Advertisement

Generalized Formulations and Solving Techniques for Selective Harmonic Elimination PWM Strategy: A Review

  • Neerparaj RaiEmail author
  • Sandeep Chakravorty
Review Paper
  • 73 Downloads

Abstract

Multilevel inverters (MLIs) are widely recommended for DC to AC power conversion as per the load requirements. The MLIs are preferred over other types of multilevel and conventional converters due to their ability to produce staircase output voltage waveforms with superior harmonics profile. However, the performance of MLIs largely depends on the modulation strategy employed. Among the various modulation techniques, the selective harmonic elimination (SHE) method is more efficient in eliminating low-order harmonics from the voltage waveform produced by MLIs. Proper mitigation of the dominant low-order harmonics results in reduction in switching losses in the semiconductor devices and improves the efficiency of the inverter. However, the analytical solution of the nonlinear SHE equations constitutes the main challenge. Over last few decades, various solving algorithms and techniques such as algebraic methods such as resultant theory, numerical techniques and optimization algorithms have been developed and proposed for selective elimination of unwanted harmonics. This review paper presents the various aspects of the problem formulations for SHE technique. Moreover, the detailed principle operation for five different SHE problem-solving techniques is also discussed in this paper. Solution trajectories corresponding to multiple solutions, PWM waveforms with single and multiple transitions at each voltage level and also for pulse-width-amplitude modulation are evaluated and presented to help the researchers gain better insight into the SHE problem and its solution.

Keywords

Selective harmonic elimination PWM formulations Multilevel inverter Iterative techniques Optimization algorithms 

Notes

References

  1. 1.
    M. Ebadi, M. Joorabian, J.S. Moghani, Multilevel cascaded transformer less inverter for connecting distributed-generation sources to network. IET Power Electron. 7(7), 1691–1703 (2014)CrossRefGoogle Scholar
  2. 2.
    R. Sajadi, H. Iman-Eini, M.K. Bakhshizadeh, Y. Neyshabouri, S. Farhangi, Selective harmonic elimination technique with control of capacitive DC-link voltages in an asymmetric cascaded H-bridge inverter for STATCOM application. IEEE Trans. Ind. Electron. 65(11), 8788–8796 (2018)CrossRefGoogle Scholar
  3. 3.
    J. Rodriguez, J.S. Lai, F.Z. Peng, Multilevel inverters: a survey of topologies, controls, and applications. IEEE Trans. Ind. Electron. 49(4), 724–738 (2002)CrossRefGoogle Scholar
  4. 4.
    Mariusz Malinowski, K. Gopa Kumar, Jose Rodriguez and Marcelo A.Perez, “ A survey on cascaded multilevel inverters”, IEEE Trans. On Ind.Electron., Vol.57, No.7, July (2010)Google Scholar
  5. 5.
    J.S. Lai, F.Z. Peng, Multilevel converters: a new breed of converters. IEEE Trans. Ind. Appl. 32(3), 509–517 (1996)CrossRefGoogle Scholar
  6. 6.
    Y. Zhang, Y.W. Li, N.R. Zargari, Z. Cheng, Improved selective harmonics elimination scheme with online harmonic compensation for high-power PWM converters. IEEE Trans. Power Electron. 30(7), 3508–3517 (2015)CrossRefGoogle Scholar
  7. 7.
    A. Tripathi, G. Narayanan, Torque ripple minimization in neutral-point-clamped three-level inverter fed induction motor drives operated at low-switching-frequency. IEEE Trans. Ind. Appl. 54(3), 2370–2380 (2018)CrossRefGoogle Scholar
  8. 8.
    A. Tripathi, G. Narayanan, High-performance off-line pulse width modulation without quarter wave symmetry for voltage-source inverter, in 2014 International Conference on Advances in Electronics Computers and Communications, IEEE, Bangalore (2014), pp. 1–6Google Scholar
  9. 9.
