Analysis Of Harmonic Mitigation Techniques For Cascaded Asymmetric Inverters

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 22 |NUMBER: 1 |2024 |MARCH Analysis O Ha monic Mi iga ion Techniques Fo Cascaded Asymme ic In e e s Lakshmi PRASANNA1, Jyo hsna.T.R.2 1Elec ical Enginee ing, Resea ch Schola , Andh a Uni e si y, Maddilapalem, Visakhapa nam, India 2Elec ical Enginee ing, P o esso , Andh a Uni e si y, Maddilapalem, Visakhapa nam, India lakshmip asanna. s@andh auni e si y.edu.in, Thummalajy[email p o ec ed] DOI: 10.15598/aeee. 22i1.5641 A icle his o y: Recei ed Dec 30, 2023; Re ised Ma 7, 2024; Accep ed Ma 22, 2024; Published Ma 31, 2024. This is an open access a icle unde he BY-CC license. Abs ac . Mul ile el in e e s (MLIs) a e a ac ing he a en ion o academics as well as indus y as a ea- sible echnology o an ex ensi e a ie y o pu poses, like enewable ene gy sou ces, and Elec ic ehicles. MLIs a e commonly employed as a pa o he sophis i- ca ed con e e con igu a ions in bo h high and medium ol age applica ions. The c ea ion o minimised swi ch MLI s uc u es emains a key objec i e o he p esen esea ch wi h he goal o achie e supe io esul s de- spi e o in ol ed a g ea e numbe o swi ches. Ba- sically, a ious layou s o asymme ical con igu a ion using enhanced cascaded b idge opologies a e iden i ied in a b ie o e iew and e alua ed agains impo an pa- ame e s. I is a me hod o designing mul iple ol age le els using iden ical swi ch coun and ewe de ices. This wo k desc ibes nume ous a ie ies o ha monic mi iga ion echniques, and i also ou lines he mos e - ec i e swi ching angle op imiza ions o p oduce a ious le els. Fu he mo e, he e ec i eness o con igu a ion is e alua ed based on minimising THD due o dec eas- ing lowe o de ha monics. THD is e alua ed agains a ious mi iga ion echniques employing ce ain p o- po ions o sou ce ol ages coming om sola ene gy /ba e ies. THD is calcula ed heo e ically and con- as ed o simula ion ou comes o he sugges ed con- igu a ions. The simula ed wa e o ms o a ious con- igu a ions a e examined using Ha dwa e in loop (HIL) applica ion. Keywo ds Asymme ic In e e , Ha monic mi iga ion echniques, Low equency scheme, To al Ha - monic Dis o ion,OPAL-RT(OP4510). 1. In oduc ion The inco po a ion o enewable ene gy sou ces in o he cu en ly ope a ing powe ne wo k signi ican ly im- p o ed sys em eliabili y. The mos impo an en i- onmen ally iendly powe sou ces a e sola and wind ene gies. Sola ene gy in e connec ion necessi a es he inclusion o con e e s, a ype o simply dc o ac con- e e s. The p ima y ea u es o implemen ing MLIs in applica ions such as elec ic ehicles and enewable en- e gy sou ces a e enhanced powe densi y, g ea e e ec- i eness, less ha monic dis o ion, mo e e ec i e ol - age con ol, lexibili y, adap abili y, and compa ibili y wi h enewable ene gy sou ces. MLIs a e a desi able op ion o a a ie y o applica ions in he enewable ene gy and elec ic ehicle sec o s due o hese ad- an ages MLIs a e equen ly u ilised o such appli- ca ions [1,2]. Classic MLI con igu a ions such as neu al poin clamped MLI (NPCMLI), cascaded H-b idge MLI (CHBMLI), and lying capaci o MLI (FCMLI) ha e become commonplace in p ac ical applica ions. The CHB in e e opology necessi a e minimal componen coun han o he con en ional in e e opologies o c ea ing an iden ical le el o ou pu . CHB in e - e s a e ansi ioning om a adi ional pe spec i e o eal-wo ld applica ions due o capabili ies ha includes high deg ee o modula i y, he abili y o sa ely link o medium ol age wi h supe io powe quali y [3,4]. As a esul , MLIs using ewe componen s a e em- ployed in ecen s udies o c ea e he iden ical num- be o le els iden ical o he adi ional con igu a ion. Despi e his, he app oach o minimizing componen coun s displays ce ain di icul ies o academics. How- e e , esea che s encoun e ed a ew obs acles while c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 36 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 22 |NUMBER: 1 |2024 |MARCH a emp ing o minimize componen coun