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Journal articles on the topic 'Synchronous Reference Frame'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Chapman, P. L., and S. D. Sudhoff. "A multiple reference frame synchronous estimator/regulator." IEEE Transactions on Energy Conversion 15, no. 2 (2000): 197–202. http://dx.doi.org/10.1109/60.867000.

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2

Golestan, Saeed, Josep M. Guerrero, Abdullah M. Abusorrah, and Yusuf Al-Turki. "Hybrid Synchronous/Stationary Reference-Frame-Filtering-Based PLL." IEEE Transactions on Industrial Electronics 62, no. 8 (2015): 5018–22. http://dx.doi.org/10.1109/tie.2015.2393835.

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3

Khatsymovsky, V. M. "On the Kerr metric in a synchronous reference frame." International Journal of Modern Physics D 30, no. 10 (2021): 2150071. http://dx.doi.org/10.1142/s0218271821500711.

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The Kerr metric is considered in a synchronous frame of reference obtained by using proper time and initial conditions for particles that freely move along a certain set of trajectories as coordinates. Modifying these coordinates in a certain way (keeping their interpretation as initial values at large distances), we still have a synchronous frame and the direct analogue of the Lemaitre metric, the singularities of which are exhausted by the physical Kerr singularity (the singularity ring).

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4

Pan, Rongcai, and Peide Sun. "Multifunctional inverter based on virtual synchronous machine implemented in synchronous reference frame." Electrical Engineering 103, no. 4 (2021): 2093–111. http://dx.doi.org/10.1007/s00202-021-01220-w.

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5

Popovici, Alexandru-Tudor, and Alexandru Onea. "Generalized Differential Mathematical Model in Stator Reference Frame for PMSM and VRSM Simulation." Bulletin of the Polytechnic Institute of Iași. Electrical Engineering, Power Engineering, Electronics Section 67, no. 4 (2021): 43–55. http://dx.doi.org/10.2478/bipie-2021-0021.

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Abstract The paper presents the deduction of a novel decoupled form (considering the differential current quantities) of the differential mathematical model in stator reference frame, useful for numeric simulation of control approaches for PMSM (permanent magnet synchronous machines) generalized for both IPMSM and SPMSM (salient and non-salient PMSM). The model is confirmed to be equivalent to the well-known model defined in the rotor synchronous reference frame using a Matlab-Simulink implementation that is verified and validated by simulation during which the power/energy conservation is mon

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6

Subash Kumar, C. S., and V. Gopalakrishnan. "Modified Synchronous Reference Frame Based Harmonic Extraction for Shunt Active Filter." International Journal of Power Electronics and Drive Systems (IJPEDS) 6, no. 4 (2015): 897. http://dx.doi.org/10.11591/ijpeds.v6.i4.pp897-905.

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<p>This paper presents the modified synchronous reference frame based Shunt Active Filter (SAF) for the instantaneous compensation of harmonic current present at the Point of Common Coupling. The harmonics generated by the non linear load are extracted using the positive frame and negative frame of the input signal using the modified synchronous reference frame theory with extended Multiple Reference Frame based PLL (EMRFPLL). Based on the harmonics extracted, pulse width modulation signals are generated using Artificial Neural Network based Space Vector Pulse width Modulation technique

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7

Svishch, V. M. "The Features of the Reference Frame Concomitant to the Cosmic Microwave Background." European Journal of Applied Physics 3, no. 6 (2021): 1–6. http://dx.doi.org/10.24018/ejphysics.2021.3.6.115.

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The features of reference frame, concomitant to the cosmic microwave background, immobile relatively cosmic microwave background, are considered. It is shown that the features of reference frame, concomitant to the cosmic microwave background (CMB), are determined by its properties. Any other object in the Universe and reference frame concomitant to it, is immersed in the CMB and moves relative to the reference frame concomitant to microwave background radiation. The zero pecular velocity of the reference frame concomitant to the microwave background radiation is analogous to the zero temperat

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8

Li, Dan, and Ting Ting Cai. "Control Strategy for VSC-HVDC under Unbalanced Grid Voltages." Applied Mechanics and Materials 863 (February 2017): 214–19. http://dx.doi.org/10.4028/www.scientific.net/amm.863.214.

