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Geomagnetically induced currents (GICs) can cause saturation of the magnetic circuit of transformers in a power system. This saturation can increase the MVAr absorption of the transformers, leading to voltage-control problems, generating significant harmonic currents, and cause heating of the internal components of the transformer itself, leading to gas relay alarm/operation as well as possible damage. This paper sets out the methods used to examine these effects using a mathematical model explicitly incorporating the electric and magnetic circuits, including the shunting effect of the tank to predict the current and flux waveforms. The model has been used to predict GIC effects for a variety of winding connections for single-, three-, and five-limb core-type transformers connected to the National Grid Company plc transmission system in England and Wales. The size and form of the return limbs along with the tank shunting effect determine the magnitude and the often complex shape of the waveforms resulting from GIC. Field and factory DC injection tests on various types of transformers have been conducted to validate the model and gain an insight into the magnetic behavior of transformers. With the aid of finite-element analysis (FEA) techniques and a consideration of the various constructional arrangements of the core and coils in the tank, it is possible to evaluate the power losses and accompanying temperature rises of the core, structural components, windings, and tank. Some guidance on the acceptable GIC current levels for various transformer types is given.