A statistical distinguishability-based PMU placement method for fault location problem in distribution networks

This paper proposes a statistical distinguishability-driven framework for optimal placement of phasor measurement units (PMUs) in distribution networks to support machine learning (ML)-based fault location. For fault classification tasks, measurement separability is quantified using the Mahalanobis distance under Gaussian uncertainty, establishing a link to the Bayes error probability. For fault parameter regression, the framework is extended via the Fisher information matrix (FIM), where the Cramér–Rao lower bound (CRLB) characterizes the fundamental limit of estimator performance.,The PMU placement problem is formulated as a worst-case optimization of the minimum pairwise Mahalanobis distance and solved using a sequential strategy that improves the least distinguishable regions of the network. A stopping criterion based on the Bayes error bound ensures that no critically indistinguishable fault scenarios remain, providing an a priori measure of classification feasibility without model training.,After this criterion is satisfied, further PMU deployment shifts the objective from classification to parameter estimation, where additional sensors increase the Fisher information content and improve CRLB-based identifiability. This defines a two-stage placement strategy separating classification-oriented separability from regression-oriented information gain.,The approach is validated on a 20 kV distribution feeder using electromagnetic transient simulations. A Random Forest (RF) model is used as an empirical benchmark, showing strong agreement between information-theoretic metrics and observed ML performance for both classification and regression tasks.