A Cascaded H-Bridge Multilevel Inverter based on Switched-Capacitor for High Frequency Ac Applications

Transcription

1 ISSN: , Volume7 Issue3, February 2018 A Cascaded HBridge Mulilevel Inverer based on SwichedCapacior for High Frequency Ac Applicaions M. S. S. Bhadri Nadh, R. V. D. Rama Rao Absrac: High frequency ac applicaions wih a reduced componen of a cascaded mulilevel inverer using swiched capacior are proposed in his projec. Here swiched capacior and HBridges are consruced in fron end and back end hrough he connecions of series and parallel conversions. An increasing he volage level by swiched capacior, oupu harmonics can be reduced. High Frequency AC Applicaions (HFAC) is alernaive o DC disribuion due o lower cos. These are mos commonly used o apply for small scale and closed elecrical nework in elecric vehicles due o moderae size and reducion of weigh for disribuion nework. The ype of mulilevel inverer used in his projec is cascaded HBridge and hey buil by he series connecion of HBridges. I is similar o dcdc converers. The cascaded HBridges needs individual inpu and four power swiches for consrucion in order o increase number of volage levels wih heir saircase oupu. However conrol sraegy is difficul because of inpu curren will be in disconinuous; herefore Elecromagneic Inerference (EMI) becomes wors. The advanages for his opology a raed oupu frequency of abou 20 khz are feasible o operae, increasing reliabiliy and high efficiency. By increasing number of volage levels, he oal harmonic disorion (THD) conen of saircase oupu can be decreased and furher in such a way ha, has a paricular meaning o simplifying he filer design. This opology will be analyzed by symmerical modulaion for 13 level inverer, which is based on swiched capacior of a cascaded mulilevel inverer for HFAC PDS. The enire sysem is simulaed in MATLAB/SIMULINK TOOL. Keywords: Cascaded HBridge, High Frequency Ac (HFAC), Mulilevel inverer, Swiched Capacior (SC), Symmerical PhaseShif Modulaion (PSM). I. INTRODUCTION HIGHFREQUENCY ac (HFAC) power disribuion sysem (PDS) poenially becomes an alernaive o radiional dc disribuion due o he fewer componens and lower cos. The exising applicaions can be found in compuer [1], elecom [2], elecric vehicle [3], and renewable energy micro grid [4], [5].However; HFACPDS has o confron he challenges from large power capaciy, high elecromagneic inerference (EMI), and severe power losses [6].A radiional HFAC PDS is made up of a highfrequency (HF) inverer, an HF ransmission rack, and numerous volageregulaion modules (VRM). HF inverer accomplishes he power conversion o accommodae he requiremen of poin of load (POL).In order o increase he power capaciy; Revised Manuscrip Received on 21 February M. S. S. Bhadri Nadh, PG Suden, Deparmen of Elecrical & Elecronics Engineering, Vishnu Insiue of Technology (JNTUK), Bhimavaram (Andhra Pradesh), India. Dr. R. V. D. RamaRao, Deparmen of Elecrical & Elecronics Engineering, Vishnu Insiue of Technology (JNTUK), Bhimavaram (Andhra Pradesh), India. The mos popular mehod is o connec he inverer oupu in series or in parallel. However, i is impracical for HF inverer, because i is complicaed o simulaneously synchronize boh ampliude and phase wih HF dynamics. Mulilevel inverer is an effecive soluion o increase power capaciy wihou synchronizaion consideraion, so he higher power capaciy is easy o be achieved by mulilevel inverer wih lower swich sress. Non pollued sinusoidal waveform wih he lower oal harmonic disorion (THD) is criically caused by long rack disribuion in HFAC PDS. The higher number of volage levels can effecively decrease oal harmonics conen of saircase oupu, hus significanly simplifying he filer design [7]. HF power disribuion is applicable for smallscale and inernal closed elecrical nework in elecric vehicle (EV) due o moderae size of disribuion nework and effecive weigh reducion [8]. The consideraion of operaion frequency has o make compromise beween he ac inducance and resisance [9], so mulilevel inverer wih he oupu frequency of