    A. Tripathi, G. Narayanan, Evaluation and minimization of low-order harmonic torque in low switching frequency inverter-fed induction motor drives. IEEE Trans. Ind. Appl. 52(2), 1477–1488 (2016)Google Scholar
  10. 10.
    A. Moeini, H. Zhao, S. Wang, A current-reference-based selective harmonic current mitigation PWM technique to improve the performance of cascaded H-bridge multilevel active rectifiers. IEEE Trans. Ind. Electron. 65(1), 727–737 (2018)CrossRefGoogle Scholar
  11. 11.
    H.S. Patel, R.G. Hoft, Generalized techniques of harmonic elimination and voltage control in thyristor inverters: part I harmonic elimination. IEEE Trans. Ind. Appl. IA–9(3), 310–317 (1973)CrossRefGoogle Scholar
  12. 12.
    H.S. Patel, R.G. Hoft, Generalized techniques of harmonic elimination and voltage control in thyristor inverters: part II voltage control techniques. IEEE Trans. Ind. Appl. IA– 10(5), 666–673 (1974)CrossRefGoogle Scholar
  13. 13.
    P.N. Enjeti, P.D. Ziogas, J.F. Lindsay, Programmed PWM techniques to eliminate harmonics: a critical evaluation. IEEE Trans. Ind. Appl. 26(2), 302–316 (1990)CrossRefGoogle Scholar
  14. 14.
    K. Yang, Z. Yuan, R. Yuan, W. Yu, J. Yuan, J. Wang, A Groebner bases theory based method for selective harmonic elimination. IEEE Trans. Power. Electron. 30(12), 6581–92 (2015)CrossRefGoogle Scholar
  15. 15.
    P. Enjeti, P.D. Ziogas, J.F. Lindsay, M.H. Rashid, A new PWM speed control system for high performance ac motor drives, in Conference Record IEEE IAS Annual Meeting (1987), pp. 303–31 1Google Scholar
  16. 16.
    G. Konstantinou, V.G. Agelidis, Bipolar switching waveform: novel solution sets to the selective harmonic elimination problem, in Proceedings of IEEE ICIT (2010), pp. 696–701Google Scholar
  17. 17.
    J. Soomro, T.D. Memon, M.A. Shah, Design and analysis of single phase voltage source inverter using unipolar and bipolar pulse width modulation techniques, in ICAEES (IEEE, Putrajaya, 2016), pp. 277–282Google Scholar
  18. 18.
    A. Kulkarni, V. John, Mitigation of lower order harmonics in a grid-connected single-phase PV inverter. IEEE Trans. Power Electron. 28(11), 5024–5037 (2013)CrossRefGoogle Scholar
  19. 19.
    J.V. Rao, A. Mahesh, Firing angle optimization of seven-level cascaded H-bridge multilevel inverter with un-equal DC sources using GSA approach, in IEEE 7th Power India International Conference (PIICON) (Bikaner, 2016), pp. 1–6Google Scholar
  20. 20.
    L.K. Haw, M.S.A. Dahidah, H.A.F. Almurib, SHE-PWM cascaded multilevel inverter with adjustable DC voltage levels control for STATCOM applications. IEEE Trans. Power Electron. 29, 6433–6444 (2014)CrossRefGoogle Scholar
  21. 21.
    S. Dutta, K. Chatterjee, A buck and boost based grid connected PV inverter maximizing power yield from two PV arrays in mismatched environmental conditions. IEEE Trans. Ind. Electron. 65(7), 5561–5571 (2018)CrossRefGoogle Scholar
  22. 22.
    C. Buccella, M.G. Cimoroni, C. Cecati, E. Babaei, Comparison between harmonic reduction procedures for 5-level inverters, in AEIT International Annual Conference (IEEE, Cagliari, 2017), pp. 1–6Google Scholar
  23. 23.
    P.L. Kamani, M.A. Mulla, Middle-level SHE pulse-amplitude modulation for cascaded multilevel inverters. IEEE Trans. Ind. Electron. 65(3), 2828–2833 (2018)CrossRefGoogle Scholar
  24. 24.