s, such as enhanced a ed ol age o swi ching de ices, losses in ex ensibili y, minimiza ion o concu en modes coun , occasionally demand o bidi ec ional swi ches, ad anced con ol me hodologies, a massi e numbe o sou ces o accomplish he an icipa ed le el coun om he exis ing opologies [5–9]. Ne e heless, by in eg a - ing sus ainable ene gy sou ces o ac as independen inpu o he cascade in e e s, his d awback can be ec i ied. In compa ison o o he con en ional in e e s uc u es, he CHBMLI needs less swi ch coun and all o he ac o s aking in o coun o c ea e iden ical ol age le els in he ou pu [10]. By u ilising imp o ed cascaded b idge opologies in asymme ical con igu a ions, i is possible o achie e mul iple ol age le els wi h a minimum numbe o swi ches by conside ing bene i s o asymme ic ol - age di ision. These con igu a ions a e desi able o a wide ange o applica ions since hey o e posi i e as- pec s like less swi ch coun , op imized numbe o le els, g ea e e iciency, and imp o ed aul ole ance. Due o ea u es such as a good ex en o modula i y, he abil- i y o secu ely connec o medium ol age, and good powe quali y CHB in e e s ansi ioned om a a- di ional iew o eal wo ld applica ions. Subjec o he le el o ou pu ol age CHBMLI is gene ally called symme ic o asymme ic. Those a e (i) equal ol - age cascaded MLI(ECHBMLI), whe e all inpu ol - ages a e in equal magni ude, (ii)na u al sequence cas- caded MLI(NSCHBMLI), whe e all inpu ol age ol- lows a i hme ic p og ession each is di e ed by one, (iii) bina y cascaded MLI(BCHBMLI), whe e succes- si e inpu ol ages a e doubled,(i ) ina y cascaded MLI(TCHBMLI), in which successi e inpu ol ages a e ipled,( )quasi-linea cascade MLI(QLCHBMLI), whe e all inpu ol ages a e kep cons an so ha he an icipa ed esul ing ol age is eached. Modula ion echniques a e he undamen al aspec s o any MLI s uc u e. In ac , sugges ing no el modu- la ion schemes ha can be implemen ed o any ype o s uc u e in o de o mee speci ied equi emen s can be iewed as a dis inc a ea o esea ch [9,13]. Modula- ion is he p ocess o con ol he ol age wa e o m us- ing swi ches o mee speci ied equi emen s. MLI mod- ula ion schemes a e commonly ca ego ized as high e- quency (HF) o low equency (LF). In [27], i een le el con igu a ion is desc ibed u ilizing high equency con- ol scheme. Hyb id modula ion scheme is employed o i een le el opology desc ibed in [26]. The low equency con ol scheme possesses nume ous signi i- can ea u es, which includes (a) highly e icien wi h low equency o undamen al equency p opo ion; (b) excellen ol age boos ing and a wide con e e ca- paci y; (c) ewe il e demands; (d) comple e omission o lowe ha monics; (e) low swi ching losses wi h e- s ic ed ha monic egula ion; and ( ) addi ionally pe - o mance index is op imised o a ious supe io as- pec s. Va ious modula ion schemes o 15-le el opol- ogy a e p esen ed [23,24]. The wo h o u ilizing a LF scheme han HF scheme a e educed swi ching losses, minimum s ess on swi ches, imp o ed de ice u iliza- ion ac o , and enhanced con e e e iciency. Selec- i e ha monic elimina ion (SHE), nea es le el con ol (NLC), and space ec o con ol (SVC) a e some o he popula LF schemes [11,12]. U ilizing NLC i een le el is de eloped in [25]. Employing NLC dis inc hi een le el opologies designed [28–30]. I g ea e he numbe o le els, SVC is a easonable echnique only issue is i does no elimina e speci ic ha monic. The abo e p ob- lem is mi iga ed using he SHE me hod by adjus ing he swi ch angles men ioned in [10,14]. Re iew o SHE echnique algo i hms desc ibed [18–20]. Minimiza ion o ha monics u ilizing Pa icle Swa m Op imiza ion (PSO) app oach o symme ical MLI con igu a ion is p esen ed [15,17]. Fu he mo e, PSO app oach [21] is lacking o es ima e swi ching angles o speci ied mod- ula ion indices (ma) based on compu a ional esul s om Gene ic Algo i hm (GA) app oach [22]. As he le el o ou pu ex en s, ob ain solu ions using SHE become mo e challenging o implemen . As a conse- quence, ano he s aigh o wa d app oach o SHE ad- d esses abo