An Implementation Mechanisms of SVM Control Strategies Applied to Five Levels Cascaded Multi-Level Inverters

Received Dec 26, 2013 Revised Mar 20, 2014 Accepted Apr 1, 2014 In the area of the energy control with high voltage and power, the multilevel inverters constitute a relatively recent research orientation. The current applications of this technology are in the domains of the high voltage (over hundred kV), variable speed drives, transport and distribution of a good quality of electrical energy (HVDC, FACTS system, ....). To improve the output voltage for such inverters, many different modulation strategies have been developed. Among these strategies, the SVM (Space Vector Modulation). The technique provide the nearest switching vectors sequence to the reference vector without involving trigonometric functions and provide the additional advantages of superior harmonic quality. In this paper, we analyze different mechanisms of the output voltage synthesis and the problem of even order harmonic production. With the proposed a new trajectory SVM, which can eliminate all the even order harmonics for five levels inverter. Show clearly how to deduce the trajectories from the sequences allowing to have better performances among several possible trajectories. It is dedicated to the application of two particular trajectories. Keyword:


INTRODUCTION
The main interest of the multilevel inverters is the remarkable improvement of the spectral quality of its output signals. Multilevel inverters can reach the increasing demand for power quality and power ratings along with lower harmonic distortion and lesser electromagnetic interference (EMI). This spectrum is, by far, relatively better than the classical two levels inverter [1]- [5].
To improve much more quality of electrical energy, we apply the space vector modulation (SVM) strategy which stands out because it offers significant flexibility to optimize switching waveforms, and because it is well suited for implementation on a digital computer [1], [2], [6]- [9]. The technique provide the nearest switching vectors sequence to the reference vector and calculates the on-state durations of the respective switching state vectors without involving trigonometric functions and provide the additional advantages of superior harmonic quality. It will be studied on a five levels cascaded three-phase inverter. This converter consists of a series-connection of two 4-quadrant converter by phase [2].
The implementation of SVM produces, for some cases, even order harmonics. We will propose a new trajectory SVM for the cascaded inverter, allowing to eliminate the even order harmonics from the output voltage and resulting in a solution where the number of commutation and hence the switching losses may be reduced in the inverter.  Figure 1 shows the simplified circuit of a five levels cascaded inverter. The output voltage of the inverter of a phase, characterize its state. It is defined by the formula (1) [2]. Theoretical tools allowing evaluating and identifying the representation of the vectors and commutations (hexagonal structure) is corresponding to the vectors of output of the 2 levels and Multilevel inverters have been studied in detail by [2], [6], [10].  It is the task of the modulator (SVM) to determine which position the switches should assume (switching state) in the α, β plane, the duration needed (duty cycle) and the triangular area in which it is, in order to synthesize the reference voltage vector [2], [6]. The generalized algorithm being used to determine, for the hexagonal structure, the exact position of the vector of reference (detection of nearest three vectors and duty cycles computation) was developed and studied in detail in [2], [5], [8] and [13]. Figure 3 illustrates a subset of a five level space vector plot, and Table 1 summarises all possible sequences for this subset that achieve the required minimum of three switching transitions per phase leg in a switching period, i.e. if we locate the exact triangle where is located, limited by some sort three switching stats (s 1 , s 2 , s 3 ) in one switching intervals T e , then the sequence is given like continuation: s 1 s 2 s 3 s 1 s 3 s 2 s 1 [2], [10]- [12].