    P. Palanivel, S.S. Dash, Control of three phase cascaded multilevel inverter using various novel multicarrier pulse width modulation techniques, in TENCON (IEEE, Fukuoka, 2010), pp. 59–64Google Scholar
  25. 25.
    E. Kabalci, I. Colak, R. Bayindir, C. Pavlitov, Modelling a 7-level asymmetrical H-bridge multilevel inverter with PS-SPWM control, in ACEMP (IEEE, Istanbul, 2011), p. 578–583Google Scholar
  26. 26.
    I.J. Pitel, S.N. Talukdar, P. Wood, Characterization of programmed-waveform pulsewidth modulation. IEEE Trans. Ind. Appl. IA–16, 707–715 (1980)CrossRefGoogle Scholar
  27. 27.
    F. Wanmin, D. Xiaoli, W. Bin, A generalized half-wave symmetry SHE-PWM formulation for multilevel voltage inverters. IEEE Trans. Ind. Electron. 57, 3030–3038 (2010)CrossRefGoogle Scholar
  28. 28.
    G. Konstantinou, V.G. Agelidis, On re-examining symmetry of two-level selective harmonic elimination PWM: novel formulations, solutions and performance evaluation. Electr. Power Syst. Res. 108, 185–197 (2014)CrossRefGoogle Scholar
  29. 29.
    A. Tripathi, G. Narayanan, Optimal pulse width modulation of voltage-source inverter fed motor drives with relaxation of quarter wave symmetry condition, in IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT) (Bangalore, 2014), pp. 1–6Google Scholar
  30. 30.
    M.S.A. Dahidah, V.G. Agelidis, Selective harmonic elimination PWM control for cascaded multilevel voltage source converters: a generalized formula. IEEE Trans. Power Electron. 23(4), 1620–1630 (2008)CrossRefGoogle Scholar
  31. 31.
    M.S.A. Dahidah, V.G. Agelidis, A hybrid genetic algorithm for selective harmonic elimination control of a multilevel inverter with non-equal DC sources, in IEEE International Conference on Power Electronics and Drives Systems (Kuala Lumpur, 2005), pp. 1205–1210Google Scholar
  32. 32.
    J. Chiasson, L. Tolbert, K. McKenzie, Z. Du, Control of a multilevel converter using resultant theory. IEEE Trans. Control Syst. Technol. 63(3–5), 197–208 (2003)zbMATHGoogle Scholar
  33. 33.
    J.N. Chiasson, L.M. Tolbert, K.J. McKenzie, Z. Du, A complete solution to the harmonic elimination problem. IEEE Trans. Power Electron. 19, 491–499 (2004)CrossRefGoogle Scholar
  34. 34.
    L.M. Tolbert, J.N. Chiasson, Z. Du, K.J. McKenzie, Elimination of harmonics in a multilevel converter with nonequal DC sources. IEEE Trans. Ind. Appl. 41(1), 75–82 (2005)CrossRefGoogle Scholar
  35. 35.
    J.N. Chiasson, L.M. Tolbert, K.J. McKenzie, Z. Du, Elimination of harmonics in a multilevel converter using the theory of symmetric polynomials and resultants. IEEE Trans. Control Syst. Technol. 13(2), 216–223 (2005)CrossRefGoogle Scholar
  36. 36.
    T.A. Lipo, D.G. Holmes, Pulse-Width Modulation for Power Converters Principles and Practice. IEEE Press Series on Power Engineering (2003)Google Scholar
  37. 37.
    F.G. Turnbull, Selected harmonic reduction in static dc–ac inverters. IEEE Trans. Commun. Electron. 83(73), 374–378 (1964)CrossRefGoogle Scholar
  38. 38.
    J. Sun, S. Beineke, H. Grotstollen, Optimal PWM based on real-time solution of harmonic elimination equations. IEEE Trans. Ind. Electron. 11, 612–621 (1996)Google Scholar
  39. 39.
