# A Two-stage Optimal Network Reconfiguration Approach for Minimizing Energy Loss of Distribution Networks Using Particle Swarm Optimization Algorithm

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## Abstract

**:**

## 1. Introduction

_{2}emissions are reduced and global warming is prevented. Constructing microgrids in industrial parks, campuses, shopping malls, off-shore islands, and remote districts is worthwhile because of the all the aforementioned advantages.

## 2. Problem Formulation

#### 2.1. Describes Network Reconfiguration Problem

- Mathematical optimization methods,
- Heuristic methods,
- Artificial intelligence methods.

#### 2.2. Describes Phase Balancing Problem

#### 2.3. Particle Swarm Optimization Algorithm

_{max}is the maximum iteration, n is the particle number, ${V}_{n}^{k}$ is the velocity of particle n at the k

^{th}iteration, ${s}_{n}^{k}$ is the k

^{th}position of particle n, c

_{1}and c

_{2}are learning factors, rand

_{1}and rand

_{2}are random numbers between 0 and 1, $pbes{t}_{n}^{k}$ is the best value of particle n at the k

^{th}iteration, and $gbes{t}^{k}$ is the global best value at the k

^{th}iteration. w, w

_{max}, and w

_{min}are acceleration coefficients, maximum weighting values, and minimum weighting values, respectively.

#### 2.4. Power Flow Algorithm

^{−1}]

^{t}

#### 2.5. Description of the Objective Function

#### 2.5.1. Three-Phase Voltage Unbalance

_{0,i}, V

_{1,i}and V

_{2,i}and n denotes the bus number.

#### 2.5.2. Energy Loss

_{avg}) and maximum load demand (P

_{peak}) in a period of time (T) is the definition of load factor (LF) as shown in Equation (14), where p(t) is the instantaneous power. The typical value of LF in a distribution system is between 30% and 70% [29], so the LF is set as 62.68% in this paper. The maximum load demands can be derived from the measured daily load curve. Furthermore, the loss factor (LSF) is defined as the ratio between the average power loss (P

_{avg,loss}) and maximum power loss (P

_{peak.loss}) in a period of time (T) as shown in Equation (15), where p

_{loss}(t) is the instantaneous power loss, and the LSF is set as 49.11% in this paper.

#### 2.5.3. Multi-Objective Function

_{i}is an adjustable weighting factor depend on the requirement; besides, ${E}_{\text{daily,loss}}^{\text{max}}$ and ${E}_{\text{daily,loss}}^{\text{min}}$ represent the maximum and minimum values of daily energy loss of the particles in a swarm; similarly, the same meanings of $T{D}_{\text{o}}^{\text{max}}$, $T{D}_{\text{o}}^{\text{min}}$, $T{D}_{2}^{\text{max}}$, and $T{D}_{2}^{\text{min}}$ in Equation (20).

_{j}denotes the current of the j

^{th}line. Meanwhile, P

_{i}and Q

_{i}denote the real and reactive power flow out of bus i, respectively; r

_{i}and x

_{i}are the resistance and reactance between bus i and i + 1; Li represents the line current between bus i and i + 1; in Equation (24), V

_{i}, V

_{Ui}, and V

_{Li}denote the voltage at bus i and its upper and lower limits, respectively. In Equations (25) and (26), ${D}_{0,i}$ and$\text{}{D}_{2,i}$ represent the zero- and negative sequence voltage factors at bus i, and ${D}_{0}^{\text{max}.}$ and ${D}_{2}^{\text{max}.}$ are the specified maximum values of zero- and negative sequence voltage factors, respectively. In Equation (27), g is the network topology; and G represents the sets of radial topologies, which cannot be closed-loop and islanding topologies, the A matrix that is the element-bus incidence matrix can be used to check the network topology, if the determinant of A equals 1 or − 1 and then it is the radial topology; otherwise, if the determinant of A equals 0 and then it is not a radial topology.

