Heat load forecasting using adaptive temporal hierarchies

Hjörleifur G. Bergsteinsson*, Jan Kloppenborg Møller, Peter Nystrup, Ólafur Pétur Pálsson, Daniela Guericke, Henrik Madsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Heat load forecasts are crucial for energy operators in order to optimize the energy production at district heating plants for the coming hours. Furthermore, forecasts of heat load are needed for optimized control of the district heating network since a lower temperature reduces the heat loss, but the required heat supply at the end-users puts a lower limit on the temperature level. Consequently, improving the accuracy of heat load forecasts leads to savings and reduced heat loss by enabling improved control of the network and an optimized production schedule at the plant. This paper proposes the use of temporal hierarchies to enhance the accuracy of heat load forecasts in district heating. Usually, forecasts are only made at the temporal aggregation level that is the most important for the system. However, forecasts for multiple aggregation levels can be reconciled and lead to more accurate forecasts at essentially all aggregation levels. Here it is important that the auto- and cross-covariance between forecast errors at the different aggregation levels are taken into account. This paper suggests a novel framework using temporal hierarchies and adaptive estimation to improve heat load forecast accuracy by optimally combining forecasts from multiple aggregation levels using a reconciliation process. The weights for the reconciliation are computed using an adaptively estimated covariance matrix with a full structure, enabling the process to share time-varying information both within and between aggregation levels. The case study shows that the proposed framework improves the heat load forecast accuracy by 15% compared to commercial state-of-the-art operational forecasts.

Original languageEnglish
Article number116872
JournalApplied Energy
Number of pages13
Publication statusPublished - 15 Jun 2021

Bibliographical note

Funding Information:
This work is funded by Innovation Fund Denmark through the projects Heat 4.0 ( 8090-00046B ), CITIES (1305-00027B), Flexible Energy Denmark ( 8090-00069B ), the IDASC, Denmark ( 18012745 ) project funded by Region H, and the Norwegian FME-ZEN project funded by the ZEN partners and the Research Council of Norway .

Publisher Copyright:
© 2021 The Authors


  • Adaptive estimator
  • Adaptive forecasting
  • Forecast reconciliation
  • Heat load forecast
  • Recursive shrinkage estimator
  • Temporal hierarchies


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