Solar thermal plants operate in a highly variable environment, with variations in both the energy source and the heat demand. Moreover, weather and load forecasts contain uncertainty. Thermal energy storage helps to decouple the heat production from the heat supply and gives the solar thermal plant more flexibility while complexifying its operation. In this work, a Dynamic Real-Time Optimization (DRTO) methodology is presented. Firstly, a planning phase determines the best storage management policy, given the estimated weather and load forecasts. An economic DRTO algorithm is then used to update the optimal trajectories to minimize the operating costs of the plant while respecting the storage management policy determined at the planning level, despite disturbances in the weather conditions. This stage uses updated forecasts and real-time information to update the optimal trajectories. This methodology is tested on a "virtual solar plant" (a detailed dynamic model of an existing plant) in a case study, with real data for the weather forecasts and measurements and a variable heat demand. Results obtained without and with DRTO adjustment are compared. In the first case, the virtual plant is operated using trajectories computed with offline dynamic optimization (DO) at the planning phase and undergoing the real-time weather and load conditions, while in the second case, real-time modification of the operating trajectories is performed. We observe an improvement in the solar fraction used to satisfy the heat demand and a reduction in the operating costs with DRTO compared to DO, without degrading the storage management significantly. The results are promising for an application to an existing plant.