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This paper describes the use of an unbalanced control strategy to solve the faults occur in AC grid side of High voltage direct current based on Voltage Source Converter (VSC-HVDC) system. This method divides the voltage and current parameters into negative-sequence and positive-sequence. It can be obtained that the negative-sequence appears as double-frequency component in the positive-sequence synchronous reference frame; while, it appears as dc component in the negative-sequence synchronous reference frame. To mitigate the unfavourable impact of the unbalance fault, such as the DC link ripp

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9

Zsigmond, Andor-Attila, and András Kelemen. "Implementation of Grid Synchronization Methods on a Real Time Development System." Acta Universitatis Sapientiae, Electrical and Mechanical Engineering 13, no. 1 (2021): 52–67. http://dx.doi.org/10.2478/auseme-2021-0005.

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Abstract The paper presents a study regarding the implementation of two representative grid synchronization methods, intended to be used in the control structure of a three phase switch mode voltage rectifier. The methods considered are the Synchronous Reference Frame Phase Locked Loop (SRF PLL) and the Double Synchronous Frame Phase Locked Loop (DSRF PLL), respectively. These synchronization methods have been compared on a real time development system type dSpace 1104 from the point of view of their performance in case of an unbalanced mains voltage system. Finally, the influence of the chose

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10

CIANFRANI, FRANCESCO, and GIOVANNI MONTANI. "SYNCHRONOUS QUANTUM GRAVITY." International Journal of Modern Physics A 23, no. 08 (2008): 1149–56. http://dx.doi.org/10.1142/s0217751x08040007.

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The implications of restricting the covariance principle within a Gaussian gauge are developed both on a classical and a quantum level. Hence, we investigate the cosmological issues of the obtained Schrödinger Quantum Gravity with respect to the asymptotically early dynamics of a generic Universe. A dualism between time and the reference frame fixing is then inferred.

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11

Hirase, Yuko, Osamu Noro, Eiji Yoshimura, Hidehiko Nakagawa, Kenichi Sakimoto, and Yuji Shindo. "Virtual Synchronous Generator Control with Double Decoupled Synchronous Reference Frame for Single-Phase Inverter." IEEJ Journal of Industry Applications 4, no. 3 (2015): 143–51. http://dx.doi.org/10.1541/ieejjia.4.143.

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12

Karimi-Ghartemani, Masoud. "A Unifying Approach to Single-Phase Synchronous Reference Frame PLLs." IEEE Transactions on Power Electronics 28, no. 10 (2013): 4550–56. http://dx.doi.org/10.1109/tpel.2012.2235185.

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13

Suul, Jon Are, Kjell Ljokelsoy, Tarjei Midtsund, and Tore Undeland. "Synchronous Reference Frame Hysteresis Current Control for Grid Converter Applications." IEEE Transactions on Industry Applications 47, no. 5 (2011): 2183–94. http://dx.doi.org/10.1109/tia.2011.2161738.

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14

Rodriguez, Pedro, Josep Pou, Joan Bergas, J. Ignacio Candela, Rolando P. Burgos, and Dushan Boroyevich. "Decoupled Double Synchronous Reference Frame PLL for Power Converters Control." IEEE Transactions on Power Electronics 22, no. 2 (2007): 584–92. http://dx.doi.org/10.1109/tpel.2006.890000.

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15

Gong, Zhen, Xiaorong Xie, Chengxi Liu, Filipe Faria da Silva, and Yonghao Gui. "Power decoupling method for synchronous reference frame-based vector control." International Journal of Electrical Power & Energy Systems 164 (March 2025): 110429. https://doi.org/10.1016/j.ijepes.2024.110429.

