Optimal Placement of HVDC-VSC in AC System Using Self-Adaptive Bonobo Optimizer to Solve Optimal Power Flows: A Case Study of the Algerian Electrical Network
Abstract
:1. Introduction
- The optimization problem incorporates the equations for the VSC stations, DC grids, and AC/DC coupling, which are modeling components.
- Optimization variables—the VSC injections of active (P) and reactive (Q) power are control variables in the optimization problem.
- Implementation of the self-adaptive bonobo optimizer (SABO) was made to find the optimal location of the HVDC line in the system to optimize desired objectives
- The proposed algorithm was tested on the IEEE 30 bus and the large-scale Algerian 114-bus electric network; the simulation results were compared with several results of algorithms mentioned in other recent literature in terms of the quality and robustness of the solution.
2. VSC-HVDC Model
- The converter transformer
- The AC filters
- The phase reactor
- The converter.
3. Formulation Problem
3.1. Objective Functions
3.1.1. Minimization of the Total Generation Costs (TGCs)
3.1.2. Minimization of the Total Active Power Transmission Losses (APTLs)
3.2. The Control and State Variables IN Hybrid AC/DC Network
3.2.1. The Control Variables
3.2.2. The State Variables
3.3. Constraints
3.3.1. The Equality Constraint
3.3.2. The Inequality Constraint
4. Self-Adaptive Bonobo Optimizer (SABO) Algorithm
4.1. The SABO Works
4.2. Using Different Mating Strategies to Create New Bonobos
4.2.1. Mating Strategies: Restrictive and Promiscuous
4.2.2. Extra-Group Mating
4.2.3. Consortship Mating
4.3. Modified Boundary Handling Technique
5. Simulation Results and Discussions
5.1. IEEE 30-Bus System
5.1.1. Case-1: Minimization of Total Generation Costs (TGCs)
5.1.2. Case-2: Minimization of Total Active Power Transmission Losses (APTLs)
5.2. Large Algerian Electrical Test System DZ114
5.2.1. Case-1: Minimization of Total Generation Costs (TGCs)
5.2.2. Case-2: Minimization of Total Active Power Transmission Losses (APTLs)
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Control Variables | Limits | Case 1: TGCs (USD/h) | ||||||
---|---|---|---|---|---|---|---|---|
Without HVDC | With HVDC | |||||||
Min | Max | JAYA [9] | SMA [7] | EEO [9] | AO-AOA [11] | SABO | SABO | |
PG1 | 50 | 200 | 177.0106 | 177.5784 | 176.7345 | 177.0037 | 177.0646 | 178.0241 |
PG2 | 20 | 80 | 48.6495 | 48.6770 | 48.78826 | 48.5782 | 48.6784 | 49.0698 |
PG5 | 15 | 50 | 21.2822 | 21.2668 | 21.35174 | 21.3235 | 21.2994 | 20.3217 |
PG8 | 10 | 35 | 21.0841 | 21.2316 | 21.59308 | 21.0818 | 21.0916 | 20.0680 |
PG11 | 10 | 30 | 11.9518 | 12.0890 | 11.90222 | 11.9328 | 11.8472 | 11.5181 |
