# A generative graph model for electrical infrastructure networks

## Abstract

We propose a generative graph model for electrical infrastructure networks that accounts for heterogeneity in both node and edge type. To inform the design of this model, we analyze the properties of power grid graphs derived from the U.S. Eastern Interconnection, Texas Interconnection, and Poland transmission system power grids. Across these datasets, we find subgraphs induced by nodes of the same voltage level exhibit shared structural properties atypical to small-world networks, including low local clustering, large diameter and large average distance. On the other hand, we find subgraphs induced by transformer edges linking nodes of different voltage types contain a more limited structure, consisting mainly of small, disjoint star graphs. The goal of our proposed model is to match both these inter and intra-network properties by proceeding in two phases: we first generate subgraphs for each voltage level and then generate transformer edges that connect these subgraphs. The first phase of the model adapts the Chung-Lu random graph model, taking desired vertex degrees and desired diameter as inputs, while the second phase of the model is based on a simpler random star graph generation process. We test the performance of our model by comparing its output across many runs tomore »

- Authors:

- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Oregon State Univ., Corvallis, OR (United States)

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1508032

- Report Number(s):
- PNNL-SA-130657

Journal ID: ISSN 2051-1310

- Grant/Contract Number:
- AC05-76RL01830

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Complex Networks

- Additional Journal Information:
- Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 2051-1310

- Publisher:
- Oxford University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; power grid graph model; Chung-Lu model; network-of-networks

### Citation Formats

```
Aksoy, Sinan G., Purvine, Emilie AH, Cotilla Sanchez, Eduardo, and Halappanavar, Mahantesh. A generative graph model for electrical infrastructure networks. United States: N. p., 2018.
Web. doi:10.1093/comnet/cny016.
```

```
Aksoy, Sinan G., Purvine, Emilie AH, Cotilla Sanchez, Eduardo, & Halappanavar, Mahantesh. A generative graph model for electrical infrastructure networks. United States. doi:10.1093/comnet/cny016.
```

```
Aksoy, Sinan G., Purvine, Emilie AH, Cotilla Sanchez, Eduardo, and Halappanavar, Mahantesh. Mon .
"A generative graph model for electrical infrastructure networks". United States. doi:10.1093/comnet/cny016. https://www.osti.gov/servlets/purl/1508032.
```

```
@article{osti_1508032,
```

title = {A generative graph model for electrical infrastructure networks},

author = {Aksoy, Sinan G. and Purvine, Emilie AH and Cotilla Sanchez, Eduardo and Halappanavar, Mahantesh},

abstractNote = {We propose a generative graph model for electrical infrastructure networks that accounts for heterogeneity in both node and edge type. To inform the design of this model, we analyze the properties of power grid graphs derived from the U.S. Eastern Interconnection, Texas Interconnection, and Poland transmission system power grids. Across these datasets, we find subgraphs induced by nodes of the same voltage level exhibit shared structural properties atypical to small-world networks, including low local clustering, large diameter and large average distance. On the other hand, we find subgraphs induced by transformer edges linking nodes of different voltage types contain a more limited structure, consisting mainly of small, disjoint star graphs. The goal of our proposed model is to match both these inter and intra-network properties by proceeding in two phases: we first generate subgraphs for each voltage level and then generate transformer edges that connect these subgraphs. The first phase of the model adapts the Chung-Lu random graph model, taking desired vertex degrees and desired diameter as inputs, while the second phase of the model is based on a simpler random star graph generation process. We test the performance of our model by comparing its output across many runs to the aforementioned real data. In nearly all categories tested, we find our model is more accurate in reproducing the unusual mixture of properties apparent in the data than the Chung-Lu model. We also include graph visualization comparisons, as well as a brief analysis of edge-deletion resiliency. Ultimately, our model may be used to generate synthetic graph data, test hypotheses and algorithms at different scales, and serve as a baseline model on top of which further electrical network properties, device models, and interdependencies to other networks, may be appended.},

doi = {10.1093/comnet/cny016},

journal = {Journal of Complex Networks},

number = 1,

volume = 7,

place = {United States},

year = {2018},

month = {8}

}

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