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UBC Theses and Dissertations

Dual-loop linear controller for LLC resonant converters Degioanni, Franco 2018

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innzr xurrznt loop vny outzr voltvgz loop hv“ “hofin numzrou“ vyBvvntvgz“A “uxh v“A tight xurrznt rzgulvtionA ovzrBxurrznt protzxtionA vny vmplz wvnyfiiythC]ofizvzrA thi“ xontrol vrxhitzxturz i“ not xommonl– implzmzntzy in aaX rz“onvnt xonvzrtzr“Avny xonvzntionvl “inglz voltvgz loop xontrollzr“ vrz zmplo–zyCihi“ fiork propo“z“ v “implz vny “trvightforfivry mzthoyolog– for yz“igning linzvr xonBtrollzr“ for aaX rz“onvnt xonvzrtzr“C V “implizy “zxony oryzr zquivvlznt xirxuit i“ yzvzlopzyvny zmplo–zy to yzrivz vll thz rzlzvvnt zquvtion“ for yz“igning propzr xompzn“vtor“C V yuvlBloop xontrol “xhzmz inxluying vn innzr xurrznt loop vny outzr voltvgz loop i“ propo“zyC ihziiiAvstruwtimplzmzntvtion of thz yuvlBloop xongurvtion proviyz“ improvzy xlo“zyBloop pzrformvnxzfor thz zntirz opzrvtionvl rvngzCihz thzorztixvl nying“ vrz “upportzy w– yztvilzy mvthzmvtixvl proxzyurz“ vny vvliyvtzyw– “imulvtion vny zflpzrimzntvl rz“ult“CivLuy gummuryeofizr xonvzrtzr“ znvwlz thz xontrol of pofizr ofi from 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C C C C C C C C C C viiList of huvlys C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C flList of Figurys C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C fliUwknowlyxgymynts C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C fliiiDyxiwution C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C flivE Introxuwtion C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C FFCF botivvtion C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C FFCG aitzrvturz gzvizfi C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C HFCGCF gz“onvnt Xonvzrtzr“ C C C C C C C C C C C C C C C C C C C C C C C C C C C IFCGCG aaX gz“onvnt Xonvzrtzr C C C C C C C C C C C C C C C C C C C C C C C C KFCGCH aaX gz“onvnt Xonvzrtzr Xontrol C C C C C C C C C C C C C C C C C C C C LFCH Xontriwution of thz lork C C C C C C C C C C C C C C C C C C C C C C C C C C C C FEFCI ihz“i“ dutlinz C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C FFviihuvly of WontyntsF Unulysis of thy LLW fysonunt Wonvyrtyr C C C C C C C C C C C C C C C C C C C FGGCF aaX gz“onvnt Xonvzrtzr C C C C C C C C C C C C C C C C C C C C C C C C C C C C FHGCFCF YX Gvin Xhvrvxtzri“tix“ of thz aaX gz“onvnt Xonvzrtzr C C C C C C C FIGCG cumzrixvl Iyzntixvtion of thz bo“t Xhvllznging dpzrvting Xonyition C C C FKGCGCF Zfltznyzy Yz“xriwing [unxtion bzthoy C C C C C C C C C C C C C C C C C FLGCGCG Zigznvvluz“ Vnvl–“i“ C C C C C C C C C C C C C C C C C C C C C C C C C C C GEGCGCH himulvtion vny Zflpzrimzntvl kvliyvtion C C C C C C C C C C C C C C C C GFGCH hummvr– C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C GIG LurgyAgignul aoxyl of thy LLW fysonunt Wonvyrtyr C C C C C C C C C C C C GKHCF Vvzrvgz boyzl of thz aaX gz“onvnt Xonvzrtzr C C C C C C C C C C C C C C C C GLHCG boyzl kvliyvtion C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C HHHCGCF himulvtion“ C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C HIHCGCG Zflpzrimzntvl co aovy htvrtBjp C C C C C C C C C C C C C C C C C C C C HJHCH hummvr– C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C HMH DuulALoop Wontrollyr for LLW fysonunt Wonvyrtyr C C C C C C C C C C C C C HNICF hmvllBhignvl boyzl of thz aaX gz“onvnt Xonvzrtzr C C C C C C C C C C C C C IEICG YuvlBaoop Xontrollzr for thz aaX gz“onvnt Xonvzrtzr C C C C C C C C C C C C IGICH Xontrollzr Yz“ign eroxzyurz vny himulvtion gz“ult“ C C C C C C C C C C C C C IJICHCF Xontrollzr Yz“ign eroxzyurz C C C C C C C C C C C C C C C C C C C C C C IKICHCG himulvtion gz“ult“ C C C C C C C C C C C C C C C C C C C C C C C C C C C C INICI Zflpzrimzntvl gz“ult“ C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C JGICJ hummvr– C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C JII Wonwlusion C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C JNJCF hummvr– C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C JNviiihuvly of WontyntsJCG [uturz lork C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C KEVivliogruphy C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C KFUppynxiwysU Efitynxyx Dyswriving Funwtion autriwys C C C C C C C C C C C C C C C C C C C C LFiflList of huvlysGCF cormvlizzy aaX evrvmztzr“ C C C C C C C C C C C C C C C C C C C C C C C C C C C GFHCF htvrt jp Zflpzrimzntvl evrvmztzr“ C C C C C C C C C C C C C C C C C C C C C C C HJICF aaX evrvmztzr“ B Xontrol Yz“ign C C C C C C C C C C C C C C C C C C C C C C C C IKflList of FigurysFCF Wloxk Yivgrvm eofizr htvgz C C C C C C C C C C C C C C C C C C C C C C C C C C C GFCG Wloxk Yivgrvm of gz“onvnt Xonvzrtzr“ C C C C C C C C C C C C C C C C C C C C C JGCF [ullBWriygz aaX gz“onvnt Xonvzrtzr C C C C C C C C C C C C C C C C C C C C C C FHGCG YX Gvin xhvrvxtzri“tix“ aaX gz“onvnt Xonvzrtzr C C C C C C C C C C C C C C C FJGCH Zigznvvluz“ of thz cormvlizzy aaX gz“onvnt Xonvzrtzr C C C C C C C C C C C C GGGCI himulvtion opznBaoop gz“pon“z of thz aaX gz“onvnt Xonvzrtzr C C C C C C C GHGCJ Zflpzrimzntvl opznBaoop gz“pon“z of thz aaX gz“onvnt Xonvzrtzr C C C C C GHHCF dpzrvting boyz“ of thz aaX gz“onvnt Xonvzrtzr vt gz“onvnt [rzquznx– C C GMHCG htvrtBup gz“pon“z of thz aaX gz“onvnt Xonvzrtzr C C C C C C C C C C C C C C HFHCH avrgzBhignvl Vvzrvgz boyzl of thz aaX gz“onvnt Xonvzrtzr C C C C C C C C C HHHCI aaX Xonvzrtzr v“ Vvzrvgz avrgzBhignvl boyzl C C C C C C C C C C C C C C C C C HIHCJ Zflpzrimzntvl htvrt jp aaX) vny aaX2 C C C C C C C C C C C C C C C C C C C C C HKHCK Zflpzrimzntvl htvrt jp aaX+ vny aaX4 C C C C C C C C C C C C C C C C C C C C C HLICF hmvllBhignvl Xirxuit of thz aaX gz“onvnt Xonvzrtzr C C C C C C C C C C C C C IFICG Xontrol [rzquznx–BtoBdutput koltvgz irvn“fzr [unxtion C C C C C C C C C C C IGICH eropo“zy YuvlBaoop Xontrollzr for thz aaX gz“onvnt Xonvzrtzr C C C C C C C IHICI himplizy irvn“fzr [unxtion“ of thz aaX gz“onvnt Xonvzrtzr C C C C C C C C IIICJ himplizy koltvgz aoop irvn“fzr [unxtion C C C C C C C C C C C C C C C C C C C IJICK Xompzn“vtzy irvn“fzr [unxtion“ C C C C C C C C C C C C C C C C C C C C C C C C ILfliList of FigurysICL Xlo“zyBloop Woyz elot of thz Yz“ignzy Xontrollzr C C C C C C C C C C C C C C C IMICM Xlo“zyBloop Woyz elot for Yiffzrznt Gvin“ C C C C C C C C C C C C C C C C C C C INICN aovy htzp“ himulvtion C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C JEICFE koltvgz gzfzrznxz htzp himulvtion C C C C C C C C C C C C C C C C C C C C C C C JFICFF Zflpzrimzntvl erotot–pz C C C C C C C C C C C C C C C C C C C C C C C C C C C C C JGICFG Zflpzrimzntvl gzfzrznxz htzp for YuvlBaoop Xontrollzr C C C C C C C C C C C C JIICFH Zflpzrimzntvl Xurrznt aovy htzp for YuvlBaoop Xontrollzr C C C C C C C C C C JJICFI Zflpzrimzntvl Xurrznt aovy htzp for YuvlBaoop Xontrollzr C C C C C C C C C C JKICFJ Zflpzrimzntvl Xurrznt aovy htzp for 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thz zfli“ting mzthoy“ vrz u“uvll– ovzrl–xomplzfl vny yiffixult to vppl– in prvxtixvl vpplixvtion“CborzovzrA mo“t of thz xurrznt litzrvturz foxu“z“ on yzvzloping “inglz voltvgz loop xonBtrollzr“ for rz“onvnt xonvzrtzr“C ihz implzmzntvtion of yuvlBloop xontrol “xhzmz“A zmplo–ingvn innzr xurrznt loop vny outzr voltvgz loop hv“ “hofin numzrou“ vyvvntvgz“ in trvyitionvlelb topologiz“C V“ v rz“ultA thzrz i“ room for zflploring vny vnvl–zing thz implzmzntvtionof yuvlBloop xontrollzr“ in rz“onvnt xonvzrtzr“CVmong thz yiffzrznt t–pz“ of rz“onvnt xonvzrtzr“A aaX'“ vrz u“uvll– przfzrrzy yuz tothzir highzr zffixiznx–A fiiyz output voltvgz rzgulvtion vny inxrzv“zy pofizr yzn“it– xompvrzyfiith othzr rz“onvnt topologiz“C V“ v rz“ultA thz fiork prz“zntzy in thi“ thz“i“ proviyz“ vxomprzhzn“ivz vnvl–“i“A moyzllingA vny xontrol of aaX rz“onvnt xonvzrtzr“ u“ing v yuvlBloopxontrol “trvtzg–CEBF Lityrutury fyviywYXBYX xonvzrtzr“ hvvz wzzn fiiyzl– u“zy in v vvrizt– of vpplixvtion“ for mvn– –zvr“A “uxh v“tzlzxommunixvtion zquipmznt pMrA xzll phonz pofizr “uppliz“ pNrA lvptop wvttzr– xhvrgzr“ pFErAvny YX motor yrivz“ pFFrC cofivyv–“A YXBYX xonvzrtzr“ vrz vl“o zmplo–zy for rznzfivwlzznzrg– vpplixvtion“ likz photovoltvxi“ pFGA FHr vny YX mixrogriy“ pFIrA vmong othzr“ pFJrCIn vll thz“z vpplixvtion“A high zffixiznx– vny high pofizr yzn“it– rzquirzmznt“ vrz thz mvinkz– rzquirzmznt“C gz“onvnt xonvzrtzr“ vrz vwlz to mzzt thz“z rzquizrmznt“ w– opzrvting vtHEBFB Lityrutury fyviywhighzr “fiitxhing frzquznxiz“ pFKrA fihilz mvintvining high zffixiznx– pFLr in xompvri“on fiithelb xonvzrtzr“Cihz mvin xhvrvxtzri“tix“ of rz“onvnt xonvzrtzr“ vrz “ummvrizzy in thz follofiing pvrvBgrvph“A vny pvrtixulvrl– thz vyvvntvgz“ of thz aaX rz“onvnt xonvzrtzr vrz zflplorzyC borzBovzrA vn zfltzn“ivz rzvizfi of thz prinxipvl xontriwution“ v“ fizll v“ thz lvtz“t vyvvnxz“ in thzmoyzllling vny xontrollzr yz“ign of rz“onvnt xonvzrtzr“ i“ prz“zntzyA highlighting thz knofini““uz“ thvt givz plvxz to thz prz“znt fiorkCEBFBE fysonunt WonvyrtyrsV YXBYX rz“onvnt xonvzrtzr xvn wz xon“truxtzy w– u“ing thz mvin “tvgz“ “hofin in [igC FCGCihz “fiitxh nztfiork proyuxz“ v “quvrz fivvz voltvgz fihixh i“ vpplizy to thz input tzrminvl“of thz rz“onvnt tvnk nztfiorkC V“ v xon“zquznxzA