A Multi-Energy System Expansion Planning Method Using a Linearized Load-Energy Curve: A Case Study in South Korea
Abstract
:1. Introduction
- The expansion planning problem for a multi-energy system, where considering various energy resources, including fuel-based generators and a renewable electrical power source, as well as a CHP unit and energy storage resources, is modeled as an MILP problem with linearized constraints.
- To model linearized constraints including a linearized load curve, we use a load-energy curve instead of the LDC, and apply a Douglas-Peucker algorithm that can approximate linear functions and minimize the distortion of the original demand function.
- To validate the use of a linearized load-energy curve, the results of optimization methods using the linearized load-energy curve and the stepwise representation of LDC are compared.
- A case study for a multi-energy system based on a benchmark case from Goyang city in South Korea is presented.
2. Multi-Energy System Overview
3. Basic Optimization Model
3.1. Objective Function
3.2. CHP Constraints
3.3. Energy Storage Constraints
3.4. Lifespan Constraints
4. Linearized Load-Energy Curve
4.1. Load-Energy Curve and Linearization
4.2. Impact of the Renewable Electrical Power Source
5. Optimization Process
5.1. Proposed Optimization Method
5.2. Comparison of Optimization Results Using Different Load Curves
6. Case Study
6.1. Data and Assumptions
6.2. Simulation Results
6.2.1. Case 1
6.2.2. Case 2
6.2.3. Case 3
6.2.4. Case 4
7. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
Indices | |
Project year index, from . | |
Electrical energy resource index, from . | |
Heat energy resource index, from . | |
Candidate unit index, from . | |
Electrical load pattern index, from . | |
Index for node point of approximated electrical load-energy curve, from . | |
Index for node point of approximated heat load-energy curve, from . | |
Index for stack of electrical energy resource, from . | |
Index for stack of heat energy resource, from . | |
Index for segment of approximated electrical load-energy curve, from . | |
Index for segment of approximated heat load-energy curve, from . | |
Variables | |
Load demand for node point, , of the electrical load-energy curve, , in project year, (MW). | |
Energy demand for node point, , of the electrical load-energy curve, , in project year, (MWh). | |
Load demand for node point, , of the heat load-energy curve in project year, (MW). | |
Energy demand for node point, , of the heat load-energy curve in project year, (MWh). | |
Special ordered sets of type 2 variable for approximated point, , in stack, , of the electrical load-energy curve, , in project year, . | |
Special ordered sets of type 2 variable for approximated point, , in stack, , of the heat load-energy curve in project year, . | |
Electrical load demand point for determining stack, , in project year, (MW). | |
Electrical energy demand point for determining stack, , in project year, (MWh). | |
Heat load demand point for determining stack, , in project year, (MW). | |
Heat energy demand point for determining stack, , in project year, (MWh). | |
