Duality derived topological model of single phase four limb transformers for GIC and DC bias studies

Doctoral Thesis


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University of Cape Town

Geomagnetic disturbances brought about by solar activity cause geo-electric fields in the Earth that drive geomagnetically induced currents through the earthed neutrals of transformers and through power transmission networks. The flow of these currents causes the magnetic cores of transformers to half-wave saturate. Saturated transformers pose problems for power system operators since they can cause harmonics, transformer heating, mal-operation of protection relays, generator heating and vibration, and consume a large reactive power that can cause voltage collapse. Network studies of slow transient phenomena such as transformer half-wave saturation require appropriate models with parameters that represent the transformer transient state aptly. In this thesis a novel duality derived reversible model is developed of a single phase four limb transformer. The test transformers' non-step lap butt type core joints are shown to be problematic and the model is developed further to include the core joints. Due to the irregular core stacking method joint parameter determination is at best an approximation and the model is reduced to a duality compliant equivalent pi model for accuracy reasons. The pi model parameters and saturation characteristics are determined through laboratory testing and a complete pi model is presented. An understanding of a single phase transformer's physical behavior to slow transients is undertaken through the use of appropriately developed test circuits. Search coils are used extensively to understand the transformer core's behaviour through flux mapping of the core and stray flux in the surrounding air space when the transformer saturates. Three phase testing is included using a three phase bank of test transformers. The electrical measurements of waveforms are analysed and fast Fourier transforms carried out to obtain the harmonic components. The effect on a motor load of the distortion caused by transformer half-wave saturation is determined. A novel method of determining the effective core joint area of the problematic non-step lap butt type core joints is developed and a joint utilization factor is proposed that can be used in the absence of transformer manufacturer design information about this joint type in other transformer models.