abou 20 khz is a feasible rial o serve as power source for HF EV applicaion. The radiional opologies of mulilevel inverer mainly are diodeclamped and capacior clamped ype [10], [11]. The former uses diodes o clamp he volage level, and he laer uses addiional capaciors o clamp he volage. The higher number of volage levels can hen be obained; however, he circui becomes exremely complex in hese wo opologies. Anoher kind of mulilevel inverer is cascaded HBridge consruced by he series connecion of HBridges [12], [13]. The basic circui is similar o he classical Hbridge DC DC converer [14]. The cascaded srucure increases he sysem reliabiliy because of he same circui cell, conrol srucure and modulaion. However, he disadvanages confroned by cascaded srucure are more swiches and a number of inpus. In order o increase wo volage levels in saircase oupu, an HBridge consruced by four power swiches and an individual inpu are needed. Theoreically, cascaded H Bridge can obain saircase oupu wih any number of volage levels, bu i is inappropriae o he applicaions of cos saving and inpu limiaion. A number of sudies have been performed o increase he number of volage levels. A swichedcapacior (SC) based mulilevel circui can effecively increase he number of volage levels. However, he conrol sraegy is complex, and EMI issue becomes worse due o he disconinuous inpu curren [15]. A singlephase fivelevel pulse widh modulaed (PWM) inverer is consiued by a full bridge of diodes, wo capaciors and a swich. 93

2 A Cascaded HBridge Mulilevel Inverer based on SwichedCapacior for High Frequency Ac Applicaions However, i only provides oupu wih five volage levels, and higher number of volage levels is limied by circui srucure[16].an SCbased cascaded inverer was presened wih SC fronend and full bridge backend. However, boh complicaed conrol and increased componens limi is applicaion [17].The furher sudy was presened using series/parallel conversion of SC. However, i is in appropriae o he applicaions wih HF oupu because of mulicarrier PWM (MPWM)[18],[19].If oupu frequency is around 20 khz, he carrier frequency reaches a couple of megaherz. Namely, he carrier frequency in MPWM is dozens imes of he oupu frequency. Since he carrier frequency deermines he swiching frequency, a high swiching loss is ineviable for he sake of highfrequency oupu. A boos mulilevel inverer based in parial charging of SC can increase he number of volage levels heoreically. However, he conrol sraegy is complicaed o implemen parial charging [20]. Therefore, i is a challenging ask o presen an SCbased mulilevel inverer wih highfrequency oupu, lowoupu harmonics, and high conversion efficiency [21]. Based on he sudy siuaion aforemenioned, a novel mulilevel inverer and simple modulaion sraegy are presened o serve as HF power source. The res of his paper is organized as follows. The discussions of ninelevel inverer are presened in Secion II, including circui opology, modulaion sraegy, operaion cycle, and Fourier analysis. The parameer deerminaion and loss analysis are discussed in chaper III. The furher enhancemen of 13level inverer is sudied in chaper IV. The performance evaluaion accomplished by simulaion is described in chaper VI followed by concluding remarks. II. SC BASED CASCADED HBRIDGE MULTI LEVEL INVERTER WITH 13LEVEL OUTPUT The proposed circui is made up of he SC fronend and cascaded HBridge backend. A. Circui Topology. Fig. 1 shows he circui opology of ninelevel inverer (N1 = 2, N2 = 2), where,,, as he swiching devices of SC circuis (S and S) are used o conver he series or parallel connecion of and.,,,,,,, are he swiching devices of cascaded HBridge. and are inpu volage. and are diodes o resric he curren direcion. iou and vo are he oupu curren and he oupu volage, respecively. The number of volage levels can be furher increased via wo approaches. One is o increase he level number generaed by SC circui. The oher one is o increase level number generaed by cascaded HBridge. Thireenlevel inverer, 2 3 srucure as shown in Fig.1 is derived by he enhancemen of HBridge circui, which needs 3 diodes, 3 capaciors, 18 swiches, and 3 dc inpus. I can be found ha 3 2 srucure requires more diodes and capaciors han 2 3 srucure. However, he number of power swiches in 3 2 srucure is less han ha in 2 3 srucure. Because he radiional cascaded Hbridge needs 24 swiches and 6 inpus o produce 13 volage levels, he numbers of power swiches and inpus are grealy decreased by proposed inverer. 