Because of the capability of large capacity thermal storage and extended operation during night and cloudy days, concentrated solar thermal power generation is getting more and more attention in the recent years. Dual-media thermal energy storage system is typically adopted in industry for reducing the use of the heat transfer fluid, which is usually expensive. In such a dual-media system, the solid filler material can be a phase change material relying on latent heat or a regular solid material using sensible heat for energy storage. Two strategies of startingup fluid charge and discharge are considered for the operation of a concentrated solar thermal power plant incorporated with a dual-media thermal storage system. These two strategies include: 1) starting daily cyclic charge and discharge operation with an initially cold tank; 2) to fully charge the thermal storage system before operation of the cyclic discharge/charge for the power plant. The energy storage efficiency and the effects to the power plant operation due to the application of these two strategies are studied in the current work based on an enthalpy-based 1-D model, and significant difference is found in starting-up process of the daily cyclic operations, which will help us decide the best strategy of operating a thermal energy storage system with more electrical energy output.