# Deduction of Optimal Control Strategies for a Sector-Coupled District Energy System

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## Abstract

**:**

## 1. Introduction

## 2. Method for the Deduction of Control Strategies

#### 2.1. Priority Lists Describing Optimal Control Strategies

- ${c}_{e}\left(t\right)$, the cost (in Units per Joule);
- ${\eta}_{e}>0$, the transmission efficiency;
- ${P}_{\mathrm{max},e}\left(t\right)>0$, the maximum power (in Watts).

#### 2.2. Deduction of Optimal Control Strategies: Classification Based on Steering Parameters

## 3. Case Study: CHP Based Heat Supply

#### 3.1. Energy System Design and Linear Optimisation

#### 3.2. Classification for the Deduction of Control Strategies

#### 3.3. Validation and Results

#### 3.3.1. Performance in Terms of Emissions

#### 3.3.2. Performance in Terms of Prices

#### 3.4. Research Boundaries

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Cbc—COIN-OR Branch and Cut |

chp—Combined heat and power |

ENaQ—Energetisches Nachbarschaftsquartier (Energetic Neighbourhood District) |

ghg—Green house gas |

oemof—Open energy modeling framework |

pv—Photovoltaic |

## References

- Klimaschutzplan 2050. 2019. Available online: https://www.bmu.de/ (accessed on 9 September 2021).
- Jakob, M.; Luderer, G.; Steckel, J.; Tavoni, M.; Monjon, S. Time to act now? Assessing the costs of delaying climate measures and benefits of early action. Clim. Chang.
**2012**, 114, 79–99. [Google Scholar] [CrossRef] - Sanderson, B.M.; O’Neill, B.C.; Tebaldi, C. What would it take to achieve the Paris temperature targets? Geophys. Res. Lett.
**2016**, 43, 7133–7142. [Google Scholar] [CrossRef] - van Soest, H.L.; de Boer, H.S.; Roelfsema, M.; den Elzen, M.G.; Admiraal, A.; van Vuuren, D.P.; Hof, A.F.; van den Berg, M.; Harmsen, M.J.; Gernaat, D.E.; et al. Early action on Paris Agreement allows for more time to change energy systems. Clim. Chang.
**2017**, 144, 165–179. [Google Scholar] [CrossRef] [Green Version] - Pajot, C.; Artiges, N.; Delinchant, B.; Rouchier, S.; Wurtz, F.; Maréchal, Y. An Approach to Study District Thermal Flexibility Using Generative Modeling from Existing Data. Energies
**2019**, 12, 3632. [Google Scholar] [CrossRef] [Green Version] - Ma, T.; Wu, Q.; Guo, G.; Fan, Y.; Chen, J. Optimal Energy Flow Calculation of Electricity-heat Integrated Energy System with Heat Pump. In Proceedings of the 2020 IEEE Sustainable Power and Energy Conference (iSPEC), Chengdu, China, 23–25 November 2020; pp. 1159–1165. [Google Scholar] [CrossRef]
- Prognos, Öko-Institut, Wuppertal-Institut. Towards a Climate-Neutral Germany. Executive Summary Conducted for Agora Energiewende, Agora Verkehrswende and Stiftung Klimaneutralität. 2020. Available online: https://www.agora-energiewende.de/en/publications/towards-a-climate-neutral-germany-executive-summary/ (accessed on 9 September 2021).
- Pilpola, S.; Arabzadeh, V.; Mikkola, J.; Lund, P.D. Analyzing National and Local Pathways to Carbon-Neutrality from Technology, Emissions, and Resilience Perspectives—Case of Finland. Energies
**2019**, 12, 949. [Google Scholar] [CrossRef] [Green Version] - Lund, P.D.; Skytte, K.; Bolwig, S.; Bolkesjö, T.F.; Bergaentzlé, C.; Gunkel, P.A.; Kirkerud, J.G.; Klitkou, A.; Koduvere, H.; Gravelsins, A.; et al. Pathway Analysis of a Zero-Emission Transition in the Nordic-Baltic Region. Energies
**2019**, 12, 3337. [Google Scholar] [CrossRef] [Green Version] - Bashir, A.A.; Lund, A.; Pourakbari-Kasmaei, M.; Lehtonen, M. Minimizing Wind Power Curtailment and Carbon Emissions by Power to Heat Sector Coupling—A Stackelberg Game Approach. IEEE Access
**2020**, 8, 211892–211911. [Google Scholar] [CrossRef] - Zhang, M.; Wu, Q.; Wen, J.; Lin, Z.; Fang, F.; Chen, Q. Optimal operation of integrated electricity and heat system: A review of modeling and solution methods. Renew. Sustain. Energy Rev.
**2021**, 135, 110098. [Google Scholar] [CrossRef] - Gandhi, O.; Rodríguez-Gallegos, C.D.; Srinivasan, D. Review of optimization of power dispatch in renewable energy system. In Proceedings of the 2016 IEEE Innovative Smart Grid Technologies—Asia (ISGT-Asia), Melbourne, Australia, 28 November–1 December 2016; pp. 250–257. [Google Scholar] [CrossRef]
- Nottrott, A.; Kleissl, J.; Washom, B. Energy dispatch schedule optimization and cost benefit analysis for grid-connected, photovoltaic-battery storage systems. Renew. Energy
