This document presents the development of an improved reluctance model of a three-phase three-limb and five-limb transformer for analyzing the conditions within the transformer during the occurrence of geomagnetically induced currents. Geomagnetically induced currents result from geomagnetic activity in Earth's atmosphere and, in power transformers, cause direct-current magnetization of the ferromagnetic core. This DC magnetization of the ferromagnetic core causes an increased and asymmetric current in the transformer's primary windings, which can lead to circuit breaker tripping and interruption of the electricity supply.
Nowadays, our lives are strongly dependent on the supply of electricity, which is why we aim to thoroughly examine phenomena that can lead to its interruption. To analyze the impact of geomagnetic currents, we therefore develop a hybrid transformer model that combines an equivalent electrical circuit with a magnetic (reluctance) circuit. The development of the model is based on the basic equivalent circuit of a transformer, in which the shunt branch representing the magnetization of the ferromagnetic core is represented by a reluctance circuit. Elements modeling the leakage magnetic flux are also added to the reluctance circuit, since its origin is magnetic in nature. The electrical part of the circuit retains the winding resistance and the induced voltage. Under DC magnetization of the ferromagnetic core, zero-sequence reluctances also strongly affect the conditions in the transformer, since the magnetic flux closes through them, and they are therefore included in the reluctance circuit.
The model is suitable for simulations in the SpiceOpus program, which is freely available and intended for the analysis of electrical circuits. The implementation of the hybrid model provides insight into the electrical and magnetic quantities that affect the conditions in the transformer. In this document, we focus on the current in the primary winding and on the magnetic conditions in the limbs and reluctances. The model is applied to two different transformer core designs, three-limb and five-limb, allowing a comparison between them and thus an assessment of which design is more resistant to the occurrence of geomagnetically induced current.
The simulations showed that the model is suitable, as it describes the transformer sufficiently well and the analysis results are comparable to other results. The model is suitable for both transformer designs, as the primary current waveforms and magnetic flux match expectations. This also confirms our calculations and the incorporation of leakage and zero-sequence reluctance into the circuit. The analysis also showed that the three-limb transformer design is more resistant to the occurrence of geomagnetically induced current, which confirms the theory and the validity of our model.
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