Analytical Determination of the Harmonic Disturbance Rejection in a Synchronous Reference Frame Phase Locked Loop

• Published in: 2023 IEEE Energy Conversion Congress and Exposition (ECCE) pp. 957 - 964
• Main Authors: Stinson, Aaron, McGrath, Brendan, Wilkinson, Richardt, Teixeira, Carlos
• Format: Conference Proceeding
• Language: English
• Published: IEEE 29.10.2023
• Subjects: Distortion measurement; Harmonic analysis; Harmonic distortion; Inverters; Phase locked loops; Phase measurement; Transforms
• ISSN: 2329-3748
• DOI: 10.1109/ECCE53617.2023.10362357

Grid-tied inverters require a phase-locked-loop (PLL) to detect the grid frequency and phase for synchronization. Grid voltage harmonics can distort the PLL phase signal, which consequently disturb the reference waveforms used by the inverter current controller and modulator. Distortion characterization is particularly challenging for PLLs that use a frame of reference transformation (i.e., the Park transform) as this process is non-linear and leads to convolution integrals in the frequency domain. This paper proposes an analytic harmonic distortion characterization method that overcomes this difficulty. The approach assigns a distortion profile to the PLL phase signal, that propagates through the Park transform, generating an infinite harmonic series with Bessel function coefficients. The phase signal resulting from the PLL loop filter acting on this series is then matched to the assigned PLL phase distortion to determine amplitude and phase coefficients for each harmonic. The accuracy of this approach has been validated by matching PSIM simulation results against theoretical results computed in MATLAB, and experimental results obtained from a practical inverter control system.