# Hierarchical Distributed Control Strategy for Electric Vehicle Mobile Energy Storage Clusters

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## Abstract

**:**

## 1. Introduction

## 2. Hierarchical Distributed Control

## 3. MESC Model

#### 3.1. Lower Layer Control Strategy

_{v}denotes the life loss cost of the EV v, Q

_{N,v}denotes the rated capacity of the EV v, Q

_{v}is the amount of output energy released by the EV v, C

_{v}is the initial investment cost of the battery of the EV v. a

_{v}and b

_{v}are coefficients.

_{agg}denotes the total life loss cost.

_{v}

_{,max}and Q

_{v}

_{,min}are the maximum and minimum output energy, respectively, that each EV can provide and Q

_{D}denotes the total demand of the system.

_{v}is the same as I

_{F,v}, where I

_{F,v}can be obtained by calculating the partial derivative of the life loss cost F

_{v}with respect to the output energy Q

_{v}, which is represented as below:

_{v}is considered as the consensus variable. According to Equations (1) and (5), the output energy offered by each EV can be expressed as follows:

_{D}is the amount of energy required by the system.

_{v}can be calculated by:

_{v}= Q

_{D}can be guaranteed, and Q

_{D}is issued through the distributed consensus control strategy. The controller calculates the required output energy according to Equations (8) and (9).

_{agg}and the total output energy ${Q}_{\mathrm{agg}}={\displaystyle \sum _{v=1}^{n}{Q}_{v}}$ during the release process could be obtained as shown in Figure 2.

#### 3.2. Upper Layer Control Strategy

_{agg,i}of cluster i is represented as follows:

_{agg,i}denotes the total life loss cost of cluster i, Q

_{agg,i}is the amount of output energy released by cluster i and I

_{agg,i}is equal to the incremental cost λ

_{agg,i}during the operation of the consensus algorithm.

_{agg,i}can be obtained by using Equations (10) and (11), which is shown as follows:

_{agg}represents the total number of clusters, λ

_{agg,j}represents the information state of cluster j that is adjacent to cluster i, h

_{ij}is the element in the sparse iterative matrix H and the sparse iterative matrix is obtained from the Laplacian matrix corresponding to the communication topology [18].

_{agg,i}, which can be calculated by:

_{Dagg}represents the total energy demand of MESS and Q

_{aggmin,i}and Q

_{aggmax,i}are the maximum and minimum output energy, respectively, that each cluster can provide.

_{agg}should be increased, and vice versa.

_{agg,i}is subject to the following constraint:

_{agg,i}will asymptotically converge to I

_{agg}.

## 4. Simulation Results

_{agg,i}of cluster i will be updated based on its neighbors’ incremental costs. In addition, the leader node has to be selected, which will control whether to increase or decrease the group incremental costs. In the example shown in Figure 5, node 3 was selected as the leader node of the five-MESCs system according to the centrality principle [20].

_{D}= 111.3019 kWh. The simulation curves are shown in Figure 9 and Figure 10 using the communication topology in Figure 6.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**Consensus variables λ

_{agg,j}in the upper layer for (

**a**) the optimal allocation method based on the consensus incremental cost, (

**b**) the average allocation method and (

**c**) the battery-capacity-based allocation method.

**Figure 8.**Output energy Q

_{agg,i}in the upper layer for (

**a**) the optimal allocation method based on the consensus incremental cost, (

**b**) the average allocation method and (

**c**) the battery-capacity-based allocation method.

Bus | The Number of EVs | BYDe6 | Tengshi |
---|---|---|---|

I | 32 | 21 | 11 |

II | 44 | 24 | 20 |

III | 28 | 15 | 13 |

IV | 40 | 28 | 12 |

V | 34 | 19 | 15 |

**Table 2.**The parameters of the five mobile energy storage clusters (MESCs) system using the optimal allocation method based on the consensus incremental cost.

Node | α | β | γ |
---|---|---|---|

1 | 0.0004 | 0.0849 | −1.3760 |

2 | 0.0003 | 0.0715 | −1.3610 |

3 | 0.0005 | 0.0738 | −1.3071 |

4 | 0.0004 | 0.0737 | −1.5293 |

5 | 0.0004 | 0.1030 | −1.6182 |

Node | α | β | γ |
---|---|---|---|

1 | 0.0003 | 0.1402 | 0.1734 |

2 | 0.0002 | 0.1503 | 0.0632 |

3 | 0.0004 | 0.1484 | 0.1242 |

4 | 0.0003 | 0.1752 | 0.0624 |

5 | 0.0003 | 0.1645 | 0.0528 |

**Table 4.**The parameters of the five-MESCs system using the battery-capacity-based allocation method.

Node | α | β | γ |
---|---|---|---|

1 | 0.0003 | 0.1276 | 0.2084 |

2 | 0.0002 | 0.1414 | 0.0728 |

3 | 0.0004 | 0.1379 | 0.1616 |

4 | 0.0003 | 0.1598 | 0.0693 |

5 | 0.0003 | 0.1531 | 0.0423 |

Node | Optimal Allocation Based on the Consensus Incremental Cost (kWh) | Average Allocation (kWh) | Battery-Capacity-Based Allocation (kWh) |
---|---|---|---|

1 | 94.7762 | 116.1089 | 117.6006 |

2 | 134.2594 | 137.6080 | 132.6827 |

3 | 89.3234 | 86.5212 | 85.9543 |

4 | 111.3019 | 78.7278 | 84.2197 |

5 | 70.3390 | 81.0341 | 79.5427 |

Allocation Method | Cost (yuan) |
---|---|

Optimal allocation based on the consensus of incremental cost | 52.6900 |

Average allocation | 93.2611 |

Battery-capacity-based allocation | 87.5728 |

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## Share and Cite

**MDPI and ACS Style**

Wu, M.; Bao, Y.-Q.; Chen, G.; Zhang, J.; Wang, B.; Qian, W.
Hierarchical Distributed Control Strategy for Electric Vehicle Mobile Energy Storage Clusters. *Energies* **2019**, *12*, 1195.
https://doi.org/10.3390/en12071195

**AMA Style**

Wu M, Bao Y-Q, Chen G, Zhang J, Wang B, Qian W.
Hierarchical Distributed Control Strategy for Electric Vehicle Mobile Energy Storage Clusters. *Energies*. 2019; 12(7):1195.
https://doi.org/10.3390/en12071195

**Chicago/Turabian Style**

Wu, Mei, Yu-Qing Bao, Gang Chen, Jinlong Zhang, Beibei Wang, and Weixing Qian.
2019. "Hierarchical Distributed Control Strategy for Electric Vehicle Mobile Energy Storage Clusters" *Energies* 12, no. 7: 1195.
https://doi.org/10.3390/en12071195