We propose metabolic models for the haptophyte microalgae Tisochyrisis lutea with different possible organic carbon excretion mechanisms. These models - based on the DRUM (Dynamic Reduction of Unbalanced Metabolism) methodology - are calibrated with an experiment of nitrogen starvation under day/night cycles, and then validated with nitrogen-limited chemostat culture under continuous light. We show that models including exopolysaccharide excretion offer a better prediction capability. It also gives an alternative mechanistic interpretation to the Droop model for nitrogen limitation, which can be understood as an accumulation of carbon storage during nitrogen stress, rather than the common belief of a nitrogen pool driving growth. Excretion of organic carbon limits its accumulation, which leads to a maximal C/N ratio (corresponding to the minimum Droop N/C quota). Although others phenomena - including metabolic regulations and dissipation of energy - are possibly at stake, excretion appears as a key component in our metabolic model, that we propose to include in the Droop model.