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16

Syed, Mazheruddin H., Efren Guillo-Sansano, Steven M. Blair, Andreas Avras, and Graeme M. Burt. "Synchronous reference frame interface for geographically distributed real-time simulations." IET Generation, Transmission & Distribution 14, no. 23 (2020): 5428–38. http://dx.doi.org/10.1049/iet-gtd.2020.0441.

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17

İnci, Mustafa, Kamil Çağatay Bayındır, and Mehmet Tümay. "Improved Synchronous Reference Frame based controller method for multifunctional compensation." Electric Power Systems Research 141 (December 2016): 500–509. http://dx.doi.org/10.1016/j.epsr.2016.08.033.

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18

Che, Yanbo, Zhaojing Yin, Shuyan Yu, and Qiang Sun. "Random Harmonic Detection and Compensation Based on Synchronous Reference Frame." Journal of Electrical and Computer Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/7239267.

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Algorithms for harmonic detection and compensation are important guarantees for an active power filter (APF) to achieve the harmonic control function and directly determine the overall performance. Existing algorithms usually need a large amount of computation, and the compensation effect of specified order harmonic is also limited. DC side capacitor voltage at sudden change of load is affected by the algorithm as well. This paper proposes a new algorithm for harmonic detection and compensation based on synchronous reference frame (SRF), in which a band-pass filter with center frequency of 6kt

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19

Hazaea Al-Sabaeei, Mohammed Najib, and Ahmad Afif Bin Nazib. "Comparative Analysis of Control Strategies for 3-Phase Grid-Connected Inverters: Stationary vs. Synchronous Frame Approaches with LCL Filtering." Journal of Physics: Conference Series 2998, no. 1 (2025): 012005. https://doi.org/10.1088/1742-6596/2998/1/012005.

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Abstract This paper presents a comprehensive analysis and comparison of the performance of stationary frame and synchronous frame control strategies for a 3-phase grid-connected inverter equipped with an LCL filter. The performance of synchronous proportional-integral (PI) controllers is analysed and compared to that of stationary proportional-resonant (PR) controllers. Key metrics such as current tracking accuracy, harmonic distortion, and system robustness are evaluated. Simulation results demonstrate that the stationary frame control provides superior performance with lower THD. In contrast

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20

Osetrin, Konstantin, Evgeny Osetrin, and Elena Osetrina. "Deviation of Geodesics, Particle Trajectories and the Propagation of Radiation in Gravitational Waves in Shapovalov Type III Wave Spacetimes." Symmetry 15, no. 7 (2023): 1455. http://dx.doi.org/10.3390/sym15071455.

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A class of exact (non-perturbative) models of strong gravitational waves based on Shapovalov type III spacetimes and Einstein’s vacuum equations is obtained. Exact solutions are found for the trajectories of particles and radiation in a gravitational wave in privileged coordinate systems. Exact solutions are obtained for the equations of geodesic deviation and tidal acceleration of particles in a gravitational wave in privileged coordinate systems. An explicit analytical law of transition from a privileged coordinate system to a synchronous reference system associated with a freely falling obs

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21

Kampitsis, Georgios E., Anastasis P. Tsoumanis, Konstantinos C. Gallos, Stavros A. Papathanassiou, and Stefanos N. Manias. "Experimental Investigation of the Response of Different PLL Algorithms to Grid Disturbances." Materials Science Forum 856 (May 2016): 291–96. http://dx.doi.org/10.4028/www.scientific.net/msf.856.291.

