# Neutral Current Reduction in Three-Phase Four-Wire Distribution Feeders by Optimal Phase Arrangement Based on a Full-Scale Net Load Model Derived from the FTU Data

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description and the Proposed Approach

#### 2.1. The Solution Procedure of the Proposed Approach

#### 2.2. Description of the Long Short Term Memory

#### 2.3. Description of the Particle Swarm Optimization

#### 2.4. The Computation Platform with the OpenDSS and Python

#### 2.5. Optimal Phase Arrangement with the Multi-objective Function

## 3. Simulation and Analysis

#### 3.1. Scenario and Simulation Parameter Setting

#### 3.2. Numerical Results

#### 3.2.1. Iterative Convergence Trend

#### 3.2.2. Neutral Current Profile

#### 3.2.3. Line Current Profile

#### 3.2.4. Bus Voltage Profile

_{0}, V

_{1}, and V

_{2}denote the zero- positive-, and negative-sequence voltage components, respectively. The zero- and negative-sequence voltage unbalance factors are defined in Equations (10) and (11), respectively. These two unbalance factors can completely reflect the voltage unbalance phenomenon caused by magnitude and phase angle deviation. Consequently, the zero- and negative-sequence voltage unbalance factors were used to estimate the performance of the proposed approach in this paper. The simulation results show that the maximum values of the zero- and negative-sequence voltage unbalance factors were near 1.7% before rephasing, but decreased to below 0.3% after rephasing (Figure 16).

