# Optimal Allocation of Large-Capacity Distributed Generation with the Volt/Var Control Capability Using Particle Swarm Optimization

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Contributions and Findings

#### 1.2. Structure

## 2. Problem Statement

- Location and VVC. DG can be installed on all buses except for a slack bus. Buses to which DG systems are connected can participate in VVC. A target voltage magnitude is set at 1.00 p.u to maximize the effect of VVC on the system.
- Capacity. In this paper, it is assumed that DG systems are connected to the transmission system in the form of a large-capacity energy resource (e.g., conventional generators, PV, or wind farms). However, the capacity of DG does not exceed the system’s base MVA (e.g., S
_{base}). - Load profile. The optimization should be in conjunction with load profile data.

## 3. Previous Method

#### 3.1. Distributed Generation

- i = bus location (e.g., bus number),
- P
_{i}^{max}= maximum active power of ith DG, - P
_{i}^{min}= minimum active power of ith DG, - P
_{DG},_{i}= active power of ith DG, - Q
_{i}^{min}= minimum reactive power of ith DG, - Q
_{i}^{max}= maximum reactive power of ith DG, - Q
_{DG,i}= reactive power of ith DG.

- P
_{DG},_{i}= generation output of ith DG, - P
_{g,i}= generation output of the ith generator, - P
_{load,i}= load or demand of the ith bus, - P
_{losses,i}= line loss of branch i.

- V
_{i}^{min}= minimum voltage magnitude of the ith bus, - V
_{i}^{max}= maximum voltage magnitude of the ith bus, - V
_{i}= voltage magnitude of the ith bus.

#### 3.2. Particle Swarm Optimization

_{best}) is created through an iterative process and converges to the best swarm position (G

_{best}),

- v = velocity,
- x = position,
- w = coefficient of inertia,
- rand = random number,
- c
_{1}and c_{2}= weight coefficient value.

_{best}). Figure 1 shows the workflow of a typical PSO algorithm for optimal DG allocation.

_{1}and c

_{2}. The values of the parameters are set as follows:

- w
_{min}= 0.4, - w
_{max}= 0.9, - c
_{1}and c_{2}= 2.

#### 3.3. Volt/Var Control

_{2}), the bus is supplied with reactive power from the DG. If the voltage rises above the set value (i.e., V

_{3}), the bus consumes reactive power. The controlled reactive power is obtained as the pu value from the result of Equation (7). Injected reactive power is used in the power flow equations. That is, the reactive power is either injected or consumed in the buses while iteratively adjusting the voltage magnitude within the set value. For example, Q(V) determined by Equation (6) iteratively calculates the new active and reactive power set point (${S}_{\mathrm{DG}}^{(i+1)}$) of DG that participates in VVC.

- ${S}_{\mathrm{rated}}$ = rated complex power of DG,
- ${S}_{\mathrm{DG}}^{(i+1)}$= complex power set point of DG at iteration (i + 1),
- Q
^{(i)}= reactive power injected by DG at iteration i.

## 4. Proposed Method

#### 4.1. Load Profile

#### 4.2. PSO with VVC

#### 4.2.1. Objective Function

- V
_{i,h}= voltage at bus i and time h, - N = the last number of buses in the test feeder,
- T = total hours,
- h = hour.

_{cost}) to the OF.

_{DG}is the average installation cost of DG in USD/kW (e.g., 3.975 USD/kW) and M is the last number of DG.

_{loss, i, h}) are also added to the OF.

_{loss}is the complex loss of branch i.

#### 4.2.2. Normalization

_{base}) in all branches.

#### 4.2.3. Objective Function Evaluation

#### 4.3. Workflow of the Proposed Method

## 5. Case Studies

#### 5.1. IEEE 30-Bus Test System

#### 5.2. IEEE 14-Bus Test System

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

DG | distributed generation |

IC | installation cost |

GA | genetic algorithm |

OF | objective function |

PSO | particle swarm optimization |

pu | per unit |

PV | photovoltaic |

VVC | Volt/Var control |

## Appendix A

#### Appendix A.1. Newton–Raphson Method Power Flow

**x**), including the angle (δ) and the magnitude (V) of the voltage,

**J**):

**x**

^{(0)}), the method continues to satisfy the following convergence:

#### Appendix A.2. Result of Genetic Algorithm

Location (bus) | Capacity (MVA) | |
---|---|---|

IEEE 30-bus | IEEE 14-bus | |

1 | 0 | 0 |

2 | 0 | 0 |

3 | 5.52 | 0 |

4 | 1.44 | 10.91 |

5 | 0 | 0.10 |

6 | 23.25 | 29.82 |

7 | 20.47 | 0.42 |

8 | 0 | 4.82 |

9 | 10.37 | 4.40 |

10 | 8.91 | 5.17 |

11 | 11.26 | 0.19 |

12 | 1.01 | 0 |

13 | 88.33 | 0 |

14 | 5.00 | 5.89 |

15 | 3.59 | - |

16 | 1.63 | - |

17 | 2.28 | - |

18 | 0.20 | - |

19 | 5.76 | - |

20 | 2.33 | - |

21 | 1.26 | - |

22 | 0.90 | - |

23 | 0.92 | - |

24 | 1.51 | - |

25 | 0.25 | - |

26 | 2.44 | - |

27 | 3.18 | - |

28 | 6.56 | - |

29 | 1.04 | - |

30 | 2.76 | - |

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**Figure 5.**IEEE 30-bus test system [33].

