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  1. 1. IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 2, FEBRUARY 2013 625 A Generalized Cascaded Multilevel Inverter Using Series Connection of Submultilevel Inverters Mohammad Farhadi Kangarlu, Student Member, IEEE, and Ebrahim Babaei, Member, IEEE Abstract—Application of multilevel inverters for higher power purposes in industries has become more popular. This is partly because of high-quality output waveform of multilevel inverters in comparison with two-level inverters. In this paper, initially a new topology for submultilevel inverter is proposed and then series connection of the submultilevel inverters is proposed as a generalized multilevel inverter. The proposed multilevel inverter uses reduced number of switching devices. Special attention has been paid to obtain optimal structures regarding different criteria such as number of switches, standing voltage on the switches, number of dc voltage sources, etc. The proposed multilevel inverter has been analyzed in both symmetric and asymmetric conditions. The validity of the proposed multilevel inverter is verified with both computer simulations using PSCAD/EMTDC software and laboratory prototype implementation. Index Terms—Generalized topology, multilevel inverter, optimal structure, submultilevel inverter. I. INTRODUCTION ULTILEVEL inverters include an array of power semiconductors and dc voltage sources, the output of which generate voltages with stepped waveforms [1]. In comparison with a two-level voltage-source inverter (VSI), the multilevel VSI enables to synthesize output voltages with reduced harmonic distortion and lower electromagnetic interference [2]. By increasing the number of levels in the multilevel inverters, the output voltages have more steps in generating a staircase waveform, which has a reduced harmonic distortion. However, a larger number of levels increase the number of devices that must be controlled and the control complexity [3]. There are three well-known types of multilevel inverters [4], [5]: the neutral point clamped (NPC) multilevel inverter, the flying capacitor (FC) multilevel inverter, and the cascaded H-bridge (CHB) multilevel inverter. The NPC multilevel inverter, also called diode-clamped, can be considered the first generation of multilevel inverter introduced by Nabae et al. [6] which was a three-level inverter. The three-level case of the NPC multilevel inverters has been widely applied in different industries. Unlike the NPC type, the FC multilevel inverter offers M Manuscript received July 30, 2011; revised November 16, 2011 and February 4, 2012; accepted May 24, 2012. Date of current version September 27, 2012. Recommended for publication by Associate Editor J. R. Rodriguez. The authors are with the Faculty of Electrical and Computer Engineering, University of Tabriz, 51664 Tabriz, Iran (e-mail: m.farhadi@tabrizu.ac.ir; e-babaei@tabrizu.ac.ir). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2012.2203339 some redundant switching states that can be used to regulate the capacitors voltage. However, the control scheme becomes complicated. Moreover, the number of capacitors increases by increasing the number of voltage levels. The CHB multilevel inverters use series-connected H-bridge cells with an isolated dc voltage sources connected to each cell. The CHB multilevel inverters can be divided into two groups from the viewpoint of values of the dc voltage sources: the symmetric and the asymmetric topology. In the symmetric topology, the values of all of the dc voltage sources are equal. This characteristic gives the topology good modularity. However, the number of the switching devices rapidly increases by increasing the number of output voltage level. In order to increase the number of output voltage level, the values of the dc voltage sources are selected to be different, these topologies are called asymmetric [7], [8]. The CHB multilevel inverters have been industrially employed in several applications fields such as pump, fans, compressors, etc. In addition, they have recently been proposed for other applications like photovoltaic power-conversion system and wind power conversion [9]. The topologies discussed previously are the conventional topologies. Many other multilevel inverter topologies have been introduced in recent years. One of the topologies is the modular multilevel inverter [10]. This topology is simpler than the cascaded four-switch H-bridge-based inverter and has several advantages, such as modular extension to any number of levels and redundancy [11]. However, the topology does not consider reduction in the number of components used. Other multilevel inverter topologies have been introduced in [12]–[15]. The multilevel inverter presented in [15] is based on symmetric topology and uses series/parallel connection of the dc voltage sources. This topology uses lower number of switches in comparison with the symmetric CHB multilevel inverter. The topologies presented in [12] and [13] consider reduction in the components. These topologies are basically based on asymmetric topologies; hence, the used dc voltage sources have different values. However, the number of switching devices still remains high in these topologies. A nine-level active NPC inverter has been presented in [16] which is the modification of the standard active NPC converter. Nami et al. [17] present a hybrid multilevel inverter using the CHB and the diode-clamped topology. This paper proposes a new multilevel inverter topology using series-connected submultilevel inverters. The proposed multilevel inverter uses reduced number of switches. Initially, the proposed submultilevel inverter is described and then the series connection of them to form a multilevel inverter is discussed. The optimal structures of the proposed multilevel inverter regarding several factors (e.g., number of switches, number of dc 0885-8993/$31.00 © 2012 IEEE
  2. 2. 626 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 2, FEBRUARY 2013 TABLE I OUTPUT VOLTAGES FOR STATES OF SWITCHES Fig. 1. Proposed generalized submultilevel inverter. voltage sources, standing voltage on the switches, etc.) are also obtained. The power loss of the proposed topology is calculated. Afterward, the proposed multilevel inverter is compared with other multilevel inverter topologies considering the number of switches. A design example is then given which is used for simulation and experimental studies. II. PROPOSED GENERALIZED MULTILEVEL INVERTER Considering Fig. 1, for each value of the output voltage of submultilevel inverter, two switches must be turned ON, one from the upper switches and the other from the lower switches. For example, to get output voltage of Vdc , the switches S1 and S2 are turned ON. In order to obtain the output voltage of (n − 1)Vdc , the switches Sn /2 and S(n +2)/2 should be turned ON. Considering Fig. 1, the following equations can be written: Nswitch,sub = 2, for n = 1 (n + 2), for n ≥ 2 (1) A. Proposed Submultilevel Inverter Ndriver,sub = Nswitch,sub (2) Fig. 1 shows the proposed submultilevel inverter. As depicted in Fig. 1, the topology consists of n dc voltage sources. In general, the dc voltage sources can have different values. However, in order to have equal voltage steps, they are considered to be the same and equal to Vdc . Each submultilevel inverter consists of n + 2 switches. Some of the switches are unidirectional and the others are bidirectional. The unidirectional switches consist of an insulated gate bipolar transistor (IGBT) with an antiparallel diode. The switches S1 , S1 , S(n +2)/2 , and S(n +2)/2 are unidirectional and the other switches are bidirectional; hence, they have to withstand both positive and negative voltages. For instance, when S(n +2)/2 is turned ON, the voltage Vdc is on the switch Sn /2 , and if the switch S(n −2)/2 is turned ON, the voltage equal to −Vdc is on the switch Sn /2 . The same conditions are valid for the other switches. Therefore, the switches have to withstand both positive and negative voltages. In addition, the switches have to conduct backward current that is as a result of inductive characteristic of the load. It can be concluded that the switches must be bidirectional. There are several circuit configurations for bidirectional switches. In this study, the common emitter topology is used as it needs one gate driver for a switch. Considering the types of the switches, 2n IGBTs are required in the proposed submultilevel inverter. It is worth mentioning that the number of the antiparallel diodes is equal to the number of IGBTs. The proposed submultilevel inverter can only generate zero and positive voltage levels. The zero output voltage is obtained when the switches S1 and S1 are turned ON simultaneously. The other voltage levels are generated by proper switching between the switches. Table I shows the states of the switches for each output voltage value. In this table, 1 means that the corresponding switch is turned ON and 0 indicates the OFF state. NIGBT,sub = 2n (3) Nsource,sub = n (4) where, Nswitch,sub , Ndriver,sub , NIGBT,sub , and Nsource,sub are the number of switches, number of switches drivers in one submultilevel inverter, number of IGBTs in one submultilevel inverter, and number of dc sources in one submultilevel inverter, respectively. For the proposed typical submultilevel inverter (see Fig. 1), the standing voltage on the switches is calculated. A switch experiences different off-state voltages in different switching combinations. Among these off-state voltages, the highest voltage is considered to be the standing voltage of the switch. This can be a criterion for voltage rating of the switch. For example, in Fig. 1, the switch S1 experiences the maximum off-state voltage when the switch S(n +2)/2 is turned ON that is equal to (n/2)Vdc . For the switch S2 , the standing voltage is (n/2 − 1)Vdc . For the switches S1 and S2 , the standing voltage is equal to (n/2)Vdc and (n/2 − 1)Vdc , respectively. This calculation can be done for any switch in the submultilevel inverter. The standing voltage for the submultilevel inverter is sum of all standing voltage on the switches in their off state [12]. For a submultilevel inverter including n dc voltage sources, the standing voltage on the switches depends on n and whether it is odd or even. For different n, the standing voltage on the switches of ith submultilevel inverter (Vstand,i ) can be obtained by (5), shown at the bottom of the next page. B. Proposed Generalized Multilevel Inverter The proposed submultilevel inverters can be connected in series to achieve the desired voltage and number of voltage
  3. 3. KANGARLU AND BABAEI: GENERALIZED CASCADED MULTILEVEL INVERTER Fig. 2. Proposed general multilevel inverter using series connection of m proposed submultilevel inverters, each one has n dc voltage sources. levels. Fig. 2 shows m submultilevel inverters in series. Each submultilevel inverter has n dc voltage source. The dc voltage sources in each submultilevel inverter are equal. The output voltage of the submultilevel inverters (and series connection of them) is always positive or zero. To operate as an inverter, it is necessary to change the voltage polarity in every half cycle. For this purpose, an H-bridge inverter is added to the output of the series connected submultilevel inverters. It is important to note that the switches of the H-bridge must withstand higher voltage. This should be considered in the design of the inverter. However, these switches are turned ON and OFF once during a fundamental cycle. So, these switches would be high-voltage low-frequency switches. Considering that the multilevel inverter shown in Fig. 2 includes m submultilevel inverter (using (1)–(4) and considering the H-bridge part), the following equations can be written: Nswitch = 2m + 4, for n = 1 m · (n + 2) + 4, for n ≥ 2 (6) Ndriver = Nswitch (7) NIGBT = 2mn + 4 (8) Nsource = mn (9) Vstand,i = 627 where Nswitch , Ndriver , NIGBT , and Nsource are the number of switches, number of switches drivers (which is equal to number of switches), number of IGBTs, and total number of dc sources, respectively. Considering (6) and (8), in general, the number of IGBTs is not equal to the number of switches in the proposed multilevel inverter; hence, some of the switches are bidirectional (which is considered as one switch) and consist of two IGBTs. The proposed topology can be extended to three-phase systems using three single-phase units. Like the other multilevel converters, the switches cannot be shared between the phases, and therefore, three single-phase structures should be used. In the extension of the proposed topology to the three-phase systems without using transformer, attention should be paid that the dc voltage sources in the different phases must be independent (isolated) so that the load can be star/delta connected. It is very important to note that also in the well-known CHB topology (extended to three-phase), independent dc voltage sources are required for different phases [18]. Therefore, from this point of view, the proposed topology acts as like as the CHB topology. Two conditions can be considered regarding the value of the dc voltage sources used in the proposed multilevel inverter; all of them can be equal leading to a symmetric topology or their values can be different leading to asymmetric topology. These two conditions are discussed as follows. 