# Multiple-Zone Synchronous Voltage Regulation and Loss Reduction Optimization of Distribution Networks Based on a Dual Rotary Phase-Shifting Transformer

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Topology and Working Principle of DRPST

#### 2.1. Topology of DRPST

#### 2.2. Working Principle Analysis

**I**

_{s}is the system line current before connection to RPST,

**I**

_{sh}is the total stator-side current,

**I**

_{s1}is the rotor-side current,

**U**

_{DRPST}is the voltage of the DRPST series flowing into the line, Z

_{sh}is the impedance attributed to the rotor side, Z

_{RPST1}and Z

_{RPST2}are the impedance attributed to the stator side, and k is the DRPST voltage variation ratio size [14,15].

## 3. Active Distribution Network Voltage Regulation Model for Multiple Zones That Considers Line Losses

#### 3.1. Active Distribution Network Model with DRPST for Multiple Zones

**U**

_{s0}is the 10 kV section bus voltage, R

_{1}+ jX

_{1}is the equivalent line impedance of the 10 kV section bus I, U

_{s1}is the parallel network voltage of the 10 kV section bus I, P

_{Li}and Q

_{Li}are the loads at node i, and P

_{DGi}and Q

_{DGi}are the active power and reactive power injected by the distributed PV connected to node i. At this moment, the line power of the 10 kV section bus I distribution station exists as P

_{i}= P

_{Li}+ P

_{DGi}, Q

_{i}= Q

_{Li}+ Q

_{DGi}. The voltage of each station parallel network and that of the first end of the 10 kV line are as follows:

_{s0}and 10 kV bus first section voltage U

_{s}after connecting DRPST can be expressed as:

_{z}is the voltage drop formed by the resistance inside DRPST. From Equation (11), DRPST can achieve continuous regulation of its string line voltage while only adjusting its stator–rotor relative angle and then controlling the access point voltage U

_{s0}. It exhibits the advantages of simple control and high stability compared with the traditional reactive power–control voltage compensation mode.

#### 3.2. Inner Layer Model That Considers Voltage Control and Line Loss

#### 3.2.1. Objective Function

#### Voltage Deviation Target

_{si}is the voltage magnitude of system node i; U

_{si}

^{*}is the reference voltage magnitude of node voltage i, and it is typically 1.0 (the standard lowest value); U

_{simax}is the maximum allowable voltage of node i; U

_{simin}is the minimum allowable voltage of node i; ω

_{si}is the weight of the load of node i; and L

_{si}is the power of the load of the node.

#### Line Loss Target

_{sGi}from the substation to the distributed power access node. The overall line loss target at that moment can be expressed as follows:

_{si}can reduce distribution network loss under the premise that PV access capacity and distribution network line length remain unchanged.

#### 3.2.2. Binding Conditions

- (1)
- Voltage deviation constraint: in accordance with “power quality supply voltage deviation” [19], voltage deviation limits that are allowed to pass through the lines of various voltage levels are different, with the voltage deviation limit for the parallel network voltage constraint.
- (2)
- DRPST equivalent voltage source magnitude phase angle constraint.
- (3)
- Power equivalence constraint.
- (4)
- Branch current constraint: to prevent the long-term overcurrent operation of the line from causing permanent damage to the line, i.e., the line carrying capacity for constraint.
- (5)
- Calculation time constraint: the application scenario of this study belongs to an online calculation scenario and, thus, the calculation time of the control variable U
_{DRPST}is constrained. When calculation time exceeds sampling time, the current U_{DRPST}value is directly outputted to the outer model.

#### 3.3. Outer-Layer Model of DRPST-Based Deviation-Free Control

_{DRPST}calculated by the inner model is set as the target of voltage inner loop control. From the value in Equation (8), a speed-limiting module is adopted in the angle’s outer loop control. The output of the actual α value can realize the function of voltage regulation.

## 4. DRPST Control Strategy

#### 4.1. Solution Strategy for the Inner-Layer Model

_{i}is the i-th particle velocity vector, c

_{1}and c

_{2}are the acceleration factors, r

_{1}and r

_{2}are the random numbers that are uniformly distributed in the interval [0, 1], v

_{i}is the i-th particle velocity vector, p

_{besti}is the individual optimal position of the i-th particle, x

_{i}is the position vector of the i-th particle, and g

_{besti}is the individual optimal position of the i-th particle.

