Solving Optimal Power Flow Using New Efficient Hybrid Jellyfish Search and Moth Flame Optimization Algorithms
<p>Flowchart of the JS-MFO algorithm.</p> "> Figure 2
<p>IEEE 30-bus single-line diagram.</p> "> Figure 3
<p>Convergence curves of JS, MFO and JS-MFO algorithms for case 1.</p> "> Figure 4
<p>Convergence rates of JS, MFO, and JS-MFO algorithms for case 2.</p> "> Figure 5
<p>Convergence rates of JS, MFO, and JS-MFO algorithms for case 3.</p> "> Figure 6
<p>Convergence rates of JS, MFO, and JS-MFO for Case 4.</p> "> Figure 7
<p>Convergence curves of JS, MFO, and JS-MFO algorithms for case 7.</p> "> Figure 8
<p>Single-line diagram of the Mauritanian electric power system 27 bus.</p> "> Figure 9
<p>Convergence characteristics of JS, MFO, and JS-MFO algorithms for case 4.</p> "> Figure 10
<p>Convergence characteristics of JS, MFO, and JS-MFO algorithms for case 5.</p> "> Figure 11
<p>Voltage profile for each RIM 27-bus case using the JS-MFO algorithm.</p> ">
Abstract
:1. Introduction
- Providing a hybrid JS-MFO algorithm to associate the advantages of both the JS optimizer in exploration and MFO in exploitation.
- The effectiveness of the proposed hybrid approach has been investigated by solving various cases related to the OPF problem.
- Applications were carried out on two test systems, the IEEE 30-bus and the Mauritanian RIM 27-bus electric power systems, to verify the JS-MFO’s performance.
2. Optimal Power Flow Problem
3. Mathematical Representation of the Optimization Technique
- Two types of jellyfish movement can be handled by the time control mechanism: moving in the jellyfish swarm or following the ocean current.
- When searching for food sources in the ocean, jellyfish move in an attractive manner towards the best locations of nutrients.
- The quantity of food found by jellyfish and its location correspond to the objective function of the problem and the corresponding solution, respectively.
4. Simulation Results and Discussion
4.1. Performance Evaluation of JS-MFO for Benchmark Functions
4.2. Implementation of JS-MFO for Solving OPF Problems
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
PG1 | Generated active power of slack bus |
PGi | Generated active power of i-th bus |
VLi | Voltage magnitude of load bus i |
QGi | Reactive power output of generator i |
PGi,min | Lower active generation capacity in i-th bus |
PGi,max | Upper active generation capacity in i-th bus |
PDi | Active power of load demand on bus i |
QDi | Reactive power of load demand on bus i |
Ng | Number of generators (power plants) |
NPQ | Number of load buses (PQ buses) |
SLi | Apparent power in transmission line i |