## 3. Numerical Results

#### 3.1. IEEE 37-Bus Test System

Stage | Parameter | ||||||
---|---|---|---|---|---|---|---|

Particle | Max. iteration | c_{1} | c_{2} | w_{1} | w_{2} | w_{3} | |

First stage | 100 | 200 | 2 | 2 | 1 | 0 | 0 |

Second stage | 500 | 200 | 2 | 2 | 0.7 | 0.15 | 0.15 |

**Table 2.**Individual phase loads before and after phase balancing arrangement at each bus of IEEE 37-bus test system.

Bus | Loads | Before phase balancing | |||||
---|---|---|---|---|---|---|---|

Phase A | Phase B | Phase C | |||||

Bus number | Phase type | P (kW) | Q (kvar) | P (kW) | Q (kvar) | P (kW) | Q (kvar) |

701 | ABC | 224.54 | 181.07 | 144.03 | 72.02 | 279.58 | 70.99 |

712 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

713 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

714 | ABC | 10.84 | −0.34 | 20.07 | 8.21 | 8.18 | 10.65 |

718 | AB | 54.21 | −1.7 | 33.24 | 42.85 | 0 | 0 |

720 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

722 | ABC | 8.18 | 10.65 | 90.36 | −0.69 | 67.09 | 72.34 |

724 | BC | 0 | 0 | 27.11 | −0.21 | 16.1 | 21.81 |

725 | BC | 0 | 0 | 27.11 | −0.21 | 16.1 | 21.81 |

727 | AC | 16.1 | 21.81 | 0 | 0 | 27.11 | −0.21 |

728 | ABC | 42 | 21 | 42 | 21 | 42 | 21 |

729 | AB | 27.11 | −0.21 | 16.1 | 21.81 | 0 | 0 |

730 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

731 | BC | 0 | 0 | 54.21 | −1.7 | 33.24 | 42.85 |

732 | AC | 16.1 | 21.81 | 0 | 0 | 27.11 | −0.21 |

733 | AB | 54.21 | −1.7 | 33.24 | 42.85 | 0 | 0 |

734 | AC | 16.1 | 21.81 | 0 | 0 | 27.11 | −0.21 |

735 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

736 | BC | 0 | 0 | 27.11 | −0.21 | 16.1 | 21.81 |

737 | AB | 90.36 | −0.68 | 53.37 | 72.7 | 0 | 0 |

738 | AB | 81.06 | −1.13 | 42.56 | 64.92 | 0 | 0 |

740 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

741 | AC | 16.1 | 21.81 | 0 | 0 | 27.11 | −0.21 |

742 | ABC | 5.16 | −0.04 | 57.27 | 2.45 | 33.24 | 42.85 |

744 | AB | 27.11 | −0.21 | 16.1 | 21.81 | 0 | 0 |

Total | 888.62 | 551.05 | 683.88 | 367.6 | 945.33 | 315.07 | |

Bus | Loads | After phase balancing | |||||

Phase A | Phase B | Phase C | |||||

Bus number | Phase type | P (kW) | Q (kvar) | P (kW) | Q (kvar) | P (kW) | Q (kvar) |

