Multilevel Multiphase Feedforward Space-Vector Modulation Technique

Multilevel Multiphase Feed-forward Space Vector Modulation Technique J. I. Leon, Member,IEEE, O. Lopez, Member, L. G. Franquelo, Fellow Member,IEEE, J. Doval-Gandoy, Member,IEEE, S. Vazquez, Member,IEEE, J. Alvarez and F. D. Freijedo, Member,IEEE Abstract—Multiphase converters are being applied to an increasing number of industrial applications in recent years. On the other hand, multilevel converters have become a mature technology mainly in medium and high power applications. One of the problems of multilevel converters is the dc voltage unbalance of the dc bus. Depending on the loading conditions and the number of levels of the converter, oscillations appear in the dc voltages of the DC-Link. This paper presents a feedforward modulation technique for multilevel multiphase converters that reduces the distortion under balanced or unbalanced dc conditions. The proposed modulation method can be applied to any multilevel converter topology with any number of levels and phases. Experimental results are shown in order to validate the proposed feed-forward modulation technique. I. INTRODUCTION MULTIPHASE variable-speed drives field has experienced a substantial growth since the beginning of this century. There has been a rapid development in some specific application areas such as: electric ship propulsion, locomotive traction, industrial high-power applications, electric and hybrid-electric vehicles, electric aircrafts, etc... [1]–[5]. Recent developments in the field of multiphase variable speed drives have led to a corresponding development of pulsewidth modulation (PWM) schemes for multiphase inverters used in these drives. Most of the existing research related to PWM control of multiphase inverters applies to two-level inverters [6]–[9]. However, the use of multilevel inverters for multiphase variable speed drives has been established as a good solution in high power applications such as electric ship propulsion and locomotive traction [10]–[13]. Multilevel topologies considered in the literature are typically either diode-clamped, flying capacitor or cascaded H-bridge converters [14]–[17]. Several space vector modulation techniques have been presented recently applied to multiphase converters of twolevel voltage source type [18]–[20]. In [21], a general space vector modulation algorithm that can be applied to multilevel multiphase converters with any number of phases and levels was presented. This algorithm, called multilevel multiphase space vector modulation (MSVM) in this paper, is based on a Manuscript received June 17, 2009. Accepted for publication September 26, 2009. Copyright c °2009 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. J. I. Leon, L. G. Franquelo and S. Vazquez are with the Electronic Engineering Department, University of Seville (Spain), (e-mail: [email protected]). O. Lopez, J. Doval-Gandoy, J. Alvarez and F. D. Freijedo are with the Electronic Engineering Department, University of Vigo (Spain). reduction of the multilevel multiphase modulation problem to a two-level multiphase modulation problem using a two-level multiphase modulator. This two-level modulator is fed with the fractional part of the reference voltage vector to obtain a matrix, which includes a displaced switching vector sequence, and the switching times. The final switching sequence is calculated adding the integer part of the reference to the vectors of that sequence. This paper introduces a new feed-forward space vector modulation technique for multilevel multiphase power converters called multilevel multiphase feed-forward space vector modulation (MFFSVM). This modulation algorithm is a feedforward version of the MSVM technique. In this way, the notation introduced in [21] has been used to explain the proposed MFFSVM strategy. This paper is organized as follows: In section II the aim of the MFFSVM technique is presented. The mathematical description of the MFFSVM strategy is introduced in section III. An example to show the good performance of the proposed idea is shown in section IV. Finally, experimental results and conclusions of the work are presented in section V and