94 D 1 S 1 V dc1 D 2 S 2 V dc2 D 3 V dc3 S 1 S 2 S 3 S 3 SC 1 SC 2 SC 3 C 1 C 2 C 3 S 1a S 1d S 2a S 2d S 3a S 3d H Bridge 1 S 1b S 1c H Bridge 2 S 2b S 2c H Bridge 3 S 3b S 3c a 1 a 2 a 3 b 2 I ou R 0 v 0 HFAC Oupu Fig.1 Circui Topology of 13Level Inverer 2 3 wih Three Dc Inpus DC POWER SUPPLY SC BASED CASCADED H BRIDGE INVERTER PSC PWM CONTROL STRATEGY LOAD Fig. 2. Block Diagram for SC based Cascaded HBridge Inverer

3 ISSN: , Volume7 Issue3, February 2018 COMP 1 AND 1 NOT 2 DFF AND 2 XOR SET D Q CLR Q XOR2 AND 3 COMP 2 SRF PWM S Q XOR 3 V in R SET CLR Q XOR 4 AND 4 NOT 1 Fig.3. (a) Circui of Symmerical PSM V V V V GATE 1 GATE 2 GATE 3 GATE 4 in Fig. 2(b). The logic operaions of gae signals are gae1 = XOR{Q(RS), Q (D)} gae2 = XOR{Q(RS), Q(D)} (1) gae3 = XOR{AND{Q(RS),NOT (PWM )}, Q(D)} gae4=xor{and{q(rs), NOT (PWM )}, Q (D)}. (2) A conrolled PWM wih pulse widh δ is symmerically generaed by he comparisons of he riangle carrier V c and modulaion signal V m. The rising edge maching of V c and V m riggers he polariy inversion of he leading bridge, while he falling edge maching of V c and V m riggers he polariy inversion of he lagging bridge. When V m has a change ΔV m, his modulaion simulaneously moves gae 1 and gae 3 in he opposie direcion. Thus, he derived Vab is symmerical wih respec o Vc. Table1. In Order o Accomplish he Saircase Oupu wih 4n 1 Volage Levels, he Componen Couns are Compared in Table1. Table1 Componens Comparison of Proposed Inverer and Cascaded hbridge. Inverer ype Proposed inverer enhanced by SC n*2 opology Proposed inverer enhanced by H Bridge 2*n opology Cascaded HBridge Swiching device 2n8 6n 8n Capacior 2n2 n 0 Diode 4n6 n 0 DC bus 2 n 2n Power Losses (2n2)loss cap nloss cap (4n6)loss diode (2n8)loss swich nloss diode 6nloss swich 8nloss swich Fig.3.(b) circui and operaional waveform of symmerical PSM (a)circui of symmerical PSM (b) Operaional waveforms of symmerical PSM. III. SYMMETRICAL MODULATION There are many modulaion mehods o regulae he mulilevel inverer, he popular modulaions are he space vecor modulaion [22], he mulicarrier PWM [23], and he selecive harmonic eliminaion [24], [25], sub harmonic pulse widh modulaion [26], ec. However, mos of hem grealy increase he carrier frequency ha is dozens imes he frequency of reference or oupu. A symmerical phaseshif modulaion (PSM) is inroduced ino he proposed mulilevel inverer. The symmerical PSM ensures he oupu volage of full bridge is symmerical o he carrier, so volage levels can be superimposed symmerically and carrier frequency is wice as ha of he oupu frequency [27]. The srucure of symmerical PSM is shown in Fig. 2(a), and he operaional waveform of symmerical PSM is shown 95 A 2*n opology needs n capaciors, 6n swiches, and n dc inpus; n*2 opology needs 2n 2 capaciors, 2n8 swiches, and 2 dc inpus. The radiional cascaded HBridge needs 8n swiches and 2n dc inpus. Wih he same number of volage levels, he proposed inverer needs less swiching devices and inpus han he radiional cascaded HBridge. Considering he power losses, he radiional cascaded H bridge has he higher swiching losses caused by more swich devices. However, he proposed inverer newly inroduces he capacior loss ha has already been examined in las secion. Moreover, a flexible circui srucure becomes possible. I is feasible for he proposed mulilevel inverer o selec suiable enhancemen ha can accommodae he requiremens from differen applicaions. For example, 2 n opology can be used for he power applicaion sourced by muliple solar panels or baeries, and n 2opology can be used for he power applicaion sourced by dual power sources.

