Time-Dependent Storage Loss Rate


I am trying to optimize dispatch of thermal storage (simple hot water tank) where the loss_rate changes with time depending on temperature. Any hints on how I may approach this?

Standing heat losses in thermal storage

Hi @aljubrmj The long defunct deeco framework supported standing heat losses in thermal storage. And would present a reasonable point of reference for new development. Working from the general to the specific.

Equation (26) on page 952 in this publication covers the overarching approach:

As indicated, these ideas were implemented in deeco which supported temperature-characterized heat transport and thermal storage. As Lindenberger et al (2004) indicate:

The non-linear and time-dependent influence of ambient temperatures, flow and return heat transport, and storage-media temperatures on energy conversion efficiencies is taken into account.

Moving to the documentation (in German unfortunately so try the deepl translator for DE→EN):

  • Bruckner, Thomas (2001). Benutzerhandbuch ‘‘deeco’’ — Version 1.0 [User handbook ‘‘deeco’’ — Version 1.0] (in German). Berlin, Germany: Institut für Energietechnik (IET), Technische Universität Berlin. doi:10.5281/zenodo.5148149. 239 pages.

And looking at the SSenH module, namely (page 139):

5.6.1 : Gut durchmischter, temperatur-ungeschichteter Wärmespeicher
5.6.1 : Well-mixed, temperature-unstratified thermal storage

And then to equation (5.31) (page 139) for the heat loss flows:

where kS is the thermal conductivity of the storage tank envelope [WK−2m−2] and the other terms are reasonably self‑explanatory.

The deeco codebase is on GitHub for archival reasons:

  • deeco contributors (28 February 2018). deeco. GitHub. Last compiled 30 September 2005.

You can examine the C++ source if you wish: class SSenH

There were some case‑studies too which I should be able to dig up on request.

One other consideration is that deeco utilized recursive dynamic optimization. If your paradigm is entire horizon optimization, then you will need to think more carefully about implementation in relation to the size of the submitted problem.

By the way, deeco was the first energy system framework to be open licensed back in 2003 and we tried to build an online community too. deeco ran off a UNIX box and devs had to compile archaic C++ on the command line using SSH into a 80 chars × 24 lines terminal. That server is sitting behind me as I type so if you want to want to go down that route, we should be able to arrange something! :smile: HTH, R

Note also these related topics:

The stratified thermal storage in oemof.thermal offers another solution. It assumes that hot and cold temperatures inside the storage are constant while the ambient temperature is fluctuating. When the storage content changes, the boundary between the two sub-volumes moves. As the ambient temperature is not influenced by the modelled energy system, it can be taken as known a-priory. This way, you can have time-dependent loss in a linear energy system model.

Note that a stratified storage has increased losses compared to a fully mixed storage of the same energy content. However, you can always safely assume that the stratified one can actually supply the upper temperature level.

Just a comment. I had guessed that domestic‑level seasonal thermal storage had fallen from favor. But the EnerMaps folk said at a recent seminar that the technology is under active investigation.

By the way, stunning documentation from the oemof project!  R

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