section VI respectively. II. AIM OF THE PROPOSED MODULATION STRATEGY In the most common multilevel converter topologies such as flying capacitor, diode-clamped, cascaded full-bridge or hybrid converters, the possible output voltages of each phase are equally distributed being an integer multiple of a fixed voltage step [14], [15]. However, in asymmetrical multilevel converters, this voltage condition is not true because unequal voltage steps are present in the power converter operation [22]–[24]. In both cases, symmetrical or asymmetrical multilevel converters, the control of the dc voltage balance can not be accurately achieved in all loading conditions. Load imbalances and nonlinear or transient loads have a significant impact on the multilevel converter dc voltages ripple (oscillations or actual values) [25]–[28]. As a consequence, transient imbalances and steady state oscillations can be present in the power converter operation. These phenomena lead to distorted output waveforms because the modulators usually do not take into account the actual dc voltage unbalance. Recently a work has been introduced in order to eliminate this distortion in three-level diode-clamped converters [29]. The previous MSVM technique can be applied to multilevel converters where the output voltage step between all the consecutive voltage levels is constant. However, under unbalanced dc voltages this voltage step is not constant in general. In this case, the MSVM technique generates errors in the modulated waveforms leading to undesired distortion. The modulation technique proposed in this work solves this problem using the feed-forward concept. Some modulation strategies present in the literature use the feed-forward concept in order to achieve modulated output waveforms with low distortion for multilevel converters [30]–[33]. The feed-forward basic idea is to measure the actual dc voltages of the multilevel converter and generate the switching of the power converter taking them into account. In this way, the averaged value of the modulated output waveforms coincides with the desired reference. The proposed feed-forward space vector modulation strategy, called in this paper MFFSVM, is a simple method that can be applied to multilevel multiphase converters. III. ENHANCED FEED-FORWARD MULTILEVEL MULTIPHASE SVM TECHNIQUE (MFFSVM) In a space-vector modulation (SVM) technique, the reference vector Vris generated by means of a sequence of space states or switching vectors {Vs1,Vs2,. . . ,Vs(P+1)}.P is the number of phases of the multilevel multiphase converter. To achieve a proper synthesis of the reference vector over a switching period Tsw, each switching vector Vsk must be applied during an interval Tk. Vr=1 Tsw P+1 X k=1 VskTk P+1 X k=1 Tk=Tsw (1) The reference vector Vris composed of the voltage reference for each phase of the system. Switching times vector T is composed of the switching times of the switching sequence. Vr= [V1 r, V 2 r,· · · , V P r]T∈RP Vsk = [V1 sk, V 2 sk,· · · , V P sk]T∈RP T= [T1, T2,· · · , TP+1]∈RP+1 (2) Each phase jof the power converter can achieve in general Ndifferent output voltage levels and each one of these voltages is described as Vj sk (possible output voltage number kof phase j). Each possible output phase voltage Vj sk is achieved by a specific and known switching configuration of the phase jof the power converter denoted Sj k. The possible switching configurations of the power converter Sj kand the corresponding phase voltages Vj sk are used to define matrices S and Mvrespectively. These matrices depend on the multilevel converter topology. This is the only step of the MFFSVM technique that depends on the topology of the power converter. S=     S1 1S1 2. . . S1 N S2 1S2 2. . . S2 N . . .. . ..... . . SP 1SP 2. . . SP N      (3) Mv=     V1 s1V1 s2. . . V 1 sN V2 s1V2 s2. . . V 2 sN . . .. . ..... . . VP s1VP s2. . . V P sN      (4) The next step of the proposed MFFSVM technique is to generate matrix Mowhich contains the elements of matrix Mvbut ordered in increasing order. Matrix So(with elements called Sj ok) is obtained from matrix Sordering their elements in the order obtained in matrix Mo. In this way, each element