Graph-Theoretic Models for Resilient Renewable Energy Networks: Applications in Smart Grid Planning, Optimization and Sustainability
Firash Zhed S. Ututalum *
Sulu State University, Capitol Site, Bangkal, Patikul 7401, Sulu, Philippines.
Rosalio G. Artes Jr.
Mindanao State University–Tawi-Tawi College of Technology and Oceanography, Sanga-Sanga, 7500 Bongao, Tawi-Tawi, Philippine.
*Author to whom correspondence should be addressed.
Abstract
Aims: This chapter develops a graph-theoretic framework for analysing resilient renewable energy networks, with emphasis on smart grid planning, distributedenergy integration, network optimization, and sustainability-oriented decision support.
Study Design: The chapter is written as a methodological review and conceptual modelling study. It synthesizes recent energy-network literature and translates selected ideas into graph models that can be used in planning and screening studies.
Methodology: Renewable energy systems are represented as weighted, directed, multilayer, and temporal graphs. Nodes denote buses, substations, distributed energy resources, storage units, loads, prosumers, and control devices, whereas edges represent physical lines, switching options, communication links, or energysharing relationships. Connectivity, centrality, algebraic connectivity, domination, spanning trees, community detection, shortest paths, and resilience indices are formulated as planning tools. Original illustrative graphs, tables, and a stepwise modelling workflow are provided to support implementation.
Results: The graph-theoretic perspective clarifies how renewable penetration modifies the structural and operational behaviour of modern grids. Centrality and vulnerability measures identify critical buses and corridors; spanning-tree and reconfiguration models support radial distribution operation; dominating-set models guide placement of sensors, controllers, storage, and renewable nodes; and
Keywords: Graph theory, renewable energy networks, smart grids, resilience, distributed energy resources, network optimization, sustainability, power system planning