# Voltage Zoning Regulation Method of Distribution Network with High Proportion of Photovoltaic Considering Energy Storage Configuration

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## Abstract

**:**

## 1. Introduction

- (1)
- Based on the k-means clustering method, the voltage deviation curves of each node in a day are clustered and analyzed, and the nodes are divided into several categories to determine the distribution network partition. The ESDs are connected to the cluster centers of each district, thus realizing the voltage partition adjustment;
- (2)
- The solution method based on PSO can effectively solve the proposed voltage regulation model;
- (3)
- Based on the proposed voltage regulation method of a distribution network considering energy storage configuration, the IEEE33 example is analyzed, and the objective function values are effectively reduced, thus improving the stability and economy of the distribution network.

## 2. Partition Configuration of Energy Storage Based on K-Means Clustering

#### 2.1. Definition of High Proportion

#### 2.2. K-Means Clustering

- (1)
- Simple principle, easy realization and fast convergence;
- (2)
- Good clustering effect;
- (3)
- Strong interpretability and intuition;
- (4)
- There is only one parameter, k.

- (1)
- Randomly selecting k sample points as initial clustering centers;
- (2)
- Calculating the distance between each cluster center and other sample points by using Euclidean distance and classifying each sample point into the nearest class;
- (3)
- Finding a new cluster center of each class, and taking it as the center to calculate the average value of each class by Equation (2);$${M}_{k}=\frac{1}{{N}_{k}}{\displaystyle \sum _{i=1}^{{N}_{k}}{D}_{ki}}$$
- (4)
- Repeating (2) and (3) until the clustering center does not change.

#### 2.3. Elbow Rule to Determine the k Value

#### 2.4. Partition Configuration of ESD

## 3. Distribution Network Voltage Regulation Model with High Proportion of PV

#### 3.1. Objective Function

- (1)
- Objective function ${F}_{2}$: the economic cost ${C}_{E\_total}$ is the lowest:${C}_{E\_total}$ consists of ESD call cost ${C}_{\mathrm{ESD}}$, power generation cost of PVs ${C}_{\mathrm{PV},m}$, power generation cost of MTs ${C}_{\mathrm{MT},ge}$, electricity purchase cost ${C}_{e,buy}$ [21] and environmental treatment cost ${C}_{pt}$, namely$${C}_{E\_total}={C}_{\mathrm{ESD}}+{C}_{\mathrm{PV},ge}+{C}_{\mathrm{MT},ge}+{C}_{e,buy}+{C}_{pt}+{C}_{nl}$$➀ ESD call cost ${C}_{\mathrm{ESD}}$$${C}_{\mathrm{ESD}}={\mu}_{\mathrm{ESD}}{P}_{\mathrm{ESD},c}+{\mu}_{\mathrm{ESD}}{P}_{\mathrm{ESD},dc}$$➁ Power generation cost of PVs: PVs are clean energy, so there is no fuel cost, so ${C}_{\mathrm{PV},ge}$ only consists of the operation and maintenance cost of PVs ${C}_{\mathrm{PV},om}$.$${C}_{\mathrm{PV},ge}={C}_{\mathrm{PV},om}={\displaystyle \sum _{t=1}^{T}{c}_{\mathrm{PV},om}{P}_{\mathrm{PV}}(t)}$$➂ Power generation cost of MTs: ${C}_{\mathrm{MT},ge}$ consists of fuel cost and operation and maintenance cost ${C}_{\mathrm{MT},om}$ (see Equation (8)). Among them, ${C}_{\mathrm{MT},fu}$ is related to factors such as natural gas price and power supply efficiency of the unit [22], and its calculation formula is shown in Equation (9). The calculation formula of ${C}_{\mathrm{MT},om}$ is shown in Equation (10).$${C}_{\mathrm{MT},ge}={C}_{\mathrm{MT},fu}+{C}_{\mathrm{MT},om}$$$${C}_{\mathrm{MT},fu}={\displaystyle \sum _{t=1}^{T}\frac{(3600/4.1868)\times {c}_{gas}}{{Q}_{gas}\eta}\cdot {P}_{\mathrm{MT},i}(t)}$$$${C}_{\mathrm{MT},om}={\displaystyle \sum _{t=1}^{T}{\displaystyle \sum _{i=1}^{{N}_{\mathrm{MT}}}{c}_{\mathrm{MT},om}}}{P}_{\mathrm{MT},i}(t)$$
^{3}; ${Q}_{gas}$ is the power generation for natural gas, kcal/m^{3}; $\eta $ is the power supply efficiency for the unit, %; ${P}_{\mathrm{MT}}(t)$ is the MT output at time t, kW; ${c}_{\mathrm{MT},om}$ is the unit operation and maintenance cost of MTs, yuan/kW.➃ Electricity purchase cost ${C}_{e,buy}$$${C}_{e,buy}={\displaystyle \sum _{t=1}^{T}\left({p}_{ph}(t)\cdot {P}_{ee}(t)\right)}$$➄ Environmental treatment cost ${C}_{pt}$: CO_{2}and NO_{x}emissions come from MTs [23]. The calculation formula of ${C}_{pt}$ is shown in Equation (12).$${C}_{pt}={\displaystyle \sum _{t=1}^{T}{c}_{po,k}{\sigma}_{po,k}{P}_{\mathrm{MT},i}}$$ - (2)
- Objective function ${F}_{3}$: the total power loss of the branch $\Delta {A}_{nl\_total}$ is the lowest.$${F}_{3}=\mathrm{min}{\displaystyle \sum _{t=1}^{T}{\displaystyle \sum _{i=1}^{b}{10}^{-3}\times \frac{\left({P}_{i}^{2}(t)+{Q}_{i}^{2}(t)\right){R}_{i}}{{U}_{i}^{2}(t)}}}\mathsf{\Delta}t$$
- (3)
- Objective function ${F}_{4}$: the installation ratio ${\gamma}_{\mathrm{ESD},\mathrm{rate}}$ of ESD is minimum.$${F}_{4}=\mathrm{min}\frac{{\displaystyle \sum _{i=1}^{{N}_{\mathrm{ESD}}}{E}_{\mathrm{ESD},i}}}{{\displaystyle \sum _{i=1}^{{N}_{\mathrm{PV}}}{E}_{\mathrm{PV},i}}}\times 100\%$$

