# Optimization Model of Electric Vehicles Charging and Discharging Strategy Considering the Safe Operation of Distribution Network

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## Abstract

**:**

## 1. Introduction

- (1)
- Summarize the impact of EV access on the indicators of the distribution network and the correlation between the impacts.
- (2)
- According to the power load planning of a certain area, combined with the distribution planning margin and the load power factor, the distribution capacity configuration model can be obtained. Calculating the distribution transformer requirements of each region under different charging modes can effectively reduce unnecessary investment.
- (3)
- Establish a multi-objective optimization function that considers the load peak, load volatility, and voltage offset of each node of the power grid. Using the distribution transformer capacity configuration model as the optimization target constraint, the improved IEEE 34-bus systems is simulated as an example, and the investment requirements of the distribution network are analyzed and compared under disorderly and orderly charging and discharging.

## 2. Literature Review

## 3. Influence of Electric Vehicles Access on Distribution Network

## 4. Analysis of Transformer Transformation in Distribution Network under Disordered Charging Mode

#### 4.1. Electric Vehicles Penetration Rate and Charging Load Simultaneous Rate

#### 4.2. The Superposition Rate of Electric vehicles Charging Load and Grid Base Load

#### 4.3. Model of Electric Vehicle Charging Load Planning Calculation

#### 4.4. Calculation Model of Power Load Planning

#### 4.5. Distribution Transformer Capacity Configuration Model

## 5. Optimization Model of Charging and Discharging Strategy for Electric Vehicles

#### 5.1. Objective Function

#### 5.2. Constraint Condition

#### 5.2.1. Battery Capacity and User Travel Constraints

#### 5.2.2. Network Trend Constraints

#### 5.2.3. Node Voltage Constraints

#### 5.2.4. Distribution Capacity Constraints

#### 5.3. Multi-Objective Particle Swarm Algorithm Solving

- Set the population number and maximum number of iterations, initial population, initialization parameters.
- To achieve the fitness value calculation, calculate the objective function of each particle to find the individual value of each particle and the current optimal solution of the particle swarm.
- Use the Pareto domination principle to select dominant particles (Pareto optimal solution) and update the individual optimal position of each particle, select the guide particles from the external archive, and generate a new population.
- Recalculate the fitness degree, update the individual optimal particle position and the global optimal particle position according to the fitness degree, determine whether to update the particle position, and record the global optimality.
- Iterate the maximum number of iterations set, constantly update the external archive, and finally obtain the Pareto optimal solution set and a set of optimal solutions in the solution set.

## 6. Calculation Example

#### 6.1. Parameter Settings

#### 6.2. Analysis of Results

## 7. Conclusions and Future Works

- The large-scale disorderly access of electric vehicles to the distribution network will exacerbate the peak-to-valley difference of the power grid, affecting the quality of power and the life of the transformers. According to the power load planning of a certain region, combined with the distribution planning margin, the load power factor can obtain the distribution capacity configuration model, calculate the distribution transformer demand of each region under different charging modes, and effectively reduce unnecessary investment.
- The orderly charging and discharging of electric vehicles is conducive to reducing the load rate of the distribution network to delay the investment and construction of the distribution network, according to the estimation that the number of electric vehicles will reach 80 million in 2030, it is expected that by 2030, the cumulative investment in the distribution network can saved CNY 147 billion, and the V2G mode of electric vehicles is conducive to helping the construction of digital power grids and promoting the process of modernizing the power grid.
- According to the simulation results, the V2G mode of electric vehicles reduces the load peak-to-valley difference of residential area by 42.66%, the load peak-to-valley difference of commercial area by 54.89%, and the load peak-to-valley difference of charging stations by 26.93%, keeping the three-phase voltage offset within the allowable range, effectively improving the power quality of the power grid and improving the reliable operation safety of the power grid.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ACSR | Aluminum core steel reinforced aluminum overhead cable |

DC | Direct current |

AC | Alternating current |

EVs | Electric vehicles |

PV | Solar photovoltaic energy |

WE | Wind energy |

FC | Fuel cell |

SC | Supercapacitor |

HEV | Hybrid electric vehicles |

RERs | renewable energy resources |

PEM | proton exchange membrane |

DG | Distribution generation |

PSO | Particle swarm algorithm |

MOPSO | Multi-objective particle swarm algorithm |

## Appendix A

kVA | kV-High | kV-Low | R-% | X-% | |
---|---|---|---|---|---|

Substation: | 2500 | 69-D | 24.9-Gr. W | 1 | 8 |

XFM-1 | 500 | 24.9-Gr.W | 4.16-Gr. W | 1.9 | 4.08 |

Node | Load Model | Ph-1 (kW) | Ph-1 (kVAr) | Ph-2 (kW) | Ph-2 (kVAr) | Ph-3 (kW) | Ph-4 (kVAr) |
---|---|---|---|---|---|---|---|