Vj ok is still related to switching configuration Sj ok. So=     S1 o1S1 o2. . . S1 oN S2 o1S2 o2. . . S2 oN . . .. . ..... . . SP o1SP o2. . . SP oN      Mo=     V1 o1V1 o2. . . V 1 oN V2 o1V2 o2. . . V 2 oN . . .. . ..... . . VP o1VP o2. . . V P oN      where Vj ok ≤Vj ok+1 (5) In order to consider any dc voltage in the multilevel power converter, voltage vectors Vrand Vsk and switching times vector Tare normalized determining respectively vectors vr and vsk and t. It is important to remark that all vrand vsk and tbelong to the multidimensional space of real numbers RP≥ 0. The normalization of the voltage vectors is done using the lowest output voltage of each phase and the difference between the highest and the lowest output voltages of each phase. On the other hand, the switching times vector is normalized using the switching period Tsw. These calculations force that the values of all the normalized voltage vector components are in the range [0,1]. vr= [υ1 r, υ2 r, . . . , υP r]T vsk = [υ1 sk, υ2 sk, . . . , υP sj]T t= [t1, t2, . . . , tP+1](6) υj r=Vj r−Vj o1 Vj oN −Vj o1 ∈R υj sk =Vsk −Vj o1 Vj oN −Vj o1 ∈R tk=Tk Tsw (7) Each element Vj ok of the output voltages matrix Mois also normalized obtaining the normalized positive matrix of possible output voltages of the power converter mo. mo=     υ1 o1υ1 o2. . . υ1 oN υ2 o1υ2 o2. . . υ2 oN . . .. . ..... . . υP o1υP o2. . . υP oN      where υj ok =Vj ok −Vj o1 Vj oN −Vj o1 ∈R(8) Each component of the normalized reference vector vris compared with the corresponding output voltages of its phase obtaining matrix mc. mc=     υ1 c1υ1 c2. . . υ1 ck υ2 c1υ2 c2. . . υ2 ck . . .. . ..... . . υP c1υP c2. . . υP ck      where υj ck =½−1if υj ok > υj r υj ok otherwise (9) The normalized reference vector vris decomposed into the sum of its nearest possible normalized positive voltage level towards to zero achieved by the power converter vnand the rest vf. vr=vn+vf vn= [υ1 n, υ2 n,· · · , υP n]T∈RP vf= [υ1 f, υ2 f,· · · , υP f]T∈RP(10) Elements of vector vncan be easily determined. Components υj nare real numbers and are equal to some element of the row jof matrix mo. Therefore, υj nare normalized values of one output voltage of phase jof the power converter present in matrix Mowhich can be directly achieved by a specific switching state Sj ok of phase jin matrix So. Therefore, vector vncan be achieved using a switching vector of the power converter. υj n=max[υj c1, υj c2,· · · , υj cN ] = υj cm (11) The rest of the voltage vector vfis determined as the difference between vrand vnas was introduced in section III. υj f=υj r−υj n(12) Vector vfalso belongs to the space RPbut it cannot be directly synthesized by means of a single switching vector. It has to be approximated with a sequence of two switching vectors. The first switching vector is vnand the second switching vector is defined as vector vn+1 that can be obtained from matrix mc. This second switching vector vn+1 is achieved by the switching state Sj om+1 of phase jin matrix So. υj n+1 =υj cm+1 (13) The final step of the proposed MFFSVM technique uses the two-level multiphase SVM algorithm presented in [21]. In order to use it, vector vfhas to be normalized using the difference between the υj nand υj n+1. In this way, the normalized reminder of the voltage vector vf∆is calculated as vf∆= [υ1 f∆, υ2 f∆,· · · , υP f∆]T∈RP υj f∆=υj f υj n+1 −υj n (14) Vector vf∆can be used directly as the input of two-level multiphase SVM algorithm introduced in [21]. The result of this method are matrix Dand vector ˆvf∆(which is vf∆vector sorted by descending values) and the switching times vector tof the switching sequence with elements tkequal to tk=   1−ˆυ1 f∆,if k= 1 ˆυk−1 f∆−ˆυk f∆,if 2≤k≤P ˆυP f∆,if k=P+ 1 (15) Matrix Dresult of the two-level multiphase SVM algorithm shows the order of the switching between the different phases of the converter. Ignoring first row and column of matrix D, reading the columns from left to right, only one element of each column changes from 0 to 1 compared with the previous one. The row’s element shows the phase that has to switch from its initial switching state to the final one in the singlephase switching sequence. IV. EXAMPLE