  This paper proposes a Voltage Stability Index (VSI) suitable for unbalanced
polyphase power systems. To this end, the grid is represented by a polyphase
multiport network model (i.e., compound hybrid parameters), and the aggregate
behavior of the devices in each node by Th\'evenin Equivalents (TEs) and
Polynomial Models (PMs), respectively. The proposed VSI is a generalization of
the known L-index, which is achieved through the use of compound electrical
parameters, and the incorporation of TEs and PMs into its formal definition.
Notably, the proposed VSI can handle unbalanced polyphase power systems,
explicitly accounts for voltage-dependent behavior (represented by PMs), and is
computationally inexpensive. These features are valuable for the operation of
both transmission and distribution systems. Specifically, the ability to handle
the unbalanced polyphase case is of particular value for distribution systems.
In this context, it is proven that the compound hybrid parameters required for
the calculation of the VSI do exist under practical conditions (i.e., for lossy
grids). The proposed VSI is validated against state-of-the-art methods for
voltage stability assessment using a benchmark system which is based on the
IEEE 34-node feeder.
