Ensemble estimation and analysis of network parameters: strengthening the GIC modelling chain

Master Thesis


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University of Cape Town

Ensemble Estimation and Analysis of Network Parameters - Strengthening the GIC Modelling Chain - Abstract Large grounded conducting networks on Earth's surface have long been known to be affected by solar activity and geomagnetic storms. Geomagnetically induced currents (GICs) in these quasiantennas are just one of the effects. In modern times, society has become more and more dependent on electrical power and, as a result, power networks. These power networks form extensive grounded conductors and are susceptible to GICs, even at mid-latitude regions. Given a large enough event now, such as the Carrington event of 1859, the direct and knock-on results can be devastating. Such an event is more than just a possibility, it is just a matter of time. With this in mind, the study of the effects of GICs and the modelling of them has become essential to ensure the future security of society in general. GIC modelling makes the assumption that the resultant GIC at a specific node in a power network is assumed to be linearly related to the horizontal vector components of the geoelectric field, which is induced by a plane-wave geomagnetic field. The linear GIC and geoelectric field relation is linked by a pair of network parameters, a and b. These parameters are not easily measurable explicitly but may be estimated empirically. Furthermore, these parameters are traditionally only seen to include network information and remain constant given a stable network. In this work, a new empirical approach to derive estimates for a and b is presented where the linear relation is solved simultaneously for all possible pair of time instances. Given a geomagnetic storm time-series (length n) of simultaneous GIC and geoelectric field data to solve for a and b, taking all possible time instance pairs yields approximately N²/2 estimates for a and b. The resulting ensembles of parameter estimates are analysed and found to be approximately Cauchy-distributed. Each individual estimate resulting from a single pair of time instances being solved is not the true state of the system, but a possible state. Taking the ensemble as a whole though gives the most probable parameter estimate, which in the case of a Cauchy distribution is the median. These ensemble parameter estimates are used in the engineering link of the modelling chain, but the ensembles themselves allow further analysis into the nature of GICs. An improvement is seen when comparing the performance of the ensemble estimates applied to an out-of-sample dataset during the Halloween Storm of 2003 with previous GIC modelling in the South African power network using the same dataset. Analysis of the ensembles has verified certain ground assumptions (specifically the plane-wave assumption and network directionality) made as a first-order approximation in GIC modelling and has also shown that errors from these assumptions are absorbed into empirically derived network parameters. Using a range of estimates from the ensemble, a GIC prediction band is produced. This in itself corresponds to an error estimate in the prediction. For the first time, it has been explicitly shown that empirically derived network parameters show a correlation to the magnitude of the produced GIC. This behaviour is then used to refine the parameter estimation further and allow for real time dynamic network parameter estimation that further improves modelling.