A solar dynamic (SD) power system composed of a concentrating solar collector and an irreversible Brayton cycle system is set lip, where the heat losses of the collector are dominated by the radiation, the heat transfer between the collector and the Brayton cycle system obeys Newton's law, and the heat transfer between the Brayton cycle system and the ambient obeys the radiant heat transfer law. The cycle model is used to investigate synthetically the influence of the radiant heat losses of the collector the finite-rate heat transfer and the irreversible adiabatic processes in the Brayton cycle system on the performance of a space SD power Brayton system. The overall efficiency of the system and the other performance parameters are optimized. The optimal values of the important parameters and their corresponding upper or lower bounds are determined. Finally, the optimal performance of an endoreversible SD power Carnot system is simply derived.