4 c A Cascaded HBridge Mulilevel Inverer based on SwichedCapacior for High Frequency Ac Applicaions A. Modes of Operaion The mode of operaion wih reference o he swiching paern given o he circui as shown in figure.1 is abulaed in able II. Mode of Operaion OnSae Swiches Oupu Volage Capacior Sae S 1a, S 1c, S 2a, S 2c, S 3a, S 3c, S 1, S 2, S 3 6V in C 1, C 2, C 3 Discharging S 1a, S 1c, S 2a, S 2c, S 3a, S 3c, S 1, S 2, S 3 5V in C 2, C 3 Discharging S 1a, S 1c, S 2a, S 2c, S 3a, S 3c, S 1, S 2, S 3 4V in C 3 Discharging S 1a, S 1c, S 2a, S 2c, S 3a, S 3c, S 1, S 2, S 3 S 1a, S 1c, S 2a, S 2c, S 3a, S 3b, S 1, S 2, S 3 S 1a, S 1c, S 2a, S 2b, S 3a, S 3b, S 1, S 2, S 3 S 1a (or)s 1c, S 2a (or)s 2c, S 3a (or)s 3c, S 1, S 2, S 3 3V in 2V in V in C 1, C 2, C 3 charging C 1, C 2, C 3 charging C 1, C 2, C 3 charging S 1b (or)s 1d, S 2b (or)s 2d, S 3b (or)s 3d, S 1, S 2, S 3 0V C 1, C 2, C 3 charging S 1b, S 1d, S 2b, S 2a, S 3b, S 3a, S 1, S 2, S 3 S 1b, S 1d, S 2b, S 2d, S 3b, S 3a, S 1, S 2, S 3 S 1b, S 1d, S 2b, S 2d, S 3b, S 3d, S 1, S 2, S 3 V in C 1, C 2, C 3 charging 2V in C 1, C 2, C 3 charging 3V in C 1, C 2, C 3 charging S 1b, S 1d, S 2b, S 2d, S 3b, S 3d, S 1, S 2, S 3 4V in C 3 Discharging S 1b, S 1d, S 2b, S 2d, S 3b, S 3d, S 1, S 2, S 3 5V in C 2, C 3 Discharging S 1b, S 1d, S 2b, S 2d, S 3b, S 3d, S 1, S 2, S 3 6V in C 1, C 2, C 3 Discharging For Posiive Half Cycle For Negaive Half Cycle For 0V: For 0V: D 1 S 1 V S 1 d c 1 C 1 S 1 a S 1 b a 1 b 1 S 1 d S 1 c I o u D 2 S 2 V d c 2 S 2 C 2 S 2 a S 2 d a 2 S 2 b S 2 c b 2 R 0 v 0 D 3 b C 3 S 3 a S 3 b S 3 a 3 b 3 d c V d c 3 S 3 S 3 d S 3 c For V in : For V in : b b d c d c 96

5 ISSN: , Volume7 Issue3, February 2018 For 2V in : For 2V in : b b d c d c \ For 3V in : For 3V in : b b d c d c For 4V in : For 4V in : b b d c d c For 5V in : For 5V in : 97

6 A Cascaded HBridge Mulilevel Inverer based on SwichedCapacior for High Frequency Ac Applicaions b b d c d c For 6V in : For 6V in : b b d c d c The above figures shows he Posiive half cycles and Negaive Half Cycles. For Posiive Half Cycle For 0V: A he insan when saisfies 0 << 1 he swiches S 1a (or)s 1c, S 2a (or)s 2c, S 3a (or)s 3c, S 1, S 2, S 3 S 1b (or)s 1d, S 2b (or)s 2d, S 3b (or)s 3d, S 1, S 2, S 3 & C 1, C 2, C 3 charging. The operaional mode 1: 0 1 V 0 =0 V 0 = 0V For V in : A he insan when saisfies 1 < 2 he swiches S 1a, S 1c, S 2a, S 2b, S 3a, S 3b, S 1, S 2, S 3 & C 1, C 2, C 3 charging. The operaional mode 1: 1 2 V dc1 V 0 =0 V 0 =V dc1 [V dc1 =V dc2 =V in ] V 0 = V in For 2V in : A he insan when saisfies 2 < 3 he swiches S 1a, S 1c, S 2a, S 2c, S 3a, S 3b, S 1, S 2, S 3 & C 1, C 2, C 3 charging. The operaional mode 1: 2 3 V dc1 V 0 V dc2 =0 V 0 = V dc1 V dc2 V 0 = 2V in 98 For 3V in : A he insan when saisfies 3 < 4 he swiches S 1a, S 1c, S 2a, S 2c, S 3a, S 3c, S 1, S 2, S 3 & C 1, C 2, C 3 charging. The operaional mode 1: 3 4 V dc1 V 0 V dc2 V dc3 =0 V 0 = V dc1 V dc2 V dc3 V 0 = 3V in For 4V in : A he insan when saisfies 4 < 5 he swiches S 1a, S 1c, S 2a, S 2c, S 3a, S 3c, S 1, S 2, S 3 & C 3 Discharging. The operaional mode 1: 4 5 V dc1 V 0 V dc2 V dc3 V c3 = 0 V 0 = V dc1 V dc2 V dc3 V c3 V 0 = 4V in For 5V in : A he insan when saisfies 5 < 6 he swiches S 1a, S 1c, S 2a, S 2c, S 3a, S 3c, S 1, S 2, S 3 & C 2, C 3 Discharging. The operaional mode 1: 5 6 V dc1 V 0 V dc2 V c2 V dc3 V c3 = 0 V 0 = V dc1 V dc2 V c2 V dc3 V c3 V 0 = 5V in For 6V in : A he insan when saisfies 6 < 7 he swiches S 1a, S 1c, S 2a, S 2c, S 3a, S 3c, S 1, S 2, S 3 & C 1, C 2, C 3 Discharging. The operaional mode 1: 6 7

