# Reactive Power Management Based Hybrid GAEO

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## Abstract

**:**

## 1. Introduction

- Solving the RPD problem using a new algorithm, GAEO, for the first time as far as the authors know based on literature review.
- The validity of the GAEO algorithm for minimizing power loss is investigated and compared with results of other techniques.
- GAEO is applied to optimize the RPD problem for the first time on three test systems: IEEE14-bus, IEEE-30bus, and IEEE57-bus.

## 2. Hybrid Genetic Algorithm Equilibrium Optimizer (GAEO)

## 3. Modelling of Power System

#### 3.1. Objective Function

_{k}, and the difference in angle between i and j is represented by ${\theta}_{k}$. The second objective function, which is the minimization of voltage deviation, can be represented by Equation (7).

#### 3.2. System Constraints

#### 3.2.1. Equality Constraints

#### 3.2.2. Inequality Constraints

## 4. Modeling and Implementation of GAEO Algorithm

#### 4.1. Initialization

#### 4.2. Main Loop

#### 4.2.1. Using GA (Crossover and Mutations)

#### 4.2.2. Using EO on the Best Half Population Members

#### 4.2.3. Balancing of Both Exploration and Exploitation

_{2}is the exploitation ability control variables. The value of the ${\mathrm{t}}_{0}$ is expressed by Equation (21).

#### 4.3. Adjusting Operating Parameters

- The exploration ability of control variables (a1).
- The exploitation ability of control variables (a2).
- Mutrate.
- Selection and participation probability of concentration updating by the generation rate control variable (GP).

## 5. Simulation and Results

#### 5.1. Case I IEEE 14-Bus System

#### 5.2. Modified IEEE 30-Bus System

#### 5.3. Case III IEEE 57-bus System

^{9}but reached the best value so far within 200 iterations.

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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IEEE 14-Bus | IEEE 30-Bus | IEEE 57-Bus | |
---|---|---|---|

Number of buses | 14 | 30 | 57 |

Number of line flow | 20 | 41 | 80 |

Generating units | 5 | 6 | 7 |

Transformer tap changer | 3 | 4 | 15 |

Reactive compensator | 2 | 3 | 3 |

Control variables | 10 | 13 | 25 |

P load (MW) | 259.0 | 283.40 | 1250.8 |

Q load (MVAR) | 73.5 | 126.20 | 336.40 |

P gen (MW) | 272.0 | 289.211 | 1279.26 |

Q gen (MVAR) | 82.44 | 108.922 | 345.45 |

P loss (MW) base case | 13.49 | 17.557 | 28.462 |

Range | Vg | Vl | tap | Qc |
---|---|---|---|---|

Minimum | 0.95 | 0.95 | 0.9 | 0 |

maximum | 1.1 | 1.5 | 1.1 | 0.3 |

Parameters | Values |
---|---|

No. of iterations | 100 |

Number of populations | 40 |

The exploration ability control variables (a1) | 2 |

The exploitation ability control variables (a2) | 1 |

Participation probability of concentration updating by the generation rate control variable (GP) | 0.3 |

Mutrate | 0.09 |

Selection | 0.5 |

Variable Name | Base Value | CBA-IV [5] | SCA [35] | ISSA [37] | GAEO |
---|---|---|---|---|---|

V1 | 1.06 | 1.092 | 1.09 | 1.1 | 1.0600 |

V2 | 1.045 | 1.0884 | 1.08 | 1.085802 | 1.0450 |

V3 | 1.01 | 1.0558 | 1.05 | 1.056346 | 1.0100 |

V6 | 1.07 | 1.0325 | 1.09 | 1.096919 | 1.0700 |

V8 | 1.09 | 1.0951 | 1.09 | 1.1 | 1.0900 |

T1 | 0.9467 | 0.9746 | 0.95 | 1.03 | 0.9780 |

T2 | 0.9524 | 1.0676 | 0.94 | 0.9 | 0.9690 |

T3 | 0.9091 | 1.0599 | 1.03 | 0.98 | 0.9320 |

Q9 | 0.18 | 0.2208 | 0.16 | 0.18 | 0.1900 |

Qc14 | 0.18 | 0.0786 | 0.05 | 0 | 0.1900 |

Real power loss (MW) | 13.49 | 12.2923 | 12.27 | 12.2834 | 12.2694 |

Parameters | Values |
---|---|

No. of iterations | 100 |

Number of populations | 40 |

The exploration ability control variables (a1) | 2 |

The exploitation ability control variables (a2) | 1 |

Participation probability of concentration updating by the generation rate control variable (GP) | 0.4 |

