Mechanisms for Choosing PV Locations That Allow for the Most Sustainable Usage of Solar Energy
Abstract
:1. Introduction
2. MCDM Methods
2.1. Determination of Weights
2.1.1. Group Eigen Value Method
- Analysts designate assessment scores to specified criteria.
- Transpose of the assessment matrix and then multiply it by the transposed one as shown in Equation (4).F = xT.x
- The power method, as employed by Qiu in 1997 [25], can be utilized to derive the eigenvector x*.
- Suppose k = 0, y0 = (1/n, 1/n,…..,1/n)T
- For k = 1, 2, 3,..., yk+1 = Fzk, and zk+1 =
- Verify if │zk→k+1│≤ ɛ, if it does, then, zk+1 equates to x*, else return to the prior step (with ɛ representing the precision and │zk→k+1│is the maximum absolute value of the difference between zk and zk+1)
- Normalization of the derived eigenvector using Equation (6).
2.1.2. Fuzzy Analytic Hierarchy Process
2.1.3. Entropy Method
2.2. Ranking Approaches
2.2.1. VIKOR Method
- Alternatives i = 1 and i = 2 if only condition C2 is not achieved or
- Alternatives i = 1, 2, …, m, if the condition C1 is not attained, where m is specified by the QM − Q1 < DQ relationship, for maximum i.
2.2.2. Grey Relation Analysis
2.3. Sensitivity Analysis
3. Data Collection
3.1. Study Area
3.2. Criteria for MCDM
- Solar radiation (C1). The yearly solar radiation is a meteorological factor that is applied to quantify the intensity of sunlight for a prospective site. The uninterrupted functioning of a PV plant relies upon solar irradiance. The opportunity for producing energy in a location increases with the amount of solar radiation available. In this research, the amount of solar radiation received by a surface is measured using the Global Horizontal Irradiance (GHI) [57]. The unit of measurement for GHI is in Watts per square meter per day (W/m2/day).
- Average air temperature (C2). The efficiency of power generation in PV systems is significantly influenced by ambient temperature [58]. The efficiency of power conversion in solar cells decreases with increasing ambient temperature, resulting in a reduction in the amount of power produced. The air temperature is measured in °C.
- Wind speed (C3). The efficacy of a PV system’s energy production is influenced by wind speed. The rate at which solar systems cool down increases with wind speed, which is accompanied by an increase in power production. It is measured in kilometers per hour (km/h).
- Sunshine hours (C4). The territory with more sun hours has the ability to generate more power when taking into account that various regions receive the same quantity of solar radiation. It is measured in hours (h).
- Sand and dust storm (C5). A suitable parameter for solar PV systems can be sand and dust storm [59]. Among the globe’s places where sand and dust storm existence are particularly intense is the Arabian Peninsula. The extent of radiation reaching the surface of PV panels is decreased with a greater incidence of storm phenomena. As a result, the amount of power generated in locations prone to higher sand storms is also decreased. It is calculated using the average yearly number of storms.
- Topography (C6). Minimal elevation fluctuations aid in lowering the high construction costs and flat topography is generally preferred for the placement of PV plants. Due to low economic viability, more change in topography or terrain is not acceptable. A maximum elevation change in a specific location can be approximated in feet.
- Population (C7). A high population in a region causes both a larger energy demand as well as a higher need for employment. Consequently, job generation increases with an increase in population. It implies that having a higher population in a specific area makes it a good location for a PV installation. As a result, the site of a solar system must be preferable to one where there is enough consumption and trained personnel to run and manage the PV system.
4. Implementation
4.1. GEM-VIKOR
4.2. FAHP-GRA
4.3. Entropy-VIKOR
5. Results and Discussion
6. Conclusions
- The fact that different strategies might produce different outcomes when used to solve the same problem is a key critique of MCDM. A decision-maker need to select a course of action that comes the closest to the ideal. As a result, the best solution can be one that is repeated by numerous MCDM procedures.
- This paper emphasizes the significance of evaluating several decision-making strategies and choosing the most suitable methodology for the specific application, without implying that any one MCDM method is superior to other methods.
- The outcomes of the different techniques might not be the same. This is explained by various weights and their distributions, as well as various solution algorithms.