7 ISSN: , Volume7 Issue3, February 2018 V dc1 V c1 V 0 V dc2 V c2 V dc3 V c3 = 0 V 0 = V dc1 V c1 V dc2 V c2 V dc3 V c3 V 0 = 6V in A he insans acive circuis for 7 < 8, 8 < 9, and 9 < 10, 10 < 11, 11 < 12 are same as he operaions in 6 < 7, 5 < 6, 4 < 5 3 < 4, 2 < 3, 1 < 2 respecively. For Negaive Half Cycle For 0V: A he insan when saisfies 0 << 1 he swiches S 1a (or)s 1c, S 2a (or)s 2c, S 3a (or)s 3c, S 1, S 2, S 3 S 1b (or)s 1d, S 2b (or)s 2d, S 3b (or)s 3d, S 1, S 2, S 3 & C 1, C 2, C 3 charging. The operaional mode 1: 0 ( 1 ) V 0 =0 V 0 = 0V For V in : A he insan when saisfies 1 < 2 he swiches S 1b, S 1d, S 2b, S 2a, S 3b, S 3a, S 1, S 2, S 3 & C 1, C 2, C 3 charging. The operaional mode 1: 1 ( 2 ) V dc1 V 0 =0 V 0 =V dc1 [V dc1 =V dc2 =V in ] V 0 = V in For 2V in : A he insan when saisfies 2 < 3 he swiches S 1b, S 1d, S 2b, S 2d, S 3b, S 3a, S 1, S 2, S 3 & C 1, C 2, C 3 charging. The operaional mode 1: 2 ( 3 ) V dc1 V 0 V dc2 =0 V 0 = V dc1 V dc2 V 0 = 2V in For 3V in : A he insan when saisfies 3 < 4 he swiches S 1b, S 1d, S 2b, S 2d, S 3b, S 3d, S 1, S 2, S 3 & C 1, C 2, C 3 charging. The operaional mode 1: 3 ( 4 ) V dc1 V 0 V dc2 V dc3 =0 V 0 = V dc1 V dc2 V dc3 V 0 = 3V in For 4V in : A he insan when saisfies 4 < 5 he swiches S 1b, S 1d, S 2b, S 2d, S 3b, S 3d, S 1, S 2, S 3 & C 3 Discharging. The operaional mode 1: 4 ( 5 ) V dc1 V 0 V dc2 V dc3 V c3 = 0 V 0 = V dc1 V dc2 V dc3 V c3 V 0 = 4V in V dc1 V 0 V dc2 V c2 V dc3 V c3 = 0 V 0 = V dc1 V dc2 V c2 V dc3 V c3 V 0 = 5V in For 6V in : A he insan when saisfies 6 < 7 he swiches S 1b, S 1d, S 2b, S 2d, S 3b, S 3d, S 1, S 2, S 3 & C 1, C 2, C 3 Discharging. The operaional mode 1: 6 ( 7 ) V dc1 V c1 V 0 V dc2 V c2 V dc3 V c3 = 0 V 0 = V dc1 V c1 V dc2 V c2 V dc3 V c3 V 0 = 6V in A he insans acive circuis for 7 < 8, 8 < 9, and 9 < 10, 10 < 11, 11 < 12 are same as he operaions in 6 < 7, 5 < 6, 4 < 5 3 < 4, 2 < 3, 1 < 2 respecively. OPERATION CYCLES Derivaion of Harmonics & Fourier Analysis for Operaion Cycles In aforemenioned ninelevel inverer, he saircase oupu v o can be divided ino four componens v 01,v 02,v 03, and v 04 as shown in Fig.4. The duraions of each componen are decided by he comparisons of reference signal (V m_1c,v m_1b, V m_1d,v m _2c,V m_2b, V m_2d ) and riangular carrier (V c ). If pulse widhs of he consiued componen are defined as δ 1, δ 2, α 1, and α 2, Fourier analysis is accomplished for his ninelevel saircase. V V01 V02 V03 V04 V05 V06 x3 x1 x2 α3 α2 α1 δ3 δ2 δ Fig.3 Oupu Volage Decomposiion for Fourier Analysis in he Operaional Mode The magniude of he harmonics is derived by α δ For 5V in : A he insan when saisfies 5 < 6 he swiches S 1b, S 1d, S 2b, S 2d, S 3b, S 3d, S 1, S 2, S 3 & C 2, C 3 Discharging. The operaional mode 1: 5 ( 6 ) α δ 99

