# Sizing and Sitting of Static VAR Compensator (SVC) Using Hybrid Optimization of Combined Cuckoo Search (CS) and Antlion Optimization (ALO) Algorithms

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. System under Study

## 3. Formulation of the Multi-Objective Function

#### 3.1. Voltage Deviations

#### 3.2. Overloads

#### 3.3. Power Loss

#### 3.4. Overall Function

_{1}+ C

_{2}+ C

_{3}= 1

#### 3.5. Constraints

#### 3.5.1. Inequality Constraints

#### 3.5.2. Equality Constraints

#### 3.6. Modelling of SVC

## 4. Proposed Methods

#### 4.1. Cuckoo Search Algorithm (CS)

#### 4.2. Antlion Optimization (ALO)

#### 4.3. Proposed Hybrid Cuckoo Search and Antlion Optimization (CS-ALO)

## 5. Simulation and Results

#### 5.1. Validation of the CS-ALO Algorithm to Benchmark Function

#### 5.2. Application of the CS-ALO Algorithm to the Optimal Sizing and Sitting of SVC Devices

#### 5.2.1. Outage in Branch 50

#### 5.2.2. Outage of Branch 41

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Pareto front for various objective functions with different probabilities of weighting factors.

**Figure A2.**Results of branch outages and their ranking in the IEEE57 bus system with their objective functions.

Rank | Branch Outage | DEV | OL | ${\mathbf{P}}_{\mathbf{l}\mathbf{o}\mathbf{s}\mathbf{s}}$ | Rank | Branch Outage | DEV | OL | ${\mathbf{P}}_{\mathbf{l}\mathbf{o}\mathbf{s}\mathbf{s}}$ |
---|---|---|---|---|---|---|---|---|---|

3 | (3–4) | 0.0164 | 0 | 0.3160 | 33 | (22–23) | 0.0469 | 0 | 0.2885 |

38 | (26–27) | 0.0351 | 0 | 0.2839 | 17 | (1–17) | 0.0133 | 0 | 0.3717 |

41 | (7–29) | 2.6699 | 0 | 0.4666 | 26 | (12–16) | 0.0157 | 0 | 0.2943 |

14 | (13–15) | 0.0159 | 0 | 0.2920 | 52 | (36–40) | 0.0276 | 0 | 0.2775 |

57 | (38–44) | 0.0174 | 0 | 0.2860 | 46 | (34–32) | 1.6464 | 0 | 0.3040 |

50 | (38–37) | 3.5657 | 0 | 0.3182 | 56 | (41–43) | 0.0205 | 0 | 0.2805 |

65 | (10–51) | 0.0314 | 0 | 0.3089 | 22 | (7–8) | 0.0268 | 0 | 0.3196 |

28 | (14–15) | 0.0144 | 0 | 0.3032 | 79 | (38–48) | 0.0518 | 0 | 0.2839 |

8 | (8–9) | 0.0345 | 0 | 0.6111 | 23 | (10–12) | 0.0139 | 0 | 0.2802 |

80 | (9–55) | 0.5577 | 0 | 0.3166 | 37 | (24–26) | 0.0300 | 0 | 0.2840 |

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**Figure 7.**Evaluation of different types of benchmark functions; (

**a**): ${\mathrm{F}}_{1}$, (

**b**): ${\mathrm{F}}_{11}$, (

**c**): ${\mathrm{F}}_{14}$.

**Figure 11.**Voltage and power loss before and after SVC installation in case of an outage in branch 41.

Generator Number | ${\mathbf{P}}_{\mathbf{g}\mathbf{m}\mathbf{i}\mathbf{n}}\left(\mathbf{M}\mathbf{W}\right)$ | ${\mathbf{P}}_{\mathbf{g}\mathbf{m}\mathbf{a}\mathbf{x}}\left(\mathbf{M}\mathbf{W}\right)$ | ${\mathbf{Q}}_{\mathbf{g}\mathbf{m}\mathbf{i}\mathbf{n}}\left(\mathbf{M}\mathbf{V}\mathbf{A}\mathbf{R}\right)$ | ${\mathbf{Q}}_{\mathbf{g}\mathbf{m}\mathbf{a}\mathbf{x}}\left(\mathbf{M}\mathbf{V}\mathbf{A}\mathbf{R}\right)$ |
---|---|---|---|---|