701 | ABC | 144.03 | 72.02 | 279.58 | 70.99 | 224.54 | 181.07 |

712 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

713 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

714 | ABC | 20.07 | 8.21 | 10.84 | −0.34 | 8.18 | 10.65 |

718 | AB | 54.21 | −1.7 | 33.24 | 42.85 | 0 | 0 |

720 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

722 | ABC | 8.18 | 10.65 | 67.09 | 72.34 | 90.36 | −0.69 |

724 | BC | 0 | 0 | 16.1 | 21.81 | 27.11 | −0.21 |

725 | BC | 0 | 0 | 27.11 | −0.21 | 16.1 | 21.81 |

727 | AC | 16.1 | 21.81 | 0 | 0 | 27.11 | −0.21 |

728 | ABC | 42 | 21 | 42 | 21 | 42 | 21 |

729 | AB | 27.11 | −0.21 | 16.1 | 21.81 | 0 | 0 |

730 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

731 | BC | 0 | 0 | 54.21 | −1.7 | 33.24 | 42.85 |

732 | AC | 27.11 | −0.21 | 0 | 0 | 16.1 | 21.81 |

733 | AB | 33.24 | 42.85 | 54.21 | −1.7 | 0 | 0 |

734 | AC | 16.1 | 21.81 | 0 | 0 | 27.11 | −0.21 |

735 | AC | 33.24 | 42.85 | 0 | 0 | 54.21 | −1.7 |

736 | BC | 0 | 0 | 27.11 | −0.21 | 16.1 | 21.81 |

737 | AB | 90.36 | −0.68 | 53.37 | 72.7 | 0 | 0 |

738 | AB | 81.06 | −1.13 | 42.56 | 64.92 | 0 | 0 |

740 | AC | 54.21 | −1.7 | 0 | 0 | 33.24 | 42.85 |

741 | AC | 16.1 | 21.81 | 0 | 0 | 27.11 | −0.21 |

742 | ABC | 57.27 | 2.45 | 33.24 | 42.85 | 5.16 | −0.04 |

744 | AB | 16.1 | 21.81 | 27.11 | −0.21 | 0 | 0 |

Total | 869.45 | 453.04 | 783.87 | 426.9 | 864.51 | 353.78 |

**Figure 4.**IEEE 37-bus test system: (

**a**) before reconfiguration; (

**b**) after the first stage reconfiguration.

^{th}and 29

^{th}iteration, respectively. The new phase connections of individual phase loads are listed in Table 2 after second stage phase balancing algorithm, the simulation result depicts that the three-phase complex powers are more balanced than before phase arrangement.

**Figure 5.**Convergence characteristics of proposed method of the IEEE 37-bus test system: (

**a**) the first stage; (

**b**) the second stage.

**Figure 6.**Simulation result of the bus voltage of the IEEE 37-bus test system: (

**a**) before optimization; (

**b**) after first stage; and (

**c**) after second stage.

**Figure 7.**Simulation result of the voltage unbalance factors of the IEEE 37-bus test system: (

**a**) zero-sequence voltage unbalance factor; and (

**b**) negative-sequence voltage unbalance factor.

#### 3.2. Institute of Nuclear Energy Research Microgrid

From bus | To bus | Line resistance (pu) | Line reactance (pu) | Z (%) | Distance (m) | Transformer rating (kV) | Transformer capacity (kVA) | X/R |
---|---|---|---|---|---|---|---|---|

1 | 2 | - | - | 3.85 | - | 11.4/0.38 | 500 | 8.02 |

2 | 3 | 0.2918 | 0.354 | - | 50 | - | - | - |

3 | 4 | - | - | 2 | - | 0.38/0.48 | 100 | 8 |

3 | 5 | 0.2918 | 0.354 | - | 50 | - | - | - |

5 | 6 | - | - | 4 | - | 0.38/0.38 | 150 | 8 |

3 | 7 | 0.2918 | 0.354 | - | 25 | - | - | - |

7 | 8 | - | - | 8 | - | 0.38/0.38 | 400 | 8 |

7 | 9 | 0.2918 | 0.354 | - | 25 | - | - | - |

9 | 10 | 0.2918 | 0.354 | - | 25 | - | - | - |

10 | 11 | - | - | - | - | 0.38/0.38 | 150 | 8 |

3 | 9 | 0.2918 | 0.354 | - | 25 | 0 | - | - |

6 | 12 | - | - | 4 | - | 0.38/0.208 | 150 | 8 |

^{th}and 21

^{th}iteration, respectively. The new phase connections of individual phase loads are shown in Table 4; the simulation result demonstrates that the three-phase complex powers are more balanced than before phase arrangement. Figure 11 shows the simulation result of the three-phase bus voltage profile of a weekday in summer. After the two-stage optimization approach, the voltage profile was better than that before optimization. Figure 12 indicates the simulation result of the voltage unbalance factors after optimization was better than that before optimization.

**Figure 10.**Optimal network reconfiguration function in energy management system (EMS) of the INER microgrid.

**Table 4.**Individual phase loads of a weekday in summer before and after phase balancing at each bus of the INER microgrid.