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In this paper, the performance of three different phase locked loop (PLL) algorithms is experimentally evaluated in a grid connected photovoltaic inverter. Robust PLL is a key requirement for ensuring system compatibility with existing grid codes. The double second order generalized integrator (DSOGI) and the decoupled double synchronous reference frame (DDSRF) PLL are compared against the conventional synchronous reference frame (SRF) PLL under grid disturbances. All synchronization algorithms are initially simulated in Matlab and subsequently transformed in discrete time for implementation i

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22

Jamshidi, Ahmad, S. Masoud Barakati, and M. Moradi Ghahderijani. "Impact of Distributed Power Flow Controller to Improve Power Quality Based on Synchronous Reference Frame Method." International Journal of Engineering and Technology 4, no. 5 (2012): 581–85. http://dx.doi.org/10.7763/ijet.2012.v4.437.

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23

Costa, Israel D. L., Danilo I. Brandao, Lourenço Matakas Junior, Marcelo G. Simões, and Lenin M. F. Morais. "Analysis of Stationary- and Synchronous-Reference Frames for Three-Phase Three-Wire Grid-Connected Converter AC Current Regulators." Energies 14, no. 24 (2021): 8348. http://dx.doi.org/10.3390/en14248348.

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The current state of the art shows that unbalance and distortion on the voltage waveforms at the terminals of a grid-connected inverter disturb its output currents. This paper compares AC linear current regulators for three-phase three-wire voltage source converters with three different reference frames, namely: (1) natural (abc), (2) orthogonal stationary (αβ), and (3) orthogonal synchronous (dq). The quantitative comparison analysis is based on mathematical models of grid disturbances using the impedance-based analysis, the computational effort assessment, as well as the steady-state and tra

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24

Bangia, Sakshi, P. R. Sharma, and Maneesha Garg. "Reference Current Generation using Sliding Mode Control and Synchronous Reference Frame for Power Quality." i-manager's Journal on Electrical Engineering 6, no. 2 (2012): 29–35. http://dx.doi.org/10.26634/jee.6.2.2057.

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25

Jeong, Horyeong, Jong Hyuk Choi, and Jae Suk Lee. "A Current Control Algorithm to Improve Command Tracking Performance and Resilience of a Grid-Connected Inverter." Applied Sciences 10, no. 23 (2020): 8642. http://dx.doi.org/10.3390/app10238642.

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This paper presents a stationary reference frame grid current control algorithm for a grid-connected inverter (GCI) to improve command tracking performance and resilience in response to disturbances, i.e., a grid voltage incident in a GCI current control system. In the proposed algorithm, disturbance rejection is applied to reduce the overcurrent at the GCI in response to a grid fault. Disturbances to the GCI current control system are estimated using a grid current observer, and the estimate applied to the grid current controller to activate the disturbance rejection. The stationary reference

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26

Fabio E. Rojas R et al.,, Fabio E. Rojas R. et al ,. "Active Power Filter Using Adaptive Filters In The Synchronous Frame Reference." International Journal of Mechanical and Production Engineering Research and Development 10, no. 6 (2020): 13–24. http://dx.doi.org/10.24247/ijmperddec20203.

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27

Golestan, Saeed, Mohammad Monfared, and Francisco D. Freijedo. "Design-Oriented Study of Advanced Synchronous Reference Frame Phase-Locked Loops." IEEE Transactions on Power Electronics 28, no. 2 (2013): 765–78. http://dx.doi.org/10.1109/tpel.2012.2204276.

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28

Philip, Riya. "Synchronous Reference Frame Detection and Hysteresis Control for Active Power Filters." International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering 03, no. 09 (2014): 12173–78. http://dx.doi.org/10.15662/ijareeie.2014.0309053.

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29

Busada, Claudio A., Sebastian Gomez Jorge, and Jorge A. Solsona. "A Synchronous Reference Frame PI Current Controller With Dead Beat Response." IEEE Transactions on Power Electronics 35, no. 3 (2020): 3097–105. http://dx.doi.org/10.1109/tpel.2019.2925705.