_{min}and ω

_{max}are the minimum and maximum values of inertia weights, respectively; c

_{1}and c

_{2}, c

_{min}, and c

_{max}are the current, minimum, and maximum values of learning factors, respectively; N is the current number of iterations; and N

_{max}is the maximum number of iterations. The initial stage of the algorithm ω is larger and, thus, beneficial for the global search of the algorithm. The later iteration of ω is gradually reduced, which is favorable for the local search of the algorithm. In the beginning of the iteration, c

_{1}is larger and c

_{2}is smaller. This condition is beneficial for the recognition of individuals by particles. Later in the iteration, c

_{1}is smaller, while c

_{2}is larger, and a particle demonstrates strong cognitive ability for global search [22].

#### 4.2. Selection of the Optimal Compromise Solution for the Inner Model

_{i}is the i-th objective function value and f

_{imin}and f

_{imax}are the upper and lower bounds of the objective function, respectively, during which the maximum value of the standardized satisfaction is solved using Equation (17), i.e., the optimal compromise solution of the inner-layer model [24,25].

#### 4.3. DRPST Control Block Diagram

- Step 1: The distribution network parameters are inputted. The network voltage parameters are collected. The objective function, constraints, and other distribution network model parameters are set.
- Step 2: The parameters of the MOPSO algorithm are initialized.
- Step 3: Particle positions, particle velocities, and external profiles are randomly initialized.
- Step 4: The objective function of each particle is calculated and the nondominated solution is stored in the external file.
- Step 5: The current inertia weights and acceleration factors, particle positions, velocities, individual optimal positions, and global optimal positions are updated in accordance with Equation (16).
- Step 6: The external archive is updated with the current particle swarm nondominated solution.
- Step 7: Whether the current time exceeds the maximum sampling time is recorded. Step 9 is skipped if it does. Proceed to Step 8 if it does not.
- Step 8: The size of the current iteration number is compared with the maximum iteration number. If the two are equal, then proceed to Step 9.
- Step 9: Searching is stopped. The external file is the Pareto optimal solution set. Pareto solution set satisfaction is calculated from Equations (17) and (18). The optimal compromise solution and the current control variables are outputted.
- Step 10: The control variable U
_{DRPSTref}in Step 9 is used as the outer model set value. A difference is made with the current U_{DRPST}and the nondifferential control of the voltage set value is realized by the PI controller. - Step 11: Using the solution of Step 10 U
_{DRPST}, the rotor angle α_{DRPST}is set by solving Equation (8) for the output DRPST. A difference is made with the actual angle α_{DRPST}to achieve the nondifferential control of the angle set value. - Step 12: Real-time rolling optimization of DRPST is achieved based on the parallel network voltage obtained from the next period of rolling acquisition.

## 5. Simulation Analysis

#### 5.1. Design of System Parameters

#### 5.2. Simulation Verification of Steady-State Regulation Characteristics

#### 5.3. Simulation Verification of Transient Regulation Characteristics

## 6. Experimental Validation of DRPST

#### Experimental Platform Construction

_{ss}; 7 is the DRPST bypass switch k

_{bp}; 8 is the RS485 interface; S is the load box; and R is the resistive element.