- All three weight calculation methods have established solar radiation and sunshine hours as the most important criteria. For instance, using GEM, solar radiation and sunlight hours are given weights of 0.1877 and 0.1744, respectively, thereby contributing 18.77% and 17.44% to the choice of the PV site. Similarly, solar radiation and sunshine hour receive the same weight value of 0.1862 from the FAHP. Solar radiation and sunlight hours have entropy weights of 0.1663 and 0.1667, respectively.
- The type of MCDM approach selected affects the decision’s quality and the amount of work necessary. The various approaches display differing degrees of difficulty and demand varying degrees of computation.
- It makes sense to employ one of the simplest techniques. However, the use of multiple techniques is suggested in order to verify consistency and improve the trustworthiness of the results.
- It should be noted that some strategies work well for large-sized problems while others are better suited for small-scale problems.
- Of all the methods utilized in this study, the FAHP-VIKOR technique is the most exhaustive with a difficulty level of 8, while Entropy-GRA is the easiest with a complexity degree of 4.
- A decision among numerous options that is replicated by several MCDM approaches can be regarded as the best option. As a result, Tabuk is the ideal location for the construction of a solar power plant. High solar radiation (GHI value of 5992 W/m2/day) and more sunshine hours (12.16 h/day) are the main factors that contribute to its selection.
- The ranking consistency among the various MCDM techniques employed in the study is reasonable, as indicated by Kendall’s coefficient of concordance value of 0.8741, which is very close to 1.
- The likelihood of uncertainty in expert decision-making as well as the lack of precise data collection is the work’s limitations. Future studies will find ways to circumvent these restrictions. Future versions of the work will also be expanded by integrating additional accurate data, expert opinions, different cities or locations, and improvised MCDM procedures.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Scenario | Description |
1 | 20% increase in weight for average temperature |
2 | 40% increase in weight for the population |
3 | 20% decrease in weight for topography |
4 | 30% increase in weight for global horizontal irradiance |
5 | 40% decrease in weight for dust storm |
6 | 30% decrease in weight for wind speed |
Cities | Criteria | ||||||
---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C4 | C5 | C6 | C7 | |
Arar | 5392 | 22 | 14 | 12.16 | 0.30 | 174 | 148,540 |
Al-Jouf | 5016 | 21.87 | 13.5 | 12.16 | 0.57 | 82 | 102,903 |
