**1. Introduction**

The conversion of DC voltage into sinusoidal AC voltage at power levels from kilowatts to megawatts with low power losses and low higher harmonics in the output voltage is a common task for modern power engineering. Multimodule multilevel converter is the best approach to generate the high-power sinusoidal voltage from HVDC bus for electrical grid consumers, propulsion electrical motor drives, etc. High-efficiency switch-mode modules, used to synthesize sinusoidal output voltage, may operate at the fundamental frequency of the sine voltage, required for the load, or at higher frequencies (the carrier frequency) using the pulse-width modulation to reduce higher harmonics of the fundamental frequency. In the last case, the output filters, required for reducing total harmonic distortion (THD) of the output voltage to the acceptable level, are significantly smaller [1–20].

for maximum output power. The bridge load Z is connected directly to the bridge outputs or via the output transformer TX. For the industrial frequency 50 Hz–60 Hz and other lowfrequency high-power applications, fully controlled thyristors are the best choice, while for the frequency range over few kilohertz, IGBTs are the preferred ones. Operation in the frequency range over 100 kHz requires fast-switching power MOSFETs. To simplify analysis of the following circuits, the switches are assumed to be ideal and have zero-switching time and

The Fourier analysis provides the expression for the full-bridge symmetrical 50% duty cycle

∑*n=1*

where *n* is the harmonic number (only odd harmonics 1, 3, 5, etc.), ω is the angular frequency,

Spectrum of the bridge output voltage with amplitude of 1 V and frequency of 1 kHz is shown on **Figure 2**. The vertical axis represents the RMS values of each harmonic starting with the

Converter output current *Iout(t)* is a combination of the fundamental harmonic and higher harmonics, each of them being a product of the harmonic voltage *Vn(t)* and load admittance *Yn*

> *n=1* ∞

first one equal to 0.9Vrms (or 1.273 V peak value). Horizontal axis is frequency.

decreasing with the harmonic number *n*:

Sequential Selective Harmonic Elimination and Outphasing Amplitude Control...

(n = 1, 3, 5, 7, etc.):

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

for

15

\_\_\_\_\_\_ *cosn*<sup>t</sup> *<sup>n</sup>* (1)

*<sup>n</sup>* (2)

*Vn(t) Yn* (3)

output voltage *Vout(t)* (**Figure 1**) as the sum of only odd harmonics *Vn*

is the full-bridge inverter DC bus voltage and *t* is time.

*<sup>V</sup>out(t)* <sup>=</sup> <sup>4</sup> *<sup>V</sup>*\_\_\_<sup>0</sup>

*Vn* <sup>=</sup> <sup>4</sup> *<sup>V</sup>*\_\_\_<sup>0</sup>

*Iout(t)* = ∑

**Figure 2.** Spectrum of the 1 kHz 50% duty cycle signal.

Each harmonic *n* has its amplitude *Vn*

zero internal losses.

*V*0

this harmonic:

The biggest problem with the phase-shift pulse-width modulation, providing the highest quality of the output sinusoidal voltage with minimum switching losses, is its control methodology, which requires complicated calculation of the necessary phase shifts in real time [8, 21, 22].

In this paper a simple method of the sequential selective harmonic elimination and amplitude control is discussed. It is based on the combination of the fixed precalculated phase shifts/ delays for harmonic elimination and variable phase shift for amplitude control. Application of this method is illustrated using two examples—the industrial-frequency DC/AC converter and the high-frequency converter used as a transmitter for the nuclear magnetic resonance (NMR) oil/gas well logging tool, operating in harsh conditions. LTspice was used for simulation in time and frequency domains. A simple expression is provided for the resulting THD vs. the number of eliminated harmonics to comply with industrial grid voltage of THD standards without the output filter. For the NMR transmitter, decreasing of conductive losses due to the harmonic elimination reduces operating temperature and increases the reliability. Improvement of the life expectancy is calculated according to the Arrhenius equation for three transmitter cases with the same number of switches but with different harmonic contents.
