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arXiv · 2608.04740

Analytical Prediction of Voltage Collapse in Current-Limited Grid-Forming Inverters

Wenhao Lin·Robin Preece·Panagiotis N. Papadopoulos
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Abstract

The limited overcurrent capability of grid-forming (GFM) inverters makes current limiting essential during large disturbances. Activation of a circular current limiter (CCL) does not always cause the operating equilibrium to disappear. This paper develops an analytical framework to predict the grid-voltage boundaries at which the CCL is activated, determine whether the operating equilibrium persists as a saturated stable equilibrium point (satSEP), and identify the voltage at which it is lost. The CCL-based GFM inverter with frozen anti-windup is formulated as a piecewise-smooth system comprising normal-control and current-limited modes, so limiter activation is interpreted as a boundary-equilibrium bifurcation (BEB). A continuation formulation that switches to a reduced current-limited model when the CCL is activated is introduced to avoid the rank deficiency caused by frozen integrator states. An equivalent circuit that includes the filter capacitor yields closed-form expressions for the lower and upper boundary voltages at which the CCL is activated. A positive lower-boundary slope predicts that a satSEP persists in the current-limited mode and is lost at a later saddle-node, whereas a nonpositive slope predicts a non-smooth fold and equilibrium loss at the BEB. The upper-boundary slope is always negative under the assumed parameter conditions. Power-angle analysis, dynamic-model continuation in single-inverter and modified 9-bus systems, and time-domain simulations validate these predictions, showing that CCL activation can either cause immediate equilibrium loss through a non-smooth fold or allow a satSEP to persist until it is lost at a later saddle-node.

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Wenhao Lin, Robin Preece, Panagiotis N. Papadopoulos. 2026-08-05. Analytical Prediction of Voltage Collapse in Current-Limited Grid-Forming Inverters. https://arxiv.org/abs/2608.04740

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