Tabuk | 5992 | 22.98 | 10 | 12.16 | 0.16 | 125 | 455,450 |
Hail | 5359 | 23.3 | 12 | 12.15 | 0.28 | 387 | 267,005 |
Dhahran | 5205 | 26.4 | 15 | 12.16 | 0.15 | 525 | 99,540 |
Al-Ahsa | 5278 | 26.9 | 12 | 12.15 | 0.91 | 157 | 293,179 |
Taif | 5671 | 22.2 | 14 | 12.15 | 0.08 | 459 | 530,848 |
Makkah | 5303 | 28.6 | 3 | 12.15 | 0.02 | 1106 | 1,323,624 |
Jeddah | 5525 | 28.1 | 13 | 12.13 | 0.17 | 112 | 2,867,446 |
Yanbu | 5765 | 27.7 | 11 | 12.14 | 0.48 | 190 | 200,161 |
Medina | 5376 | 27.2 | 11 | 12.14 | 0.09 | 276 | 1,300,000 |
Riyadh | 6040 | 27 | 11 | 12.15 | 0.16 | 200 | 4,205,961 |
Abha | 5674 | 19.2 | 11 | 12.15 | 0.05 | 1942 | 210,886 |
Jizan | 4663 | 28.55 | 11 | 12.13 | 0.60 | 190 | 105,198 |
Najran | 6684 | 23.9 | 11 | 12.15 | 0.26 | 1486 | 258,573 |
Criteria | E1 | E2 | E3 |
---|---|---|---|
C1 | 9 | 10 | 9 |
C2 | 8 | 7 | 8 |
C3 | 7 | 8 | 6 |
C4 | 9 | 9 | 8 |
C5 | 7 | 8 | 6 |
C6 | 6 | 5 | 5 |
C7 | 4 | 6 | 4 |
k | 0 | 1 | 2 | 3 |
---|---|---|---|---|
ykT | (0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14) | (199.14, 162.71, 150, 185, 150, 113.57, 100.29) | (539.20, 440.77, 406.01, 500.91, 406.01, 307.58, 271.36) | (539.20, 440.77, 406.01, 500.91, 406.01, 307.58, 271.36) |
- | 410.262 | 1110.79 | 1110.79 | |
zkT | - | (0.4854, 0.3966, 0.3656, 0.4509, 0.3656, 0.2768, 0.2444) | (0.4854, 0.3968, 0.3655, 0.4509, 0.3655, 0.2769, 0.2443) | (0.4854, 0.3968, 0.3655, 0.4509, 0.3655, 0.2769, 0.2443) |
Cities | Criteria | ||||||
---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C4 | C5 | C6 | C7 | |
Arar | 0.0471 | 0.0346 | 0.0433 | 0.0451 | 0.0293 | 0.0065 | 0.0026 |
Al-Jouf | 0.0438 | 0.0344 | 0.0417 | 0.0451 | 0.0557 | 0.0031 | 0.0018 |
Tabuk | 0.0523 | 0.0361 | 0.0309 | 0.0451 | 0.0158 | 0.0047 | 0.0078 |
Hail | 0.0468 | 0.0366 | 0.0371 | 0.0450 | 0.0276 | 0.0145 | 0.0046 |
Dhahran | 0.0455 | 0.0415 | 0.0464 | 0.0451 | 0.0146 | 0.0197 | 0.0017 |
Al-Ahsa | 0.0461 | 0.0423 | 0.0371 | 0.0450 | 0.0886 | 0.0059 | 0.0050 |
Taif | 0.0495 | 0.0349 | 0.0433 | 0.0450 | 0.0076 | 0.0173 | 0.0091 |
Makkah | 0.0463 | 0.0449 | 0.0093 | 0.0450 | 0.0020 | 0.0416 | 0.0228 |
Jeddah | 0.0483 | 0.0441 | 0.0402 | 0.0450 | 0.0166 | 0.0042 | 0.0493 |
Yanbu | 0.0504 | 0.0435 | 0.0340 | 0.0450 | 0.0466 | 0.0071 | 0.0034 |
Medina | 0.0470 | 0.0427 | 0.0340 | 0.0450 | 0.0089 | 0.0104 | 0.0224 |
Riyadh | 0.0528 | 0.0424 | 0.0340 | 0.0450 | 0.0159 | 0.0075 | 0.0723 |
Abha | 0.0496 | 0.0302 | 0.0340 | 0.0450 | 0.0046 | 0.0730 | 0.0036 |
Jizan | 0.0407 | 0.0448 | 0.0340 | 0.0450 | 0.0588 | 0.0071 | 0.0018 |
Najran | 0.0584 | 0.0375 | 0.0340 | 0.0450 | 0.0249 | 0.0559 | 0.0044 |
Criteria | |||||||
---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C4 | C5 | C6 | C7 | |
