[Paper Review] A Network of Networks Approach to Interconnected Power Grids

Paul Schultz, Frank Hellmann+2 more|arXiv (Cornell University)|Dec 31, 2016

Complex Network Analysis Techniques26 references3 citations

TL;DR

This paper introduces two novel network models—static glue stick construction (GSC) and interconnected layer growth (ILG)—to simulate multi-layer power grids as networks of networks. The GSC model builds fixed topologies using predefined inter-layer connections, while the ILG model grows networks dynamically from heuristics. Both models replicate key topological features of real power grids, such as geometric degree distributions and exponential edge length scaling, with GSC showing stronger realism in scale separation between layers.

ABSTRACT

We present two different approaches to model power grids as interconnected networks of networks. Both models are derived from a model for spatially embedded mono-layer networks and are generalised to handle an arbitrary number of network layers. The two approaches are distinguished by their use case. The static glue stick construction model yields a multi-layer network from a predefined layer interconnection scheme, i.e. different layers are attached with transformer edges. It is especially suited to construct multi-layer power grids with a specified number of nodes in and transformers between layers. We contrast it with a genuine growth model which we label interconnected layer growth model.

Motivation & Objective

• To address the lack of systematic models for interconnected transmission and distribution power grids in multi-layer network frameworks.
• To develop a flexible, scalable approach for generating realistic multi-layer power grid topologies that reflect hierarchical, spatially embedded structures.
• To compare static (GSC) and dynamic (ILG) construction methods for modeling power grid evolution and inter-layer connectivity.
• To analyze network characteristics such as degree distribution, edge length, and clustering across both models to assess realism and scalability.

Proposed method

• The static glue stick construction (GSC) model assembles multi-layer networks by defining inter-layer connections via transformer edges, based on predefined node and link distributions across layers.
• The interconnected layer growth (ILG) model simulates network evolution through a stochastic growth process, where new nodes are added with spatial proximity and redundancy preferences.
• Both models incorporate spatial embedding by assigning 2D coordinates to nodes and using distance-dependent attachment rules.
• The GSC model uses fixed parameters for intra- and inter-layer connections, while the ILG model uses dynamic rules involving node density, edge redundancy, and splitting rates.
• Network characteristics are evaluated using ensemble analysis across 50 realizations, with metrics including degree distribution, edge length, and clustering.
• Efficient data structures like R+-trees are used to manage spatial distances without storing full distance matrices, enabling low memory usage.

Experimental results

Research questions

• RQ1 How do static and dynamic multi-layer network construction methods compare in replicating real-world power grid topologies?
• RQ2 To what extent do the GSC and ILG models reproduce key topological features such as degree distribution and edge length scaling?
• RQ3 How does the inclusion of spatial embedding and inter-layer connectivity affect network resilience and stability in multi-layer power grids?
• RQ4 What role does inter-layer connection structure play in determining the hierarchical organization of transmission and distribution networks?
• RQ5 Can the ILG model generate realistic power grid topologies without relying on empirical data from real grids?

Key findings

• The GSC model produces a two-sided exponential edge length distribution with slopes of approximately 0.9 (left) and -1.8 (right), closely matching real-world North American and Mexican power grids.
• The ILG model generates networks with geometric degree distributions per layer, showing higher-degree nodes predominantly in upper layers, with observable gaps due to node projection.
• Both models exhibit a positive correlation between node degree and spatial density, particularly in higher layers, reflecting real grid hierarchies.
• The GSC model demonstrates stronger inter-layer scale separation, with clearer distinction between high-voltage transmission and lower-voltage distribution networks.
• The ILG model achieves realistic network formation with low memory usage by using spatial data structures like R+-trees and avoiding full distance matrix storage.
• Ensemble analysis confirms that both models produce networks with realistic clustering and spatial embedding, supporting their use in studying grid stability and resilience.