Vi, Vj | Voltage magnitudes at node i and node j, respectively |
SLi,min | Lower limit of apparent power in transmission line i |
SLi,max | Upper limit of apparent power in transmission line i |
VLi,min | Lower limit of voltage magnitude in load bus i |
VLi,max | Upper limit of voltage magnitude in load bus i |
QGi,min | Lower reactive generation capacity in i-th bus |
QGi,max | Upper reactive generation capacity in i-th bus |
VGi | Voltage magnitude of generator connected to bus i |
Qci | Reactive power injected by shunt VAR compensator in i-th bus |
VGi,min | Minimum voltage magnitude of generator connected to bus i |
VGi,max | Maximum voltage magnitude of generator connected to bus i |
δi, δj | Voltage angles of buses i and j, respectively |
δij | Difference angle between voltage angles δi and δj, respectively |
Bij | Susceptance of the transmission line between buses i and j (imaginary part of the admittance) |
Gij | Conductance of the transmission line between buses i and j (real part of the admittance) |
Nt | Number of regulating transformers |
NB | Number of buses |
Nl | Number of the transmission lines |
NC | Number of shunt compensators |
NPV | Number of generator buses (PV buses) |
Ti | Tap setting of i-th transformer |
Ti,min | Lower tap setting of i-th transformer |
Ti,max | Upper tap setting of i-th transformer |
PG1 | Generated active power of slack bus |
Ng | Number of generator buses |
VLj | Voltage magnitude of load bus j |
NPQ | Number of load buses (PQ buses) |
QGi | Reactive power output of generator i |
QDi | Active power of load demand on bus i |
SLi | Apparent power in transmission line i |
Vi, Vj | Voltage magnitudes at node i and node j, respectively |
PGi | Active power output of generator i |
PDi | Active power of load demand on bus i |
VGi | Voltage magnitude of generator connected to bus i |
Qci | Reactive power injected by shunt VAR compensator in i-th bus |
Bij | Susceptance of the transmission line between buses i and j (imaginary part of the admittance) |
Gij | Conductance of the transmission line between buses i and j (real part of the admittance) |
NT | Number of regulating transformers |
NB | Number of buses |
Ti | Tap setting of transformer i |
NC | Number of shunt compensators |
NPV | Number of generator buses (PV buses) |
Nl | Number of the transmission lines |
δij | Difference angle between voltage anglesδi and δj, respectively |
δi,δj | Voltage angles of buses i and j, respectively |
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Fun | Equation | B | Min | D | T |
---|---|---|---|---|---|
[−100, 100] | 0 | 30 | Unimodal | ||