- (1)
- Variable voltage setting experiment

- (2)
- Constant voltage setting experiment

## 7. Conclusions

- (1)
- In this study, a new regulating structure based on DRPST is proposed. A simplified circuit model of DRPST is constructed, its control characteristics are analyzed, and its regulating performance is verified through experiments. DRPST string-in line voltage is only affected by rotor angle. The constructed model exhibits the advantages of bidirectional continuous voltage regulation and simple control.
- (2)
- A two-layer optimization model and its control strategy are proposed for the optimization of voltage regulation and loss reduction in multiple-zone active distribution networks.
- (3)
- DRPST is an electromagnetic voltage regulator that exhibits better shock resistance and reliability than power electronic voltage regulators. The generated loss and harmonic content will be considerably reduced. Manufacturing, operation, and maintenance costs are relatively low, providing an effective complement to future active distribution network voltage regulation schemes.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Zhong, Y.; Ji, L.; Jiang, Y.; Li, J.; Wang, Z.; Wang, Y. Fine-grained Calculation Method of Accepting Distributed Generation Capacity in Distribution Network for Virtual Power Plant. In Proceedings of the 2023 IEEE 6th International Electrical and Energy Conference (CIEEC), Hefei, China, 12–14 May 2023; pp. 159–164. [Google Scholar]
- Lin, Z.Y.; Jiang, F.; Tu, C.; Xiao, Z. Distributed Coordinated Voltage Control of Photovoltaic and Energy Storage System Based on Dynamic Consensus Algorithm. In Proceedings of the 2021 IEEE/IAS Industrial and Commercial Power System Asia (I&CPS Asia), Chengdu, China, 18–21 July 2021; pp. 1223–1228. [Google Scholar]
- Navarro-Espinosa, A.; Ochoa, L.F. Increasing the PV hosting capacity of LV networks: OLTC-fitted transformers vs. reinforcements. In Proceedings of the 2015 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), Washington, DC, USA, 18–20 February 2015; pp. 1–5. [Google Scholar]
- Liu, X.; Niu, X.S.; Zhu, Y.; Zhu, C. Influence of Regulation of OLTC Transformation Ratio on Voltage Stability. In Proceedings of the 2013 Fourth International Conference on Digital Manufacturing & Automation, Shinan, China, 29–30 June 2013; pp. 696–700. [Google Scholar]
- Zhang, L.; Zhu, Y.; Xiao, Y. Voltage Segment Coordinated Control Strategy for Isolated DC Microgrid with Multiple Energy Storage Units. In Proceedings of the 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 11–14 August 2019; pp. 1–5. [Google Scholar]
- Weber, H.; Baskar, P.; Ahmed, N. Nodal Voltage Angle Control of Power Systems with Renewable Sources, Storages and Power Electronic Converters. In Proceedings of the 2018 International Conference on Smart Energy Systems and Technologies (SEST), Seville, Spain, 10–12 September 2018; pp. 1–6. [Google Scholar]
- Ba, A.O.; Peng, T.; Lefebvre, S. Rotary Power-Flow Controller for Dynamic Performance Evaluation—Part I: RPFC Modeling. IEEE Trans. Power Deliv.
**2009**, 24, 1406–1416. [Google Scholar] [CrossRef] - Ba, A.O.; Peng, T.; Lefebvre, S. Rotary Power Flow Controller Performance in Power Systems Part I—RPFC Modeling. In Proceedings of the IEEE International Symposium on Industrial Electronics, Cambridge, UK, 30 June–2 July 2008. [Google Scholar]
- Tan, Z.; Zhang, C.; Jiang, Q. Research on Characteristics and Power Flow Control Strategy of Rotary Power Flow Controller. In Proceedings of the 5th International Youth Conference on Energy (IYCE), Pisa, Italy, 27–30 May 2015. [Google Scholar]
- Abardeh, M.H.; Ghazi, R. Rotary power flow controller (RPFC) characteristics analysis. In Proceedings of the 2011 5th International Power Engineering and Optimization Conference, Shah Alam, Malaysia, 6–7 June 2011; pp. 358–363. [Google Scholar]
- Li, T.; Wu, H.; Chen, H. Based on Deep Reinforcement Learning Algorithm, Energy Storage Optimization and Loss Reduction Strategy for Distribution Network with High Proportion of Distributed Generation. In Proceedings of the 2023 8th Asia Conference on Power and Electrical Engineering (ACPEE), Tianjin, China, 14–16 April 2023; pp. 1863–1868. [Google Scholar]
- Yu, W.; You, R.; Zhou, J. Research on Operation Optimization of Active Distribution Networks Based on Multi-Port SOP Integrated Energy Storage System. In Proceedings of the 2021 6th International Conference on Power and Renewable Energy (ICPRE), Shanghai, China, 17–20 September 2021; pp. 707–712. [Google Scholar]
- Lu, L.; Liu, J.; Wang, J. A distributed hierarchical structure optimization algorithm based poly-particle swarm for reconfiguration of distribution network. In Proceedings of the 2009 International Conference on Sustainable Power Generation and Supply, Nanjing, China, 6–7 April 2009; pp. 1–5. [Google Scholar]
- Ba, A.O.; Peng, T.; Lefebvre, S. Rotary Power-Flow Controller for Dynamic Performance Evaluation—Part II: RPFC Application in a Transmission Corridor. IEEE Trans. Power Deliv.
**2009**, 24, 1417–1425. [Google Scholar] [CrossRef] - Peng, T.; Ba, A.O.; Lefebvre, S. Rotary power flow controller performance in power systems part II—RPFC performances in a transmission corridor. In Proceedings of the 2008 IEEE International Symposium on Industrial Electronics, Cambridge, UK, 30 June–2 July 2008; pp. 1476–1482. [Google Scholar]
- Yan, X.; Shao, C.; Peng, W. Flexible Loop Closing and Emergency Power Control Method for Active Distribution Network Based on the Rotary Power Flow Controller. Proc. Chin. Soc. Electr. Eng.
**2023**, 43, 6192–6204. [Google Scholar] - Ba, A.O.; Peng, T.; Lefebvre, S. Rotary Power Flow Controller modeling for dynamic performance evaluation. In Proceedings of the 2008 IEEE Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century, Pittsburgh, PA, USA, 20–24 July 2008; pp. 1–10. [Google Scholar]
- Shang, L.; Hu, R.; Wei, T.; Ci, H.; Zhang, W.; Chen, H. Multiobjective optimization for hybrid AC/DC distribution network structure considering reliability. In Proceedings of the 2021 IEEE Sustainable Power and Energy Conference (iSPEC), Nanjing, China, 23–25 July 2021; pp. 3034–3041. [Google Scholar]
- IEEE Std C57.12.80-2010; IEEE Standard Terminology for Power and Distribution Transformers. Revision of IEEE Std C57.12.80-2002; IEEE Standard Association: Piscataway, NJ, USA, 2010; pp. 1–60. [CrossRef]
- Li, L.; Gao, M.; Gan, L.; Li, W.; You, G.; Tao, Z.; Wang, J. Two-level Capacity Optimization Strategy for Generations in Multi-energy Gathering Center Considering the Flexibility. In Proceedings of the 2020 IEEE 4th Conference on Energy Internet and Energy System Integration (EI2), Wuhan, China, 30 October–1 November 2020; pp. 2599–2604. [Google Scholar]
- Su, W.; Xiao, X.; Yang, X.; Fang, X. Research on distribution network expansion planning based on load feature library and load simultaneous rate. In Proceedings of the 2022 IEEE 10th Joint International Information Technology and Artificial Intelligence Conference (ITAIC), Chongqing, China, 17–19 June 2022; pp. 1471–1475. [Google Scholar]
- Zhao, L.; He, D.; Zeng, X.; Wu, J. Distributed Photovoltaic Energy Storage Configuration Method for Distribution Network Considering Voltage Constraint. In Proceedings of the 2023 IEEE 3rd International Conference on Information Technology, Big Data and Artificial Intelligence (ICIBA), Chongqing, China, 26–28 May 2023; pp. 485–489. [Google Scholar]
- Ren, C.; Zhou, J.; Xu, X.; Mao, W.; Ma, Y.; Wang, B. Load Balance and Recovery Optimization of Distribution Network Based on Binary Particle Swarm Optimization Algorithm. In Proceedings of the 2022 5th International Conference on Renewable Energy and Power Engineering (REPE), Beijing, China, 28–30 September 2022; pp. 103–107. [Google Scholar]
- Zhang, M.J.; Zhang, Z.Y.; Yi, H.; Tang, X. Demand Response Featured Dynamic Voltage Regulation of Active Distribution Network. In Proceedings of the 58th IEEE/IAS Industrial and Commercial Power Systems Technical Conference Asia (IEEE I and CPS Asia), Shanghai, China, 8–11 July 2022. [Google Scholar]
- Zhou, S.C.; Zhou, Y.P.; Wei, Y.C.; Kang, L.; Zhang, X. Multi-Objective Optimal Control for Distribution Network Loop-Closing Operation Using PE-MOPSO Algorithm. In Proceedings of the 6th International Conference on Smart Grid and Electrical Automation (ICSGEA), Kunming, China, 29–30 May 2021. [Google Scholar]
- Zogg, R.; Lawrence, T.; Ofer, D. Distributed Energy Storage. Ashrae J.
**2007**, 49, 90. [Google Scholar]