vj+ | 0.0584 | 0.0302 | 0.0464 | 0.0451 | 0.0020 | 0.0031 | 0.0723 |
vj− | 0.0407 | 0.0449 | 0.0093 | 0.0450 | 0.0886 | 0.0730 | 0.0017 |
Cities | Criteria | Si | Ri | Qi | ||||||
---|---|---|---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C4 | C5 | C6 | C7 | ||||
Arar | 0.0471 | 0.0346 | 0.0433 | 0.0451 | 0.0293 | 0.0065 | 0.0026 | 0.3206 | 0.1200 | 0.1929 |
Al-Jouf | 0.0438 | 0.0344 | 0.0417 | 0.0451 | 0.0557 | 0.0031 | 0.0018 | 0.3983 | 0.1550 | 0.4497 |
Tabuk | 0.0523 | 0.0361 | 0.0309 | 0.0451 | 0.0158 | 0.0047 | 0.0078 | 0.2961 | 0.0863 | 0.0000 |
Hail | 0.0468 | 0.0366 | 0.0371 | 0.0450 | 0.0276 | 0.0145 | 0.0046 | 0.4335 | 0.1231 | 0.3309 |
Dhahran | 0.0455 | 0.0415 | 0.0464 | 0.0451 | 0.0146 | 0.0197 | 0.0017 | 0.3955 | 0.1374 | 0.3601 |
Al-Ahsa | 0.0461 | 0.0423 | 0.0371 | 0.0450 | 0.0886 | 0.0059 | 0.0050 | 0.5856 | 0.1414 | 0.5866 |
Taif | 0.0495 | 0.0349 | 0.0433 | 0.0450 | 0.0076 | 0.0173 | 0.0091 | 0.3284 | 0.0941 | 0.0737 |
Makkah | 0.0463 | 0.0449 | 0.0093 | 0.0450 | 0.0020 | 0.0416 | 0.0228 | 0.6066 | 0.1535 | 0.6692 |
Jeddah | 0.0483 | 0.0441 | 0.0402 | 0.0450 | 0.0166 | 0.0042 | 0.0493 | 0.5073 | 0.1744 | 0.6644 |
Yanbu | 0.0504 | 0.0435 | 0.0340 | 0.0450 | 0.0466 | 0.0071 | 0.0034 | 0.5586 | 0.1388 | 0.5446 |
Medina | 0.0470 | 0.0427 | 0.0340 | 0.0450 | 0.0089 | 0.0104 | 0.0224 | 0.5049 | 0.1306 | 0.4458 |
Riyadh | 0.0528 | 0.0424 | 0.0340 | 0.0450 | 0.0159 | 0.0075 | 0.0723 | 0.3219 | 0.1274 | 0.2305 |
Abha | 0.0496 | 0.0302 | 0.0340 | 0.0450 | 0.0046 | 0.0730 | 0.0036 | 0.4024 | 0.1071 | 0.2182 |
Jizan | 0.0407 | 0.0448 | 0.0340 | 0.0450 | 0.0588 | 0.0071 | 0.0018 | 0.7553 | 0.1877 | 1.0000 |
Najran | 0.0584 | 0.0375 | 0.0340 | 0.0450 | 0.0249 | 0.0559 | 0.0044 | 0.3910 | 0.0908 | 0.1256 |
Importance | Explanation | Trapezoidal Fuzzy Number | Importance | Trapezoidal Fuzzy Number |
---|---|---|---|---|
1 | Equal importance | (1,1,1,1) | 1 | (1,1,1,1) |
3 | Moderate importance | (2, 2.5, 3.5, 4) | 0.3333 | (0.25, 0.286, 0.4, 0.5) |
5 | Strong importance | (4, 4.5, 5.5, 6) | 0.2 | (0.167, 0.182, 0.222, 0.25) |
7 | Very strong importance | (6, 6.5, 7.5, 8) | 0.1429 | (0.125, 0.133, 0.154, 0.167) |
9 | Extreme importance | (9, 9, 9, 9) | 0.1111 | (0.111, 0.111, 0.111, 0.111) |
2 | Intermediate values | (1, 1.5, 2.5, 3) | 0.5 | (0.333, 0.4, 0.667, 1) |
4 | (3, 3.5, 4.5, 5) | 0.25 | (0.2, 0.222, 0.286, 0.333) | |
6 | (5, 5.5, 6.5, 7) | 0.1667 | (0.143, 0.154, 0.182, 0.2) | |
8 | (7, 7.5, 8.5, 9) | 0.125 | (0.111, 0.118, 0.133, 0.143) |
Criteria | C1 | C2 | C3 | C4 | C5 | C6 | C7 |
---|---|---|---|---|---|---|---|
C1 | (1,1,1,1) | (1, 1.5, 2.5, 3) | (2, 2.5, 3.5, 4) | (1,1,1,1) | (2, 2.5, 3.5, 4) | (3, 3.5, 4.5, 5) | (5, 5.5, 6.5, 7) |
