Efficient temperature estimation for thermally stratified storage tanks with buoyancy and mixing effects

Estimating the state thermal storage devices is key to use them efficiently to reduce the uncertainty of renewable sources. Although stratified storage tanks are one of the most efficient and cost-effective storage systems, they lack accurate state estimation methods. In this paper, we propose a general methodology for estimating the state of thermally stratified storage tanks of different topologies and capacity. The method is based on a simple moving horizon estimation technique and a 1-D smooth model that can integrate buoyancy effects into a smooth equation. The novelty of the proposed approach is that it is the first state estimation approach that considers both buoyancy and mixing effects. This distinction is paramount to an adequate estimation of the temperature distribution in the storage tank which can then be used for different aims, namely as a basis for model predictive controls. Besides the novel state estimation approach, the paper has three more contributions: (i) it shows how a model for seasonal storage devices can be further extended to smaller stratified tanks with different topologies; (ii) it modifies such a model so that the model equations can be integrated into a single dynamical equation; (iii) it proposes the most complete case study to date for modeling and estimating temperature distribution inside small stratified storage tanks. The analysis of the proposed approach is done in several stages. First, to validate the applicability of the model to small tanks and multiple topologies, we perform a model identification and parameter estimation for three different stratified tanks. Second, we test the accuracy of the proposed state estimation approach in those three stratified tanks employing the estimated parameters in the first experimental study and the models also previously defined. Finally, to further validate the models, we perform a simulation for each of the three tanks and we compare the accuracy of the simulation against real data. As we show, both the state estimation approach and the model are satisfactorily accurate as they display average mean errors below 2 °C.