Time-Domain Symmetrical Components for Detection and Analysis of Unbalanced Faults in Three-Phase Systems

Author

Ryan Pospichal, California Polytechnic State University, San Luis ObispoFollow

Available at: https://digitalcommons.calpoly.edu/theses/3202

Date of Award

12-2025

Degree Name

MS in Electrical Engineering

Department/Program

Electrical Engineering

College

College of Agriculture, Food, and Environmental Sciences

Advisor

Majid Poshtan

Advisor Department

Electrical Engineering

Advisor College

College of Engineering

Abstract

Unbalanced faults in three-phase power systems degrade performance, increase losses, and threaten equipment reliability. Traditional frequency-domain approaches using phasor analysis and symmetrical components offer valuable steady-state insights but respond too slowly for transient or rapidly changing conditions. This thesis investigates time-domain symmetrical components (ISCs) as a faster, physically interpretable method for detecting and analyzing unbalanced faults directly from instantaneous voltages and currents. Two ISC computation techniques were developed and compared: a polar-form method, applying one-third and two-thirds cycle time delays, and a rectangular-form method, which achieves equivalent phase shifts using only a quarter-cycle delay. Simulations in Microsoft Excel verified both methods, with the rectangular approach demonstrating superior accuracy and reduced latency. Experimental validation was performed using a mechanically coupled three-phase synchronous motor-generator system under controlled fault and imbalance scenarios. Results confirmed that time-domain decomposition reliably identifies fault types and sequence behavior consistent with theoretical expectations. These findings indicate that instantaneous symmetrical components can enable sub-cycle fault detection, supporting faster, more reliable protective relaying for modern, dynamically evolving power systems.