C2 | (0.333, 0.4, 0.667, 1) | (1,1,1,1) | (1, 1.5, 2.5, 3) | (0.333, 0.4, 0.667, 1) | (1, 1.5, 2.5, 3) | (2, 2.5, 3.5, 4) | (4, 4.5, 5.5, 6) |
C3 | (0.25, 0.286, 0.4, 0.5) | (0.333, 0.4, 0.667, 1) | (1,1,1,1) | (0.25, 0.286, 0.4, 0.5) | (1,1,1,1) | (1, 1.5, 2.5, 3) | (3, 3.5, 4.5, 5) |
C4 | (1,1,1,1) | (1, 1.5, 2.5, 3) | (2, 2.5, 3.5, 4) | (1,1,1,1) | (2, 2.5, 3.5, 4) | (3, 3.5, 4.5, 5) | (5, 5.5, 6.5, 7) |
C5 | (0.25, 0.286, 0.4, 0.5) | (0.333, 0.4, 0.667, 1) | (1,1,1,1) | (0.25, 0.286, 0.4, 0.5) | (1,1,1,1) | (1, 1.5, 2.5, 3) | (3, 3.5, 4.5, 5) |
C6 | (0.2, 0.222, 0.286, 0.333) | (0.25, 0.286, 0.4, 0.5) | (0.333, 0.4, 0.667, 1) | (0.2, 0.222, 0.286, 0.333) | (0.333, 0.4, 0.667, 1) | (1,1,1,1) | (2, 2.5, 3.5, 4) |
C7 | (0.143, 0.154, 0.182, 0.2) | (0.167, 0.182, 0.222, 0.25) | (0.2, 0.222, 0.286, 0.333) | (0.143, 0.154, 0.182, 0.2) | (0.2, 0.222, 0.286, 0.333) | (0.25, 0.286, 0.4, 0.5) | (1,1,1,1) |
Criteria | E1 | E2 | E3 | Aggregated | Normalized |
---|---|---|---|---|---|
C1 | 0.1780 | 0.1888 | 0.1835 | 0.1834 | 0.1862 |
C2 | 0.1780 | 0.1384 | 0.1835 | 0.1654 | 0.1679 |
C3 | 0.1566 | 0.1762 | 0.1476 | 0.1597 | 0.1622 |
C4 | 0.1780 | 0.1888 | 0.1835 | 0.1834 | 0.1862 |
C5 | 0.1566 | 0.1762 | 0.1476 | 0.1597 | 0.1622 |
C6 | 0.1186 | 0.0404 | 0.1042 | 0.0794 | 0.0806 |
C7 | 0.0344 | 0.0910 | 0.0500 | 0.0539 | 0.0547 |
C1 | C2 | C3 | C4 | C5 | C6 | C7 |
---|---|---|---|---|---|---|
0.3607 | 0.7021 | 0.9167 | 1.0000 | 0.6857 | 0.9505 | 0.0119 |
0.1747 | 0.7160 | 0.8750 | 1.0000 | 0.3799 | 1.0000 | 0.0008 |
0.6576 | 0.5979 | 0.5833 | 1.0000 | 0.8415 | 0.9769 | 0.0867 |
0.3444 | 0.5638 | 0.7500 | 0.6667 | 0.7045 | 0.8360 | 0.0408 |
0.2682 | 0.2340 | 1.0000 | 1.0000 | 0.8546 | 0.7618 | 0.0000 |
0.3043 | 0.1809 | 0.7500 | 0.6667 | 0.0000 | 0.9597 | 0.0472 |
0.4988 | 0.6809 | 0.9167 | 0.6667 | 0.9353 | 0.7973 | 0.1050 |
0.3167 | 0.0000 | 0.0000 | 0.6667 | 1.0000 | 0.4495 | 0.2981 |
0.4265 | 0.0532 | 0.8333 | 0.0000 | 0.8321 | 0.9839 | 0.6740 |
0.5453 | 0.0957 | 0.6667 | 0.3333 | 0.4859 | 0.9419 | 0.0245 |
0.3528 | 0.1489 | 0.6667 | 0.3333 | 0.9203 | 0.8957 | 0.2923 |
0.6813 | 0.1702 | 0.6667 | 0.6667 | 0.8396 | 0.9366 | 1.0000 |
0.5002 | 1.0000 | 0.6667 | 0.6667 | 0.9700 | 0.0000 | 0.0271 |
0.0000 | 0.0053 | 0.6667 | 0.0000 | 0.3443 | 0.9419 | 0.0014 |
1.0000 | 0.5000 | 0.6667 | 0.6667 | 0.7364 | 0.2452 | 0.0387 |
C1 | C2 | C3 | C4 | C5 | C6 | C7 |
---|---|---|---|---|---|---|
0.6393 | 0.2979 | 0.0833 | 0.0000 | 0.3143 | 0.0495 | 0.9881 |
0.8253 | 0.2840 | 0.1250 | 0.0000 | 0.6201 | 0.0000 | 0.9992 |
0.3424 | 0.4021 | 0.4167 | 0.0000 | 0.1585 | 0.0231 | 0.9133 |
0.6556 | 0.4362 | 0.2500 | 0.3333 | 0.2955 | 0.1640 | 0.9592 |