1 | 0 | 575.88 | −140 | 200 |

2 | 0 | 100 | −17 | 50 |

3 | 0 | 140 | −10 | 60 |

6 | 0 | 100 | −8 | 25 |

8 | 0 | 550 | −140 | 200 |

9 | 0 | 100 | −3 | 9 |

12 | 0 | 410 | −150 | 155 |

Algorithm | Specific Parameters | Value |
---|---|---|

PSO | Inertia weight w, Inertia Weight Damping Ratio, c1, and c2 | 1, 0.99, 1.5, 2 |

GSA | Alpha, G0, Rnorm, Rpower | 20, 100, 2, 1 |

CS | Discovery rate | 0.25 |

ALO | popsize, 𝑀𝑎𝑥_𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛 | 30, 1000 |

CS-ALO | Discovery rate, popsize, 𝑀𝑎𝑥_𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛 | 0.25, 30, 1000 |

Function | Stats | PSO | GSA | CS | ALO | CS-ALO |
---|---|---|---|---|---|---|

${\mathrm{F}}_{1}$ | Ave | 4.6653 × 10^{−6} | 2.0950 × 10^{−17} | 0.0036 | 9.6514 × 10−6 | 7.0132 × 10^{−18} |

Std | 1.1056 × 10^{−6} | 7.2306 × 10^{−18} | 0.0026 | 8.1485 × 10^{−6} | 1.1014 × 10^{−17} | |

Min | 3.1615 × 10^{−7} | 1.0235 × 10^{−17} | 8.8569 × 10^{−4} | 8.5855 × 10^{−7} | 3.7131 × 10^{−19} | |

${\mathrm{F}}_{2}$ | Ave | 0.0296 | 5.3973 × 10^{−}^{8} | 0.2982 | 98.0542 | 2.5484 × 10^{−11} |

Std | 0.0202 | 1.3423 × 10^{−}^{9} | 0.1847 | 1.4454 × 10^{−14} | 1.2883 × 10^{−11} | |

Min | 7.1882 × 10^{−}^{4} | 2.7989 × 10^{−}^{8} | 0.1215 | 98.0542 | 8.7168 × 10^{−12} | |

${\mathrm{F}}_{3}$ | Ave | 7.2588 | 461.3663 | 303.7764 | 1.1582 × 10^{3} | 0.448 |

Std | 15.4066 | 182.0644 | 71.7279 | 522.6452 | 0.2563 | |

Min | 0.2636 | 181.0675 | 156.4354 | 374.8212 | 0.0597 | |

${\mathrm{F}}_{4}$ | Ave | 0.6348 | 1.4477 | 5.6706 | 12.6565 | 0.11 |

Std | 0.2771 | 1.2543 | 2.1251 | 4.7648 | 0.064 | |

Min | 0.2252 | 9.6847 × 10^{−}^{9} | 1.2383 | 3.917 | 0.0374 | |

${\mathrm{F}}_{5}$ | Ave | 51.2677 | 35.3128 | 51.5287 | 29.1538 | 22.033 |

Std | 43.8051 | 23.4802 | 40.1303 | 7.2269 × 10^{−}^{15} | 19.1713 | |

Min | 3.6562 | 25.7798 | 21.5784 | 29.1538 | 1.4643 | |

${\mathrm{F}}_{6}$ | Ave | 3.0054 × 10^{−}^{10} | 1.0634 × 10^{−}^{16} | 0.0036 | 7.6753 × 10^{−}^{6} | 6.5789 × 10^{−18} |

Std | 1.3491 × 10^{−}^{9} | 3.4396 × 10^{−}^{17} | 0.0025 | 4.9301 × 10^{−}^{6} | 9.0468 × 10^{−18} | |

Min | 6.3484 × 10^{−}^{17} | 4.9508 × 10^{−}^{17} | 8.7930 × 10^{−}^{4} | 8.2654 × 10^{−}^{7} | 1.6541 × 10^{−19} | |