PG13 | 12 | 40 | 12.0048 | 12.0000 | 12.01063 | 12.0035 | 12.0000 | 12.0000 |
VG1 | 0.95 | 1.1 | 1.1000 | 1.1000 | 1.081652 | 1.09530 | 1.1000 | 1.1000 |
VG2 | 0.95 | 1.1 | 1.0882 | 1.0879 | 1.083692 | 1.06812 | 1.0877 | 1.0839 |
VG5 | 0.95 | 1.1 | 1.0625 | 1.0618 | 1.034161 | 1.05370 | 1.0613 | 1.0780 |
VG8 | 0.95 | 1.1 | 1.0695 | 1.0701 | 1.040193 | 1.04973 | 1.0690 | 1.0698 |
VG11 | 0.95 | 1.1 | 1.1000 | 1.1000 | 1.058904 | 1.09511 | 1.1000 | 1.1000 |
VG13 | 0.95 | 1.1 | 1.1000 | 1.1000 | 1.035318 | 1.04431 | 1.1000 | 1.1000 |
T11 | 0.9 | 1.1 | 1.0239 | 1.0259 | 0.049801 | 1.04510 | 1.0363 | 1.0448 |
T12 | 0.9 | 1.1 | 0.9000 | 0.9010 | 0.035215 | 0.91041 | 0.9033 | 0.9000 |
T15 | 0.9 | 1.1 | 0.9741 | 0.9803 | 0.04999 | 0.96710 | 0.9772 | 0.9824 |
T36 | 0.9 | 1.1 | 0.9595 | 0.9568 | 0.96527 | 0.9593 | 0.9633 | |
QC10 | 0 | 5 | 5.000 | 4.3806 | 1.039025 | 4.49630 | 5.0000 | 5.0000 |
QC12 | 0 | 5 | 4.9197 | 4.7790 | 0.9264 | 3.63150 | 5.0000 | 4.9998 |
QC15 | 0 | 5 | 5.000 | 4.8272 | 0.963273 | 4.63540 | 5.0000 | 4.9997 |
QC17 | 0 | 5 | 5.000 | 4.9942 | 0.971492 | 4.88170 | 5.0000 | 5.0000 |
QC20 | 0 | 5 | 4.9949 | 2.5651 | 0.045018 | 4.20613 | 4.2704 | 4.3136 |
QC21 | 0 | 5 | 4.9698 | 2.8396 | 0 | 4.97820 | 5.0000 | 5.0000 |
QC23 | 0 | 5 | 4.9892 | 3.4609 | 0.049426 | 4.95210 | 2.6829 | 2.7305 |
QC24 | 0 | 5 | 5.000 | 4.9957 | 0.048943 | 4.99160 | 5.0000 | 5.0000 |
QC29 | 0 | 5 | 2.0948 | 1.1562 | 0.043546 | 2.11586 | 2.2158 | 2.4387 |
PS1 | −100 | 100 | - | - | - | - | - | −92.09 |
QS1 | −100 | 100 | - | - | - | - | - | 10.64 |
PSslack | −100 | 100 | - | - | - | - | - | 90.35 |
QSslack | −100 | 100 | - | - | - | - | - | 0.00 |
Optimal location of HVDC line | - | - | - | - | - | Line 5 Bus (2–5) | ||
TGCs (USD/h) | 798.9386 | 798.9709 | 800.4145 | 800.0239 | 798.8979 | 795.0720 | ||
(MW) | 8.58378 | 8.5752 | 8.99217 | 8.873080 | 8.5813 | 5.866 | ||
(MW) | - | - | - | - | - | 1.5257 | ||
(MW) | - | - | - | - | - | 0.21 | ||
APTLs (MW)of AC/DC system | - | - | - | - | - | 7.6017 | ||
The convergence time (second) | - | - | - | - | 63.8806 | 510.717 |
Control Variables | Limits | Case 2: APTLs (MW) | ||||||
---|---|---|---|---|---|---|---|---|
Without HVDC | With HVDC | |||||||
Min | Max | JAYA [9] | SMA [7] | EEO [9] | AO-AOA [11] | SABO | SABO | |
PG1 | 50 | 200 | 51.5290 | 51.2614 | 51.49013 | 51.4988 | 51.2295 | 51.2490 |
PG2 | 20 | 80 | 80.000 | 80.0000 | 79.99994 | 80.000 | 80.0000 | 80.0000 |
PG5 | 15 | 50 | 50.000 | 50.0000 | 49.99974 | 50.000 | 50.0000 | 49.9996 |
PG8 | 10 | 35 | 35.000 | 34.9999 | 34.99917 | 35.000 | 35.0000 | 35.0000 |
PG11 | 10 | 30 | 30.000 | 30.0000 | 30.000 | 30.000 | 29.9999 | 29.9999 |
PG13 | 12 | 40 | 40.000 | 40.0000 | 39.99999 | 40.000 | 40.0000 | 39.9999 |
