Hierarchical and Distributed Monitoring of Voltage Stability in Distribution Networks

We consider the problem of quantifying and assessing the steady-state voltage stability in radial distribution networks. Our approach to the voltage stability problem is based on a local, approximate, and yet highly accurate characterization of the determinant of the Jacobian of the power flow equations parameterized according to the branch-flow model. The proposed determinant approximation allows us to construct a voltage stability index that can be computed in a fully distributed or in a hierarchical fashion, resulting in a scalable approach to the assessment of steady-state voltage stability. Finally, we provide upper hounds for the approximation error and we numerically validate the quality and the robustness of the proposed approximation with the IEEE 123-bus test feeder.