Modelling Grid Constraints in a Multi-Energy Municipal Energy System Using Cumulative Exergy Consumption Minimisation
Abstract
:1. Introduction
2. State of Research and Research Objective
2.1. Cumulative Exergy Consumption
2.2. Multi-Energy-Systems
2.3. Load Flow Calculations
2.4. Research Objective and Paper Outline
- System design: How can the optimum capacity of storages and conversion units be determined?
- System operation: How can such a system be operated while always meeting the demand?
- What is the impact of maximum grid capacities on installed RES, storage and conversion unit capacities and their operation?
- What is the impact of different load flow representations (network flow vs. power flow)?
- What influence do the spatially unevenly distributed RE potentials have? High potentials typically exist in thinly populated rural regions, low potentials in densely populated cities.
3. Methodology
3.1. Formulation of the Optimisation Problem
3.2. Cumulative Exergy Consumption Minimisation
3.3. Energy System Components
3.3.1. Energy Imports, Loads and Excess Energy
3.3.2. RES
3.3.3. Conversion Units
3.3.4. Storages
3.3.5. Energy Transmission
3.3.6. Busses
4. Case Study
4.1. System Description
4.2. Results
5. Discussion and Conclusions
5.1. Model Discussion and Comparison
5.2. Conclusion and Outlook
Author Contributions
Funding
Conflicts of Interest
Abbreviations
AC | alternating current |
CExC | cumulative exergy consumption |
CHP | combined heat and power |
DC | direct current |
EU | European Union |
HP | heat pump |
MES | multi energy system |
MILP | mixed integer linear programming |
NF | network flow |
OECD | Organisation for Economic Co-operation and Development |
OPF | optimal power flow |
PF | power flow |
RES | renewable energy sources |
TES | thermal energy storage |
Nomenclature
cross section | exergy factor | ||
CExC-yield | CExC-factor | ||
CExC-expenditures | equivalent periodic CExC-factor | ||
storage capacity | state of energy | ||
diameter | time period | ||
specific energy | time series | ||
length | reactance | ||
mass | density | ||
power | efficiency | ||
pressure | voltage angle | ||
resistance | friction factor | ||
Reynolds number | time step |
Appendix A. Linearisation of the Heat and Gas Flows and Pressure Losses
Heat Pipe | Gas Pipe | |
---|---|---|
Diameter | 350 mm | 300 mm |
Length | 1000 m | 1000 m |
Temperature difference Supply/return | 50 °C | |
Gross calorific value | 11 kWh/Nm3 | |
Pipe roughness | 1 mm | 0.3 mm |
Max. power | 50 MW | 163 MW |
Natural Gas | District Heat | ||
---|---|---|---|
1 | 0.0 | 0.000 | 0.000 |
2 | 0.2 | 0.062 | 0.040 |
3 | 0.4 | 0.158 | 0.160 |
4 | 0.6 | 0.358 | 0.360 |
5 | 0.8 | 0.637 | 0.640 |
6 | 1.0 | 1.000 | 1.000 |
Appendix B. Component Properties and Equivalent Periodic CExC-Factors
Technology | Inflow Efficiency | Outflow Efficiency | Capacity Loss | Equivalent Periodic CExC-Factor |
---|---|---|---|---|
- | - | |||
Battery | ||||
TES | ||||
H2-Storage |
Type | Efficiency | Equivalent Periodic CExC-Factor |
---|---|---|
- | ||
Biomass boiler | ||
Gas boiler | ||
Heat pump | ||
PEM electrolyser | ||
PEM fuel cell | ||
Resistance heater | ||
Biomass CHP | ||
Gas CHP |