thz tvnk xurrznt i“ z““zntivll– v “inu“oiyvlfivvzformC W– vyju“ting thz “fiitxhing frzquznx– =vs)A xlo“zr toA or furthzr fromA thz tvnk rz“Bonvnt frzquznx– =vy)A thz mvgnituyz of thz xurrznt xvn wz xontrollzyC [invll–A thz “inu“oiyvlrz“onvnt tvnk output xurrznt i“ rzxtizy vny ltzrzy to “uppl– v YX lovy pFMrC V vvrizt– ofrz“onvnt tvnk nztfiork“ xvn wz zmplo–zyA owtvining yiffzrznt output xhvrvxtzri“tix“C ihrzz ofthz mo“t xommon rz“onvnt tvnk xongurvtion“ vrz illu“trvtzy in [igC FCGC ihz rz“onvnt tvnkin thz “zriz“ rz“onvnt xonvzrtzr i“ formzy w– onz xvpvxitor vny onz inyuxtor xonnzxtzy in“zriz“A fihilz in thz pvrvllzl rz“onvnt xonvzrtzrA thz xvpvxitor i“ xonnzxtzy in pvrvllzl fiith thzrzxtizr nztfiork pFNrC Yivzr“z “zriz“Bpvrvllzl rz“onvnt xonvzrtzr xonvzrtzr“ xvn wz owtvinzyw– xomwining thz rz“onvnt tvnk“ of thz “zriz“ vny pvrvllzl xonvzrtzr“A fiith onz xomwinvtionAthz aaX rz“onvnt xonvzrtzrA “hofin in [igC FCGC In “omz xongurvtion“A v high frzquznx–voltvgz trvn“formzr i“ plvxzy wztfizzn thz rz“onvnt tvnk vny thz rzxtizr to “xvlz yofinDupthz output rz“onvnt tvnk voltvgz vny xurrzntCihz mvin vyvvntvgz of rz“onvnt xonvzrtzr“ i“ thzir high zffixiznx– vny pofizr yzn“it–C ihzzffixiznx– of pofizr xonvzrtzr“ i“ mvinl– yztzrminzy w– thz lo““z“ in thz “zmixonyuxtor zlzBIEBFB Lityrutury fyviywSwitch NetworkResonantTankRectifierNetworkOutputFilterVin Vo+-RLfsCs CpLs CsLsLpLsSeriesResonantTankParallelResonantTankLLCResonantTank[igurz FCGO Gznzrvl wloxk yivgrvm of rz“onvnt xonvzrtzr“Cmznt“A vny it xvn wz yiviyzy into xonyuxtion lo““z“ vny “fiitxhing lo““z“C hfiitxhing lo““z“xvn wz minimizzy w– mvking thz turnBon vnyDor turnBoff trvn“ition“ of thz vvriou“ xonvzrtzr“zmixonyuxtor zlzmznt“ vt zzro xro““ing“ of thz rz“onvnt xonvzrtzr quv“iB“inu“oiyvl fivvzBform“ pGFrC ihz“z tzxhniquz“ vrz knofin v“ zzroBxurrznt “fiitxhing =oXh)A vny zzroBvoltvgz“fiitxhing =okh) pGErC gz“onvnt xonvzrtzr“ vrz vwlz to guvrvntzz okh vny oXh opzrvtionvt yiffzrznt xonyition“A rzyuxing “fiitxhing lo““z“ vny znvwling opzrvtion vt highzr “fiitxhingfrzquznxiz“ thvn xompvrvwlz elb xonvzrtzr“C borzovzrA thz rzyuxtion of “fiitxhing lo““z“though okh rzyuxz“ zlzxtromvgnztix intzrfzrznxz =ZbI) gznzrvtzy w– thz xonvzrtzr pGGrCV“ yoxumzntzy in pGHrA thz “zriz“ vny pvrvllzl rz“onvnt topologiz“ hvvz “zvzrvl limitingfvxtor“ fihixh mvkz thzm v lz““Bpopulvr xhoixz for prvxtixvl vpplixvtion“C [or thz “zriz“rz“onvnt xonvzrtzrA lightBlovy opzrvtion rzquirz“ v vzr– fiiyz rvngz of “fiitxhing frzquznxiz“in oryzr to rztvin output voltvgz rzgulvtionC Xompvrzy to thz “zriz“ rz“onvnt xonvzrtzrA thzpvrvllzl rz“onvnt topolog– yoz“ not rzquirz v fiiyz rvngz of “fiitxhing frzquznxiz“ to mvintvinoutput voltvgz rzgulvtionC ]ofizvzrA vt high input voltvgz xonyition“A thz xonvzrtzr “hofi“fior“z xonyuxtion lo““z“A vny highzr turnBoff xurrznt“CJEBFB Lityrutury fyviywEBFBF LLW fysonunt Wonvyrtyrihz aaX rz“onvnt xonvzrtzr xomwinz“ thz vyvvntvgz“ of wothA “zriz“ vny pvrvrvllzl topoloBgiz“C It xvn fiork in v fiiyz output voltvgz rvngz fiith rzlvtivzl– “mvll rvngz vvrivtion ofthz “fiitxhing frzquznx–A offzring fiiyzr output rzgulvtion thvn “zriz“ vny pvrvllzl rz“onvntxonvzrtzr“ pGI{GKrC ihi“ xonvzrtzr hv“ wzzn introyuxzy in v lvrgz numwzr of vpplixvtion“ “uxhv“ wvttzr– xhvrgzr“ pGLA GMrA photovoltvix vpplixvtion“ pGNA HErA fuzlBxzll“ pHFrA highBzffixiznx–pofizr “uppliz“ pHGr vny YX mixrogriy“ pHHrA vmong mvn– othzr intzrz“ting vpplixvtion“ pHI{HKrCV“ illu“trvtzy in [igC FCGA thz rz“onvnt tvnk of thz aaX xonvzrtzr i“ xompo“zy of onz “zriz“inyuxtorA onz “zriz“ xvpvxitor vny onz pvrvllzl inyuxtorC dnz of thz prvxtixvl vyvvntvgz“ ofthz aaX xonvzrtzr i“ thvt thz mvgnztix xomponznt“ xvn wz zv“il– intzgrvtzy into v highfrzquznx– trvn“formzr pHLrC ihz aaX rz“onvnt xonvzrtzr vxhizvz“ okh xonyition“ vt thzinput “fiitxhz“ vny oXh xonyition“ vt thz output rzxtizrA thu“ vxhizving pIGrA vxhizvinghighzr zffixiznx– lzvzl“A vny thz mvflimum zffixiznx– point i“ owtvinzy vt rz“onvnt frzquznx–opzrvtionCbzthoy“ wv“zy on thz [ir“t ]vrmonix Vpproflimvtion =[]V) vrz u“uvll– zmplo–zy tony thz trvn“fzr rvtio of thz xonvzrtzr pFMA HMA HNrC ihz []V vpprovxh i“ wv“zy on thzv““umption thvt thz pofizr trvn“fzr from thz “ourxz to thz lovy through thz rz“onvnt tvnki“ xomplztzl– v““oxivtzy to thz funyvmzntvl hvrmonix of thz [ourizr zflpvn“ion of thz xurBrznt“ vny voltvgz“ involvzyC ihz hvrmonix“ of thz “fiitxhing frzquznx– vrz thzn nzglzxtzyvny thz tvnk fivvzform“ vrz v““umzy to wz purzl– “inu“oiyvl vt thz funyvmzntvl “fiitxhingfrzquznx– pIEA IFrCKEBFB Lityrutury fyviywEBFBG LLW fysonunt Wonvyrtyr Wontrolbo“t of thz vforzmzntionzy vpplixvtion“ rzquirz tight voltvgz vny xurrznt rzgulvtion vt thzoutputC [or thi“ rzv“onA v fzzywvxk loop mu“t wz implzmzntzy in oryzr to vxhizvz thz yz“irzypzrformvnxz vny guvrvntzz “tvwilit– vt thz outputC ihz yz“ign of thz xontrol loop“ i“ u“uvll–wv“zy on “mvllB“ignvl moyzl“ vny linzvr xontrollzr“ vrz xommonl– implzmzntzyCIn trvyitionvl elb xonvzrtzr“A “mvllB“ignvl moyzl“ vrz fizll knofin vny hvvz wzzn yzBvzlopzy vny vnvl–zzy for mo“t of thz xontrol mzthoy“C hinxz thz nvturvl frzquznx– of thzoutput ltzr i“ muxh lofizr thvn thz “fiitxhing frzquznx–A vvzrvging tzxhniquz“ vrz u“uvll–zmplo–zy to yzrivz thz mvthzmvtixvl moyzl“ pIH{IKrC [or “inglzBloop =voltvgz moyz) xonBtrolA thz vvzrvging xonxzpt fiv“ r“t propo“zyA vny thzn rzprz“zntzy in “tvtzB“pvxzC ihz“zmzthoy“ proviyz v xontinuou“Btimz “mvllB“ignvl moyzl fihixh i“ vxxurvtz up to onz hvlf of thzoutput ripplz frzquznx–C elb xonvzrtzr“ vl“o zmplo– yuvlBloop =xurrzntBmoyz) xontrol inoryzr to vxhizvz highzr wvnyfiiyth“C ihz vvzrvging xonxzpt hv“ wzzn vl“o zfltznyzy to owtvinmoyzl“ for thi“ yuvlBloop xongurvtion pILrC]ofizvzrA thz “xznvrio i“ xomplztzl– yiffzrznt for rz“onvnt xonvzrtzr“ wzxvu“z “omz of thz“tvtz vvrivwlz“ =xurrznt“ vny voltvgz“ in thz rz“onvnt tvnk) yo not xontvin YX xomponznt“Avny xontvin lvrgz xomponznt“ of thz “fiitxhing frzquznx– vny it“ hvrmonix“C ihzrzforzAowtvining “mvllB“ignvl moyzl“ i“ not v“ “trvightforfivry v“ in elb xonvzrtzr“A “inxz xonvznBtionvl vvzrvging mzthoy“ xvnnot wz yirzxtl– vpplizyC Yuz to thz o“xillvtor– nvturz of “omzof thz “tvtz vvrivwlz“A thz “fiitxhing frzquznx– intzrvxt“ fiith thz rz“onvnt frzquznx– of thzrz“onvnt tvnkC ihi“ intzrvxtion i“ u“uvll– knofin v“ thz wzvt frzquznx– y–nvmix“ pIMrA vny itxvnnot wz invz“tigvtzy w– u“ing trvyitionvl vvzrvging xonxzpt“ fihixh nzglzxt thz “fiitxhingfrzquznx– xomponznt vny it“ hvrmonix“CYivzr“z mzthoy“ hvvz wzzn propo“zy to yzrivz “mvllB“ignvl“ moyzl“ for rz“onvnt xonvzrtBzr“C V “vmplzByvtv mzthoy i“ vpplizy in pIN{JFrC ihi“ vpprovxh proviyz“ yi“xrztz “mvllB“ignvlLEBFB Lityrutury fyviywmoyzl“ fihixh vrz v “zt of yivzr“z yiffzrznxz zquvtion“ fiith thz “fiitxhing pzrioy v“ thz “vmBpling intzrvvlC ihz yi“xrztz moyzl xvpturz“ thz inhzrznt “vmpling nvturz vny i“ vwlz to przyixtthz “mvllB“ignvl wzhvvior of rz“onvnt xonvzrtzr“ up to thz “fiitxhing frzquznx–C ]ofizvzrA thz“vmplzByvtv vnvl–“i“ tzxhniquz “hofi“ onl– zquvtion“ thvt nzzy to wz “olvzy numzrixvll– vnyyoz“ not proviyz muxh ph–“ixvl in“ight for prvxtixvl implzmzntvtionCIn pJGrA vn zffort to zfltzny thz “tvtzB“pvxz vvzrvging tzxhniquz to moyzlling rz“onvntxonvzrtzr“ i“ prz“zntzyC ihi“ mzthoy propo“z“ “tvtzB“pvxz vnvl–“i“ fiithout linzvr ripplz vpBproflimvtionP in“tzvy onl– xon“iyzring thz YX xomponznt =v“ it i“ yonz for elb xonvzrtzr“)vny thz vmplituyz of thz “fiitxhing frzquznx– hvrmonix“C V xontinuou“Btimz “mvllB“ignvlmoyzl fiv“ yzrivzy for v “zriz“ rz“onvnt xonvzrtzr vny thz owtvinzy rz“ult“ for thz xontrolBtoBoutput voltvgz trvn“fzr funxtion vrz “hofin to wz vzr– vxxurvtz in xompvri“on fiith thzzflpzrimzntvl rz“ult“C ]ofizvzrA thz mzthoy i“ wv“zy on mvtrifl zquvtion“ vny it rzquirz“numzrixvl xomputvtion in oryzr to owtvin thz “mvllB“ignvl moyzlCVn vpprovxh u“ing thz hvrmonix wvlvnxz tzxhniquz i“ propo“zy in pJHrC ihi“ mzthoyyz“xriwz“ thz “–“tzm in frzquznx–Byomvin v“ v “zt of nonlinzvr zquvtion“ thvt yz“xriwz thzhvrmonix“ of thz “–“tzmC ihi“ “zt of zquvtion“ i“ “olvzy w– “zlzxting thz hvrmonix“ vt thzfrzquznx– of thz “timulu“ vny thz trvn“fzr funxtion xvn wz owtvinzyC [urthzrmorzA v gznzrBvlizzy vpprovxh i“ propo“zy in pJIrC ]ofizvzrA woth mzthoy“ rzquirz numzrixvl xvlxulvtion“to owtvin thz xorrz“ponying trvn“fzr funxtion vny thz– yo not proviyz xlo“zy form “olution“CIn pJJrA thz lovy prz“zntzy to thz VX “iyz of thz rzxtizr i“ moyzlzy v“ v timz vvr–Bing rz“i“torC j“ing xonvzr“ion mvtrifl tzxhniquz“ vny vn itzrvtivz proxzyurz thz mvgnituyzvny phv“z of thz timz vvr–ing impzyvnxz xvn wz owtvinzyC Vl“oA xommunixvtion thzor– i“zmplo–zy in pJKr to yzrivz thz “mvllB“ignvl moyzl for vn aaX rz“onvnt xonvzrtzrC ihz vpBprovxhz“ yz“xriwzy hzrz vrz vl“o wv“zy on thz “olution of xomplzfl mvthzmvtixvl vnvl–“i“ vnythz– vrz not “trvightforfivry to vppl– in prvxtixvl vpplixvtion“CMEBFB Lityrutury fyviywihz Zfltznyzy Yz“xriwing [unxtion =ZY[) mzthoy fiv“ introyuxzy in pJLr to yzrivz “mvllB“ignvl moyzl“ for rz“onvnt xonvzrtzr“C ihz yz“xriwing funxtion tzxhniquz i“ zfltznyzy to vmorz gznzrvlizzy multiBvvrivwlz xv“zC ihi“ mzthoy xomwinz“ thz timzByomvin vny frzquznx–yomvin vnvl–“i“ vny zfltrvxt“ thz moyzl w– yiviying moyulvtzy fivvzform“ into “inz vnyxo“inz fivvzform“C ihi“ vpprovxh hv“ wzzn fiiyzl– zmplo–zy in