Synthesis of the reference vector
The best way to synthesize the voltage reference vector is by using the nearest three vectors (V , V and V ) and their duty cycles (d , d and d ) [2]: With the additional constraint: For example, for triangles (b) and (d), there are two possible sequences. For triangles (a) and (c) the correct sequence can be identified from the possible alternatives by ensuring that no extra switching transitions occur when moving between triangles. For example, sequence c(iii) (or c(iv)) should be used when moving from triangle (b) to (c) since it begins with the same state as the sequence in (b), or sequence c(i) (or c(ii)) should be used when moving from triangle (c) to (d) since it begins with the same state as the sequence in (d). Applying this principle to triangle (a) means that sequences a(i) to a(iv) cannot be used because they will introduce extra switching transitions when moving into triangle (c). Table 2 shows two seven-segment switching sequences for falling into region (a 2 ). V It is interesting to note that for sequence 1, the switching sequence of the three vectors, V , V and V , in the first three segment rotates in a counter clockwise (CCW) direction in the space vector diagram shown in Figure 4, whereas for sequence 2, the switching sequence for these vectors rotating in a clockwise (CW) direction. Thees notations "+" and "-" indicate the direction of the switching sequence rotation. While basing itself on the sequence 1, the switching sequence for all the triangular regions is shown in Figure 5. The modulation index 0.7 and 1.15 for sampling frequency 600 12 and 650 13 . with ; : fundamental frequency=50Hz.
We obtain the results given in Figure 6. In the spectrum of output signal, the amplitude of fundamental is equal to 100%. By analyzing the spectrum of the SVM signal on five levels, it is noted that it is made up, in addition to the fundamental one which is at the frequency and whose peak value is equal to , components of harmonics gathered in families. However, the above discussed trajectory SVM produces even order harmonics for even values of because of the no-symmetry of the output voltage.
To explain that, now consider the region (Figure 7) which is symmetrical by report to the origin with the area represented on Figure 3. When lies in regions (a 2 ) and (a 3 ) (which are 180° apart in space), the switching sequence and corresponding waveform of are shown in Figure 8. To eliminate even order harmonics, the waveforms have to be of half-wave symmetry.
Obviously, the waveforms shown in Figure 8 do not meet this condition, which indicates that it contains even order harmonics. This phenomenon can be more clearly demonstrated in Figure 6(a), where the inverter phase voltage for one cycle of the fundamental frequency is shown. None of the waveforms is half-wave symmetrical.

EVEN ORDER HARMONIC ELIMINATION (SECOND TRAJECTORY)
As discussed earlier, waveform with half-wave symmetry does not contain any even order harmonics. To achieve this, the switching sequence should be arranged such that the inverter phase voltage Consider two regions (a 2 ) and (a 3 ), which are symmetrical to the origin of the space diagram. To make the waveform of for in region (a 2 ) a mirror image of that for in region (a 3 ), the switching sequence of the three vectors, V , V and V , should be changed from its original CCW to CW. The resultant waveform of is shown in Figure 9, which becomes a mirroreste image of that shown in Figure 8(b). It is worth noting that although the waveforms of in Figure 9 and Figure 8(a) seems quite different. Figure 10 shows a new switching sequence arrangement, where the switching sequences, in some areas, are modified for even order harmonic elimination.

SIMULATION AND INTERPRETATION OF THE RESULTS
We made a simulation test for a five levels inverter supplying an asynchronous motor, for (r=0.9, m=25), then for (r=0.9, m=26). In the Figures 11 and 12, we have represented the output voltages , and its spectral analysis, the current and the speed.
The switch trigger signal is plotted in Figure 13. For the trajectory 1 (Figure 11), we note that there is no symmetry of simple voltage in halfwave for even values of , thus, in addition to the odd harmonics, the voltage contains both even order harmonics. In addition, the harmonic spectre shows that all the even order harmonics are eliminated for odd , and gather in family centered around the multiple frequencies of • . For the trajectory 2 ( Figure 12), we note that there is no symmetry of simple voltage in halfwave for odd values of , thus, in addition to the odd harmonics, the voltage contains both even order harmonics. In addition, the harmonic spectre shows that all the even order harmonics are eliminated for even , and gather in family centered around the multiple frequencies of • . This is understandable since the switching pattern generation mechanism, including the selection of the stationary vectors and dwell time calculations, is the same for both trajectories. The only difference is that some of the switching sequences are rearranged for the new trajectory.  It should be pointed out that the device switching frequency of the SVM trajectory 2 is slightly higher than that of the trajectory 1 for a given sampling frequency data corresponding to odd. However, the device switching frequency of the SVM trajectory 1 is slightly higher than that of the trajectory 2 for a given sampling frequency data corresponding to even ( Figure 13).

CONCLUSION
Two space vector modulation trajectories are proposed for five levels cascaded inverters. The main feature lies in its ability to eliminate even order harmonics in the inverter output voltage of the modulation trajectory 1 for even and of the modulation trajectory 2 for odd .
Considering the similar form of the hexagonal structure of the SVM for the multilevel inverters, we thus can carry out an algorithm which uses either trajectory 1 or trajectory 2, according to the value of , so as to obtain output signals which contain only odd harmonics, and this for any levels of voltage.
The advantage of the SVM technique is that all the even order harmonics can be eliminated. This is favorable in the industry applications.