A numerically efficient mathematical model of a proton exchange membrane fuel cell (PEMFC) stack is presented. The aim of this model is to study the dynamic response of a PEMFC stack subjected to load changes under the restriction of short computing time. This restriction was imposed in order for the model to be applicable for nonlinear model predictive control (NMPC). The dynamic, non-isothermal model is based on mass and energy balance equations, which are reduced to ordinary differential equations in time. The reduced equations are solved for a single cell and the results are upscaled to describe the fuel cell stack. This approach makes our calculations computationally efficient. We study the feasibility of capturing water balance effects with such a reduced model. Mass balance equations for water vapor and liquid water including the phase change as well as a steady-state membrane model accounting for the electro-osmotic drag and diffusion of water through the membrane are included. Based on this approach the model is successfully used to predict critical operating conditions by monitoring the amount of liquid water in the stack and the stack impedance. The model and the overall calculation method are validated using two different load profiles on realistic time scales of up to 30min. The simulation results are used to clarify the measured characteristics of the stack temperature and the stack voltage, which has rarely been done on such long time scales. In addition, a discussion of the influence of flooding and dry-out on the stack voltage is included. The modeling approach proves to be computationally efficient: an operating time of 0.5h is simulated in less than 1s, while still showing sufficient accuracy.