**2013**, 55, 230–240. [Google Scholar] [CrossRef] - Lin, W.; Wu, G.; Wang, X.; Li, K. An Artificial Neural Network Approach to Power Consumption Model Construction for Servers in Cloud Data Centers. IEEE Trans. Sustain. Comput.
**2020**, 5, 329–340. [Google Scholar] [CrossRef] - Lissa, P.; Deane, C.; Schukat, M.; Seri, F.; Keane, M.; Barrett, E. Deep reinforcement learning for home energy management system control. Energy AI
**2021**, 3, 100043. [Google Scholar] [CrossRef] - do Amaral Burghi, A.C.; Hirsch, T.; Pitz-Paal, R. Artificial Learning Dispatch Planning with Probabilistic Forecasts: Using Uncertainties as an Asset. Energies
**2020**, 13, 616. [Google Scholar] [CrossRef] [Green Version] - Roege, P.E.; Collier, Z.A.; Mancillas, J.; McDonagh, J.A.; Linkov, I. Metrics for Energy Resilience. Energy Policy
**2014**, 72, 249–256. [Google Scholar] [CrossRef] - Huang, L.; Walrand, J.; Ramchandran, K. Optimal demand response with energy storage management. In Proceedings of the 2012 IEEE Third International Conference on Smart Grid Communications (SmartGridComm), Tainan, Taiwan, 5–8 November 2012; pp. 61–66. [Google Scholar] [CrossRef] [Green Version]
- Scheller, F.; Bruckner, T. Energy system optimization at the municipal level: An analysis of modeling approaches and challenges. Renew. Sustain. Energy Rev.
**2019**, 105, 444–461. [Google Scholar] [CrossRef] - De Carolis, J.; Daly, H.; Dodds, P.; Keppo, I.; Li, F.; McDowall, W.; Pye, S.; Strachan, N.; Trutnevyte, E.; Usher, W.; et al. Formalizing best practice for energy system optimization modelling. Appl. Energy
**2017**, 194, 184–198. [Google Scholar] [CrossRef] [Green Version] - Pfenninger, S.; Hawkes, A.; Keirstead, J. Energy systems modeling for twenty-first century energy challenges. Renew. Sustain. Energy Rev.
**2014**, 33, 74–86. [Google Scholar] [CrossRef] - Clancey, W.J. Classification Problem Solving; Stanford University: Stanford, CA, USA, 1984. [Google Scholar]
- Hilpert, S.; Kaldemeyer, C.; Krien, U.; Günther, S.; Wingenbach, C.; Plessmann, G. The Open Energy Modelling Framework (Oemof)—A New Approach to Facilitate Open Science in Energy System Modelling. Energy Strategy Rev.
**2018**, 22, 16–25. [Google Scholar] [CrossRef] [Green Version] - Oemof Documentation. Available online: https://oemof.readthedocs.io/en/stable/ (accessed on 9 September 2021).
- Krien, U.; Schönfeldt, P.; Launer, J.; Hilpert, S.; Kaldemeyer, C.; Pleßmann, G. oemof.solph—A model generator for linear and mixed-integer linear optimisation of energy systems. Softw. Impacts
**2020**, 6, 100028. [Google Scholar] [CrossRef] - Schönfeldt, P.; Grimm, A.; Neupane, B.; Torio, H.; Duran, P.; Klement, P.; Hanke, B.; von Maydell, K.; Agert, C. Simultaneous optimisation of temperature and energy in linear energy system models. arXiv
**2020**, arXiv:2012.12664. [Google Scholar] - Schönfeldt, P.; Schmeling, L.; Wehkamp, S. Model Template for Residential Energy Supply Systems (MTRESS). Available online: https://github.com/mtress/mtress (accessed on 9 September 2021).
- Vigerske, S.; Santos, H.G.; Ralphs, T.; Hafer, L.; Kristjansson, B.; Lubin, M.; Saltzman, M. Coin-or/Cbc: Version 2.10.5. Zenodo
**2020**. [Google Scholar] [CrossRef] - CBC User’s Guide. Available online: https://coin-or.github.io/Cbc/ (accessed on 9 September 2021).
- Fazlollahi, S.; Becker, G.; Maréchal, F. Multi-objectives, multi-period optimization of district energy systems: II—Daily thermal storage. Comput. Chem. Eng.
**2014**, 71, 648–662. [Google Scholar] [CrossRef] - Juhrich, K. CO
_{2}-Emissionsfaktoren für fossile Brennstoffe; Technical Report; Umweltbundesamt: Dessau-Roßlau, Germany, 2016. [Google Scholar] - Grimm, A. Deduction of Emissions-, Exergy- and Price-Optimised Control Strategies for a Sector-Coupled District Energy System. 2020. Available online: https://elib.dlr.de/138503/ (accessed on 9 September 2021).
- Wehkamp, S.; Schmeling, L.; Vorspel, L.; Roelcke, F.; Windmeier, K.L. District Energy Systems: Challenges and New Tools for Planning and Evaluation. Energies
**2020**, 13, 2967. [Google Scholar] [CrossRef] - Entsoe—Day-Ahead Prices. Available online: https://transparency.entsoe.eu/transmission-domain/r2/dayAheadPrices/show (accessed on 9 September 2021).
- Reddy, T.A. Applied Data Analysis and Modeling for Energy Engineers and Scientists; Springer: New York, NY, USA, 2011. [Google Scholar]
- Linear and Quadratic Discriminant Analysis—Scikit-Learn 0.23.2 Documentation. Available online: https://scikit-learn.org/stable/modules/lda_qda.html#lda-qda (accessed on 9 September 2021).

