**7. Conclusion**

**Figure 20.** Higher harmonic (blue) elimination decreases total output current (red).

is the power switch total power dissipation, *Psw* is the power of switching losses, *Iout*

*E\_\_\_A*

of the switch die over the ambient temperature *TA* depends

<sup>2</sup> ) (13)

according to the Arrhenius law:

*kTj* (14)

is the RMS value of switch current and *Rdson* is the switch resistance drain to source, which for

on the thermal resistance *R*th from the switch die to the ambient temperature *TA* and current

affects the switch life expectancy *tv*

silicon MOSFET is the function of the temperature and current [36].

28 Power System Harmonics - Analysis, Effects and Mitigation Solutions for Power Quality Improvement

**Figure 19.** Antenna voltage (Vp(t)) and RF pulses with Hann envelope.

*Tj* = *TA* + ∆*T* = *TA* + *Rth* ∗ (*Psw* + *Iout*

*tv* = *C* ∗ *e*

where *Ps*

*I out*:

Additional temperature rise *∆T<sup>j</sup>*

The die temperature *T<sup>j</sup>*

The sequential harmonic elimination provides a simple method of removing higher harmonics from the output voltage of the multimodule multilevel converters operating with the fundamental switching frequency and using identical modules, generating 50% duty cycle output voltages. A simple algorithm for the control circuitries used to eliminate harmonics and regulate output voltage from zero to maximum maintaining stable phase is discussed. A simple expression for THD of the output voltage vs. the number of eliminated harmonics, derived from simulation results, is provided for design evaluation against IEEE 519 standard requirements. The application of this method to the NMR transmitters operating in the high-temperature environment eliminates the most dangerous output current harmonics and shows more than twice the gain in the life expectancy. This method was validated for NMR downhole logging equipment, and two patents were granted.

[9] Rodriguez J, Lai J-S, Peng FZ. Multilevel inverters: A survey of topologies, controls, and applications. IEEE Transactions on Industrial Electronics. August 2002;**49**(4):724-738. DOI:

Sequential Selective Harmonic Elimination and Outphasing Amplitude Control...

http://dx.doi.org/10.5772/intechopen.72198

31

[10] Tolbert L, Peng F, Habetler T. Multilevel converters for large electric drives. IEEE Transactions on Industrial Applications. Jan/Feb 1999;**35**:36-44. DOI: 10.1109/28.740843 [11] Du Z, Tolbert L, Chiasson J. Harmonic Elimination for Multilevel Converter with Programmed PWM Method. IEEE IAS; 2004. pp.2210-2215. DOI: 10.1109/IAS.2004.1348783

[12] Rodrigues J, Bernet S, Wu B, Pontt J, Kouro S. Multilevel voltage-source-converter topologies for industrial medium-voltage drives. IEEE Transactions on Industrial Electronics.

[13] Rodriuez P, Bellar MD, Munoz-Aguilar RS, Busgues-Monge S, Blaabjerg F. Multilevel-Clamped Multilevel Converters (MLC). 3, s.l. IEEE. 2012;**27**:1055-1060. DOI: 10.1109/TPEL.

[14] Dahidah M, Agelidis V. Selective harmonic elimination PWM control for cascaded multilevel voltage source converters: A generalized formula. IEEE Transactions on Power

[15] Dahidah M, Konstantinou G, Agelidis VA. Review of multilevel selective harmonic elimination PWM: Formulations, solving algorithms, implementation and applications. IEEE Transactions on Power Electronics. 2014;**99**:1-16. DOI: 10.1109/TPEL.2014.2355226 [16] Darus R, Konstantinou G, Pou J, Ceballos S, Agelidis V. Comparison of Phase-Shifted and Level-Shifted PWM in the Modular Multilevel Converter. In: IEEE International Power Electronics Conference (IPEC–ECCE Asia) 2014. Hiroshima, Japan: IEEE; 2014. DOI:

[17] Gnanasambandam K, Rathor AK, Edpuganti A, Srinivasan D, Rodriguez J. Current-Fed Multilevel Converters: An Overview of Circuit Topologies, Modulation Techniques, and Applications. IEEE Transactions on Power Electronics. 2017;**32**:3382-3402. DOI: 10.1109/

[18] Ilves K, Antonopoulos A, Norrga S, Nee HP. A new modulation method for the modular multilevel converter allowing fundamental switching frequency. Proc. IEEE ICPE

[19] Ilves K, Harnefors L, Norrga S, Nee H-P. Analysis and operation of modular multilevel converters with phase-shifted carrier PWM. IEEE Transactions on Power Electronics. Jan

[20] Konstantinou G, Pulikanti S, Agelidis V. Harmonic Elimination Control of a Five-Level DC-AC Cascaded H-Bridge Hybrid Inverter. s.l. 2nd IEEE International Symposium on Power Electronics for Distributed Generation Systems, 2010. 2010. DOI: 10.1109/

[21] Li B, Yang R, Xu D, Wang G, Wang W, Xu D. Analysis of the phase-shifted carrier modulation for modular multilevel converters. IEEE Transactions on Power Electronics. Jan

December 2007;**54**:2930-2945. DOI: 10.1109/TIE.2007.907044

Electronics. 2008;**23**(4):1620-1630. DOI: 10.1109/TPEL.2008.925179

(ECCE Asia). June 2011:991-998. DOI: 10.1109/ICPE.2011.5944672

2015;**30**(1):268-296. DOI: 10.1109/TPEL.2014.2321049

2015;**30**(1):297-310. DOI: 10.1109/TPEL.2014.2299802

10.1109/TIE.2002.801052

2011.2172224

10.1109/IPEC.2014.6870039

TPEL.2016.2585576

PEDG.2010.5545762