8 A Cascaded HBridge Mulilevel Inverer based on SwichedCapacior for High Frequency Ac Applicaions Where, n= 1, 3, 5... In operaional mode 1 δ 1 =, α 1 = δ 2 =, α 2 = δ 3 =, α 3 = (2) To furher describe he relaions of oupu THD and pulse widhs α 1, α 2, α 3, δ 1, δ 2, δ 3 six parameers are predefined k 1 =, k 2 =, k 3 =, x =, x 2 =, x 3 =, (3) The oupu waveforms can be characerized by hese four consans. According o he definiions as (THD = ( /V 1 ) 100%), THD of oupu volage can be calculaed by he harmonic magniudes. The relaions of oupu THD o x 1, x 2, x 3 are given wih he fixed k 1, k 2 and k 3. IV. DETERMINATION OF CAPACITANCE As shown in Fig.3.2, he capaciors are charged when hey are in parallel wih power source, and he capaciors are discharged when hey are in series wih power source. The swich S 1 and S 1 are driven alernaively during he half of oupu cycle. Therefore, he driven frequency of S 1 and S 1 is wice he frequency of oupu volage, as well as he driven frequency of S 1a S 1d is he same as he frequency of oupu volage. The capaciance of C i is deermined by he volage ripple of C i ha denoes he volage flucuaion of mulilevel oupu. The larger capaciance has he fewer ripple volage. The volage flucuaion over a narrow scope has a smaller power losses and higher capacior efficiency. The appropriaed mehod of capaciance calculaion is ha he maximum volage ripple is 10% of he maximum capacior volage [28]. Before obaining he capaciance of C i, wo assumpions are given o simplify he derivaions: 1) The oupu load is pure resisive load, and 2) The same duraion is given in each level of saircase oupu. Therefore, he ime poins in Fig. 3.2 are 0 =0, 1 = s, 2 = s, 3 = s, 4 = s, 5 = s, 6 = s, 7 = s, 8 = s (1) where s is he period of he oupu volage derived by s = (2) Where f s is he frequency of he oupu volage. In he operaional mode 1, as shown in Fig.3.2 (a), he longes discharging cycle of C 1 is beween 4 and 5, and he longes discharging cycle of C 2 is beween 3 and 6. In he operaional mode 2, as shown in Fig.3.2 (b), he longes discharging cycle of C 1 is he same as he operaional mode 1, while he longes discharging cycle of C 2 is beween 2 and 7. Therefore, he maximum discharging amoun of C 1 is Q c1 and is defined as Where, Q c1 = (3) I ou is he ampliude of he oupu curren i ou and Φ is he phase difference beween he oupu volage v o and curren i ou.if 10% ripple volage is considered, Qc1 should be less han 10% of he maximum charge of C 1, i.e. C 1. (4) Furhermore, he maximum discharging amoun of C 2 is Q c2 and is defined as Then, mode 1 (5),mode 2 (6) C 2 (7) I can be seen from he equaions ha he operaional mode 2 needs larger C 2 han ha in operaional mode 1. When he load is resisive, he phase of load curren is agreed wih he load volage. The maximum discharging amoun of capacior is obained in resisive load, because he peak load curren is he midpoin of inegraion period. In oher words, if he capaciance of C i is derived in pure resisive load, i also mainains he less volage ripples in inducive load. The peak curren of he capacior C i is derived by Where, V Ci is he volage on he capaciors C i, V df is he forward volage drop of diode, r c is he equivalen series resisance (ESR) of he capaciors, r on is he inernal onsae resisance of he swiching device and r d is he inernal onsae resisance of he diode. Because of a small volage difference of V in and, he peak curren I ci is fewer for he larger C i. Thus, he larger capacior is needed o cu down undesirable peak curren and prolong he capacior lifeime. The analysis of swiching loss is similar o he radiional cascaded Hbridge, while he capacior losses consising of ripple loss P rip and conducion loss P cond are newly inroduced by he proposed inverer. When he capacior C i is conneced from series o parallel, he ripple is derived by he difference beween he inpu volage V in and he capacior volage. The volage ripple of C i is Δ (9) (8) 100

