• BOUROUNECH CHARAF Department of Electrical Engineering, Mira A. University , Bejaia, Algeria Author
  • LEHOUCHE HOCINE Department of Electrical Engineering, Mira A. University , Bejaia, Algeria Author
  • MENDIL BOUBEKEUR Department of Electrical Engineering, Mira A. University , Bejaia, Algeria Author




Matrix Converter, Venturini method, Lyapunov’s functions


This paper presents the contribution of a matrix converter for frequency stabilization for an energy source. Venturini optimal amplitude method is used. The energy source frequency is assumed to be purely random. A new approach based on the concept of Lyapunov's functions is revealed. The study is done for an electrical network with a random variable frequency, following the normal distribution and a typical RL load. The approach is tested using simulations under MATLAB® /Simulink® environment. The criteria used in the analysis are signal form, frequency analysis, and THD. The performances obtained are discussed.


(1) L. Huber, D. Borojevic, Space vector modulated three-phase to three-phase matrix converter with input power factor correction, IEEE Transactions On Industry Applications, 31, 6, pp. 1234–1246, 1995.

(2) T.F. Podlesak, D.C. Katsis, P.W. Wheeler, J.C. Clare, L. Empringham, M. Bland, A 150-kVA vector-controlled matrix converter induction motor drive, IEEE Trans. Ind. Appl., 41, 3, pp. 841–847, 2005.

(3) A. Benyoussef, S. Barkat, direct torque control based on space vector modulation with balancing strategy of dual star induction motor, Rev. Roum. Sci. Techn.– Électrotechn. et Énerg., 67, 1, pp. 15–20, Bucarest, 2022.

(4) A. Dendouga, R Abdessemed, M.L Bendaas, Active and reactive powers control of a doubly-fed induction generator fed by matrix converter, E.P.E. Journal, 19, 1, pp. 50–56, 2009.

(5) L. Gyugyi, B.R. Pelly. Static power frequency changers. John Wiley & Sons, New York, NY, 1976.

(6) M. Venturini, A. Alesina, New sine wave in sine wave out, conversion technique which eliminates reactive elements, Proc Powercon, 7, 3, pp 242–252, 1980. E3_1-E3_15

(7) A. Alesina, M. Venturini. Analysis and design of optimum-amplitude nine switch direct ac-ac converters. IEEE Transaction. Power Electronics, 4,1, pp 101–112, 1989.

(8) D. Casadei, G. Serra, A. Tani, Reduction of the input current harmonic content in matrix converters under input/output unbalance, IEEE Transactions on Industrial Electronics, 45, 3, pp. 401-409, 1998.

(9) H. Karaca, R. Akkaya. A matrix converter controlled with the optimum amplitude-direct transfer function approach, 6th International Conference On Electrical Engineering ICEENG, Cairo Egypt, 2008.

(10) P.W. Wheeler, J. Rodriguez, J.C. Clare, L. Empringham, A. Weinstein, Matrix converters: a technology review, IEEE Trans. Ind. Electron, 49, 2, pp. 276–288, 2002.

(11) V. Veera, D. Pavel, J. Martin, B. Bedrich, New modification of a single-phase ac-ac matrix converter with auxiliary resonant circuits for ac locomotives, Rev. Roum. Sci. Techn.– Électrotechn. et Énerg, 61, 1, pp. 73–77, Bucarest, 2016.

(12) P. Patel, A. Mulla, Space vector modulated three-phase to three-phase direct matrix converter, IEEE. 16th International Conference on Environment and Electrical Engineering EEEIC, 7-10 June 2016.

(13) J.J. Rodriguez, E. Peralta, O. Carranza, R. Ortega, Optimal venturini modulation for a three-phase four-wire matrix converter, IEEE Latin America Transactions, 14, 2, pp. 617–623, 2016.

(14) A. Boukadoum, T.Bahi, D. Dib, Fuzzy logic control based matrix converter for improvement output current waveforms based wind turbine system, International Journal of Renewable Energy Research, 3, 3, pp. 586–591, 2013.

(15) H. Chaoui, B. Hamane, M. Doumbia, Adaptive control of Venturini modulation-based matrix converters using interval type-2 fuzzy sets, J. Control Autom. Electr. Syst., 27, pp. 132–143, 2016.

(16) H. Karaca, R. Akkaya, Modelling and simulation of matrix converter under distorted input voltage conditions, Simulation Modelling Practice and Theory, 19, 2, pp. 673–684, 2011.

(17) M. Galea, G. Buticchi, L. Empringham, L. de Lillo, C. Gerada, Design of a high force density tubular motor, IEEE Trans. on Industry Applications, 50, 4, pp. 2523–2532, 2014.

(18) K. Khalil, Nonlinear Systems, Prentice Hall, 2001.

(19) D. Liberzon, A. S. Morse, Basic problems in stability and design of switched systems, IEEE Control Systems Magazine, 19, 5, pp. 59–70, 1999.

(20) S. Pettersson, B. Lennartson, LMI for stability and robustness of hybrid systems, Proceedings of the 1997 American Control Conférence, Albuquerque NM USA, 6 June 1997.

(21) M.S. Braniky, Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control, 43, 4, pp. 475–482. 1998.

(22) R.A. Decarlo, M.S. Branicky, S. Pettersson, B. Lennartson, Perspectives and results on the stability and stabilizability of hybrid systems, Proceedings of the IEEE, 88, 7, pp. 1069–1082, 2000.

(23) V.F. Montagner, V.J.S. Leite, R.C.L.F. Olineira, P.L.D. Pers, State feedback control of switched linear systems an LMI approach, Journal of Computational and Applied Mathematics, 194, 2, pp. 192–206, 2006.

(24) A.V. Savkin, E. Skafidas, R.J. Evans, Robust output feedback stabilizability via controller switching, Automatica, 35, 1, pp. 69–74, 1999.

(25) G.S. Zhai, H. Lin, P.J. Antsaklis, Quadratic stabilizability of switched linear systems with polytopic uncertainties, Internat. J. Control, 76, 7, pp. 747–753, 2003.






Électrotechnique et électroénergétique | Electrical and Power Engineering

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