Topology-Adaptive Piecewise Linearization for Three-Phase Power Flow Calculations in Distribution Grids

The rapidly growing number of distributed energy resources is increasing uncertainty and variability in distribution system operations. At the same time, better access to measurement data is enabling new, data-driven methods for state estimation and analysis. Unfortunately, topology changes pose a significant challenge to existing methods, which are geared towards approximating the power flow (PF) equations in a continuous manner. To address this gap, this paper proposes a data-driven topology-adaptive piecewise PF linearization approach which inherently adapts to topology changes in the distribution system. The approach leverages measurements of a topology-identifying variable that helps cluster the data according to the system topology, without requiring explicit information about the topology status. Specifically, when we fit a three-phase piecewise linear PF model using a K-plane regression algorithm while integrating the topology-identifying variables, we observe that each linear piece only incorporates samples from a single topology. Numerical tests demonstrate that the resulting piecewise linear PF model enables high-accuracy PF calculations, even under system topology changes.