    J. Sun, H. Grotstollen, Solving nonlinear equations for selective harmonic eliminated PWM using predicted initial values, in Proceedings of IEEE IECON 1992, 9–13 Nov (SanDiego, CA, USA, 1992), pp. 259–264Google Scholar
  40. 40.
    B. Ozpineci, L.M. Tolbert, J.N. Chiasson, Harmonic optimization of multilevel converters using genetic algorithms, IEEE power electron.spec. conf.; (2004), p. 3911-6Google Scholar
  41. 41.
    B. Ozpineci, L.M. Tolbert, J.N. Chiasson, Harmonic optimization of multilevel converters using genetic algorithms. IEEE Power Electron. Lett. 3(3), 92–5 (2005)CrossRefGoogle Scholar
  42. 42.
    K.S. Neralwar, P.M. Meshram, V. Borghate, GA based hybrid selective harmonic elimination (SHE) technique applied to five-level nested neutral point clamped (NNPC) converter, in ICPEICES (IEEE, Delhi, 2016), pp. 1–6Google Scholar
  43. 43.
    M. Hajizadeh, S.H. Fathi, Selective harmonic elimination strategy for cascaded H-bridge five-level inverter with arbitrary power sharing among the cells. IET Power Electron. 9(1), 95–101 (2016)CrossRefGoogle Scholar
  44. 44.
    S.S. Lee, B. Chu, N.R.N. Idris, H.H. Goh, Y.E. Heng, Switched-battery boost-multilevel inverter with GA optimized SHEPWM for standalone application. IEEE Trans. Ind. Electron. 63(4), 2133–2142 (2016)CrossRefGoogle Scholar
  45. 45.
    J. Kennedy, R. Eberhart, Particle swarm optimization, in IEEE Proceedings of International Conference on Neural Networks, Perth, WA, Australia, vol. 4 (1995), pp. 1942–1948Google Scholar
  46. 46.
    D. Yadav and J. Kumar, Harmonic minimization using PSO technique for CMLI with unequal and equal DC sources, IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), Delhi, (2016), pp. 1-5Google Scholar
  47. 47.
    H. Taghizadeh, M. Tarafdar Hagh, Harmonic elimination of cascade multilevel inverters with nonequal DC sources using particle swarm optimization. IEEE Trans. Ind. Electron. 57(11), 3678–3684 (2010)CrossRefGoogle Scholar
  48. 48.
    H.M. Tarafdar, H. Taghizadeh, K. Razi, Harmonic minimization in multilevel inverters using modified species-based particle swarm optimization. IEEE Trans. Power Electron. 24(10), 2259–67 (2009)CrossRefGoogle Scholar
  49. 49.
    M.A. Memon, S. Mekhilef, M. Mubin, Selective harmonic elimination in multilevel inverter using hybrid APSO algorithm. IET Power Electron. 11(10), 1673–1680 (2018)CrossRefGoogle Scholar
  50. 50.
    K.P. Panda, G. Panda, Application of swarm optimisation-based modified algorithm for selective harmonic elimination in reduced switch count multilevel inverter. IET Power Electronics 11(8), 1472–1482 (2018)CrossRefGoogle Scholar
  51. 51.
    A. Niknam Kumle, S.H. Fathi, F. Jabbarvaziri, M. Jamshidi, S.S. Heidari Yazdi, Application of memetic algorithm for selective harmonic elimination in multi-level inverters. IET Power Electron. 8(9), 1733–1739 (2015)CrossRefGoogle Scholar
  52. 52.
    M.H. Etesami, N. Farokhnia, S.H. Fathi, Colonial competitive algorithm development toward harmonic minimization in multilevel inverters. IEEE Trans Ind Inform 11(2), 459–66 (2015)Google Scholar
  53. 53.
    E.E. Espinosa, A new modulation method for a 13-level asymmetric inverter toward minimum THD. IEEE Trans. Ind. Appl. 50(3), 1924–1933 (2014)CrossRefMathSciNetGoogle Scholar
  54. 54.