e issue ha e been execu ed in [16], ha is ha monic mi iga ion which in ol es ema kable mini- miza ion o lowe o de ha monics a he han en i ely e adica ing hem. An asymme ical cascaded b idge MLI opology is p oposed in his wo k, as well as mi iga ion echniques. The ollowing posi i e aspec s a e o e ed by he ec- ommended wo k: •The applica ion o mi iga ion echniques has been e icien ly ca ied ou , i is easily esol ed o con- igu e up ma hema ical analysis and leads o lowe ol age s ess. •I ope a es e icien ly wi h a wide ange o loads. •The a icle ou lines an open-loop s uc u e and new cascade asymme ic in e e s ha a e es ed using he OPAL-RT simula o . This wo k has he ollowing s uc u e Sec ion 2. con on s p oposed opologies wi h all swi ching s a es o hi een and i een espec i ely. Sec ion 3. o- cuses on mi iga ion echniques, Vol age s ess analysis and Loss analysis. Sec ion 4. explo es simula ion esul s, The mal modelling and HIL Implemen a ion, Sec ion 5. compa es p oposed asymme ical con igu- a ions wi h o he opologies and Sec ion 6. e e s o conclusion o wo k. c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 37 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 22 |NUMBER: 1 |2024 |MARCH Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + Fig. 1: P oposed Topology 2. P oposed Topology Figu e 1 shows he planned H-b idge con igu a ion be- o e lea ning mo e abou con igu a ions. I has h ee ol age sou ces and wel e swi ches ha a e IGBTs in an ipa allel wi h diodes. The ollowing subsec ions de- ail he swi ching s a es and modes o ope a ion o he ol age sou ces ha a e classed as 13-le el, and 15-le el con igu a ions based on a ings. 2.1. Thi een-Le el Con igu a ion Figu e 2 shows he swi ching s a es o his me hod, which is a pa o he NSCHBMLI. In Figu e 2, ed deno es he conduc ing pa h o he ma ching swi ches, while g een deno es he non-conduc ing pa h. Twel e swi ches a e in iew wi h h ee p e e ed ol age sou ces a e a anged as a na u al sequence magni udes while c ea ing le els. Since ol age sou ces a e a ed he same, all swi ches a e also a ed he same. a- ble 1 ep esen s he swi ching capabili ies o swi ches o c ea ing he equi ed le el o ol age. Table 1 dis- plays 0 o no conduc i i y and 1 o conduc i i y o he swi ches. The emaining swi ches, such as S4,S3, S8,S7,S12, and S11 illus a ed in igu e 2, a e comple- men a y ope a ions o he swi ches as indica ed abo e and a e shown in able1 as S1,S2,S5,S6,S9, and S10. The ope a ing mode o his con igu a ion is based on NSCHBMLI he e o e, he peak ou pu is exp essed as equa ion (1). The ollowing de ails he con igu a ion’s ope a ing mode: Vopeak = ∞ X n=1 n(n+ 1) 2Vdc.(1) 0Vdc: To achie e ze o ou pu ol age le el in his mode o ope a ion, ei he S1,S3,S6,S8,S9, and S11 conduc o S2,S4,S5,S7,S10, and S12 conduc , as shown in Figu e 2(d)&2( ) and Table 1(7) mode, e- spec i ely. ±1Vdc:S1,S2,S6,S8,S9, and S11 conduc in ac- co dance wi h he indica ions in Figu e 2(c) and Table 1(6) mode o ob ain +1Vdc as he ou pu ol age le el. To ob ain −1Vdc as he ou pu ol age le el, S3,S4, Tab. 1: Ope a ing modes o 13-le el con igu a ion Swi ching Ac ion Mode Vou pu S1S2S5S6S9S10 1 1 1 1 1 1 1 +6Vdc 1 0 1 1 1 1 2 +5Vdc 0 0 1 1 1 1 3 +4Vdc 1 0 0 1 1 1 4 +3Vdc 1 0 1 1 1 0 5 +2Vdc 1 1 0 1 1 0 6 +1Vdc 1 0 0 1 1 0 7 0 0 0 1 0 0 1 8 −1Vdc 0 1 0 0 0 1 9 −2Vdc 0 1 1 0 0 0 10 −3Vdc 1 1 0 0 0 0 11 −4Vdc 0 1 0 0 0 0 12 −5Vdc 0 0 0 0 0 0 13 −6Vdc S5,S7,S10, and S12 conduc as shown in Figu e 2( ) and Table 1(8) mode espec i ely. ±2Vdc:S1,S3,S5,S6,S9, and S11 conduc as shown in Figu e 2(b) and Table 1(5) mode o each +2Vdc as he ou pu ol age le el. To ob ain −2Vdc as he ou pu ol age le el, S2,S4,S7,S8,S10, and S12 conduc as shown in Figu e 2( ) and Table 1(9) mode espec i ely. ±3Vdc:S1,S3,S6,S7,S9, and S10 conduc as shown in Figu e 2(c) and Table 1(4) mode, in o de o p o- duce +3Vdc as he ou pu ol age le el. S2,S4,S5,S7, S11, and S12 conduc in he o de depic ed in Figu e 2(j) and Table 1(10) mode espec i ely, o p oduce an ou pu ol age le el o −3Vdc. ±4Vdc: