# End-to-End Deep Graph Convolutional Neural Network Approach for Intentional Islanding in Power Systems Considering Load-Generation Balance

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## Abstract

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## 1. Introduction

#### 1.1. Intentional Islanding

#### 1.2. Graph Neural Networks

- The proposed method is the first to incorporate an end-to-end deep learning solution for the intentional islanding problem. It incorporates four loss functions in total.
- The load-generation imbalance is minimised at each island using a deep learning loss formulation, enhancing the stability of the power system after the islanding process.
- A loss function is defined to determine the cluster for each bus in the system.
- A loss function is also defined to ensure the coherency of generators in the formed islands and avoid loss of power supply.
- An additional loss function is defined to balance the number of nodes in each partition.

## 2. Related Work

## 3. Deep Learning Based Method for Intentional Islanding

#### 3.1. Graph Partition

#### 3.1.1. GAP

#### 3.1.2. Min-Cut

#### 3.2. Islanding Using Deep Learning

#### 3.3. Coarse-Fine Adjustment

#### 3.4. Graph Representation of the Power System

## 4. Evaluation Experiments

#### 4.1. Model Implementation

#### 4.2. Simulation Results

#### 4.3. Ablation Study

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CNN | Convolutional neural network |

GAP | Generalisable Approximate Partitioning |

GNN | Graph neural network |

MILP | Mixed-integer linear programming |

ML | Machine learning |

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**Figure 2.**Model structure, showing the layers that comprise the proposed neural network for intentional islanding.

**Figure 3.**Example of a graph CNN’s function. For every node (coloured black in this instance), it takes the one-hop or two-hop neighbor as the receptive field. The blue nodes indicate the selected receptive field or neighbouring nodes, while the yellow ones are not selected for the black node. Graph CNNs use a filter to perform convolution on the selected nodes ${X}_{i}$, resulting in the new status ${Z}_{i}$, where the blue nodes are considered to calculate the black value in the right subfigure.

**Figure 4.**The test cases used in the simulation experiments. Starting from top left and moving horizontally, the images display the power system of cases: 9, 14, ieee 24, 30, ieee 30, 39, 57, 89, 118, 145 and 200.

**Figure 5.**Clustering visualisation of the results obtained by using the GAP loss function. Each color represents a specific cluster. The first row displays the results from case 14, followed by case 30 and case 118.

**Figure 6.**Clustering visualisation of the results obtained by using the min-cut loss function. Each color represents a specific cluster. The first row displays the results from case 14, followed by case 30 and case 118.

**Figure 7.**Min-cut clustering results without (

**top**) and with (

**bottom**) balance cut and bus injection loss functions.

Layer | Output Dimension |
---|---|

Graph CNN layer | 96 |

128 | |

256 | |

Linear layer | 256 |

128 | |

g |

Case | Imbalance (MW) | Lines Disconnected | ||
---|---|---|---|---|

GAP | Min-Cut | GAP | Min-Cut | |

9 | 4.95 | 4.95 | 2 | 2 |

30 | 2.44 | 2.44 | 9 | 9 |

ieee30 | 17.56 | 17.56 | 9 | 7 |

57 | 27.86 | 27.86 | 16 | 13 |

118 | 132.91 | 132.91 | 28 | 21 |

200 | 23.42 | 23.42 | 33 | 24 |

Method | Imbalance (MW) | Lines Disconnected | No. of Islands |
---|---|---|---|

Kyriacou et al. [10] | 240.03 | n/a | 4 |

Proposed (Min-cut) | 132.91 | 24 | 4 |

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## Share and Cite

**MDPI and ACS Style**

Sun, Z.; Spyridis, Y.; Lagkas, T.; Sesis, A.; Efstathopoulos, G.; Sarigiannidis, P.
End-to-End Deep Graph Convolutional Neural Network Approach for Intentional Islanding in Power Systems Considering Load-Generation Balance. *Sensors* **2021**, *21*, 1650.
https://doi.org/10.3390/s21051650

**AMA Style**

Sun Z, Spyridis Y, Lagkas T, Sesis A, Efstathopoulos G, Sarigiannidis P.
End-to-End Deep Graph Convolutional Neural Network Approach for Intentional Islanding in Power Systems Considering Load-Generation Balance. *Sensors*. 2021; 21(5):1650.
https://doi.org/10.3390/s21051650

**Chicago/Turabian Style**

Sun, Zhonglin, Yannis Spyridis, Thomas Lagkas, Achilleas Sesis, Georgios Efstathopoulos, and Panagiotis Sarigiannidis.
2021. "End-to-End Deep Graph Convolutional Neural Network Approach for Intentional Islanding in Power Systems Considering Load-Generation Balance" *Sensors* 21, no. 5: 1650.
https://doi.org/10.3390/s21051650