# Sizing and Energy Management of Parking Lots of Electric Vehicles Based on Battery Storage with Wind Resources in Distribution Network

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## Abstract

**:**

## 1. Introduction

## 2. Problem Formulation

#### 2.1. Objective Function

- Cost of power loss

- Cost of purchased power from main network

- Cost of wind power

- Cost of parking lots

#### 2.2. Constraints

- Power balance

- Power purchased from the main network

- Vehicle’s battery capacity

- Voltage

- Power of wind generator

- Allowable power of network lines (thermal limit)

#### 2.3. Energy Management Strategy

- If the power output of wind turbines is more than the load demand and if the amount of parking battery charge is less than the maximum allowable value, then the parking battery will be charged based on the allowable charging capacity.
- If the power output of wind turbines is less than the load demand and if the amount of parking battery charge is more than the maximum allowable value, then considering the allowable charging capacity, the parking battery will be discharged to load supply.
- If the capacity of wind resources in addition to charging electric parking lots is less than the demand, then in proportion to the load shortage, the power can be purchased from the main grid.

## 3. Proposed Optimization Method

#### 3.1. Overview of AOA

#### 3.1.1. Preparation Stage

#### 3.1.2. Exploration Stage

_{i}(C_Iter + 1) represents the ith next iteration solution, x

_{i,j}(C_Iter) is the jth position of the ith solution in the present iteration, best (x

_{j}) is the jth position in the best solution, $\epsilon $ represents a very small number, UB

_{j}and LB

_{j}specify the upper and lower limits of the j position, and μ is the control parameter (equal to 0.5) [23].

#### 3.1.3. Exploitation Phase

#### 3.2. Implementation of the AOA

**Step 1.**The problem variables are randomly determined for the AOA population. The population of the algorithm is selected as 50 and the maximum iteration of the AOA is considered to be 300.

**Step 2.**For each of the AOA population members, the energy contribution of the parking lots and also wind energy resources are considered and the operating conditions are checked. In this study, backward–forward load flow is used. The voltage constraints and also thermal limits should be satisfied.

**Step 3.**The value of the objective function for the variables selected in step 1 is calculated for each of the AOA population members and the best solution is determined. The variable set with a lower objective function value is considered as the best set of the variables in this step.

**Step 4.**Using the AOA, the population is updated in this step and then the variables are randomly determined again. Then, the objective function is evaluated for the new variable set.

**Step 5.**If the convergence conditions such as achieving the best value of the objective function and maximum iteration are met, we go to step 6; otherwise, we go to step 2.

**Step 6.**In this step, after the determination of the optimal variable set, we stop the AOA to save the optimal variable.

## 4. Simulation Results

#### 4.1. Test Network

#### 4.2. Simulation Cases

**Case 1#**OSPF with minimizing the cost of power losses,

**Case 2#**OSPF with minimizing the voltage deviations, and

**Case 3#**OSPF with minimizing the total objective (Equation (1)). The results of the OSPF based on the AOA for the allocation of parking lots integrated with wind turbines are implemented in three cases. The convergence curve of the AOA in the problem solution is depicted in Figure 9. The convergence process of the AOA in the optimization of the problem and achieving the optimal variables is plotted in this figure for the three cases.

#### 4.3. Comparison of the Results

#### 4.3.1. Power Loss

#### 4.3.2. Minimum Voltage

#### 4.3.3. Grid Power

#### 4.3.4. Contribution of the Wind Resources and Grid

#### 4.3.5. Charge and Discharge of the Batteries

#### 4.4. Comparison of the AOA Results with PSO and ABC

#### 4.5. Comparison Results of the AOA with Previous Studies

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Hierarchy of AOs in AOA with exploration and operation phases adopted from [23].

**Figure 2.**How to update AOA operators to the optimal region adopted from [23].

**Figure 4.**The 33-bus distribution network [33].

**Figure 5.**Wind speed profile for 24 h [34].

**Figure 7.**Loading coefficients of the distribution network for 24 h [34].

**Figure 14.**Charging and discharging of electric parking lot batteries with and without OSPF via the AOA for 24 h.

Item | Cost of Power Loss (USD) | Cost of Grid Power (USD) | Total Cost (USD) | Min Voltage (p.u) |
---|---|---|---|---|