${\mathrm{F}}_{7}$ | Ave | 0.0163 | 0.0583 | 0.0421 | 0.0983 | 0.0179 |

Std | 0.0052 | 0.0185 | 0.0159 | 0.0245 | 0.0092 | |

Min | 0.0080 | 0.0300 | 0.0209 | 0.0403 | 0.0055 |

Function | Stats | PSO | GSA | CS | ALO | CS-ALO |
---|---|---|---|---|---|---|

${\mathrm{F}}_{8}$ | Ave | −6.2103 × 10^{3} | −2.5413 × 10^{3} | −8.5857 × 10^{3} | −5.6850 × 10^{3} | −6.7474 × 10^{3} |

Std | 923.4325 | 377.5468 | 294.6083 | 617.4115 | 568.8082 | |

Min | −8.8187 × 10^{3} | −3.2992 × 10^{3} | −9.2405 × 10^{3} | −8.3628 × 10^{3} | −1.0711 × 10^{4} | |

${\mathrm{F}}_{9}$ | Ave | 30.8471 | 26.5986 | 75.3270 | 79.6629 | 38.5049 |

Std | 10.7542 | 7.5364 | 10.4607 | 20.1800 | 10.8053 | |

Min | 15.9193 | 13.9294 | 51.7229 | 45.7681 | 18.9042 | |

${\mathrm{F}}_{10}$ | Ave | 0.0683 | 8.0603 × 10^{−9} | 1.1229 × 10^{−4} | 2.1124 | 6.2630 × 10^{−9} |

Std | 0.3480 | 1.6945 × 10^{−9} | 1.4341 × 10^{−4} | 0.6619 | 2.0012 × 10^{−8} | |

Min | 3.9460 × 10^{−9} | 5.3680 × 10^{−9} | 1.2382 × 10^{−5} | 1.1551 | 4.9253 × 10^{−10} | |

${\mathrm{F}}_{11}$ | Ave | 0.0421 | 0.0738 | 0.0695 | 0.0140 | 0.0107 |

Std | 0.0492 | 0.0854 | 0.0503 | 0.0126 | 0.0111 | |

Min | 4.7629 × 10^{−14} | 5.2457 × 10^{−10} | 0.0055 | 3.5451 × 10^{−4} | 0.000 | |

${\mathrm{F}}_{12}$ | Ave | 4.9720 × 10^{−4} | 1.6556 × 10^{−9} | 9.6072 × 10^{−5} | 6.2029 | 0.1694 |

Std | 0.0013 | 4.9501 × 10^{−1}0 | 2.5802 × 10^{−4} | 3.9109 | 0.2336 | |

Min | 1.7475 × 10^{−7} | 8.6483 × 10^{−10} | 5.4287 × 10^{−7} | 1.8516 | 3.8621 × 10^{−18} | |

${\mathrm{F}}_{13}$ | Ave | 9.8245 × 10^{−4} | 3.6627 × 10^{−4} | 4.9824 × 10^{−6} | 0.1569 | 0.0044 |

Std | 0.0028 | 0.0020 | 3.7307 × 10^{−6} | 0.3956 | 0.0055 | |

Min | 2.0979 × 10^{−7} | 1.3857 × 10^{−8} | 8.7312 × 10^{−7} | 6.3967 × 10^{−6} | 5.5347 × 10^{−20} |

Function | Stats | PSO | GSA | CS | ALO | CS-ALO |
---|---|---|---|---|---|---|

${\mathrm{F}}_{14}$ | Ave | 3.3274 | 4.2276 | 0.9980 | 1.5605 | 0.9980 |

Std | 2.9242 | 3.3261 | 0 | 0.8104 | 0 | |

Min | 0.9980 | 0.9980 | 0.9980 | 0.9980 | 0.9980 | |

${\mathrm{F}}_{15}$ | Ave | 0.0018 | 0.0030 | 3.0781 × 10^{−}^{4} | 0.0015 | 4.9062 × 10^{−}^{4} |

Std | 0.0051 | 0.0018 | 1.7909 × 10^{−}^{6} | 0.0036 | 3.7254 × 10^{−}^{4} | |

Min | 3.0749 × 10^{−}^{4} | 0.0016 | 3.0749 × 10^{−}^{4} | 6.5332 × 10^{−4} | 3.0749 × 10^{−}^{4} | |

