A solid oxide electrolysis cell (SOEC) stack tower formed by piling several stacks is a general approach to scaling up SOEC due to its simplicity and compactness. Enhanced fluid and thermal inhomogeneity are the main factors limiting the stack tower performance when increasing serial cell number and single-cell area. Multiphysics models widely used in stack-level research can accurately simulate stack tower inhomogeneity. However, their complex forms and high computational costs hinder investigating the impacts of various operating and geometrical parameters, such as current density, serial cell number, and single-cell area. To fill the gap, this study proposes a coupled fluid-thermal-electric equivalent circuit model of an SOEC stack tower, which reduces the computational cost by more than three orders of magnitude with an error of less than 0.8% compared with the 3D multiphysics model. With this model, explicit expressions for inhomogeneity indices and corresponding maximum current density are derived, which quantify the relationship between the maximum current density and the size of a stack tower. A 21.7% and a 13.9% reduction in maximum current density are observed when the serial cell number is increased from 30 to 150, and the single-cell area is reduced from 68 cm² to 544 cm², respectively. Moreover, the optimal scale-up path to improve the economy shows that the serial cell number should be preferentially increased when it is lower than 80, after which the single-cell area should be enlarged. However, even if following the optimal path, scaling up the total cell area from 5000 cm² to 25000 cm² reduces the maximum current density from 0.75 A⋅cm^-2 to 0.62 A⋅cm^-2, indicating that the contradiction between the maximum current density and the size of a stack tower is inevitable.