Long-Term Hydropower Planning for Ethiopia: A Rolling Horizon Stochastic Programming Approach with Uncertain Inflow
Abstract
:1. Introduction
2. Mathematical Model
2.1. Problem Definition
2.2. Assumptions
2.3. Stochastic Optimization Model
2.3.1. Objective Function
2.3.2. Risk Measures
2.4. Stochastic Model in a Weekly Rolling Horizon Framework
Algorithm 1 Risk-neutral stochastic rolling horizon model |
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Algorithm 2 Risk-averse stochastic rolling horizon model |
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3. Results and Discussion
3.1. Risk-Neutral Model
3.2. Risk-Averse Model
3.3. Rolling Horizon Model
- What is the total load shedding during a year?
- How much water is saved for the future?
- How is load shedding distributed throughout the year?
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Indices: | |
i | Index for hydropower plants: |
m | Index for export area: |
n | Index for wind power plants: |
Index for inflow scenarios: | |
t | Planning period of one year with a weekly time resolution: |
Parameters: | |
C | Penalty cost of load shedding |
Load forecast during week t | |
Maximal generation in power plant i | |
I | Number of reservoirs |
Index set of all power plants downstream of reservoir i | |
Index set of power plants upstream of reservoir i | |
Starting contents of reservoir i | |
Maximal contents of reservoir i | |
Minimal contents of reservoir i | |
Minimal contents of reservoir i at the end of planning period T | |
Power export to area m during week t | |
M | Number of export areas |
N | Number of wind power plants |
Power generation of waste to energy plants during week t | |
Minimal discharge of power plant i | |
Maximal discharge of power plant i | |
T | Number of weeks in the planning horizon |
Local inflow to reservoir i during week t for scenario | |
Total wind power generation during week t | |
Confidence level of Conditional Value at Risk () | |
risk factor | |
Production equivalent of power plant i, | |
Value of future electricity generation | |
Number of scenarios | |
Probability of inflow scenario | |
Variables: | |
Generation of hydropower plant i during week t for scenario | |
Contents of reservoir i at the end of week t for scenario | |
Discharge from power plant i during week t for scenario | |
Spillage from reservoir i during week t for scenario | |
Load shedding during week t for scenario | |
Auxiliary variables for calculating |
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Load Level Increase | Optimal Value (M USD) | Quality Metric | |
---|---|---|---|
Z | Z | ||
0% | 1598.42 | 1520.88 | 77.54 |
35% | 1015.44 | 984.75 | 30.69 |
50% | 134.08 | 120.86 | 13.82 |
USD 50 | USD 200 | USD 500 | USD 750 | USD 1000 |
---|---|---|---|---|
Optimal value (M USD) | 1213.65 | 1015.44 | 852.83 | 690.22 |
Energy in Stored Water (TWh) | 26.97 | 26.81 | 26.81 | 26.81 |
Load shedding(TWh) | 0.67 | 0.65 | 0.65 | 0.65 |
Risk-Averse | USD/MWh, USD/MWh | ||||
---|---|---|---|---|---|
Risk measures for stored water (Case-a) | Optimal value without the risk measure (M USD) | 1015.44 | 1005.50 | 865.93 | −6872.34 |
Energy in stored water (TWh) | 26.81 | 26.88 | 27.75 | 37.05 | |
Load shedding (TWh) | 0.65 | 0.68 | 1.04 | 17.45 | |
(M USD) | 421.35 | 647.32 | 1840.70 | 1849.95 | |
Risk measures for load shedding (Case-b) | Optimal value without the risk measure (M USD) | 1015.44 | 1015.44 | 1015.44 | 883.27 |
Energy in stored water (TWh) | 26.81 | 26.81 | 26.81 | 26.16 | |
Load shedding (TWh) | 0.65 | 0.65 | 0.65 | 0.85 | |
(M USD) | 0.00 | −377.29 | −750.80 | −754.57 | |
Risk measures for entire objective function (Case-c) | Optimal value without the risk measure (M USD) | 1015.44 | 1015.44 | 1015.44 | 639.04 |
Energy in stored water (TWh) | 26.81 | 26.81 | 26.81 | 24.94 | |
Load shedding (TWh) | 0.65 | 0.65 | 0.65 | 1.22 | |
(M USD) | 0.00 | 265.77 | 528.88 | 531.54 |
Load Level Increase () | Deterministic (Case-D) | Risk-Neutral Stochastic (Case-RN) | Risk-Averse Stochastic (Case-RA-1) | Risk-Averse Stochastic (Case-RA-2) | |
---|---|---|---|---|---|
Total L.sh () | 35% | 1.17 | 0.82 | 0.77 | 1.32 |
50% | 2.23 | 2.38 | 2.00 | 3.34 | |
Maximum L.sh () | 35% | 0.20 | 0.07 | 0.07 | 0.05 |
50% | 0.26 | 0.12 | 0.14 | 0.11 | |
Energy Stored (TWh) | 35% | 28.29 | 28.35 | 28.30 | 28.48 |
50% | 28.26 | 28.28 | 28.21 | 28.48 | |
Energy Spilled (TWh) | 35% | 0.50 | 0.41 | 0.38 | 0.44 |
50% | 0.26 | 0.37 | 0.35 | 0.41 |
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Dires, F.G.; Amelin, M.; Bekele, G. Long-Term Hydropower Planning for Ethiopia: A Rolling Horizon Stochastic Programming Approach with Uncertain Inflow. Energies 2023, 16, 7399. https://doi.org/10.3390/en16217399
Dires FG, Amelin M, Bekele G. Long-Term Hydropower Planning for Ethiopia: A Rolling Horizon Stochastic Programming Approach with Uncertain Inflow. Energies. 2023; 16(21):7399. https://doi.org/10.3390/en16217399
Chicago/Turabian StyleDires, Firehiwot Girma, Mikael Amelin, and Getachew Bekele. 2023. "Long-Term Hydropower Planning for Ethiopia: A Rolling Horizon Stochastic Programming Approach with Uncertain Inflow" Energies 16, no. 21: 7399. https://doi.org/10.3390/en16217399
APA StyleDires, F. G., Amelin, M., & Bekele, G. (2023). Long-Term Hydropower Planning for Ethiopia: A Rolling Horizon Stochastic Programming Approach with Uncertain Inflow. Energies, 16(21), 7399. https://doi.org/10.3390/en16217399