# Design of Renewable and System-Beneficial District Heating Systems Using a Dynamic Emission Factor for Grid-Sourced Electricity

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## Abstract

**:**

## 1. Importance of a Dynamic Emission Factor in Sector-Coupled Energy Systems

_{2}) attributed to one kilowatt-hour electricity from the upstream electricity grid. A constant emission factor means a fixed value regardless of the time, at which electricity is sourced from the grid. A dynamic emission factor implies that individual emission factors are used for each point in time, depending on the upstream power grid.

_{2}emissions, all mentioned models are using a constant emission factor for grid-sourced electricity, or do not explicitly state that a dynamic emission factor is used. Only one article was found, which explicitly mentions that a dynamic emission factor was used as input parameter for grid-sourced electricity [17].

## 2. Introduction of the Applied Optimization Method and Case Study

#### 2.1. General Model Description

#### 2.2. Mathematical Model Description

#### 2.2.1. Objective Function and Global Constraints

#### 2.2.2. Node Constraints

#### 2.3. Case Study

#### 2.3.1. Structure of the Energy System

#### 2.3.2. Emission Scenarios of Grid-Sourced Electricity

#### 2.3.3. Concept and Generation of Local Emission Factor

#### 2.3.4. Parameters of Case Study

_{2}-equivalent of the consumed commodities are provided in Table A5 and explained in detail in Section 2.3.2 and Section 2.3.3 in case of electricity. For the feed-in of electricity in the upstream power system, no emission credits are assumed (see Table A5). The investment costs of the energy converter and storage technologies are based on actual manufacturer data (see Appendix A.1). Both the efficiency and maximum power output of the air-source heat pump results from preceding calculations depending on the outside temperature and district heating supply temperature.

## 3. Results of the Case Study

#### 3.1. Total Costs and Total Emission

#### 3.2. Energy System Design Decisions

#### 3.3. Unit Commitment and System-Beneficial Design

## 4. Discussion of Method and Results

#### 4.1. Parameters and Methodology

#### 4.2. Energy System Design

_{2}emission in the long run, if fossil gas is used.

## 5. Conclusions and Outlook

## 6. Model and Data Availability

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CHP | combined heat and power plant |

CO_{2} | carbon dioxide |

COP | coefficient of performance |

DSO | distribution grid operator |

EF | emission factor |

GSC_{abs} | absolute grid support coefficient |

HP | heat pump |

HV | high voltage |

IEA | International Energy Agency |

LP | linear problem |

MV | medium voltage |

PV | photovoltaic system |

SoC | state of charge |

TSO | transmission system operator |

## Symbols

$\mathsf{\Delta}t$ | time step width |

${\delta}_{n,t}$ | energy loss factor |

${\eta}_{n,i,t}$ | conversion factor of inflow i at time step t |

${\eta}_{n,o,t}$ | conversion factor of outflow o at time step t |

${c}_{(i,o),invest}$ | investment costs of flow $(i,o)$ |

${c}_{(i,o),t}$ | variable costs of flow $(i,o)$ at time step t |

${C}_{invest}$ | total investment costs |

${C}_{total}$ | total costs |

${C}_{var}$ | total variable costs |

$cape{x}_{(i,o)}$ | capital expenditure per installed capacity of flow $(i,o)$ |

${e}_{(i,o),t}$ | energy-specific emission factor of flow $(i,o)$ at time step t |

${E}_{limit}$ | global emission limit |

${E}_{total}$ | total emission |

$fixope{x}_{(i,o)}$ | fixed operation costs of flow $(i,o)$ |

${n}_{(i,o)}$ | technical lifetime of investment flow $(i,o)$ |

${P}_{(i,o),invest,max}$ | maximum investment flow $(i,o)$ |

${P}_{(i,o),invest}$ | investment flow $(i,o)$ |

${P}_{(i,o),t,max}$ | maximum power flow $(i,o)$ at time step t |

${P}_{(i,o),t}$ | power flow $(i,o)$ at time step t |

${W}_{n,t}$ | stored energy of storage n at time step t |

$wacc$ | weighted average cost of capital |

## Appendix A. Parameters of the Case Study

#### Appendix A.1. Technology Parameter Data

Investment | Fixed Operating | Variable Operating | Lifetime | |
---|---|---|---|---|

