# African Vulture Optimization Algorithm-Based PI Controllers for Performance Enhancement of Hybrid Renewable-Energy Systems

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## Abstract

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## 1. Introduction

- Applying the incremental-conductance method combined with the PI controllers for the MPP tracking of PV and wind systems.
- Introducing a novel algorithm called the African Vultures Optimization Algorithm for tuning the PI controllers in the hybrid system.
- Comparing the results of the application of the AVOA with the PSO method.
- Implementing a storage system to smooth the fluctuations in the output of renewable systems, i.e., wind and PV systems, because of the irregular nature of wind speed and solar irradiance.

## 2. Hybrid DC Microgrid System

#### 2.1. AC System

#### 2.2. PV System

#### 2.3. Wind System

#### 2.4. Storage System

## 3. Methodology

#### 3.1. Incremental-Conductance Algorithm

#### 3.2. African Vulture Optimization Algorithm

- The African vulture population has N vultures, and each vulture’s position space is specified in d dimensions.
- The population of vultures is separated into three groups. The vultures’ quality position is determined by the feasible solution’s fitness value; the best solution is recognized as the best and first vulture, the second solution is recognized as the second-best vulture, and the other vultures are assigned to the third group.
- In the population, the three groups are created so that the most important natural role of vultures could be formulated. As a result, various vulture species play distinct roles.
- Also, the fitness value of the possible solution can reflect the benefits and drawbacks of vultures. Therefore, the weakest and most hungry vultures correlate to the worst vultures. The strongest and most numerous vultures, on the other hand, correlate to the best vulture at the time. Generally, all vultures in the AVOA aim to be near the best vultures while avoiding the worst.

- Phase 1: Population Grouping

- b.
- Phase 2: The Rate of Starvation of Vultures

- c.
- Phase 3: Exploration Stage

- d.
- Phase 4: Exploitation (First Stage)

- e.
- Phase 5: Exploitation (Second Stage)

## 4. Results and Discussion

#### 4.1. Optimization Results

#### 4.2. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

AC-Generator Ratings | |
---|---|

Line-to-line voltage | 25 kV |

Frequency | 60 Hz |

Base power | 50 MVA |

Base voltage | 25 kV |

X/R ratio | 7 |

Transformer ratings | |

Nominal power | 111.11 kVA |

Primary voltage | 25 kV |

Secondary voltage | 380 V |

Frequency | 60 Hz |

Universal Bridge (IGBT) ratings | |

Snubber-resistance R_{s} | 100 kΩ |

Snubber-capacitance C_{s} | inf |

R_{on}, L_{on} | 1 mΩ, 0 H |

Forward voltage (V_{f}) | 0 V |

Parameter | Rating |
---|---|

Module type | Tata Power Systems TP240MBZ |

$\mathrm{Maximum}\text{}\mathrm{power}\text{}({P}_{m}$) | 238.95 W |

Number of cells | 60 |

Open-circuit voltage (V_{oc}) | 36.5 V |

Max-power voltage (V_{mp}) | 29.5 V |

Short-circuit current (I_{sc}) | 8.78 A |

Max-power current (I_{mp}) | 8.1 A |

$\mathrm{Series}\text{}\mathrm{resistance}\text{}({R}_{s}$) | 0.32793 Ω |

$\mathrm{Shunt}\text{}\mathrm{resistance}\text{}({R}_{sh}$) | 113.1517 Ω |

Voltage-temp. coefficient | −0.33 (%V/°C) |

Current-temp. coefficient | 0.063804 (%/°C) |

Parameter | Rating |
---|---|

Input DC Voltage | 253.7 V |

Output DC Voltage | 500 V |

Switching frequency | 5 kHz |

L | 1.6 mH |

${C}_{pv}$ | 1.6 mF |

${C}_{out}$ | 12 mF |

Wind Turbine | |
---|---|

Nominal mechanical-output power | 10 (kW) |

Wind speed at nominal speed | 11 (m/s) |

2-Mass Drive Train | |

Wind-turbine inertia constant H | 4.32 (s) |

Shaft-spring constant | 0.3 (p.u.) |

Shaft mutual damping | 1.5 (p.u.) |

Turbine initial speed | 1 (p.u.) |

Initial output torque | 1 (p.u.) |

Synchronous generator ratings | |

Power | 11.11 kVA |

Frequency | 60 Hz |

Line to line voltage | 220 V |

Reactances [Xd, Xd′, Xd″, Xq, Xq″] in p.u. | [1.305, 0.296, 0.252, 0.474, 0.243] |