    U. Choi, F. Blaabjerg, K. Lee, Control strategy of two capacitor voltages for separate MPPTs in photovoltaic systems using neutral-point-clamped inverters. IEEE Trans. Ind. Appl. 51(4), 3295–3303 (2015)CrossRefGoogle Scholar
  55. 55.
    M.S.A. Dahidah, G. Konstantinou, V.G. Agelidis, A review of multilevel selective harmonic elimination PWM: formulations, solving algorithms, implementation and applications. IEEE Trans Power Electron 30(8), 4091–106 (2015)CrossRefGoogle Scholar
  56. 56.
    L. Li, D. Czarkowski, L. Yaguang, P. Pillay, Multilevel selective harmonic elimination PWM technique in seriesconnected voltage inverters. IEEE Trans. Ind. Appl. 36, 160–170 (2000)CrossRefGoogle Scholar
  57. 57.
    J.R. Wells, B.M. Nee, P.L. Chapman, P.T. Krein, Selective harmonic control: a general problem formulation and selected solutions. IEEE Trans. Power Electron. 20, 1337–1345 (2005)CrossRefGoogle Scholar
  58. 58.
    M.S.A. Dahidah, G. Konstantinou, N. Flourentzou, V.G. Agelidis, On comparing the symmetrical and non-symmetrical selective harmonic elimination pulse-width modulation technique for two-level three-phase voltage source converters. IET Power Electron. 3, 829–842 (2010)CrossRefGoogle Scholar
  59. 59.
    M.S.A. Dahidah, V.G. Agelidis, M.V. Rao, On abolishing symmetry requirements in the formulation of a fivelevel selective harmonic elimination pulse-width modulation technique. IEEE Trans. Power Electron. 21, 1833–1837 (2006)CrossRefGoogle Scholar
  60. 60.
    M. Sabahi, A.R. Marami Iranaq, K.M. Bahrami, K.M. Bahrami, M.B.B. Sharifian, Harmonics elimination in a multilevel inverter with unequal DC sources using genetic algorithm, in International Conference on Electrical Machines and Systems, Beijing (2011), pp. 1–5Google Scholar
  61. 61.
    M. Veenstra, A. Rufer, Control of a hybrid asymmetric multilevel inverter for competitive medium-voltage industrial drives. IEEE Trans. Ind. Appl. 41(2), 655–664 (2005)CrossRefGoogle Scholar
  62. 62.
    J. Lee, K. Lee, Optimal phase shifted method to reduce current ripples for parallel grid-connected voltage source inverter under unequal DC-link voltages, in IEEE Energy Conversion Congress and Exposition (ECCE) (Cincinnati, OH, 2017), pp. 4589–4594Google Scholar
  63. 63.
    I. Abdalla, J. Corda, L. Zhang, Multilevel DC-link inverter and control algorithm to overcome the PV partial shading. IEEE Trans. Power Electron. 28(1), 14–18 (2013)CrossRefGoogle Scholar
  64. 64.
    A. Moeini, H. Iman-Eini, A. Marzoughi, DC link voltage balancing approach for cascaded H-bridge active rectifier based on selective harmonic elimination-pulse width modulation”. IET Power Electron. 8, 583–590 (2015)CrossRefGoogle Scholar
  65. 65.
    M. Najjar, A. Moeini, M.K. Bakhshizadeh, F. Blaabjerg, S. Farhangi, Optimal selective harmonic mitigation technique on variable DC link cascaded H-bridge converter to meet power quality standards. IEEE J. Emerg. Sel. Top. Power Electron 4(3), 1107–1116 (2016)CrossRefGoogle Scholar
  66. 66.
    A. Mokhberdoran, A. Ajami, Symmetric and Asymmetric Design and Implementation of New Cascaded Multilevel Inverter Topology. IEEE Transactions on Power Electronics 29(12), 6712–6724 (2014)CrossRefGoogle Scholar
  67. 67.