**Figure 3.**Simplified circuit model and voltage regulation vector diagram of DRPST. (

**a**) Simplified circuit diagram of DRPST. (

**b**) Regulating vector diagram of DRPST when crossing the lower limit. (

**c**) Regulating vector diagram of DRPST when the upper limit is crossed.

**Figure 8.**24 h PV output and load curve. (

**a**) Variation of station load in 24 hours. (

**b**) The change of photovoltaic output in 24 h.

**Figure 9.**Connection point voltage and system grid loss before and after adding DRPST. (

**a**) Voltage change of each station area after DRPST is connected. (

**b**) Network loss changes after DRPST is connected.

**Figure 11.**The process of solving multi-objective particle swarm algorithm before and after improvement. (

**a**) Optimization search process for t = 0 s. (

**b**) Optimization search process for t = 15 s. (

**c**) Optimization search process for t = 30 s.

**Figure 12.**Experimental platform of DRPST. (1) is the DSP controller. (2) and (3) are the two RPST main structures. (4) is the current transformer. (5) is the RPST energy side input switch, which is automatically closed when the power supply generates excitation to the stator windings, and automatically disconnected when the excitation is cancelled. (6) is the DRPST series switch k

_{ss}. (7) is the DRPST bypass switch k

_{bp}. (8) is the RS485 interface.

