This paper deals with the analysis of a Microalgae Anaerobic Digestion model (MAD model), to study the influence of the ammonia on the fermentation of such protein- rich substrate. Using the operating diagram of the model, we show the key role of the operating parameters: Dilution rate (D) and the nitrogen input concentration (Nin), on the process performances. To investigate the ammonia toxicity phenomenon and its subsequent impact, we focus on the variation Free ammoniacal Nitrogen (FAN) concentration and the biogas yield with respect to the changes of D and Nin. Numerical simulations provide the FAN critical concentration leading to bacteria inhibition as well as the ideal values of the control parameters allowing to maximize biogas production, on the one hand, and to avoid any process failure, on the other hand. Our study highlights the effectiveness of the modeling to detect ammonia inhibition risk, that can then be used for control and optimization purposes of such anaerobic digestion process.