OF THE PROPOSED FEED-FORWARD SVM TECHNIQUE FOR MULTILEVEL MULTIPHASE CONVERTERS The same example presented in [21] has been used in order to validate the proposed feed-forward extension of the multilevel multiphase SVM algorithm. In this way, the fivephase multilevel two-cell cascaded converter shown in Fig. 1 is used. In order to show that the proposed feed-forward SVM technique can work with any dc voltage in the DC-Link of the multilevel converter, in the example the upper and the lower H-bridge of all the phases are charged with different voltages shown in Table I. This is a simple example but it should be noticed that the proposed MFFSVM technique can deal with any dc voltage in the H-bridges. This example has been chosen in order to clarify the proposed MFFSVM highlighting the very simple calculations needed to determine the switching sequence and the switching times of the power converter. In this example, as shown in [21], the voltage reference to be modulated is Vr= [28.6,22.6,−14.6,−31.6,−5.0]TV(16) Vdck j - + H-Bridge1 1 H-Bridge2 1 H-Bridge1 2 H-Bridge2 2H-Bridge2 3 H-Bridge1 3H-Bridge1 4 H-Bridge2 4H-Bridge2 5 H-Bridge1 5 H-Bridgek j - + - + - + - + - + - + - + - + - + - + - + Tk1 j Tk1 j Tk2 j Tk2 j Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 Fig. 1. Multilevel multiphase cascaded H-bridge converter The first step of the MFFSVM technique is to determine the phase voltages of the power converter and the results lead to building of matrices Sand Mv. In the case of the two-cell cascaded converter shown in Fig. 1, the possible switching states of the phase jcan be denoted using factors T rj kto define the trigger signals for the power semiconductors. These trigger signals can be denoted using variables Hj kfor the H- bridge number kof phase j. Each factor Hj kcan take values 0, 1 or 2 if the output H-bridgej kvoltage is −Vj dck,0or Vj dck respectively. The correspondence between these factors and the trigger signals of the power semiconductors is summarized in Table II. The switching factors Sj kare defined as a possible H-bridge states configuration Hj 1Hj 2. In the multilevel two-cell cascaded converter case, nine different output phase voltages can be achieved in general. Therefore, nine factors Sj k(k=1,2,· · · ,9) have to be defined. These factors are summarized in Table III. Taking into account the dc voltage values of the converter summarized in Table I, using Table II and Table III matrices Sand Mocan be defined. TABLE I DC VOLTAGES OF THE H-BRIDGES OF THE FIVE-PHASE TWO-CELL MULTILEVEL CASCADED CONVERTER Phase number Vj dc1(V) Vj dc2(V) 1 25 40 2 15 30 3 20 25 4 30 10 5 20 20 TABLE II POSSIBLE TRIGGER SIGNAL CONFIGURATIONS OF PHASE jOF THE MULTILEVEL TWO-CELL CASCADED CONVERTER Trigger signals H-bridge states Tj 11Tj 12Tj 21Tj 22 Hj 1Hj 2 0000 11 0001 10 0010 12 0011 11 0100 01 0101 00 0110 02 0111 01 1000 21 1001 20 1010 22 1011 21 1100 11 1101 10 1110 12 1111 11 S=     00 01 02 10 11 12 20 21 22 00 01 02 10 11 12 20 21 22 . . .. . .. . .. . .. . .. . .. . .. . .. . . 00 01 02 10 11 12 20 21 22      (17) Mv=       -65 -25 15 -40 0 40 -15 25 65 -45 -15 15 -30 0 30 -15 15 45 -45 -20 5 -25 0 25 -5 20 45 -40 -30 -20 -10 0 10 20 30 40 -40 -20 0 -20 0 20 0 20 40       (18) The next step of the MFFSVM technique is to summarize the output voltage levels of the power converter described in (18) using matrix Mowhere the elements of each row are ordered in increasing order. In addition, matrix So(with elements called Sj ok) is determined using matrix Sand following TABLE III Sj kFACTORS DEFINITION OF THE MULTILEVEL TWO-CELL CASCADED CONVERTER. Switching Trigger signals Phase voltage Sj kHj 1Hj 2Vj sk Sj 100 −Vj dc1−Vj dc2 Sj 201 −Vj dc1 Sj 302 −Vj dc1+Vj dc2 Sj 410 −Vj dc2 Sj 511 0 Sj 612 Vj dc2 Sj 720 Vj dc1−Vj dc2 Sj 821 Vj dc1 Sj 922 Vj dc1+Vj dc2 the order of the elements achieved in Mo. Mo=       -65 -40 -25 -15 0 15 25 40 65 -45 -30 -15 -15 0 15 15 30 45 -45 -25 -20 -5 0 5 20 25 45 -40 -30 -20 -10 0 10 20 30 40 -40 -20 -20 0 0 0 20 20 40       (19) So=       00 10 01 20 11 02 21 12 22 00 10 01 20 11 02 21 12 22 00 10 01 20 11 02 21 12 22 00 01 02 10 11 12 20 21 22 00 01 10 20 11 02 21 12 22       (20) The