resistor to the grounding resistance of the substation.…”

Geomagnetically induced currents in the Irish power network during geomagnetic storms

“…The introduction of a new node at the neutral point in a transformer which connects different voltage levels of a modeled network will account for this flow without adding off‐diagonal elements to the earthing impedance matrix Z , allowing for simple calculation. In this study, the 400 kV substations were treated as wye‐wye transformers using the approach of Boteler and Pirjola []. Although wye‐wye transformers are not usually used to connect different voltage networks, this approach gave good agreement between the predicted and measured GIC levels at the sole Hall effect probe in Ireland.…”

The South Atlantic Anomaly throughout the solar cycle

“…Also important to stress is the hazard due to the unusually high flux of high energy particles in the SAA region, resulting in significant space weather effects in space, such as satellite outages (Heirtzler, 2002) or even on ground, as in communications, induced currents in pipelines and transmission lines (Pulkkinen et al, 2012;Boteler and Pirjola, 2014). High energy protons affect the oscillator of space clocks in the SAA region (Belli et al, 2015;Capdeville et al, 2016).…”