Large-Signal Models of the Park Transformation and Phase-Locked Loop Algorithms

Authors

  • Edhuardo Francisco Celli Grabovski Power Electronics Institute - Federal University of Santa Catarina, Florianópolis – Santa Catarina, Brazil https://orcid.org/0000-0002-5403-9336
  • Samir Ahmad Mussa Power Electronics Institute - Federal University of Santa Catarina, Florianópolis – Santa Catarina, Brazil https://orcid.org/0000-0003-1102-422X
  • Marcelo Lobo Heldwein Technical University of Munich, Chair of High-Power Converter Systems – Munich, Germany https://orcid.org/0000-0001-8869-7137

DOI:

https://doi.org/10.18618/REP.2005.1.045052

Keywords:

ac power electronic systems, control oriented models, dynamic phasor modeling, harmonic state-space modeling, large-signal modeling, time-periodic systems

Abstract

The control of modern grid-connected converters often relies on Park Transform and synchronization algorithms. These are highly nonlinear subsystems integrated into even larger systems that include other nonlinearities. Thus, strictly speaking, large-signal models are required when analysing and designing such systems. However, a limited number of mathematical tools is available to that end. This work proposes a nonlinear time-invariant model for the Park Transformation and the Synchronous Reference Frame Phase-Locked Loop (SRF-PLL), which are based on the Harmonic State-Space (HSS) in a stationary coordinate frame. The HSS modeling technique is reviewed as a basis for nonlinear models of functions based on polynomial nonlinear systems. This serves as an appropriate formal basis for the model of 2-D rotations as means of modeling the SRF-PLL and other similar algorithms. The models are validated through simulations to verify their accuracy when compared to the original Nonlinear Time-Periodic (NLTP) Systems.

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Published

2024-07-08

How to Cite

[1]
E. F. C. Grabovski, S. A. Mussa, and M. L. Heldwein, “Large-Signal Models of the Park Transformation and Phase-Locked Loop Algorithms”, Eletrônica de Potência, vol. 29, p. e202417, Jul. 2024.

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Original Papers