    M.D. Manjrekar, P.K. Steimer, T.A. Lipo, Hybrid multilevel power conversion system: a competitive solution for high-power applications. IEEE Trans. Ind. Appl. 36, 834–841 (2000)CrossRefGoogle Scholar
  68. 68.
    K.A. Corzine, Y.L. Familiant, A new cascaded multilevel Hbridge drive. IEEE Trans. Power Elect. 17, 125–131 (2002)CrossRefGoogle Scholar
  69. 69.
    M.S.A. Dahidah, V.G. Agelidis, Non-symmetrical SHEPWM technique for five-level cascaded converter with nonequal DC sources, in IEEE PECon 2nd International (2008), pp. 775–780Google Scholar
  70. 70.
    H. Ghoreishy, A.Y. Varjani, S. Farhangi, M. Mohamadian, Hybrid cascaded H-bridge inverter with even power distribution and improved total harmonic distortion: analysis and experimental validation. IET Power Electron. 5, 1245–1253 (2012)CrossRefGoogle Scholar
  71. 71.
    L. Kah Haw, M.S.A. Dahidah, G. Konstantinou, V.G. Agelidis, SHE-PWM cascaded multilevel converter with adjustable DC sources control for STATCOM applications, in IEEE IPEMC (2012), pp. 330–334Google Scholar
  72. 72.
    Y. Liu, H. Hong, A.Q. Huang, Real-time algorithm for minimizing THD in multilevel inverters with unequal or varying voltage steps under staircase modulation. IEEE Trans. Ind. Electron. 56(6), 2249–2258 (2009)CrossRefGoogle Scholar
  73. 73.
    P.L. Kamani, M.A. Mulla, Simpson’s rule based SHE pulse-amplitude modulation for cascaded multilevel inverters, in IEEE International Conference on Power Systems (ICPS) (Pune, 2017), pp. 585–590Google Scholar
  74. 74.
    A. Moeini, H. Iman-Eini, M. Bakhshizadeh, Selective harmonic mitigation-pulse-width modulation technique with variable DC-link voltages in single and three-phase cascaded H-bridge inverters. IET Power Electron. 7(4), 924–932 (2014)CrossRefGoogle Scholar
  75. 75.
    Y. Zhang, G. Adam, S. Finney, B. Williams, Improved pulse-width modulation and capacitor voltage-balancing strategy for a scalable hybrid cascaded multilevel converter. IET Power Electron. 6(4), 783–97 (2013)CrossRefGoogle Scholar
  76. 76.
    A. Edpuganti, R. Akshay Kumar, New optimal pulsewidth modulation for single dc-link dual-inverter fed open-end stator winding induction motor drive. IEEE Trans. Power Electron. 30(8), 4386–93 (2015)CrossRefGoogle Scholar
  77. 77.
    O. Dordevic, E. Levi, M. Jones, A vector space decomposition based space vector PWM algorithm for a three-level seven-phase voltage source inverter. IEEE Trans. Power Electron. 28(2), 637–649 (2013)CrossRefGoogle Scholar
  78. 78.
    X. Guo, D. Xu, B. Wu, Four-leg current-source inverter with a new space vector modulation for common-mode voltage suppression. IEEE Trans. Ind. Electron. 62(10), 6003–6007 (2015)CrossRefGoogle Scholar
  79. 79.
    M. Abarzadeh, H.M. Kojabadi, L. Chang, A modified static ground power unit based on active natural point clamped converter, in IEEE Energy Conversion Congress and Exposition (ECCE) (Montreal, QC, 2015), pp. 3508–3514Google Scholar
  80. 80.
    P. Palanivel, S.S. Dash, Analysis of THD and output voltage performance for cascaded multilevel inverter using carrier pulse width modulation techniques. IET Power Electron. 4(8), 951–8 (2011)CrossRefGoogle Scholar
  81. 81.
    A.M.Y.M. Ghias, M. Ciobotaru, J. Pou, V.G. Agelidis, Performance evaluation of a five level flying capacitor converter with reduced DC bus capacitance under two different modulation schemes, in PEDG (IEEE, 2012)Google Scholar
  82. 82.
