Understanding the Geometry of Faulted Power Systems under High Penetration of Inverter-Based Resources via Ellipse Fitting and Geometric Algebra

摘要

Power systems with high penetration of inverter-based resources (IBR) present significant challenges for conventional protection schemes, with traditional distance protection methods failing to detect line-to-line faults during asymmetric conditions. This paper presents a methodology for electrical fault detection and classification using ellipse fitting and geometric algebra applied to voltage and current space curves. The approach characterizes electrical faults by fitting ellipses to voltage vector data, enabling fault detection with only a quarter-cycle. The method employs bivector components for line-to-ground fault classification, while ellipse parameters identify line-to-line and three-phase faults. The geometric representation preserves voltage or current curve shapes in three-dimensional space, overcoming Clarke transform limitations when zero-sequence components are present. Validation using simulations and laboratory experiments demonstrates accurate fault identification and magnitude estimation, providing enhanced power system protection capabilities.