As most biological species, photosynthetic lifeforms have evolved to function optimally, despite thermal disorder and with fault tolerance. It remains a challenge to understand how this is achieved. To address this challenge, the function of the protein-pigment complex photosystem I (PSI) of the cyanobacterium Synechococcus elongatus is investigated theoretically. The recently obtained high-resolution structure of this complex exhibits an aggregate of 96 chlorophylls that are electronically coupled to function as a light-harvesting antenna complex. This paper constructs an effective Hamiltonian for the chlorophyll aggregate to describe excitation transfer dynamics and spectral properties of PSI. For this purpose, a new kinetic expansion method, the sojourn expansion, is introduced. Our study shows that at room temperature fluctuations of site energies have little effect on the calculated excitation lifetime and quantum yield, which compare favorably with experimental results. The efficiency of the system is found to be robust against "pruning" of individual chlorophylls. An optimality of the arrangement of chlorophylls is identified through the quantum yield in comparison with an ensemble of randomly oriented chlorophylls, though the quantum yield is seen to change only within a narrow interval in such an ensemble.