VG1 | 0.95 | 1.1 | 1.0500 | 1.1000 | 1.061175 | 1.06193 | 1.1000 | 1.1000 |
VG2 | 0.95 | 1.1 | 1.0477 | 1.0979 | 1.057169 | 1.05172 | 1.0977 | 1.0962 |
VG5 | 0.95 | 1.1 | 1.0292 | 1.0793 | 1.037851 | 1.03225 | 1.0799 | 1.0892 |
VG8 | 0.95 | 1.1 | 1.0364 | 1.0876 | 1.043643 | 1.03964 | 1.0869 | 1.0879 |
VG11 | 0.95 | 1.1 | 1.0500 | 1.1000 | 1.050452 | 1.05861 | 1.1000 | 1.1000 |
VG13 | 0.95 | 1.1 | 1.0500 | 1.1000 | 1.051736 | 1.05512 | 1.1000 | 1.1000 |
T11 | 0.9 | 1.1 | 1.0372 | 1.0331 | 0.049996 | 1.04764 | 1.0630 | 1.0658 |
T12 | 0.9 | 1.1 | 0.9000 | 0.9193 | 0.029683 | 0.90000 | 0.9038 | 0.9001 |
T15 | 0.9 | 1.1 | 0.9846 | 0.9870 | 0.05 | 0.98360 | 0.9864 | 0.9887 |
T36 | 0.9 | 1.1 | 0.9664 | 0.9834 | 0.018962 | 0.96880 | 0.9675 | 0.9739 |
QC10 | 0 | 5 | 4.3257 | 1.0281 | 1.02419 | 4.52370 | 4.9974 | 4.9949 |
QC12 | 0 | 5 | 5.000 | 0.2155 | 0.933052 | 0.95180 | 4.9993 | 4.9993 |
QC15 | 0 | 5 | 5.000 | 4.7108 | 0.990881 | 4.57320 | 4.7827 | 4.8029 |
QC17 | 0 | 5 | 4.9979 | 2.4109 | 0.973498 | 4.66150 | 5.0000 | 4.9955 |
QC20 | 0 | 5 | 4.1615 | 4.9982 | 0.049819 | 4.15290 | 3.7924 | 3.9913 |
QC21 | 0 | 5 | 5.000 | 4.9042 | 0.03386 | 4.22410 | 5.0000 | 4.9995 |
QC23 | 0 | 5 | 3.3293 | 0.3454 | 0.049166 | 3.11720 | 2.4482 | 2.5848 |
QC24 | 0 | 5 | 5.000 | 4.9181 | 0.049966 | 4.63050 | 4.9997 | 4.9982 |
QC29 | 0 | 5 | 1.8872 | 2.8276 | 0.039794 | 2.18670 | 1.9277 | 2.2502 |
PS1 | −100 | 100 | - | - | - | - | - | −55.64 |
QS1 | −100 | 100 | - | - | - | - | - | 11.06 |
PSslack | −100 | 100 | - | - | - | - | - | 54.58 |
QSslack | −100 | 100 | - | - | - | - | - | 0.00 |
Optimal location of HVDC line | - | - | - | - | - | Line 5 Bus (2–5) | ||
TGCs (USD/h) | 967.7316 | 967.0437 | 967.5845 | 967.6703 | 966.9680 | 967.0105 | ||
(MW) | 3.1291 | 2.8612 | 3.088974 | 3.017910 | 2.8295 | 1.781 | ||
(MW) | - | - | - | - | - | 0.99 | ||
(MW) | - | - | - | - | - | 0.08 | ||
APTLs (MW)of AC/DC system | - | - | - | - | - | 2.8483 | ||
The convergence time (second) | - | - | - | - | 64.533 | 514.580 |
Control Variables | Limits | Case 1: TGCs (USD/h) | Case 2: APTLs (MW) | |||
---|---|---|---|---|---|---|
Min | Max | Without HVDC | With HVDC | Without HVDC | With HVDC | |
PG 4 | 135 | 1350 | 449.1546 | 450.5743 | 502.9009 | 519.8323 |
PG 5 | 135 | 1350 | 445.4603 | 448.1035 | 506.9725 | 487.2334 |
PG 11 | 10 | 100 | 99.8786 | 99.9825 | 99.8891 | 99.6393 |
PG 15 | 30 | 300 | 194.1843 | 193.5099 | 116.9265 | 127.2726 |
PG 17 | 135 | 1350 | 448.1758 | 447.5191 | 608.1340 | 639.7914 |
PG 19 | 34.5 | 345 | 195.4801 | 193.2714 | 205.3335 | 150.0935 |
PG 22 | 34.5 | 345 | 189.3318 | 190.0804 | 131.5792 | 154.8630 |
PG 52 | 34.5 | 345 | 190.3655 | 186.5989 | 120.8845 | 120.7498 |
