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72              Renewable Energy Devices and Systems with Simulations in MATLAB  and ANSYS ®
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            achieved, while high efficiency is still maintained. Besides the higher costs of the SiC and GaN, new
            challenges need to be dealt with, like radiated and conducted EMI [31].
              The drive for higher efficiencies has led to the use of multilevel topologies like neutral point
            clamped (NPC) [32] or T type [33], also sketched in Figure 4.3, resulting in a decrease in filter
            requirements and increase in the overall efficiency of the system, thanks to the multilevel output
            voltage. Some of these multilevel topologies are also preferred in high power applications, due to the
            reduced voltage stress of the power devices, compared to a traditional two-level converter. Several
            companies use these multilevel topologies in their MCIs within a range of 10–60 kW and these
            MCIs are being used in MW-sized PV plants, where the modularity given by this topology is a huge
            advantage during installation, operation, and maintenance.
              In order to maintain high efficiency over a wide range of power levels and to ensure fault-tolerant
            operation for the converter, a new trend is to apply modular topologies, such as modular multilevel
            converters (MMC) or paralleled converters. The MMC consist of series-connected cells, usually
            with half- or full-bridge topology [34]. The number of cells used in a phase of the MMC will define
            the discrete voltage levels at the output of the converter; thus, the size of the passive filters between
            the MMC and grid can be reduced considerably. Another advantage of such topology is the pos-
            sibility of using LV power switches. By adding redundant cells on each phase of the converter,
            fault-tolerant operation can be ensured [35]. By paralleling inverters, a flat efficiency profile can be
            achieved over a wide power range, where the number of parallel-connected inverters depends on the
            available power from the solar panels [36]. The parallel configuration for the central inverter ensures
            also fault-tolerant operation. By using interleaving between the modulation carrier wave, the current
            THD can be reduced considerably [37].


            4.4  CONTROL BUILDING BLOCKS FOR PV INVERTERS

            4.4.1  Modulation Strategies for Three-Phase PV Inverters
            From the two-level inverter topologies, the most commonly used three-phase solution consists of
            six power switches, each one equipped with an antiparallel diode, and a DC-link capacitor as shown
            in Figure 4.3. PWM method is the most commonly used technique for on/off pulse generation for
            the switches. One of the earliest methods to generate the switching function, called sine triangular
            (ST)-PWM, is based on a comparison between a high-frequency triangular carrier wave with three
            reference phase voltages. In Figure 4.4, one fundamental period of the ST-PWM reference signals
            together with the carrier waveform and the resultant PWM switching function waveform is illus-
            trated. The method is not used for three-phase inverters due to its reduced linear operating range. An
            improved modulation scheme can be achieved by third harmonic injection (THI) in the common-
            mode voltage (CMV). The method is based on the fact that the line-to-line voltage is equal to the
            difference of the two-phase voltages. Thus, in case all the three-phase voltage levels are increased
            or decreased with the same value, the line-to-line voltage is not affected [38]. However, the sum of
            the three-phase voltages will not be equal to zero anymore; thus, this additional voltage appears as
            CMV. By adding the third harmonic, the sinusoidal phase voltage is transformed to a quasi-trapezoi-
            dal signal, obtaining a peak amplitude reduction of approximately 15% [39].
              The most often used modulation method for three-phase inverters is the space vector modulation
            (SVM). This modulation method uses the advantage of signal injection in the CMV as the THI-
            PWM method; however, in the beginning, it was treated as a totally different modulation technique.
            By analyzing all the possible switching states in a VSI, six active and two zero-sequence voltage
            vectors (when either the three upper or the three lower switches are simultaneously on) can be
            generated. In a d–q plane, the six active vectors form a hexagon as shown in the red hexagon in
            Figure 4.4.
              With the SVM method, during one modulation period, two adjacent vectors are generated con-
            secutively; thus, the position of the resultant voltage vector (V ) in the sector is defined by the ratio
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