860 | Y-PQ | 20 | 16 | 20 | 16 | 20 | 16 |

840 | Y-I | 9 | 7 | 9 | 7 | 9 | 7 |

844 | Y-Z | 135 | 105 | 135 | 105 | 135 | 105 |

848 | D-PQ | 20 | 16 | 20 | 16 | 20 | 16 |

890 | D-I | 150 | 75 | 150 | 75 | 150 | 75 |

830 | D-Z | 10 | 5 | 10 | 5 | 25 | 10 |

Total | 344 | 224 | 344 | 224 | 359 | 229 |

Regulator ID: | 1 | Regulator ID: | 2 | ||||

Line Segment: | 814–850 | Line Segment: | 852–832 | ||||

Location: | 814 | Location: | 852 | ||||

Phases: | A-B-C | Phases: | A-B-C | ||||

Connection: | 3-Ph,LG | Connection: | 3-Ph,LG | ||||

Monitoring Phase: | A-B-C | Monitoring Phase: | A-B-C | ||||

Bandwidth: | 2.0 volts | Bandwidth: | 2.0 volts | ||||

PT Ratio: | 120 | PT Ratio: | 120 | ||||

Primary CT Rating: | 100 | Primary CT Rating: | 100 | ||||

Compensator Settings: | Ph-A | Ph-B | Ph-C | Compensator Settings: | Ph-A | Ph-B | Ph-C |

R—Setting: | 2.7 | 2.7 | 2.7 | R—Setting: | 2.5 | 2.5 | 2.5 |

X—Setting: | 1.6 | 1.6 | 1.6 | X—Setting: | 1.5 | 1.5 | 1.5 |

Volltage Level: | 122 | 122 | 122 | Volltage Level: | 124 | 124 | 124 |

Node A | Node B | Length (ft.) | Config. |
---|---|---|---|

800 | 802 | 2580 | 300 |

802 | 806 | 1730 | 300 |

806 | 808 | 32,230 | 300 |

808 | 810 | 5804 | 303 |

808 | 812 | 37,500 | 300 |

812 | 814 | 29,730 | 300 |

814 | 850 | 10 | 301 |

816 | 818 | 1710 | 302 |

816 | 824 | 10,210 | 301 |

818 | 820 | 48,150 | 302 |

820 | 822 | 13,740 | 302 |

824 | 826 | 3030 | 303 |

824 | 828 | 840 | 301 |

828 | 830 | 20,440 | 301 |

830 | 854 | 520 | 301 |

832 | 858 | 4900 | 301 |

832 | 888 | 0 | XFM-1 |

834 | 860 | 2020 | 301 |

834 | 842 | 280 | 301 |

836 | 840 | 860 | 301 |

836 | 862 | 280 | 301 |

842 | 844 | 1350 | 301 |

844 | 846 | 3640 | 301 |

846 | 848 | 530 | 301 |

850 | 816 | 310 | 301 |

852 | 832 | 10 | 301 |

854 | 856 | 23,330 | 303 |

854 | 852 | 36,830 | 301 |

858 | 864 | 1620 | 302 |

858 | 834 | 5830 | 301 |

860 | 836 | 2680 | 301 |

862 | 838 | 4860 | 304 |

888 | 890 | 10,560 | 300 |

Node (A) | Node (B) | Load Model | Ph-1 (kW) | Ph-1 (kVAr) | Ph-2 (kW) | Ph-2 (kVAr) | Ph-3 (kW) | Ph-3 (kVAr) |
---|---|---|---|---|---|---|---|---|

802 | 806 | Y-PQ | 0 | 0 | 30 | 15 | 25 | 14 |

808 | 810 | Y-I | 0 | 0 | 16 | 8 | 0 | 0 |

818 | 820 | Y-Z | 34 | 17 | 0 | 0 | 0 | 0 |

820 | 822 | Y-PQ | 135 | 70 | 0 | 0 | 0 | 0 |

816 | 824 | D-I | 0 | 0 | 5 | 2 | 0 | 0 |

824 | 826 | Y-I | 0 | 0 | 40 | 20 | 0 | 0 |

824 | 828 | Y-PQ | 0 | 0 | 0 | 0 | 4 | 2 |

828 | 830 | Y-PQ | 7 | 3 | 0 | 0 | 0 | 0 |

854 | 856 | Y-PQ | 0 | 0 | 4 | 2 | 0 | 0 |

832 | 858 | D-Z | 7 | 3 | 2 | 1 | 6 | 3 |

858 | 864 | Y-PQ | 2 | 1 | 0 | 0 | 0 | 0 |

858 | 834 | D-PQ | 4 | 2 | 15 | 8 | 13 | 7 |

834 | 860 | D-Z | 16 | 8 | 20 | 10 | 110 | 55 |

860 | 836 | D-PQ | 30 | 15 | 10 | 6 | 42 | 22 |

836 | 840 | D-I | 18 | 9 | 22 | 11 | 0 | 0 |

862 | 838 | Y-PQ | 0 | 0 | 28 | 14 | 0 | 0 |

842 | 844 | Y-PQ | 9 | 5 | 0 | 0 | 0 | 0 |

844 | 846 | Y-PQ | 0 | 0 | 25 | 12 | 20 | 11 |

846 | 848 | Y-PQ | 0 | 0 | 23 | 11 | 0 | 0 |

Total | 262 | 133 | 240 | 120 | 220 | 114 |

Config. | Phasing | Phase (ACSR) | Neutral (ACSR) | Spacing ID |
---|---|---|---|---|