mvn– yiffzrznt vpplixvtion“to zfltrvxt thz “mvllB“ignvl moyzl of rz“onvnt xonvzrtzr“ pJM{KErCVlthough thz vforzmzntionzy moyzl“ gznzrvtzy vxxurvtz rz“ult“A thz– rzquirzy xomplzflmvthzmvtixvl vnvl–“i“ in“tzvy of u“ing xirxuit rzprz“zntvtionC homz vttzmpt“ hvvz wzznmvyz in oryzr to “implif– thz vnvl–“i“ vny yzrivz “mvllB“ignvl zquivvlznt xirxuit“ for rz“onvntxonvzrtzr“C Vn zquivvlznt xirxuit i“ owtvinzy in pKFr w– vppl–ing thz zfltznyzy yz“xriwingfunxtion xonxzptC Yz“pitz thz fvxt thvt thz owtvinzy moyzl i“ v fth oryzr “–“tzmA numzrixvl“olution“ “hofi thvt u“ing v lofizr oryzr “–“tzm i“ vxxurvtz znough to moyzl thz wzhvviorof thz xonvzrtzr pJIrC borzovzrA thz trvn“fzr funxtion“ vrz “till yzrivzy wv“zy on numzrixvl“olution“ vny no zflplixit vnvl–tixvl “olution“ vrz proviyzyC V “implizy thiry oryzr “–“tzm i“proviyzy in pKGA KHrC ihi“ zquivvlznt xirxuit proviyz“ vnvl–tix zflprz““ion“ vny vxxurvtz rz“ult“C]ofizvzrA thz owtvinzy zflprz““ion“ vrz “till xomplzfl to zvvluvtz vny hvry to implzmzntCihz high mvthzmixvl xomplzflit– involvzy rzquirz“ zmpirixvl mzthoyologiz“A “uxh v“ “oftfivrz“imulvtion pKIr vny hvryfivrz mzv“urzmznt“ pKJrA v“ v mzvn“ to owtvin thz frzquznx– rz“pon“zof aaX rz“onvnt xonvzrtzr“C VlthoughA thz“z vpprovxhz“ proviyz vxxurvtz rz“ult“A thz– yonot proviyz gznzrvl xlo“zy form zflprz““ion“Cihz przviou“ moyzlling mzthoyologiz“ vrz u“uvll– zmplo–zy to yz“ign v “inglz voltvgzxontrol loopA rvthzr thvn v yuvlBloop xontrol “xhzmzC ihz implzmzntvtion of xurrzntBmoyzxontrollzr“ hv“ wzzn vv“tl– zflplorzy for elb Wuxk vny Woo“t xonvzrtzr“ pKK{KNrA wut thzrzi“ not muxh rz“zvrxh yonz for aaX rz“onvnt xonvzrtzr“C ihz wznzt“ of zmplo–ing xurrzntBmoyz in aaX xonvzrtzr“ i“ “hofin pLEA LFrC Zmplo–ing “omz intzrz“ting zmpirixvl mzthoy“thz trvn“fzr funxtion“ vrz owtvinzy vny yz“xriwzyC ]ofizvzrA in oryzr to vugmznt thz unyzrBNEB3B Wontrivution of thy kork“tvnying of aaX xonvzrtzr“A xlo“zyBform zflprz““ion“ thvt yz“xriwz thz “–“tzm wzhvvior foryiffzrznt pvrvmztzr“ vrz nzzyzy vny hvvz –zt to wz “tuyizyCEBG Wontrivution of thy korkihi“ fiork introyuxz“ vvluvwlz thzorztixvl xonxzpt“ to thz zly of xontrol for aaX rz“onvntxonvzrtzr“ v“ fizll v“ u“zful prvxtixvl vpplixvtion of thz iyzv“ yzvzlopzyO• Iyzntixvtion vny vnvl–“i“ of thz mo“t xhvllznging xonyition from v moyzlling vnyxontrol point of vizfiC• V lvrgzB“ignvl moyzl of thz aaX rz“onvnt xonvzrtzr opzrvting vt rz“onvnt frzquznx–C• ihz yzrivvtion of v linzvrizzy moyzl to owtvin vll thz rzquirzy trvn“fzr funxtion“ foryz“igning xontrol loop“C• Implzmzntvtion of v yuvlBloop xontrol “xhzmz fiith innzr rzxtizyBxurrznt loop vnyoutzr outputBvoltvgz loopCV“ v rz“ultA vn zffzxtivz vny “trvightforfivry mzthoyolog– i“ vxhizvzyC ihz propo“zy xonBtrollzr i“ formzy w– vn innzr xurrznt loop vny outzr voltvgz loop zmplo–ing thz vvzrvgzyrzxtizy xurrznt vny output voltvgz v“ fzzywvxk “ignvl“ rz“pzxtivzl–C ihz vpplixvtion of vyuvlBloop “xhzmz znvwlz“ “ignixvnt vyvvntvgz“A v“ yztvilzy in thi“ fiorkC iho“z vyvvntvgz“inxluyz tight xurrznt rzgulvtionA ovzrBxurrznt protzxtionA vny vmplz xontrollzr wvnyfiiythCborzovzrA thz implzmzntvtion of vn innzrBxurrznt loop znvwlz“ yz“irvwlz xlo“zyBloop pzrBformvnxz ovzr v fiiyz rvngz of opzrvting xonyition“C In thi“ fiv–A thi“ fiork introyuxz“ vnvxxurvtz linzvr moyzl for aaX xonvzrtzr“ vvliy for thz mo“t xhvllznging xontrol xonyitionAthz vpplixvtion of yuvlBloop xontrollzr“ to “uxxz““full– xompzn“vtz thz xomplzfl aaX rz“onvntxonvzrtzr topolog–A vny v u“zful tool thvt znvwlz“ “implz vny “trvightforfivry linzvr xontrollzryz“ignCFEEB4B hhysis cutlinyEBH hhysis cutlinyihi“ fiork i“ orgvnizzy v“ follofi“P• In Xhvptzr G thz mvin zquvtion“ vny xhvrvxtzri“tix“ of thz aaX rz“onvnt xonvzrtzrvrz vnvl–zzy vny thz y–nvmix wzhvvior of thz aaX rz“onvnt xonvzrtzr i“ “tuyizyC ihzZfltznyzy Yz“xriwing [unxtion mzthoy i“ zmplo–zy to owtvin thz linzvrizzy moyzl ofthz xonvzrtzrC V pvrvmztrix vnvl–“i“ of v normvlizzy aaX xonvzrtzr i“ pzrformzy to“tuy– thz polz yi“plvxzmznt vt yiffzrznt opzrvting xonyition“C• In xhvptzr H thz vvzrvgz lvrgzB“ignvl moyzl of thz aaX xonvzrtzr opzrvting vt rz“onvntfrzquznx– i“ introyuxzyC Zquvtion“ vrz proviyzy to owtvin thz zquivvlznt y–nvmixinyuxtvnxz of thz zquivvlznt xirxuitC himulvtion vny zflpzrimzntvl rz“ult“ vrz proviyzyto vvliyvtz thz propo“zy moyzlC• In xhvptzr I thz propo“zy yuvlBloop xontrol “xhzmz i“ introyuxzyC V “implizy “mvllB“ignvl moyzl i“ yzrivzy to owtvin vll thz rzquirzy trvn“fzr funxtion“ to yz“ign thz xonBtrollzr“C V xontrol yz“ign proxzyurz zflvmplz i“ “hofinA vny thz xonpzn“vtor for wothinnzr vny outzr loop vrz yz“ignzyC ihz pzrformvnxz of thz xontrollzr i“ vzrizy w–“imulvtion“ vny zflpzrimzntvl rz“ult“ vt yiffzrznt opzrvting point“C• [invll–A in Xhvptzr J v “ummvr– vny xonxlu“ion“ of thi“ fiork vrz prz“zntzyA vlong fiith“omz yztvil“ of futurz rz“zvrxh iyzv“CFFWhuptyr FUnulysis of thy LLW fysonuntWonvyrtyreofizr “uppliz“ fiith highzr zffixiznx– vny pofizr yzn“it– vrz highl– yz“irzy in pofizr zlzxtronix“vpplixvtion“C gz“onvnt xonvzrtzr“ vrz vwlz to vxhizvz tho“z rzquirzmznt“ fiith lofi “fiitxhinglo““z“ znvwling highzr frzquznx– opzrvtionC In pvrtixulvrA thz aaX xonvzrtzr “tvny“ out forit“ fiiyz output voltvgz rzgulvtion vxhizving “oftB“fiitxhing ovzr thz zntirz opzrvting rvngzCV“ v u“uvl prvxtixzA moyzlling zffort“ vim to moyzl thz yominvnt wzhvvior“ of thz “–“tzmAfihilz nzglzxting othzr in“ignixvnt phznomznvC himplizy tzrminvl zquvtion“ of thz xompoBnznt zlzmznt“ vrz u“zyA vny mvn– v“pzxt“ of thz “–“tzm rz“pon“z vrz nzglzxtzy vltogzthzrCihz rz“ulting “implizy moyzl –izly“ ph–“ixvl in“ight into thz “–“tzm wzhvviorA “implif–ingthz vnvl–“i“ proxzyurzC ihu“A thz moyzlling proxz““ involvz“ u“z of vpproflimvtion“ to nzBglzxt lz““ “ignixvnt xomplixvtzy phznomznvA in vn vttzmpt to unyzr“tvny fihvt i“ thz mo“timportvntCIn thi“ xhvptzr thz opzrvtion prinxiplz“ vny xonvzntionvl moyzlling tzxhniquz“ for aaXrz“onvnt xonvzrtzr“ vrz vnvl–zzyC [ir“tA thz YX gvin xhvrvxtzri“tix“ in “tzvy–B“tvtz opzrvtionof thz xonvzrtzr vrz “tuyizyC In thz “zxony pvrt of thz xhvptzrA thz “mvllB“ignvl wzhvvior of thzaaX rz“onvnt xonvzrtzr vt yiffzrznt opzrvting point i“ vnvl–zzyC ihz Zfltznyzy Yz“xriwing[unxtion mzthoy i“ yzvzlopzy vny zflplvinzyC V numzrixvl vnvl–“i“ of thz zigznvvluz“ of thz“–“tzm i“ pzrformzyC [invll–A “imulvtion vny zflpzrimzntvl rz“ult“ vrz proviyzy to vvliyvtzthz thzorztixvl vnvl–“i“CFGFBEB LLW fysonunt WonvyrtyrFBE LLW fysonunt Wonvyrtyrihz “xhzmvtix xirxuit of thz aaX rz“onvnt xonvzrtzr i“ “hofin in [igC GCFC ihz “quvrz fivvzBform gznzrvtzy w– thz fullBwriygz invzrtzr i“ vpplizy to thz rz“onvnt tvnk xompo“zy w– thrzzrz“onvnt zlzmznt“A thz rz“onvnt “zriz“ inyuxtor =Ly)A thz “zriz“ rz“onvnt xvpvxitor =Sy) vnythz pvrvllzl mvgnztizing inyuxtor =Lm)C ihz ltzrzy xurrznt i“ “xvlzy w– v thz turn“ rvtion R upusfor thz high frzquznx– trvn“formzr vny rzxtizy w– thz output rzxtizr fiith ltzrxvpvxitor to owtvin v YX voltvgz vt thz outputC[rom thz “xhzmvtix xirxuit “hofin in [igC GCFA thz nonlinzvr zquvtion“ thvt yz“xriwz thzwzhvvior of thz xonvzrtzr xvn wz zflprz““zy v“LytiLy=t)ttR fpu − vCy=t)− n siwn =iLy=t)− iLm=t)) vv=t) =GCF)Sytvj=t)ttR iLy=t) =GCG)LmtiLm=t)ttR n siwn =iLy=t)− iLm=t)) vv=t) =GCH)Svtvv=t)ttR n|iLy=t)− iLm=t)| − vv=t)bL=GCI)S4S3S2S1Vin vinvD1D2Co voRLCr LrLmiLr iLmirecnsnsnp[igurz GCFO [ullBWriygz aaX gz“onvnt XonvzrtzrCFHFBEB LLW fysonunt Wonvyrtyrihz “tvtz vvrivwlz“ vrz yznzy in funxtion of thz “zriz“ inyuxtor xurrznt =iLy)A “zriz“xvpvxitor voltvgz =vj)A pvrvllzl mvgnztizing inyuxtor =iLm) vny thz output xvpvxitor voltvgz=vv)CFBEBE DW Guin Whuruwtyristiws of thy LLW fysonunt Wonvyrtyrihz gvin xhvrvxtzri“tix“ of thz xonvzrtzr thvt rzlvtz thz output voltvgz vny thz “fiitxhingfrzquznx– vrz mvinl– yznzy w– thz ltzr nvturz of thz rz“onvnt tvnkC bzthoy“ wv“zy on[ir“t ]vrmonix Vpproflimvtion vrz u“uvll– zmplo–zy to ny thz “tzvy–B“tvtz xhvrvxtzri“tix“of rz“onvnt xonvzrtzr“C ihz proxzyurz mv– wz “ummvrizzy v“• gzprz“znt thz input “quvrzBfivvz voltvgz vny xurrznt fiith thzir funyvmzntvl xompoBnznt“A ignoring vll thz highzrBoryzr hvrmonix“C• Ignorz thz zffzxt“ from thz output xvpvxitorA v““uming xon“tvnt voltvgz vt thz outputyuring onz “fiitxhing x–xlzC• gzfzr thz owtvinzy “zxonyvr–B“iyz vvrivwlz“ to thz primvr– “iyz of thz trvn“formzrCW– follofiing thz“z “tzp“A thz nonlinzvr wzhvvior of rz“onvnt xonvzrtzr“ i“ vpproflimvtzyw– v linzvr moyzl zflxitzy w– vn zffzxtivz “inu“oiyvl input “ourxzC ihz “implizy moyzl xvnwz “olvzy w– u“ing xonvzntionvl xirxuit thzor– vny thz zflprz““ion thvt rzlvtz“ thz outputvoltvgz in funxtion of thz “fiitxhing frzquznx– i“ yzrivzyC ihi“ zflprz““ion i“ fizllBknofin inthz litzrvturz vny i“ givzn w–Mv RnfvfpuRv 2u=m− F)√=m=v 2u − F))2 + v 2u=v 2u − F)2=m− F)2a2=GCJ)lithFIFBEB LLW fysonunt Wonvyrtyr0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.511.52OverloadGainNo LoadRegion IIZVSRegion IZVSRegion IIINo ZVS  M vΔ f s,maxf s,minLighterLoadQ1Q2Q3Q4M =1vNormalized Switching Frequencyfsfr Normalized DC GainV o V  inn[igurz GCGO YX Gvin xhvrvxtzri“tix“ aaX rz“onvnt xonvzrtzrCa RFbaj√LySy; baj RM2n2bL; vs Rvsvy; vy RFG√LySy; m R=Ly + Lm)Ly=GCK)W– u“ing zquvtion =GCJ)A thz normvlizzy voltvgz gvin v“ normvlizzy “fiitxhing frzquznx–xhvrvxtzri“tix of thz aaX rz“onvnt xonvzrtzr i“ plottzy in [igC GCGC