Harmonics Elimination in Multilevel Inverter Using Linear Fuzzy Regression

Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

Abstract:

Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1058669

References:

[1] A. Bardossy, "Note on fuzzy regression," Fuzzy Sets and Systems, vol. 37, pp. 65-75, 1990/8/15 1990.
[2] J. K. Kim and H.-R. Chen, "A Comparison of fuzzy and nonparametric linear regression," Computers Ops Res, vol. 24, pp. 505-519, 1997.
[3] G. Peters, "Fuzzy linear regression with fuzzy intervals," Fuzzy Sets and Systems, vol. 63, pp. 45-55, 1994/4/11 1994.
[4] R.Dieck, "Measurement Uncertainty Methods and Applications," Instrument Society of America 1995.
[5] A. Abur and M. K. Celik, "Least absolute value state estimation with equality and inequality constraints," Power Systems, IEEE Transactions on, vol. 8, pp. 680 - 686, May 1993.
[6] H. Singh, F. L. Alvarado, and W.-H. E. Liu, "Constrained LAV state estimation using penalty functions," Power Systems, IEEE Transactions on, vol. 12, pp. 383 - 388, Feb. 1997.
[7] K. A. Clements, P. W. Davis, and K. D. Frey, "Treatment of inequality constraints in power system state estimation," Power Systems, IEEE Transactions on, vol. 10, pp. 567 - 574, May 1995.
[8] F. C. Schweppe, Uncertain dynamic systems. Englewood Cliffs, N.J.: Prentice-Hall, 1973.
[9] F. Shabani, N. R. Prasad, and H. A. Smolleck, "A fuzzy-logic-supported weighted least squares state estimation," Electric Power Systems Research, vol. 39, pp. 55-60, 1996/10 1996.
[10] H. Tanaka, S. Uejima, and K. Asai, "Fuzzy linear regression model," Int. Congr. on Applied Systems Research and CyberneticsAcapulco, Mexico, 1980, pp. 2933-2938.
[11] T. Ross, Fuzzy Logic with Engineering Applications, 2nd ed.: John Wiley & Sons, Ltd, April 2005.
[12] H. Moskowitz and K. Kim, "On assessing the H value in fuzzy linear regression," Fuzzy Sets and Systems, vol. 58, pp. 303-327, 1993.
[13] H. Tanaka, S. Uejima, and K. Asai, "Linear regression analysis with fuzzy model," IEEE Transactions on Systems, Man and Cybernetics, vol. SMC-12, pp. 903-907, 1982/11/ 1982.
[14] J. J. Grainger and W. D. Stevenson, Power system analysis. New York: McGraw-Hill, 1994.
[15] D. T. Redden and W. H. Woodall, "Further examination of fuzzy linear regression," Fuzzy Sets and Systems, vol. 79, pp. 203-211, 1996/4/22 1996.
[16] "Optimization Toolbox for use with Matlab user's guide," 2 ed: The Math works inc.
[17] M. M. Adibi and D. K. Thorne, "Remote measurement calibration," Power Systems, IEEE Transactions on, vol. PWRS-1, pp. 194-202, May 1986.
[18] M. M. Adibi, K. A. Clements, R. J. Kafka, and J. P. Stovall, "Remote measurement calibration," IEEE Computer Applications in Power, vol. 3, pp. 37 - 42, Oct. 1990.
[19] T. J. Ross, Fuzzy logic with engineering applications. Chichester: Wiley, 2004.