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30

Bangarraju, J., V. Rajagopal, and A. Jayalaxmi. "Unit Template Synchronous Reference Frame Theory Based Control Algorithm for DSTATCOM." Journal of The Institution of Engineers (India): Series B 95, no. 2 (2014): 135–41. http://dx.doi.org/10.1007/s40031-014-0087-y.

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31

Subramanian, Chandrasekaran, and Ragavan Kanagaraj. "Rapid Tracking of Grid Variables Using Prefiltered Synchronous Reference Frame PLL." IEEE Transactions on Instrumentation and Measurement 64, no. 7 (2015): 1826–36. http://dx.doi.org/10.1109/tim.2014.2366275.

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32

Somkun, Sakda. "Unbalanced synchronous reference frame control of singe-phase stand-alone inverter." International Journal of Electrical Power & Energy Systems 107 (May 2019): 332–43. http://dx.doi.org/10.1016/j.ijepes.2018.12.011.

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33

D., Uma, and Vijayarekha K. "Modeling and Simulation of VSI Fed Induction Motor Drive in Matlab/Simulink." International Journal of Electrical and Computer Engineering (IJECE) 7, no. 2 (2017): 584–95. https://doi.org/10.11591/ijece.v7i2.pp584-595.

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The theory of reference frames and switching functions are effective in analyzing the performance of the induction motor fed from VSI (Voltage Source Inverter). In this work, mathematical model of Adjustable Speed Drive (ASD) is developed by taking synchronous reference frame equations for induction motor, switching function concept for VSI and non-switching concept for diode bridge rectifier. Simulation model of induction machine is implemented using dq0 axis transformations of the stator and rotor variables in the arbitrary reference frame. The corresponding equations are given in the beginn

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34

Rinkevičienė, Roma, Benas Kundrotas, and Sonata Tolvaišienė. "Model of Six-Phase Induction Motor." Solid State Phenomena 220-221 (January 2015): 510–14. http://dx.doi.org/10.4028/www.scientific.net/ssp.220-221.510.

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35

Grib, Andrey A., and Yuri V. Pavlov. "Some properties of energies in nonsynchronous reference frames in cosmology." Journal of Physics: Conference Series 2081, no. 1 (2021): 012004. http://dx.doi.org/10.1088/1742-6596/2081/1/012004.

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Abstract It is shown that use of non synchronous reference frame in cosmology can lead to unusual behavior of the energy of particles: it can have not only positive but also negative and zero energies. A special example of the model with the scale factor a(t) ∼ t is considered.

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36

Ilioudis, Vasilios C. "A Study of MTPA Applied to Sensorless Control of the Synchronous Reluctance Machine (SynRM)." Automation 6, no. 1 (2025): 11. https://doi.org/10.3390/automation6010011.

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The present paper proposes a new Maximum Torque Per Ampere (MTPA) algorithm applied to sensorless speed control for the Synchronous Reluctance Machine (SynRM). The SynRM mathematical model is suitably modified and expressed in the γδ estimated reference frame, which could be applied in sensorless implementations. In the controller–observer scheme, an MTPA controller is coupled with a sliding mode observer (SMO) of first order. The provided equivalent control inputs are directly utilized by a modified EMF observer to estimate the rotor speed and position. Also, the MTPA control, SMO, and modifi

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37

Al-Othman, A. K., M. E. AlSharidah, Nabil A. Ahmed, and Bader N. Alajmi. "Model Predictive Control for Shunt Active Power Filter in Synchronous Reference Frame." Journal of Electrical Engineering and Technology 11, no. 2 (2016): 405–15. http://dx.doi.org/10.5370/jeet.2016.11.2.405.

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38

Hans, Florian, Walter Schumacher, and Lennart Harnefors. "Small-Signal Modeling of Three-Phase Synchronous Reference Frame Phase-Locked Loops." IEEE Transactions on Power Electronics 33, no. 7 (2018): 5556–60. http://dx.doi.org/10.1109/tpel.2017.2783189.

