Monitoring and control of distribution systems in the presence of renewable energy sources is enabled by active management approaches that utilise real-time information from the network. Such approaches typically rely on knowledge of the distribution system topology and parameters, and use physics-based models that must adequately capture system behaviour; these models become more complex to build or maintain in large, unbalanced and partially observed systems with significant penetration of renewables. An under-explored alternative is to construct simpler, low-order empirical models from time-series measurements of system variables, i.e., system identification; first, however, it needs to be determined which measurements are useful. This paper lays the foundations for such an approach by proposing and investigating new metrics that aim to characterize the controllability and observability of the system with respect to the power–voltage relationship. We propose to use voltage electric distance and statistical tools based on voltage covariance and correlation indicators. We show how these metrics provide useful information about the spatio-temporal variations in system voltages following power injections, potentially enabling the identification of critical nodes for control and observation.