Superposition theorem for flexible grids

TL;DR

This work generalizes the classical Superposition Theorem to include topology changes in flexible grids, introducing the Extended Superposition Theorem (EST) that expresses power flows under a target topology as a weighted combination of flows under a reference topology and unitary topology changes. Coefficients are found by solving a small linear system of topology sensitivity factors (TSFs), enabling rapid computation of flows for diverse topological actions without re-solving full power-flow equations. The framework unifies line disconnections, line reconnections, node splitting, and node merging, and yields interpretable metrics (TSFs, LCDFs) that illuminate the interactions among concurrent actions. Experiments show more than an order-of-magnitude speed-up over fast power-flow solvers on real grids, with improved AC load-flow accuracy in many cases, and demonstrates practical use in Remedial Action search and Topological Action Security Analysis. The approach holds promise for tight integration with optimization workflows (e.g., OPF) and for accelerating topology-aware grid operations in large-scale networks.

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.

Figures (4)

• Figure 1: EST example on IEEE14, starting from a meshed topology (top left) to which 2 node splitting actions at substations 4 and 5 are applied (bottom right). Displayed EST coefficients are derived from initial and unitary action states.
• Figure 2: Top left, power Flows in the reference topology for the two lines to disconnect. Right and bottom left, the two lines disconnected in two equivalent models: the standard one with physical line disconnections on top, and the canceling flow model at the bottom. The lines remains virtually connected but with equivalent null flow: the virtual induced flow $vf_l$ gets canceled out by the reversed direction canceling flow $cf_l$.
• Figure 3: The box plots of accuracy error distributions to AC load flow for DC approximation (orange) and the EST method (blue) in the case of influenced actions.
• Figure 4: Comparing security analysis computation time in second (s) across grid sizes for EST and 2 reference DC power flow solvers LightSim2Grid lightsim2grid, PandaPower thurner2018pandapower. LODF is the most optimized computation specifically for DC.

Theorems & Definitions (3)

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