0.7318 | 0.7660 | 0.0000 | 0.0000 | 0.1454 | 0.2382 | 1.0000 |
0.6957 | 0.8191 | 0.2500 | 0.3333 | 1.0000 | 0.0403 | 0.9528 |
0.5012 | 0.3191 | 0.0833 | 0.3333 | 0.0647 | 0.2027 | 0.8950 |
0.6833 | 1.0000 | 1.0000 | 0.3333 | 0.0000 | 0.5505 | 0.7019 |
0.5735 | 0.9468 | 0.1667 | 1.0000 | 0.1679 | 0.0161 | 0.3260 |
0.4547 | 0.9043 | 0.3333 | 0.6667 | 0.5141 | 0.0581 | 0.9755 |
0.6472 | 0.8511 | 0.3333 | 0.6667 | 0.0797 | 0.1043 | 0.7077 |
0.3187 | 0.8298 | 0.3333 | 0.3333 | 0.1604 | 0.0634 | 0.0000 |
0.4998 | 0.0000 | 0.3333 | 0.3333 | 0.0300 | 1.0000 | 0.9729 |
1.0000 | 0.9947 | 0.3333 | 1.0000 | 0.6557 | 0.0581 | 0.9986 |
0.0000 | 0.5000 | 0.3333 | 0.3333 | 0.2636 | 0.7548 | 0.9613 |
C1 | C2 | C3 | C4 | C5 | C6 | C7 |
---|---|---|---|---|---|---|
0.4389 | 0.6267 | 0.8571 | 1.0000 | 0.6141 | 0.9100 | 0.3360 |
0.3773 | 0.6377 | 0.8000 | 1.0000 | 0.4464 | 1.0000 | 0.3335 |
0.5935 | 0.5542 | 0.5455 | 1.0000 | 0.7593 | 0.9558 | 0.3538 |
0.4327 | 0.5341 | 0.6667 | 0.6000 | 0.6285 | 0.7530 | 0.3426 |
0.4059 | 0.3950 | 1.0000 | 1.0000 | 0.7747 | 0.6773 | 0.3333 |
0.4182 | 0.3790 | 0.6667 | 0.6000 | 0.3333 | 0.9254 | 0.3442 |
0.4994 | 0.6104 | 0.8571 | 0.6000 | 0.8854 | 0.7116 | 0.3584 |
0.4225 | 0.3333 | 0.3333 | 0.6000 | 1.0000 | 0.4759 | 0.4160 |
0.4658 | 0.3456 | 0.7500 | 0.3333 | 0.7486 | 0.9688 | 0.6054 |
0.5237 | 0.3561 | 0.6000 | 0.4286 | 0.4931 | 0.8960 | 0.3389 |
0.4358 | 0.3701 | 0.6000 | 0.4286 | 0.8625 | 0.8274 | 0.4140 |
0.6108 | 0.3760 | 0.6000 | 0.6000 | 0.7571 | 0.8874 | 1.0000 |
0.5001 | 1.0000 | 0.6000 | 0.6000 | 0.9434 | 0.3333 | 0.3395 |
0.3333 | 0.3345 | 0.6000 | 0.3333 | 0.4326 | 0.8960 | 0.3336 |
1.0000 | 0.5000 | 0.6000 | 0.6000 | 0.6548 | 0.3985 | 0.3422 |
Cities | C1 | C2 | C3 | C4 | C5 | C6 | C7 | Sum | Rank |
---|---|---|---|---|---|---|---|---|---|
Arar | 0.0817 | 0.1052 | 0.1390 | 0.1862 | 0.0996 | 0.0733 | 0.0184 | 0.7035 | 1 |
Al-Jouf | 0.0703 | 0.1071 | 0.1297 | 0.1862 | 0.0724 | 0.0806 | 0.0183 | 0.6645 | 6 |
Tabuk | 0.1105 | 0.0931 | 0.0884 | 0.1862 | 0.1231 | 0.0770 | 0.0194 | 0.6978 | 2 |
Hail | 0.0806 | 0.0897 | 0.1081 | 0.1117 | 0.1019 | 0.0607 | 0.0188 | 0.5715 | 9 |
Dhahran | 0.0756 | 0.0663 | 0.1622 | 0.1862 | 0.1256 | 0.0546 | 0.0182 | 0.6887 | 3 |
Al-Ahsa | 0.0779 | 0.0636 | 0.1081 | 0.1117 | 0.0541 | 0.0746 | 0.0188 | 0.5088 | 13 |
Taif | 0.0930 | 0.1025 | 0.1390 | 0.1117 | 0.1436 | 0.0573 | 0.0196 | 0.6668 | 5 |
Makkah | 0.0787 | 0.0560 | 0.0541 | 0.1117 | 0.1622 | 0.0384 | 0.0228 | 0.5237 | 12 |
Jeddah | 0.0867 | 0.0580 | 0.1216 | 0.0621 | 0.1214 | 0.0781 | 0.0331 | 0.5611 | 10 |
Yanbu | 0.0975 | 0.0598 | 0.0973 | 0.0798 | 0.0800 | 0.0722 | 0.0185 | 0.5051 | 14 |
