# A Privacy-Preserving Distributed Optimal Scheduling for Interconnected Microgrids

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

#### 2.1. Renewable Energy Resources

#### 2.2. Diesel Generation

#### 2.3. BESS

#### 2.4. Optimal Scheduling Model of MGs

#### 2.5. Optimal Scheduling Model of the IMG

## 3. Distributed Optimization

#### 3.1. ADMM

#### 3.2. Decentralizing the Problem

Algorithm 1 Distributed scheduling algorithm |

1: procedure DISPATCHING(${\mathit{x}}_{n},n=[1,2,\dots ,N]$) |

2: Initiate u,ρ,k |

3: while ${\parallel r\parallel}_{2}^{2}>\epsilon $ do |

4: ${\mathit{x}}_{n}^{k+1}=arg\underset{\mathit{x}}{min}{h}_{n}(\mathit{x})+\frac{\rho}{2}{\parallel {x}_{n}^{in}-{x}_{n}^{i{n}^{k}}+{\overline{x}}^{i{n}^{k}}+{u}^{k}\parallel}_{2}^{2}$ |

5: ${\overline{x}}^{i{n}^{k+1}}=\frac{1}{N}{\sum}_{n=1}^{N}{x}_{n}^{i{n}^{k+1}}$ |

6: ${u}^{k+1}={u}^{k}+{\overline{x}}^{i{n}^{k+1}}$ |

7: ${r}_{k+1}=\frac{1}{N}{\sum}_{n=1}^{N}{x}_{n}^{i{n}^{k+1}}$ |

8: $k=k+1$ |

9: end while |

10: end procedure |

## 4. Privacy-Preserving Strategy

#### 4.1. Basic Theory of the Paillier Cryptosystem

#### 4.1.1. Key Generation

#### 4.1.2. Encryption

#### 4.1.3. Decryption

#### 4.2. Protocol of EEP Sharing

#### 4.3. Security Analysis of the Protocol

- For the first scenario, the sensitive data of each MG ${x}_{n}^{in}$ are encrypted and delivered on a fixed path. The AU can receive the ciphertext of summing EEP $E({\sum}_{n=1}^{N}{x}_{n})$. Although the plaintext can be decrypted as ${\sum}_{n=1}^{N}{x}_{n}$, the actual data of arbitrary MGs cannot be deduced.
- For the second scenario, as the EEP of each MG is encrypted by the public key of AU $E({x}_{n}^{in})$, even if there are a number of collusive MGs, the plaintext of any MGs cannot be obtained without the private key of AU.
- For the third scenario, we assume that there are ${N}_{c}$ collusive MGs. (a) When ${N}_{c}=N-1$, that is only one non-collusive MG exists (denoted as MG-a), then, the MG-a is the target of the collusive MGs. In this case, if all of the collusive MGs can share their own plaintexts with the AU or set their EEPs to zero, the AU can get the privacy data of MG-a. Otherwise, the privacy of MG-a still can be guaranteed. However, this condition is difficult to achieve, since it would also affect the privacy of the collusive MGs or make it easy to be detected by MG-a. (b) When ${N}_{c}<N-1$, that is the number of non-collusive MGs is not less than two. Similar to the condition of ${N}_{c}=N-1$, the untrustful AU can only get the sum of EEPs from the non-collusive MGs (e.g. ${\sum}_{n=1}^{N-{N}_{c}}{x}_{n}$) even with the worst conditions.

## 5. Case Study

#### 5.1. Basic Data

#### 5.2. Result and Analysis of the Distributed Optimal Scheduling

#### 5.3. Comparison with the Centralized Optimization

#### 5.4. Comparison of Operation Cost between the Isolated Mode and Interconnected Mode

#### 5.5. Operation Cost Analysis for the Different Configured Capacities of BESS

#### 5.6. Analysis for the Impact of Forecasting Errors

#### 5.7. Efficiency Analysis of the Privacy-Preserving Protocol

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 10.**Errors between the operation cost of centralized optimization and distributed optimization.

DER | Rated Capacity (kW) | DER | Rated Capacity (kW) |
---|---|---|---|

MG1.WT1 | 500 | MG3.PV3 | 800 |

MG1.PV1 | 500 | MG1.DG1 | 500 |

MG2.PV2 | 800 | MG2.DG2 | 800 |

MG3.WT3 | 500 | MG3.DG3 | 1000 |

BESS | Rated Power (kW) | Rated Energy (kWh) | I (CYN) |
---|---|---|---|

MG1.BESS1 | 250 | 800 | 800,000 |

MG2.BESS2 | 350 | 1000 | 1,000,000 |

MG3.BESS3 | 400 | 1200 | 1,200,000 |

MGs | Centralized Optimization (CNY) | Distributed Optimization (CNY) |
---|---|---|

MG1 | 3211.63 | 3213.14 |

MG2 | 6754.12 | 6747.35 |

MG3 | 5515.76 | 5520.88 |

Total | 15,481.52 | 15,481.37 |

**Table 4.**Cost and discarded renewable energy resources (RES) energy in isolated and interconnected operation.

MGs | Cost of Isolated Operation (CNY) | Discarded RES Energy of Isolated Operation (kWh) | Cost of Interconnected Operation (CNY) | Discarded RES Energy of Interconnected Operation (kWh) |
---|---|---|---|---|

MG1 | 190.21 | 1128.13 | 2815.83 | 0 |

MG2 | 18,616.30 | 0 | 5856.92 | 0 |

MG3 | 4622.87 | 846.46 | 5307.43 | 0 |

Total | 23,429.38 | 1974.59 | 15,481.37 | 0 |

MGs | Distributed Scheduling (CNY) | Considering Forecasting Error (CNY) | Cost Errors (%) |
---|---|---|---|

MG1 | 3213.14 | 3040.24 | −5.38 |

MG2 | 6747.35 | 6758.25 | +0.16 |

MG3 | 5520.88 | 5396.10 | −2.2 |

Total | 15,481.37 | 15,194.60 | −1.85 |

Scheduling (s) | Encryption (s) | Transmission (s) | Decryption (s) | |
---|---|---|---|---|

Average | 0.0269 | 0.0042 | 1.887 | 0.0039 |

Minimize | 0.0146 | 0.0032 | 1.33 | 0.0036 |

Maximize | 0.0617 | 0.0098 | 3.15 | 0.0052 |

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**MDPI and ACS Style**

Liu, N.; Wang, C.; Cheng, M.; Wang, J.
A Privacy-Preserving Distributed Optimal Scheduling for Interconnected Microgrids. *Energies* **2016**, *9*, 1031.
https://doi.org/10.3390/en9121031

**AMA Style**

Liu N, Wang C, Cheng M, Wang J.
A Privacy-Preserving Distributed Optimal Scheduling for Interconnected Microgrids. *Energies*. 2016; 9(12):1031.
https://doi.org/10.3390/en9121031

**Chicago/Turabian Style**

Liu, Nian, Cheng Wang, Minyang Cheng, and Jie Wang.
2016. "A Privacy-Preserving Distributed Optimal Scheduling for Interconnected Microgrids" *Energies* 9, no. 12: 1031.
https://doi.org/10.3390/en9121031