As illus a ed in Figu e 2(b) and Table 1(3) mode, he swi ching pa e n o p oducing +4Vdc as he ou pu ol age le el. The conduc i i y pa e n o he swi ches is depic ed in Figu e 2(k) and Table 1(11) mode espec i ely o ob ain −4Vdc as he ou pu ol - age le el. ±5Vdc: Figu e 2(a) and Table 1(2) mode, which demons a e he swi ching pa e ns used o p o ide +5Vdc as he ou pu ol age le el, espec i ely. As illus a ed in Figu e 2(l) and Table 1(12) mode, he swi ching pa e n used o gene a e −5Vdc as he ou - pu ol age le el. ±6Vdc:S1,S2,S5,S6,S9, and S10 conduc in he manne depic ed in Figu e 2(a) and Table 1(1) mode espec i ely, o p oduce an ou pu ol age le el o +6Vdc.S3,S4,S7,S8,S11, and S12 conduc as il- lus a ed in Figu e 2(h) and Table 1(13) espec i ely, o p oduce an ou pu ol age le el o −6Vdc. 2.2. Fi een-Le el Con igu a ion This design is a a ia ion on he BCHBMLI, and Fig- u es 2&3 illus a es hei ways o swi ching ope a ion. The con igu a ion used in his ins ance is a bina y one wi h all ol age sou ce a ings. Simila o he example c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 38 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 22 |NUMBER: 1 |2024 |MARCH Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (a) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (b) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (c) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (d) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (e) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + ( ) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (g) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (h) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (i) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (j) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (k) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (l) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (m) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (n) Fig. 2: Ope a ing modes o 13-le el con igu a ion wi h (a) V0= +6Vdc, (b) V0= +5Vdc, (c) V0= +4Vdc, (d) V0= +3Vdc, (e) V0= +2Vdc, ( ) V0= +1Vdc, (g) V0= 0, (h) V0= 0, (i) V0=−1Vdc, (j) V0=−2Vdc, (k) V0=−3Vdc, (l) V0=−4Vdc, (m) V0=−5Vdc, (n) V0=−6Vdc. c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 39 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 22 |NUMBER: 1 |2024 |MARCH Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (a) Load S4 S2 S1 S3 S5 S7 S8 S6 S12 S10 S9 S11 V1 V2 V3 - V0 + (b) Fig. 3: Two ope a ing modes o 15-le el con igu a ion wi h (a) V0= +3Vdc, (b) V0=−3Vdc. (m-1)/2 -(m-1)/2 Le els ω α1α2π/2 α(m-2) α(m-1) αm α(m+1) α(3m-1)/2 3π /2 α3(m-1)/2 α(2m-3) α2(m-1) α(m-1)/2 π 2π α(m+1)/2 0 Fig. 4: Mul i- le el in e e ou pu ol age wa e o m gi en abo e, he a ings o he i s H-b idge swi ch a e di e en om hose o he nex wo. The swi ch- ing beha iou o a ious ope a ing modes is shown in Table 2. The peak ou pu ol age o his con igu a ion is indica ed as equa ion (2). I adhe es o he same se o ci cums ances as desc ibed in Table 1. He e is an explana ion o how he modes o ope a ion ansi ion. Vopeak = ∞ X n=1 (−(1 −2n))Vdc.(2) Tab. 2: Swi ching modes o 15-le el con igu a ion Swi ching Ac ion Mode Vou pu S1S2S5S6S9S10 1 1 1 1 1 1 1 +7Vdc 1 0 1 1 1 1 2 +6Vdc 1 1 0 1 1 1 3 +5Vdc 1 0 0 1 1 1 4 +4Vdc 1 1 1 1 1 0 5 +3Vdc 1 0 1 1 1 0 6 +2Vdc 1 1 0 1 1 0 7 +1Vdc 1 0 0 1 1 0 8 0 0 0 1 0 0 1 9 −1Vdc 0 1 0 0 0 1 10 −2Vdc 0 0 0 0 0 1 11 −3Vdc 0 1 1 0 0 0 12 −4Vdc 0 0 1 0 0 0 13 −5Vdc 0 1 0 0 0 0 14 −6Vdc 0 0 0 0 0 0 15 −7Vdc 0Vdc: As p e iously men ioned in Table 1(7) mode, he analogous swi ches a e conduc ed in he same man- ne o his con igu a ion o achie e ze o ou pu ol age le el, as demons a ed in Figu e 2(g)&2(h) and Table 2(8) mode espec i ely. ±1Vdc: As p e iously men ioned Table 1(6) mode, he pa h i akes is depic ed in Figu e 2( ) and Table 2(7) mode espec i ely, o he c ea ion o +1Vdc as he ou pu ol age le el. Simila o how Table 1(8) was ep oduced in Figu e 2(i) and Table 2(9), i is possible o acqui e he ou pu ol age le