Optimal Reconfiguration of Distributed Battery Networks Under Connectivity and Energy Constraints

Pranay KC, Amin Taghieh, Maria Angel Palacios, Mohammadali Rashidioun, Petras Swissler, SangWoo Park

Networked battery systems arise in industrial automation, distributed energy applications, and multi-agent systems, where terminals consume energy locally and recharge only when connected to a source. Resource constraints often limit the number of simultaneous connections, requiring networks to be dynamically reconfigured to maintain system functionality. Managing such networks in dynamic environments is challenging, particularly when low-energy terminals must be prioritized for timely replenishment. This paper presents a battery-aware topology optimization algorithm that extends the GeoSteiner framework with a tailored Mixed-Integer Linear Program (MILP) formulation for Full Steiner Tree (FST) aggregation. The formulation minimizes network length while prioritizing low-battery terminals through a weighted objective subject to a global budget constraint, enabling partial network formation under realistic resource limits. An overlap-correction term is introduced that prevents double-counting when selected trees share terminals. To capture the network reconfiguration cost between time steps, a graph-distance metric penalizes frequent topology changes, resulting in 72.2% reduction compared to a baseline without penalty. Simulations on a 20-terminal network demonstrate battery levels are effectively managed as the lowest battery level improved from 2.7% to 68.6% over 30 iterations while maintaining the topology stability and budget utilization (92%). The framework offers a principled approach to designing energy-aware, adaptive connectivity in power-limited multi-agent systems.