1) Proposed Symmetric Multilevel Inverter: For the symmetric multilevel inverter, all of the dc voltage sources are considered to be equal. Therefore, the following equations can be written for the symmetric topology: Vdc,1 = Vdc,2 = · · · = Vdc,m Nlevel = 2mn + 1 (11) where Nlevel is the number of output voltage levels. Since in the case of the symmetric topology the cascaded submultilevel inverters have the same condition, the following ⎧ ( n −1 ) −1 ⎪ ( n + 1 −1 )/2 4 2 ⎪ ⎪ 3n2 n−1 n+1 5 n−1 ⎪ ⎪2 − k Vdc,i + 2 − k Vdc,i + Vdc,i = +n+ Vdc,i ⎪ ⎪ ⎪ 2 2 4 8 8 ⎪ k =0 k =0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ n−1 ⎪ ⎪ is even if n is odd and ⎪ ⎪ 2 ⎪ ⎪ ⎪ ⎪ n −1 ⎪ ⎪ ( 2 −1 )/2 ( n + 1 −1 ) ⎪ 4 ⎪ ⎪ 3n2 n−1 n+1 5 n+1 ⎪2 ⎪ − k Vdc,i + 2 − k Vdc,i + Vdc,i = +n+ Vdc,i ⎪ ⎪ 2 2 4 8 8 ⎨ k =0 k =0 ⎪ n−1 ⎪ ⎪ ⎪ is odd if n is odd and ⎪ ⎪ 2 ⎪ ⎪ ⎪ ⎪ n ⎪ ( −1 )/2 ⎪ 2 ⎪ ⎪ 3n2 n 1 n ⎪ ⎪ ⎪4 − k Vdc,i = +n+ Vdc,i , if n is even and is odd ⎪ ⎪ 2 8 2 2 ⎪ ⎪ k =0 ⎪ ⎪ ⎪ ⎪ n ⎪ ( −1 ) ⎪ 4 ⎪ ⎪ 3n2 n n n ⎪ ⎪4 − k Vdc,i + Vdc,i = + n Vdc,i if n is even and is even ⎪ ⎩ 2 2 8 2 k =0 (10) (5)
  4. 4. 628 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 2, FEBRUARY 2013 relations can be expressed regarding the standing voltage on the switches: Vstand,1 = Vstand,2 = · · · = Vstand,m (12) Vstand,total = m · Vstand,1 + 4mnVdc,1 Nlevel − 1 2n Nlevel − 1 2 Vstand,1 + 4Vdc,1 n · (15) 2) Proposed Asymmetric Multilevel Inverter: For the asymmetric topology, the value of the dc voltage sources is different from a submultilevel inverter to another. In other words, if the dc sources of the first submultilevel inverter is Vdc,1 , the dc sources of the second submultilevel inverter is Vdc,2 . To get maximum number of level for the output voltage, there must be no redundancy. This is achieved when the value of the dc voltage sources in submultilevel inverters have the following relation: Vdc,2 = (n + 1) · Vdc,1 Vdc,3 = (n + 1)Vdc,1 + nVdc,2 = (n + 1)Vdc,1 + n(n + 1)Vdc,1 = (n + 1)(n + 1)Vdc,1 = (n + 1)2 Vdc,1 . (16) Therefore, in general, the following relation should be valid for the dc sources of the submultilevel inverters: Vdc,i = (n + 1)i−1 · Vdc,1 , i = 1, 2, 3, . . . , m (17) where Vdc,i is the value of the dc sources in the ith submultilevel inverter. The maximum value of the output voltage (sum of all dc voltage sources) for the proposed asymmetric topology can be obtained as follows: m Vo,m ax = n Vdc,i . (18) i=1 Using (17) and (18), the maximum value of the output voltage can be written as Vo,m ax = [(n + 1)m − 1]Vdc,1 . (19) With the aforementioned arrangement of the dc voltage sources, the number of voltage levels will be equal to Nlevel = 2(n + 1)m − 1. (20) For the asymmetric topology, the total standing voltage of the switches (Vstand,total ) is sum of standing voltages on the switches of the submultilevel inverters ( m Vstand,i ) and i=1 also the standing voltage on the switches of the H-bridge part (4Vo,m ax ). Therefore, it can be written as follows: m Vstand,total = Vstand,i + 4Vo,m ax . i=1 Using (20) and (22), the total standing voltage in terms of number of output voltage level and n can be expressed as follows: Vstand,total = . (21) (n + 1)m − 1 n · Vstand,1 + 4[(n + 1)m − 1] · Vdc,1 . (22) (14) From (13) and (14), the following equation is obtained: Vstand,total = Vstand,total = (13) where Vstand,total is the total standing voltage on the switches of the multilevel inverter. Using (11), m is obtained as follows: m= Using (5), (17), (19), and (21), the total standing voltage of the switches can be written as follows: Nlevel − 1 2 · Vstand,1 + 4Vdc,1 n . (23) C. Optimal Structures In this section, the aim is to determine the optimal structures considering different aspects. For the proposed multilevel inverter, there are two design parameters. The first parameter is the number of dc sources in each submultilevel inverter n and the other is the number of series connected submultilevel inverters, m. Both m and n affect maximum value of the output voltage. However, one of them can be used as a parameter for topology optimization and the other should be left to meet the desired maximum value of the output voltage (output voltage rating of the multilevel inverter). Here, m is used to meet the required nominal voltage. Therefore, n is used as a variable to determine the optimal structures. In the following, the optimal structures are discussed for the proposed symmetric and asymmetric multilevel inverters. 1) Optimal Structures of the Symmetric Topology: The aim is to determine the parameter n in order to use minimum number of IGBTs for a specific number of levels. Using (8) and (11), NIGBT can be written as follows: NIGBT = Nlevel + 3. (24) The aforementioned equation shows that for a specific value of the number of levels, the number of IGBTs is independent of n and it is constant. Therefore, variation of the parameter n does not affect the number of IGBTs. The same result is obtained for the case in which the aim is to have maximum number of voltage levels for a given number of IGBTs. Another aspect for optimization of the topology can be using the minimum number of gate driver circuits for a constant number of voltage levels. Using (6), (7), and (11), the number of the gate drivers (and its normalization) can be written as follows: ⎧ for n = 1 ⎨ (Nlevel − 1) + 4, Ndriver = n + 2 ⎩ (Nlevel − 1) + 4, for n ≥ 2 2n ⎧ 1, for n = 1 Ndriver − 4 ⎨ = n+2 Normalized Ndriver = ⎩ Nlevel − 1 , for n ≥ 2. 2n (25) Fig. 3 shows variation of the normalized value of the number of drivers versus n for a given number of voltage levels. The figure indicates that as n increases, the number of required