Medina | 0.0812 | 0.0621 | 0.0973 | 0.0798 | 0.1399 | 0.0667 | 0.0227 | 0.5496 | 11 |
Riyadh | 0.1137 | 0.0631 | 0.0973 | 0.1117 | 0.1228 | 0.0715 | 0.0547 | 0.6349 | 8 |
Abha | 0.0931 | 0.1679 | 0.0973 | 0.1117 | 0.1530 | 0.0269 | 0.0186 | 0.6685 | 4 |
Jizan | 0.0621 | 0.0562 | 0.0973 | 0.0621 | 0.0702 | 0.0722 | 0.0183 | 0.4382 | 15 |
Najran | 0.1862 | 0.0840 | 0.0973 | 0.1117 | 0.1062 | 0.0321 | 0.0187 | 0.6362 | 7 |
Cities | Criteria | ||||||
---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C4 | C5 | C6 | C7 | |
Arar | 0.8067 | 1.1458 | 0.9333 | 1.0000 | 14.4000 | 2.1220 | 0.0353 |
Al-Jouf | 0.7504 | 1.1391 | 0.9000 | 1.0000 | 27.4400 | 1.0000 | 0.0245 |
Tabuk | 0.8965 | 1.1969 | 0.6667 | 1.0000 | 7.7600 | 1.5244 | 0.1083 |
Hail | 0.8018 | 1.2135 | 0.8000 | 0.9992 | 13.6000 | 4.7195 | 0.0635 |
Dhahran | 0.7787 | 1.3750 | 1.0000 | 1.0000 | 7.2000 | 6.4024 | 0.0237 |
Al-Ahsa | 0.7896 | 1.4010 | 0.8000 | 0.9992 | 43.6400 | 1.9146 | 0.0697 |
Taif | 0.8484 | 1.1563 | 0.9333 | 0.9992 | 3.7600 | 5.5976 | 0.1262 |
Makkah | 0.7934 | 1.4896 | 0.2000 | 0.9992 | 1.0000 | 13.4878 | 0.3147 |
Jeddah | 0.8266 | 1.4635 | 0.8667 | 0.9975 | 8.1600 | 1.3659 | 0.6818 |
Yanbu | 0.8625 | 1.4427 | 0.7333 | 0.9984 | 22.9200 | 2.3171 | 0.0476 |
Medina | 0.8043 | 1.4167 | 0.7333 | 0.9984 | 4.4000 | 3.3659 | 0.3091 |
Riyadh | 0.9037 | 1.4063 | 0.7333 | 0.9992 | 7.8400 | 2.4390 | 1.0000 |
Abha | 0.8489 | 1.0000 | 0.7333 | 0.9992 | 2.2800 | 23.6829 | 0.0501 |
Jizan | 0.6976 | 1.4870 | 0.7333 | 0.9975 | 28.9600 | 2.3171 | 0.0250 |
Najran | 1.0000 | 1.2448 | 0.7333 | 0.9992 | 12.2400 | 18.1220 | 0.0615 |
Criteria | C1 | C2 | C3 | C4 | C5 | C6 | C7 |
---|---|---|---|---|---|---|---|
Hj | 0.9987 | 0.9975 | 0.9873 | 1.0000 | 0.8778 | 0.8237 | 0.7382 |
m | 15 | ||||||
ln m | 2.7081 | ||||||
1 − Hj | 0.0013 | 0.0025 | 0.0127 | 0.0000 | 0.1222 | 0.1763 | 0.2618 |
n − ∑ Hj | 0.5767 | ||||||
wj | 0.0022 | 0.0043 | 0.0219 | 0.0000 | 0.2118 | 0.3057 | 0.4540 |
1 − wj | 0.9978 | 0.9957 | 0.9781 | 1.0000 | 0.7882 | 0.6943 | 0.5460 |
Normalized wj | 0.1663 | 0.1659 | 0.1630 | 0.1667 | 0.1314 | 0.1157 | 0.0910 |
MCDM Approach | Ideal Location |
---|---|
GEM-VIKOR | Tabuk |
FAHP-VIKOR | Tabuk |
Entropy-VIKOR | Tabuk or Taif |
GEM-GRA | Tabuk |
FAHP-GRA | Arar (Tabuk is second-ranked) |
Entropy-GRA | Arar (Tabuk is second-ranked) |
MCDM Technique | GEM-VIKOR | FAHP-VIKOR | Entropy-VIKOR | GEM-GRA | FAHP-GRA | Entropy-GRA |
---|---|---|---|---|---|---|
W | 0.9598 | 0.9759 | 0.9694 | 0.9752 | 0.9821 | 0.9841 |
Technique | Combination | Ideal Alternative | Benefits | Limitations | Difficulty | Problem Size | |
---|---|---|---|---|---|---|---|
Weights | Ranking | ||||||