el o −1Vdc. ±2Vdc:S1,S3,S5,S6,S9, and S11 conduc s a e de- pic ed in Figu e 2(e) and Table 2(6) mode espec i ely, o o ma ion o +2Vdc as ou pu ol age le el. S2,S4, S7,S8,S10, and S12 conduc s a e illus a ed in Figu e 2(j) and Table 2(10) mode espec i ely, o p o iding −2Vdc as ou pu ol age le el. ±3Vdc: In o de o p o ide he +3Vdc ou pu ol - age le el depic ed in Figu e 3(a) and Table 2(5) mode, S1,S2,S5,S6,S9, and S11 conduc , espec i ely. As demons a ed in Figu e 3(b) and Table 2(11) mode, e- spec i ely, S3,S4,S7,S8,S10, and S12 conduc in he same way o gene a e he −3Vdc ou pu ol age le el. ±4Vdc: In he same way as Table 1(1) mode was de- sc ibed be o e, Table 2(4) mode and Figu e 2(d) bo h display he +4Vdc ou pu ol age le el. The ou pu ol age le el o −4Vdc is p oduced in he same manne as ha desc ibed in Table 1(7) mode and is depic ed in Figu e 2(k) and Table 2(12) mode, espec i ely. ±5Vdc: I ollows he same conduc ion pa h pa e n as in Figu e 2(c) and p oduces an ou pu ol age le el o +5Vdc, which is depic ed in Table 2(3) mode. Simila o he conduc ion pa e n exhibi ed in Figu e 2(l), i yields −5Vdc as he ou pu ol age le el depic ed in Table 2(13) mode. ±6Vdc:S1,S3,S5,S6,S9, and S10 conduc s a e illus- a ed in Figu e 2(b) and Table 2(2) mode espec i ely, o o ma ion o +6Vdc as ou pu ol age le el. S2,S4, S7,S8,S11, and S12 conduc s a e illus a ed in Figu e 2(m) and Table 2(14) mode espec i ely, o p o iding −6Vdc as ou pu ol age le el. ±7Vdc: The same pa e n o he swi ches’ conduc ion pa h, obse ed in Figu e 2(a), is ollowed and esul s in he ou pu ol age le el o +7Vdc, which is ep esen ed c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 40 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 22 |NUMBER: 1 |2024 |MARCH in Table 2(1) mode. Following he same conduc ion pa h as he swi ches in Figu e 2(n), i p oduces he ou pu ol age le el o −7Vdc, which is illus a ed in Table 2(15) mode. 3. Mi iga ion Techniques, Vol age S ess Analysis and Loss Analysis 3.1. Mi iga ion Techniques The swi ching angles conside ed o a qua e wa e symme y is shown in Figu e 4. The e a e 2(m-1) swi ching angles a e exp essed in he wa e o m o an m-le el (m is an odd numbe ) ou pu ol age wa e o m. As seen om Figu e 4, swi ching angles a e di ided in o ou quad an s. The i s quad an ( ange om 0 o π/2) swi ching angles a e called as main swi ch- ing angles. By using main swi ching angles emaining quad an angles a e calcula ed easily. In Fi s quad an in e al (0-π/2), main swi ching angles a e deno ed as α1, α2, ......, α(m−1)/2.(3) In second Quad an in e al (π/2−π), he swi ching angles a e ep esen ed as α(m+1)/2=π−α(m−1)/2, ...., α(m−1) =π−α1.(4) In hi d quad an in e al(π−3π/2), he swi ching angles a e indica ed as αm=π+α1, ...., α3(m−1)/2=π+α(m−1)/2.(5) In ou h quad an in e al(3π/2−2π), he swi ching angles a e indica ed as α(3m−1)/2= 2π−α(m−1)/2, ...., α2(m−1) = 2π−α1. (6) Equal phase me hod: The o mula (7) is capable o being u ilized o c ea e an assessmen o swi ching angles in his me hod. The swi ching angles a e equally dis ibu ed, wi h an a e age spec um o 0-π/2. The numbe m deno es he gene a ed numbe o le els. αi=i∗180 m,(7) whe e i= 1,2,...,(m−1)/2 Hal equal phase me hod: Since he ou pu is oo na ow as well as he esul ing wa e o m appea s as a iangle in EPM, he HEPM app oach has been c ea ed o ob ain a la ge and mo e e ec i e ou pu om he MLIs. The swi ching angles in he 0-π/2spec um a e calcula ed using he o mula as ollows: αi=i∗180 (m+ 1).(8) Hal Heigh me hod: E en hough he i s wo me hods can smoo hly a ange he main swi ching an- gles, he ou pu wa e o m does no look like a sinu- soidal. By using his me hod, he swi ching angles in i s quad an a e es ima ed depending on he sine unc ion. The heo y is ha when sine unc ion alue aises o hal he al i ude o he le el, he swi ching an- gle is posi ioned, leading o an imp o ed ou pu wa e o m. The ollowing o mula speci ies he main swi ch- ing angles. αi= sin−12i−1 m−1.