V“ “hofinA thz mvflimumvoltvgz gvin vvriz“ vxxorying to thz lovy xonyitionC [or lightzr lovy“ =a yzxrzv“z“)A thz pzvkgvin i“ highzr vny it movz“ to lofizr frzquznxiz“A rzvxhing vy2 R)2√(Lm+Lr)Crfor no lovyxonyitionC dn thz othzr hvnyA vt rz“onvnt frzquznx– vyA unitvr– gvin i“ vxhizvzy for vll lovyxonyition“ inxluying “hortBxirxuit opzrvtionCFJFBFB bumyriwul Ixyntiwution of thy aost Whullynging cpyruting Wonxitionihz YX gvin xhvrvxtzri“tix“ xvn wz yiviyzy in thz thrzz mvin rzgion“ “hofin in [igC GCGCIn oryzr to guvrvntzz okhA thz xonvzrtzr mu“t opzrvtz fiithin gzgion I vny IIC lhzn thzxonvzrtzr'“ “fiitxhing frzquznx– i“ vwovz rz“onvnxz =wuxk rzgion)A thz voltvgz gvin i“ lofizrthvn onzC Vrouny rz“onvnxzA thz gvin of thz xonvzrtzr wzxomz“ xlo“z to onzA vny for frzquznBxiz“ wzlofi rz“onvnxz thz gvin wzxomz“ highzr thvn onz =woo“t moyz)C ihzrzforzA thz outputvoltvgz xvn wz xontrollzy w– vvr–ing thz “fiitxhing frzquznx– of thz mvin “fiitxhz“Cihz opzrvting rvngz of thz aaX xonvzrtzr yzpzny“ on thz lovy xonyition v“ “hofin in[igC GCGC ]ofizvzrA fihzn thz “fiitxhing frzquznx– i“ vyA xonvzrtzr'“ gvin xhvrvxtzri“tix“ vrzinyzpznyznt of thz lovy xonyitionC ihzrzforzA opzrvtion vrouny rz“onvnt frzquznx– i“ u“uvll–yz“irzy to minimizz thz “fiitxhing frzquznx– vvrivtion vt yiffzrznt lovyC borzovzrA vt rz“onvntfrzquznx– opzrvtion thz xonvzrtzr vxhizvz“ thz highz“t zffixiznx– opzrvting pointCFBF bumyriwul Ixyntiwution of thy aost Whullyngingcpyruting WonxitionYuz to thz nonlinzvr xhvrvxtzri“tix“ of thz “–“tzmA opzrvtion vt yiffzrznt “fiitxhing frzquznBxiz“ lzvy“ to yiffzrznt trvn“iznt rz“pon“z“C In thi“ “zxtionA thz zfltznyzy yz“xriwing funxtionmzthoy i“ vpplizy to vnvl–zz thz “mvllB“ignvl wzhvvior of thz xonvzrtzr vrouny yiffzrznt opBzrvting xonyition“C Iyzntif–ing thz mo“t xhvllznging xonyition from v xontrol point of vizfivny yzriving v “implizy moyzl vt thvt point i“ v hvny– vny xommon “trvtzg– to yz“ignlinzvr xompzn“vtor“CFKFBFB bumyriwul Ixyntiwution of thy aost Whullynging cpyruting WonxitionFBFBE Efitynxyx Dyswriving Funwtion aythoxihz yz“xriwing funxtion vnvl–“i“ i“ v tzxhniquz xommonl– zmplo–zy to “tuy– frzquznx– rzB“pon“z of nonlinzvr “–“tzm“C It i“ vn zfltzn“ion of linzvr frzquznx– rz“pon“z vnvl–“i“C Inlinzvr “–“tzm“A trvn“fzr funxtion“ yzpzny onl– on thz frzquznx– of thz input “ignvlC ]ofizvzrAin nonlinzvr “–“tzm“A fihzn v “pzxix xlv““ of input “ignvl “uxh v“ “inu“oiyvl i“ vpplizy to vnonlinzvr zlzmzntA thz “–“tzm xvn wz rzprz“zntzy w– v funxtion thvt yzpzny“ not onl– onfrzquznx– wut vl“o on input vmplituyzC ihi“ funxtion i“ rzfzrrzy to v“ v yz“xriwing funxBtionC In oryzr to u“z “inu“oiyvlBinput yz“xriwing funxtion vnvl–“i“ thz “–“tzm mu“t “vti“f–thz follofiing xonyition“O• conlinzvritiz“ vrz timzBinvvrivntC• conlinzvritiz“ yo not gznzrvtz vn– “uwBhvrmonix v“ v rz“pon“z to thz “inu“oiyvl inputC• ihz “–“tzm ltzr“ out thz hvrmonix“ gznzrvtzy w– thz nonlinzvritiz“CV“ rz“onvnt xonvzrtzr“ “vti“f– vll thz“z xonyition“A thz ZY[ mzthoy hv“ wzzn fiiyzl– u“zyto moyzl thz wzhvvior of thz“z xonvzrtzr“CHurmoniw UpprofiimutionYuz to thz rz“onvnt tvnk ltzr xhvrvxtzri“tix“A thz xurrznt through thz rz“onvnt inyuxtorvny thz voltvgz in thz rz“onvnt xvpvxitor vrz nzvrl– “inu“oiyvl fivvzform“C ihz– xvn wzvpproflimvtzy w– thzir funyvmzntvl xomponznt“A fihzrzv“ thz xurrznt vny voltvgz vt thzoutput xvn wz vpproflimvtzy w– thzir YX tzrm“C W– u“ing []VA thz VX “tvtz vvrivwlz“mv– wz yznzy v“ v xomwinvtion of “inz vny xo“inz xomponznt“ in funxtion of thz “fiitxhingfrzquznx–C ihz rz“onvnt xurrznt“ vny thz rz“onvnt voltvgz vrz vpproflimvtzy w–OiLy=t) R iys=t) “in=!st)− iyj=t) xo“=!st) =GCL)FLFBFB bumyriwul Ixyntiwution of thy aost Whullynging cpyruting WonxitioniLm=t) R ims=t) “in=!st)− imj=t) xo“=!st) =GCM)vj=t) R vjs=t) “in=!st)− vyj=t) xo“=!st) =GCN)ihz yzrivvtivz“ vrz givzn w–tiLy=t)ttR(tiys=t)tt+ !siyj=t))“in=!st)−(tiyj=t)tt− !siys=t))xo“=!st) =GCFE)tiLm=t)ttR(tims=t)tt+ !simj=t))“in=!st)−(timj=t)tt− !sims=t))xo“=!st) =GCFF)tvj=t)ttR(tvjs=t)tt+ !svjj=t))“in=!st)−(tvjj=t)tt− !svjs=t))xo“=!st) =GCFG)ihz tzrm“ iys vny iyj rzprz“znt“ thz “inz vny xo“inz xomponznt“ of thz xurrznt in thzrz“onvnt tvnkC ihz “vmz xonxzpt xvn wz vpplizy for im=t) vny vj=t)C ihi“ yzxompo“itionintroyuxz“ tfio “tvtz“ for zvxh vx vvrivwlzA rz“ulting in v “zvznthBoryzr y–nvmix moyzlCEfitynxyx Dyswriving Funwtion aythoxV“ “tvtzy wzforzA thz ZY[ mzthoy xomwinz“ timz yomvin vny frzquznx– yomvin vnvl–“i“Azfltrvxting thz moyzl w– yiviying moyulvtzy fivvzform“ into “inz vny xo“inz xomponznt“Cihz nonlinzvr tzrm“ xvn w– vpproflimvtzy zithzr w– thz funyvmzntvl xomponznt or thz YXxomponzntC ihz ZY['“ vrz yznzy v“V)=t; fpu) RIfpu=GCFH)V2=iss; isj; fv) RIissipvv =GCFI)V+=iss; isj; fv) RIisjipvv =GCFJ)V4=iss; isj) RGip =GCFK)FMFBFB bumyriwul Ixyntiwution of thy aost Whullynging cpyruting Wonxitionip R√=iys − ims)2 + =iyj − imj)2 =GCFL)fihzrz fpu i“ thz input voltvgz vny y i“ thz yut– x–xlz =flzy JE:)A iss vny isj vrz thz “inzvny xo“inz xomponznt“ of thz “zxonyvr– of thz trvn“formzrA vny ip i“ thz xurrznt ofiing inthz primvr– of thz trvn“formzr yznzy w– zquvtion =GCFL)C [rom zquvtion“ =GCFH) B =GCFK)Athz nonlinzvr tzrm“ of thz “tvtz zquvtion“ =GCF) B =GCI) xvn wz vpproflimvtzy w–fpu R V)=t; fpu) “in=!st) =GCFM)siwn=iLy − iLm)vv=t) R V2=iss; isj; fv) “in=!st)− V+=iss; isj; fv) xo“=!st) =GCFN)is R V4=iss; ijs) =GCGE)ihz xurrznt is i“ thz onz ofiing vt thz “zxonyvr– of thz trvn“formzrC huw“tituting thz quv“iB“inu“oiyvl fivvzform“ vny thz nonlinzvr tzrm“ of thz “tvtz zquvtion“ w– thzir vpproflimvtion“Athz xontinuou“ “tvtz zquvtion“ vrz owtvinzy v“ follofi“LytiysttRIfpu− Ly!siys − vjs − In=iys − ims)ipvv =GCGF)LytiyjttR Ly!siyj − vjj − In=iyj − imj)ipvv =GCGG)SytvjsttR −Sy!svjj + iys =GCGH)SytvjjttR Sy!svjs + iyj =GCGI)LmtimsttR −Lm!simj + In=iys − ims)ipvv =GCGJ)LmtimjttR Lm!sims +In=iyj − imj)ipvv =GCGK)SvtvvttRGnip − nbLvv =GCGL)FNFBFB bumyriwul Ixyntiwution of thy aost Whullynging cpyruting Wonxitionihi“ “zt of zquvtion“ yz“xriwz“ thz vpproflimvtzy lvrgzB“ignvl moyzl of thz aaX rz“onvntxonvzrtzrC [or owtvining thz “tzvy–B“tvtz opzrvting pointA thz timz yzrivvtivz“ mu“t wz“zt to zzroC W– yzning thz opzrvting point =bL; !s)A thz zquvtion xvn wz “olvzy vnyowtvin thz “tzvy–B“tvtz vzxtor X R pIys; Iyj; Ims; Imj; fjj; fjs; fvrC ]ofizvzrA thi“ moyzlxontinuz“ hvving “omz nonlinzvr tzrm“ vri“ing from thz proyuxt of tfio or morz timzBvvr–ingquvntitiz“C ihz “–“tzm xvn wz linzvrizzy vrouny onz opzrvting pointC ihz linzvrizzy moyzlxvn wz zflprz““zy in v “tvtz “pvxz rzprz“zntvtion tx=t) R Qx=t) + Ru=t)A fihzrz V vny W vrzthz Jvxowivn mvtrixz“ of thz “–“tzm givzn w–Qpq R@v=x=t); u=t))@xq=t)xo;uo=GCGM)Rpq R@v=x=t); u=t))@uq=t)xo;uo=GCGN)ihz vforzmzntionzy zflprz““ion“ vny yzrivvtion“ vrz highlightzy in yztvil in VppznyiflCZquvtion =GCGM) vny =GCGN) vrz mvtrixz“ of yimzn“ion L× L vny L× F rz“pzxtivzl–CFBFBF Eigynvuluys Unulysisihz zigznvvluz“ =p) of mvtrifl V rzprz“znt thz polz“ of thz linzvrizzy moyzl vrouny v quiz“xzntopzrvting pointA vny thzir po“ition in thz xomplzfl plvnz yz“xriwz“ thz y–nvmix wzhvviorof thz “–“tzmC Yuz to thz high oryzr of thz “–“tzmA owtvining vnvl–tixvl zflprz““ion vrzhvry to yzrivzC V numzrixvl vnvl–“i“ i“ zmplo–zy to zvvluvtz thz y–nvmix wzhvvior of thzxonvzrtzrC io gvin gznzrvlit–A thz “uw“zquznt vnvl–“i“ i“ yonz u“ing thz normvlizzy aaXrz“onvnt xonvzrtzr “hofin in ivwlz GCFA zmplo–ing thz follofiing wv“z quvntitiz“ vvuA Zv R√LrCrA ivu Rvoaovny vu R)2√LrCrCihz loxvtion of thz zigznvvluz“ of thz normvlizzy xonvzrtzr i“ plottzy in [igC GCH foryiffzrznt “fiitxhing frzquznxiz“C V“ “hofin in thz gurzA thz zigznvvluz“ go through yiffzrzntGEFBFB bumyriwul Ixyntiwution of thy aost Whullynging cpyruting Wonxitionivwlz GCFO cormvlizzy evrvmztzr“Parameter FaleeVpu 1Vy)2Cy)2Vm 3Vyfy 1n 1linz“ of xon“tvnt yvmping =) vny nvturvl frzquznx– =!u) v“ vs xhvngz“C In aaX rz“onvntxonvzrtzr“A thz rz“onvnt tvnk zlzmznt“ vrz u“uvll– “mvll xompvrzy fiith thz output ltzrpvrvmztzr“ in oryzr to vxhizvz high “fiitxhing frzquznxiz“ fiith lofi ripplz xomponznt“ vt thzoutput voltvgzC ihzrzforzA thz y–nvmix“ of thz rz“onvnt tvnk vrz muxh fv“tzr vny it i“ onl–yznzy w– thz rz“onvnt tvnk zlzmznt“C dn thz othzr hvnyA thzrz i“ v lofi frzquznx– xomponzntyztzrminzy w– thz intzrvxtion wztfizzn thz output ltzr xvpvxitor vny thz zquivvlznt y–nvmiximpzyvnxz of thz rz“onvnt tvnkC [rom thz gurzA v pvir of yominvnt polz“ xvn wz iyzntizyChinxz thz moyzlling zffort“ foxu“ on xhvrvxtzrizing thz xonvzrtzr'“ lofi frzquznx– y–nvmix“Athz “potlight of thi“ fiork i“ put in thz yominvnt polz“Cihz yi“plvxzmznt of thz yominvnt polz“ for yiffzrznt lovy xonyition“ i“ yztvilzy in [igCGCH=w)C V“ illu“trvtzy in thz gurzA thz zigznvvluz“ “hofi thz lofiz“t yvmping rvtio vt rz“onvntfrzquznx–C lhzn thz lovy i“ yzxrzv“zyA thz polz“ movz ovzr linz“ of xon“tvnt !u fihilzxro““ing yivzr“z  linz“C Vt xon“tvnt “fiitxhing frzquznx– thz minimum yvmping i“ owtvinzyfor minimum lovy vny opzrvting vt rz“onvnt frzquznx–CFBFBG gimulution unx Efipyrimyntul Vulixutionihz numzrixvl vnvl–“i“ pzrformzy “hofi“ thz minimum yvmping opzrvtion hvppzn“ vt thzrz“onvnt frzquznx–C ihi“ wzhvvior xvn wz vl“o ow“zrvzy in thz timz yomvin rz“pon“z of thzGFFBFB bumyriwul Ixyntiwution of thy aost Whullynging cpyruting WonxitionIm(λ )iIm(λ )iConstant ζ Lines(a) (b)ζminfrConstant ω  LinesnR =1nR = 2.5nR =5n R =10nLight LoadDominant Polesfor DifferentLoadsRe(λ )ifsfsf s>f rf s<f rDominant PolesRe(λ )i[igurz GCHO Zigznvvluz“ of thz normvlizzy aaX rz“onvnt xonvzrtzr of ivwlz GCF =v) zigznvvluz“yi“plvxzmznt for yiffzrznt opzrvting xonyition“ yznzy w– thz vsA v pvir of yominvnt polz i“iyzntizyC cotz thvt thz rz“onvnt frzquznx– “hofi“ thz lz““ yvmpzy opzrvting xonyition vnythi“ i“ v xritixvl point for xontrol xompzn“vtionC =w) Yi“plvxzmznt of thz yominvnt polz“ foryiffzrznt lovy xonyition“A thz yvmping fvxtor yzxrzv“z“ fiith thz lovyCxonvzrtzr vt yiffzrznt opzrvting xonyition“C ihz output voltvgz rz“pon“z for v frzquznx– “tzpvrouny yiffzrznt opzrvting xonyition“ i“ “hofin in [igC GCICihz voltvgz rz“pon“z for thz normvlizzy rz“onvnt xonvzrtzr vrouny yiffzrznt opzrvtingxonyition“ vftzr vppl–ing v G: frzquznx– “tzp i“ illu“trvtzy in [igC GCI =v) to =x)C V“ zflpzxtzyAthz trvn“iznt rz“pon“z vt yiffzrznt opzrvting xonyition“ “hofi“ yi“tinxtivz xhvrvxtzri“tix“C ihzvoltvgz yi“plv–“ vn o“xillvtor– wzhvvior wzlofi vny vrouny thz rz“onvnt pointC Vt rz“onvntopzrvtionA thz o“xillvtion“ “hofi thz lvrgzr rzlvtivz ovzr“hoot vny “zttling timzA mzvning“mvllzr yvmping fvxtorC Vt highzr frzquznxiz“A thz yvmping fvxtor inxrzv“z“A vny thz outputhv“ vn ovzrByvmpzy rz“pon“z vny no o“xillvtion“ vrz proyuxzyCGGFBFB bumyriwul Ixyntiwution of thy aost Whullynging cpyruting Wonxition1.161.181.21.220 200 400v onv onv ontn tn tnBelow Resonance0 200 4000.9811.021.04Resonance0 200 4000.770.790.810.83Above Resonance(b) (c)(a)[igurz GCIO dutput voltvgz rz“pon“z of thz normvlizzy aaX xonvzrtzr unyzr v “mvll frzquznx–“tzp =G:)C =v) Wzlofi rz“onvnxzA =w) vrouny rz“onvnxzA =x) vwovz rz“onvnxzC2%vo,around resonance f( )rvo,below resonance 0.7f( )rvo,above resonance 1.3f( )rfrequency[igurz GCJO Zflpzrimzntvl trvn“iznt rz“pon“z unyzr v “mvll frzquznx– “tzp =G:) vrouny yifBfzrznt opzrvting point“CVn zflpzrimzntvl rz“pon“z of vn aaX rz“onvnt xonvzrtzr plvtform i“ “hofin in [igC GCJCihz y–nvmix rz“pon“z of thz output voltvgz vftzr vppl–ing v “mvll “fiitxhing frzquznx– “tzpGHFB3B gummury=G:) vt thrzz yiffzrznt opzrvting xonyition“ xvn wz ow“zrvzyC [or opzrvtion vwovz rz“onvntfrzquznx–A thz ovzrByvmpzy wzhvvior xvn wz ow“zrvzy vny thz output yoz“ not “hofi ovzr“hootor o“xillvtion“C Vt lofizr frzquznx– opzrvting point“A v“ rz“onvnxz vny wzlofi rz“onvnxzA thzoutput voltvgz “hofi“ vn ovzr“hoot vny o“xillvtor– rz“pon“zC ]ofizvzrA thz minimum yvmpingfvxtor i“ vxhizvzy vt rz“onvnt frzquznx– opzrvtionA “hofiing lvrgzr rzlvtivz pzrxzntvgz ofovzr“hoot vny longzr o“xillvtion“CVn VX ripplz xomponznt v““oxivtzy fiith thz high frzquznx– polz“ of mvtrifl V xvn wz“zzn in [igC GCJC [or yiffzrznt “fiitxhing frzquznxiz“A thz“z high frzquznx– polz“ vrz movingin thz xomplzfl plvnzP v“ “uxhA thz voltvgz ripplz hv“ yiffzrznt vmplituyz“ yzpznying on thzopzrvting pointC lhzn opzrvting wzlofi thz rz“onvnt frzquznx–A thz output voltvgz of thzxonvzrtzr i“ lvrgzr vny “hofi“ v mvflimum voltvgz ripplz of JEE mkC ]ofizvzrA fihzn opzrvtingvt highzr frzquznxiz“A thz ripplz xomponznt i“ rzyuxzy =vpproflimvtzl– FEE mk for opzrvtionvt F:H vy)C [or vll opzrvting point“A rzgvrylz““ of thz “fiitxhing frzquznx–A thz voltvgz ripplzxomponznt i“ lz““ thvn J: of thz output voltvgz vny xvn wz nzglzxtzy in thz y–nvmix vnvl–“i“of thz “–“tzmC ihzrzforzA thz v““umption“ in hzxtion GCGCF vny thz vnvl–“i“ in hzxtion GCGCGvrz vvliyvtzyCFBG gummuryIn thi“ xhvptzr thz mvin zquvtion“ of thz aaX rz“onvnt xonvzrtzr fizrz introyuxzy vny vnBvl–zzyC ihz zfltznyzy yz“xriwing funxtion mzthoy fiv“ pzrformzy to owtvin v mvthzmvtixvlmoyzl of thz aaX rz“onvnt xonvzrtzrC ihz “tzvy–B“tvtz zquvtion“ of thz “–“tzm fizrz linBzvrizzy vrouny yiffzrznt opzrvting xonyition“C Yuz to thz high mvthzmvtixvl xomplzflit–A vnumzrixvl vnvl–“i“ fiv“ pzrformzy in thz normvlizzy yomvin to iyzntif– thz y–nvmix wzhvvBior of thz aaX xonvzrtzrC ihz polz yi“plvxzmznt of thz “–“tzm fiv“ vnvl–zzy unyzr yiffzrzntfrzquznx– vny lovy opzrvting xonyitionC himulvtion“ vny zflpzrimzntvl rz“ult“ fizrz proviyzyGIFB3B gummuryto vzrif– thz timz yomvin rz“pon“z of thz xonvzrtzrC V pvir of xomplzfl yominvnt polz“ fizrziyzntizyC ihz lofi frzquznx– xomponznt of thz “–“tzm i“ yztzrminzy w– thz po“ition oftho“z yominvnt polz“C ihz polz“ rzvxh thz minimum yvmping opzrvtion fihzn thz xonvzrtzropzrvtz“ vt rz“onvnt frzquznx–A yzning thi“ v“ thz mo“t xhvllznging xonyition from v xontrolpoint of vizfiCGJWhuptyr GLurgyAgignul aoxyl of thy LLWfysonunt Wonvyrtyrihz wzhvvior of thz aaX rz“onvnt xonvzrtzr opzrvting vrouny rz“onvnxz i“ yznzy w– v pvirof yominvnt polz“C ]ofizvzrA thz ZY[ mzthoy rzquirz“ highl– xomplzfl mvthzmvtixvl vnvl–“i“vny numzrixvl xvlxulvtion to “tuy– thz xonvzrtzr'“ rz“pon“z for prvxtixvl vpplixvtion“C ihzu“z of zquivvlznt xirxuit“ i“ v ph–“ixvl vny intuitivz vpprovxh fihixh znvwlz“ thz vpplixvtionof thz fizllBknofin xirxuit vnvl–“i“ tzxhniquz“C [oxu“ing on thz lofi frzquznx– xomponznt“of thz fivvzform i“ hzlpful to vxhizvz u“vwlz moyzl“ for thz xonvzrtzrA w– foxu“ing on thz“zyominvnt fzvturz“A thz wzhvvior of thz xonvzrtzr xvn wz moyzlzy v“ v rzyuxzy oryzr “–“tzmCIn thi“ xhvptzrA vn vvzrvgz lvrgzB“ignvl moyzl of thz aaX rz“onvnt xonvzrtzr opzrvting vtrz“onvnt frzquznx– i“ yzrivzyC ihz owtvinzy “zxony oryzr xirxuit przyixt“ thz lofi frzquznx–wzhvvior of thz “–“tzm fihzn it i“ opzrvting vt rz“onvnt frzquznx–C ihz y–nvmix impzyvnxzof thz rz“onvnt tvnk i“ moyzlzy v“ vn zquivvlznt inyuxtor yznzy w– thz pvrvmztzr“ of thzrz“onvnt tvnk vny output ltzrC It i“ “hofin thvt thz vvzrvgz nvturvl rz“pon“z of thz “–“tzm i““imilvr to v rzxtizy aX xirxuit vny thz xhvrvxtzri“tix zquvtion“ xvn wz founyC ihz owtvinzyxirxuit xvn wz yirzxtl– “olvzy to xvlxulvtz thz vvzrvgz output voltvgz vny rzxtizy xurrzntC[invll–A “imulvtion vny zflpzrimzntvl xvpturz“ vrz proviyzy to vzrif– thz vxxurvx– of thzowtvinzy zquivvlznt moyzlCGK3BEB Avyrugy aoxyl of thy LLW fysonunt WonvyrtyrGBE Uvyrugy aoxyl of thy LLW fysonunt WonvyrtyrVt rz“onvnt frzquznx– opzrvtionA thz aaX xonvzrtzr hv“ onl– tfio opzrvtion moyz“ yzpznyingon thz po“ition of thz fullBwriygz “fiitxhz“C V “implizy zquivvlznt xirxuit for zvxh onz of thzopzrvting moyz“ i“ v“ “hofin in [igC HCFC lhzn thz “fiitxhz“ cF vny cI vrz turnzy on=“truxturz I )A thz voltvgz fpu−nfv i“ vpplizy to thz rz“onvnt tvnk vny thz xonvzrtzr wzhvvz“v“ “hofin in [igC HCF =v)C dn thz othzr hvnyA fihzn c2 vny c+ vrz xonyuxting =“truxturz II )Athz rz“onvnt tvnk voltvgz i“ yznzy w– nfv − fpu v“ “hofin in [igC HCF =w)C V“ thz xonvzrtzropzrvtz“ vt rz“onvnt frzquznx–A thz intzrvvl of timz of zvxh “uw“truxturz i“ yznzy w–tr R k√LySy; fiith k R E; F; G; H; I::: =HCF)ihz xonvzrtzr opzrvtz“ in htruxturz I yuring hvlf x–xlz k =tr L t L tr+)) vny it “fiitxhz“ tohtruxturz II yuring hvlf x–xlz =k + F) =tr+) L t L tr+2)C ihz xonvzrtzr i“ “fiitxhing wztfizzn“truxturz I vny II vt zvzr– “fiitxhing vxtion yznzy w– vyC[rom [igC HCF =v)A “truxturz I xvn wz yznzy w– thz follofiing yiffzrzntivl zquvtion“fpu R LytiLy=t)tt+ vCy=t) + nvv=t) =HCG)nvv=t) R Lmtim=t)tt=HCH)iLy=t) R SytvCy=t)tt=HCI)iylj=t) RSvnnvv=t)tt=HCJ)iylj=t) R n=iLy=t)− iLm=t)) =HCK)W– “olving =HCG) B =HCJ) thz “olution“ for iLy=t)A iLm=t)A vCy=t)A vv=t) vny iylj=t) vrz owtvinzyCIn prvxtixzA Sv >> SyA vny “implizy xurrznt vny voltvgz “olution“ inxluying onl– onzGL3BEB Avyrugy aoxyl of thy LLW fysonunt Wonvyrtyr(b)(a)nvOCrLrLmVin imirecnn2iLr vCrVin vOCrLrLmim COiLr vCrD1D2S4S1 S3S2Vin vOCrLrLmimiLr vCrS4S1 S3S2D1D2vinvCrLrLmVin imirecnn2iLr vCrnvOCOCOCOvinvn:1n:1[igurz HCFO dpzrvting moyz“ of thz aaX rz“onvnt xonvzrtzr vt rz“onvnt frzquznx–O v) htruxBturz IA “fiitxh hF vny hI vrz dcA thz vpplizy voltvgz in thz rz“onvnt tvnk i“ po“itivzC w)htruxturz IIA hG vny hH vrz dcA thz vpplizy voltvgz in thz rz“onvnt tvnk i“ nzgvtivzC“inu“oiyvl xomponznt of frzquznx– !y R√LySy vrz owtvinzy v“iLm=t) R iLm=tr) +nvv=tr)Lmt =HCL)iLy=t) R iLy=tr) +(SvSv + n2Sy) (fpu − nvv=tr)− vCy=tr)Zv)“in=!yt) +nvv=tr)Lmt =HCM)vCy=t) R vCy=tr) +(SvSv + n2Sy)=fpu − nvv=tr)− vCy=tr))=F− xo“=wyt)) + nvv=tr)GLmt2 =HCN)vv=t) R vv=tr) +(nSySv + n2Sy)=fpu − nvv=tr)− vCy=tr))=F− xo“=wyt)) =HCFE)iylj=t) R n(SvSv + n2Sy)=fpu − nvv=tr)− vCy=tr)) “in=wyt) =HCFF)GM3BEB Avyrugy aoxyl of thy LLW fysonunt Wonvyrtyrdn thz othzr hvnyA thz yiffzrzntivl zquvtion“ for “truxturz II vrz givzn w–− fpu R Ly tiLy=t)tt+ vCy=t)− nvv=t) =HCFG)− nvv=t) R Lmtim=t)tt=HCFH)iLy=t) R SytvCy=t)tt=HCFI)iylj=t) R −Svnnvv=t)tt=HCFJ)iylj=t) R −n=iLy=t)− iLm=t)) =HCFK)W– “olving =HCFG) through =HCFK)A thz xurrznt vny voltvgz“ in thz xonvzrtzr fihzn it i“ opzrBvting in “truxturz II vrz givzn w–iLm=t) R iLm=tr+))− nvv=tr+))Lmt =HCFL)iLy=t) R iLy=tr+)) +(SvSv + n2Sy)(−fpu + nvv=tr+))− vCy=tr+))Zv)“in=!yt)− nvv=tr+))Lmt =HCFM)vCy=t) R vCy=tr+)) +(SvSv + n2Sy)=−fpu + nvv=tr+))− vCy=tr+)))=F− xo“=wyt))− nvv=tr+))GLmt2 =HCFN)vv=t) R vv=tr+))−(nSySv + n2Sy)=−fpu + nvv=tr+))− vCy=tr+)))=F− xo“=wyt)) =HCGE)iylj=t) R −n(SvSv + n2Sy)=−fpu + nvv=tr+))− vCy=tr+))) “in=wyt) =HCGF)GN3BEB Avyrugy aoxyl of thy LLW fysonunt WonvyrtyrV“ thz xonvzrtzr “fiitxhz“ wztfizzn “truxturz I vny IIA thz initivl xonyition“ for zvxh “uwBintzrvvl vrz yznzy w– thz nvl “tvtz in thz przviou“ “truxturz vny thz– nzzy to wz “olvzyin v x–xlzBw–Bx–xlz mvnnzrC