  5. 5. KANGARLU AND BABAEI: GENERALIZED CASCADED MULTILEVEL INVERTER 629 Fig. 3. Normalized N d rive r and normalized total standing voltage on the switches versus n for the symmetric topology. gate driver circuits decreases. Therefore, higher n gives better topology from the viewpoint of number of gate drivers. Standing voltage on the switches is the other factor which is considered for optimization of the topology. The aim is to determine n in a way that the total standing voltage is minimized for a given number of voltage levels. Using (15), the following equation is obtained: Vstand,total Vstand,1 −2= . (Nlevel − 1) · Vdc,1 2nVdc,1 (26) Fig. 3 also shows the variation of the normalized total standing voltage on the switches versus n. It is clear from the figure that the standing voltage on the switches is minimum for both n = 1 and n = 2. The higher values of n lead to a topology with higher standing voltage. In other words, the topology with n = 1 and n = 2 give the best topology from the viewpoint of standing voltage. From the previous discussion, it can be concluded that the value of n does not affect the number of IGBTs. However, as n goes up (higher than 2), the number of gate drivers decreases and, on the contrary, the standing voltage increases. This implies that a tradeoff may be considered between the number of gate drivers and standing voltage. For instance, n = 3 can be a candidate for the better topology in the symmetric condition. 2) Optimal Structures of the Asymmetric Topology: The first optimal structure is to determine n to obtain the maximum voltage level for a constant number of switches (or driver circuits). Using (6) and (20), the number of voltage levels in terms of number of switches is as follows: ⎧ N s w i t c h −4 2 ⎨ 2(2) − 1, for n = 1 Nlevel = N s w i t c h −4 ⎩ 2(n + 1) ( n + 2 ) − 1, for n ≥ 2 ⎧ 1 ⎨ 2(2 2 )N s w i t c h −4 − 1, for n = 1 = 1 (N s w i t c h −4) ⎩ 2 (n + 1) ( n + 2 ) − 1, for n ≥ 2. Normalized Vstand,total = (27) In (27), the number of switches is considered as a constant. Therefore, the number of voltage levels is maximized for such an n that maximizes the following term: 1 22 , D= (n + 1) for n = 1 1 (n + 2) , for n ≥ 2. (28) Fig. 4 shows the variation of D versus n. As the figure indicates, n = 1 gives the optimal structure from the viewpoint of number of switches. Fig. 4. Variation of D, (29), 2(n + 1)1 / 2 n , and n/ ln(n + 1) versus n. Similarly, another optimal structure can be obtained for minimizing the number of switches for a constant number of voltage levels. In this case, using (27), the following equation can be written: ⎧ 2 ⎪ for n = 1 ⎪ ⎨ ln 2 , Nswitch − 4 (29) = ⎪ (n + 2) ln N l e v2e l −4 ⎪ ⎩ , for n ≥ 2. ln(n + 1) The variation of (29) versus n is also depicted in Fig. 4. It is clear that n = 1 gives again the optimal structure. Considering (7), the number of gate drivers is equal to the number of switches. Therefore, n = 1 also gives the optimal structure from the viewpoint of minimum gate drivers. In the previous analysis, the number of switches was considered as a criterion for determining the optimal structures. As mentioned before, the number of switches is not equal to the number of IGBTs. If the number of IGBTs is used as a criterion, the results will be the same. Considering (8) and (20), the number of voltage levels as a function of n for a constant number of IGBTs is as follows: Nlevel = 2(n + 1) N I G B T −4 2n = 2 (n + 1) 1 2n −1 (N I G B T −4) − 1. (30) Taking into account that the number of IGBTs has been considered to be constant, in (30), the number of voltage levels will be maximum if the term 2(n + 1)1/2n is maximum. Fig. 4 also shows the variation of 2(n + 1)1/2n versus n. As this figure shows, the number of levels decreases as n increases. Therefore, the maximum number of voltage level for a constant number of IGBTs is obtained when n is equal to 1. The same result can be obtained for the minimum number of IGBTs for a constant number of voltage levels. The number of the dc voltage sources Nsource is the other variable which is used to obtain optimal topology. The aim is to minimize the number of required dc voltage sources for a specific number of voltage levels. Using (9) and (20), Nsource can be written as follows in terms of the number of output voltage levels and the number of dc voltage sources in each submultilevel inverter: Nsource = n · ln ln(n + 1) Nlevel + 1 2 . (31)
  6. 6. 630 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 2, FEBRUARY 2013 The aforementioned equation gets its minimum value when the term n/ ln(n + 1) is minimum. Variation of this term versus n is also shown in Fig. 4. It is clear that the minimum value is achieved when n = 1. To obtain the optimal structure from viewpoint of standing voltage on the switches, using (23), the normalized total standing voltage is obtained as follows: Vstand,total Vstand,1 −2= . (Nlevel − 1) · Vdc,1 2nVdc,1 (32) This equation is same as (26). Therefore, for the asymmetric topology (like the symmetric topology), the optimal structure considering the total standing voltage on the switches is achieved for n = 1 and n = 2. It is important to note that the standing voltage on the switches is the same for these two values of n. This is clear from Fig. 1 for n = 1 and n = 2. It can be concluded from the previous analysis that the optimal structure (for the asymmetric topology) from the viewpoint of the number of used switches, IGBTs, dc voltage sources, and the value of the standing voltage on the switches is obtained when n is 1. Normalized Vstand,total = III. CALCULATION OF LOSSES Typically, two kinds of losses are associated with power electronic converters. The conduction losses are caused by equivalent resistance and the on-state voltage drop of the semiconductor devices. The switching losses are caused by nonideal operation of switches. Calculation of the losses of the proposed multilevel inverter is discussed as follows. proposed submultilevel inverter can be calculated as follows: Pc,sub,j = 1 π π x(t)VT ,j + y(t)VD ,j +x(t)RT ,j iβ (t) + y(t)RD ,j i(t) 0 i(t) × d(ωt). (35) The specifications of the switches used in different submultilevel inverters may be different. Therefore, the index j in the aforementioned equation is used in order to refer to the jth submultilevel inverter. As the losses are calculated for the typical jth submultilevel inverter, it can be extended to other cascaded submultilevel inverters. As the conduction power loss of the cascaded submultilevel inverters are calculated one by one, they are added together to obtain the total conduction power loss Pc, sub of the cascaded submultilevel inverters: m Pc,sub = Pc,sub,j . (36) j =1 In the power loss calculated previously, the H-bridge part of the proposed multilevel inverter has not been considered. If the power factor angle is ϕ, then in every half cycle, the diodes and transistors of the H-bridge part conduct for time interval corresponding to ϕ and π−ϕ, respectively. If the output current is considered to be sinusoidal as i(t) = Im sin(ωt), the conduction power loss of the H-bridge