${\mathrm{F}}_{16}$ | Ave | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 |

Std | 6.7752 × 10^{−}^{16} | 5.6835 × 10^{−}^{16} | 6.7752 × 10^{−}^{16} | 8.0540 × 10^{−}^{14} | 6.7752 × 10^{−}^{16} | |

Min | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | |

${\mathrm{F}}_{17}$ | Ave | 0.3979 | 0.3979 | 0.3979 | 0.3979 | 0.3979 |

Std | 0 | 0 | 0 | 0 | 0 | |

Min | 0.3979 | 0.3979 | 0.3979 | 0.3979 | 0.3979 | |

${\mathrm{F}}_{18}$ | Ave | 3.0000 | 3.0000 | 3.0000 | 3.0000 | 3.0000 |

Std | 6.0599 × 10^{−}^{16} | 3.3831 × 10^{−}^{15} | 1.9305 × 10^{−}^{15} | 3.2372 × 10^{−}^{13} | 2.1138 × 10^{−}^{15} | |

Min | 3.0000 | 3.0000 | 3.0000 | 3.0000 | 3.0000 | |

${\mathrm{F}}_{19}$ | Ave | −3.8370 | −3.8628 | −3.8628 | −3.8628 | −3.8628 |

Std | 0.1411 | 2.3397 × 10^{−}^{15} | 2.7101 × 10^{−}^{15} | 1.6256 × 10^{−}^{14} | 2.7101 × 10^{−}^{15} | |

Min | −3.8628 | −3.8628 | −3.8628 | −3.8628 | −3.8628 | |

${\mathrm{F}}_{20}$ | Ave | −3.2982 | −3.3220 | −3.3220 | −3.2784 | −3.3220 |

Std | 0.0484 | 1.4402 × 10^{−}^{15} | 1.4189 × 10^{−}^{13} | 0.0583 | 1.3550 × 10^{−}^{15} | |

Min | −3.3220 | −3.3220 | −3.3220 | −3.3220 | −3.3220 | |

${\mathrm{F}}_{21}$ | Ave | −7.3140 | −5.8832 | −10.1532 | −7.5399 | −10.1532 |

Std | 3.3952 | 3.4533 | 7.1740 × 10^{−}^{15} | 2.9214 | 7.2269 × 10^{−}^{15} | |

Min | −10.1532 | −10.1532 | −10.1532 | −10.1532 | −10.1532 | |

${\mathrm{F}}_{22}$ | Ave | −6.6128 | −10.4029 | −10.4029 | −7.0935 | −10.4029 |

Std | 3.6550 | 1.1893 × 10^{−}^{15} | 2.1733 × 10^{−}^{14} | 3.2464 | 8.0799 × 10^{−}^{16} | |

Min | −10.4029 | −10.4029 | −10.4029 | −10.4029 | −10.4029 | |

${\mathrm{F}}_{23}$ | Ave | −6.5285 | −10.1069 | −10.5364 | −6.8672 | −10.5364 |

Std | 3.8524 | 1.6822 | 2.2734 × 10^{−}^{12} | 3.3537 | 1.8949 × 10^{−}^{15} | |

Min | −10.5364 | −10.5364 | −10.5364 | −10.5364 | −10.5364 |

PSO [23] | GSA [23] | CS | ALO | CS-ALO | |
---|---|---|---|---|---|

Mean | 0.1809 | 0.1826 | 0.1801 | 0.1804 | 0.1799 |

Std | 0.0002 | 0.0003 | 0.0000 | 0.0002 | 0.0000 |

Min | 0.1806 | 0.1822 | 0.1800 | 0.1801 | 0.1798 |

Max | 0.1811 | 0.1831 | 0.1801 | 0.1808 | 0.1801 |

Without SVC | With SVC | |||||
---|---|---|---|---|---|---|

PSO [23] | GSA [23] | CS | ALO | CS-ALO | ||

DEV | 3.5657 | 0.0144 | 0.0192 | 0.0081 | 0.0080 | 0.0081 |

${\mathrm{J}}_{1}$ | 1 | 0.0040 | 0.0054 | 0.0023 | 0.0022 | 0.0023 |

${\mathrm{P}}_{\mathrm{loss}}$ | 0.3183 | 0.2840 | 0.2855 | 0.2844 | 0.2845 | 0.2841 |

