Optimal Electrification Using Renewable Energies: Microgrid Installation Model with Combined Mixture k-Means Clustering Algorithm, Mixed Integer Linear Programming, and Onsset Method
Abstract
1. Introduction
2. Theoretical Background
2.1. Scientific Models of Microgrid Technologies
2.2. Scientific Methods for Microgrid Deployment
2.2.1. Clustering Techniques
k-Means Clustering Model
Elbow Method
2.2.2. Haversine Method
2.2.3. Open-Source Spatial Planning for Electrification Method: Onsset
2.3. Bibliographical Reviews
3. Materials and Methods
3.1. Materials
3.2. Methods
3.2.1. Microgrid System Model
3.2.2. Optimizations Problem Formulation
- Enter data for each vector
- Initialize the position of the centers:
- Calculate mk averages of vectors in cluster k
- -
- Until there are no more changes in the mk
- -
- Assign each Vi point to the nearest cluster
- -
- Calculate new mk
- -
- End As long as
3.2.3. Data
4. Results and Discussion
4.1. Optimization Results
4.1.1. Results for Cluster Formation: Physical Allocation of Microgrid Centers
4.1.2. Renewable Energy Resource Availability Results
4.1.3. Optimization Results for Technology Selection
4.1.4. Capacity and Connection Optimization Results
- (a)
- Scenario 1: results for voltage rate profile/distance
- (b)
- Scenario 2: influence of load capacity
4.1.5. Results of Microgrid Formation Evaluation Studies in Togo
4.2. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
solar power variable | |
charging (80%) and discharging (20%) rates | |
performance | |
performance rate | |
area | |
temperature differential | |
decision variable | |
standard temperature | |
battery storage at t + 1 | |
battery storage at t | |
battery power | |
number of batteries | |
battery capacity | |
battery volatge | |
battery efficiency | |
wind power | |
air density | |
area swept by the turbine | |
wind power efficiency | |
wind decision variable | |
probability density | |
scale factor | |
wind speed | |
standard deviation | |
average speed | |
average power | |
gamma function | |
hydroelectric power | |
density of water | |
acceleration | |
water flow rate | |
waterfall height | |
hydroelectric efficiency | |
i | index |
load vector matrix | |
vector i | |
, | latitudes |
, | longitudes |
j | substation index |
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Months | Solar Radiation (W/m2) | Temperature (Degrees) | Relative Humidity (%) | Wind Speed (m/s) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Min | Max | Min | Max | Min | Max | Min | Max | |||||||||
Jan | 85.46 | 115.71 | 99.01 | 5.87 | 26.12 | 28.41 | 27.59 | 0.59 | 60.56 | 85.62 | 75.25 | 6.92 | 2.04 | 4.45 | 3.27 | 0.68 |
Fev | 85.98 | 113.63 | 103.63 | 6.95 | 27.58 | 28.57 | 28.05 | 0.23 | 69.75 | 85.19 | 80.92 | 2.97 | 2.21 | 5.17 | 3.94 | 0.76 |
Mar | 84.98 | 122.43 | 108.85 | 9.69 | 27.83 | 28.96 | 28.38 | 0.23 | 78.44 | 86.31 | 81.99 | 1.89 | 3.99 | 6.11 | 4.78 | 0.57 |
Apr | 109.64 | 137.14 | 127.32 | 7.0 | 26.95 | 28.38 | 27.67 | 0.46 | 78.31 | 88.31 | 83.72 | 2.35 | 1.86 | 5.49 | 3.7 | 0.91 |
May | 108.89 | 132.91 | 126.36 | 4.72 | 26.49 | 28.11 | 27.41 | 0.41 | 76.19 | 88.62 | 85.21 | 2.59 | 1.91 | 4.47 | 3.41 | 0.56 |
June | 112.42 | 128.5 | 121.95 | 3.63 | 25.09 | 27.42 | 26.25 | 0.73 | 79.0 | 92.88 | 87.34 | 3.28 | 1.9 | 5.6 | 3.69 | 0.85 |
Jul | 117.48 | 129.11 | 123.56 | 2.93 | 24.44 | 25.9 | 25.10 | 0.36 | 82.19 | 90.81 | 87.35 | 2.33 | 3.42 | 6.55 | 5.06 | 0.66 |
Aug | 117.97 | 134.07 | 127.02 | 3.74 | 23.64 | 25.35 | 24.34 | 0.46 | 82.62 | 92.31 | 87.89 | 2.0 | 2.4 | 7.82 | 5.29 | 1.36 |
Sep | 125.77 | 140.23 | 134.24 | 3.19 | 24.95 | 25.87 | 25.45 | 0.24 | 82.88 | 91.5 | 87.28 | 2.18 | 3.26 | 6.55 | 4.85 | 0.88 |
Oct | 113.06 | 133.61 | 125.49 | 4.72 | 25.17 | 27.4 | 26.32 | 0.63 | 84.62 | 90.69 | 87.60 | 1.55 | 2.16 | 5.55 | 3.19 | 0.89 |