9 ISSN: , Volume7 Issue3, February 2018 Where i Ci is he ransien curren of he capacior C i, and he discharging inerval is denoed by and. For C 1 in operaional mode 1, and are 4 and 5, respecively. For C 2 in operaional mode 1, and are 3 and 6, respecively. Thus, he loss from volage ripple is resuled by Δ (10) Where, k is he number of swiched capaciors (SCs), and f s is he frequency of he oupu volage. I can be found ha he ripple loss is inversely proporional o he capacior C i. The conducion losses can be furher calculaed by (11) The larger capacior curren leads o a large conducion loss. Lasly, he losses from SCs are denoed by P sc = P rip P cond. (12) Boh ripple loss and conducion loss are proporional o he frequency of he oupu volage and number of capaciors. I is concluded ha a larger capacior can improve efficiency and prolong capacior lifeime. However, he larger capacior leads o he higher cos. Thus, a rade off of cos and efficiency need o be aken ino accoun. According o (4), (7), and (9), he relaion curves of SCs (C i ) and ripple volage are illusraed in Fig.4.3(a) wih he fixed 25 khz oupu frequency, and relaion curves of SC (C i ) and oupu frequency are illusraed in Fig.5.2(b) wih he fixed 10% ripple volage. I can be found from Fig.4.3 (a) ha he less capaciance leads o larger ripple volage. Operaional mode 2 needs larger capaciance han mode 1 o keep he ripples low. The gradien of capacior o ripple is larger in lowripple zone, and he gradien of capacior o ripple is lower in highripple zone. The gradien variaion is caused by inversely proporional relaion beween capaciance wih ripple volage. I can be found from Fig.4.3 (b) ha he less capaciance is required for higher frequency applicaions o mainain 10% ripple volage. Thus, capacior cos can be grealy saved for HF applicaion compared wih lowfrequency counerpar. V. PERFORMANCE EVALUTION The SC based cascaded HBridge inverer for 13level using phase shif carrier modulaion are as shown in fig1 are developed in MATLAB/SIMULINK ool. The parameers of he SC based cascaded HBridge inverer are lised in able III. Table III Parameers of he SC based Cascaded H Bridge Inverer Inverer ype 13Level Swiching devices 18 Capaciors 3 Diodes 3 DC buses 3 The waveforms of oupu volage v o, capacior currens (i, i, i ) and capacior volages (v, v, v ) are shown in Fig.6.1 The waveforms for 13level SC based cascaded inverer is aken as V in =12v, C 1 =100µf, C 2 =120µf, C 3 =220µf, Ro=50Ω. The oupu frequency f s is 25 khz. Fig.4.1 (a) Curves of Fronend Capacior Versus Volage Ripple wih 25 khz Oupu Frequency. (a)volage (V 0 ) versus Time(S) Fig.4.2 (b) Curves of fronend capacior versus oupu frequency wih 10% volage ripple. 101