Desired capacity of the electrical energy resource, , to which stack, , is allocated in project year, (MW). | |
Utilized energy of the electrical energy resource, , to which stack, , is allocated in project year, (MWh). | |
Desired capacity of the heat energy resource, , to which stack, , is allocated in project year, (MW). | |
Utilizing energy of the heat energy resource, , to which stack, , is allocated in project year, (MWh). | |
Charging electrical energy of stack, , in project year, (MWh). | |
Charging thermal energy of stack, , in project year, (MWh). | |
Binary Variables | |
Status of candidate segment, , in stack, , of the electrical load-energy curve, , in project year, . | |
Status of candidate segment, , in stack, , of heat load-energy curve in project year, . | |
Status of candidate electrical energy resource, , to which stack, , is allocated in project year, . | |
Status of candidate heat energy resource, , to which stack, , is allocated in project year, . | |
Status of candidate generating unit, , of electrical energy resource, , in project year, . | |
Status of candidate generating unit, , of heat energy resource, , in project year, . | |
Status of candidate electrical load-energy curve, , in project year, . | |
Parameters | |
Capacity of candidate generating unit, , of electrical energy resource, . | |
Capacity of candidate generating unit, , of heat energy resource, . | |
Capital cost of electrical energy resource, . | |
Capital cost of heat energy resource, . | |
Fixed operation and maintenance cost of electrical energy resource, . | |
Fixed operation and maintenance cost of heat energy resource, . | |
Fuel cost of electrical energy resource, . | |
Fuel cost of heat energy resource, . | |
Variable operation and maintenance cost of electrical energy resource, . | |
Variable operation and maintenance cost of heat energy resource, . | |
Lifetime of electrical energy resource, . | |
Lifetime of heat energy resource, . | |
Index of CHP unit in electrical energy resource, . | |
Index of CHP unit in heat energy resource, . | |
Index of electrical energy storage in electrical energy resource, . | |
Index of thermal energy storage in heat energy resource, . | |
Index of renewable electrical power source in electrical energy resource, . | |
Heat-to-power ratio | |
Interest rate |
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Unit | Fixed Cost ($/MW) (Capital Cost + Fixed Operations & Maintenance Cost) | Variable Cost ($/MWh) (Fuel Cost + Variable Operations & Maintenance Cost) |
---|---|---|
G1 | 60,000 | 100 |
G2 | 10,000 | 200 |
Model No. | Type of Curve | Total Cost (M$) | Desired Capacity of G1 (MW) | Utilized Energy of G1 (GWh) | Desired Capacity of G2 (MW) | Utilized Energy of G2 (GWh) |
---|---|---|---|---|---|---|
0 | LDC | 858.9 | 1087.2 | 7885 | 126.0 | 19.9 |
1 | Stepwise representation of LDC | 866.8 (0.92%) | 1028.8 (5.37%) | 7780 (1.33%) | 184.4 (46.35%) | 126.1 (533.7%) |
2 | Piecewise linear load-energy curve | 861.5 (0.31%) | 1080 (0.66%) | 7855 (0.38%) | 133.2 (5.68%) | 49.7 (150.3%) |