[−10, 10] | 0 | 30 | Unimodal | ||
[−30, 30] | 0 | 30 | Unimodal | ||
[−10, 10] | 0 | 30 | Unimodal | ||
[−32, 32] | 0 | 30 | Multimodal | ||
[−5.12, 5.12] | 0 | 30 | Multimodal | ||
[−50, 50] | 0 | 30 | Multimodal | ||
[−50, 50] | 0 | 30 | Multimodal |
Algorithm | Index | Unimodal Functions | Multimodal Functions | ||||||
---|---|---|---|---|---|---|---|---|---|
JS | Mean | 2.00 × 10−18 | 2.03 × 10−19 | 0.7100 | 2.67 × 10−10 | 3.49 × 10−10 | 12.585 | 8.68 × 10−5 | 0.0098 |
SD | 2.84 × 10−18 | 2.68 × 10−19 | 0.8835 | 2.65 × 10−10 | 1.49 × 10−10 | 9.0885 | 1.94 × 10−4 | 0.0368 | |
Best | 9.14 × 10−20 | 1.57 × 10−20 | 0.0179 | 3.97 × 10−11 | 1.50 × 10−10 | 3.0574 | 1.36 × 10−6 | 1.57 × 10−5 | |
Time (s) | 1.2488 | 1.2332 | 1.0741 | 1.3384 | 1.4780 | 1.4203 | 2.4955 | 2.7288 | |
MFO | Mean | 2.67 × 103 | 383.527 | 1.88 × 104 | 32.0936 | 11.1412 | 139.56 | 4.5098 | 1.36 × 107 |
SD | 5.20 × 103 | 505.098 | 3.64 × 104 | 20.3943 | 8.7387 | 27.52 | 2.8850 | 7.48 × 107 | |
Best | 0.3104 | 0.0524 | 178.5437 | 0.1066 | 0.1323 | 77.67 | 0.4706 | 0.2722 | |
Time (s) | 0.7218 | 0.7127 | 0.8212 | 0.8202 | 1.2363 | 0.9198 | 2.0499 | 2.2922 | |
JS-MFO | Mean | 6.53 × 10−83 | 4.94 × 10−60 | 0.0520 | 2.59 × 10−39 | 3.13 × 10−15 | 3.89 × 10−13 | 5.08 × 10−29 | 2.41 × 10−25 |
SD | 3.43 × 10−82 | 1.79 × 10−59 | 0.1296 | 1.40 × 10−38 | 1.74 × 10−15 | 1.98 × 10−12 | 1.88 × 10−28 | 1.31 × 10−24 | |
Best | 2.38 × 10−89 | 1.19 × 10−72 | 1.00 × 10−8 | 1.25 × 10−46 | 8.88 × 10−16 | 0 | 3.63 × 10−32 | 1.62 × 10−32 | |
Time (s) | 1.7842 | 1.7561 | 1.9401 | 1.9434 | 2.6328 | 2.0638 | 4.1697 | 4.6286 |
Study Case | Index | Method | ||
---|---|---|---|---|
JSO | MFO | JS-MFO | ||
Case 1 Quadratic total fuel cost (USD/h) | Minimum | 801.023 | 800.79 | 799.08 |
Average | 801.84 | 801.92 | 799.09 | |
Maximum | 803.41 | 802.87 | 799.14 | |
SD | 0.781 | 1.040 | 0.0133 | |
Case 3 Total fuel cost with valve point effect (USD/h) | Minimum | 929.48 | 924.02 | 918.07 |
Average | 943.60 | 929.06 | 925.61 | |
Maximum | 959.14 | 984.18 | 952.54 | |
SD | 12.07 | 13.59 | 12.05 | |
Case 4 Total active losses (MW) | Minimum | 3.232 | 3.049 | 2.881 |
Average | 3.189 | 3.443 | 2.909 | |
Maximum | 3.266 | 3.75 | 3.095 | |
SD | 0.053 | 0.2147 | 0.033 |
Control Variables/Objectives | Case 1 | Case 2 | Case 3 | ||||||
---|---|---|---|---|---|---|---|---|---|
JS | MFO | JS-MFO | JS | MFO | JS-MFO | JS | MFO | JS-MFO | |
PG1(MW) | 177.68 | 178.13 | 177.15 | 64.529 | 63.804 | 63.921 | 199.60 | 199.60 | 199.589 |
PG2(MW) | 48.689 | 49.146 | 48.727 | 67.393 | 67.79 | 67.490 | 20.144 | 20.000 | 20.002 |
PG5(MW) | 21.448 | 21.824 | 21.329 | 49.958 | 50.00 | 49.999 | 19.625 | 22.290 | 22.027 |
