**2. Full-bridge module operation and spectrum of the output voltage**

The building block or module for multimodule multilevel converter (MMC) is a full-bridge DC/AC converter utilizing maximum voltage and current ratings of the power switches S1–S4 (**Figure 1**), powered from bus V0 , producing rectangular voltage pulses with 50% duty cycle

**Figure 1.** Full-bridge stage and output voltage waveform.

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 zero internal losses.

The Fourier analysis provides the expression for the full-bridge symmetrical 50% duty cycle output voltage *Vout(t)* (**Figure 1**) as the sum of only odd harmonics *Vn* (n = 1, 3, 5, 7, etc.):

$$V\_{out(t)} = \frac{4\,\mathrm{V\_0}}{\pi} \sum\_{n=1} \frac{\cos n\mathrm{rot}}{n} \tag{1}$$

where *n* is the harmonic number (only odd harmonics 1, 3, 5, etc.), ω is the angular frequency, *V*0 is the full-bridge inverter DC bus voltage and *t* is time.

Each harmonic *n* has its amplitude *Vn* decreasing with the harmonic number *n*:

$$\mathbf{V}\_u = \frac{4\,\mathrm{V}\_0}{\pi m} \tag{2}$$

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

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* for this harmonic:

$$I\_{out0} = \sum\_{n=1}^{n} \mathbf{V}\_{n \, t \, 0} \mathbf{Y}\_n \tag{3}$$

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

**Figure 1.** Full-bridge stage and output voltage waveform.

(**Figure 1**), powered from bus V0

the acceptable level, are significantly smaller [1–20].

**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

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

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.

**2. Full-bridge module operation and spectrum of the output voltage**

The building block or module for multimodule multilevel converter (MMC) is a full-bridge DC/AC converter utilizing maximum voltage and current ratings of the power switches S1–S4

, producing rectangular voltage pulses with 50% duty cycle

Several load types such as resistive, inductive, capacitive and resonant ones have different current vs. frequency characteristics as shown in **Figure 3**, which is obtained in LTspice environment under 1 V sinusoidal test signal.

Only resistive load current replicates the spectrum of the input voltage. Inductive load decreases high-frequency current components, but capacitive and resonant loads significantly increase relative values of the high-frequency current harmonics compared to the spectrum of the applied voltage. Voltage harmonics and resulting currents affect both load and voltage sources (converter) in different ways. Excessive current harmonics increase power losses and create electrical noise (EMI) affecting electronic equipment.

Maximum voltage harmonic content for the industrial AC lines is regulated by IEEE 519 2014 standard [23, 24]. Limits for total harmonic distortion (THD) and maximum amplitude of the highest harmonic are provided in **Table 1**.

which is 150 Hz and 180 Hz for the EU and USA, respectively. Eliminating the most powerful higher harmonics from the output voltage in the process of DC to AC conversion and reducing the highest-frequency harmonic leftovers with a simple output filters are the most efficient

High-voltage systems can have up to 2% THD where the cause is an HVDC terminal where effects will have attenuated

Sequential Selective Harmonic Elimination and Outphasing Amplitude Control...

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

17

For the high-frequency converters operating as transmitter with the resonant loads at elevated temperature, the output current's higher harmonics cause additional heating, which results in the reliability problems. In this case the effectiveness of the harmonic elimination is reducing

Multimodule multilevel converters (**Figure 4**) have their outputs connected in series to produce the so-called modified sinusoidal voltage or ladder-style voltage (**Figure 5**). DC inputs may be connected in parallel with the transformer combining the output voltages or in series for HVDC

the power component temperature and increasing the converter life expectancy.

**Bus voltage (V) at PCC Individual harmonic (%) Total harmonic distortion (THD) (%)**

V ≤ 1.0 kV 5.0 8.0 kV < V ≤ 69 kV 3.0 5.0 kV < V ≤ 161 kV 1.5 2.5 kV < V 1.0 1.5

at the point in the network where future users may be connected.

**Figure 4.** Multimodule converters with different DC line feeds.

**3. Multimodule converters and synthesis of the quasi-sinusoidal** 

ways to comply with THD standard.

**Table 1.** Voltage distortion limits.

**output voltage**

THD and individual harmonic maximum values are different for different line voltages. The power distributor should keep total harmonic distortion (THD) for voltages <1 kV under 8% and individual harmonic value less than 5% of the fundamental one at the point of consumer connection (PCC). In the process of conversion of HVDC bus voltage into lower-level AC, the switch-mode converters create higher harmonics as unwanted byproduct. For full-bridge DC/ AC converter output voltage spectrum (**Figure 2**) of THD is 0.483 or 48.3% [25]. To comply with THD limits, the simple DC/AC converters include the output filters reducing higher harmonics to the acceptable level. Those filters introduce additional losses and have significant size, weight and cost especially if the filter has to remove harmonics starting with the third one,

**Figure 3.** Load current vs. frequency for different loads.


High-voltage systems can have up to 2% THD where the cause is an HVDC terminal where effects will have attenuated at the point in the network where future users may be connected.

**Table 1.** Voltage distortion limits.

Several load types such as resistive, inductive, capacitive and resonant ones have different current vs. frequency characteristics as shown in **Figure 3**, which is obtained in LTspice envi-

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

Only resistive load current replicates the spectrum of the input voltage. Inductive load decreases high-frequency current components, but capacitive and resonant loads significantly increase relative values of the high-frequency current harmonics compared to the spectrum of the applied voltage. Voltage harmonics and resulting currents affect both load and voltage sources (converter) in different ways. Excessive current harmonics increase power losses and

Maximum voltage harmonic content for the industrial AC lines is regulated by IEEE 519 2014 standard [23, 24]. Limits for total harmonic distortion (THD) and maximum amplitude of the

THD and individual harmonic maximum values are different for different line voltages. The power distributor should keep total harmonic distortion (THD) for voltages <1 kV under 8% and individual harmonic value less than 5% of the fundamental one at the point of consumer connection (PCC). In the process of conversion of HVDC bus voltage into lower-level AC, the switch-mode converters create higher harmonics as unwanted byproduct. For full-bridge DC/ AC converter output voltage spectrum (**Figure 2**) of THD is 0.483 or 48.3% [25]. To comply with THD limits, the simple DC/AC converters include the output filters reducing higher harmonics to the acceptable level. Those filters introduce additional losses and have significant size, weight and cost especially if the filter has to remove harmonics starting with the third one,

ronment under 1 V sinusoidal test signal.

highest harmonic are provided in **Table 1**.

**Figure 3.** Load current vs. frequency for different loads.

create electrical noise (EMI) affecting electronic equipment.

which is 150 Hz and 180 Hz for the EU and USA, respectively. Eliminating the most powerful higher harmonics from the output voltage in the process of DC to AC conversion and reducing the highest-frequency harmonic leftovers with a simple output filters are the most efficient ways to comply with THD standard.

For the high-frequency converters operating as transmitter with the resonant loads at elevated temperature, the output current's higher harmonics cause additional heating, which results in the reliability problems. In this case the effectiveness of the harmonic elimination is reducing the power component temperature and increasing the converter life expectancy.