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39

Ramezani, Malek, Shuhui Li, and Saeed Golestan. "Analysis and controller design for stand‐alone VSIs in synchronous reference frame." IET Power Electronics 10, no. 9 (2017): 1003–12. http://dx.doi.org/10.1049/iet-pel.2016.0883.

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40

Golestan, Saeed, and Josep M. Guerrero. "Conventional Synchronous Reference Frame Phase-Locked Loop is an Adaptive Complex Filter." IEEE Transactions on Industrial Electronics 62, no. 3 (2015): 1679–82. http://dx.doi.org/10.1109/tie.2014.2341594.

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41

Jiang, Baohong, and Xinian Li. "A Novel Fast Voltage Sequence Component Detector of Unbalanced Three-Phase System." MATEC Web of Conferences 173 (2018): 01036. http://dx.doi.org/10.1051/matecconf/201817301036.

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The fast and accurate voltage sequence component detection of unbalanced three-phase system is of major importance for the industrial continuous processing. The traditional method is to calculate the voltage in dq synchronous reference frame. This results in low order harmonics and long detection time. A novel fast voltage sequence components detector is proposed in this paper. It is to calculate the sequence component projection on dq rotating reference frame with h times the fundamental angular velocity. Simulation results demonstrate the validity of the algorithm.

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42

Rinkeviciene, Roma, and Andrius Petrovas. "Model of Vector Controlled Induction Drive." Solid State Phenomena 147-149 (January 2009): 149–54. http://dx.doi.org/10.4028/www.scientific.net/ssp.147-149.149.

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The paper presents the model of vector controlled induction motor. Induction motor model is carried out in reference frame, fixed on stator. Elaborated model of the drive is suitable for investigation dynamics because output signals appear as real currents, flux linkages and other variables. Vector control law model is implemented for variables in synchronous reference frame; therefore controller operates with transformed variables. Structure of designed model reflects the real variable speed drive. Model of vector controlled induction drive comprise model of induction motor, feedback signals

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43

Moradian, Mohammadreza, Jafar Soltani, Mohamed Benbouzid, and Abbas Najjar-Khodabakhsh. "A Parameter Independent Stator Current Space-Vector Reference Frame-Based Sensorless IPMSM Drive Using Sliding Mode Control." Energies 14, no. 9 (2021): 2365. http://dx.doi.org/10.3390/en14092365.

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In this paper, a sliding mode control is presented for direct torque and stator flux control of interior permanent magnet synchronous motor in a rotor speed sensorless drive system. The control scheme is developed in a specific synchronous rotating reference frame (X-Y) in which the stator current space vector coincides with the direct (X) axis. For this control technique no need to have any knowledge of machine parameters such as stator two-axis inductances, rotor permanent magnets flux linkage, and even the rotor initial position. However, the on-line actual stator resistance value is requir

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44

Yong, Yang. "Direct Instantaneous Power Control of Three-level Grid-connected." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 3 (2016): 1260. http://dx.doi.org/10.11591/ijece.v6i3.8193.

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Power electronic grid-connected inverters are widely applied as grid interface in renewable energy sources. This paper presents direct instantaneous power control of a three-phase three-level Neutral Point Clamped (NPC) grid-connected inverter in photovoltaic generation systems. The system consists of a PV array, DC/DC converter, three-level NPC LC filter and the grid. In order to achieve maximum power point tracking (MPPT), an adaptive perturb and observe MPPT is used. For balancing the neutral point (NP) voltage, the control scheme through proportional integral (PI) control according to the

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45

Yong, Yang. "Direct Instantaneous Power Control of Three-level Grid-connected." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 3 (2016): 1260. http://dx.doi.org/10.11591/ijece.v6i3.pp1260-1273.