Parameter | Value |
---|---|
Project lifetime (Year) | 7 |
Interest rate (%) | 3.91 |
Demand growth rate (%) | 2.5 |
Approximation error tolerance (%) | 1 |
Resource Type | Unit Name | Overnight Capital Cost ($/MW) | Fixed O&M Cost ($/MW) | Fuel Cost ($/MWh) | Variable O&M Cost ($/MWh) | Life Span (Yr) | Candidate Capacity (MW) |
---|---|---|---|---|---|---|---|
Fuel-based Power Generator | DG1 | 900,000 | 15,000 | 33.2925 | 6.1 | 20 | 800, 700, 600, 500, 400, 300 |
DG2 | 650,000 | 15,000 | 182.3 | 15 | 20 | 90, 80, 70, 60, 50, 40 | |
DG3 | 875,000 | 17,500 | 46.75 | 12.5 | 20 | 90, 80, 70, 60, 50, 40 | |
Heat Only Boiler | HOB1 | 720,000 | 12,000 | 26.634 | 4.88 | 20 | 500, 450, 400, 350, 300, 250 |
HOB2 | 520,000 | 15,000 | 182.3 | 15 | 20 | 400, 350, 300, 250, 200, 150 | |
CHP | CHP | 1,150,000 | 5850 | 22.77 | 2.75 | 20 | 900, 800, 700, 600, 500, 400 (Heat-to-Power ratio: 0.92) |
Electrical Energy Storage | EES | 3,092,000 | 42,000 | 0 | 35 | 7 | 24, 20, 16, 12, 8, 4 |
Thermal Energy Storage | TES | 3,184,000 | 52,000 | 0 | 35 | 7 | 24, 20, 16, 12, 8, 4 |
Renewable Electrical Power Source | PV | 1,375,000 | 10,500 | 0 | 0 | 20 | 13.3 |
Case Number | Fuel-Based Power Generator | Heat Only Boiler | CHP | Storage | Renewable Electrical Power Source | |
---|---|---|---|---|---|---|
Electrical Energy | Thermal Energy | |||||
1 | ◯ | ◯ | ◯ | - | - | - |
2 | ◯ | ◯ | ◯ | ◯ | ◯ | - |
3 | ◯ | ◯ | ◯ | - | - | ◯ |
4 | ◯ | ◯ | ◯ | ◯ | ◯ | ◯ |
Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
---|---|---|---|---|---|---|---|---|---|
Case No. | Forced Allocated of RES | Unit | Installed Capacity (MW)/Utilized Energy (GWh) | ||||||
1 | - | DG1 | 700/5553 | 700/5692 | 700/5834 | 700/5980 | 700/6110 | 700/6114 | 700/6118 |
DG2 | - | - | - | - | - | - | - | ||
DG3 | - | - | - | - | 40/18.83 | 40/168.3 | 40/321.5 | ||
HOB1 | 250/152.3 | 250/155.7 | 250/159.3 | 250/162.9 | 250/166.7 | 250/170.5 | 250/174.4 | ||
HOB2 | 250/9.488 | 250/10.062 | 250/10.65 | 250/11.25 | 250/11.87 | 250/12.51 | 250/13.16 | ||
CHP * | 700/2352(2164) | 700/2411(2218) | 700/2471(2273) | 700/2533(2330) | 700/2596(2388) | 700/2661(2448) | 700/2728(2509) | ||
2 | - | DG1 | 700/5553 | 700/5692 | 700/5840 | 700/6010 | 700/6110 | 700/6114 | 700/6118 |
DG2 | - | - | 60/0.2462 | 60/0.7965 | 60/1.349 | 60/1.915 | 60/2.576 | ||
DG3 | - | - | - | - | 50/75.33 | 50/252.1 | 50/417.8 | ||
HOB1 | 300/155.0 | 300/158.4 | 300/167.5 | 300/192.8 | 300/220.7 | 300/249.4 | 300/263.0 | ||
HOB2 | 250/6.792 | 250/7.366 | 250/8.264 | 250/9.619 | 250/11.01 | 250/12.43 | 250/15.63 | ||
EES | - | - | - | - | - | - | - | ||
TES | - | - | - | - | - | - | 8/14.08 | ||
CHP * | 600/2352(2164) | 600/2411(2218) | 600/2465(2267) | 600/2502(2302) | 600/2538(2335) | 600/2575(2369) | 600/2629(2418) | ||
3 | No | DG1 | 700/5553 | 700/5692 | 700/5834 | 700/5980 | 700/6110 | 700/6114 | 700/6118 |
DG2 | - | - | - | - | - | - | - | ||
DG3 | - | - | - | - | 40/18.83 | 40/168.3 | 40/321.5 | ||
HOB1 | 250/152.3 | 250/155.7 | 250/159.3 | 250/162.9 | 250/166.7 | 250/170.5 | 250/174.4 | ||
HOB2 | 250/9.488 | 250/10.062 | 250/10.65 | 250/11.25 | 250/11.87 | 250/12.51 | 250/13.16 | ||