PG8(MW) | 19.436 | 19.307 | 20.897 | 34.974 | 34.99 | 34.999 | 24.920 | 27.904 | 23.029 |
PG11(MW) | 13.069 | 11.740 | 11.924 | 29.983 | 30.00 | 29.999 | 15.038 | 10.003 | 14.982 |
PG13(MW) | 12.276 | 12.426 | 12.005 | 39.993 | 40.00 | 39.999 | 14.528 | 14.576 | 13.192 |
VG1(p.u) | 1.0804 | 1.1000 | 1.1000 | 1.0600 | 1.059 | 1.099 | 1.0660 | 1.023 | 1.097 |
VG2(p.u) | 1.0607 | 1.0811 | 1.0876 | 1.0551 | 1.054 | 1.095 | 1.0352 | 0.999 | 1.076 |
VG5(p.u) | 1.0268 | 1.0491 | 1.0605 | 1.0198 | 1.035 | 1.076 | 0.9867 | 0.950 | 1.043 |
VG8(p.u) | 1.0353 | 1.0503 | 1.0684 | 1.0406 | 1.047 | 1.083 | 1.0032 | 0.966 | 1.058 |
VG11(p.u) | 1.0669 | 1.0363 | 1.1000 | 1.0613 | 1.100 | 1.097 | 1.0606 | 1.099 | 1.096 |
VG13(p.u) | 1.0633 | 0.9500 | 1.0991 | 1.0418 | 1.100 | 1.099 | 0.9937 | 1.087 | 1.098 |
T11(6_9) | 1.0092 | 1.0919 | 1.0666 | 0.9850 | 1.019 | 1.050 | 1.0399 | 0.921 | 0.988 |
T12(6_10) | 0.9600 | 1.0405 | 0.9061 | 1.0259 | 0.901 | 0.914 | 0.9871 | 0.985 | 1.022 |
T15(4_12) | 1.0236 | 1.0600 | 1.0099 | 1.0353 | 0.972 | 0.991 | 1.0016 | 1.082 | 1.031 |
T36(28_27) | 1.0080 | 1.0745 | 0.9748 | 0.9918 | 0.950 | 0.972 | 0.9932 | 0.931 | 0.968 |
QC10(MVar) | 3.6054 | 5.0000 | 4.9914 | 1.8390 | 3.675 | 4.984 | 1.6452 | 0 | 2.657 |
QC12(MVar) | 3.8140 | 3.4313 | 4.9341 | 3.6168 | 0 | 4.739 | 1.9352 | 0.017 | 3.497 |
QC15(MVar) | 2.0583 | 4.9744 | 4.9263 | 3.5515 | 5.0000 | 4.764 | 2.1570 | 0 | 1.655 |
QC17(MVar) | 2.7145 | 0 | 4.9544 | 1.8804 | 4.716 | 4.900 | 1.5654 | 0.137 | 2.442 |
QC20(MVar) | 2.8758 | 4.9988 | 4.8532 | 2.7821 | 2.839 | 4.906 | 3.1875 | 4.931 | 4.492 |
QC21(MVar) | 2.5908 | 4.7493 | 4.9983 | 3.8469 | 4.999 | 4.963 | 2.8867 | 5.00 | 1.828 |
QC23(MVar) | 2.3790 | 4.9460 | 4.0653 | 3.8902 | 1.710 | 4.369 | 4.2100 | 4.193 | 3.439 |
QC24(MVar) | 2.9189 | 5.0000 | 4.9839 | 2.9350 | 5.000 | 4.7945 | 3.4187 | 3.224 | 2.184 |
QC29(MVar) | 1.7836 | 5.0000 | 3.2182 | 3.7881 | 3.714 | 2.9024 | 4.0090 | 0.043 | 3.073 |
($/h) | 801.02 | 800.79 | 799.085 | 944.30 | 944.6 | 943.690 | 922.48 | 924.02 | 918.07 |
(ton/h) | 0.3673 | 0.3689 | 0.3663 | 0.2049 | 0.2048 | 0.2047 | 0.4395 | 0.4403 | 0.439 |
(MW) | 9.2026 | 9.179 | 8.6368 | 3.4324 | 3.195 | 3.0095 | 10.466 | 10.975 | 9.424 |
(p.u) | 0.532 | 0.9889 | 1.6486 | 0.3994 | 1.486 | 1.9257 | 0.4706 | 0.329 | 1.195 |
0.1383 | 0.1145 | 0.1182 | 0.1339 | 0.120 | 0.1158 | 0.1433 | 0.1431 | 0.124 |
Control Variables and Objectives | Case 4 | Case 7 | Case 8 | ||||||
---|---|---|---|---|---|---|---|---|---|
JS | MFO | JS-MFO | JS | MFO | JS-MFO | JS | MFO | JS-MFO | |