V“ thz xonvzrtzr i“ opzrvting vt rz“onvnxzA thz lzngth of zvxh“uwBintzrvvl i“ yznzy w– ds R)2mrA vny =HCN)B=HCGE) xvn wz zflprz““zy in yi“xrztz yomvin v“vCy=k + F) R vCy=k) + G(SvSv + n2Sy)=fpu − nvv=k)− vCy=k)) + nvv=k)MLmv 2y=HCGG)vv=k + F) R vv=k) + G(nSySv + n2Sy)=fpu − nvv=k)− vCy=k)) =HCGH)vCy=k+G) R vCy=k+F)+G(SvSv + n2Sy)=−fpu+nvv=k+F)−vCy=k+F))− nvv=k + F)MLmv 2y=HCGI)vv=k + G) R vv=k + F)− G(nSySv + n2Sy)=−fpu + nvv=k + F)− vCy=k + F)) =HCGJ)ihz “tvrtBup rz“pon“z of thz aaX xonvzrtzr i“ illu“trvtzy in [ig HCGC ihz rz“pon“z przB“zntzy w– thz lofi frzquznx– xomponznt“ of thz rzxtizy xurrznt vny output voltvgz rz“zmwlz“v “inu“oiyvl fivvzform “imilvr to tho“z of v “zxony oryzr aX xirxuitC ihz yi“xrztz vvluz“ ofthz output voltvgz vt zvzr– “fiitxhing vxtion xvn wz przyixtzy w– =HCGG) B =HCGJ)C ihi“ lofifrzquznx– rz“pon“z of thz xonvzrtzr xvn wz moyzlzy w– v “zxony oryzr “–“tzm w– nzglzxtingthz high frzquznx– y–nvmix“C In oryzr to ny thz xlo“zyBform timz thvt inxluyz“ thz yi“xrztz“olution“A thz vvrivwlz“ vCy=k)A vv=k)A vCy=k + F) vny vv=k + F) vrz rzyznzy v“ x)=k)A x2=k)Ax+=k) vny x4=k) rz“pzxtivzl–A vny vj vny vv xvn wz rzfirittzn in vn mvtrifl form v“ “hofinin =HCGL)C Yzninga RSvSv + n2SyP r RSySv + n2SyP =HCGK)HE3BEB Avyrugy aoxyl of thy LLW fysonunt WonvyrtyrirecStttAverageResponseLLCConverterLLCConverterIterative Solutionvon2VinT2sT2eq[igurz HCGO htvrtBup rz“pon“z of thz aaX rz“onvnt xonvzrtzr vt rz“onvnt frzquznx–C ihzyi“xrztz zquvtion“ przyixt thz y–nvmix rz“pon“z of thz xonvzrtzr vt zvxh “fiitxhing vxtionCihz lofi frzquznx– rz“pon“z xvn wz moyzlzy w– v “zxony oryzr “–“tzm w– nzglzxting thz highfrzquznx– y–nvmix“C266666664x)=k + F)x2=k + F)x+=k + F)x4=k + F)377777775R266666664E E F− Ga −GnaE E −Gnr F− Gn2rF− Ga Gna E EGnr F− Gn2r E E377777775266666664x)=k)x2=k)x+=k)x4=k)377777775+266666664anr−anr377777775Gfpu =HCGL)HF3BEB Avyrugy aoxyl of thy LLW fysonunt Wonvyrtyrihz yi“xrztz zflprz““ion =HCGL) xvn wz “olvzy w– vppl–ing thz ZBtrvn“formC holving for vvthz output voltvgz zflprz““ion in Z yomvin i“ givzn w– thz follofiingx2=z) R vv=z) R fpuGnrz=z + F)=z − F) pz2 + G =n2r− a) z + =Ga− F)r =HCGM)ihz Z trvn“form for v xo“inz fivvzform of vmplituyz Q vny pzrioy d fiith YX xomponznti“ givzn w– thz follofiingZ =Q=F− xo“=!kd ))) R =F− xo“=!d ))=z + F)z=z − F)=z2 − Gz xo“=!d ) + F) =HCGN)Vxxorying to =HCGM) vny =HCGN)A vny xon“iyzring thvt Sv >> SyA thz output voltvgz xvnwz zflprz““zy v“vv=k) Rfpun=F− xo“=!lxdsk)) =HCHE)fiith ds R)2mrC W– Xompvring =HCHE) vny =HCGM) thz follofiing zflprz““ion i“ owtvinzyxo“(!lxFGvy)RSvSv + n2Sy(F− n2SySv)=HCHF)ihz lofi frzquznx– wzhvvior of thz xonvzrtzr xvn wz moyzlzy w– thz zquivvlznt xirxuit“hofin in [igC HCHC ihz inyuxtor Llx rzprz“znt“ thz impzyvnxz of thz rz“onvnt tvnk vtrz“onvnt frzquznx–A fihzrzv“ thz yioyz“ T) vny T2 moyzl thz output rzxtizrC ihz nvturvlfrzquznx– of thz vvzrvgz moyzl i“ yznzy w– !lx Ru√LeqCoA vny Llx xvn wz yzrivzy from =HCHF)v“Llx Rn2SySv2Lyxo“−)264 SvSv+u2Cr0B@F− n2SySv1CA3752 =HCHG)HG3BFB aoxyl VulixutionDIo voLeqVinirecCon:1[igurz HCHO himplizy lvrgzB“ignvl zquivvlznt xirxuit of thz aaX rz“onvnt xonvzrtzr thvtmoyzl“ thz vvzrvgz wzhvvior of thz xonvzrtzr opzrvting vt rz“onvnt frzquznx–Cv“ in prvxtixzA Sv >> Sy vny =HCHG) xvn wz vpproflimvtzy w– iv–lor “zriz“ v“Llx=Sy)|Cr5( R(FI+n2SrKSv− n4S4yKES2v+Mn6S2yNIJSv− :::)2Ly ∼R 2ILy =HCHH)ihi“ zquvtion “hofi“ thz “implizy mvthzmvtixvl zflprz““ion “–nthz“i“ of thz zquivvlzntinyuxtor introyuxzy in [igC HCHC ihi“ zquivvlznt inyuxtvnxz rzprz“znt“ thz y–nvmix zquivvlzntimpzyvnxz of thz rz“onvnt tvnk yz“xriwzy in Xhvptzr GC ihz intzrvxtion wztfizzn Llx vnySv xvn wz rzprz“zntzy v“ v “zxony oryzr xirxuit thvt znvwlz“ moyzlling thz lofi frzquznx–y–nvmix wzhvvior of thz aaX rz“onvnt xonvzrtzr opzrvting vt rz“onvnt frzquznx–CGBF aoxyl VulixutionIn thi“ “zxtionA thz yzrivzy lvrgzB“ignvl moyzl i“ xompvrzy vny vzrizy fiith thz aaX rz“onvntxonvzrtzrC himulvtion rz“ult“ vny zflpzrimzntvl xvpturz“ vrz proviyzy to vvliyvtz thz propo“zymoyzlC [ir“tA “imulvtion“ of thz aaX rz“onvnt xonvzrtzr vny it“ vvzrvgz moyzl vrz vnvl–zzyChzxonyl–A zflpzrimzntvl “tvrtBup rz“pon“z“ of thz aaX xonvzrtzr vrz “hofinC ihz owtvinzymzv“urzmznt“ vrz xon“i“tznt fiith thz xvlxulvtzy timz“ owtvinzy w– u“ing thz vvzrvgz moyzlAit i“ vwlz to przyixt thz lofi frzquznx– wzhvvior of thz aaX rz“onvnt xonvzrtzrCHH3BFB aoxyl VulixutionGBFBE gimulutionsihz “tvrtBup trvn“iznt rz“pon“z of thz normvlizzy aaX rz“onvnt xonvzrtzr vny it“ zquivvlzntvvzrvgz xirxuit of vrz “hofin in [igC HCIC ihz gurz illu“trvtz“ thz output voltvgz vny rzxtizyxurrznt fihzn thz xonvzrtzr i“ opzrvting vt rz“onvnt frzquznx–C V“ “hofinA thz moyzl i“ vwlzto przyixt lofi frzquznx– wzhvvior of thz aaX xonvzrtzrC Woth voltvgz vny xurrznt “hofi v lofifrzquznx– “inu“oiyvl fivvzform xhvrvxtzri“tix of aX xirxuit“C ihz moyzl przyixt“ thz wzhvviornzglzxting thz “fiitxhing ripplz in thz output voltvgz vny thz rz“onvnt xurrznt in thz rzxtizrCihz nvturvl frzquznx– of thz xonvzrtzr i“ yznzy w– thz intzrvxtion wztfizzn thz rz“onvnttvnkA moyzlzy v“ vn zquivvlznt inyuxtor givzn w– =HCHH)A vny thz output ltzr xvpvxitor SvCihz zquvtion thvt yznz“ thi“ funyvmzntvl frzquznx– i“ givzn w–vlx RnG√LlxSv=HCHI)Teq0120120480480 10 20 30 40 50 0 10 20 30 40 50Output Voltage Rectified Currentv oni recni recnvo LLC Converter irec LLC Converter vo Average Model irec Average Model v ontn tnThe low frequency component is predicted by the average model[igurz HCIO Xompvri“on wztfizzn aaX Xonvzrtzr vny Vvzrvgz avrgzBhignvl boyzlHI3BFB aoxyl VulixutionV“ it i“ “hofin in [igC HCIA thz y–nvmix wzhvvior of woth thz aaX xonvzrtzr vny thz vvzrvgzmoyzl vrz thz “vmzC borzovzrA thz xurrznt through Llx rz“zmwlz“ thz vvzrvgz wzhvvior ofthz rzxtizy xurrzntCGBFBF Efipyrimyntul bo Loux gturtAipYiffzrznt zflpzrimzntvl “tvrtBup rz“pon“z“ of thz aaX opzrvting vt rz“onvnt frzquznx– vnyno lovy vrz prz“zntzy in [igC HCJ B HCKC ihz xvpturz“ “hofi thz trvn“iznt rz“pon“z for yiffzrzntrz“onvnt tvnk vny output ltzr pvrvmztzr“ yz“xriwzy in ivwlz HCFC ihz owtvinzy rz“pon“z““hofi“ thz przyixtzy “zxony oryzr vvzrvgz wzhvviorC ]ofizvzrA v“ zflpzxtzyA thz ri“ing timz“ forthz output voltvgz vny rzxtizy xurrznt vrz yiffzrznt yzpznying on thz xonvzrtzr'“ pvrvmztzr“CYuring “tvrtBup trvn“iznt vt no lovy xonyitionA thz ri“ing timz of thz output voltvgz in vrzxtizy aX xirxuit i“ hvlf of thz nvturvl pzrioy of thz “–“tzmC In thi“ xv“zA it i“ givzn w–dlxGRFGvlxRn√LlxSv =HCHJ)V“ “hofin in [igC HCJ vny HCKA for yiffzrznt “zt of output xvpvxitor vny rz“onvnt tvnkpvrvmztzr“A thz “tvrt up rz“pon“z hv“ v funyvmzntvl “inu“oiyvl xomponzntC ihz mzv“urzyivwlz HCFO htvrt jp Zflpzrimzntvl evrvmztzr“Parameter LL3) LL32 LL3+ LL34Vy 81H 81H 81H 39:7HCy 32nP 32nP 32nP 18:9nPCv 16:5P 32P 50P 39:6Pn 5:33 5:33 5:33 7:8Vlx 199:86H 199:86H 199:86H 97:95HTlx 67:7s 94:27s 117:84s 50:17sHJ3BFB aoxyl Vulixution(a)(b)T2eqT=2eq Calculated 34 μs  Measured 37 μs  T2eqT=2eq Calculated 47 μs  Measured 52 μs  [igurz HCJO htvrtBup aaX rz“onvnt xonvzrtzr vt rz“onvnt frzquznx–C evrvmztzr“O =v) [ullBWriygzA aaX)C =w) [ullBWriygzA aaX2CHK3BFB aoxyl Vulixution(a)(b)T2eqT=2eq Calculated 58 μs  Measured 61 μs  T2eqT=2eq Calculated 25 μs  Measured 27.5 μs  [igurz HCKO htvrtBup aaX rz“onvnt xonvzrtzr vt rz“onvnt frzquznx–C evrvmztzr“O =v) [ullBWriygzA aaX+C =w) ]vlfBWriygzA aaX4CHL3B3B gummurydlx for zvxh tvnkBoutput ltzr xongurvtion i“ “imilvr to thz xvlxulvtzy vvluz“ zmplo–ing=HCHJ)CGBG gummuryIn thi“ xhvptzrA v lvrgzB“ignvl vvzrvgz moyzl of thz aaX rz“onvnt xonvzrtzr fiv“ yzrivzyC ihzowtvinzy moyzl przyixt“ thz lofi frzquznx– xomponznt of thz xonvzrt fihzn it i“ opzrvtingvt rz“onvnt frzquznx–C ihz y–nvmix“ of thz rz“onvnt tvnk vrz moyzlzy v“ v zquivvlzntinyuxtvnxz Llx thvt intzrvxt“ fiith thz output ltzr to yznz thz lofi frzquznx– rz“pon“z ofthz xonvzrtzrC ihz owtvinzy xirxuit xvn wz yirzxtl– “olvzy to xvlxulvtz thz vvzrvgz outputvoltvgz vny rzxtizy xurrzntC himulvtion vny zflpzrimzntvl xvpturz“ fizrz proviyzy to vzrif–thz yzrivzy vnvl–tixvl moyzlCHMWhuptyr HDuulALoop Wontrollyr for LLWfysonunt Wonvyrtyrihz zvzr inxrzv“ing yzmvny to proviyz tight rzgulvtion vt thz output voltvgz vny xurrznt rzBquirz“ thz implzmzntvtion of xlo“zyBloop xontrollzr“C bo“t of thz fiork founy in thz litzrvturzhv“ foxu“zy on yzvzloping “inglzBloop xontrollzr“ for rz“onvnt xonvzrtzr“C bzvnfihilzA zmplo–Bing vn innzrBxurrzntBloop vny outzrBvoltvgzBloop i“ v fiiyzl– vyoptzy mzthoy to xontrol elbxonvzrtzr“C dnz of thz mvin vyvvntvgz“ of xurrznt moyz xontrol i“ it“ “implzr y–nvmix“C ihztrvn“fzr funxtion xurrzntBtoBvoltvgz xontvin“ onz lz““ polz thvn thz xontrolBtoBoutputBvoltvgztrvn“fzr funxtionC borzovzrA thz vyyition of xurrznt mzv“urzmznt i“ rzquirzy for protzxtionvgvin“t zflxz““ivz xurrznt“ yuring trvn“iznt vny fvult xonyition“C Zmplo–ing v “imilvr “xhzmzfor v rz“onvnt xonvzrtzr mv– znvwlz “uxh vyvvntvgz“ v“ tho“z mzntionzy vwovzCihi“ xhvptzr introyuxz“ thz propo“zy yuvlBloop xontrol “xhzmzA zmplo–ing vn innzr xurrzntloop vny outzr voltvgz loopC [ir“tA v “implizy “mvllB“ignvl moyzl of thz aaX rz“onvntxonvzrtzr vvliy for thz mo“t xhvllznging xonyition from v xontrol point of vizfi i“ yzrivzyCihznA thz vnvl–“i“ of thz rzquirzy trvn“fzr funxtion“ for yz“igning thz yuvlBloop xontrollzri“ pzrformzyC V xontrollzr