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A mathematical model of hourly solar radiation with weather variability is proposed based on the simple sky model. The model uses a superposition of trigonometric functions with short and long periods. We investigate the effects of the model variables on the clearness (kD) and the probability of persistence (POPD) indices and also evaluate the proposed model for all of the kD-POPD weather classes. A simple solar organic Rankine cycle (SORC) system with thermal storage is simulated using the actual weather conditions, and then, the results are compared with the simulation results using the proposed model and the simple sky model. The simulation results show that the proposed model provides more accurate system operation characteristics than the simple sky model.