Abstract
The increasing penetration of inverter-based resources (IBRs) is challenging conventionaldirectional protection schemes that were originally developed for synchronous generator
(SG)-dominated power systems. Converter current limiting, altered fault-current
characteristics, and the suppression of sequence-current components can reduce the dependability
of traditional phasor-based directional elements, particularly during highresistance
and unbalanced fault conditions. This dissertation investigates the application
of the real-time stationary wavelet transform (RT-SWT) as a fast and reliable directional
protection technique for hybrid SG-IBR transmission systems. The proposed framework
constructs phase-, positive-, negative-, and zero-sequence directional indicators through
a wavelet-domain torque-factor formulation computed directly from scaling-coefficient
energies, with the wavelet (detail) coefficients providing fast transient detection at fault
inception. For the sequence-domain elements, the directional contributions of phases A,
B, and C are aggregated into single total positive- and negative-sequence signals, reducing
phase-dependent variation and improving the stability of the directional response. By
operating directly in the wavelet domain, the method eliminates the need for full-cycle
phasor estimation, enabling faster directional decisions during transient conditions while
maintaining sensitivity in converter-dominated environments. The RT-SWT framework
is implemented using PSCAD/EMTDC simulations with MATLAB-based COMTRADE
post-processing and evaluated across 440 fault cases per system configuration, spanning
different fault types, fault locations, and fault resistances in both SG-dominated and
hybrid SG-IBR transmission systems, including targeted cases with negative-sequence
current injection disabled and with the inverter operating at 10%, 50%, and 100% of
rated output. The performance of the proposed approach is compared with conventional
discrete Fourier transform (DFT)-based directional elements. Results demonstrate that
the positive- and zero-sequence RT-SWT directional indicators provide the most reliable and consistent directional response across the investigated fault conditions. The
positive-sequence indicator additionally enables dependable discrimination of balanced
three-phase faults, for which negative-sequence information is unavailable, while the zerosequence
indicator produces distinctive signatures for ground faults and maintains dependable
directional performance. The negative-sequence indicator operates reliably for
unbalanced faults when sufficient negative-sequence current is available, but may lose
dependability under high-resistance faults or when inverter controls suppress negativesequence
current injection. The phase power-factor indicator generally provides correct
directional identification but exhibits reduced robustness in some high-resistance fault
scenarios. Compared with conventional DFT-based directional elements, the RT-SWT
approach produces smoother and more stable directional responses under transient and
converter-limited conditions. While the DFT-based method can reach the directional
threshold marginally earlier in some hybrid SG-IBR cases, these early crossings often
occur during the transient oscillatory period; the principal advantage of the RT-SWT
approach in converter-dominated systems is therefore improved directional dependability
rather than raw operating speed. These simulation-validated findings indicate that
RT-SWT-based directional protection is an effective directional protection technique for
hybrid SG-IBR transmission networks. The positive- and zero-sequence wavelet-domain
signatures provide reliable directional classification across the investigated fault conditions,
while the distinctive behavior of the phase power-factor signature suggests its
potential application for fault-type classification in future research.