**5. Amplitude control**

Multimodule converter with eliminated the first four harmonics (Case E, 16 modules) complies with IEEE 519 2014 [23] requirements for voltage <1 kV, with five eliminated harmonics (Case F) for 1 kV to 69 kV and with six eliminated harmonics (Case G) from 69 kV to 161 kV without using any output power line filters. Eq. (9) may be useful for approximate calculation of THD of the MMC output voltage after canceling the first *k* harmonics using this method:

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

**Configuration A B C D E F G** Number of modules 1 2 4 8 16 32 64 Harmonics canceled + 0 3 5 7 11 13 17

THD 0.4834 0.3103 0.1752 0.1166 0.0575 0.0360 0.0238

**Table 3.** Simulation results for voltage THD and maximum high harmonic left.

**Figure 10.** Harmonic elimination topology and phase-shift control.

Phase shift per next module set

Relative change of the first harmonic

Combined output value

First harmonic *k* value

Max higher harmonic

Max harmonic value

Max harmonic relative to the

(Vrms)

number

(Vrms)

first harmonic

V1 (Vrms) *THDk* ≈ *0.5* ∗ *e <sup>−</sup>0.5k* (9)

0 π/3 π/5 π/7 π/11 π/13 π/17

1.0000 0.8660 0.9511 0.9749 0.9898 0.9927 0.9957

1.0000 0.8165 0.7528 0.7278 0.7167 0.7108 0.7076

0.9003 0.7798 0.7415 0.7229 0.7156 0.7103 0.7074

3 5 7 11 17 29 29

0.3001 0.1559 0.0658 0.0526 0.0160 0.0127 0.0113

0.3333 0.1999 0.0887 0.0728 0.0224 0.0179 0.0160

MMC with fixed phase shifts produces low THD sinusoidal output voltage with the amplitude proportion to the DC bus voltage. To regulate the output voltage amplitude from zero to maximum without affecting the harmonic elimination results, two identical voltages V1 and V2 have to be combined with the variable symmetrical phase shift [32, 33] (**Figure 13**).

The variable phase-shift symmetry maintains stable phase of the resulting output voltage at the load during the amplitude regulation. This method (also known as outphasing) was originally developed for AM transmitters and assumed two sinusoidal combining voltages, now widely used for high-efficiency communication transmitters [34]. The amplitude of the combined output voltage *V*c depends upon the phase shift ϕ as shown on phasor diagram (**Figure 13**):

$$V\_c = 2\text{ V}\_o \text{Simp} \tag{11}$$

**6. RF transmitter current harmonics and life expectancy**

**Figure 14.** DC/AC multimodule multilevel converter with outphasing amplitude control.

which is proportional to the output current.

**Figure 15.** Switch-mode outphasing transmitter.

The simplified schematic of the two module switch-mode outphasing transmitters is shown in **Figure 15** [35]. Two full-bridge converters, named leading and lagging, have their output voltages combined using their output transformers TX1 and TX2. The load is a resonant antenna consisting of the antenna inductor La, parallel-tuned capacitor Ca and resistor Ra representing antenna losses and defying antenna Q. The load impedance has its maximum at the operating frequency of the parallel resonance equal to Ra. For the higher harmonics of the output voltage, antenna impedance is capacitive and drops at higher frequency. Higher harmonics of the transmitter output current are limited by the output filters Lf and Cf. This filter is tuned to the series resonance at the operating frequency to introduce minimum output filter voltage drop

Sequential Selective Harmonic Elimination and Outphasing Amplitude Control...

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

25

For the high-power applications, the switch-mode converters are used instead of the sine generators (**Figure 14**) where two sets of power modules Mod A and Mod B are controlled from two multiple outputs of fixed delay modules A and B. Delay modules may be shift registers or digital delay lines (for RF transmitters). Inputs of delay lines controlling leading vector A and lagging vector B are connected to the outputs of symmetrical phase-shift modulator with amplitude control voltage and sinusoidal carrier voltage inputs. The shown output transformers are the simplest way to combine output voltages and to form regulated output. For power conversion with the strict requirements to the harmonic content of the regulated sinusoidal voltage at the output, each of two DC/AC converters shall comply with those requirements, and the number of modules is chosen based in **Figure 11** data.

Sinusoidal carrier voltage (not triangular or sawtooth voltage) provides linear modulation characteristic for the resulting fundamental harmonic, which allows direct control of the RF output pulses restored at the resonant antenna without the real-time negative feedback. In some cases the correction of the total system gain depending on the DC bus voltage may be done between RF pulses [29].

**Figure 13.** Outphasing modulation phasor diagram for the fundamental harmonic.

Sequential Selective Harmonic Elimination and Outphasing Amplitude Control... http://dx.doi.org/10.5772/intechopen.72198 25

**Figure 14.** DC/AC multimodule multilevel converter with outphasing amplitude control.

mum without affecting the harmonic elimination results, two identical voltages V1 and V2

The variable phase-shift symmetry maintains stable phase of the resulting output voltage at the load during the amplitude regulation. This method (also known as outphasing) was originally developed for AM transmitters and assumed two sinusoidal combining voltages, now widely used for high-efficiency communication transmitters [34]. The amplitude of the combined output voltage *V*c depends upon the phase shift ϕ as shown on phasor diagram (**Figure 13**):

*Vc* = 2 *V0 Sin* (11)

For the high-power applications, the switch-mode converters are used instead of the sine generators (**Figure 14**) where two sets of power modules Mod A and Mod B are controlled from two multiple outputs of fixed delay modules A and B. Delay modules may be shift registers or digital delay lines (for RF transmitters). Inputs of delay lines controlling leading vector A and lagging vector B are connected to the outputs of symmetrical phase-shift modulator with amplitude control voltage and sinusoidal carrier voltage inputs. The shown output transformers are the simplest way to combine output voltages and to form regulated output. For power conversion with the strict requirements to the harmonic content of the regulated sinusoidal voltage at the output, each of two DC/AC converters shall comply with those require-

Sinusoidal carrier voltage (not triangular or sawtooth voltage) provides linear modulation characteristic for the resulting fundamental harmonic, which allows direct control of the RF output pulses restored at the resonant antenna without the real-time negative feedback. In some cases the correction of the total system gain depending on the DC bus voltage may be

ments, and the number of modules is chosen based in **Figure 11** data.

**Figure 13.** Outphasing modulation phasor diagram for the fundamental harmonic.

done between RF pulses [29].

have to be combined with the variable symmetrical phase shift [32, 33] (**Figure 13**).

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