can be obtained as follows: Pc,H = = A. Conduction Losses 1 π φ π 2pc,D (t)d(ωt) + 0 2pc,T (t)d(ωt) φ 2 2 RD ,H Im (2φ − sin(2φ)) VD ,H Im (1 − cos φ) + π 4 + VT ,H Im (1 + cos φ) In order to calculate the conduction losses, first conduction losses of a typical power transistor and diode are calculated; then they are developed to the multilevel inverter. The instantaneous conduction losses of a transistor (pc,T (t)) and diode (pc,D (t)) can be written as follows: π β + RT ,H Im+1 sinβ +1 (ωt)d(ωt) . (37) φ pc,T (t) = [VT + RT iβ (t)] i(t) (33) In the aforementioned equation, the index H indicates the parameters related to the H-bridge. The total conduction loss of the proposed multilevel inverter is obtained as follows: pc,D (t) = [VD + RD i(t)] i(t) (34) Pc = Pc,sub + Pc,H . where VT and VD are the on-state voltage of the transistor and diode, respectively. RT and RD are the equivalent resistance of the transistor and diode, respectively, and β is a constant related to the specification of the transistor. In the proposed submultilevel inverter, consider that there are x(t) transistors and y(t) diodes in the current path in any instant of time. The value of x(t) and y(t) depends on the output voltage level and operating conditions (mainly direction of the current). Considering Fig. 1, depending on the voltage level and current direction, in the proposed submultilevel inverter there might be two diodes, two transistors, one transistor and one diode, two diodes and one transistor, two transistors and one diode, and two transistors and two diodes in the current path. Therefore, using (33) and (34), the average conduction power loss of the (38) B. Switching Losses The switching losses are calculated for a typical switch, and then, the results are extended for the proposed multilevel inverter. For this calculation, the linear approximation of the voltage and current during switching period is used. Using this approximation, energy loss during the turn-off period of a switch can be obtained as follows: Eoff ,k to f f = to f f v(t)i(t)dt = 0 = 1 Vsw ,k I toff 6 0 Vsw ,k t toff − I toff (t − toff ) dt (39)
  7. 7. KANGARLU AND BABAEI: GENERALIZED CASCADED MULTILEVEL INVERTER Fig. 5. (a) Number of IGBTs and (b) number of driver circuits versus number of levels for the symmetric topologies. 631 Fig. 6. Standing voltage on the switches versus number of levels for the symmetric topologies. where Eoff ,k is the turn-off loss of the switch k, toff is the turnoff time of the switch, I is the current through the switch before turning OFF, and Vsw ,k is the off-state voltage on the switch. The turn-on loss of the switch can be calculated as follows: to n Eon,k = v(t)i(t)dt 0 to n Vsw ,k t ton = 0 − I (t − ton ) ton Fig. 7. (a) Per-unit conduction power loss and (b) per-unit switching power loss versus number of levels for the symmetric topologies (R T = 0.15 Ω, V T = 2.5 V, R D = 0.1 Ω, V D = 1.5 V, n = 3, to n = to ff = 2 μs). dt 1 = Vsw ,k I ton (40) 6 where Eon,k is the turn-on loss of the switch k, ton is the turn-on time of the switch, and I is the current through the switch after turning ON. The switching losses depend on the number of switching transitions. Therefore, it depends on the modulation method. Generally, the average switching power loss can be written as follows: ⎛ ⎞⎤ ⎡ Nsw itch Psw = 2f ⎣ ⎝ Non ,k Eon,k i + i=1 k =1 No ff , k Eoff ,k i ⎠⎦ (41) i=1 where f is the fundamental frequency, Non,k and Noff ,k are the number of turning ON and OFF the switch k during a half fundamental cycle. Also, Eon,k i is the energy loss of the switch k during the ith turning ON and Eoff ,k i is the energy loss of the switch k during the ith turning OFF. Using (38) and (41), the total losses of the multilevel inverter will be PLoss = Pc + Psw . (42) IV. COMPARISON OF THE PROPOSED TOPOLOGY WITH THE OTHER TOPOLOGIES A. Symmetric Topology Fig. 5(a) shows the number of IGBTs versus the number of voltage levels in different topologies. As the figure shows, for any specific value of Nlevel , the proposed topology uses lower number of IGBTs in comparison with [15] and CHB. The required number of gate driver circuits in the aforementioned topologies versus Nlevel is shown in Fig. 5(b). The figure clearly shows that the proposed topology uses the least Ndriver . Standing voltage on the switches of the topologies is presented in Fig. 6. The figure shows that the CHB has the best characteristic from the viewpoint of standing voltage on the switches and the proposed topology is better than [15] in terms of standing voltage on the switches. Fig. 7(a) and (b) shows the calculated per-unit conduction and switching power loss of the topologies, respectively. To draw the figures, n is considered to be 3 (n = 3) and m varies as the number of levels varies. Also, for all of the transistors, the on-state resistance and voltage drop are considered to be 0.15 Ω (RT = 0.15 Ω) and 2.5 V (VT = 2.5 V), respectively. The on-state resistance and voltage drop of the diodes are assumed to be 0.1 Ω (RD = 0.1 Ω) and 1.5 (VD = 1.5 V), respectively. The on-time ton and off-time toff of the switches is assumed 2 μs. Each dc voltage source has the value of 100 V. The resistance of the load is 45 Ω and its inductance is 55 mH so that ϕ = 21◦ . It is important to note that the base value for the per-unit losses is the converter rated output power. As Fig. 7(a) shows, the proposed topology and that of [15] have lower conduction loss than the CHB. Also, the conduction power loss of the proposed topology is lower than that of [15]. This result was predictable since the number of semiconductor devices in the current path in any instant of time for the proposed topology is lower than that of the other two topologies. However, this number is close for the proposed topology and [15]. According to Fig. 7(b), switching power loss of the proposed topology is lower than that of [15]. However, the switching power loss of the proposed topology is higher than that of CHB. It is worth mentioning that the conduction losses are the major part of the losses. Despite the number of IGBTs, in the proposed symmetric topology, variety of the switches in terms of the voltage ratings is higher than the symmetric CHB topology. This can be considered a disadvantage for the proposed symmetric topology when comparing with the symmetric CHB topology. In the proposed symmetric topology with n = 3, three different kinds of switches in terms of voltage ratings are required. However, the proposed topology considerable reduces the total number of switches.
