A nonlinear, lumped-parameter mathematical model of direct reforming carbonate fuel cell stack is extended by deriving an explicit set of differential equations for computer simulation. The equilibrium assumption used for the water-gas shift reaction results in an implicit equation set, previously solved using numerical techniques. An explicit equation set is derived by eliminating a key variable associated with the water-gas shift reaction. In addition, results are improved by incorporating a fuel cell performance model to account for reversible cell potential and polarization losses. This requires determination of intermediate gas composition at the cell anode inlet, resulting in additional computations. All results and physical data used are specific to a lumped 16-stack 2-MW system design, a precursor to a demonstration plant that had been operated at the City of Santa Clara, CA. Steady state results are validated for several load points over the upper region of operation and transient results are provided for sudden load change.