Comparative analysis of classical, advanced, and geometric frequency estimation techniques for modern power systems

Accurate frequency estimation is essential for the stable operation of modern three-phase power systems, where large-scale integration of inverter-based renewable energy is reducing grid inertia and intensifying frequency dynamics. This thesis presents a comparative analysis of four frequency estimation methods: the Synchronous Reference Frame Phase-Locked Loop (SRF-PLL), the Dual Second-Order Generalised Integrator with Frequency-Locked Loop (DSOGI-FLL), the Three-Level Discrete Fourier Transform (3L-DFT), and a Geometric Frequency Estimator based on the Frenet–Serret differential geometry framework. The aim of the work is to quantify the improvement introduced in the frequency estimation by this new geometric interpretation of the power system based on geometric invariants. Each method was implemented in Python and evaluated against seven synthetic test scenarios and two real measurement datasets representing a transformer energization event and a short-circuit event. The results show that no single method performs best under all conditions. The DSOGI-FLL proves the most universally robust established method. The 3L-DFT achieves perfect harmonic rejection for stationary signals but reveals a persistent steady-state offset under real sub-nominal grid conditions. The Frenet–Serret Geometric Estimator achieves the best accuracy and a mathematically guaranteed zero settling time in four of seven synthetic scenarios, and uniquely detects individual fault sub-events in the real short-circuit dataset — capabilities unavailable in any tuned closed-loop or filter-based estimator. Its two known limitations, sensitivity to unbalance and harmonic distortion, are shown to have well-defined solutions. The Frenet Frame is identified as the most promising direction for further research in real-time power system frequency monitoring.