Approximating Voltage Stability Boundary Under High Variability of Renewables Using Differential Geometry

TL;DR

This paper introduces a differential geometry-based method to efficiently approximate voltage stability boundaries in power systems with high renewable variability, enabling better stability analysis in complex, renewable-rich grids.

Contribution

It develops a novel geometric approach using Levi-Civita connections and geodesics to predict voltage collapse points, improving computational efficiency over traditional methods.

Findings

Accurately predicts voltage collapse points in high-dimensional systems

Reduces computational cost compared to numerical continuation methods

Provides new insights into voltage stability in renewable-rich power systems

Abstract

This paper proposes a novel method rooted in differential geometry to approximate the voltage stability boundary of power systems under high variability of renewable generation. We extract intrinsic geometric information of the power flow solution manifold at a given operating point. Specifically, coefficients of the Levi-Civita connection are constructed to approximate the geodesics of the manifold starting at an operating point along any interested directions that represent possible fluctuations in generation and load. Then, based on the geodesic approximation, we further predict the voltage collapse point by solving a few univariate quadratic equations. Conventional methods mostly rely on either expensive numerical continuation at specified directions or numerical optimization. Instead, the proposed approach constructs the Christoffel symbols of the second kind from the Riemannian metric tensors to characterize the complete local geometry which is then extended to the proximity of the stability boundary with efficient computations. As a result, this approach is suitable to handle high-dimensional variability in operating points due to the large-scale integration of renewable resources. Using various case studies, we demonstrate the advantages of the proposed method and provide additional insights and discussions on voltage stability in renewable-rich power systems.