Costs | Costs | Costs | ||

€/kW | €/(kW · a) | €/kWh | a | |

Gas boiler | 72 | 1.44 | 0 | 20 |

CHP ${}^{1}$ | 1795 | 0 | 0.028 | 10 |

Heat pump air-source ${}^{2}$ | 450 | 4.5 | 0 | 15 |

Heat pump ground-source | 3000 | 6 | 0 | 40 |

Photovoltaic | 1000 | 0 | 0 | 25 |

Thermal | Electrical | Maximum | Maximum | |
---|---|---|---|---|

Efficiency | Efficiency | Full Load Hours | Capacity | |

- | - | h | kW | |

Gas boiler | 0.95 | - | - | 5000 |

CHP ${}^{1}$ | 0.55 | 0.38 | - | 5000 |

Heat pump air-source ${}^{2}$ | time series | - | - | 5000 |

Heat pump ground-source | 2.8 | - | 2500 | 622 |

Photovoltaic system | - | time series | - | 3600 |

Investment | Lifetime | |
---|---|---|

Costs | ||

€/kWh | a | |

Thermal Storage | 20 ${}^{1}$ [37] | 40 |

Electrical Storage | 500 [34] | 10 |

Inflow | Outflow | Discharge | Maximum | |
---|---|---|---|---|

Efficiency | Efficiency | Rate | Capacity | |

- | - | 1/h | kWh | |

Thermal Storage | 1 | 1 | 0.0001 | 84,000 |

Electrical Storage | 0.95 | 0.95 | - | 5000 |

#### Appendix A.2. Commodity Parameter Data

Buy | Sell | |||
---|---|---|---|---|

Variable | Emission | Variable | Emission | |

Costs | Factor | Costs | Factor | |

€/kWh | kg/kWh | €/kWh | kg/kWh | |

Electricity (grid) | 0.17 | emission scenarios | −0.044 | 0 |

Natural Gas | 0.05 | 0.25 | - | - |

#### Appendix A.3. Energy Demand

Peak Load | Annual Energy Demand | |
---|---|---|

kW | MWh | |

Heat demand | 1757 | 5268 |

Electricity demand | 311 | 1104 |

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**Figure 1.**Schematic representation of the district energy system. On the left, the upstream energy system, represented by the gas and electricity grid as sources and sinks. On the right, the heat demand of the district heating system and the electricity demand of the buildings. In the center, the energy hub with the options of energy converter and storage units for supplying the district.

**Figure 3.**Pareto fronts of energy system optimization based on historical data for the emission factor.

**Figure 4.**Pareto fronts of energy system optimization of future renewable scenarios of the emission factor.

**Figure 5.**Investment decisions of emission scenario “local emission factor—2018”. EF: emission factor.

**Figure 6.**Investment decisions of emission scenario “national emission factor—2018”. EF: emission factor.

**Figure 7.**Investment decisions of emission scenario “national emission factor—2030”. EF: emission factor.

**Figure 8.**Investment decisions of emission scenario “national emission factor—2050”. EF: emission factor.

**Figure 9.**Unit commitment of scenario “dynamic local emission factor—2018” at an emission limit of 84.8 g/kWh. SoC: state of charge.

**Figure 10.**Emission factor of heat generation units of emission scenario “local emission factor—2018”. Red dots: operation points. Black box: second and third quartile of operation points. Whiskers: first and fourth quartile of operation points. EF: emission factor. HP: heat pump. CHP: combined heat and power plant.

**Table 1.**Results of key values at an emission limit of 84.8 g/kWh of the scenario “dynamic local emission factor—2018”. EF: emission factor, GSC

_{abs}: absolute grid-support coefficient according to Klein et al. [30].

Total Costs | CAPEX | OPEX | Av. EF | GSC_{abs}(EF) | |
---|---|---|---|---|---|

ct/kWh | ct/kWh | ct/kWh | g/kWh | - | |

Dynamic emission factor | 8.56 | 6.12 | 2.44 | 113.7 | 0.321 |

Constant emission factor | 11.27 | 8.31 | 2.96 | 354.2 | 0.973 |

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## Share and Cite

**MDPI and ACS Style**

Röder, J.; Beier, D.; Meyer, B.; Nettelstroth, J.; Stührmann, T.; Zondervan, E. Design of Renewable and System-Beneficial District Heating Systems Using a Dynamic Emission Factor for Grid-Sourced Electricity. *Energies* **2020**, *13*, 619.
https://doi.org/10.3390/en13030619

**AMA Style**

Röder J, Beier D, Meyer B, Nettelstroth J, Stührmann T, Zondervan E. Design of Renewable and System-Beneficial District Heating Systems Using a Dynamic Emission Factor for Grid-Sourced Electricity. *Energies*. 2020; 13(3):619.
https://doi.org/10.3390/en13030619

**Chicago/Turabian Style**

Röder, Johannes, David Beier, Benedikt Meyer, Joris Nettelstroth, Torben Stührmann, and Edwin Zondervan. 2020. "Design of Renewable and System-Beneficial District Heating Systems Using a Dynamic Emission Factor for Grid-Sourced Electricity" *Energies* 13, no. 3: 619.
https://doi.org/10.3390/en13030619