A Generalized Index for Static Voltage Stability of Unbalanced Polyphase Power Systems including Th\'evenin Equivalents and Polynomial Models

TL;DR

This paper introduces a generalized Voltage Stability Index (VSI) for unbalanced polyphase power systems that incorporates Thévenin equivalents and polynomial models, enabling efficient and accurate stability assessment for complex distribution and transmission grids.

Contribution

It develops a novel VSI that extends the L-index to unbalanced systems using compound parameters, Thévenin equivalents, and polynomial models, suitable for practical, lossy grids.

Findings

VSI accurately predicts voltage stability margins.

The method is computationally efficient for large systems.

Validation on IEEE 34-node feeder confirms effectiveness.

Abstract

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.