(9) Tab. 3: Swi ching angles o hi een le el opology Me hod Main swi ching angle α1α2α3α4α5α6 EPM 13.84 27.69 41.54 55.38 69.23 83.07 HEPM 12.85 25.71 38.57 51.42 64.28 77.14 HHM 4.78 14.47 24.62 35.68 48.59 66.44 FFM 2.39 7.23 12.31 17.84 24.29 33.22 Feed Fo wa d me hod: Unlike o he app oaches, his me hod was designed o minimize he di e ence be ween he wo hal cycles o he ou pu wa e o m, as shown by he equa ion (10) αi=1 2sin−12i−1 m−1(10) As a esul , he main swi ching angles a e e ec- i ely ob ained o ’m’ numbe o le els by using ou Equa ions (7)-(10). The calcula ion o swi ching an- gle is independen wi h espec o o he me hods as seen om equa ions (7)-(10). Fo hi een le el, i een le el opologies, he main swi ching angles a e calcu- la ed based on he ou me hods and depic ed in Table 3&Table 4 espec i ely. The o mula o Modula ion Index (MI) in e ms o undamen al maximum ol age (Vm) is exp essed as equa ion (11). F om equa ion (12) i seems ha mod- ula ion index is modi ied due o he a ia ion o main swi ching angles espec i ely. The e o e, depending on he in e e con igu a ion op imized alue o MI changes o a ious main swi ching angles espec i ely. MI =Vm V1+V2+..... +Vn ,(11) Vm=4 πV1cos α1+V2cos α2+.... +Vncos α(m−1)/2 (12) c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 41 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 22 |NUMBER: 1 |2024 |MARCH (a) (b) Fig. 5: Vol age s ess o swi ches o dis inc con igu a ion wi h (a) 13-Le el, (b) 15-Le el. Tab. 4: Swi ching angles o i een le el opology Me hod Main swi ching angle α1α2α3α4α5α6α7 EPM 12 24 36 48 60 72 84 HEPM 11.25 22.5 33.75 45 56.25 67.5 78.75 HHM 4.10 12.37 20.92 30.00 40.01 51.79 68.21 FFM 2.05 6.18 10.46 15.00 20.00 25.89 34.10 Tab. 5: Calcula ed %THD o 13-le el and 15-le el con igu a- ions Mi iga ion Me hod %THD 13-le el 15-le el EPM 20.26 18.84 HEPM 18.61 17.54 HHM 6.35 5.5 FFM 21.15 20.67 Theo e ical calcula ion o THD: By using he equa- ion (13) To al Ha monic Dis o ion (THD) is calcu- la ed. Whe e P is he swi ching angle coun and αis he main swi ching angle espec i ely. Fo example, in case o 13-le el in e e P becomes 6 and he i s e m o nume a o changes as π2∗36/8. The emaining wo e ms is exp essed as equa ion (14) & (15) espec- i ely. Using Table 4 he main swi ching angles o hi een le el con igu a ion o indi idual me hod us- ing equa ion 14 %THD is calcula ed. In he same ash- ion o o he sugges ed con igu a ion, THD o mula is exp essed. Fo all he ou me hods %THD calcula ed alue is exp essed in able 5 3.2. Vol age S ess Analysis Maximum ol age s ess o complemen a y swi ches has iden ical magni udes. The maximum ol age s ess o de ices is exp essed as (16), (17), and (18). Vs1=Vs2=Vs3=Vs4=Vdc,(16) Vs5=Vs6=Vs7=Vs8= 2Vdc,(17) Vs9=Vs10 =Vs11 =Vs12 = 3Vdc.(18) whe e VSn ep esen s peak ol age o swi ch when i is u n-o . Fo his s uc u e, he o al s anding ol age (TSV) is deno ed as equa ion (19) TSV = 4 ∗(Vs1+Vs5+Vs9) = 24Vdc.(19) The p opo ion o sum o swi ch u n-o ol ages o peak ol age seems h ough he load is TSV (p.u.). I is 4p.u. in p esen s a e o he p oposed opology. Fig- u e5 po ays a ba cha demons a ing ol age s ess o indi idual swi ching de ice. A his ins ance o 13- le el con igu a ion TSV (p.u.) is 4. Conside ing iden- ical app oach o 15-le el con igu a ion ol age s ess and TSV a e calcula ed. TSV (p.u.) is iden ical o 13- le el o 15-le el con igu a ion. Fo 13-le el con igu a- ion blocking ol age o swi ches depic ed as ba cha shown in Figu e 5(a). F om Figu e 5(a), a +6Vdc le el S1,S2,S5,S6,S9and S10 swi ches a e conduc ing and emaining swi ches a e appea ed as a nonconduc i e elemen . As a esul , he blocking ol age o swi ches S3and S4is 1Vdc,S7and S8a e 2Vdc, and S11 and S12 is 3Vdc, espec i ely. Figu e 5(a) depic s he blocking ol age o swi ches o a 13-le el con igu a ion in he same way ha i does o o he modes o ope a ion. In simila ashion o 15-le el con igu a ion depic ed in Figu e 5(b). 