Nov | 106.05 | 122.58 | 114.64 | 4.22 | 26.64 | 27.83 | 27.24 | 0.3 | 79.44 | 87.0 | 83.24 | 1.78 | 1.65 | 4.77 | 3.03 | 0.71 |
Dec | 90.72 | 111.33 | 103.36 | 4.46 | 25.9 | 27.8 | 27.01 | 0.35 | 61.62 | 86.62 | 78.24 | 6.64 | 1.62 | 4.3 | 2.94 | 0.61 |
Indicators | Min | Max | |||
---|---|---|---|---|---|
Data | 100 | 0.028 | 0.9 | 0.455 | 0.25 |
Costs/Systems | PV (USD/kW) | Batteries/6 V (USD/Unit) | Wind (USD/kW) | Hydraulic (USD/kW) | Biodiesel (USD/kW) |
---|---|---|---|---|---|
Installation cost | 800–2000 | 900–1300 | 1800 | 2000 | 650 |
Maintenance and operating costs | 8–200 | 9–14 | 700–1000 | 100/year | 20/year |
Replacement cost | 700 | 1300 | - | - | - |
Centroid/Axis | x | y |
---|---|---|
Centroid 1 | 0.92463054 | 0.11527094 |
Centroid 2 | 0.75952381 | 0.74047619 |
Centroid 3 | 0.29246429 | 0.48892857 |
Month/Resources | Objective Function | Batteries (Injection/Consumption) | Storage | Solar | Wind | Hydro |
---|---|---|---|---|---|---|
Cost (USD) | P (kW) | E (kWh) | P (kW) | P (kW) | P (kW) | |
January | 86,993.372 | −5.9521873 | 125 | 32.78232 | 1.2654927 | 5.05 |
February | 107,862.57 | −4.3408207 | 119.04781 | 33.91956 | 1.7396193 | 5.05 |
March | 137,518.88 | −2.1732186 | 114.70699 | 35.40348 | 2.4233014 | 5.05 |
April | 113,170.6 | 2.9308321 | 112.53377 | 41.62752 | 1.3033121 | 5.05 |
May | 102,321.29 | 2.0975483 | 115.46461 | 41.04108 | 1.0564683 | 5.05 |
Jun | 106,827.33 | 1.7328749 | 117.56215 | 40.5162 | 1.2166749 | 5.05 |
Jully | 162,312.84 | 3.5950199 | 119.29503 | 40.9212 | 2.6738199 | 5.05 |
August | 177,942.34 | 5.0149667 | 122.89005 | 42.00336 | 3.0116067 | 5.05 |
September | 154,083.06 | 4.4502273 | 127.90502 | 42.08436 | 2.3658673 | 5.05 |
October | 91,055.383 | 0.5818162 | 132.35524 | 39.72888 | 0.8529362 | 5.05 |
November | 79,623.893 | −2.4906887 | 132.93706 | 36.73836 | 0.7709513 | 5.05 |
December | 69,867.2 | −5.44637 | 130.44637 | 33.8256 | 0.72803 | 5.05 |
Horizon/Years | 2024–2030 | 2030–2050 | ||
Population | 8,095,498 | >12,000,000 | ||
Scenarios | Scenario 2 | Scenario 4 | ||
Technologies/costs | Capacity (MW) | Investment (In million USD) | Capacity (MW) | Investment (In million USD) |
Mini-grid PV hybrid | 320 | 564 | 720 | 1371 |
Mini-grid hydraulic | <1 | 1.12 | 1 | 4.42 |
Mini-grid wind, biodiesel | 0 | 0 | 0 | 0 |
Extension | - | - | 274 | 964 |
Stand-alone PV systems | - | - | 62 | 280 |
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Kabe, M.; Bokovi, Y.; Sedzro, K.S.; Takouda, P.; Lare, Y. Optimal Electrification Using Renewable Energies: Microgrid Installation Model with Combined Mixture k-Means Clustering Algorithm, Mixed Integer Linear Programming, and Onsset Method. Energies 2024, 17, 3022. https://doi.org/10.3390/en17123022
Kabe M, Bokovi Y, Sedzro KS, Takouda P, Lare Y. Optimal Electrification Using Renewable Energies: Microgrid Installation Model with Combined Mixture k-Means Clustering Algorithm, Mixed Integer Linear Programming, and Onsset Method. Energies. 2024; 17(12):3022. https://doi.org/10.3390/en17123022
Chicago/Turabian StyleKabe, Moyème, Yao Bokovi, Kwami Senam Sedzro, Pidéname Takouda, and Yendoubé Lare. 2024. "Optimal Electrification Using Renewable Energies: Microgrid Installation Model with Combined Mixture k-Means Clustering Algorithm, Mixed Integer Linear Programming, and Onsset Method" Energies 17, no. 12: 3022. https://doi.org/10.3390/en17123022
APA StyleKabe, M., Bokovi, Y., Sedzro, K. S., Takouda, P., & Lare, Y. (2024). Optimal Electrification Using Renewable Energies: Microgrid Installation Model with Combined Mixture k-Means Clustering Algorithm, Mixed Integer Linear Programming, and Onsset Method. Energies, 17(12), 3022. https://doi.org/10.3390/en17123022