Exploration of Superposition Theorem in Spectrum Space for Composite Event Analysis in an ADN

This study presents a formulation of the Superposition Theorem (ST) in the spectrum space, tailored for the analysis of composite events in an active distribution network (ADN). Our formulated ST enables a quantitative analysis on a composite event, uncovering the property of additivity among independent atom events in the spectrum space. This contribution is a significant addition to the existing literature and has profound implications in various application scenarios. To accomplish this, we leverage random matrix theory (RMT), specifically the asymptotic empirical spectral distribution, Stieltjes transform, and R transform. These mathematical tools establish a nonlinear, model-free, and unsupervised addition operation in the spectrum space. Comprehensive details, including a related roadmap, theorems, deductions, and proofs, are provided in this work. Case studies, utilizing field data, validate our newly derived ST formulation by demonstrating a remarkable performance. Our ST formulation is model-free, non-linear, non-supervised, theory-guided, and uncertainty-insensitive, making it a valuable asset in the realm of composite event analysis in ADN.