# A Real Distribution Network Voltage Regulation Incorporating Auto-Tap-Changer Pole Transformer Multiobjective Optimization

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## Abstract

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^{®}environment to compare and evaluate performance of the proposed network under different situations and scenarios.

## 1. Introduction

## 2. Characteristics of the System Model and Problem Description

## 3. Methodology

#### 3.1. Multiobjective Optimization Using Genetic Algorithm

#### 3.2. Objective Functions

#### 3.3. Optimal Placement Problem

## 4. Simulation Result and Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

${a}_{i}$ | The number of introduced ATCTr at each node $i$ |

${F}_{1},{F}_{2}$ | Objective functions |

${g}_{A}~{g}_{C}$ | The numbers of tap change position |

$N$ | Total number of buses |

$\mathbb{P}$ | The placement of installed ATCTrs in overall nodes |

${T}_{i}$ | The tap position of node $i$ |

${T}_{min}$,${T}_{max}$ | Lower and upper tap position limits |

${V}_{i}$ | Distribution voltage of node $i$ |

${V}_{i,t}$ | Voltage deviation on each node $i$ at time $t$ |

${V}_{min}$,${V}_{max}$. | Voltage’s lower and upper limits respectively |

${x}_{t}$ | The number of taps changing positiont time $t$ |

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**Figure 4.**Real distribution network model: (

**a**) Daily load profile; (

**b**) hourly voltage profile (uncontrolled); (

**c**) voltage profile using ATCTrs (controlled); (

**d**) Pareto optimal solutions.

**Figure 5.**Node voltages of solution A for all tap position constraints (${g}_{A}\u2013{g}_{C}$). (

**a**) Node voltages (equality constraint of ${g}_{A}$); (

**b**) node voltages (equality constraint of ${g}_{B}$); (

**c**) node voltages (equality constraint of ${g}_{C}$).

**Figure 6.**Node voltages of solution B for all tap position constraints (${g}_{A}\u2013{g}_{C}$). (

**a**) Node voltages (equality constraint of ${g}_{A}$); (

**b**) node voltages (equality constraint of ${g}_{B}$); (

**c**) node voltages (equality constraint of ${g}_{C}$).

**Figure 7.**Node voltages of solution C for all tap position constraints (${g}_{A}\u2013{g}_{C}$). (

**a**) Node voltages (equality constraint of ${g}_{A}$); (

**b**) node voltages (equality constraint of ${g}_{B}$); (

**c**) node voltages (equality constraint of ${g}_{C}$).

**Figure 8.**Node voltages of solution D for all tap position constraints (${g}_{A}\u2013{g}_{C}$). (

**a**) Node voltages (equality constraint of ${g}_{A}$); (

**b**) node voltages (equality constraint of ${g}_{B}$); (

**c**) node voltages (equality constraint of ${g}_{C}$).

Line Number | Bus Code | Length (km) | R (pu) | X (pu) | |
---|---|---|---|---|---|

From | To | ||||

1 | 1 | 2 | 0.75 | 0.246 | 0.072375 |

2 | 2 | 3 | 0.8 | 0.2624 | 0.0772 |

3 | 3 | 4 | 0.6 | 0.1968 | 0.0579 |

4 | 3 | 12 | 0.4 | 0.1312 | 0.0386 |

5 | 4 | 5 | 0.65 | 0.2132 | 0.062725 |

6 | 5 | 6 | 0.95 | 0.3116 | 0.091675 |

7 | 5 | 13 | 0.7 | 0.2296 | 0.06755 |

8 | 6 | 7 | 0.65 | 0.2132 | 0.062725 |

9 | 6 | 14 | 1.4 | 0.4592 | 0.1351 |

10 | 14 | 15 | 0.6 | 0.1968 | 0.0579 |

11 | 7 | 8 | 0.8 | 0.2624 | 0.0772 |

12 | 7 | 16 | 0.65 | 0.2132 | 0.062725 |

13 | 16 | 17 | 0.6 | 0.1968 | 0.0579 |

14 | 17 | 18 | 0.55 | 0.1804 | 0.053075 |

15 | 8 | 9 | 0.65 | 0.2132 | 0.062725 |

16 | 9 | 10 | 0.4 | 0.1312 | 0.0386 |

17 | 9 | 19 | 0.8 | 0.2624 | 0.0772 |

18 | 19 | 20 | 0.45 | 0.1476 | 0.043425 |

19 | 20 | 21 | 0.4 | 0.1312 | 0.0386 |

20 | 21 | 22 | 0.4 | 0.1312 | 0.0386 |

21 | 10 | 11 | 0.45 | 0.1476 | 0.043425 |

Node Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Installed position | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Node Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Equality constraint of g_{A} | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Equality constraint of g_{B} | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Equality constraint of g_{C} | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Node Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Equality constraint of g_{A} | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |

Equality constraint of g_{B} | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |

Equality constraint of g_{C} | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |

Node Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Equality constraint of g_{A} | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |

Equality constraint of g_{B} | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |

Equality constraint of g_{C} | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |

Node Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Equality constraint of g_{A} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

Equality constraint of g_{B} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

Equality constraint of g_{C} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

Solution A | Solution B | Solution C | Solution D | |
---|---|---|---|---|

Voltage magnitude for ${g}_{A}$ | 0.8995 | 0.9397 | 0.9413 | 0.9487 |

Voltage magnitude for ${g}_{B}$ | 0.9157 | 0.9457 | 0.9642 | 0.9711 |

Voltage magnitude for ${g}_{C}$ | 0.9251 | 0.9641 | 0.9703 | 0.9786 |

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## Share and Cite

**MDPI and ACS Style**

Danish, S.M.S.; Shigenobu, R.; Kinjo, M.; Mandal, P.; Krishna, N.; Hemeida, A.M.; Senjyu, T. A Real Distribution Network Voltage Regulation Incorporating Auto-Tap-Changer Pole Transformer Multiobjective Optimization. *Appl. Sci.* **2019**, *9*, 2813.
https://doi.org/10.3390/app9142813

**AMA Style**

Danish SMS, Shigenobu R, Kinjo M, Mandal P, Krishna N, Hemeida AM, Senjyu T. A Real Distribution Network Voltage Regulation Incorporating Auto-Tap-Changer Pole Transformer Multiobjective Optimization. *Applied Sciences*. 2019; 9(14):2813.
https://doi.org/10.3390/app9142813

**Chicago/Turabian Style**

Danish, Sayed Mir Shah, Ryuto Shigenobu, Mitsunaga Kinjo, Paras Mandal, Narayanan Krishna, Ashraf Mohamed Hemeida, and Tomonobu Senjyu. 2019. "A Real Distribution Network Voltage Regulation Incorporating Auto-Tap-Changer Pole Transformer Multiobjective Optimization" *Applied Sciences* 9, no. 14: 2813.
https://doi.org/10.3390/app9142813