3.3. Loss Analysis Swi ching and conduc ion losses a e di e en ypes o powe losses expe ienced by swi ching de ices. Con- duc ion losses a e b ough on by on-s a e esis ance c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 42 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 22 |NUMBER: 1 |2024 |MARCH THD = u u π2p2 8−π 4p−1 P i=0 (2i−1) αi−p P i=1 cos αi2! p P i=1 cos αi,(13) 2nd e m =π 4(α1+ 3α2+ 5α3+ 7α4+ 9α5+ 11α6),(14) 3 d e m = cos α1+ cos α2+ cos α3+ cos α4+ cos α5+ cos α6.(15) while swi ching losses a e a esul o delays in he swi ch’s on/o p ocesses. I is possible o exp ess he swi ching loss du ing he u n-on p ocess as Pswl u non(i) = ca ie Z on 0 ( )i( )d = ca ie Z on 0Vswo ,i on ( on − )ion,i on d =1 6 ca ie ∗Vswo ,i ∗ion,i ∗ on,(20) Pswl u no (i) = ca ie Z o 0 ( )i( )d = ca ie Z o 0Vswo ,i o io ,i o ( o − )d =1 6 ca ie ∗Vswo ,i ∗io ,i ∗ o .(21) whe e Pswl u non(i),Pswl uno (i)and Vswo deno es he i h swi ch’s u n on, u n o loss, and o -s a e swi ching ol age, espec i ely. Cu en s du ing he swi ch’s on- and o -s a es, espec i ely, a e called Ion and Io . To al swi ching losses (Psw) a e calcula ed by summing u n-on and u n-o losses. Psw(To al) = Nsw X i=1   XNon(i) j=1 Pswlon (ij) +XNo (i) j=1 Pswlo (ij)  (22) whe e Nswis he o al numbe o swi ches o he p o- posed MLI. Conduc ion losses a e appea ed in a swi ch du ing he conduc ion pe iod due o on-s a e esis ance and ol age d op ac oss he swi ch. Gene alized equa ion o conduc ion losses o diode and swi ch as ollows PDcon =VDon ∗iDa g +RDon ∗i2 D ms (23) Pswcon =Vswon ∗iswa g +Rswon ∗i2 sw ms,(24) whe e PDcon and Pswcon a e diode and swi ch conduc- ion losses, VDon and Vswon a e on-s a e ol age d op o diode and swi ch espec i ely. RDon and Rswon a e on-s a e esis ances o diode and swi ch, iDa g,iswa g, iD ms and isw ms a e a e age and RMS cu en s o swi ch espec i ely. 4. Resul s & Discussion 4.1. Simula ion Resul s All he sugges ed con igu a ions in he simula ion a e de eloped and simula ed in an open-loop a chi ec u e employing he simula ion ool MATLAB/Simulink. In he beginning, he swi ching angles o all echniques is de e mined ela ed o i s quad an , and hen he as- socia ed angles o he emaining quad an s es ima ed u ilising qua e -wa e symme y es ima ions. Subse- quen ly acqui ing all swi ching angles o each cycle using he espec i e me hod, he co esponding swi ch- ing ime o each o he swi ching angles du ing ha pe iod is calcula ed nume ically. A his ins ance, o 13-le el con igu a ion en i ely 24 swi ching angles mus be compu ed implying ha 24 swi ching imes accumu- la e using a o emen ioned me hods o a cycle du a ion 50Hz. The swi ching modes as well as ime ha e been implemen ed o ope a e in a manne i he e is a ab- sence o ga e pulse, i ep esen s as null ou pu ha co esponds o ze o swi ching. Topology and modu- la ion make su e ze o swi ching a he beginning and in e media e poin s conce ning posi i e cycle as well as nega i e cycle. A s anda d g id il e is in ended o ensu ing he easibili y o he sugges ed asymme ical con igu a ions o in eg a ion in o he g id since he esul an ol age is s epped wa e he eby ende ing i pu e sinusoidal when he sys em is o open loop. This app oach is ad- di ionally employed o u he esea ch wi h RL loads in o de o make su e he eliabili y o he sugges ed in e e s. In simple e ms, an o dina y low pass pas- si e T/π il e is buil i e a i ely o equency o 50 Hz conside ing equa ion (25) =1 π√LC .(25) I ough o be poin ed ou ha dis inc THD al- ues ela ed o a ious modula ion index (MI) o all he me hods add essed he e a e capable o being ac- complished h ough modi ica ion o dc ol ages solely since he swi ching angles emain unchanged o e e y c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 43 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 22 |NUMBER: 1 |2024 |MARCH Fig. 6: Swi ching pulses o 13-le el con igu a ion Fig. 7: Ou pu s o each b idge o HHM (13-le el con igu a ion) (a) (b) (c) (d) Fig. 8: Ou pu Vol age and cu en o 13-le el con igu a ion wi h (a) R-load, (b) Va ious load scena ios, (c) Dis inc RL-loads, (d) Change o sou ce ol ages. c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 44 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 