The ACUREX collector field together with a thermal storage tank and a power conversion system forms the Small Solar Power Systems plant of the Plataforma Solar de Almería, a facility that has been used for research for the last 25 years. A simulator of the collector field produced by the last author has been available to and used as a test-bed for control strategies. Up to now, however, there is not a model for the whole plant. Such model is needed for hierarchical control schemes also proposed by the authors. In this paper a model of the thermal storage tank is derived using the Simultaneous Perturbation Stochastic Approximation technique to adjust the parameters of a serial grey-box model structure. The benefits of the proposed approach are discussed in the context of the intended use, requiring a model capable of simulating the behavior of the storage tank with low computational load and low error over medium to large horizons. The model is tested against real data in a variety of situations showing its performance in terms of simulation error in the temperature profile and in the usable energy stored in the tank. The results obtained demonstrate the viability of the proposed approach.