CHP * | 700/2352(2164) | 700/2411(2218) | 700/2471(2273) | 700/2533(2330) | 700/2596(2388) | 700/2661(2448) | 700/2728(2509) | ||
PV | - | - | - | - | - | - | - | ||
3 | Yes | DG1 | 700/5551 | 700/5690 | 700/5832 | 700/5978 | 700/6110 | 700/6114 | 700/6118 |
DG2 | - | - | - | - | - | - | - | ||
DG3 | - | - | - | - | 40/16.78 | 40/166.2 | 40/319.4 | ||
HOB1 | 250/152.3 | 250/155.7 | 250/159.3 | 250/162.9 | 250/166.7 | 250/170.5 | 300/177.1 | ||
HOB2 | 250/9.49 | 250/10.06 | 250/10.65 | 250/11.25 | 250/11.87 | 250/12.51 | 200/10.46 | ||
CHP * | 700/2352(2164) | 700/2411(2218) | 700/2471(2273) | 700/2533(2330) | 700/2596(2388) | 700/2661(2448) | 700/2728(2509) | ||
PV | 13.3/2.079 | 13.3/2.079 | 13.3/2.079 | 13.3/2.079 | 13.3/2.079 | 13.3/2.079 | 13.3/2.079 |
Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
---|---|---|---|---|---|---|---|---|---|
Case No. | Forced Allocation of RES | Unit | Installed Capacity (MW)/Utilized Energy (GWh) | ||||||
4 | No | DG1 | 700/5553 | 700/5692 | 700/5840 | 700/6010 | 700/6110 | 700/6114 | 700/6118 |
DG2 | - | - | 60/0.2462 | 60/0.7965 | 60/1.349 | 60/1.915 | 60/2.576 | ||
DG3 | - | - | - | - | 50/75.33 | 50/252.1 | 50/417.8 | ||
HOB1 | 300/155.0 | 300/158.4 | 300/167.5 | 300/192.8 | 300/220.7 | 300/249.4 | 300/263.0 | ||
HOB2 | 250/6.792 | 250/7.366 | 250/8.264 | 250/9.619 | 250/11.01 | 250/12.43 | 250/15.63 | ||
EES | - | - | - | - | - | - | - | ||
TES | - | - | - | - | - | - | 8/14.08 | ||
CHP * | 600/2352(2164) | 600/2411(2218) | 600/2465(2267) | 600/2502(2302) | 600/2538(2335) | 600/2575(2369) | 600/2629(2418) | ||
PV | - | - | - | - | - | - | - | ||
4 | Yes | DG1 | 700/5551 | 700/5690 | 700/5838 | 700/6008 | 700/6110 | 700/6114 | 700/6118 |
DG2 | - | - | 60/0.246 | 60/0.798 | 60/1.352 | 60/1.920 | 60/2.582 | ||
DG3 | - | - | - | - | 50/73.24 | 50/250.0 | 50/415.7 | ||
HOB1 | 300/155.0 | 300/158.4 | 300/167.5 | 300/192.8 | 300/220.7 | 300/249.4 | 300/263.0 | ||
HOB2 | 250/6.793 | 250/7.367 | 250/8.264 | 250/9.619 | 250/11.01 | 250/12.43 | 250/15.63 | ||
EES | - | - | - | - | - | - | - | ||
TES | - | - | - | - | - | - | 8/14.08 | ||
CHP * | 600/2352(2164) | 600/2411(2218) | 600/2465(2267) | 600/2502(2302) | 600/2538(2335) | 600/2575(2369) | 600/2629(2418) | ||
PV | 13.3/2.079 | 13.3/2.079 | 13.3/2.079 | 13.3/2.079 | 13.3/2.079 | 13.3/2.079 | 13.3/2.079 |
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Ko, W.; Park, J.-K.; Kim, M.-K.; Heo, J.-H. A Multi-Energy System Expansion Planning Method Using a Linearized Load-Energy Curve: A Case Study in South Korea. Energies 2017, 10, 1663. https://doi.org/10.3390/en10101663
Ko W, Park J-K, Kim M-K, Heo J-H. A Multi-Energy System Expansion Planning Method Using a Linearized Load-Energy Curve: A Case Study in South Korea. Energies. 2017; 10(10):1663. https://doi.org/10.3390/en10101663
Chicago/Turabian StyleKo, Woong, Jong-Keun Park, Mun-Kyeom Kim, and Jae-Haeng Heo. 2017. "A Multi-Energy System Expansion Planning Method Using a Linearized Load-Energy Curve: A Case Study in South Korea" Energies 10, no. 10: 1663. https://doi.org/10.3390/en10101663