Frequency-adaptive PI–PR-Notch controlled phase locked loop for three-phase grid-connected inverters under nominal grid disturbances

Stable and uninterrupted operation of grid-integrated inverter-based resources (GI-IBRs) interfacing renewable energy systems (RESs) relies on accurate and reliable synchronisation with the utility grid. Variations in grid frequency and voltage magnitude can alter control-loop dynamics and degrade phase-locking performance. Conventional synchronous-reference-frame phase-locked loops (SRF-PLLs) employing fixed-gain proportional-integral (PI) controllers face a trade-off between fast synchronisation and effective suppression of nominal voltage harmonics and frequency disturbances. To address these limitations, this article proposes an improved PLL architecture incorporating adaptive PI-PR control interfaced with a frequency-adaptive notch filter (FANF). A bandwidth-tuning law derived from a small-signal design model adaptively adjusts the PI gains according to the estimated grid frequency, thereby maintaining approximately invariant closed-loop dynamics across the operating frequency range. Furthermore, a normalised quadrature-axis error, eq=vq/V^d, reduces the dependence of the PLL loop gain on grid-voltage magnitude. Frequency-adaptive notch filters tuned to 2ω^, 6ω^, and 12ω^ attenuate dominant harmonic-induced disturbances. Closed-loop stability across the operating range is assessed using frozen-time small-signal analysis. Comparative simulation and experimental results against state-of-the-art methods demonstrate that the proposed controller achieves faster synchronisation, lower phase-estimation error, and reduced frequency and phase oscillations.