**Figure 9.**IEEE 14-bus test system [36].

Setpoint (V, Q) | V_{1} | V_{2} | V_{3} | V_{4} |
---|---|---|---|---|

Value (pu) | 0.98 | 0.99 | 1.01 | 1.02 |

Setpoint (Q) | Q_{1} | Q_{2} | Q_{3} | Q_{4} |

Value (pu) | 1 | 0 | 0 | −1 |

1st Previous Method (PSO without VVC and Load Profile) | 2nd Previous (PSO with Load Profile without VVC) | Proposed Method (PSO/VVC with Load Profile) | |||
---|---|---|---|---|---|

Location | Capacity (MVA) | Location | Capacity (MVA) | Location | Capacity (MVA) |

6 | 0.49 | 5 | 27.76 | 7 | 20.87 |

9 | 100 | 8 | 10.36 | 11 | 86.21 |

15 | 23.92 | 11 | 88.81 | 21 | 14.31 |

16 | 8.54 | 15 | 13.19 | 28 | 25.44 |

18 | 11.01 | 21 | 10.22 | 29 | 5.23 |

20 | 8.99 | 27 | 35.46 | - | - |

21 | 25.14 | - | - | - | - |

25 | 22.15 | - | - | - | - |

27 | 5.77 | - | - | - | - |

30 | 16.29 | - | - | - | - |

Model | V (%) | Loss (%) | IC | OF |
---|---|---|---|---|

Without DG | 0.0742 (100%) | 0.0194 (100%) | 0 | 0.0936 |

1st previous method | 0.0341 (45.96%) | 0.0048 (24.74%) | 0.0247 | 0.0637 |

2nd previous method | 0.0271 (36.52%) | 0.0025 (12.89%) | 0.0206 | 0.0502 |

GA method | 0.0152(20.49%) | 0.0040(20.62%) | 0.0236 | 0.0427 |

Proposed method | 0.0193 (26.01%) | 0.0053 (27.32%) | 0.0169 | 0.0415 |

1st Previous Method (PSO without VVC and Load Profile) | 2nd Previous (PSO with Load Profile without VVC) | Proposed Method (PSO/VVC with Load Profile) | |||
---|---|---|---|---|---|

Location | Capacity (MVA) | Location | Capacity (MVA) | Location | Capacity (MVA) |

3 | 15.57 | 3 | 16.64 | 6 | 31.58 |

9 | 18.55 | 8 | 75.39 | 10 | 11.54 |

10 | 32.34 | 14 | 22.34 | 14 | 5.51 |

14 | 34.20 | - | - | - | - |

Model | V (%) | Losses (%) | IC | OF |
---|---|---|---|---|

Without DG | 0.0407 (100%) | 0.0325 (100%) | 0 | 0.0732 |

1st previous method | 0.0275 (67.57%) | 0.0183 (56.31%) | 0.0240 | 0.0698 |

2nd previous method | 0.0216 (53.07%) | 0.008 (24.62%) | 0.0272 | 0.0568 |

GA method | 0.0198(48.65%) | 0.0161(49.54%) | 0.0147 | 0.0506 |

Proposed method | 0.0218 (53.56%) | 0.0167 (51.38%) | 0.0116 | 0.0500 |

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**MDPI and ACS Style**

Lee, D.; Son, S.; Kim, I.
Optimal Allocation of Large-Capacity Distributed Generation with the Volt/Var Control Capability Using Particle Swarm Optimization. *Energies* **2021**, *14*, 3112.
https://doi.org/10.3390/en14113112

**AMA Style**

Lee D, Son S, Kim I.
Optimal Allocation of Large-Capacity Distributed Generation with the Volt/Var Control Capability Using Particle Swarm Optimization. *Energies*. 2021; 14(11):3112.
https://doi.org/10.3390/en14113112

**Chicago/Turabian Style**

Lee, Donghyeon, Seungwan Son, and Insu Kim.
2021. "Optimal Allocation of Large-Capacity Distributed Generation with the Volt/Var Control Capability Using Particle Swarm Optimization" *Energies* 14, no. 11: 3112.
https://doi.org/10.3390/en14113112