Thermocline thermal storage modeling towards its predictive optimal management

Co-optimization of a high temperature thermal storage as per its modeling accuracy

“…In this formulation, the algebraic solution for thermocline HTTES is given as polynomial function, and allowing for any initial temperature profile to predict the storage temperature evolution. [8] suggested a metamodel based on data issued from 1D -PDE model simulations, representing a suitable trade-off between accuracy and computation time. In case of manufacturing defects or highly dimension-dependent phenomena like flow channeling, this metamodel can be constructed on data issued from experimental measures.…”

“…Here, the storage energy state and losses evolution in function of the power command are required for the controller to design and manage the system. This section will be dedicated for describing two 0D models, a 1D based on PDE model as well as a 1D metamodel as explained in [8], whereas 2D models are out of the scope of this work.…”

“…This subsection presents the metamodeling approach, based on a 1D -PDE model simulations, that has been developed in [8]. Depending on the initial storage temperature 𝑇 𝑡 (𝑥) and the power command 𝑃 𝑠𝑡𝑜 , it is possible to calculate the evolution of the storage temperature 𝑇 𝑡+𝛥𝑡 (𝑥) after a fixed period of time 𝛥𝑡.…”

“…2 illustrated the main calculation steps in the metamodel. 1D -MM showed a trade-off between accuracy and computation time as discussed in [8], thanks to the pre-built matrix that avoids solving PDE in the simulation stage. Therefore, it seems adequate to use 1D -MM inside a predictive controller, which will be the subject of next sections in this work.…”

“…TES technologies are multiple and can be categorized based on their temperature, physical principle, geometry, storage medium (HSM) and heat transfer fluid (HTF) as discussed in [7]. Here, a sensible thermocline high temperature thermal energy storage (HTTES), using air as HTF and rocks as HSM, will be studied [8]. This technology has proven to be cost effective and recently undergone numerous developments as shown in [9][10][11].…”