PG1(MW) | 63.591 | 51.483 | 51.349 | 178.73 | 177.89 | 176.174 | 174.09 | 179.01 | 177.466 |
PG2(MW) | 68.150 | 80.00 | 79.988 | 48.711 | 48.76 | 48.826 | 48.904 | 49.483 | 48.746 |
PG5(MW) | 49.993 | 50.00 | 49.997 | 22.006 | 21.03 | 21.970 | 21.632 | 22.102 | 21.785 |
PG8(MW) | 34.962 | 35.00 | 34.950 | 18.213 | 21.49 | 21.356 | 22.195 | 16.766 | 20.639 |
PG11(MW) | 29.969 | 29.965 | 29.998 | 12.433 | 12.239 | 12.722 | 13.182 | 11.959 | 11.458 |
PG13(MW) | 39.965 | 39.999 | 39.997 | 13.246 | 12.008 | 12.133 | 12.351 | 13.317 | 12.015 |
VG1(p.u) | 1.087 | 1.064 | 1.099 | 1.0497 | 1.033 | 1.044 | 1.086 | 1.092 | 1.100 |
VG2(p.u) | 1.076 | 1.056 | 1.096 | 1.0429 | 1.009 | 1.026 | 1.066 | 1.07 | 1.084 |
VG5(p.u) | 1.055 | 1.039 | 1.077 | 1.0134 | 0.996 | 1.010 | 1.023 | 1.024 | 1.053 |
VG8(p.u) | 1.070 | 1.045 | 1.084 | 1.0000 | 1.004 | 1.0065 | 1.045 | 1.044 | 1.058 |
VG11(p.u) | 1.069 | 1.0993 | 1.100 | 1.0038 | 1.073 | 1.0575 | 1.083 | 1.100 | 1.099 |
VG13(p.u) | 1.081 | 1.0994 | 1.099 | 1.0446 | 1.0187 | 0.9899 | 1.078 | 1.093 | 1.097 |
T11(6_9) | 0.976 | 0.9735 | 1.072 | 1.0780 | 1.1000 | 1.0779 | 1.078 | 0.940 | 0.990 |
T12(6_10) | 1.025 | 0.9323 | 0.900 | 1.0690 | 0.9110 | 0.9010 | 1.069 | 0.900 | 0.933 |
T15(4_12) | 0.996 | 0.9693 | 0.999 | 1.0320 | 0.9987 | 0.9416 | 1.032 | 0.953 | 0.969 |
T36(28_27) | 0.988 | 0.9448 | 0.978 | 1.0680 | 0.9615 | 0.9671 | 1.068 | 0.921 | 0.948 |
QC10(MVar) | 3.388 | 3.7029 | 4.870 | 2.9344 | 5.000 | 4.1739 | 4.119 | 4.989 | 4.979 |
QC12(MVar) | 3.112 | 5.0000 | 4.984 | 0.6209 | 0.468 | 0.3890 | 3.651 | 4.995 | 4.999 |
QC15(MVar) | 3.713 | 5.0000 | 4.946 | 4.7753 | 5.000 | 4.9032 | 4.494 | 5.000 | 4.983 |
QC17(MVar) | 3.072 | 5.0000 | 4.964 | 2.8538 | 5.000 | 0.0844 | 3.350 | 4.660 | 4.648 |
QC20(MVar) | 2.838 | 3.9215 | 4.815 | 4.4568 | 4.781 | 4.9859 | 2.208 | 5.000 | 4.552 |
QC21(MVar) | 2.560 | 4.0782 | 4.810 | 2.5250 | 5.000 | 4.9713 | 3.417 | 1.153 | 4.985 |
QC23(MVar) | 2.860 | 3.435 | 3.893 | 3.8349 | 5.000 | 4.9970 | 4.128 | 4.899 | 4.800 |
QC24(MVar) | 3.114 | 4.742 | 4.977 | 4.0013 | 4.901 | 4.9836 | 3.787 | 4.964 | 4.897 |
QC29(MVar) | 2.915 | 3.915 | 2.865 | 2.7291 | 1.756 | 2.3740 | 4.334 | 0 | 4.680 |
($/h) | 945.10 | 967.46 | 967.02 | 803.57 | 803.93 | 803.554 | 801.16 | 800.96 | 799.318 |
(ton/h) | 0.2048 | 0.207 | 0.207 | 0.3700 | 0.3681 | 0.3631 | 0.357 | 0.3712 | 0.367 |
(MW) | 3.232 | 3.049 | 2.881 | 9.9491 | 10.043 | 9.7845 | 8.958 | 9.244 | 8.711 |
(p.u) | 1.174 | 1.639 | 1.8806 | 0.1480 | 0.1136 | 0.0993 | 1.282 | 1.872 | 1.8981 |
0.126 | 0.118 | 0.1166 | 0.1371 | 0.1361 | 0.1370 | 0.117 | 0.1182 | 0.1141 |
Technique | Total Fuel Cost (USD/h) | Technique | Total Fuel Cost (USD/h) |