22 |NUMBER: 1 |2024 |MARCH Tab. 6: Compa ison o Dis inc 13-le el Con igu a ions Pa ame e s [28] [29] [30] P oposed NLe els 13 13 13 13 NSw 15 16 12 12 TSV 6 5 6 4 H-B idge No No No No Modula ion NLC NLC NLC HHM Scheme Pswloss Low Low Low Low THD Medium Medium Medium Low Tab. 7: Compa ison o Va ious 15-le el Con igu a ions Pa ame e s [25] [26] [27] P oposed NLe els 15 15 15 15 NSw 16 14 12 12 TSV 6 5.5 5 4 H-B idge No No No No Modula ion NLC Hyb id LSPWM HHM Scheme Pswloss Low Medium High Low THD Medium Medium High Low 5. Compa ison In his sec ion, dis inc MLI con igu a ions ela ed o hi een le el and i een le el a e p esen ed in Table 6 and Table 7 espec i ely. The con igu a ion in [28] equi es 15 swi ches and ope a ing scheme is NLC. In [29], he swi ches coun is 16 and in simila o [28] i also ope a es u ilizing NLC scheme. In [30] swi ches coun is in same ashion as p oposed and ope a ing scheme is NLC. In compa ison o o he me hods HHM p o ides minimum swi ching loss as well as THD. Coming in o i een le el con igu a ions [26] wo k- ing on hyb id me hodology (combina ion o HF scheme and LF scheme) and coun o swi ches is 14. The unc- ioning o con igu a ion [27] is ela ed o HF scheme and swi ches coun is 12. Due o HF scheme losses a e mo e han LF scheme and i is also ela ed o wo king applica ion. [29] needs 16 swi ches and con ol me hod- ology is NLC. In con as o o he con igu a ions p o- posed asymme ic con igu a ion p o ides op imized e- sul s. 6. Conclusion The ecommended Cascaded b idge in e e u ilizing asymme ical ope a ion p esen s ancho ed swi ching de ices along wi h all h ee dc sou ces o p oduce ou - pu ol age pa e ns employing hi een and i een le els. The p esen s udy buil a simple con ol as well as modula ion app oach employing a ma hema i- cal swi ching me hod. By using PLECS so wa e o al losses a e measu ed. In addi ion, he sugges ed con- igu a ion has educed conduc ion and swi ching losses o accomplishing unique c i e ia in e ms o cos ac- o s and e ec i eness. Likewise, he modi ied module using each kind o une en dc sou ces, he sugges ed cascaded b idge s uc u e can be implemen ed o dis- inc le els. Fu he mo e, THD in he p oposed in- e e ou pu is minimum, as IEEE 519-2014 speci ica- ions. Fo HHM, op imized swi ching angle compu a- ion ha e been achie ed by using nume ical and simula- ion analysis, along wi h in he HIL app oach o all he con igu a ions. 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Kuma , "A Thi een Le el Ladde Type G id-Tied Sola Powe Con e e in Va ying I adiance Con- di ions," 2023 IEEE Renewable Ene gy and Sus ainable E-Mobili y Con e ence (RESEM), Bhopal, India, 2023, pp. 1-6, DOI: 10.1109/RE- SEM57584.2023.10236018. [29] A. Rou ay, K. Shilu e u, A. Singh, R. K. Singh, and R. Mahan y, “Reduced ol age s ess hi een-le el ex endable swi ched capac- i o mul ile el in e e ,” in P oc. IEEE En- e gy Con . Cong . Expo., 2019, pp. 6224– 6230, DOI: 10.1109/ECCE.2019.8912869. [30] J. Zeng, W. Lin, D. Cen, and L. Jun eng, “No el K- ype mul ile el in e e wi h educed compo- nen s and sel -balance,” IEEE J. Eme g. Sel. Top- ics Powe Elec ., ol. 8, no. 4, pp. 4343–4354, Dec. 2020, DOI: 10.1109/JESTPE.2019.2939562. Abou Au ho s Lakshmi PRASANNA (co esponding au ho ) was bo n in Rajahmund y, India. She ecei ed he B.E. and M. Tech om Andh a Uni e si y and VJTI in 2008 and 2010, espec i ely. P esen ly she is wo king as a Resea ch Schola a Andh a Uni e si y, Visakha- pa nam. He esea ch in e es includes Mul ile el in e e s, Elec ic D i es and Elec ic Vehicles. Jyo hsna. T.R. was bo n in Visakhapa nam, India. She ecei ed he M. Tech and Ph.D. om Andh a Uni e si y, Visakhapa nam in 1997 and 2012 espec i ely. P esen ly she is wo king as a P o esso in he Depa men o Elec ical Enginee ing, Andh a Uni e si y, Visakhapa nam. He esea ch in e es includes Double ed Induc ion Gene a o (DFIG), Op imiza ion echniques, Mul ile el in e e s, Elec ic D i es and Elec ic Vehicles. c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 53