normalization proposed in (7) and (8) is applied and vector vrand matrix moare obtained. vr= [0.72,0.751,0.338,0.105,0.437]T(21) mo=       0 0.192 0.308 0.385 0.5 0.615 0.692 0.808 1 0 0.167 0.333 0.333 0.5 0.666 0.666 0.833 1 0 0.222 0.278 0.444 0.5 0.555 0.722 0.777 1 0 0.125 0.250 0.375 0.5 0.625 0.750 0.875 1 0 0.250 0.250 0.500 0.5 0.500 0.750 0.750 1       (22) Matrix mcis determined by comparing each normalized reference voltage component of vector vrand the components of matrix mousing (8). mc=       0 0.192 0.308 0.385 0.5 0.615 0.692 -1 -1 0 0.167 0.333 0.333 0.5 0.666 0.666 -1 -1 0 0.222 0.278 -1 -1 -1 -1 -1 -1 0-1 -1 -1 -1 -1 -1 -1 -1 0 0.250 0.250 -1 -1 -1 -1 -1 -1       (23) Using (11) and (13), the elements of vectors vnand vn+1 are determined. vn= [0.692,0.666,0.278,0,0.25]T vn+1 = [0.808,0.833,0.444,0.125,0.5]T(24) The switching configurations corresponding to these vectors are determined. The elements of matrix Sowith the same positions (same row and column) of the elements determined by (11) and (13) in matrix mohave to be used to form the switching sequence. This concept is shown in previous calculations (19)-(23) where the elements of the matrices have been highlighted in order to clarify the readiness of the MFFSVM technique. Using the highlighted elements of matrix Sothe first and the last switching states Hs1and Hs6of the switching sequence are known. Hs1= [S1 o7, S2 o7, S3 o3, S4 o1, S5 o3]T= [21,21,01,00,10]T Hs6= [S1 o8, S2 o8, S3 o4, S4 o2, S5 o4]T= [12,12,20,01,20]T (25) In order to find out the switching times, vector vfis determined using (12). vf= [0.028,0.085,0.060,0.105,0.187]T(26) Vector vfis normalized using (14). vf∆= [0.241,0.509,0.361,0.840,0.748]T(27) This vector vf∆is used as the input of the proposed MFFSVM technique. It uses the two-level multiphase SVM algorithm presented in [21] and vector ˆvf∆is obtained, thus providing the values of the switching times of the switching vectors. In fact, ˆvf∆vector is equal to vf∆but sorted by decreasing value. ˆvf∆= [0.840,0.748,0.509,0.361,0.241]T(28) Using ˆvf∆, the switching times are directly determined applying (15). t= [0.160,0.092,0.239,0.148,0.120,0.241] (29) Matrix Dresult of the two-level multiphase SVM technique is D=         1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 11 1 0 0 0 0 11 011 1 1 1 0 0 11 1 1         (30) Ignoring first row and column of matrix D, reading the columns from left to right, only one element of each column changes from 0 to 1 compared with the previous one. These factors are highlighted in (30) to clarify the idea. Reading from left to right, the row’s highlighted element shows the phase that TABLE IV EXPERIMENTAL DC VOLTAGES OF THE H-BRIDGES OF THE FIVE-PHASE TWO-CELL MULTILEVEL CASCADED CONVERTER Phase number Vj dc1Vj dc2 1 30.3 64.0 2 60.1 33.0 3 50.3 64.0 4 62.7 42.5 5 50.0 50.0 has to switch from its initial switching state to the final one in the single-phase switching sequence. Finally, the switching sequence can be written using Hs1and Hs6determined in (25) and the switching times determined in (29). Hs1= [21,21,01,00,10]T, t1= 0.160 Hs2= [21,21,01,01,10]T, t2= 0.092 Hs3= [21,21,01,01,20]T, t3= 0.239 Hs4= [21,12,01,01,20]T, t4= 0.148 Hs5= [21,12,20,01,20]T, t5= 0.120 Hs6= [12,12,20,01,20]T, t6= 0.241 (31) V. RESULTS OF THE PROPOSED MODULATION TECHNIQUE In order to test the proposed MFFSVM, experimental results are presented comparing the results with the previous MSVM presented in [21]. A five-level five-phase cascaded full-bridge inverter as shown in Fig. 1 has been used to obtain the results. The experimental setup includes a FPGA, a dSPACE platform, the inverter and the load. The dSPACE DS1103 PPC Controller Board provides the reference vectors to the FPGA which generates the trigger signals of the power semiconductors. The load is a five-phase distributed-concentrated winding induction motor with four poles. This motor was specifically built for the tests by rewinding the stator phases on the 30 stator slots of a 1.1-kW three-phase motor. In the experiments, a purely sinusoidal voltage is generated as the reference voltage of the power converter. The amplitude of the reference sinusoidal waveform is 80 V