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Power electronic grid-connected inverters are widely applied as grid interface in renewable energy sources. This paper presents direct instantaneous power control of a three-phase three-level Neutral Point Clamped (NPC) grid-connected inverter in photovoltaic generation systems. The system consists of a PV array, DC/DC converter, three-level NPC LC filter and the grid. In order to achieve maximum power point tracking (MPPT), an adaptive perturb and observe MPPT is used. For balancing the neutral point (NP) voltage, the control scheme through proportional integral (PI) control according to the

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46

Campo-Ossa, Daniel D., Enrique A. Sanabria-Torres, Jesus D. Vasquez-Plaza, Omar F. Rodriguez-Martinez, Oscar D. Garzon-Rivera, and Fabio Andrade. "Novel Rotated Virtual Synchronous Generator Control for Power-Sharing in Microgrids with Complex Line Impedance." Electronics 12, no. 10 (2023): 2156. http://dx.doi.org/10.3390/electronics12102156.

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Virtual synchronous generator (VSG) control is based on the fact that the line impedance in a microgrid is highly inductive. This assumption was made due to the emulation of the stator winding of an electrical machine. This concept can affect the controllability of a microgrid with complex line impedance, generating deviations in the chosen operation point. To overcome this issue, additional techniques must be implemented. This paper describes a novel mathematical approach that uses the power line characteristics in a microgrid to rotate the power control reference frame and proposes a new con

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47

Olarinoye, G. A., M. F. Akored, and S. N. Okhuegbe. "Analysis and Performance Evaluation of Three-Phase Induction Motor Model with Zero Quadrature Axis Flux Component." Nigerian Journal of Technological Development 18, no. 4 (2022): 344–51. http://dx.doi.org/10.4314/njtd.v18i4.9.

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Modeling of three phase induction motor has been extensively discussed in literature. Several models have been developed and applied by different authors to solve different problems. This paper presents a differentmodel of the symmetrical three phase induction motor in which there is an alignment of the direct axis component of the rotor flux vector to direct axis of the reference frame. The alignment reduces the quadrature axis flux component to zero, removes the dependencies associated with the d-q components of the stator current and simplifies the rotor dynamics. The model is not commonly

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48

Mirzakhani, Ali, Reza Ghandehari, and S. Alireza Davari. "Modeling and dynamic response of double-feed induction generator and back-to-back converters in unbalanced grid voltage conditions." Wind Engineering 44, no. 4 (2019): 361–72. http://dx.doi.org/10.1177/0309524x19849857.

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Double-feed induction generators are one of the most commonly used generators in wind power plants. Therefore, studying this type of generators in different grid conditions such as unbalanced grid voltage is of great importance. In this article, double-feed induction generators, in synchronous reference frame, and back-to-back converters are reviewed and modeled. The advantage of this model, compared with previous ones, is that it can be used in unbalanced grid voltage conditions. Hence, different parts of the generator in synchronous positive reference frame are studied and governing equation

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49

Uma, D., and K. Vijayarekha. "Modeling and Simulation of VSI Fed Induction Motor Drive in Matlab/Simulink." International Journal of Electrical and Computer Engineering (IJECE) 7, no. 2 (2017): 584. http://dx.doi.org/10.11591/ijece.v7i2.pp584-595.

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The theory of reference frames and switching functions are effective in analyzing the performance of the induction motor fed from VSI (Voltage Source Inverter). In this work, mathematical model of Adjustable Speed Drive (ASD) is developed by taking synchronous reference frame equations for induction motor, switching function concept for VSI and non-switching concept for diode bridge rectifier. The developed model is implemented using MATLAB/Simulink as it is an important tool for the validation of the proposed model. The performance of induction motor is analysed for different frequencies. The

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Li, Xiaoning, Yuan Wu, Shijun Shen, and Xianfeng Zhao. "The Inverse System Decoupling Control of the Permanent Magnet Synchronous Motor in D-q Synchronous Rotating Reference Frame." Procedia Engineering 24 (2011): 78–82. http://dx.doi.org/10.1016/j.proeng.2011.11.2605.

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