A transient mathematical model for managing microalgae derived hydrogen production as a source of renewable energy is developed for large scale compact photobioreactors (PBR). The model allows for the determination of microalgae and hydrogen mass fractions produced by the photobioreactor with respect to time. A Michaelis-Menten type expression is proposed for modeling the rate of hydrogen production, which introduces a mathematical expression to calculate the resulting effect on H2 production rate after genetically modifying the microalgae species. The so called indirect biophotolysis process was used. Therefore, a singular opportunity was identified to optimize the aerobic to anaerobic stages time ratio of the cycle for maximum H2 production rate, i.e., the process rhythm. A coarse mesh was used (6048 volume elements) to obtain converged results for a large compact PBR computational domain (5m x 2m x 8m). The largest computational time required for obtaining results was 560 s. Experiments were conducted in the laboratory for the wild species microalgae to assess H2 production model numerical results, which are in good qualitative agreement with the measured data. Then, with the experimentally validated model, a system thermodynamic optimization was conducted through the complete model equations to find accurately the optimal system operating rhythm for maximum hydrogen production rate, and how wild and genetically modified species compare to each other. The maxima found are sharp, showing up to a ~60% variation in hydrogen production rate for the optimal anaerobic stage time ± 1 day, which highlights the importance of system operation in optimal rhythm. Therefore, the model is expected to be useful to investigate microalgae growth biophysics aiming at biofuels, food, pharmaceuticals and other high valued bioproducts, and also for design, control and optimization of hydrogen large scale production as a source of renewable energy.