Multi-Objective Optimal Power Flow Solution Using a Non-Dominated Sorting Hybrid Fruit Fly-Based Artificial Bee Colony
Abstract
1. Introduction
2. Problem Formulation
Ramp Rate Limit
3. Objective Functions
3.1. Generation Fuel Cost Minimization
3.2. Transmission Loss Minimization
3.3. Severity Value Minimization
4. Hybrid Fruit Fly-Based Artificial Bee Colony (HFABC)
- Step-1: Initialization
- Step-2: Employed bee phase
- Step-3: Osphersis foraging phase
- Step-4: Vision foraging phase
- Step-5: Stop Off Criteria
5. Multi-Objective Control Strategy
Decision Variables
6. Results and Analysis
6.1. Single-Objective Optimization
6.1.1. Himmelblau Test Function
6.1.2. Booth’s Test Function
6.1.3. Electrical IEEE 30 Bus Test System
6.1.4. Electrical IEEE 118 Bus Test System
6.2. Multi-Objective Optimization
6.2.1. Schaffer1 (SCH1) function
6.2.2. Schaffer2 (SCH2) Function
6.2.3. Kursawe Function
6.2.4. IEEE 30 Bus Test Systems
- Case-4: Cost–Loss combination
- Case-5: Cost–Severity combination
- Case-6: Loss–Severity combination
- Case-7: Cost–Loss–Severity combination
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
OPF | Optimal power flow |
ABC | Artificial bee colony |
HFABC | Hybrid fruit fly-based artificial bee colony |
NSHFAB | Non-dominated sorting hybrid fruit fly-based artificial bee colony |
TLBO | Teaching learning-based optimization |
DG | Distributed generation |
ABC-FF | Artificial bee colony with firefly |
QOMJaya | Quasi-oppositional modified Jaya |
TSA | Tree seed algorithm |
PSO | Particle swarm optimization |
FACTS | Flexible alternating current transmission system |
CSA | Cuckoo search algorithm |
DSLC-FOA | Diminishing step and logistic chaos- fruit fly optimization algorithm |
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Parameters | Value |
---|---|
Swarm size | 50 |
Employed bees | 25 |
Food sources | 25 |
Λ | [0, 1] |
[−1, 1] |
Parameters | Existing GA [31] | Existing PSO [31] | Existing ABC | Proposed HFABC |
---|---|---|---|---|
3.003 | 2.9960 | 3.002734964 | 3.000095287 | |
1.994 | 2.0172 | 2.0042859276 | 2.000263891 | |
Function value | 1.000 × 10−3 | 0.004287118 | 8.2451 × 10−4 | 2.0229 × 10−6 |
Standard deviation | 1.7288 | 0.788 | ||
Time (s) | -- | 4.6052 | 3.0274 | 0.4326 |
Parameters | Existing PSO [1] | Existing CSA [1] | Existing ABC | Proposed HFABC |
---|---|---|---|---|
x | 1.012698 | 1.00224 | 1.000 | 1.000 |
y | 2.98924 | 2.99197 | 3.000 | 3.000 |
Minimum function value | 0.00029 | 0.00020 | 2.9285 × 10−7 | 1.6234 × 10−12 |
Standard deviation | 0.086 | 0.035 | ||
Time (s) | 8.23299 | 6.9547 | 2.12912 | 0.5297 |
Control Variable | Generation Fuel Cost (USD/h) Case-1 | Transmission Loss (MW) Case-2 | Severity Value Case-3 | |||
---|---|---|---|---|---|---|
Case-A | Case-B | Case-A | Case-B | Case-A | Case-B | |