  8. 8. 632 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 2, FEBRUARY 2013 Fig. 11. Sum of the standing voltage on the switches for different topologies. Fig. 8. Number of IGBTs versus the number of output voltage level in the submultilevel inverters. Fig. 9. Standing voltage on the switches versus the number of output voltage level in the submultilevel inverters. Fig. 10. Number of IGBTs versus the number of output voltage levels. B. Asymmetric Topology The proposed topology in this paper is compared with the topologies presented in [12] and [13] and the asymmetric CHB topology. Initially, the proposed submultilevel inverter (see Fig. 1) is compared with the submultilevel inverters proposed in [12] and [13]. It is noticeable that the submultilevel inverter is called as basic unit in [12] and [13]. The number of IGBTs versus the number of voltage levels is shown in Fig. 8 for the proposed submultilevel inverter and the basic units presented in [12] and [13]. As shown in Fig. 8, the proposed submultilevel inverter uses lower number of IGBTs in comparison with the others. Fig. 9 shows the sum of the standing voltage on the switches for the submultilevel inverters. As shown in the figure, the proposed submultilevel inverter has a better condition from the viewpoint of standing voltage on the switches. In the previous comparison, the submultilevel inverters have been compared together. Here, the aim is to compare the multilevel inverters resulted from series connection of the submultilevel inverters. For the comparison purpose, the required number of IGBTs for each number of output voltage levels is depicted in Fig. 10. It can be seen from this figure that the proposed topology uses a considerable lower number of IGBTs for any specific number of output voltage level in comparison with the topologies presented in [12] and [13] and the asymmetric CHB topology. For the topology presented in [13], the optimal topology derived in [19] is used for comparison. Fig. 12. (a) Per-unit conduction losses and (b) per-unit switching losses for the proposed asymmetric topology and the asymmetric CHB topology (R T = 0.15 Ω, V T = 2.5 V, R D = 0.1 Ω, V D = 1.5 V, n = 1, to n = to ff = 2 μs). The other aspect of comparison is the standing voltage on the switches. Fig. 11 shows the sum of standing voltage on the switches for different topologies. The standing voltage is stated in per unit where the base value is the value of the dc voltage source in the first submultilevel inverter (i.e., Vdc,1 = 1 p.u.). As shown in the figure, the standing voltage on the switches of the proposed topology is lower than the topology presented in [12] and [13]. However, the standing voltage of the CHB topology is lower than all of the topologies. Fig. 12(a) and (b), respectively, shows the per-unit conduction and switching losses of the proposed topology and that of the asymmetric CHB topology. The characteristic of the switches and the load data is the same as the symmetric one given in the previous section. The base value for per unit is the rated converter output power. In this case, the value of n is considered to be 1. Fig. 12(a) shows that the proposed topology has lower conduction losses due to lower number of semiconductor devices that are in the current path in any instant of time. Also, according to Fig. 12(b), the switching power loss of the proposed topology is slightly lower than that of the asymmetric CHB. The topologies in [12] and [13] are not considered in this comparison since they need snubber circuits for their bidirectional switches, which makes the calculation of their losses different. Also, the snubber circuit will increase the losses of [12] and [13]. The variety of the switches in the proposed asymmetric topology (with n = 1) and the asymmetric CHB topology is shown in Fig. 13. The variety of the switches indicates requirement for switches with different voltage ratings. As shown in the figure, both of the topologies need switches with different voltage ratings. However, for any number of levels, the proposed asymmetric topology needs one more different switch than the asymmetric topology. Therefore, the requirement for different switches is almost equal for both of the topologies.
  9. 9. KANGARLU AND BABAEI: GENERALIZED CASCADED MULTILEVEL INVERTER 633 TABLE II TYPICAL IGBTS IN DIFFERENT VOLTAGE RATINGS Fig. 13. Variety of the switches versus the number of output voltage levels. V. MEDIUM-VOLTAGE APPLICATION CONSIDERATIONS Theoretically, the proposed topologies can be designed for any voltage level. However, practically there are limitations when applying the topologies in medium- and high-voltage applications. Considering the switches used in the H-bridge part of the proposed topologies (T1 − T4 ), these switches must be able to tolerate a voltage equal to the rated output voltage of the multilevel inverter. These switches turn ON and OFF once during a fundamental cycle. Also, they are switched in zero voltage condition; hence, the switches of the submultilevel inverters provide zero voltage level when the switches operate. Besides these facts, the four mentioned switches restrict the application of the proposed topologies for high voltage. It is very important to note that this problem is not just for the proposed topology. The topologies in which a high-voltage H-bridge is used (e.g., the topologies presented in [12], [15], and [20]) have the same problem. In these topologies, the switches of the high-voltage H-bridge have to tolerate a voltage equal to sum of all dc voltage sources. In other words, in the proposed topology and that of, e.g., [12], [15], and [20], there are four switches that must be able to operate in the rated voltage of the inverter. As a result, it is necessary to determine the voltage level in which the application of the proposed topology is advantageous. One main criterion is to avoid series connection of the switches to form a high-voltage switch, otherwise the proposed topology will not show its advantages. Assume that the highest voltage common commercial IGBT has a voltage rating equal to VIGBT,m ax . Then, the maximum operating voltage (three-phase line–line rms voltage) of the proposed topology can be written as follows: Vrated = 3 VIGBT,m ax · 2 α (43) where Vrated is the rated three-phase line–line rms voltage of the proposed multilevel inverter and α (safety factor) is a factor to ensure the safe operation of the IGBT in practice. It may be considered about α = 1.7. If (43) is satisfied, then the series connection of the switches will not be required. In other words, (43) can be used to determine the voltage rating of the proposed topology based on the availability of the IGBT or it can be used to determine the voltage rating of the highest voltage IGBT required for a specific rated voltage of the multilevel inverter. Two examples of medium-voltage design are given as follows. For the first example, suppose that the highest voltage commercially available IGBT voltage rating is 3300 V (VIGBT,m ax = 3300 V). Using (43), the rated three-phase line– line voltage will be equal to about 2.3 kV. If the proposed 31-level asymmetric topology (with n = 1 as shown in Fig. 16) is considered, to produce such a voltage, the values of the dc sources will be 125.2, 250.4, 500.8, and 1001.6 V. Table II shows an example of commercially common IGBT voltage ratings. Considering the commercial IGBTs and taking into account Fig. 16, two 250-V IGBTs for switches S1 and S1 , two 600-V IGBTs for switches S2 and S2 , two 1200-V IGBTs for switches S3 and S3 , two 1700-V IGBTs for switches S4 and S4 , and four 3300-V IGBTs for switches T1 − T4 are required in the proposed topology. It is very important to note that although these switches are high-voltage switches, they operate in fundamental frequency and zero voltage