Time constants [Td′, Td″, Tq″] in seconds | [4.49, 0.0681, 0.0513] |

Inertia constant H(s), friction factor F(p.u.), and pairs of poles | [0.62, 0.01, 4] |

Rectifier (Diodes) | |

Snubber-resistance R_{s} | 0.15 Ω |

Snubber-capacitance C_{s} | 0.55 µF |

R_{on}, L_{on} | 1 µΩ, 0 H |

Forward voltage (V_{f}) | 0 V |

Parameter | Rating |
---|---|

Type | Lithium-Ion |

Nominal voltage | 120 V |

Rated capacity | 800 Ah |

Initial state of charge | 50 % |

Buck-boost-converter ratings | |

C_{in} | 1.6 mF |

C_{out} | 12 mF |

L | 0.3 mH |

Diodes of buck-boost converter | |

Internal resistance (R_{on}) | 1 mΩ |

Snubber resistance (R_{s}) | 100 kΩ |

Snubber capacitance (C_{s}) | Inf |

Parameter | Rating |
---|---|

DC-bus voltage | 500 V |

${\mathrm{Load}}_{1}\left({\mathrm{R}}_{1}\right)$ | 5 Ω |

${\mathrm{Load}}_{2}\left({\mathrm{R}}_{2}\right)$ | 6.25 Ω |

${\mathrm{Load}}_{3}\left({\mathrm{R}}_{3}\right)$ | 8.33 Ω |

${\mathrm{Load}}_{4}\left({\mathrm{R}}_{4}\right)$ | 25 Ω |

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**Figure 13.**Convergence curves for tuning of PI controllers of the PV system using AVOA and PSO methods.

**Figure 15.**Convergence curves for tuning of PI controllers in the wind system using AVOA and PSO methods.

**Figure 17.**Convergence curves for tuning of PI controllers in the storage system using AVOA and PSO methods.

Parameter | Method | |
---|---|---|

AVOA | PSO | |

No. of particles/populations | 30 | 30 |

No. of iterations | 100 | 100 |

Dimension (No. of variables) | 2 | 2 |

Control parameters p1, p2, p3 | 0.6, 0.4, 0.6 | --- |

α | 0.8 | --- |

β | 0.2 | --- |

γ | 2.5 | --- |

Inertia weight (w) | --- | 0.9~0.4 |

Cognitive factor (${c}_{1}$) | --- | 1.5 |

Social factor (${c}_{2}$) | --- | 1.5 |

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## Share and Cite

**MDPI and ACS Style**

Ghazi, G.A.; Hasanien, H.M.; Al-Ammar, E.A.; Turky, R.A.; Ko, W.; Park, S.; Choi, H.-J.
African Vulture Optimization Algorithm-Based PI Controllers for Performance Enhancement of Hybrid Renewable-Energy Systems. *Sustainability* **2022**, *14*, 8172.
https://doi.org/10.3390/su14138172

**AMA Style**

Ghazi GA, Hasanien HM, Al-Ammar EA, Turky RA, Ko W, Park S, Choi H-J.
African Vulture Optimization Algorithm-Based PI Controllers for Performance Enhancement of Hybrid Renewable-Energy Systems. *Sustainability*. 2022; 14(13):8172.
https://doi.org/10.3390/su14138172

**Chicago/Turabian Style**

Ghazi, Ghazi A., Hany M. Hasanien, Essam A. Al-Ammar, Rania A. Turky, Wonsuk Ko, Sisam Park, and Hyeong-Jin Choi.
2022. "African Vulture Optimization Algorithm-Based PI Controllers for Performance Enhancement of Hybrid Renewable-Energy Systems" *Sustainability* 14, no. 13: 8172.
https://doi.org/10.3390/su14138172