#### 3.2. Constraints

#### 3.2.1. Power Balance Constraints

#### 3.2.2. Unit Output Constraints

#### 3.2.3. Voltage Constraints

#### 3.2.4. Energy Storage Operation Constraints

#### 3.2.5. Power Purchase Constraints

#### 3.3. Mathematical Model of Voltage Regulation

#### 3.4. Determination of the Weighting Factor of the Objective Function

## 4. Mathematical Model Solving Method

## 5. Example Analysis

#### 5.1. Basic Data

#### 5.2. Determine the Scheme

#### 5.3. DNVR Result Analysis Based on PSO

## 6. Conclusions

- (1)
- When establishing a DNVR model with the lowest total voltage deviation, the lowest total cost, including fuel cost, operation and maintenance cost, electricity purchase cost, and environmental treatment cost, the lowest total power loss, and the lowest installation ratio of the ESD as the goal, the model is relatively perfect. It can be more in line with the actual operation of a distribution network and has a good adjustment effect by comprehensively considering many constraints such as power flow constraints, voltage deviation constraints and energy storage constraints;
- (2)
- After high-proportion PV access, node k-means clustering is performed on the voltage deviation curve of each node. The system is divided into different areas, and then FCE is used to determine the weighting factor of each objective function, thus making the determination of energy storage access location more reasonable and the subsequent adjustment effect better;
- (3)
- The results of the PSO algorithm show that the calculation results of the proposed method can effectively adjust the voltage, reduce the cost, reduce the power loss and reduce the installation ratio of ESD, thus improving the economy and security of power grid operation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Voltage deviation curves: (

**a**) before high proportion PV grid connection; and (

**b**) after high proportion PV grid connection.

**Figure 11.**MT output results under various schemes (

**a**) scheme 1; (

**b**) scheme 2; (

**c**) scheme 3; (

**d**) scheme 4; (

**e**) scheme 5.

**Figure 12.**ESD output results under various schemes (

**a**) scheme 1; (

**b**) scheme 2; (

**c**) scheme 3; (

**d**) scheme 4; (

**e**) scheme 5.

**Figure 13.**Voltage deviation results under various schemes (

**a**) scheme 1; (

**b**) scheme 2; (

**c**) scheme 3; (

**d**) scheme 4; (

**e**) scheme 5.

Behavior | PSO |
---|---|

Bird | Particle |

Forest | Solution space |

The amount of food | Objective function value |

The position of each bird | A solution in space (Particle position) |

$\mathrm{The}\mathrm{postion}\mathrm{with}\mathrm{the}\mathrm{most}\mathrm{food}$ | Global optimal solution |

Parameter | Value |
---|---|

${P}_{i,\mathrm{max}}$ | 200 |

${P}_{i,\mathrm{min}}$ | 100 |

${U}_{i}^{\mathrm{max}}$ | 13.293 |

${U}_{i}^{\mathrm{min}}$ | 11.394 |

${U}_{dev}^{\mathrm{max}}$ | 0.633 |

${U}_{dev}^{\mathrm{min}}$ | −0.633 |

${P}_{\mathrm{ESD},c}^{\mathrm{max}}$ | −250 |

${P}_{\mathrm{ESD},dc}^{\mathrm{max}}$ | 250 |

${P}_{ee,\mathrm{max}}$ | 5000 |

${\mathrm{SOC}}_{\mathrm{max}}$ | 1000 |

${\mathrm{SOC}}_{\mathrm{min}}$ | 100 |

Parameter | Value |
---|---|

${\mu}_{\mathrm{ESD}}$ | 0.045 |

${c}_{\mathrm{PV},om}$ | 0.0096 |

${c}_{gas}$ | 2.20 |

${Q}_{gas}$ | 8500 |

$\eta $ | 32 |

${c}_{\mathrm{MT},om}$ | 0.082 |

Pollutant Type | ${\mathit{c}}_{\mathit{p}\mathit{o},\mathit{k}}$ | ${\mathit{\sigma}}_{\mathit{p}\mathit{o},\mathit{k}}$ |
---|---|---|