PG1 (MW) | 174.297 | 179.337 | 51.524 | 51.731 | 126.569 | 121.997 |
PG2 (MW) | 48.123 | 44.109 | 80.000 | 80.000 | 39.026 | 43.171 |
PG5 (MW) | 22.026 | 19.893 | 50.000 | 50.000 | 48.258 | 41.608 |
PG8 (MW) | 20.833 | 22.584 | 35.000 | 35.000 | 35.000 | 30.000 |
PG11 (MW) | 12.741 | 13.000 | 30.000 | 30.000 | 18.774 | 24.626 |
PG13(MW) | 14.027 | 14.000 | 40.000 | 40.000 | 22.684 | 30.253 |
VG1 (p.u.) | 1.099 | 1.100 | 1.100 | 1.100 | 1.053 | 0.913 |
VG2 (p.u.) | 1.082 | 0.968 | 1.096 | 1.064 | 0.979 | 0.900 |
VG5 (p.u.) | 1.055 | 1.042 | 1.093 | 1.100 | 0.937 | 1.033 |
VG8 (p.u.) | 1.054 | 1.091 | 1.100 | 1.099 | 0.998 | 0.999 |
VG11 (p.u.) | 1.069 | 1.100 | 0.943 | 1.0533 | 0.989 | 0.977 |
VG13 (p.u.) | 1.091 | 1.100 | 1.100 | 1.0979 | 1.029 | 0.953 |
TAP,6–9 (p.u.) | 0.948 | 1.089 | 1.001 | 0.900 | 1.042 | 0.936 |
TAP,6–10 (p.u.) | 1.009 | 0.984 | 1.079 | 1.100 | 1.051 | 0.927 |
TAP,4–12 (p.u.) | 0.987 | 1.040 | 1.100 | 0.900 | 0.955 | 0.900 |
TAP,28–27 (p.u.) | 0.996 | 1.100 | 1.002 | 0.9522 | 1.036 | 0.900 |
QC10 (MVAr) | 22.848 | 5.000 | 30.000 | 29.998 | 21.378 | 6.179 |
QC24 (MVAr) | 10.427 | 14.632 | 10.218 | 5.0160 | 9.065 | 5.763 |
COST (USD/h) | 800.212 | 802.922 | 967.7189 | 968.2135 | 871.9846 | 865.4640 |
Standard deviation | 4.238 | 4.234 | ||||
P LOSS (MW) | 8.6462 | 9.5228 | 3.124 | 3.4527 | 6.9107 | 8.2548 |
Severity value | 1.304 | 1.534 |
Existing Methods | Generation Fuel Cost ($/h) | Transmission Power Loss (MW) |
---|---|---|
MSFLA [2] | 802.287 | --- |
SFLA [2] | 802.5092 | --- |
PSO [2] | 802.190 | --- |
MDE [2] | 802.376 | --- |
IEP [2] | 802.465 | --- |
IPSO [2] | --- | 5.0732 |
RGA [2] | --- | 4.57401 |
CLPSO [2] | --- | 4.6282 |
DE [2] | --- | 5.011 |
CMAES [2] | --- | 4.945 |
HAS [2] | --- | 4.9059 |
HCSA [2] | 802.0347 | 3.208022 |
EP [35] | 802.62 | |
TS [35] | 802.29 | |
SGA [35] | 803.699 | |
EGA [35] | 802.06 | |
ACO [35] | 802.578 | |
FGA [35] | 802 | |
IPSO [35] | 801.978 | |
Proposed HFABC | 800.212 | 3.124 |
Existing Methods | Generation Fuel Cost (USD/h) | Transmission Power Loss (MW) |
---|---|---|
BSA [36] | 135,333.4743 | --- |
MPSO [18] | 132,039.2120 | --- |
PSO [37] | --- | 137.2831 |
HPSO [37] | --- | 133.1005 |
RGA [38] | --- | 71.89 |
BBO [38] | --- | 51.43 |
Proposed HFABC | 131,400.6342 | 50.153 |
Control Variable | Case 4 | Case 5 | Case 6 | Case 7 | ||||
---|---|---|---|---|---|---|---|---|
Case A | Case B | Case A | Case B | Case A | Case B | Case A | Case B | |
PG1(MW) | 133.9825 | 144.1367 | 138.3332 | 140.3535 | 58.22553 | 82.56956 | 138.1317 | 134.6141 |
PG2 (MW) | 61.64107 | 49.41045 | 57.50178 | 63 | 80 | 63 | 49.28703 | 63 |
PG5 (MW) | 26.58247 | 33.49581 | 25.38848 | 24.45096 | 50 | 49 | 25.16808 | 21.65767 |
PG8 (MW) | 35 | 30 | 35 | 30 | 35 | 30 | 35 | 29.24235 |