Parameters | Value | Parameters | Value | Parameters | Value |
---|---|---|---|---|---|

Frequency/Hz | 50 | Capacity/MW | 3 | Rotational speed | 20°/s |

U_{s}/kV | $10\angle {0}^{\circ}$ | Z_{sh}/Ω | 0.3 | Station area 1 load level | Level 1 |

R_{1} + jX_{1}/Ω | 2.61 + j2.134 | Z_{RPST}/Ω | 0.15 | Station area 2 load level | Level 2 |

R_{2} + jX_{2}/Ω | 2.7 + j2.208 | R_{3} + jX_{3}/Ω | 2.025 + j1.656 | Station area 3 load level | Level 3 |

Parameters | Value | Parameters | Value | Parameters | Value |
---|---|---|---|---|---|

Number of iterations | 50 | ${c}_{\mathrm{max}}$ | 0.2 | ${\omega}_{\mathrm{max}}$ | 0.5 |

Population size | 100 | ${c}_{\mathrm{min}}$ | 0.1 | ${\omega}_{\mathrm{min}}$ | 0.001 |

External population file size | 100 | ${v}_{\mathrm{max}}$ | 1.2 | ${v}_{\mathrm{min}}$ | 0.8 |

Parameters | t = 0 s | t = 15 s | t = 30 s | Parameters | t = 0 s | t = 15 s | t = 30 s |
---|---|---|---|---|---|---|---|

Station area 1 load/MVA | 0.55 + j052 | 0.55 + j052 | 0.87 + j0.39 | PV for station area 1/MW | 3.32 | 0.66 | 0.66 |

Station area 2 load/MVA | 2.05 + j0.68 | 2.05 + j0.68 | 2.26 + j0.60 | PV for station area 2/MW | 2.71 | 0.41 | 0.41 |

Station area 3 load/MVA | 0.56 + j0.21 | 0.56 + j0.21 | 0.55 + j0.22 | PV for station area 3/MW | 1.75 | 0.44 | 0.44 |

Parameters | Value | Parameters | Value | Parameters | Value |
---|---|---|---|---|---|

U_{s}/V | 380 | Capacity/kVA | 40 | Stator–rotor ratio | 380:100 |

Frequency/Hz | 50 | S/kVA | 1.1 + j0.5 | R/W | 5 |

Experiment (1)/V | t_{0}–t_{1} | t_{1}–t_{2} | t_{2}–t_{3} | t_{3}–t_{4} | t_{4}–t_{5} | t_{5}–t_{6} |

220 | 200 | 185 | 260 | 240 | 220 | |

Experiment (2)/kVA | t_{0}–t_{1} | t_{1}–t_{2} | t_{2}–t_{3} | t_{3}–t_{4} | t_{4}–t_{5} | |

uninvested | 1.1 + j0.5 | 3.3 + j1.8 | 3.3 + j0.6 | 2 + j1.5 |

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## Share and Cite

**MDPI and ACS Style**

Shao, C.; Yan, X.; Yang, Y.; Aslam, W.; Jia, J.; Li, J.
Multiple-Zone Synchronous Voltage Regulation and Loss Reduction Optimization of Distribution Networks Based on a Dual Rotary Phase-Shifting Transformer. *Sustainability* **2024**, *16*, 1029.
https://doi.org/10.3390/su16031029

**AMA Style**

Shao C, Yan X, Yang Y, Aslam W, Jia J, Li J.
Multiple-Zone Synchronous Voltage Regulation and Loss Reduction Optimization of Distribution Networks Based on a Dual Rotary Phase-Shifting Transformer. *Sustainability*. 2024; 16(3):1029.
https://doi.org/10.3390/su16031029

**Chicago/Turabian Style**

Shao, Chen, Xiangwu Yan, Yaohui Yang, Waseem Aslam, Jiaoxin Jia, and Jiayao Li.
2024. "Multiple-Zone Synchronous Voltage Regulation and Loss Reduction Optimization of Distribution Networks Based on a Dual Rotary Phase-Shifting Transformer" *Sustainability* 16, no. 3: 1029.
https://doi.org/10.3390/su16031029