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« on: November 23, 2011, 02:10:24 am »
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International Journal of Scientific & Engineering Research Volume 2, Issue 10, October-2011
ISSN 2229-5518

AbstractThis paper proposed a new modulation strategy to eliminate common mode voltages in multilevel inverters. In this scheme which is explained for a 5-level modular inverter, all voltage vectors with zero common mode voltages can be classified into four categories and each two adjacent categories composed a segment. Synthesized voltage vectors that are an approximation to the reference vector belong to the segment in which the reference vector lies. Dwell times of these voltage vectors, depend on the distance between reference vector and the voltage vectors. This scheme leads to a good linearity relationship and low total harmonic distortion.

Index Terms Common mode voltage, Multilevel modular inverter, Modulation, Linearity, THD

1      INTRODUCTION
The main purpose of the control for multilevel inverters is to synthesize the output voltages corresponding to the desired sinusoidal waveforms. Many modulation schemes have been developed with considerations to harmonic generation, linearity relationship or common mode voltage eliminations [1-3]. Due to the resulting overall inverter performance, simplicity both in hardware and software, space vector modulation is still considered as a suitable choice for multilevel PWM inverters .
One of the simplest ideas to control the output voltages based on SVM is to select adjacent voltage vectors. The dwell times of these vectors is based on time-averaging principle which may lead to complicated calculations. In some schemes to achieve simpler calculations, only nearest vector to the reference vector will be delivered [1, 5]. Figure 1(a) shows a modular five-level PWM inverter. Each leg consists of four bidirectional chopper-cells which have been shown in figure 1(b).

These cells which are the basic components of the MMC topology known as a sub-module. Each sub-module consists of a dc capacitor and two IGBTs which composed a bidirectional chopper. Its output voltage is either equal to the capacitor voltage Vc or zero. Also it should be noted that to avoid short-circuiting, operation of the switches has a complementary role in a sub-module. So when either of the sub-modules is turned-on, the other one of the same sub-module must be switched off. Since the number of chopper-cells per leg is four, five-level (9-level in line-to-line) PWM waveforms will be produced.

2  PROPOSED MODULATION ALGORITHM
One of the easiest space vector modulation methods is to deliver the nearest voltage vector with respect to the reference vector . Figure 2 represents the phase voltages, line to line voltage, and common mode voltage in a five-level inverter controlled by this scheme (using nearest vectors), operating with a modulation index of m=.9 and fundamental frequency of 50Hz. Considering figure 2 (b) this modulation method generates an important amount of common mode voltages. Common mode voltages commutations can generate circulating currents that is the cause of bearing failures . Therefore, to avoid these failures, this scheme is not recommended.
Figure 2.    (a) Phase voltages, (b) common mode voltage, (c) line to line voltage, and  (d) spectrum of line to line voltage in a five level inverter using nearest vectors method with m=.9
To modify this scheme, only voltage vectors which have zero common mode voltages can be used. This restriction of vectors increases the distance between reference vector and the vectors of space vector diagram. So the error of the generated voltage with respect to the reference will be increased. Consequently as shown in figure 3, the linear relationship between fundamental voltage and modulation index will be decreased . The proposed method in this paper, will completely eliminate common mode voltages, and will improve the linear relationship.

Figure 3.    Comparsion of fundamental voltage (a1) versus index modulation (m) in a 5-level inverter (1pu=Vcc)
In the proposed method, voltage vectors with zero common mode voltages are classified into four categories and each category is located on a hexagonal in space vector diagram as shown in figure 4. It should be noted that the zero voltage vector (2, 2, 2) by itself is a category.
Figure 4.    Representation of voltage vectors with zero common mode in a five-level inverter.
Each of categories creates a circle. Therefore as shown in figure 5, circles with radiuses R1 and R3 have been embeded in green and blue hexagonals respectively. Second hexagonal that is red colored, has been embebed in the circle with radius R2.
It should be noted that the first category which is a zero vector, is a circle with zero radius, (i.e. a simple dot). Each two adjacent circles compose a segment as shown in Table 1. Thus d-q plane is divided into 3 segments.
Considering table 1, each of centric circles with R1 and R2 radiuses has been used in two segments. Therefore to specify the border of each segment it should be determined that reference vector is closer to which of adjacent circles.
Figure 5.    Representation of circles with radiuses R0, R1, R2 and R3
TABLE 1
TWO ADJACENT CIRCLES IN EACH SEGMENT
Numer of segments   Used circles
1   Circle 0 & circle 1
2   Circle 1 & circle 2
3   Circle 2 & circle 3

For example to determine the border of segment 1:
(1)
So :
(2)
When the reference vector falls in one of the segments the voltage vectors in that segment are selected to synthesize the desired voltage vector. the dwell times of these vectors depend on distance between reference vector and them. To determine the dwell times, parameter m is defined as:
(3)
The main idea of this scheme is based on specifying  of each sector as shown in figure 6, to the voltage vectors which are located on circle with radius Ri. The residue of sector is specified to the vectors of other circle which is composed the segment. So if the reference vector will be closer to circle with radius Ri, the section of sector which is dedicated to this circle will be greater.