${\mathrm{CO}}_{2}$ | 724 | 0.994 |

$\mathrm{NO}$ | 0.0036 | 0.00653 |

${\mathrm{NO}}_{2}$ | 0.2 | 0.00312 |

Actual Value | Value |
---|---|

${d}_{ac,1}$/kV | 2.0639 |

${d}_{ac,2}$/yuan | 3017.94 |

${d}_{ac,3}$/kW | 0.3368 |

${d}_{ac,4}$/% | 0.1056 |

Maximum Allowable Value | Value |
---|---|

${d}_{ma,1}$/kV | 2.5400 |

${d}_{ma,2}$/yuan | 3796.01 |

${d}_{ma,3}$/kW | 0.5549 |

${d}_{ma,4}$/% | 0.1234 |

Weighing Factor | Value |
---|---|

${m}_{1}$ | 0.2646 |

${m}_{2}$ | 0.2590 |

${m}_{3}$ | 0.1977 |

${m}_{4}$ | 0.2787 |

Cluster Sequence Number | Node Division | Cluster Center (Node Configured with ESD) |
---|---|---|

1 | 1, 2, 19~22 | 19 |

2 | 6~9, 26~33 | 8 |

3 | 10~18 | 13 |

4 | 3~5, 23~25 | 24 |

Subitem | ${\mathit{C}}_{\mathbf{ESD}}$/Yuan | ${\mathit{C}}_{\mathbf{PV},\mathit{g}\mathit{e}}$/Yuan | ${\mathit{C}}_{\mathbf{MT},\mathit{g}\mathit{e}}$/Yuan | ${\mathit{C}}_{\mathit{e},\mathit{b}\mathit{u}\mathit{y}}$/Yuan | ${\mathit{C}}_{\mathit{p}\mathit{t}}$/Yuan |
---|---|---|---|---|---|

Before DNVR | 0 | 280.0 | 0 | 40,315.1 | 0 |

scheme 1 | 270.0 | 280.0 | 6085.8 | 31,144.2 | 1311.1 |

scheme 2 | 540.0 | 280.0 | 5997.6 | 30,259.0 | 1292.0 |

scheme 3 | 769.7 | 280.0 | 6645.7 | 28,384.1 | 1431.6 |

scheme 4 | 1080.0 | 280.0 | 6262.2 | 25,538.2 | 1349.0 |

scheme 5 | 1280.8 | 280.0 | 5897.2 | 27,352.3 | 1266.5 |

Subitem | ${\mathit{U}}_{\mathit{d}\mathit{e}\mathit{v}\_\mathit{t}\mathit{o}\mathit{t}\mathit{a}\mathit{l}}$/kV | ${\mathit{C}}_{\mathit{E}\_\mathit{t}\mathit{o}\mathit{t}\mathit{a}\mathit{l}}$/Yuan | ${\mathit{A}}_{\mathit{n}\mathit{l}\_\mathit{t}\mathit{o}\mathit{t}\mathit{a}\mathit{l}}$/kWh | ${\mathit{\gamma}}_{\mathbf{ESD},\mathbf{rate}}$/% |
---|---|---|---|---|

Before DNVR | 48.1080 | 40,595 | 6.5324 | 0 |

scheme 1 | 35.6493 | 39,091 | 5.8300 | 12.34 |

scheme 2 | 35.1966 | 38,369 | 5.6184 | 10.97 |

scheme 3 | 34.0495 | 37,511 | 5.5829 | 10.29 |

scheme 4 | 32.3250 | 34,509 | 5.2677 | 9.60 |

scheme 5 | 33.8130 | 36,059 | 5.5074 | 9.60 |

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## Share and Cite

**MDPI and ACS Style**

Zheng, F.; Meng, X.; Xu, T.; Sun, Y.; Zhang, N.
Voltage Zoning Regulation Method of Distribution Network with High Proportion of Photovoltaic Considering Energy Storage Configuration. *Sustainability* **2023**, *15*, 10732.
https://doi.org/10.3390/su151310732

**AMA Style**

Zheng F, Meng X, Xu T, Sun Y, Zhang N.
Voltage Zoning Regulation Method of Distribution Network with High Proportion of Photovoltaic Considering Energy Storage Configuration. *Sustainability*. 2023; 15(13):10732.
https://doi.org/10.3390/su151310732

**Chicago/Turabian Style**

Zheng, Fangfang, Xiaofang Meng, Tiefeng Xu, Yongchang Sun, and Nannan Zhang.
2023. "Voltage Zoning Regulation Method of Distribution Network with High Proportion of Photovoltaic Considering Energy Storage Configuration" *Sustainability* 15, no. 13: 10732.
https://doi.org/10.3390/su151310732