300 | B A C N | 1/0 | 1/0 | 500 |

301 | B A C N | #2 6/1 | #2 6/1 | 500 |

302 | A N | #4 6/1 | #4 6/1 | 510 |

303 | B N | #4 6/1 | #4 6/1 | 510 |

304 | B N | #2 6/1 | #2 6/1 | 510 |

Node | Ph-A (kVAr) | Ph-B (kVAr) | Ph-C (kVAr) |
---|---|---|---|

844 | 100 | 100 | 100 |

848 | 150 | 150 | 150 |

Total | 250 | 250 | 250 |

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**Figure 3.**The impact of electric vehicle charging loads on various indicators of the distribution network.

**Figure 7.**Load curves of disordered charging mode and V2G mode in various regions. (

**a**) Load curves in residential areas; (

**b**) the load curves of the business district; (

**c**) charging station load curves.

Ref. | Research Direction | Specific Research Content |
---|---|---|

[26,27,28] | Multi-objective optimization of electric vehicles access to distribution network | Evaluate the voltage security of the distribution networks in the presence of electric vehicles in the optimization framework, including the maximization of voltage security margin and minimization of operational cost as target optimization functions. |

An optimal scheduling model of the distribution network, considering the demand response side load is established, and the optimal scheduling problem is solved by using the firefly optimization algorithm. | ||

The economic cost of the distribution network and the unsatisfactory value of electric vehicle users are proposed as the optimization goals. | ||

[29,30,31] | The impact of electric vehicle discharge behavior on the distribution network | Propose a distributed generation equivalent method based on the discharge behavior of electric vehicles. |

Analyze the impact of electric vehicle access on power quality in distribution networks. | ||

Study the demand characteristics of electric charging and the treatment method and model of access to the network. Analyze the impact on the distribution network load, the network loss, and voltage through different electric vehicles capacities. | ||

[32] | evaluate the reliability of the distribution network incorporating electric vehicles | The effects of electric vehicles penetration, discharging threshold, and battery capacity on reliability of both distribution networks and electric vehicles are studied. |

[33,34,35] | New technologies and Strategies | Propose an input–output methodology applied to a case study in a representative urban context. |

propose a distributed framework for vehicle grid integration taking into account the communication and physical networks. | ||

Propose a charging and discharging strategy along with two price-based and voltage-based load management programs to manage the penetration of electric vehicles for economic and technical purposes. |

**Table 2.**Comparison of distribution network evaluation indicators in the disordered charging mode and V2G mode in residential area.

Evaluation Indicators | Disordered Charging | V2G |
---|---|---|

Load overlay rate | 0.96 | 0.82 |

Number of distribution transformers (units) | 9 | 12 |

Maximum load rate | 81.38% | 59.71% |

Peak-to-valley difference (kW) | 4693.6 | 2691.2 |

Load standard deviation (kW) | 1409.46 | 704.09 |

**Table 3.**Comparison of distribution network evaluation indicators in the disordered charging mode and V2G mode in commercial area.

Evaluation Indicators | Disordered Charging | V2G |
---|---|---|

Load overlay rate | 0.88 | 0.79 |

Number of distribution transformers (units) | 7 | 6 |

Maximum load rate | 72.16% | 68.46% |

Peak-to-valley difference (kW) | 3318.02 | 1496.6 |

Load standard deviation (kW) | 838.41 | 403.95 |

**Table 4.**Comparison of distribution network evaluation indicators in disordered charging mode and V2G mode in charging station.

Evaluation Indicators | Disordered Charging | V2G |
---|---|---|

Load overlay rate | - | - |

Number of distribution transformers (units) | 26 | 23 |

Maximum load rate | 90.28% | 87.12% |

Peak-to-valley difference (kW) | 23.47 | 17.15 |

Load standard deviation (kW) | 8.20 | 6.73 |

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## Share and Cite

**MDPI and ACS Style**

Zou, M.; Yang, Y.; Liu, M.; Wang, W.; Jia, H.; Peng, X.; Su, S.; Liu, D.
Optimization Model of Electric Vehicles Charging and Discharging Strategy Considering the Safe Operation of Distribution Network. *World Electr. Veh. J.* **2022**, *13*, 117.
https://doi.org/10.3390/wevj13070117

**AMA Style**

Zou M, Yang Y, Liu M, Wang W, Jia H, Peng X, Su S, Liu D.
Optimization Model of Electric Vehicles Charging and Discharging Strategy Considering the Safe Operation of Distribution Network. *World Electric Vehicle Journal*. 2022; 13(7):117.
https://doi.org/10.3390/wevj13070117

**Chicago/Turabian Style**

Zou, Mengjiao, Ye Yang, Mingguang Liu, Wen Wang, Heping Jia, Xiaofeng Peng, Shu Su, and Dunnan Liu.
2022. "Optimization Model of Electric Vehicles Charging and Discharging Strategy Considering the Safe Operation of Distribution Network" *World Electric Vehicle Journal* 13, no. 7: 117.
https://doi.org/10.3390/wevj13070117