Mutrate | 0.09 |

Selection | 0.5 |

Variable Name | Base Value | DEPSO [38] | CPSMOEA [36] | GAEO |
---|---|---|---|---|

V1 | 1.06 | 0.9925 | 1.01 | 1.0600 |

V2 | 1.043 | 0.9989 | 1.0778 | 1.0450 |

V5 | 1.01 | 1.0646 | 1.0417 | 1.0100 |

V8 | 1.01 | 1.0017 | 1.0478 | 1.0100 |

V11 | 1.082 | 1.0448 | 1.0393 | 1.0820 |

V13 | 1.071 | 1.0252 | 1.0293 | 1.0710 |

T1 | 0.98 | 1.017 | 1.05 | 0.9780 |

T2 | 0.97 | 1.0461 | 1.05 | 0.9690 |

T3 | 0.93 | 1.0363 | 1.05 | 0.9320 |

T4 | 0.97 | 1.0299 | 1 | 0.9680 |

Q3 | 5 | 14.7 | 12 | 19.0000 |

Q10 | 19 | 13.99 | 20 | 4.3000 |

Q24 | 4 | 12.03 | 12 | 0.9000 |

Real power loss | 17.55 | 17.52 | 16.17 | 16.0428 |

Parameters | Values |
---|---|

No. of iterations | 200 |

Number of populations | 40 |

The exploration ability control variables (a1) | 2 |

The exploitation ability control variables (a2) | 1 |

Participation probability of concentration updating by the generation rate control variable (GP) | 0.2 |

Mutrate | 0.09 |

Selection | 0.5 |

Variable Name | SCA [35] | CBA-IV [5] | GAEO |
---|---|---|---|

V1 | 1.096 | 1.0964 | 1.0400 |

V2 | 1.089 | 1.0949 | 1.0100 |

V3 | 1.083 | 1.0906 | 0.9850 |

V6 | 1.082 | 1.0838 | 0.9800 |

V8 | 1.091 | 1.100 | 1.0050 |

V9 | 1.075 | 1.0869 | 0.9800 |

V12 | 1.070 | 1.0822 | 1.0150 |

T4-18 | 1.004 | 0.9002 | 0.9700 |

T4-18 | 1.029 | 0.9005 | 0.9780 |

T21-20 | 1.039 | 0.9958 | 1.0430 |

T24-25 | 1.022 | 1.0086 | 1.0430 |

T7-29 | 0.99 | 0.9061 | 0.9670 |

T34-32 | 1.029 | 0.9990 | 0.9750 |

T11-41 | 0.998 | 0.9087 | 0.9550 |

T15-45 | 1.023 | 0.9003 | 0.9550 |

T14-46 | 1.016 | 0.9002 | 0.9000 |

T10-51 | 0.999 | 0.9123 | 0.9300 |

T13-49 | 1.022 | 0.9002 | 0.8950 |

T11-43 | 0.998 | 0.9000 | 0.9580 |

T40-56 | 1.022 | 1.0267 | 0.9580 |

T39-57 | 0.992 | 0.9729 | 0.9800 |

T9-55 | 0.984 | 0.9220 | 0.9400 |

Qc18 | 0.066 | 0.1827 | 10.0000 |

Qc25 | 0.046 | 0.1335 | 5.9000 |

Qc53 | 0.030 | 0.0858 | 6.3000 |

Active power loss | 24.05 | 21.9627 | 23.2514 |

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## Share and Cite

**MDPI and ACS Style**

Hemeida, M.; Senjyu, T.; Alkhalaf, S.; Fawzy, A.; Ahmed, M.; Osheba, D.
Reactive Power Management Based Hybrid GAEO. *Sustainability* **2022**, *14*, 6933.
https://doi.org/10.3390/su14116933

**AMA Style**

Hemeida M, Senjyu T, Alkhalaf S, Fawzy A, Ahmed M, Osheba D.
Reactive Power Management Based Hybrid GAEO. *Sustainability*. 2022; 14(11):6933.
https://doi.org/10.3390/su14116933

**Chicago/Turabian Style**

Hemeida, Mahmoud, Tomonobu Senjyu, Salem Alkhalaf, Asmaa Fawzy, Mahrous Ahmed, and Dina Osheba.
2022. "Reactive Power Management Based Hybrid GAEO" *Sustainability* 14, no. 11: 6933.
https://doi.org/10.3390/su14116933