condition. On the other hand, if the asymmetric CHB topology is considered, four 250-V, four 600-V, four 1200-V, and four 1700-V IGBTs will be required. As another example of high-voltage, another design is considered for three-phase 6-kV rms line–line voltage. So, the peak voltage will be about 4.9 kV. Considering the 31-level inverter (see Fig. 16), the value of the dc voltage sources will be about 327, 654, 1307, and 2612 V. Therefore, considering the voltage rating of the commercial IGBTs, the IGBTs with the voltage ratings of 600 V (for S1 and S1 ), 1200 V (for S2 and S2 ), 2500 V (for S3 and S3 ), and 4500 V (for S4 and S4 ) can be used which are available. For high-voltage operation, the switches may be connected in series [21], [22], and for high-current application they may be connected in parallel [21], [23]. However, special attention should be paid to distribute the voltage on them equally and synchronous operation of them. In order to equally distribute voltage on the switches, balancing resistors should be used [21], [24]. For the mentioned example, the switches T1 − T4 of the proposed topology will need series-connected IGBTs (each of the switches may require two 3300-V or two 4500-V IGBTs). Therefore, application of the proposed multilevel inverter in this voltage level is challenging (although it is possible). As a result, it is recommended that (43) to be satisfied when using the proposed topology in medium-voltage applications. Form the two examples discussed previously, it can be concluded that with today’s semiconductor technology, the proposed topology and the topologies presented in [12], [15], and [20] are not well suited for higher voltages since they use an H-bridge, the switches of which have to withstand a voltage equal to rated voltage of the multilevel inverter. Therefore, with the existing IGBTs, they are recommended for low-voltage applications. However, the semiconductor technology is progressing with a considerable rate. Some years back, IGBTs even with voltage ratings presented in Table II (e.g., 3300 V, 4500 V) did not exist. Considering the progressing trend of the semiconductor technology, in future higher voltage IGBTs will be produced
  10. 10. 634 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 2, FEBRUARY 2013 Fig. 14. Thirteen-level inverter based on the proposed symmetric topology with n = 3 and m = 2. Fig. 16. Thirty-one-level inverter based on the proposed optimal structure with n = 1 and m = 4 (used for simulations and experimentation). operates as a low-pass filter for the current. The load current has also phase difference with the load voltage because of inductive characteristic of the load. Fig. 15. Simulation results for the 13-level symmetric topology. B. Asymmetric Topology commercially. This will make the mentioned topologies suitable for medium-voltage applications. VI. SIMULATION AND EXPERIMENTAL RESULTS This section deals with the simulation and experimental validation of the proposed multilevel inverter topology. For the proposed symmetric multilevel inverter, only the simulation results are presented, but, for the asymmetric topology both simulation and experimental results are given. For all of the studies, the load is an RL load with the value of 45 Ω and 55 mH. The output voltage frequency is assumed 50 Hz. There are many control methods for multilevel inverter. It is noticeable that the staircase control method is used in this paper [1]. The term staircase control method is used to state that in this method, transition from one level of voltage to the next level happens once as shown in Fig. 15 (for example). This control method tends to generate a staircase voltage which minimizes the error with respect to the reference voltage. It is worth noting that the calculation of optimal switching angles for different goals, such as elimination of the selected harmonics and minimizing total harmonic distortion (THD), is not the objective of this paper. A. Symmetric Topology Fig. 14 shows the 13-level inverter based on the proposed symmetric multilevel inverter with n = 3. Six dc voltage sources each of them 100 V have been used so that the maximum output voltage will be 600 V. The number of IGBTs for a 13-level inverter in the proposed topology is 16. For the same number of voltage levels, the topology of [15] and CHB use 19 and 24 IGBTs, respectively, which are higher than that of the proposed topology. Fig. 15 shows the load voltage and scaled load current of the 13-level inverter. As the figure shows, all of the expected voltage levels are generated at the output voltage. The load voltage is sine-waved current as a result of the RL load which For the asymmetric topology, first a design example of the proposed multilevel inverter is given and then it is used for simulation and experimental studies. 1) Design Example: The aim is to design a peak 150-V multilevel inverter with minimum 30 levels of output voltage. As discussed before, the proposed multilevel inverter is optimal for n = 1 from different points of view. In order the number of output voltage level to be higher than its minimum (i.e., 30), the number of cascaded submultilevel inverters should be 4 (m = 4). Therefore, a 31-level 150-V inverter based on the proposed generalized multilevel inverter regarding the optimal structures will be as shown in Fig. 16 in which the values of the dc voltage sources are shown in the figure. The proposed 31-level inverter in Fig. 16 uses 12 IGBTs. The number of the dc sources is 4 with binary increment. On the other hand, a 21-level inverter based on the topology presented in [13] uses 20 IGBTs which is much more than the number of IGBTs in the proposed topology, and at the same time, the number of output voltage level is lower than that of the proposed topology. A 17-level inverter based on [12] uses 16 IGBTs and 4 dc voltage sources. In comparison with the proposed topology, shown in Fig. 16, the topology presented in [12] uses more IGBTs, and at the same time, the number of output voltage levels is considerably lower. 2) Simulation and Experimental Results: The validity of the proposed multilevel inverter is demonstrated with both simulation and experimental results. For the simulation and experimentation, the 31-level inverter shown in Fig. 16 is used. The BUP306D-type IGBTs are used. Also the AT89C52 microcontroller is used to prepare gate signals for the switches. Tektronix TDS 2024B four-channel digital storage oscilloscope is used for measurements in laboratory. Each switch has a driver circuit. The driver circuit used in this paper consists of an optoisolator, a Schmit trigger, and a buffer. For a switch in the inverter, an isolated driver circuit is required. The isolation is achieved using optoisolators. The states of the switches in different voltage levels have been stored in the microcontroller as a lookup table. The microcontroller provides the switching signals for the driver circuits and the driver circuits drive the switches. In the