Value | 57.02 | 75,011 | 75,068 | 0.9134 |

Size/@Bus | WT 1 | WT 2 | WT 3 |
---|---|---|---|

Case#1 | 429/@6 | --/-- | 500/@30 |

Case#2 | 500/@8 | --/-- | 500/18 |

Case#3 | 500/@6 | 500/@18 | 500/@30 |

Size/@Bus | PHEV 1 | PHEV 2 | PHEV 3 | PHEV 4 | PHEV 5 | PHEV 6 | PHEV 7 | PHEV 8 |
---|---|---|---|---|---|---|---|---|

Case#1 | 2000/@12 | 2000/@15 | 2000/@17 | 2000/@28 | 2000/@32 | 2000/@21 | --/-- | 2000/@24 |

Case#2 | --/-- | 1601/@17 | --/-- | 1974/@21 | --/-- | 1697/@24 | --/-- | 1204/@32 |

Case#3 | --/-- | 1059/@8 | --/-- | 1789/@16 | --/- | 1195/@28 | 1059/@32 | --/-- |

Item/Case | Case#1 | Case#2 | Case#3 |
---|---|---|---|

Cost of power loss (USD) | 29.68 | 31.25 | 44.60 |

Cost of grid (USD) | 47012 | 45,876 | 29,271 |

Cost of PHEV (USD) | 547.16 | 312.84 | 201.28 |

Cost of WTs (USD) | 995.17 | 1071.22 | 1606.84 |

Total cost (USD) | 48,584 | 47,291 | 31,123 |

Voltage deviation (p.u) | 0.1779 | 0.0504 | 0.0631 |

**Table 5.**Size and installation location of WTs in 33-bus distribution network using different methods.

Method/Size/@Bus | WT 1 | WT 2 | WT 3 |
---|---|---|---|

AOA | 500/@6 | 500/@18 | 500/@30 |

PSO | 500/@8 | 500/@16 | 500/@29 |

ABC | 495/@6 | 467/@18 | 495/@28 |

**Table 6.**Size and installation location of PHEVs in 33-bus distribution network using different methods.

Method/Size/@Bus | PHEV 1 | PHEV 2 | PHEV 3 | PHEV 4 | PHEV 5 | PHEV 6 | PHEV 7 | PHEV 8 |
---|---|---|---|---|---|---|---|---|

AOA | --/@-- | 1059/@8 | --/@-- | 1789/@16 | --/@- | 1195/@28 | 1059/@32 | --/@-- |

PSO | --/@-- | 2000/@12 | --/@-- | 2000/@17 | --/@-- | --/@-- | 2000/@28 | 2000/@32 |

ABC | --/@-- | 1536/@15 | --/@-- | 1962/@21 | --/@- | 1006/@30 | --/@-- | --/@-- |

Item/Case | AOA | PSO | ABC |
---|---|---|---|

Cost of power loss (USD) | 44.60 | 44.81 | 45.07 |

Cost of grid (USD) | 29,271 | 29,364 | 30,690 |

Cost of PHEV (USD) | 201.28 | 238.50 | 184.33 |

Cost of WTs (USD) | 1606.84 | 1617.35 | 1560.77 |

Total cost (USD) | 31,123 | 31,264 | 32,480 |

Voltage deviation (p.u) | 0.0631 | 0.0648 | 0.0726 |

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**MDPI and ACS Style**

Shahrokhi, S.; El-Shahat, A.; Masoudinia, F.; Gandoman, F.H.; Abdel Aleem, S.H.E. Sizing and Energy Management of Parking Lots of Electric Vehicles Based on Battery Storage with Wind Resources in Distribution Network. *Energies* **2021**, *14*, 6755.
https://doi.org/10.3390/en14206755

**AMA Style**

Shahrokhi S, El-Shahat A, Masoudinia F, Gandoman FH, Abdel Aleem SHE. Sizing and Energy Management of Parking Lots of Electric Vehicles Based on Battery Storage with Wind Resources in Distribution Network. *Energies*. 2021; 14(20):6755.
https://doi.org/10.3390/en14206755

**Chicago/Turabian Style**

Shahrokhi, Saman, Adel El-Shahat, Fatemeh Masoudinia, Foad H. Gandoman, and Shady H. E. Abdel Aleem. 2021. "Sizing and Energy Management of Parking Lots of Electric Vehicles Based on Battery Storage with Wind Resources in Distribution Network" *Energies* 14, no. 20: 6755.
https://doi.org/10.3390/en14206755