A Triode Solid Oxide Fuel Cell is a novel cell architecture that consists of two circuits: an auxiliary circuit, operated in electrolysis mode, and a conventional main fuel cell circuit. During triode operation, performance enhancement can be expected especially when a significant electrode overpotential is present. A two-dimensional stationary isothermal model is implemented in a commercial software, COMSOL Multiphysics. The model, able to predict conventional and triode operation, gives guidelines for the electrodes geometry design that needs to be adopted in order to favor the expected improvements. The interaction between the main and auxiliary circuits is then discussed in terms of equipotential and current lines in a cross section of the cell for two different geometries: anode and electrolyte supported cells. The improvements achievable in triode operation are also calculated in terms of electric current surplus that is possible to obtain in the fuel cell circuit.