    C.F. Liang, J. Agelidis, V.G. Green, T.C, A multi-modular system based on parallel-connected multilevel flying capacitor converters controlled with fundamental frequency SPWM, in IECON (IEEE, Paris, 2006), p. 2360–2365Google Scholar
  83. 83.
    C. Hu, G. Holmes, W. Shen, X. Yu, Q. Wang, F. Luo, Neutral-point potential balancing control strategy of three-level active NPC inverter based on SHEPWM. IET Power Electron. 10(14), 1943–1950 (2017)CrossRefGoogle Scholar
  84. 84.
    A. Marzoughi, H. Imaneini, Optimal selective harmonic elimination for cascaded Hbridge-based multilevel rectifiers. IET Power Electron. 7(2), 350–6 (2014)CrossRefGoogle Scholar
  85. 85.
    R. Pindado, C. Jaén, J. Pou, Robust method for optimal PWM harmonic elimination based on the Chebyshev function, in Proceedings of IEEE ICHQP, 14–18 Oct (Athens, Greece, 1998), pp. 976–981Google Scholar
  86. 86.
    J.-W. Chen, T.J. Liang, S.H. Wang, A novel design and implementation of programmed PWM to eliminated harmonics, in Proceedings of IEEE IECON, 6–10 Nov (Raleigh, NC, USA, 2005), pp. 1278–1283Google Scholar
  87. 87.
    A. Kouzou, M.O. Mahmoudi, M.S. Boucherit, Application of SHE-PWM for seven-level inverter output voltage enhancement based on particle swarm optimization, in IEEE 7th International Multi-Conference on Systems, Signals and Devices, Amman (2010), pp. 1–6Google Scholar
  88. 88.
    K. Shen, D. Zhao, J. Mei, L. Tolbert, W. Jianze, M. Ban et al., Elimination of harmonics in a modular multilevel converter using particle swarm optimization-based staircase modulation strategy. IEEE Trans. Ind. Electron. 61(10), 5311–5322 (2014)CrossRefGoogle Scholar
  89. 89.
    T.J. Liang, R.G. Hoft, Walsh function method of harmonic elimination, in APEC 1993, 7–11 Mar (IEEE, San Diego, CA, USA, 1993), pp. 847–853Google Scholar
  90. 90.
    T.J. Liang, R.M. O’onnell, R.G. Hoft, Inverter harmonic reduction using Walsh function harmonic elimination method. IEEE Trans. Power Electron. 12(6), 971–982 (1997)CrossRefGoogle Scholar
  91. 91.
    T. Kato, Sequential homotopy-based computation of multiple solutions for selected harmonic elimination in PWM inverters. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 46(5), 586–93 (1999)CrossRefGoogle Scholar
  92. 92.
    A.G. Hosseini, Optimised active harmonic elimination technique for threelevel T-type inverters. IET Power Electron. 6(3), 425–33 (2013)CrossRefMathSciNetGoogle Scholar
  93. 93.
    M.G. Hosseini Aghdam, S.H. Fathi, G.B. Gharehpetian, Elimination of harmonics in a multi-level inverter with unequal DC sources using the homotopy algorithm, in IEEE International Symposium on Industrial and Electronics (2007), pp. 578–583Google Scholar
  94. 94.
    K. Yang, D. Lu, X. Kuang, Z. Yuan, W. Yu, Harmonic elimination for multilevel converters with unequal DC levels by using the polynomial homotopy continuation algorithm, in IEEE, Chengdu (2016), pp. 9969–9973Google Scholar
  95. 95.
    J. Chiasson, L. Tolbert, K. McKenzie, Zhong Du, Eliminating harmonics in a multilevel converter using resultant theory, in IEEE 33rd Annual Power Electronics Specialists Conference. Proceedings, Australia, vol. 2 (2002), pp. 503–508Google Scholar
  96. 96.
