Superposition theorem for flexible grids

TL;DR

This paper extends the superposition theorem to flexible power grid topologies, enabling faster and more interpretable analysis of topological changes such as line reconnections and bus splitting, with significant computational speed-ups.

Contribution

The authors develop a unified superposition framework for varying grid topologies using distribution factors, applicable to all topological changes, and demonstrate its effectiveness in speed and interpretability.

Findings

Achieves over tenfold speed-up in power flow calculations

Validates the approach with numerical experiments on real-sized grids

Enhances remedial action search and security analysis post-topology change

Abstract

Flexible grid topology has become a key enabler of flexibility in modern power grids, particularly for congestion management. Studying the effects of combinatorial topological changes is therefore of significant interest, though it remains computationally intensive in most cases. To address this, we revisit the superposition theorem, which has served as the foundation for the decomposition of numerous power system problems over the past decades, particularly those involving changes in generation and loads. However, its application has traditionally been restricted to fixed grid topologies, breaking down as soon as a topology change occurs. In this paper, we extend the superposition theorem to accommodate varying grid topologies by leveraging well-known distribution factors. This unified framework applies to all types of topological changes, including line disconnection and reconnection, as well as bus splitting and merging. We provide numerical experiments to validate our approach and highlight its advantages in terms of speed-up and interpretability. Finally, we demonstrate its application in two key use cases: remedial action search and updated security analysis following a topological change. Our results show that the proposed approach achieves more than an order-of-magnitude speed-up for real-sized grids compared to the fastest power flow solvers.