and the switching frequency is 5 kHz. First of all, the MSVM technique is applied to the converter shown in Fig. 1 connected to a five-phase motor drive. In the experiment, the dc voltages summarized in Table IV are imposed for the dc sources of the converter. As the MSVM technique does not take into account the actual imbalances in the dc voltages, the obtained phase voltages are highly distorted as can be observed from Fig. 2 where the phase voltages, their filtered versions and the phase currents are represented. Secondly, the proposed MFFSVM technique is applied considering again the dc voltages summarized in Table IV. The obtained modulated phase voltages, their filtered versions and the corresponding phase currents are shown in Fig. 3 showing that the MFFSVM technique can work with any dc voltage generating phase voltages with low distortion. The proposed MFFSVM technique and the previous MSVM technique can be directly compared observing Fig. 2 (MSVM results) and Fig. 3 (FFMSVM results). Under the same unbalanced dc voltage conditions, the proposed MFFSVM improves the behavior of the power converter achieving a high quality of the output waveforms. A summary of the obtained results is shown in Table V where the harmonic spectrum data of the filtered phase voltages using both modulation techniques are written. It is clear that using the proposed MFFSVM technique, the low harmonic distortion present with the MSVM method under unbalanced dc conditions is reduced. This means that the THD values obtained with the MFFSVM technique are improved when compared to those achieved by the MSVM, as can be observed in the last row of Table V. It has to be noticed that, in the experimental results, nonzero values for either zero-sequence harmonics (5th, 15th, etc) or the even harmonics are present. The proposed algorithm applied to an ideal converter obtains negligible low order harmonics in the output waveform. The low order harmonics present in the measured output voltage waveform are due to nonlinearities of the converter: dead times, turn on/off delays, voltage drop across power devices, etc [34], [35]. In addition, the harmonics amplitude are not the same for all phases, it is due to the different number of steps in the output voltage of every leg. In addition it has to be noticed that, in general, a phase with two H-bridges with different dc voltages achieves up to nine output voltage levels and the proposed MFFSVM uses all these levels to generate the phase voltages. These phase voltages have lower distortion because of the higher number of levels taking advantage of the multilevel operation of the power converter. This phenomenon can be clearly seen comparing the results of phase 4 and 5 from Fig. 3. The dc voltages of phase 4 lead to achieve nine output voltages generating phase voltages with low distortion (2.52%). On the other hand, the phase 5 has balanced dc voltages achieving only five output voltage levels achieving consequently a higher THD value (3.75%). Finally, the proposed MFFSVM technique has been tested under dynamic unbalanced dc conditions in order to show the dynamic response of the modulator. In this experiment, in phase 1 the voltage of H-bridge2is equal to 64 V while the voltage of H-bridge1is variable. In this way, a 100 Hz sinusoidal oscillation is added to V1 dc2so that its mean value is 50 V while it oscillates between 30 to 70 V. The obtained results are shown in Fig. 4 where the phase voltage, the phase voltage filtered, the variable dc voltage of the cell and the harmonic spectrum of the phase voltage are represented. It can be seen that a high performance of the dynamic response of the MFFSVM technique is achieved. Other experiment has been done in order to test the good dynamic performance of the proposed MFFSVM technique. In this case, the peak voltage of the reference voltage of phase 1 is equal to 60 V. The dc voltage of H-bridge2of phase 1 is constant (V1 dc2=64 V) whilst a drastic change in the voltage of H-bridge1of phase 1 (V1 dc1) is applied. Its value is changed from its desired value (V1 dc1=30.3 V) to zero and vice versa. The obtained results are shown in Fig. 5 where the phase voltage, its low-pass filtered version and the voltage of both H-bridges of phase 1 (V1 dc1and V1 dc2) are represented. It can be Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 Fig. 2. Results using the previous multilevel multiphase SVM technique applied under unbalanced dc voltage conditions. Phase voltages (channel 1), filtered phase voltages (channel 2) and phase currents (channel 3) using the dc voltage values summarized in Table IV. Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 Fig. 3. Results using the proposed feed-forward multilevel multiphase SVM technique applied under unbalanced dc voltage conditions. Phase voltages (channel 1), filtered phase voltages (channel 2) and phase currents (channel 3) using the dc voltage values summarized in Table IV. observed that the MFFSVM technique takes into account the measured dc voltages in order to generate the phase voltage correctly. This experiment shows that the MFFSVM technique still operates achieving high performance even when one of the cells of the multilevel converter has failed. In order to test that the proposed MFFSVM technique can achieve multi-frequency outputs, other experiment has been Phase 1 V dc2 1= 64V V dc1 1=’variable’ a) b) Fig. 4. Dynamic response results using the proposed feed-forward multilevel multiphase SVM technique applied under dynamic unbalanced dc voltage conditions. a) Phase voltage, low-pass filtered phase voltage, phase current b) Harmonic spectrum of the phase voltage carried out. In this case, the voltage reference is the same of experiment shown in Fig. 6 but it is added a third harmonic content with amplitude equal to 25 V. The results also show the good performance of the MFFSVM method to achieve multi-frequency outputs. a) b) Fig. 5. Dynamic response results using the proposed feed-forward multilevel multiphase SVM technique applied under a drastic change of a dc voltage H- bridge of the multilevel cascaded converter. a) DC voltage changes from its desired value to zero b) DC voltage changes from zero to its desired value VI. CONCLUSIONS A feed-forward space vector modulation technique called MFFSVM has been presented in this paper. This modulation TABLE V EXPERIMENTAL RESULTS USING THE MSVM AND THE PROPOSED FFMSVM TECHNIQUES UNDER UNBALANCED DC VOLTAGES OF TABLE IV Harmonic MSVM harmonic content results % FFMSVM harmonic content results % order (n) Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 1 100 100 100 100 100 100 100 100 100 100 2 0.17 0.52 0.12 0.17 0.31 0.01 0.15 0.07 0.25 0.06 3 8.86 7.05 4.43 1.57 1.26 1.59 1.33 1.73 1.36 1.43 4 0.30 0.20 0.32 0.14 0.29 0.07 0.14 0.25 0.13 0.21 5 0.68 0.58 0.77 0.47 0.84 0.64 0.63 0.81 0.74 0.58 6 0.19 0.37 0.10 0.31 0.07 0.21 0.16 0.45 0.26 0.07 7 1.30 0.65 0.85 0.91 0.84 0.36 0.18 0.51 0.26 0.28 8 0.84 0.60 0.82 0.67 0.71 0.07 0.04 0.49 0.29 0.87 9 0.32 0.51 0.24 0.35 0.22 0.29 0.08 0.27 0.11 0.17 10 0.69 0.69 0.71 0.81 0.68 0.30 0.35 0.07 0.12 0.69 11 0.43 0.18 0.31 0.29 0.16 0.17 0.12 0.22 0.11 0.20 12 0.17 0.13 0.17 0.09 0.14 0.25 0.07 0.06 0.04 0.16 13 0.25 0.11 0.13 0.05 0.19 0.07 0.09 0.19 0.13 0.12 14 0.07 0.15 0.05 0.05 0.13 0.63 0.61 0.22 0.08 0.05 15 0.19 0.12 0.17 0.05 0.15 0.12 0.08 0.12 0.07 0.11 THD 9.52 8.14 5.58 4.22 3.89 2.99 2.76 2.83 2.52 3.75 −100 0 100 −100 −50 0 50 100 −100 0 100 −100 −50 0 50 100 Vd1 [V]Vd2 [V] Vq1 [V ] Vq2 [V ] a) b) c) Fig. 6. Response of the proposed MFFSVM technique when the reference voltage includes a third harmonic content with amplitude equal to 25 V. a) Channel 1: Phase 1 voltage, channel 2: Filtered phase 1 voltage b) Harmonic spectrum of the phase voltage c) Trajectories of the output voltage (gray) and its filtered version (black) in stationary dq axis technique has been designed for multilevel multiphase power converters. Measuring the actual dc voltages of the converter and thanks to the feed-forward control, the proposed technique can operate with any dc voltage value in the DC-link capacitor voltages achieving good results without using any prestored off-line tables. Previous modulation techniques do not consider the possible voltage imbalances and generate output waveforms with high distortion. 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