#### 3.2.5. Power Loss Profile

#### 3.3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Siddique, A.; Yadava, G.; Singh, B. Effects of voltage unbalance on induction motors. In Proceedings of the Conference Record of the 2004 IEEE International Symposium on Electrical Insulation ELINSL-04, Indianapolis, IN, USA, 19–22 September 2005; pp. 26–29. [Google Scholar]
- Weckx, S.; González, C.; Driesen, J. Reducing grid losses and voltage unbalance with PV inverters. In Proceedings of the 2014 IEEE PES General Meeting|Conference & Exposition; Institute of Electrical and Electronics Engineers (IEEE), National Harbor, MD, USA, 27–31 July 2014; pp. 1–5. [Google Scholar]
- Otcenasova, A.; Bolf, A.; Altus, J.; Regula, M. The Influence of Power Quality Indices on Active Power Losses in a Local Distribution Grid. Energies
**2019**, 12, 1389. [Google Scholar] [CrossRef][Green Version] - Farughian, A.; Kumpulainen, L.; Kauhaniemi, K. Earth Fault Location Using Negative Sequence Currents. Energies
**2019**, 12, 3759. [Google Scholar] [CrossRef][Green Version] - Lowczowski, K.; Lorenc, J.; Andruszkiewicz, J.; Nadolny, Z.; Zawodniak, J. Novel Earth Fault Protection Algorithm Based on MV Cable Screen Zero Sequence Current Filter. Energies
**2019**, 12, 3190. [Google Scholar] [CrossRef][Green Version] - Shao, W.; Bai, J.; Cheng, Y.; Zhang, Z.; Li, N. Research on a Faulty Line Selection Method Based on the Zero-Sequence Disturbance Power of Resonant Grounded Distribution Networks. Energies
**2019**, 12, 846. [Google Scholar] [CrossRef][Green Version] - Tu, C.-S.; Tsai, M.-T. Optimal Phase Arrangement of Distribution Transformers for System Unbalance Improvement and Loss Reduction. Energies
**2020**, 13, 545. [Google Scholar] [CrossRef][Green Version] - Chen, T.H.; Cherng, J.T. Optimal phase arrangement of distribution transformers connected to a primary feeder for system unbalance improvement and loss reduction using a genetic algorithm. In Proceedings of the 21st International Conference on Power Industry Computer Applications. Connecting Utilities. PICA 99. To the Millennium and Beyond (Cat. No. 99CH36351), Santa Clara, CA, USA, 21 May 1999; Volume 15, pp. 994–1000. [Google Scholar]
- Huang, M.-Y.; Chen, C.-S.; Lin, C.-H.; Kang, M.-S.; Chuang, H.-J.; Huang, C.-W. Three-phase balancing of distribution feeders using immune algorithm. IET Gener. Transm. Distrib.
**2008**, 2, 383–392. [Google Scholar] [CrossRef] - Hooshmand, R.-A.; Soltani, S. Fuzzy Optimal Phase Balancing of Radial and Meshed Distribution Networks Using BF-PSO Algorithm. IEEE Trans. Power Syst.
**2011**, 27, 47–57. [Google Scholar] [CrossRef] - Arias, J.; Calle, M.; Turizo, D.; Guerrero, J.; Candelo-Becerra, J.E. Historical Load Balance in Distribution Systems Using the Branch and Bound Algorithm. Energies
**2019**, 12, 1219. [Google Scholar] [CrossRef][Green Version] - Lin, C.-H.; Chen, C.; Chuang, H.-J.; Huang, M.-Y.; Huang, C.-W. An Expert System for Three-Phase Balancing of Distribution Feeders. IEEE Trans. Power Syst.
**2008**, 23, 1488–1496. [Google Scholar] - Soltani, S.; Rashidinejad, M.; Abdollahi, A. Stochastic Multiobjective Distribution Systems Phase Balancing Considering Distributed Energy Resources. IEEE Syst. J.
**2017**, 12, 2866–2877. [Google Scholar] [CrossRef] - Peng, C.; Xu, L.; Gong, X.; Sun, H.; Pan, L. Molecular Evolution Based Dynamic Reconfiguration of Distribution Networks With DGs Considering Three-Phase Balance and Switching Times. IEEE Trans. Ind. Inform.
**2019**, 15, 1866–1876. [Google Scholar] [CrossRef] - Chen, C.; Tsai, C.-T.; Lin, C.-H.; Hsieh, W.-L.; Ku, T.-T. Loading Balance of Distribution Feeders With Loop Power Controllers Considering Photovoltaic Generation. IEEE Trans. Power Syst.
**2011**, 26, 1762–1768. [Google Scholar] [CrossRef] - 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. [Google Scholar] [CrossRef][Green Version] - Bouktif, S.; Fiaz, A.; Ouni, A.; Serhani, M.A. Multi-Sequence LSTM-RNN Deep Learning and Metaheuristics for Electric Load Forecasting. Energies
**2020**, 13, 391. [Google Scholar] [CrossRef][Green Version] - Yudantaka, K.; Kim, J.-S.; Song, H. Dual Deep Learning Networks Based Load Forecasting with Partial Real-Time Information and Its Application to System Marginal Price Prediction. Energies
**2019**, 13, 148. [Google Scholar] [CrossRef][Green Version] - Santra, A.S.; Lin, J.-L. Integrating Long Short-Term Memory and Genetic Algorithm for Short-Term Load Forecasting. Energies
**2019**, 12, 2040. [Google Scholar] [CrossRef][Green Version] - Tian, C.; Ma, J.; Zhang, C.; Zhan, P. A Deep Neural Network Model for Short-Term Load Forecast Based on Long Short-Term Memory Network and Convolutional Neural Network. Energies
**2018**, 11, 3493. [Google Scholar] [CrossRef][Green Version] - Kim, S.H.; Lee, G.; Kwon, G.-Y.; Kim, D.-I.; Shin, Y.-J. Deep Learning Based on Multi-Decomposition for Short-Term Load Forecasting. Energies
**2018**, 11, 3433. [Google Scholar] [CrossRef][Green Version] - OpenDSS-EPRI. Available online: https://www.epri.com/#/pages/sa/opendss?lang=en (accessed on 21 February 2020).
- Kim, H.; Kim, K.; Park, S.; Kim, H.; Kim, H. CoSimulating Communication Networks and Electrical System for Performance Evaluation in Smart Grid. Appl. Sci.
**2018**, 8, 85. [Google Scholar] [CrossRef][Green Version] - Xiao, H.; Pei, W.; Dong, Z.; Kong, L.; Wang, D. Application and Comparison of Metaheuristic and New Metamodel Based Global Optimization Methods to the Optimal Operation of Active Distribution Networks. Energies
**2018**, 11, 85. [Google Scholar] [CrossRef][Green Version] - Misra, R.; Paudyal, S.; Ceylan, O.; Mandal, P. Harmonic Distortion Minimization in Power Grids with Wind and Electric Vehicles. Energies
**2017**, 10, 932. [Google Scholar] [CrossRef][Green Version] - Martinez-Velasco, J.; Guerra, G. Reliability Analysis of Distribution Systems with Photovoltaic Generation Using a Power Flow Simulator and a Parallel Monte Carlo Approach. Energies
**2016**, 9, 537. [Google Scholar] [CrossRef][Green Version] - Chemali, E.; Kollmeyer, P.; Preindl, M.; Ahmed, R.; Emadi, A.; Kollmeyer, P. Long Short-Term Memory Networks for Accurate State-of-Charge Estimation of Li-ion Batteries. IEEE Trans. Ind. Electron.
**2017**, 65, 6730–6739. [Google Scholar] [CrossRef] - Ospina, J.; Newaz, A.; Faruque, M.O. Forecasting of PV plant output using hybrid wavelet-based LSTM-DNN structure model. IET Renew. Power Gener.
**2019**, 13, 1087–1095. [Google Scholar] [CrossRef] - Brownlee, J. Long Short-term Memory Networks with Python: Develop Sequence Prediction Models with Deep Learning; Machine Learning Mastery: Melbourne, Australia, 2017. [Google Scholar]
- Jamian, J.J.; Aman, M.M.; Mustafa, M.W.; Jasmon, G.B.; Mokhlis, H.; Bakar, A.H.A.; Abdullah, M.N. Optimum multi DG units placement and sizing based on voltage stability index and PSO. In Proceedings of the 2012 47th International Universities Power Engineering Conference (UPEC), Middlesex, UK, 4–7 September 2012; pp. 1–6. [Google Scholar]
- Montenegro, D.; Hernandez, M.; Ramos, G.; Montenegro-Martinez, D. Real time OpenDSS framework for distribution systems simulation and analysis. In Proceedings of the 2012 Sixth IEEE/PES Transmission and Distribution: Latin America Conference and Exposition (T&D-LA), Montevideo, Uruguay, 3–5 September 2012; pp. 1–5. [Google Scholar]