${\mathrm{J}}_{3}$ | 1 | 0.8922 | 0.8970 | 0.8935 | 0.8938 | 0.8926 |

J | 0.8 | 0.1809 | 0.1826 | 0.1801 | 0.18043 | 0.1799 |

SVC Number | Optimal Bus Number | Optimal Susceptance |
---|---|---|

1 | 17 | 10.000000 |

2 | 30 | 3.374653 |

3 | 41 | 9.999994 |

4 | 40 | 6.385686 |

5 | 42 | 6.747763 |

6 | 39 | 2.641199 |

7 | 49 | −0.999999 |

8 | 34 | 4.574809 |

9 | 31 | 2.886868 |

10 | 28 | 2.721426 |

11 | 53 | 6.609649 |

12 | 29 | 9.890116 |

PSO [23] | GSA [23] | CS | ALO | CS-ALO | |
---|---|---|---|---|---|

Mean | 0.1754 | 0.2048 | 0.1709 | 0.1713 | 0.1705 |

Std | 0.0016 | 0.0360 | 0.0001 | 0.0004 | 0.0001 |

Min | 0.1730 | 0.1777 | 0.1707 | 0.1706 | 0.1704 |

Max | 0.1767 | 0.2564 | 0.1710 | 0.1722 | 0.1709 |

Without SVC | With SVC | |||||
---|---|---|---|---|---|---|

PSO [23] | GSA [23] | CS | ALO | CS-ALO | ||

DEV | 2.6699 | 0.0178 | 0.1563 | 0.0118 | 0.0123 | 0.0124 |

${\mathrm{J}}_{1}$ | 1 | 0.0067 | 0.0585 | 0.0044 | 0.0046 | 0.0046 |

${\mathrm{P}}_{\mathrm{loss}}$ | 0.4666 | 0.3999 | 0.3958 | 0.3921 | 0.3917 | 0.3912 |

${\mathrm{J}}_{3}$ | 1 | 0.8571 | 0.8483 | 0.8403 | 0.8395 | 0.8384 |

J | 0.8 | 0.1754 | 0.2048 | 0.1709 | 0.1713 | 0.1705 |

SVC Number | Optimal Bus Number | Optimal Susceptance |
---|---|---|

1 | 54 | 9.832125 |

2 | 55 | 9.999988 |

3 | 53 | 9.390575 |

4 | 31 | 3.960381 |

5 | 29 | 9.633920 |

6 | 44 | 4.091333 |

7 | 26 | 6.876093 |

8 | 32 | 5.164825 |

9 | 52 | 5.260811 |

10 | 28 | 8.862748 |

11 | 41 | 8.578958 |

12 | 40 | 9.412178 |

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## Share and Cite

**MDPI and ACS Style**

Merah, H.; Gacem, A.; Ben Attous, D.; Lashab, A.; Jurado, F.; Sameh, M.A.
Sizing and Sitting of Static VAR Compensator (SVC) Using Hybrid Optimization of Combined Cuckoo Search (CS) and Antlion Optimization (ALO) Algorithms. *Energies* **2022**, *15*, 4852.
https://doi.org/10.3390/en15134852

**AMA Style**

Merah H, Gacem A, Ben Attous D, Lashab A, Jurado F, Sameh MA.
Sizing and Sitting of Static VAR Compensator (SVC) Using Hybrid Optimization of Combined Cuckoo Search (CS) and Antlion Optimization (ALO) Algorithms. *Energies*. 2022; 15(13):4852.
https://doi.org/10.3390/en15134852

**Chicago/Turabian Style**

Merah, Hana, Abdelmalek Gacem, Djilani Ben Attous, Abderezak Lashab, Francisco Jurado, and Mariam A. Sameh.
2022. "Sizing and Sitting of Static VAR Compensator (SVC) Using Hybrid Optimization of Combined Cuckoo Search (CS) and Antlion Optimization (ALO) Algorithms" *Energies* 15, no. 13: 4852.
https://doi.org/10.3390/en15134852