Grey-Box Modelling of District Heating Networks Using Modified LPV Models
The International Energy Agency (IEA) 2023 report highlights that global energy losses have persisted over the years, with 32% of the energy supply lost in 2022 alone. To mitigate this, this research adopts optimisation to enhance the efficiency of district heating networks (DHNs), a key global ener...
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2025-03-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/18/7/1626 |
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| author | Olamilekan E. Tijani Sylvain Serra Patrick Lanusse Rachid Malti Hugo Viot Jean-Michel Reneaume |
| author_facet | Olamilekan E. Tijani Sylvain Serra Patrick Lanusse Rachid Malti Hugo Viot Jean-Michel Reneaume |
| author_sort | Olamilekan E. Tijani |
| collection | DOAJ |
| description | The International Energy Agency (IEA) 2023 report highlights that global energy losses have persisted over the years, with 32% of the energy supply lost in 2022 alone. To mitigate this, this research adopts optimisation to enhance the efficiency of district heating networks (DHNs), a key global energy supply technology. Given the dynamic nature of DHNs and the challenges in predicting disturbances, a dynamic real-time optimisation (DRTO) approach is proposed. However, this research does not implement DRTO; instead, it develops a fast grey-box linear parameter varying (LPV) model for future integration into the DRTO algorithm. A high-fidelity physical model replicating theoretical time delays in pipes serves as a reference for model validation. For a single pipe, the grey-box model achieved a 91.5% fit with an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> value of 0.993 and operated 5 times faster than the reference model. At the DHN scale, it captured 98.64% of the reference model’s dynamics, corresponding to an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> value of 0.9997, while operating 52 times faster. Low-fidelity physical models (LFPMs) were also developed and validated, proving to be more precise and faster than the grey-box models. This research recommends performing dynamic optimisation with both models to determine which better identifies local minima. |
| format | Article |
| id | doaj-art-e10abe2e93a0494d9a97bf82339f6743 |
| institution | OA Journals |
| issn | 1996-1073 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj-art-e10abe2e93a0494d9a97bf82339f67432025-08-20T02:17:00ZengMDPI AGEnergies1996-10732025-03-01187162610.3390/en18071626Grey-Box Modelling of District Heating Networks Using Modified LPV ModelsOlamilekan E. Tijani0Sylvain Serra1Patrick Lanusse2Rachid Malti3Hugo Viot4Jean-Michel Reneaume5LaTEP, Universite de Pau et des Pays de l’Adour, 64075 Pau, FranceLaTEP, Universite de Pau et des Pays de l’Adour, 64075 Pau, FranceUniversite de Bordeaux, CNRS, Bordeaux INP, IMS, UMR 5218, 33400 Talence, FranceUniversite de Bordeaux, CNRS, Bordeaux INP, IMS, UMR 5218, 33400 Talence, FranceNobatek, 67 rue de Mirambeau, 64600 Anglet, FranceLaTEP, Universite de Pau et des Pays de l’Adour, 64075 Pau, FranceThe International Energy Agency (IEA) 2023 report highlights that global energy losses have persisted over the years, with 32% of the energy supply lost in 2022 alone. To mitigate this, this research adopts optimisation to enhance the efficiency of district heating networks (DHNs), a key global energy supply technology. Given the dynamic nature of DHNs and the challenges in predicting disturbances, a dynamic real-time optimisation (DRTO) approach is proposed. However, this research does not implement DRTO; instead, it develops a fast grey-box linear parameter varying (LPV) model for future integration into the DRTO algorithm. A high-fidelity physical model replicating theoretical time delays in pipes serves as a reference for model validation. For a single pipe, the grey-box model achieved a 91.5% fit with an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> value of 0.993 and operated 5 times faster than the reference model. At the DHN scale, it captured 98.64% of the reference model’s dynamics, corresponding to an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> value of 0.9997, while operating 52 times faster. Low-fidelity physical models (LFPMs) were also developed and validated, proving to be more precise and faster than the grey-box models. This research recommends performing dynamic optimisation with both models to determine which better identifies local minima.https://www.mdpi.com/1996-1073/18/7/1626district heating networksgrey boxlinear parameter varyingmodelling and simulation |
| spellingShingle | Olamilekan E. Tijani Sylvain Serra Patrick Lanusse Rachid Malti Hugo Viot Jean-Michel Reneaume Grey-Box Modelling of District Heating Networks Using Modified LPV Models Energies district heating networks grey box linear parameter varying modelling and simulation |
| title | Grey-Box Modelling of District Heating Networks Using Modified LPV Models |
| title_full | Grey-Box Modelling of District Heating Networks Using Modified LPV Models |
| title_fullStr | Grey-Box Modelling of District Heating Networks Using Modified LPV Models |
| title_full_unstemmed | Grey-Box Modelling of District Heating Networks Using Modified LPV Models |
| title_short | Grey-Box Modelling of District Heating Networks Using Modified LPV Models |
| title_sort | grey box modelling of district heating networks using modified lpv models |
| topic | district heating networks grey box linear parameter varying modelling and simulation |
| url | https://www.mdpi.com/1996-1073/18/7/1626 |
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