**Figure 7.**Various connections between the individual distribution transformer and the lateral and tapped-off points in the feeder main.

**Figure 10.**The iterative convergence diagram: (

**a**) fitness function, (

**b**) neutral current, (

**c**) total energy loss, and (

**d**) rephasing number.

**Figure 11.**The single line diagram of LCO protective relay in the three-phase, four-wire distribution systems.

**Figure 12.**The neutral current spread and PDF of neutral current: (

**a**) before rephrasing and (

**b**) after rephasing.

**Figure 13.**The neutral current profile in each line section: (

**a**) before rephrasing and (

**b**) after rephasing.

**Figure 14.**Line current profiles: (

**a**) phase A: before rephasing, (

**b**) phase A: after rephasing, (

**c**) phase B: before rephasing, (

**d**) phase B: after rephasing, (

**e**) phase C: before rephasing, and (

**f**) phase C: after rephasing.

**Figure 15.**Bus voltage profiles: (

**a**) phase A: before rephasing, (

**b**) phase A: after rephasing, (

**c**) phase B: before rephasing, (

**d**) phase B: after rephasing, (

**e**) phase C: before rephasing, and (

**f**) phase C: after rephasing.

**Figure 16.**Zero- and negative-sequence voltage unbalance factors: (

**a**) Zero-sequence: before rephasing, (

**b**) Zero-sequence: after rephasing, (

**c**) Negative-sequence: before rephasing, and (

**d**) Negative-sequence: after rephasing.

**Figure 18.**The iterative convergence diagram of Case 2: (

**a**) fitness function and rephasing number and (

**b**) neutral current and total energy loss.

**Figure 19.**The iterative convergence diagram of Case 3: (

**a**) fitness function and rephasing number and (

**b**) neutral current and total energy loss.

**Figure 20.**The iterative convergence diagram of Case 4: (

**a**) fitness function and rephasing number and (

**b**) neutral current and total energy loss.

Case | Parameter | |||||||
---|---|---|---|---|---|---|---|---|

Swarm Size | Iterations | $\mathit{\omega}$ | ${\mathit{\phi}}_{\mathit{p}}$ | ${\mathit{\phi}}_{\mathit{g}}$ | ${\mathit{w}}_{1}$ | ${\mathit{w}}_{2}$ | ${\mathit{w}}_{3}$ | |

Case 1 | 100 | 100 | from 0.9 to 0.4 during iteration | 0.5 | 0.5 | 1 | 0 | 0 |

Case 2 | 0.8 | 0 | 0.2 | |||||

Case 3 | 0.4 | 0.3 | 0.3 | |||||

Case 4 | 150 | 1 | 0 | 0 |

Case | Result | |||
---|---|---|---|---|

Fitness Function | Maximunm Neutral Current (A) | Total Energy Loss (kWh) | Rephasing Number | |

Original | - | 72.17 | 11,317.21 | - |

Case 1 | 0.678675 | 48.98 | 8261.55 | 30 |

Case 2 | 0.720195 | 54.95 | 9074.69 | 18 |

Case 3 | 0.699720 | 54.56 | 8980.33 | 20 |

Case 4 | 0.691161 | 49.88 | 8636.6 | 26 |

Connection | Original | Case 1 | Case 2 | Case 3 | Connection | Original | Case 1 | Case 2 | Case 3 | ||
---|---|---|---|---|---|---|---|---|---|---|---|