Type | CExC-Factor | Equivalent Periodic CExC-Factor |
---|---|---|
PV | ||
Wind |
Appendix C. PF Equations, Multi-Cell Models and Result Quality
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Electricity | Natural Gas | Waste Heat | Biomass | |
---|---|---|---|---|
CExC-factor in | 2.0 | 1.21 | 0.21 | 1.1 |
Electricity | Natural Gas | Heat | ||
---|---|---|---|---|
CI-Slack | Max. cap. | 600 MW | 1000 MW | 20 MW |
CI-CC | Max. cap. | 36 MW | 163 MW | 30 MW |
Efficiency | 99.9% | 99.9% | 85% | |
CI-CS | Max. cap. | 36 MW | 141 MW | 30 MW |
Efficiency | 99.9% | 99.9% | 85% | |
CC-CS | Max. cap. | 36 MW | 100 MW | |
Efficiency | 99.9% | 99.9% | ||
CI-CR | Max. cap. | 36 MW | ||
Efficiency | 99.9% |
CI-CC | 2.5 | 0.0729 | 40.5 | 119.1 |
CI-CS | 5.0 | 0.0729 | 40.5 | 119.1 |
CC-CS | 7.5 | 0.0729 | 40.5 | |
CI-CR | 10.0 | 0.0729 |
Cell | Electricity | Domestic Heat | Process Heat | PV | Wind | ||
---|---|---|---|---|---|---|---|
CC | Ann. Demand | GWh | 137.5 | 405.0 | 31.8 | ||
Max. Power | MW | 26.1 | 162.2 | 62.5 | |||
CS | Ann. Demand | GWh | 110.0 | 315.0 | 65.5 | ||
Max. Power | MW | 20.9 | 140.4 | 50 | |||
CI | Ann. Demand | GWh | 220.0 | 72.0 | 130.9 | ||
Max. Power | MW | 52.8 | 22.1 | 100 | |||
CR | Ann. Demand | GWh | 82.5 | 180.0 | 49.1 | 697.1 | |
Max. Power | MW | 17.6 | 92.5 | 37.5 | 330 |
CI | CC | CS | CR | Total | Gap | ||
---|---|---|---|---|---|---|---|
MW | MW | MW | MW | MW | MW | ||
Gas boiler PH | NF | 22.1 | 22.1 | 0.0 | |||
PF | 22.1 | 22.1 | |||||
Resistance heater PH | NF | 20.8 | 20.8 | 0.0 | |||
PF | 20.8 | 20.8 | |||||
Heat pump | NF | 163.0 | 145.4 | 240.2 | 548.6 | +1.8 | |
PF | 138.8 | 171.6 | 240.0 | 550.4 | |||
Biomass CHP | NF | 7.1 | 7.1 | +3.9 | |||
PF | 11.0 | 11.0 | |||||
Fuel Cell | NF | 20.0 | 20.0 | 0.0 | |||
PF | 20.0 | 20.0 | |||||
Electrolyser | NF | 66.3 | 66.3 | −0.2 | |||
PF | 66.1 | 66.1 | |||||
Wind | NF | 214.9 | 214.9 | +0.1 | |||
PF | 215.0 | 215.0 | |||||
PV | NF | 100 | 62.5 | 50 | 212.5 | 0.0 | |
PF | 100 | 62.5 | 50 | 212.5 |
CI | CC | CS | CR | Total | Gap | ||
---|---|---|---|---|---|---|---|
MWh | MWh | MWh | MWh | MWh | MWh | ||
Battery | NF | 22.0 | 96.3 | 73.1 | 443.3 | 634.7 | +1.5 |
PF | 22.0 | 162.5 | 6.9 | 444.8 | 636.2 | ||
TES | NF | 1340.0 | 1625.2 | 8614.2 | 11579.4 | −15.8 | |
PF | 1728.8 | 1219.7 | 8614.2 | 11,563.6 | |||
H2 storage | NF | 13,474.0 | 13,474.0 | −12.8 | |||
PF | 13,461.2 | 13,461.2 |
- | |||||||
---|---|---|---|---|---|---|---|
CI | Gas boiler PH | NF | 0.39 | 8.6 | 0.0 | 22.1 | 8.4 |
PF | 0.39 | 8.6 | 0.0 | 22.1 | 8.4 | ||
Resistance heater PH | NF | 0.08 | 1.7 | 0.0 | 20.8 | 0.0 | |
PF | 0.08 | 1.7 | 0.0 | 20.8 | 0.0 | ||
PV | NF | 0.15 | 14.9 | 0.0 | 85.0 | 0.5 | |
PF | 0.15 | 14.9 | 0.0 | 85.0 | 0.5 | ||
CC | Heat Pump | NF | 0.21 | 34.2 | 0.0 | 163.0 | 0.3 |
PF | 0.23 | 31.9 | 0.0 | 138.8 | 3.7 | ||
Biomass CHP | NF | 0.05 | 0.4 | 0.0 | 7.1 | 0.0 | |
PF | 0.10 | 1.1 | 0.0 | 11.0 | 0.0 | ||
PV | NF | 0.15 | 9.3 | 0.0 | 53.1 | 0.3 | |
PF | 0.15 | 9.3 | 0.0 | 53.1 | 0.3 | ||
CS | Heat Pump | NF | 0.20 | 29.4 | 0.0 | 145.4 | 0.0 |
PF | 0.18 | 30.7 | 0.0 | 171.6 | 0.0 | ||
PV | NF | 0.15 | 7.5 | 0.0 | 42.5 | 0.3 | |
PF | 0.15 | 7.5 | 0.0 | 42.5 | 0.3 | ||
