Duty Cycle-Rotor Angular Speed Reverse Acting Relationship Steady State Analysis Based on a PMSG d–q Transform Modeling

José Genaro González-Hernández and Rubén Salas-Cabrera
Additional contact information
José Genaro González-Hernández: Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Av. Primero de Mayo, Ciudad Madero 89440, Tamaulipas, Mexico
Rubén Salas-Cabrera: Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Av. Primero de Mayo, Ciudad Madero 89440, Tamaulipas, Mexico

Mathematics, 2022, vol. 10, issue 5, 1-17

Abstract: Multilevel converters have been broadly used in wind energy conversion systems (WECS) to set the generator angular speed to a certain value, which allows maximizing wind power extraction; nevertheless, power that is drawn out from WECS strongly depends on the power coefficient and the ability to operate at the optimal tip speed ratio that corresponds to the maximum power coefficient. This work presents a novel and formal steady-state analysis to demonstrate the reverse relationship between the duty cycle of a multilevel boost converter (MBC) and the angular speed of a permanent magnet synchronous generator (PMSG). The study was based on the d–q transformation using the rotor reference frame. It was carried out by employing a reduced order dynamic system that included an equivalent electrical load resistance as a representation for the subsystems that were cascade-connected at the terminals of the PMSG. The steady-state characteristic was obtained by using the definition of equilibrium point. The set of nonlinear equations that represents the steady state of this WECS was solved by using the Newton method; besides, an analysis that considers the equivalent load as a bifurcation parameter demonstrates that the number of equilibria never changes.

Keywords: bifurcation analysis; d–q transform modeling; dynamic systems control; permanent magnet synchronous generator; multilevel boost converter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/5/762/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/5/762/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:5:p:762-:d:760013

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().