Bus No. | Bus No. | ||||||||||

6_1 | BC | BA | BC | BA | 21_11 | AB | AB | AB | AB | ||

11_4 | A | A | A | A | 21_13 | BC | BA | BA | BC | ||

11_5 | BC | AB | BC | BA | 21_14 | BC | BA | BC | BA | ||

11_6 | C | A | A | A | 21_15 | C | B | C | A | ||

11_7 | A | A | A | A | 27_1 | A | A | A | A | ||

11_9 | BC | BC | BC | BC | 27_7 | AC | BC | AC | AC | ||

11_10 | C | C | B | C | 28_1 | B | B | B | B | ||

11_12 | B | B | B | B | 30_0 | A | A | A | A | ||

11_16 | B | B | B | B | 33_2 | B | B | B | B | ||

11_17 | B | B | B | B | 36_0 | ABC | ABC | ABC | ABC | ||

11_27 | AB | AB | AB | AB | 35_1 | AB | AB | AB | AB | ||

11_28 | B | B | B | B | 38_2 | B | B | B | B | ||

13_1 | B | B | B | B | 38_3 | AC | AB | AC | AC | ||

13_9 | C | A | A | A | 38_5 | AC | AC | AC | AC | ||

13_10 | C | B | A | A | 38_6 | BC | BC | BC | BC | ||

15_2 | AC | AB | AC | AC | 39_0 | BC | BA | BC | BA | ||

15_3 | B | B | B | B | 40_3 | AC | AC | AC | AC | ||

15_4 | B | A | B | B | 40_4 | AC | AC | BC | AB | ||

16_2 | B | B | B | B | 40_5 | AC | AC | AC | AC | ||

16_7 | BC | BC | BA | BC | 40_27 | A | A | A | A | ||

16_10 | B | B | B | B | 40_28 | C | A | C | C | ||

16_15 | C | B | B | C | 40_31 | AC | AC | AC | AB | ||

16_20 | A | A | A | A | 40_33 | B | B | B | B | ||

17_20 | A | A | A | A | 40_34 | C | B | A | A | ||

17_22 | B | A | B | B | 47_0 | AC | AC | AC | AC | ||

17_23 | B | B | B | B | 49_1 | A | A | A | A | ||

17_25 | B | B | B | B | 50_0 | AC | BC | AB | AB | ||

17_26 | BC | AB | BA | BC | 51_0 | AC | AC | AC | AC | ||

18_0 | BC | AB | BA | BC | 54_0 | AC | AC | AC | AC | ||

19_0 | C | A | C | C | 54_2 | AC | AC | AC | BC | ||

19_4 | C | B | A | C | 54_6 | C | B | C | C | ||

19_5 | B | B | B | B | 54_10 | C | A | C | A | ||

19_7 | B | B | B | B | 54_11 | AB | AB | AB | AB | ||

19_8 | A | A | A | A | 54_12 | B | B | B | B | ||

19_9 | AB | AB | AB | AB | 54_13 | BC | BA | BA | BA | ||

20_3 | C | C | A | A | 54_14 | AB | AB | AB | AB | ||

20_9 | AC | AC | AC | AB | 54_15 | B | B | B | B | ||

20_10 | BC | BA | BA | BC | 54_16 | AC | BC | AB | BC | ||

20_11 | C | A | C | C | 57_0 | AC | AB | BC | BC | ||

21_9 | AC | AC | AC | AC | 57_1 | AC | BC | AC | AC | ||

21_10 | C | B | A | B | Note: Bus No._n^{th} Transformer(lateral) |

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## Share and Cite

**MDPI and ACS Style**

Lee, Y.-D.; Jiang, J.-L.; Ho, Y.-H.; Lin, W.-C.; Chih, H.-C.; Huang, W.-T. Neutral Current Reduction in Three-Phase Four-Wire Distribution Feeders by Optimal Phase Arrangement Based on a Full-Scale Net Load Model Derived from the FTU Data. *Energies* **2020**, *13*, 1844.
https://doi.org/10.3390/en13071844

**AMA Style**

Lee Y-D, Jiang J-L, Ho Y-H, Lin W-C, Chih H-C, Huang W-T. Neutral Current Reduction in Three-Phase Four-Wire Distribution Feeders by Optimal Phase Arrangement Based on a Full-Scale Net Load Model Derived from the FTU Data. *Energies*. 2020; 13(7):1844.
https://doi.org/10.3390/en13071844

**Chicago/Turabian Style**

Lee, Yih-Der, Jheng-Lun Jiang, Yuan-Hsiang Ho, Wei-Chen Lin, Hsin-Ching Chih, and Wei-Tzer Huang. 2020. "Neutral Current Reduction in Three-Phase Four-Wire Distribution Feeders by Optimal Phase Arrangement Based on a Full-Scale Net Load Model Derived from the FTU Data" *Energies* 13, no. 7: 1844.
https://doi.org/10.3390/en13071844