**Figure 2.**Obtaining a linear discriminant function and the classification-based priority lists from the class-definition-based priority lists and the steering parameters.

**Figure 3.**Energy system graph with the energy sectors electricity in green, heat in orange, and gas in yellow. The purple dots mark costs considered in the model, see Table 1 for details.

Cost | Emissions [kg/MWh] | Price [EUR/MWh] |
---|---|---|

${c}_{1}$ | 167…797 | 34.07…280.65 |

${c}_{2}$ | 0 | −249.84 |

${c}_{3}$ | 0 | −50.00 |

${c}_{4}$ | 0 | −72.90 |

${c}_{5}$ | 0 | 67.56 |

${c}_{6}$ | 201 | 42.57 |

${c}_{7}$ | 0 | −5.50 |

${c}_{8}$ | 0 | −243.52…3.06 |

${c}_{9}$ | 0 | 27.56 |

Class | pv | chp | Grid |
---|---|---|---|

Class 1 | 1 | 2 | 3 |

Class 2 | 1 | 3 | 2 |

Class 3 | 2 | 1 | 3 |

Class 4 | 3 | 1 | 2 |

Class 5 | 2 | 3 | 1 |

Class 6 | 3 | 2 | 1 |

Case | Condition | Share pv | Share chp | Share Grid | Class |
---|---|---|---|---|---|

A | pv full- and chp part-load | ${\widehat{f}}_{\mathrm{pv}}=1$ | $0<{\widehat{f}}_{\mathrm{chp}}<1$ | ${\widehat{f}}_{\mathrm{g}}<1$ | 1 |

B | pv full-load and chp off | ${\widehat{f}}_{\mathrm{pv}}=1$ | ${\widehat{f}}_{\mathrm{chp}}=0$ | ${\widehat{f}}_{\mathrm{g}}<1$ | 2 |

C | pv part- and chp full-load | $0<{\widehat{f}}_{\mathrm{pv}}<1$ | ${\widehat{f}}_{\mathrm{chp}}=1$ | ${\widehat{f}}_{\mathrm{g}}=0$ | 3 |

D | pv and chp full-load | ${\widehat{f}}_{\mathrm{pv}}=1$ | ${\widehat{f}}_{\mathrm{chp}}=1$ | ${\widehat{f}}_{\mathrm{g}}<1$ | 1 or 3 → 1 |

Observed Hour | pv | chp | Grid |
---|---|---|---|

09–10 | 1 | 2 | 3 |

10–11 | 1 | 2 | 3 |

11–12 | 1 | 2 | 3 |

12–13 | 1 | 3 | 2 |

13–14 | 1 | 3 | 2 |

Linear | Class | Full | Electricity | Top Priority |
---|---|---|---|---|

Optimum | Assignment | Classification | Classification | Classification |

237 | 250 | 253 | 251 | 298 |

( $100.0$%) | ( $105.5$%) | ( $106.8$%) | ( $105.7$%) | ( $125.6$%) |

Linear | Class | Full | Electricity | Top Priority |
---|---|---|---|---|

Optimum | Assignment | Classification | Classification | Classification |

$-68.66$ | $-67.22$ | $-65.23$ | $-60.71$ | $-41.67$ |

( $100.0$%) | ( $97.9$%) | ( $95.0$%) | ( $88.4$%) | ( $60.7$%) |

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**MDPI and ACS Style**

Grimm, A.; Schönfeldt, P.; Torio, H.; Klement, P.; Hanke, B.; von Maydell, K.; Agert, C.
Deduction of Optimal Control Strategies for a Sector-Coupled District Energy System. *Energies* **2021**, *14*, 7257.
https://doi.org/10.3390/en14217257

**AMA Style**

Grimm A, Schönfeldt P, Torio H, Klement P, Hanke B, von Maydell K, Agert C.
Deduction of Optimal Control Strategies for a Sector-Coupled District Energy System. *Energies*. 2021; 14(21):7257.
https://doi.org/10.3390/en14217257

**Chicago/Turabian Style**

Grimm, Adrian, Patrik Schönfeldt, Herena Torio, Peter Klement, Benedikt Hanke, Karsten von Maydell, and Carsten Agert.
2021. "Deduction of Optimal Control Strategies for a Sector-Coupled District Energy System" *Energies* 14, no. 21: 7257.
https://doi.org/10.3390/en14217257