The saturation model of the transformer is one of the core tools of multi-physics simulation. By combining it with multi-physics simulation, researchers can more comprehensively evaluate the performance of a transformer in actual applications. Geomagnetically induced currents (GIC) induce DC bias in transformers, leading to core saturation and a host of adverse effects. Traditional transformer models often struggle to accurately capture the behavior of the core under nonlinear saturation conditions. To address these challenges, a saturable transformer unified magnetic-equivalent (UMEC) model that directly takes the B-H magnetization curve to represent a transformer’s core nonlinear characteristics is proposed. The saturable transformer model is based on the model of a magnetic circuit of the transformer core. An estimation method to obtain a transformer’s essential parameters for saturation simulation is presented. GIC effects on transformer saturation are also studied through the proposed saturable transformer and estimation method.