10 A Cascaded HBridge Mulilevel Inverer based on SwichedCapacior for High Frequency Ac Applicaions (b)curren (i c1 ) versus Time(S) (f) Curren (i c3 ) versus Time(S) (c)volage (V c1 ) versus Time(S) (d)curren (i c2 ) versus Time(S) (g)volage (V c3 ) versus Time(S) The Above Fig.5 Shows [a,b,c,d,e,f,g] In The Simulaion waveforms of 13level SC based cascaded inverer. I can be found from Fig.5 ha he volage drop is indisincive in each sep of sair case oupu because he discharging periods of SCs become shorer for 13level inverer. The oupu specrums of 13level inverer are illusraed in below Fig.6 respecively. The fundamenal frequency is 25 khz ha is he same as oupu frequency. I can be observed ha he fundamenal harmonic is significanly higher han he oher harmonics. The magniude of fundamenal componen is 55V for a 13level inverer. (e) Volage (V c2 ) versus Time(S) 102

11 ISSN: , Volume7 Issue3, February 2018 Oupu volage & oupu specrum of 13level inverer The above fig.6 shows he Simulaion waveforms of 13level inverer The calculaed THD 9.13% for 13level inverer. A 13level inverer has fewer high order harmonics han ninelevel inverer. I can be esimaed ha he harmonics can be furher cu down along wih he increasing number of volage levels. Thus, he proposed inverer produces near sinusoidal saircase oupu, and wo mehods can make i more sinusoidal. One is o opimize he duraion of volage levels; he oher one is o increase he number of volage levels. MATLAB/Simulink for 13 level cascaded hbridge inverer. 103

12 A Cascaded HBridge Mulilevel Inverer based on SwichedCapacior for High Frequency Ac Applicaions MATLAB/Simulink for 13 Level Cascaded hbridge Inverer for a Sub Sysem. 104

13 ISSN: , Volume7 Issue3, February 2018 VI. CONCLUSION A novel SCbased cascaded mulilevel inverer was proposed. 13level circui opology are examined in deph. Compared wih convenional cascaded mulilevel inverer, he proposed inverer can grealy decrease he number of swiching devices. A single carrier modulaion named by symmerical PSM, was presened wih he low swiching frequency and simple implemenaion. The accordan resuls of simulaion furher confirm he feasibiliy of proposed circui and modulaion mehod. Comparing wih radiional cascade Hbridge, he number of volage levels can be furher increased by SC fronend. For insance, he number of volage levels increases hree imes in half cycle of 13 level circui. Wih he exponenial increase in he number of volage levels, he harmonics are significanly cu down in saircase oupu, which is paricularly remarkable due o simple and flexible circui opology. Meanwhile, he magniude conrol can be accomplished by pulse widh regulaion of volage level, so he proposed mulilevel inverer can serve as HF power source wih conrolled magniude and fewer harmonics. This paper mainly analyzes 13level inverers. The mehod of analysis and design is also applicable o oher members of he proposed inverer. The proposed inverer can be applied o he elecrical inducion cooker. FUTURE SCOPE OF WORK The proposed inverer can also be applied o gridconneced phoovolaic sysem and elecrical nework of EV, because he muliple dc sources are available easily from solar panel, baeries, ulra capaciors, and fuel cells. The hardware can also be implemened o he proposed mulilevel inverer for he given parameers in simulaion. REFERENCES 1. Junfeng Liu, K. W. E. 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