Toward efficient control of energy systems: an application of proper generalized decomposition to thermal storage

The need of a sustainable use of energy resources is undeniable. This can be achieved only through 1) design of efficient energy systems and 2) optimal control of energy systems during operation. Traditionally, these two tasks are tackled through opposite modelling strategies. Complex and computationally expensive models (CFD, finite elements, etc.) are used for designing purposes; simplified inexpensive models (black box models, transfer functions, etc.) are employed for control purposes. In this paper we consider and alternative approach called Proper Generalized Decomposition (PGD) that combines the accuracy of CFD with the "lightness" of black box models. A thermocline thermal energy storage (TES) system is considered in the present analysis to show the attractive features of PGD. An accurate, but at the same time computationally inexpensive model is developed considering a solution in a separate form (i.e. a PGD solution) of the energy equation that describes the evolution of the TES temperature both in time and space. More thrillingly, we show how to include a priori in the solution the effect of design/operational parameters by finding once for all a generalized solution which, beside space and time, contains the parameters as further "dimensions". To summarize, this work presents a novel approach to energy systems modelling which combines both accuracy, computational efficiency, and flexibility. These features make PGD an attractive methodology which is worth of further use in the field of energy systems design and control.