PG11 (MW) | 14.82879 | 19.14705 | 15.28843 | 15.74895 | 30 | 28 | 22.61887 | 28 |
PG13 (MW) | 17.97686 | 14 | 18.96543 | 18.31494 | 33.29999 | 35 | 20.31096 | 14 |
VG 1 (p.u.) | 1.1 | 1.084887 | 1.059755 | 1.0449 | 1.1 | 1.041552 | 1.076465 | 1.076605 |
VG 2 (p.u.) | 1.1 | 1.037541 | 1.049932 | 0.959809 | 1.094372 | 1.031484 | 0.985134 | 1.052951 |
VG 5 (p.u.) | 1.06103 | 1.038822 | 1.017991 | 1.045268 | 1.076186 | 1.030485 | 1.01856 | 1.031196 |
VG 8 (p.u.) | 1.085257 | 1.029494 | 1.022296 | 1.014201 | 1.082601 | 1.021 | 1.015163 | 1.020506 |
VG 11 (p.u.) | 0.916737 | 1.080233 | 1.095377 | 1.011141 | 1.061172 | 1.1 | 0.991042 | 1.003952 |
VG 13 (p.u.) | 1.1 | 1.1 | 1.044095 | 0.985591 | 1.076334 | 1.1 | 1.039085 | 1.081282 |
TAP,6–9 (p.u.) | 1.019361 | 1.081856 | 0.934663 | 1.059802 | 1.042781 | 0.973826 | 0.997074 | 0.956768 |
TAP,6–10 (p.u.) | 0.956273 | 0.9 | 0.983163 | 1.07789 | 1.052493 | 0.92203 | 1.046692 | 0.963351 |
TAP,4–12 (p.u.) | 1.1 | 0.942512 | 0.940031 | 1.1 | 1.006434 | 0.926004 | 1.08331 | 0.905993 |
TAP,28–27 (p.u.) | 0.954972 | 0.932137 | 0.952542 | 1.05998 | 0.997475 | 0.986524 | 0.986524 | 0.946003 |
QC10 (MVAr) | 13.31924 | 29.13522 | 5 | 12.12297 | 30 | 5 | 11.49146 | 23.46145 |
QC24 (MVAr) | 7.605346 | 11.93253 | 9.521084 | 15.95451 | 11.34165 | 20.20976 | 5.732153 | 12.01105 |
COST (USD/h) | 816.3544 | 817.5049 | 814.1558 | 817.887 | --- | --- | 817.1957 | 820.532 |
P LOSS (MW) | 6.611724 | 6.789968 | --- | --- | 3.125514 | 4.169562 | 7.116676 | 7.114076 |
Severity value | --- | --- | 1.18808 | 1.322637 | 0.752894 | 1.021353 | 1.04962 | 1.210963 |
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Mallala, B.; Papana, V.P.; Sangu, R.; Palle, K.; Chinthalacheruvu, V.K.R. Multi-Objective Optimal Power Flow Solution Using a Non-Dominated Sorting Hybrid Fruit Fly-Based Artificial Bee Colony. Energies 2022, 15, 4063. https://doi.org/10.3390/en15114063
Mallala B, Papana VP, Sangu R, Palle K, Chinthalacheruvu VKR. Multi-Objective Optimal Power Flow Solution Using a Non-Dominated Sorting Hybrid Fruit Fly-Based Artificial Bee Colony. Energies. 2022; 15(11):4063. https://doi.org/10.3390/en15114063
Chicago/Turabian StyleMallala, Balasubbareddy, Venkata Prasad Papana, Ravindra Sangu, Kowstubha Palle, and Venkata Krishna Reddy Chinthalacheruvu. 2022. "Multi-Objective Optimal Power Flow Solution Using a Non-Dominated Sorting Hybrid Fruit Fly-Based Artificial Bee Colony" Energies 15, no. 11: 4063. https://doi.org/10.3390/en15114063
APA StyleMallala, B., Papana, V. P., Sangu, R., Palle, K., & Chinthalacheruvu, V. K. R. (2022). Multi-Objective Optimal Power Flow Solution Using a Non-Dominated Sorting Hybrid Fruit Fly-Based Artificial Bee Colony. Energies, 15(11), 4063. https://doi.org/10.3390/en15114063