CR | Heat Pump | NF | 0.09 | 21.8 | 0.0 | 240.2 | 0.0 |
PF | 0.09 | 21.8 | 0.0 | 240.0 | 0.0 | ||
Fuel Cell | NF | 0.26 | 6.9 | 0.0 | 26.7 | 0.0 | |
PF | 0.26 | 6.9 | 0.0 | 26.7 | 0.0 | ||
Electrolyser | NF | 0.11 | 5.1 | 0.0 | 20.0 | 0.0 | |
PF | 0.11 | 5.1 | 0.0 | 20.0 | 0.0 | ||
Wind | NF | 0.24 | 51.8 | 0.1 | 212.9 | 39.6 | |
PF | 0.24 | 51.8 | 0.1 | 212.9 | 39.6 |
- | |||||||
---|---|---|---|---|---|---|---|
CI | Battery | NF | 108.1 | 3.9 | 0 | 22.0 | 0.0 |
PF | 135.4 | 4.7 | 0 | 22.0 | 0.0 | ||
CC | Battery | NF | 131.8 | 50.6 | 0 | 96.3 | 51.7 |
PF | 129.2 | 82.5 | 0 | 162.5 | 79.1 | ||
TES | NF | 55.6 | 285.5 | 0 | 1339.8 | 138.7 | |
PF | 50.9 | 327.8 | 0 | 1728.8 | 153.8 | ||
CS | Battery | NF | 137.1 | 38.8 | 0 | 73.1 | 39.4 |
PF | 128.7 | 3.4 | 0 | 6.9 | 2.9 | ||
TES | NF | 40.0 | 297.3 | 0 | 1625.2 | 125.1 | |
PF | 38.9 | 204.3 | 0 | 1219.7 | 32.3 | ||
CR | Battery | NF | 72.4 | 221.9 | 0 | 443.3 | 212.2 |
PF | 72.8 | 277.9 | 0 | 444.8 | 303.0 | ||
TES | NF | 13.2 | 1583.5 | 0 | 8614.2 | 692.7 | |
PF | 13.2 | 1577.5 | 0 | 8614.2 | 684.7 | ||
H2-storage | NF | 4.5 | 8738.7 | 0 | 13,474.0 | 9881.4 | |
PF | 4.5 | 8698.5 | 0 | 13,461.2 | 9823.1 |
CI-CC Heat | NF | 11.8 | 0.0 | 20.8 | 13.4 |
PF | 13.1 | 0.0 | 20.8 | 10.7 | |
CI-CS Heat | NF | 6.8 | 0.0 | 20.5 | 6.8 |
PF | 5.4 | 0.0 | 20.8 | 6.4 | |
CC-CS Electricity | NF | −0.1 | −5.9 | 0.0 | 0.0 |
PF | 2.3 | −16.6 | 18.4 | 1.7 | |
CI-CC Electricity | NF | 17.8 | −27.2 | 36.0 | 14.7 |
PF | 19.1 | −31.7 | 36.0 | 18.9 | |
CI-CR Electricity | NF | −29.6 | −36.0 | 36.0 | −36.0 |
PF | −29.6 | −36.0 | 36.0 | −36.0 | |
CI-CS Electricity | NF | 15.4 | −21.1 | 36.0 | 11.2 |
PF | 13.0 | −20.2 | 36.0 | 10.7 |
Expenditures in GWh | Yields in GWh | ||||||
---|---|---|---|---|---|---|---|
RES | Import | Infrastructure | Total | Load | Excess | Total | |
NW | 732.1 | 454.8 | 133.3 | 1320.2 | 766.0 | 19.9 | 785.9 |
PF | 732.2 | 455.7 | 133.6 | 1321.5 | 766.0 | 19.9 | 785.9 |
Electricity | Gas | Heat | Biomass | |
---|---|---|---|---|
GWh | GWh | GWh | GWh | |
NF | 312.6 | 95.9 | 36.4 | 9.9 |
PF | 294.5 | 95.9 | 36.4 | 28.9 |
NF | PF | ||
---|---|---|---|
Electricity grids | High voltage/transmission | X | |
Medium voltage/distribution | X | ||
Low voltage/distribution | X | ||
District heating networks | Large scale | X | |
Small scale | X | ||
Gas networks | High pressure/transmission | X | |
Low pressure/distribution | X |
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Kriechbaum, L.; Gradl, P.; Reichenhauser, R.; Kienberger, T. Modelling Grid Constraints in a Multi-Energy Municipal Energy System Using Cumulative Exergy Consumption Minimisation. Energies 2020, 13, 3900. https://doi.org/10.3390/en13153900
Kriechbaum L, Gradl P, Reichenhauser R, Kienberger T. Modelling Grid Constraints in a Multi-Energy Municipal Energy System Using Cumulative Exergy Consumption Minimisation. Energies. 2020; 13(15):3900. https://doi.org/10.3390/en13153900
Chicago/Turabian StyleKriechbaum, Lukas, Philipp Gradl, Romeo Reichenhauser, and Thomas Kienberger. 2020. "Modelling Grid Constraints in a Multi-Energy Municipal Energy System Using Cumulative Exergy Consumption Minimisation" Energies 13, no. 15: 3900. https://doi.org/10.3390/en13153900