---|---|---|---|
JS-MFO | 799.085 | DA [13] | 802.316 |
JS | 801.02 | AGTLBO [14] | 800.481 |
MFO | 800.79 | PSO-PS [21] | 799.8723 |
NISSO [35] | 799.762 | DA-PSO [23] | 802.124 |
FFA [15] | 802.130 | HF-PSO [24] | 799.123 |
MSA [15] | 802.223 | HF-ABC [26] | 800.212 |
ESCA [36] | 800.219 | HFA-JAYA [27] | 800.480 |
SOS [35] | 801.5733 | ||
HHO [16] | 801.829 |
Technique | Total Gas Emissions (ton/h) | Technique | Total Gas Emissions (ton/h) |
---|---|---|---|
JS-MFO | 0.2047 | AGTLBO [14] | 0.2048 |
JS | 0.2049 | SSO [35] | 0.2315 |
MFO | 0.2048 | NISSO [35] | 0.2048 |
HHO [16] | 0.2850 | SSA [37] | 0.205 |
TFWO [17] | 0.2050 | PSO-SSA [37] | 0.205 |
DA-PSO [23] | 0.2048 |
Technique | Total Fuel Cost (USD/h) | Technique | Total Fuel Cost (USD/h) |
---|---|---|---|
JS-MFO | 918.093 | TLBO [39] | 919.394 |
JS | 922.48 | Gbest-ABC [40] | 931.745 |
MFO | 924.02 | GABC1 [41] | 919.597 |
ISSA [38] | 919.191 | GABC2 [41] | 918.435 |
SSA [38] | 920.706 | ||
IHS [38] | 919.843 |
Technique | Total Transmission Losses (MW) | Technique | Total Transmission Losses (MW) |
---|---|---|---|
JS-MFO | 2.881 | DA [23] | 3.198 |
JS | 3.232 | DA-PSO [23] | 3.189 |
MFO | 3.049 | HFA-JAYA [27] | 4.529 |
AGTLBO [14] | 3.090 | SS0 [35] | 3.911 |
FFA [15] | 3.643 | NISSO [35] | 2.945 |
MSA [15] | 3.649 | ESCA [36] | 3.021 |
DE-HS [22] | 3.054 | AMTPG-JAYA [42] | 3.080 |
Technique | Total Fuel Cost FC (USD/h) | Total Voltage Deviation FVD (p.u) |
---|---|---|
JS-MFO | 803.5549 | 0.0993 |
JS | 803.5727 | 0.1480 |
MFO | 803.93 | 0.1136 |
AGTLBO [14] | 803.738 | 0.0947 |
DA-PSO [23] | 803.66 | 0.1163 |
HFA-JAYA [27] | 803.7036 | 0.0948 |
ESCA [36] | 804.9968 | 0.09163 |
PSO-SSA [37] | 803.989 | 0.0940 |
MVO [43] | 803.908 | 0.1056 |
ECHT-DE [44] | 803.719 | 0.0945 |
Technique | Total Fuel Cost FC (USD/h) | Voltage Stability Index FLmax |
---|---|---|
JS-MFO | 799.3187 | 0.1141 |
JS | 801.1621 | 0.1171 |
MFO | 800.963 | 0.1182 |
ESCA [36] | 800.410 | 0.1224 |
PSO-SSA [38] | 830.352 | 0.1250 |
AMTPG-JAYA [42] | 840.901 | 0.1240 |
MVO [43] | 802.466 | 0.1146 |
ECHT-DE [44] | 800.420 | 0.1374 |
Control Variables and Objective | Case 4 | Case 5 | Case 6 | ||||||
---|---|---|---|---|---|---|---|---|---|
JS | MFO | JS-MFO | JS | MFO | JS-MFO | JS | MFO | JS-MFO | |
PG1(MW) | 85.67 | 82.044 | 83.6279 | 90.667 | 49.75 | 36.9530 | 77.5546 | 108.26 | 109.0601 |
PG8(MW) | 20.49 | 21.971 | 21.8570 | 20.005 | 50.00 | 49.8027 | 18.176 | 5.553 | 6.5210 |
PG10(MW) | 19.27 | 19.327 | 17.8151 | 11.789 | 14.42 | 27.6150 | 25.6081 | 29.95 | 10.4073 |
PG23(MW) | 9.345 | 8.581 | 9.0237 | 4.6829 | 9.936 | 3.0152 | 12.6120 | 14.66 | 3.5084 |
