Article by: Robert Boschetti & Loau Al-Bahrani

Introduction

With the increasing penetration of renewable energy sources into the power grid, optimal siting and sizing of generators such as solar PV and wind have become a major challenge for transmission system planners.

In the Australian National Electricity Market (NEM), planning for renewable integration requires not only technical feasibility and economic benefit analysis but also consideration of network constraints and topological robustness.

Graph theory has emerged as a powerful analytical framework for modelling complex power systems and determining optimal placements of distributed energy resources (DERs). This report explores the use of graph theory approaches for optimal renewable placement in the NEM, highlighting recent case studies and visual models to support the findings.

Graph Theory in Power Network Planning

Graph theory enables the abstraction of a power grid as a graph, where nodes represent buses (substations, loads, or generation points) and edges denote transmission lines or cables. Graph metrics-such as degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality-can be used to analyse the topological importance of various nodes. These metrics help in identifying critical nodes for placing new generation assets to ensure better connectivity, reduced transmission losses, improved system resilience, and enhanced controllability.

In the NEM, particularly in regions such as Victoria and New South Wales, where significant renewable expansion is underway, graph theory is integrated with traditional planning tools such as PSSE and PLEXOS to validate renewable investment and placement decisions under the Regulatory Investment Test for Transmission (RIT-T) and ISP frameworks.

Methodology

A typical graph-based renewable siting approach involves the following steps:

• Model the power grid as an undirected or directed graph.
• Calculate centrality measures to identify topologically important nodes.
• Introduce candidate renewable generators at selected nodes.
• Evaluate network performance with candidate sites using power flow simulations and resilience metrics.
• Select optimal placements based on multi-criteria analysis, including centrality, load proximity, and voltage stability.

Case Studies

Case Study 1 – Optimal Renewable Siting Using Graph Centrality

This case study models a simplified network consisting of six buses (N1–N6) and introduces two potential PV generators. Using Network X in Python, degree and betweenness centrality were computed to identify nodes N2 and N5 as high-centrality locations. These sites were selected for PV placement as they offer topological benefits such as high connectivity and strong bridging positions within the network.

Figure 1 illustrates the resulting network where PV1 is placed at N2 and PV2 at N5. This model demonstrates how centrality-driven siting can improve grid access and operational efficiency. In real NEM applications, this methodology aligns with AEMO’s approach in the Western Victoria Renewable Integration project, where high-centrality zones such as Bulgana and Horsham were selected for renewable development based on network topology and power transfer capabilities (AEMO, 2022).

Case Study 2 – Grid Resilience with PV, Battery, and Load Integration

In this second case study, a resilience-focused topology is modelled, incorporating substations, solar PV, battery storage, and load centers. The graph includes nodes for substations SubA, SubB, and SubC, load centers LoadX and LoadY, PV generators (PV1, PV2), and one battery energy storage system (BESS). Redundant connections between substations ensure grid flexibility, while distributed generation and storage enable localized resilience.

Figure 2 illustrates the layout where SubC hosts both PV2 and a BESS, enhancing its role as a resilient hub. This configuration supports fast recovery during faults and improved voltage support. In the NEM, similar architecture is applied in projects like the Onslow DER trial in Western Australia, which integrates PV and BESS with grid-forming capabilities to sustain supply in islanded or constrained conditions (Horizon Power, 2021).

Discussion

The case studies demonstrate how graph theory enables planners to identify optimal renewable locations based on network structure, independent of real-time load and generation profiles. This topological perspective complements traditional power flow-based methods by providing initial insights into network bottlenecks, redundancy, and control node identification. Especially in weak grids or fringe-of-grid areas within the NEM, this approach aids in maximising renewable hosting capacity and improving operational resilience.

The integration of BESS and distributed PV using graph-based resilience modelling also highlights the role of DERs in modern power networks. Projects incorporating grid-forming inverters and localised storage, such as the fringe-of-grid deployments in South Australia, directly benefit from such modelling approaches to support both market participation and system security.

Conclusion

Graph theory provides a valuable toolkit for supporting renewable energy planning and resilience analysis in the NEM. By leveraging network centrality and connectivity insights, planners can optimise the siting of new renewable generators, storage systems, and load centers in a way that enhances system performance and supports regulatory objectives. The case studies presented affirm the practicality of graph-based methods and their relevance to ongoing energy transition efforts in Australia.

References

AEMO. (2022). Integrated System Plan. Retrieved from: AEMO | Integrated System Plan (ISP).

HORIZON POWER (2021). Onslow DER Project. Retrieved from: https://arena.gov.au/projects/onslow-der-project/Onslow Distributed Energy Resources Management System (DERMS).

AEMO (no date). Regulatory investment tests for transmission. Retrieved from AEMO | Regulatory investment tests for transmission.