Solar organic Rankine cycle (SORC) is a promising approach for solar energy utilization under low and moderate temperatures due to low investment and small-to-medium scale. The stable output of the SORC system under variable solar irradiation conditions is necessary to weaken the impact on the power grid and provide a base load. A novel operating mode was designed to obtain the stable output of 1 MWe for a SORC system operated under variable solar irradiation for 1 day. The parabolic trough collector was selected for solar heat reception, and a two-tank direct thermal storage unit was used for heat storage. Given the variations in solar irradiation, the mass flow rate of the heat transfer fluid (HTF) in the solar collectors was adjusted to guarantee a constant HTF inlet temperature for the ORC unit, and the mass flow rate of the HTF from the hot tank to the ORC unit was kept constant. Thus, the SORC system could operate under stable conditions. Four organic working fluids and two cycle types were subjected to thermodynamic analysis and parametric optimization. Results show that as the HTF inlet temperature increases, the optimal efficiency of system with non-recuperative cycle and toluene increases, whereas those of systems with non-recuperative cycles and cyclohexane, hexamethyldisiloxane, and pentane as working fluids first increase and then remain constant. The increment in the superheat degree increases the efficiency of the system with recuperation. By contrast, the system with non-recuperation demonstrates the maximum system efficiency in the absence of or at a low superheat degree. The maximum system efficiency reaches 17.9%. The system efficiency of this novel operating mode is 4.2% higher than that of an unstable output operating mode when operated for 1 day.