    J. Chiasson, L.M. Tolbert, K. McKenzie, Z. Du, Elimination of harmonics in a multilevel converter using the theory of symmetric polynomials and resultants, in IEEE International Conference on Decision and Control, Maui, HI, vol. 4 (2003), pp. 3507–3512Google Scholar
  97. 97.
    K. Yang, Q. Zhang, R. Yuan, W. Yu, J. Wang, Selective harmonic elimination with Groebner bases and symmetric polynomials. IEEE Trans. Power Electron. 31(4), 689–94 (2015)Google Scholar
  98. 98.
    X. Che, Y. Luo, J. Yang, Z. He, Application of universal grey algorithm to solutions of algebraic based on Wu elimination method, ion Fourth International Conference on Natural Computation (IEEE, Jinan, 2008), pp. 289–293Google Scholar
  99. 99.
    G. Mohaddes, P.G. McLaren, Harmonic elimination in PWM inverters using neural networks, in Proceedings of Canadian Conference on Electrical and Computer Engineering, Canada, vol. 1 (IEEE, 1994), pp. 64–67Google Scholar
  100. 100.
    F. Filho, S. Member, L.M. Tolbert, S. Member, Y. Cao, S. Member, Real-time selective harmonic minimization for multilevel inverters connected to solar panels using artificial neural network angle generation. IEEE Trans. Ind. Appl. 47(5), 2117–24 (2011)CrossRefGoogle Scholar
  101. 101.
    F. Filho, H.Z. Maia, T.H.A. Mateus, B. Ozpineci, L.M. Tolbert, J.O.P. Pinto, Adaptive selective harmonic minimization based on ANNs for cascade multilevel inverters with varying DC sources. IEEE Trans. Ind. Electron. 60(5), 1955–62 (2013)CrossRefGoogle Scholar
  102. 102.
    M. Balasubramonian, V. Rajamani, Design and real-time implementation of SHEPWM in single-phase inverter using generalized Hopfield neural network. IEEE Trans. Ind. Electron. 61(11), 6327–36 (2014)CrossRefGoogle Scholar
  103. 103.
    E. Deniz, O. Aydogmus, Z. Aydogmus, GA-based optimization and ANN-based SHEPWM generation for two-level inverter, in IEEE International Conference on Industrial Technology (ICIT), Seville (2015), pp. 738–744Google Scholar
  104. 104.
    M.R. Banaei, P.A. Shayan, Solution for selective harmonic optimisation in diode-clamped inverters using radial basis function neural networks. IET Power Electron. 7(7), 1797–1804 (2014)CrossRefGoogle Scholar
  105. 105.
    H.R. Baghaee, M. Mirsalim, G.B. Gharehpetian, H.A. Talebi, A. Niknam-Kumle, Notice of violation of IEEE publication principles: A hybrid ANFIS/ABC-based online selective harmonic elimination switching pattern for cascaded multi-level Inverters of microgrids. IEEE Trans. Ind. Electron.  https://doi.org/10.1109/TIE.2017.2694403 (2017)
  106. 106.
    A. Kavousi, B. Vahidi, R. Salehi, M.K. Bakhshizadeh, N. Farokhnia, S.H. Fathi, Application of the bee algorithm for selective harmonic elimination strategy in multilevel inverters. IEEE Trans. Power Electron. 27(4), 1689–1696 (2012)CrossRefGoogle Scholar
  107. 107.
    H. Lou, C. Mao, D. Wang, J. Lu, PWM optimisation for three-level voltage inverter based on clonal selection algorithm. IET Electr. Power Appl. 1(6), 870–878 (2007)CrossRefGoogle Scholar
  108. 108.
    H.R. Massrur, T. Niknam, M. Mardaneh, A.H. Rajaei, Harmonic elimination in multilevel inverters under unbalanced voltages and switching deviation using a new stochastic strategy. IEEE Trans. Ind. Inform. 12(2), 716–725 (2016)CrossRefGoogle Scholar

Copyright information

© The Institution of Engineers (India) 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringIndus Institute of Technology and EngineeringAhmedabadIndia

Personalised recommendations