PG 80 | 34.5 | 345 | 195.3247 | 191.6183 | 272.5870 | 254.6253 |
PG 83 | 30 | 300 | 192.0720 | 192.0580 | 179.0298 | 170.1840 |
PG 98 | 30 | 300 | 187.2295 | 192.1012 | 251.4170 | 265.6369 |
PG 100 | 60 | 600 | 599.9521 | 599.9732 | 387.0482 | 391.4905 |
PG 101 | 20 | 200 | 199.9881 | 199.9941 | 198.5835 | 199.9958 |
PG 109 | 10 | 100 | 99.8483 | 99.9396 | 99.4402 | 99.4404 |
PG 111 | 10 | 100 | 99.9404 | 99.9277 | 99.9706 | 100.0000 |
VG 4 | 0.9 | 1.1 | 1.0545 | 1.0539 | 1.0614 | 1.0804 |
VG 5 | 0.9 | 1.1 | 1.0471 | 1.0456 | 1.0504 | 1.0736 |
VG 11 | 0.9 | 1.1 | 1.0489 | 1.0553 | 1.0493 | 1.0674 |
VG 15 | 0.9 | 1.1 | 1.0563 | 1.0541 | 1.0608 | 1.0799 |
VG 17 | 0.9 | 1.1 | 1.0561 | 1.0613 | 1.0695 | 1.0813 |
VG 19 | 0.9 | 1.1 | 1.0012 | 1.0271 | 1.0567 | 1.0386 |
VG 22 | 0.9 | 1.1 | 1.0053 | 1.0241 | 1.0573 | 1.0499 |
VG 52 | 0.9 | 1.1 | 1.0326 | 1.0330 | 1.0428 | 1.0568 |
VG 80 | 0.9 | 1.1 | 1.0375 | 1.0436 | 1.0513 | 1.0266 |
VG 83 | 0.9 | 1.1 | 1.0747 | 1.0750 | 1.0832 | 1.0548 |
VG 98 | 0.9 | 1.1 | 1.0634 | 1.0803 | 1.0793 | 1.0759 |
VG 100 | 0.9 | 1.1 | 1.0819 | 1.0949 | 1.0962 | 1.0788 |
VG 101 | 0.9 | 1.1 | 1.0617 | 1.0827 | 1.0772 | 1.0776 |
VG 109 | 0.9 | 1.1 | 1.0718 | 1.0954 | 1.0848 | 1.0947 |
VG 111 | 0.9 | 1.1 | 1.0268 | 1.0541 | 1.0811 | 1.0489 |
Control Variables | Limits | Case 1: TGCs (USD/h) | Case 2: APTLs (MW) | |||
---|---|---|---|---|---|---|
Min | Max | Without HVDC | With HVDC | Without HVDC | With HVDC | |
T 160 | 0.9 | 1.1 | 0.9004 | 0.9022 | 0.9006 | 0.9023 |
T 161 | 0.9 | 1.1 | 0.9231 | 0.9135 | 0.9614 | 0.9438 |
T 162 | 0.9 | 1.1 | 0.9412 | 0.9156 | 0.9674 | 0.9688 |
T 163 | 0.9 | 1.1 | 0.9413 | 0.9727 | 0.9605 | 0.9717 |
T 164 | 0.9 | 1.1 | 0.9726 | 0.9711 | 0.9646 | 0.9558 |
T 165 | 0.9 | 1.1 | 0.9710 | 0.9844 | 0.9486 | 0.9742 |
T 166 | 0.9 | 1.1 | 0.9888 | 1.0044 | 1.0013 | 0.9886 |
T 167 | 0.9 | 1.1 | 0.9552 | 1.0142 | 0.9648 | 1.0145 |
T 168 | 0.9 | 1.1 | 0.9597 | 0.9922 | 0.9392 | 0.9857 |
T 169 | 0.9 | 1.1 | 1.0034 | 0.9954 | 0.9605 | 0.9869 |
T 170 | 0.9 | 1.1 | 1.0331 | 1.0239 | 0.9898 | 1.0063 |
T 171 | 0.9 | 1.1 | 0.9572 | 0.9324 | 0.9600 | 0.9653 |
T 172 | 0.9 | 1.1 | 1.0237 | 1.0071 | 0.9561 | 1.0309 |
T 173 | 0.9 | 1.1 | 0.9824 | 1.0074 | 0.9988 | 0.9989 |
T 174 | 0.9 | 1.1 | 0.9619 | 1.0076 | 0.9587 | 0.9605 |
T 175 | 0.9 | 1.1 | 0.9238 | 1.0801 | 1.0198 | 1.0652 |
Control Variables | Limits | Case 1: TGCs (USD/h) | Case 2: APTLs (MW) | |||
---|---|---|---|---|---|---|
Min | Max | Without HVDC | With HVDC | Without HVDC | With HVDC | |
QC41 | 0 | 25 | 20.3355 | 19.3062 | 22.8674 | 21.9126 |
QC50 | 0 | 25 | 11.2038 | 12.8306 | 10.1334 | 6.7341 |
QC55 | 0 | 25 | 16.0482 | 19.4523 | 19.6093 | 22.4936 |
QC66 | 0 | 25 | 23.8080 | 23.9402 | 22.2982 | 23.7515 |