GEM-VIKOR | GEM | VIKOR | Tabuk | Higher decision reliability. Precise and consistent evaluation. Suitable for medium-scale problems. | Generation of the judgment matrix is relatively difficult, i.e., shortlisting experts and collecting precise information from them is a hectic task. | 6 | Medium-sized |
FAHP-VIKOR | FAHP | VIKOR | Tabuk | Higher precision in small data problems. Checks inconsistency through the consistency index. Utilizes inherent information of criteria. | Large-sized problems can be demanding. Rank reversal problem—the final ranking can be reversed with the addition or elimination of an alternative. Geometric aggregation approach is used, so there is a possibility that some information may be lost. | 8 | Small-sized |
Entropy-VIKOR | Entropy | VIKOR | Tabuk or Taif | Unbiased results. Capable of handling multiple inputs and outputs. Flexible to fit small and medium-sized problems. | Sensitive to inconsistent data. | 5 | Large -sized |
GEM-GRA | GEM | GRA | Tabuk | Straightforward and uncomplicated method. Require precise information. Suitable for medium and small-sized problems. | Generation of judgement matrix is relatively difficult. Can be difficult for large-sized problems. | 5 | Medium-sized |
FAHP-GRA | FAHP | GRA | Arar (Tabuk is second-ranked) | Takes into account uncertainty and vagueness. Checks inconsistency through consistency index. Full use of inherent information of criteria. Suitable for small-sized problems. | Complicated and computationally exhaustive even for medium-sized problems. Possibility of rank reversal. | 6 | Small-sized |
Entropy-GRA | Entropy | GRA | Arar (Tabuk is second-ranked) | Suitable for large-sized problems. Simple and easy to use. Easy to understand. Number of steps remains the same regardless of the number of criteria. | Consistency is not controlled. Results may differ from other methods. | 4 | Large-sized |
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Mian, S.H.; Moiduddin, K.; Alkhalefah, H.; Abidi, M.H.; Ahmed, F.; Hashmi, F.H. Mechanisms for Choosing PV Locations That Allow for the Most Sustainable Usage of Solar Energy. Sustainability 2023, 15, 3284. https://doi.org/10.3390/su15043284
Mian SH, Moiduddin K, Alkhalefah H, Abidi MH, Ahmed F, Hashmi FH. Mechanisms for Choosing PV Locations That Allow for the Most Sustainable Usage of Solar Energy. Sustainability. 2023; 15(4):3284. https://doi.org/10.3390/su15043284
Chicago/Turabian StyleMian, Syed Hammad, Khaja Moiduddin, Hisham Alkhalefah, Mustufa Haider Abidi, Faraz Ahmed, and Faraz Hussain Hashmi. 2023. "Mechanisms for Choosing PV Locations That Allow for the Most Sustainable Usage of Solar Energy" Sustainability 15, no. 4: 3284. https://doi.org/10.3390/su15043284