Localized structure in secondary distribution system voltage sensitivity matrices

Secondary systems comprise the localized groups of nodes located downstream of low-voltage service transformers. Models of secondary electric power distribution systems are often unknown or unavailable, motivating the use of measurements to model them. This paper studies the structure of sensitivity matrices relating changes in nodal voltage magnitudes to changes in active and reactive power injections in distribution systems with multiple radial secondary systems. In such problem settings, we propose that voltage sensitivity matrices take on a block diagonal-or localized-structure. Each sensitivity submatrix represents a localized model of the secondary system, which allows each secondary to be modeled individually. This contrasts with feeders that only model the primary network, which admits dense voltage sensitivity matrices with rapidly decreasing singular values. We propose efficient algorithms that exploit the structure of secondary distribution networks for measurement-based modeling of distribution systems. Specifically, we show that this structure can provide speed and accuracy improvements in model-free hosting capacity and state estimation algorithms. Intuitive physical explanations and simulations using a test case with multiple secondary system topologies verify the proposed matrix structure.