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

Edhuardo Francisco Celli Grabovski; Samir Ahmad Mussa; Marcelo Lobo Heldwein

doi:10.18618/REP.2005.1.045052

Authors

Edhuardo Francisco Celli Grabovski Universidade Federal de Santa Catarina https://orcid.org/0000-0002-5403-9336
Samir Ahmad Mussa Universidade Federal de Santa Catarina https://orcid.org/0000-0003-1102-422X
Marcelo Lobo Heldwein Technical University of Munich 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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Author Biographies

Edhuardo Francisco Celli Grabovski, Universidade Federal de Santa Catarina

received the B.S. and M.S. degreesin electrical engineering from the Federal University of Santa Catarina(UFSC), Florianopolis, Brazil, in 2016 and 2018, respectively, currentlyworking towards the Ph.D. degree in electrical engineering from INEP–UFSC. He is currently a Senior Power Electronics Engineer, consultantfor Huawei Technologies Sweden, AB, Stockholm, Sweden. His researchinterests include power electronics, modeling, control and stability analysisof power converter systems and optimal design of power converters.

Samir Ahmad Mussa, Universidade Federal de Santa Catarina

received the B.S. degree from the Federal Universityof Santa Maria (UFSM) in 1988, and the M.S. and Ph.D. degrees fromthe Federal University of Santa Catarina (UFSC), in 1994 and 2003,respectively. He is currently a Full Professor at the Electrical and ElectronicsEngineering Department (EEL) of the Federal University of Santa Catarina(UFSC) and researcher at the Power Electronics Institute (INEP). Hisresearch interests include PFC rectifiers, Digital Signal Processing, DSP,FPGA and microprocessor-based systems. Dr. Mussa is a member of theBrazilian Power Electronic Society (SOBRAEP) and IEEE.

Marcelo Lobo Heldwein, Technical University of Munich

received the B.S. and M.S. degrees in electricalengineering from the Federal University of Santa Catarina (UFSC), Flo-rian ́opolis, Brazil, in 1997 and 1999, respectively, and the Ph.D. degreefrom the Swiss Federal Institute of Technology (ETH Z ̈urich), in 2007.From 1999 to 2003, he worked with industry, including research anddevelopment activities at the Power Electronics Institute, Brazil and EmersonNetwork Power, Brazil and Sweden. He was a Postdoctoral Fellow at theETH Z ̈urich and at the UFSC, from 2007 to 2009. From 2010 to 2022,he was a Professor with the Department of Electronics and ElectricalEngineering, UFSC. He is currently the Head of the Chair of High–PowerConverter Systems (HLU), at the Technical University of Munich (TUM).His research interests include power electronics, advanced power distributiontechnologies, and electromagnetic compatibility. He is a member of theBrazilian Power Electronic Society (SOBRAEP), a Senior member of theIEEE and a member of the Advisory Board of PCIM Europe.

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