  11. 11. KANGARLU AND BABAEI: GENERALIZED CASCADED MULTILEVEL INVERTER 635 Fig. 19. Experimental results. From top to bottom, the traces are output voltage of cascaded submultilevel inverters, load voltage, and load current. Fig. 17. Output voltage of each submultilevel inverter: from top to bottom traces are first, second, third, and fourth submultilevel inverter output voltage, respectively. Fig. 18. (Upper trace) Output voltage of cascaded submultilevel inverters. (Lower trace) Load voltage and scaled load current. experimental prototype, the constant dc supplies existing in the laboratory have been used as the dc voltage sources. In order to generate the triggering signals for the switches used in the inverter, the reference output voltage is compared with the available voltage levels. These levels are determined by the available dc voltage sources and operation modes of the inverter. Then, the switches that generate the nearest voltage level to the reference output voltage are turned on. As an example, when the voltage level of 30 V (in Fig. 16) is nearest to the reference output voltage, the switches S1 , S2 , S3 , and S4 are turned ON and the other switches are turned OFF. Fig. 17 shows the output voltage of each submultilevel inverter shown in Fig. 16. Clearly, the output voltage of each submultilevel inverter corresponds to its dc voltage sources. Considering the figure, the first submultilevel inverter operates with the lowest voltage, but in return its operating frequency is highest among the submultilevel inverters. Inversely, the last submultilevel inverter operates with highest voltage and lowest frequency. The switching frequency of the switches S1 –S4 is 1500, 720, 300, and 100 Hz, respectively. Fig. 18 shows the output voltage of the cascaded submultilevel inverters, load voltage, and scaled load current. As shown in the figure, the output voltage of the cascaded submultilevel inverters is always nonnegative. The polarity of the voltage is changed using the H-bridge connected to the output of the submultilevel inverters. The load current is scaled to become visible in the same frame with the load voltage. In the test condition (R = 45 Ω, L = 55 mH, Vo,m ax = 150 V), the power loss of the proposed multilevel inverter, shown in Fig. 16, is about 12 W. However, the power loss of the asymmetric CHB topology with the same conditions (with the same value of voltage and load) is about 15.5 W. This can be as a result of the fact that in the proposed topology, less semiconductor devices are in the current path in any instant of time in comparison with the asymmetric CHB topology. In this condition, output active power of the inverter is about 217 W. Also, the specification of the switches (their resistance and on-state voltage) is as given in Section IV. Fig. 19 shows the experimental results. The upper trace of the figure shows the total output voltage of the cascaded submultilevel inverters. The middle trace shows the load voltage and the lower trace shows the load current. The load voltage and current THD is %1.44 and %0.2, respectively. The figures show a good correspondence with the simulation results. In practice, the switches are not ideal and they have voltage drop in their on-state due to resistance and reverse on-state voltage of them. Therefore, the peak of the output voltage may not reach 150 V because of some voltage drop on the switches. VII. CONCLUSION In this paper, initially, a submultilevel inverter has been proposed and then the cascaded submultilevel inverters have been considered as a generalized multilevel inverter in both symmetric and asymmetric conditions. The number of the dc voltage sources in each submultilevel inverter is equal, but their values are different from one submultilevel inverter to another. Therefore, the proposed multilevel inverter can be categorized in asymmetric group. The optimal structures for the proposed multilevel inverter were obtained considering several factors such as the number of switching devices, number of dc voltage sources, number of output voltage levels, standing voltage on the switches etc. For the asymmetric topology, almost all of the
  12. 12. 636 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 2, FEBRUARY 2013 factors dictate that the number of dc voltage sources per submultilevel inverter should be 1. The comparison between the proposed topology and the topologies presented in [12], [13], and [15] and the CHB topologies has been presented considering several factors. The simulation results of a 13-level symmetric topology based on the proposed multilevel inverter have been presented. In the case of asymmetric topology, the simulation and experimental results have been presented for a 31-level inverter based on the proposed optimal structure to validate the ability of the proposed topology in generating of desired output voltage. REFERENCES [1] J. Rodriguez, J. S. Lai, and F. Z. Peng, “Multilevel inverters: A survey of topologies, controls, and applications,” IEEE Trans. Ind. Electron., vol. 49, no. 4, pp. 724–738, Aug. 2002. [2] J. H. Kim, S. K. Sul, and P. N. 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Electron., vol. 58, no. 8, pp. 2643–2650, Aug. 2010. [16] J. Li, S. Bhattacharya, and A. Q. Huang, “A new nine-level active NPC (ANPC) converter for grid connection of large wind turbines for distributed generation,” IEEE Trans. Power Electron., vol. 26, no. 3, pp. 961–972, Mar. 2010. [17] A. Nami, F. Zare, A. Ghosh, and F. Blaabjerg, “A hybrid cascade converter topology with series-connected symmetrical and asymmetrical diodeclamped H-bridge cells,” IEEE Trans. Power Electron., vol. 26, no. 1, pp. 51–64, Jan. 2011. [18] L. M. Tolbert, F. Z. Peng, and T. G. Habetler, “Multilevel converters for large electric drives,” IEEE Trans. Ind. App., vol. 35, no. 1, pp. 36–44, Jan./Feb. 1999. [19] E. Babaei, “Optimal topologies for cascaded sub-multilevel inverters,” J. Power Electron., vol. 10, no. 3, pp. 251–261, May 2010. [20] W. K. Choi and F. S. Kang, “H-bridge based multilevel inverter using PWM switching function,” in Proc. Int. Telecomm. Energy Conf., 2009, pp. 1–5. [21] J. F. Chen, J. N. Lin, and T. H. Ai, “The techniques of the serial and paralleled IGBTs,” in Proc. IEEE Ind. Electron. Soc., 1994, vol. 2, pp. 999– 1004. [22] Y. Xiao, B. Wu, F. A. DeWinter, and Reza Sotudeh, “A dual GTO currentsource converter topology with sinusoidal inputs for high-power applications,” IEEE Trans. Ind. Appl., vol. 34, no. 4, pp. 878–884, Jul./Aug. 1998. [23] B. Abdi, A. H. Ranjbar, G. B. Gharehpetian, and J. Milimonfared, “Reliability considerations for parallel performance of semiconductor switches in high-power switching power supplies,” IEEE Trans. Ind. Electron., vol. 56, no. 6, pp. 2133–2139, Jun. 2009. [24] M. H. Rashid, Power Electronics: Circuits, Devices and Applications, 3rd ed. Upper Saddle River, NJ: Pearson Education, 2003. Mohammad Farhadi Kangarlu (S’09) was born in Kangarlu, East Azerbaijan, Iran, in 1987. He received the B.S. and M.S. degrees (first class Hons.) both in electrical power engineering from the University of Tabriz, Tabriz, Iran, in 2008 and 2010, respectively, where he is currently working toward the Ph.D. degree in electrical power engineering (power electronics and systems). He is the author or coauthor of more than 25 journal and conference papers and one book. He also holds seven patents in the area of power electronics. His research interests include power electronic converters analysis and design, power quality, and custom power devices. Dr. Farhadi Kangarlu received the Best Researcher Award of the East Azerbaijan Province in 2011. He also received the Distinguished Student Award of the University of Tabriz in 2007 and 2011. Ebrahim Babaei (M’10) was born in Ahar, Iran, in 1970. He received the B.S. and M.S. degrees (first class Hons.) in electrical engineering from the Department of Engineering, University of Tabriz, Tabriz, Iran, in 1992 and 2001, respectively, where he also received the Ph.D. degree in electrical engineering from the Department of Electrical and Computer Engineering, in 2007. In 2004, he joined the Faculty of Electrical and Computer Engineering, University of Tabriz. He was an Assistant Professor from 2007 to 2011 and has been an Associate Professor since 2011. He is the author of more than 140 journal and conference papers. His current research interests include the analysis and control of power electronic converters, matrix converters, multilevel converters, flexible ac transmission systems devices, power system transients, and power system dynamics.

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