QC67 | 0 | 25 | 16.3570 | 2.3715 | 17.9964 | 12.8060 |
QC77 | 0 | 25 | 11.5375 | 5.5738 | 6.6413 | 6.9476 |
QC93 | 0 | 25 | 24.6758 | 21.9619 | 24.5343 | 24.7118 |
PS1 | −100 | 100 | - | −18.4787 | −15.0939 | |
QS1 | −100 | 100 | - | 29.3269 | - | 21.8249 |
PSslack | −100 | 100 | - | 17.85 | - | 14.49 |
QSslack | −100 | 100 | - | 6.97 | - | −6.27 |
Control Variables | Limits | Case 1: TGCs (USD/h) | Case 2: APTLs (MW) | |||
---|---|---|---|---|---|---|
Min | Max | Without HVDC | With HVDC | Without HVDC | With HVDC | |
Optimal location of HVDC line | - | Line 99 Bus 73–67 | - | Line 99 Bus 73–67 | ||
TGCs (USD/h) | 18,928,4612 | 18,917.4349 | 20,468.7419 | 20,498.3401 | ||
(MW) | 59.3861 | 57.622 | 53.6965 | 53.242 | ||
(MW) | - | 0.62 | - | 0.59 | ||
(MW) | - | 0.01 | - | 0.01 | ||
APTLs (MW) of AC/DC system | - | 58.2520 | - | 53.8482 | ||
The convergence time (second) | 97.1380 | 533.601 | 123.180 | 542.842 |
Methods | TGCs (USD/h) | Method Description |
---|---|---|
MOALO [44] | 19,355.859 | Multi-objective ant lion algorithm |
DE [45] | 19,203.340 | Differential evolution |
GA-ED-PS [46] | 19,199.444 | Hybrid GA-DE-PS |
GOA [7] | 19,178.818 | Grasshopper optimization algorithm |
GWO [47] | 19,171.958 | Grey wolf optimizer |
SMA [7] | 19,170.205 | Slime mould algorithm |
SABO | 18,928,4612 | Self-adaptive bonobo optimizer |
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Alouache, H.E.; Sayah, S.; Bosisio, A.; Hamouda, A.; Kouadri, R.; Shirvani, R. Optimal Placement of HVDC-VSC in AC System Using Self-Adaptive Bonobo Optimizer to Solve Optimal Power Flows: A Case Study of the Algerian Electrical Network. Electronics 2024, 13, 3848. https://doi.org/10.3390/electronics13193848
Alouache HE, Sayah S, Bosisio A, Hamouda A, Kouadri R, Shirvani R. Optimal Placement of HVDC-VSC in AC System Using Self-Adaptive Bonobo Optimizer to Solve Optimal Power Flows: A Case Study of the Algerian Electrical Network. Electronics. 2024; 13(19):3848. https://doi.org/10.3390/electronics13193848
Chicago/Turabian StyleAlouache, Houssam Eddine, Samir Sayah, Alessandro Bosisio, Abdellatif Hamouda, Ramzi Kouadri, and Rouzbeh Shirvani. 2024. "Optimal Placement of HVDC-VSC in AC System Using Self-Adaptive Bonobo Optimizer to Solve Optimal Power Flows: A Case Study of the Algerian Electrical Network" Electronics 13, no. 19: 3848. https://doi.org/10.3390/electronics13193848
APA StyleAlouache, H. E., Sayah, S., Bosisio, A., Hamouda, A., Kouadri, R., & Shirvani, R. (2024). Optimal Placement of HVDC-VSC in AC System Using Self-Adaptive Bonobo Optimizer to Solve Optimal Power Flows: A Case Study of the Algerian Electrical Network. Electronics, 13(19), 3848. https://doi.org/10.3390/electronics13193848