PG24(MW) | 33.43 | 35.939 | 35.9926 | 30.700 | 36.00 | 35.9595 | 19.6385 | 10.71 | 23.6076 |
PG25(MW) | 13.48 | 14.073 | 13.3123 | 24.333 | 2.745 | 29.9992 | 29.0962 | 12.86 | 29.9499 |
VG1(p.u) | 0.934 | 0.9618 | 0.9200 | 0.9570 | 0.954 | 0.9559 | 0.9518 | 0.9379 | 0.9445 |
VG8(p.u) | 0.941 | 0.9705 | 0.9271 | 0.9744 | 0.992 | 0.9936 | 0.9647 | 0.9398 | 0.9392 |
VG10(p.u) | 0.938 | 0.9663 | 0.9235 | 0.9648 | 0.966 | 0.9724 | 0.9646 | 0.9500 | 0.9492 |
VG23(p.u) | 0.935 | 0.9641 | 0.9219 | 0.9574 | 0.959 | 0.9574 | 0.9511 | 0.9422 | 0.9411 |
VG24(p.u) | 0.929 | 0.9504 | 0.9200 | 0.9374 | 0.941 | 0.9415 | 0.9421 | 0.9313 | 0.9303 |
VG25(p.u) | 0.970 | 0.9691 | 0.9431 | 0.9719 | 0.920 | 0.9993 | 0.9240 | 0.9200 | 0.9673 |
QC12(MVar) | −19.67 | −19.948 | −19.994 | −19.73 | −20 | −19.998 | −16.248 | −19.34 | −19.903 |
QC14(MVar) | −9.774 | −9.9932 | −9.9996 | −9.907 | −10 | −9.971 | −7.9491 | −9.760 | −7.072 |
QC16(MVar) | −24.97 | −25.000 | −24.998 | −24.944 | −25 | −24.999 | −24.216 | −25.00 | −15.7419 |
(MW) | 3.354 | 3.5621 | 3.2562 | 3.9357 | 4.470 | 4.9235 | 4.3556 | 3.8866 | 4.9284 |
(p.u) | 0.916 | 0.6045 | 1.2402 | 0.6547 | 0.732 | 0.6144 | 0.8005 | 0.9306 | 0.9650 |
0.426 | 0.3796 | 0.4597 | 0.3869 | 0.391 | 0.3876 | 0.3861 | 0.4201 | 0.3389 |
State Variables | Case 4 | Case 5 | Case 6 |
---|---|---|---|
Generated Reactive Power | JS-MFO | JS-MFO | JS-MFO |
QG1(MVAR) | −79.6379 | −104.3660 | −99.8009 |
QG8(MVAR) | −13.7852 | −6.2700 | −17.1219 |
QG10(MVAR) | −15.8118 | −6.1590 | −8.9077 |
QG23(MVAR) | −7.5879 | −5.8648 | −11.5592 |
QG24(MVAR) | −5.9939 | −25.0052 | −17.6271 |
QG25(MVAR) | 0.3272 | 5.1091 | 4.5488 |
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© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Mayouf, C.; Salhi, A.; Haidara, F.; Aroua, F.Z.; El-Sehiemy, R.A.; Naimi, D.; Aya, C.; Kane, C.S.E. Solving Optimal Power Flow Using New Efficient Hybrid Jellyfish Search and Moth Flame Optimization Algorithms. Algorithms 2024, 17, 438. https://doi.org/10.3390/a17100438
Mayouf C, Salhi A, Haidara F, Aroua FZ, El-Sehiemy RA, Naimi D, Aya C, Kane CSE. Solving Optimal Power Flow Using New Efficient Hybrid Jellyfish Search and Moth Flame Optimization Algorithms. Algorithms. 2024; 17(10):438. https://doi.org/10.3390/a17100438
Chicago/Turabian StyleMayouf, Chiva, Ahmed Salhi, Fanta Haidara, Fatima Zahra Aroua, Ragab A. El-Sehiemy, Djemai Naimi, Chouaib Aya, and Cheikh Sidi Ethmane Kane. 2024. "Solving Optimal Power Flow Using New Efficient Hybrid Jellyfish Search and Moth Flame Optimization Algorithms" Algorithms 17, no. 10: 438. https://doi.org/10.3390/a17100438