Bus | Loads | Before phase balancing | |||||
---|---|---|---|---|---|---|---|

Phase A | Phase B | Phase C | |||||

Bus number | Phase type | P (kW) | Q (kvar) | P (kW) | Q (kvar) | P (kW) | Q (kvar) |

2 | ABC | 0.5342 | 0.3106 | 0.5342 | 0.3106 | 0.5342 | 0.3106 |

3 | ABC | 0.0694 | 0.0404 | 0.0694 | 0.0404 | 0.0694 | 0.0404 |

5 | ABC | 24 | 4 | 19.8 | 3.3 | 16.2 | 2.7 |

6 | ABC | −18.5647 | 0.0932 | −18.5647 | 0.0932 | −18.5647 | 0.0932 |

7 | ABC | 0.4274 | 0.2485 | 0.4274 | 0.2485 | 0.4274 | 0.2485 |

8 | ABC | −6.5333 | 0 | −6.5333 | 0 | −6.5333 | 0 |

9 | ABC | 24 | 0 | 19.8 | 0 | 16.2 | 0 |

10 | ABC | 12.1603 | 2.0932 | 10.0603 | 1.7432 | 8.2603 | 1.4432 |

11 | ABC | −3.2667 | 0 | −3.2667 | 0 | −3.2667 | 0 |

12 | ABC | 14.5001 | 0.1118 | 11.9626 | 0.0922 | 9.7876 | 0.0755 |

Total | 47.3267 | 6.8977 | 34.2892 | 5.8281 | 23.1142 | 4.9114 | |

Bus | Loads | After phase balancing | |||||

Phase A | Phase B | Phase C | |||||

Bus number | Phase type | P (kW) | Q (kvar) | P (kW) | Q (kvar) | P (kW) | Q (kvar) |

2 | ABC | 0.5342 | 0.3106 | 0.5342 | 0.3106 | 0.5342 | 0.3106 |

3 | ABC | 0.0694 | 0.0404 | 0.0694 | 0.0404 | 0.0694 | 0.0404 |

5 | ABC | 19.8 | 3.3 | 24 | 4 | 16.2 | 2.7 |

6 | ABC | −18.5647 | 0.0932 | −18.5647 | 0.0932 | −18.5647 | 0.0932 |

7 | ABC | 0.4274 | 0.2485 | 0.4274 | 0.2485 | 0.4274 | 0.2485 |

8 | ABC | −6.5333 | 0 | −6.5333 | 0 | −6.5333 | 0 |

9 | ABC | 19.8 | 0 | 16.2 | 0 | 24 | 0 |

10 | ABC | 10.0603 | 1.7432 | 12.1603 | 2.0932 | 8.2603 | 1.4432 |

11 | ABC | −3.2667 | 0 | −3.2667 | 0 | −3.2667 | 0 |

12 | ABC | 14.5001 | 0.1118 | 9.7876 | 0.0755 | 11.9626 | 0.0922 |

Total | 36.8267 | 5.8477 | 34.8142 | 6.8614 | 33.0892 | 4.9281 |

**Figure 11.**Simulation result of the bus voltage of a weekday in summer of the INER microgrid: (

**a**) before optimization; (

**b**) after first stage; and (

**c**) after second stage.

**Figure 12.**Simulation result of the Voltage Unbalance Factors of a weekday in summer of the INER microgrid: (

**a**) zero-sequence voltage unbalance factor; (

**b**) negative-sequence voltage unbalance factor.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Huang, W.-T.; Chen, T.-H.; Chen, H.-T.; Yang, J.-S.; Lian, K.-L.; Chang, Y.-R.; Lee, Y.-D.; Ho, Y.-H.
A Two-stage Optimal Network Reconfiguration Approach for Minimizing Energy Loss of Distribution Networks Using Particle Swarm Optimization Algorithm. *Energies* **2015**, *8*, 13894-13910.
https://doi.org/10.3390/en81212402

**AMA Style**

Huang W-T, Chen T-H, Chen H-T, Yang J-S, Lian K-L, Chang Y-R, Lee Y-D, Ho Y-H.
A Two-stage Optimal Network Reconfiguration Approach for Minimizing Energy Loss of Distribution Networks Using Particle Swarm Optimization Algorithm. *Energies*. 2015; 8(12):13894-13910.
https://doi.org/10.3390/en81212402

**Chicago/Turabian Style**

Huang, Wei-Tzer, Tsai-Hsiang Chen, Hong-Ting Chen, Jhih-Siang Yang, Kuo-Lung Lian, Yung-Ruei Chang, Yih-Der Lee, and Yuan-Hsiang Ho.
2015. "A Two-stage Optimal Network Reconfiguration Approach for Minimizing Energy Loss of Distribution Networks Using Particle Swarm Optimization Algorithm" *Energies* 8, no. 12: 13894-13910.
https://doi.org/10.3390/en81212402