yz“ign proxzyurz zflvmplz i“ “hofinA vny propzr xompzn“vtor“ forwoth xurrznt vny voltvgz loopA vrz yz“ignzy to guvrvntzz “tvwlz opzrvtionC [invll–A “imulvtionvny zflpzrimzntvl rz“ult“ of thz xlo“zyBloop “–“tzm unyzr yiffzrznt opzrvting xonyition“ vrzproviyzy to vzrif– thz pzrformvnxz of thz xontrollzrCHN4BEB gmullAgignul aoxyl of thy LLW fysonunt WonvyrtyrHBE gmullAgignul aoxyl of thy LLW fysonuntWonvyrtyrj“uvll– “mvllB“ignvl moyzl“ vrz zmplo–zy to przyixt hofi thz vvrivtion“ in thz xontrol vvrivwlz“vffzxt thz outputC Xonvzntionvl pzrturwvtion vny linzvrizvtion tzxhniquz“ v““umz thvt vnvvzrvgzy voltvgz or xurrznt xon“i“t“ of v xon“tvnt xomponznt vny v “mvllB“ignvl VX vvrivtionvrouny thz YX xomponzntC ihzrzforzA thz lvrgzB“ignvl vvzrvgz moyzl yzvzlopzy in Xhvptzr“ Gvny H xvn wz zfltznyzy to owtvin v linzvrizzy moyzl of thz pofizr plvntC dwtvining rzlivwlzvny vxxurvtz “mvllB“ignvl moyzl“ xvn wz zmplo–zy to yzrivz thz rzquirzy trvn“fzr funxtionfor yz“igning linzvr xontrollzr“CWzforz vppl–ing xonvzntionvl linzvrizvtion tzxhniquz“A thz y–nvmix gvin of thz moyzl nzzy“to wz owtvinzyC ihi“ gvin rzprz“znt hofi muxh i“ thz vvrivtion of thz output voltvgz vnyxurrznt fihzn v “mvll pzrturwvtion i“ vpplizy in thz xontrol vvrivwlzC [or thz aaX xonvzrtzrAthz xontrol vvrivwlz i“ thz “fiitxhing frzquznx–C ihzrzforzA thz y–nvmix rzlvtion“hip wztfizznthz output voltvgz vny thz “fiitxhing frzquznx– xvn wz founy v“ thz “lopz of thz YX gvinvoltvgz xhvrvxtzri“tix“ givzn w– =GCJ)C ivking thz pvrtivl yzrivvtivzA thz “lopz i“ founy v“@M@vuR −Lyvu=GLmLyv2u + GL2m=v2u − F) + Lya2=v 6u − v 2u))L+m[(v 2u(LrLm+ F)− F)2+ L2rQ2m2n(m2n−))2L2m] 32=ICF)V“ thz moyzl hv“ wzzn yzrivzy v““uming rz“onvnt opzrvtionA vy R vsA vny vu R FC ihzy–nvmix “mvllB“ignvl gvin xvn wz yzrivzy v“km R@fv@vsR −MfpunLmLyFvy=ICG)IE4BEB gmullAgignul aoxyl of thy LLW fysonunt WonvyrtyrRL~sCo1irec;avgsLeqn2fs~kfnvo~[igurz ICFO hmvllBhignvl Zquivvlznt Xirxuit of thz aaX rz“onvnt xonvzrtzr vt rz“onvnt frzBquznx–C ihi“ linzvrizzy moyzl i“ zmplo–zy to yzrivz thz trvn“fzr funxtion“ for yz“igning thzpropo“zy yuvlBloop xontrollzrCainzvrizing thz vvzrvgz moyzl “hofin in [igC HCHA thz “mvllB“ignvl moyzl vrouny thz rz“oBnvnt frzquznx– xvn wz owtvinzy v“ “hofin in [igC ICFC ihz output voltvgz to xontrol frzquznx–trvn“fzr funxtion =Gvm ) xvn wz owtvinzy from thz linzvrizzy moyzl v“Gvm =s) Rvv=s)vs=s)RkmF + s LeqRLu2+ s2LeqCou2=ICH)ihz Woyz plot of thz trvn“fzr funxtion Gvm i“ illu“trvtzy in [igC ICGC ihz y–nvmix rz“pon“zof thz aaX rz“onvnt xonvzrtzr rz“zmwlz“ thz “mvllB“ignvl moyzl of v Wuxk xonvzrtzrC ihz“fiitxhing to nvturvl frzquznx– rvtio of v wuxk xonvzrtzr i“ xritixvl to vxhizvz high wvnyfiiythxontrollzr“C In xv“z of aaX xonvzrtzr“C thz rvtio wztfizzn thz rz“onvnt vny thz youwlz polzfrzquznxiz“ i“ yznzy w–rmj RvyvlxRGn√SvSy=ICI)fihixh i“ yzpznyvnt on thz xonvzrtzr pvrvmztzr“Cihz xontrol to output voltvgz trvn“fzr funxtion fiv“ yzrivzy in thi“ “zxtion wv“zy on thz“mvllB“ignvl moyzl “hofin in [igC ICFC ihz “vmz mzthoyolog– xvn wz zmplo–zy to owtvinthz xontrol to rzxtizy xurrznt trvn“fzr funxtionA vny thz rzxtizy xurrznt to output voltvgztrvn“fzr funxtion rzquirzy for yz“igning v yuvlBloop xontrollzrCIF4BFB DuulALoop Wontrollyr for thy LLW fysonunt WonvyrtyrFrequency  [Hz]0180Phase [deg]R1R2R3Magnitude [dB]rfcrfeqf=frfeqrfcGv0[igurz ICGO ihz xontrolBfrzquznx– to outputBvoltvgz trvn“fzr funxtion of aaX rz“onvnt xonBvzrtzr prz“znt“ v “zxony oryzr frzquznx– rz“pon“zCHBF DuulALoop Wontrollyr for thy LLW fysonuntWonvyrtyrIn opznBloop opzrvtionA in prz“znxz of yi“turwvnxz“A thz output voltvgz mv– “hofi o“xillvtion“Aovzr“hoot vny “tzvy–B“tvtz zrrorC V xlo“zyBloop xontrollzr xvn wz zmplo–zy to minimizz thz“zi““uz“C In thi“ “zxtionA v yuvlBloop xontrol “xhzmz zmplo–ing vn innzr xurrznt vny vn outzrvoltvgz loop i“ propo“zy for thz aaX rz“onvnt xonvzrtzr vny illu“trvtzy in [igC ICHC ImplzBmznting v yuvlBloop “xhzmz znvwlz“ “ignixvnt vyvvntvgz“ “uxh v“ tight xurrznt rzgulvtionvny ovzrBxurrznt protzxtionC V“ “hofin in thz gurzA thz yz“irzy output voltvgz i“ zmplo–zyv“ v “ztBpoint for thz outzr loopA fihzrzv“ thz innzrBloop xurrznt rzfzrznxz i“ xommvnyzyw– thz voltvgzBloop xompzn“vtorC ihz vvzrvging of thz rzxtizy xurrznt i“ inxluyzy in thzIG4BFB DuulALoop Wontrollyr for thy LLW fysonunt WonvyrtyrOuter Voltage LoopInner Current LoopLLCev irecirecGv(s) Gvi(s)Gif(s)Gi(s)Avgvovrefei f iref[igurz ICHO ihz propo“zy xontrol “xhzmz for thz aaX rz“onvnt xonvzrtzrC ihz xontrol yz“ignproxzyurz i“ “implizy w– zmplo–ing thz linzvrizzy moyzl of thz aaX pofizr xonvzrtzrCfzzywvxk pvth of thz innzr loopA vny thz xurrznt loop xompzn“vtor vyju“t“ thz “fiitxhingfrzquznx– in oryzr to trvxk thz vvzrvgz xurrznt rzfzrznxzCihz xontrol frzquznx– to rzxtizy xurrznt trvn“fzr funxtion i“ givzn w–Gpm =s) Riylj;avn=s)vs=s)Rkm()RL+ sSv)F + s Lequ2RL+ s2LeqCou2=ICJ)V“ it xvn wz ow“zrvzy in thz zquvtionA thz trvn“fzr funxtion hv“ v youwlz polz loxvtzy vt!lx Ru√LeqCoA vny v zzro yznzy w– thz intzrvxtion of thz output xvpvxitor vny thz lovyCihz gvin km i“ nzgvtivz v“ v xon“zquznxz of thz nzgvtivz on thz YX xhvrvxtzri“tix“ of thz aaXxonvzrtzrA fihixh trvn“lvtz into v −FME◦ phv“z yzlv– of thz YX xomponzntC ihz Woyz plotof =ICJ) “hofin in [igC ICI =v) inxluyz“ thz yi“xrztizvtion zffzxt givzn w– thz vvzrvging wloxkvny xontrollzr “vmpling frzquznx– =vs R GvNy)C V“ thz xontrol loop wvnyfiiyth i“ yz“irzy towz wztfizzn vlx vny vNyA thz rvtio wztfizzn thz“z frzquznxiz“ =yfc2) i“ xritixvl for thz xontrollzryz“ign v“ “hofin in [igC ICI =v)Ceroviyzy znough wvnyfiiyth yiffzrznxz wztfizzn thz tfio xontrol loop“A thz innzr loop xvnwz xon“iyzrzy v“ v xontrollzy xurrznt “ourxz “implif–ing thz loop y–nvmix“ to v r“t oryzrIH4BFB DuulALoop Wontrollyr for thy LLW fysonunt Wonvyrtyr2rfc2fr1fr2Gvi3Gvi2Gvi1fz3 fz2 fz1R1R2R3Gvi3 Gvi2 Gvi12rfc2fNy2feq fNy1-3600Frequency  [Hz] Frequency  [Hz]Phase [deg]Magnitude [dB]-90-450Phase [deg]Magnitude [dB]Same f  eqDifferent f r(a) (b)Frequency-to-Current Current-to-Voltage[igurz ICIO =v) Xontrol frzquznx–BtoBvvzrvgz rzxtizy xurrznt trvn“fzr funxtion xon“iyzringtfio rz“onvnt frzquznxiz“C ihz rvtio wztfizzn vy vny vlx i“ xritixvl in thz xontrollzr yz“ignC=w) Vvzrvgz rzxtizy xurrzntBtoBoutput voltvgz trvn“fzr funxtionC ihz outzr voltvgz loop hv“wzzn “implizyC“–“tzm v“ “hofin in gurz“ ICI =w) vny ICJC ihz rzxtizy xurrznt to output voltvgz trvn“fzrfunxtion i“ thzn givzn w–Gvp Rvv=s)iylj;avn=s)RF)RL+ sSv=ICK)dnxz thz trvn“fzr funxtion“ hvvz wzzn yznzy for woth innzr vny outzr loop“A linzvr xonBtrollzr“ xvn wz implzmzntzy w– zmplo–ing xonvzntionvl tzxhniquz“C In thi“ fiv–A rzyuxing thzII4B3B Wontrollyr Dysign drowyxury unx gimulution fysults(b)(a)Outer Voltage LoopInner Current Loopev Gv(s) Gvi(s)Gi  CL(s) vovrefiref irecRLsCo1vo~iref[igurz ICJO himplizy zquivvlznt xirxuit of thz outzr loop for yz“igning thz voltvgz xontrollzrOv) xirxuit moyzlA w) xlo“zyBloop wloxk xontrol yivgrvmC ihz implzmzntvtion of vn innzrxurrznt loop “impliz“ thz voltvgz loop xontrollzr yz“ignCaaX rz“onvnt xonvzrtzr y–nvmix“ to v “zxony oryzr “–“tzm znvwlz“ “implz vny “trvightforBfivry xontrollzr yz“ign proxzyurzCHBG Wontrollyr Dysign drowyxury unx gimulutionfysultsihz “mvllB“ignvl moyzl yzrivzy in thz przviou“ xhvptzr i“ u“zy in thz follofiing “zxtion“to yz“ign zvxh xontrol loopC Vyying v fzzywvxk loop xvn xvu“z vn othzrfii“z fizllBwzhvvzyxirxuit to zflhiwit o“xillvtion“A ovzr“hootA vny othzr unyz“irvwlz wzhvviorC j“uvll–A lzvyBlvgxompzn“vtor“ vrz u“zy to improvz thz phv“z mvrgin vny zfltznyzy thz wvnyfiiyth of thzfzzywvxk loopA fihilz proportionvl intzgrvl xontrollzr“ vrz u“zy to inxrzv“z thz lofiBfrzquznx–loop gvinC ihi“ lzvy“ to wzttzr rzjzxtion of yi“turwvnxz“ vny “mvll “tzvy–B“tvtz zrrorCIJ4B3B Wontrollyr Dysign drowyxury unx gimulution fysultsHBGBE Wontrollyr Dysign drowyxury[ir“tA thz xurrznt loop mu“t wz yz“ignzyC ihz xontrolBtoBrzxtizy xurrznt trvn“fzr funxBtion =ICJ) fiv“ illu“trvtzy in [igC ICI =v)C Vxxorying to thz pvrvmztzr“ in ivwlz ICFA in thi“xv“z thz po“ition of thz youwlz polz =vlx) i“ G:H k]zA fiith vmr2of JE k]zC dwtvining lvrgzrwvnyfiiyth“ thvn vlx guvrvntzz“ thvt thz xurrzntBloop i“ vwlz to vttznuvtz thz o“xillvtion“yuz to thz zffzxt of thz youwlz polzC dn thz othzr hvnyA thi“ i“ v “vmplz yvtv “–“tzm vny thzmvflimum thzorztixvl wvnyfiiyth i“ yznzy w– thz c–qui“t frzquznx–C ihzrzforzA thz xomBpzn“vtor zmplo–zy in thz innzr xurrzntBloop mu“t wz yz“ignzy to “vti“f– v loop wvnyfiiythvlx vnymr2C V wvnyfiiyth of FE k]z i“ “zlzxtzy to “vti“f– thi“ xonyitionCihz “zxony “tzp i“ yz“ignzy thz outzr voltvgz loop xontrollzrC V“ it fiv“ zflplvinzy inXhvptzr IA thz implzmzntvtion of vn innzr xurrznt loop “impliz“ thz voltvgz loop trvn“fzrfunxtionA vny thz rzxtizy xurrzntBtoBoutput voltvgz trvn“fzr funxtion =ICK) i“ zmplo–zyC]ofizvzrA in thi“ xv“zA thz xompzn“vtor mu“t wz yz“ignzy to vxhizvz v muxh lofizr wvnyfiiyththvn thz innzrBloopA fihixh lzvy“ to v “zlzxtion of v F k]z frzquznx–C In thi“ fiv–A thz y–nvmix“of thz xurrznt loop xvn wz nzglzxtzy fihzn vnvl–zing thz wzhvvior of thz fiholz “–“tzmCivwlz ICFO aaX evrvmztzr“ B Xontrol Yz“ignParameter FaleeVpu 120 FVy 81 8Cy 32 n6Vm 227 8fy 98 k8zPv 150 Wn 5:33Cv 660 6flx 2:3 k8zIK4B3B Wontrollyr Dysign drowyxury unx gimulution fysultseroportionvl Intzgrvl =eI) xontrollzr“ vrz zmplo–zy v“ xompzn“vtor“ for zvxh xontrol loopCihz xompzn“vtzy opznBloop Woyz plot“ vrz “hofin in [igC ICK =v) vny ICK =w) for thz innzrvny outzr loop“ rz“pzxtivzl–C V“ it xvn wz ow“zrvzy thz yz“irzy wvnyfiiyth“ vrz vxhizvzy fiithphv“z mvrgin“ =.m) of JL◦ vny LN◦ rz“pzxtivzl– fihixh guvrvntzz “tvwlz opzrvtionCio vzrif– thz yz“ign of thz xurrznt vny voltvgz xontrollzr“A thz y–nvmix“ of woth innzr vnyoutzr xontrol loop“ vrz inxluyzy in thz xlo“zyBloop rz“pon“z of [igC ICL vny ICMC Yz“igningthz outzr loop wvnyfiiyth tzn timz“ “lofizr thvn thz innzrBloop znvwlz“ v −HyW wvnyfiiyth-135-180-90-4504580604020-200150 W 15 W 101100102103104 fr2f = 2.3 kHzeqFrequency  [Hz] Frequency  [Hz]Phase [deg]Magnitude [dB]GciGfi1GciGfi2GciGfi1GciGfi2-50050100-180-150-120-90φm=79°ΔBW = 1 kHz150 W 15 W 101100102103104GcvGiv1GcvGiv2GcvGiv2GcvGiv1φm=57°ΔBW = 10 kHzCompensated Current Loop Compensated Voltage Loop(a) (b)[igurz ICKO =v) Xompzn“vtzy xontrolBfrzquznx– to rzxtizyBxurrznt trvn“fzr funxtionC ihzwvnyfiiyth loop i“ “zlzxtzy to vttznuvtz thz youwlzBpolz vt vlxC =w) Xompzn“vtzy rzxtizyBxurrznt to outputBvoltvgz trvn“fzr funxtionC ihz wvnyfiiyth of thz voltvgz loop i“ tzn timz“lofizr thvn thz innzrBloop wvnyfiiythCIL4B3B Wontrollyr Dysign drowyxury unx gimulution fysultsof F:J k]z xlo“zyBloop wvnyfiiyth v“ “hofin in [igC ICLC V“ mzntionzy wzforzA thz rzlvtivzyi“tvnxz wztfizzn xontrol loop“ i“ xritixvl to guvrvntzz xlo“zyBloop “tvwilit–C V pvrvmztrixvnvl–“i“ of thz xlo“zyBloop Woyz rz“pon“z i“ pzrformzy in [igC ICM for yiffzrznt voltvgz xontrolloop wvnyfiiyth“C V“ “hofin in thz gurzA thz xlo“zyBloop −H yW wvnyfiiyth vvriz“ fiith thzgvin of thz voltvgz xontrollzrC avrgzr wvnyfiiyth in thz outzr loop znvwlz“ highzr xlo“zyBloopwvnyfiiyth“A hofizvzr yz“igning thz outzr loop fiith lvrgz gvin“ mv– xrzvtz o“xillvtion“ yuzto thz intzrvxtion wztfizzn woth xontrol loop“C-360-1800100-10-20-60-403 dBΔBW = 1.5 kHz101100102103104 fr2Frequency  [Hz]Phase [deg]Magnitude [dB]150 W 15 W GCL1GCL2GCL2GCL1[igurz ICLO Xlo“zyBloop Woyz plot of thz propo“zy yuvlBloop xontrol “xhzmz for thz aaXrz“onvnt xonvzrtzr of ivwlz ICFC ihz owtvinzy xlo“zyBloop H yW wvnyfiiyth i“ F:J k]zC ihzoutzr voltvgz loop gvin i“ vyju“tzy to wz owtvin v voltvgz wvnyfiiyth tzn timz “lofizr thvnthz innzr xurrznt loop to przvznt thz intzrvxtion wztfizzn xontrol loop“CIM4B3B Wontrollyr Dysign drowyxury unx gimulution fysults20100-10-30-20-360-270-180-9000.1 Kv0.3 Kv 0.6 Kv 1 Kv 1.5 Kv 3.5 Kv5.5 KvControl Loops InterferenceLowBandwidth101100102103104 fr2Frequency  [Hz]Phase [deg]Magnitude [dB]GCLkGCLk[igurz ICMO Yiffzrznt xlo“zyBloop woyz plot“ of thz propo“zy yuvlBloop “xhzmz for yiffzrzntoutzr loop wvnyfiiyth“C avrgzr gvin“ in thz voltvgz loop znvwlz highzr wvnyfiiyth vny fv“tzrrz“pon“z“ in thz xlo“zyBloop “–“tzmC ]ofizvzrA lvrgz gvin“ mv– xrzvtz o“xillvtion wztfizznwoth xontrol loop“CHBGBF gimulution fysultsIn thi“ pvrtA thz aaX rz“onvnt xonvzrtzr u“ing thz pvrvmztzr“ of ivwlz ICF i“ “imulvtzy unyzryiffzrznt opzrvting xonyition“ implzmznting thz yz“ignzy yuvlBloop xontrollzrChimulvtion rz“ult“ of thz propo“zy yuvlBloop “xhzmz unyzr yiffzrznt lovy “tzp“ vny voltBvgz rzfzrznxz “ztBpoint“ vrz “hofin in [igC ICN vny xompvrzy fiith thz opznBloop rz“pon“z“=xon“tvnt vs)C ihz uppzr plot illu“trvtz“ thz rz“pon“z of vv for v xurrznt lovy “tzp from F toL VC V“ zflpzxtzyA thz xlo“zyBloop “–“tzm rz“pon“z “hofi“ no o“xillvtion“ vny zzro “tzvy–B“tvtzzrror unyzr thz vpplizy yi“turwvnxz“ vt yiffzrznt opzrvting point“CIN4B3B Wontrollyr Dysign drowyxury unx gimulution fysults18222630343860801001201401600 2 4 6 8048ref v = 34 Vref v = 30 Vref v = 26 Vref v = 22 Vref v = 18 V119 KHz98 KHz102 KHz145 KHz88 KHz79 KHz73 KHz83 KHz76 KHz70 KHzf[KHz]si[A]Loadv[V]oUnregulated Open-Loop Tight Closed-LoopSimilar ResponsesOver a Wide Range of Operating ConditionsWide Range of Frequencies}6 At [ms][igurz ICNO himulvtion rz“ult“ for thz propo“zy yuvlBloop xontrollzr for thz aaX xonvzrtzrof ivwlz ICF unyzr v lovy “tzp for yiffzrznt opzrvting point“C ihz xlo“zyBloop “–“tzm i“ “tvwlzunyzr v fiiyz rvngz of opzrvting xonyition“ wzlofi vny vwovz thz rz“onvnxzCihz “zxony pvrt of [igC ICN illu“trvtz“ thz vvrivtion of thz “fiitxhing frzquznx– yuringthz trvn“iznt“C V“ “hofinA thz yuvlBloop xontrollzr i“ vwlz to xompzn“vtz thz output ovzr vJE4B3B Wontrollyr Dysign drowyxury unx gimulution fysults1820222426283032v[V]oVoltageReferencei  1 [A]Loadi  3.5 [A]Loadi  7 [A]LoadTight Closed-Loop0 5 10 15 20 25708090100110120f[KHz]sSwitching Frequencyt [ms]Wide Range of Frequencies}Zero Steady-State ErrorNo Overshoot[igurz ICFEO himulvtion rz“ult“ for thz propo“zy yuvlBloop xontrollzr for thz aaX xonvzrtzr ofivwlz ICF unyzr v voltvgz rzfzrznxz “tzp for yiffzrznt lovy xonyition“C ihz xontrollzr opzrvtz“in v fiiyz rvngz of “fiitxhing frzquznxiz“Cfiiyz rvngz of frzquznxiz“ vwovz vny wzlofi rz“onvnxzC It xvn wz ow“zrvzy thvt thz xontrollzrxontinuz“ opzrvting propzrl– for rzfzrznxz “ztBpoint“ thvt rzvxh HI vny FM k fiith “fiitxhingfrzquznxiz“ rvnging from LE to FJE k]zCihz output voltvgz wzhvvior unyzr v “ztBpoint “tzp i“ illu“trvtzy in [igC ICFEC ihz gurz“hofi“ v xompvri“on wztfizzn yiffzrznt lovying xonyition for xlo“zyBloop opzrvtionA vny illu“Btrvtz“ hofi thz “fiitxhing frzquznx– mu“t xhvngz in oryzr to trvxk thz xhvnging “ztBpointC V““hofinA thz xlo“zyBloop “–“tzm i“ “tvwlz unyzr v fiiyz rvngz of opzrvting point“ wzlofi vnyvwovz thz rz“onvnxzCJF4B4B Efipyrimyntul fysultsHBH Efipyrimyntul fysultsV FJE l protot–pz of v fullBwriygz aaX rz“onvnt xonvzrtzr fiv“ implzmzntzy zmplo–ing thzpvrvmztzr“ givzn w– ivwlz ICFC ihz yuvlBloop xontrollzrA innzr xurrznt vny outzr voltvgz i“implzmzntzy wv“zy on thz yz“ign of Xhvptzr ICHC ihz zflpzrimzntvl protot–pz of thz fullBwriygz aaX rz“onvnt xonvzrtzr i“ “hofin in [igC ICFFC ihz propo“zy xontrollzr i“ implzmzntzyin v izflv“ In“trumznt yigitvl mixroxontrollzr for thz “zriz“ XGEEE =bheHGE[GMHHJ Yhe)Cihz output of thz protot–pz i“ xonnzxtzy to v zlzxtronix lovy Xhromv KHGEI xongurzy inxon“tvnt xurrznt lovy moyz vnyA vt thz inputA v YX pofizr “uppl– horzn“z“n hGV IEEDHM i“xonnzxtzyC Zflpzrimzntvl rz“ult“ for thz trvn“iznt rz“pon“z of thz FJE l protot–pz unyzr vyiffzrznt xonyition“ vrz prz“zntzy in [igC ICFG B [igC ICFKC Vll thz “ignvl“ fizrz xvpturzy w– vizlzy–nz azxro– lvvzgunnzr KEIoi o“xillo“xopzCInverter BoardControl Board Input VoltageOutput (to load)Resonant TankRectifier andOutput Filter[igurz ICFFO FJE l fullBwriygz aaX rz“onvnt xonvzrtzr zflpzrimzntvl protot–pzCJG4B4B Efipyrimyntul fysultsihz zflpzrimzntvl xvpturz“ “hofiing thz y–nvmix rz“pon“z of thz aaX xonvzrtzr fiith thzyzvzlopzy yuvlBloop xontrollzr xurrznt lovy “tzp opzrvting vt yiffzrznt voltvgz “ztBpoint“ vrz“hofin in [igC ICFG vny ICFHC ihz rz“pon“z of thz xonvzrtzr for v voltvgz rzfzrznxz of FM ki“ “hofin in [igC ICFG =v)C V“ “hofinA thz “ztting timz i“ G:G m“ vny F:G m“ for v lovy xurrznt“tzpByofin vny “tzpBupA fihilz thz ovzr“hoot i“ F:G k vny F:J m“ rz“pzxtivzl–C [or v “ztBpointof GG kA thz xonvzrtzr opzrvtz“ vrouny thz rz“onvnt pointA v“ “hofin in [ig ICFG =w) fiith“zttling timz vny ovzr“hoot vvluz“ of KE mk vny F:G m“ rz“pzxtivzl–C ihz wzhvviour ofthz xlo“zy loop “–“tzm fiith thz xonvzrtzr opzrvting wzlofi vy i“ illu“trvtzy in ICFG =v) vnyICFG =w)C V“ it xvn wz ow“zrvzyA woth xv“z“ “hofi “imilvr “zttling timz vny ovzr“hot vvluz“Cihz implzmzntvtion of vn innzrBxurrznt loop improvz“ thz y–nvmix of thz “–“tzm ovzr v fiiyzrvngz of “fiitxhing frzquznxiz“Cihz y–nvmix rz“pon“z of thz zflpzrimzntvl plvtform unyzr v voltvgz “ztBpoint “tzp i““hofin in [igC ICFIC ihz xvpturz illu“trvtz“ thz output voltvgz vny “fiitxhing frzquznx– ofthz xonvzrtzr for thrzz yiffzrznt lovying xonyition“C V“ “hofinA thz output voltvgz rzvxhz“thz rzfzrznxz point fiith no ovzr“hot vny no o“xillvtion“ for vll lovying xonyition C Yuring thz“tzpBupA thz output “hofi“ “imilvr rz“pon“z“ for vll lovying xonyition“C ]ofizvzrA yuring “tzpByofinA lightzr lovy“ tvkz longzr timz to “zttlz yuz to thz xonvzrtzr zntzring in yi“xontinuou“xonyuxtion moyzCV xonvzntionvl voltvgz moyz xontrollzr hv“ wzzn implzmzntzy to xompvrz thz y–nvmixrz“pon“z of thz yuvlBloop xontrollzrC ihz zflpzrimzntvl rz“ult“ for lovy trvn“iznt rz“pon“z ofthz FJE l protot–pz vrz “hofin in [igC ICFJ B ICFKC V“ ow“zrvzyA thz yuvlBloop xontrol “hofi““upzrior trvn“iznt wzhvvior ovzr v fiiyz rvngz of opzrvting xonyition“C Vpvrt from rzyuxzthz oryzr vny “implif– thz voltvgz loopA thz innzr xurrznt loop minimizz“ thz vvrivtion of thz“mvllB“ignvl xhvrvxtzri“tix“ of thz xonvzrtzr vt yiffzrznt opzrvting xonyition“CJH4BIB gummuryHBI gummuryihi“ xhvptzr introyuxzy v yuvlBloop xontrollzr for aaX rz“onvnt xonvzrtzr“C ihz xon“iyzrvBtion“ for thz vnvl–“i“ vny yz“ign of woth innzr vny outzr loop fizrz prz“zntzyC V “mvllB“ignvlmoyzl of thz aaX rz“onvnt xonvzrtzr opzrvting vt rz“onvnt frzquznx– fiv“ yzrivzy from thzvvzrvgz lvrgzB“ignvl moyzl w– vppl–ing xonvzntionvl linzvrizvtion tzxhniquz“C ihz “mvllB“ignvl moyzl i“ v “zxony oryzr “–“tzm fiith v youwlz polz loxvtzy vt thz rz“onvnt frzquznx–yznzy w– Llx vny SvC ihz “mvllB“ignvl moyzl fiv“ zmplo–zy to yzrivzy propzr trvn“fzrfunxtion“ for thz yz“ign of xompzn“vtor“ in v “implz vny “trvightforfivry mvnnzrC [invll–Av yz“ign xontrollzr zflvmplz fiv“ pzrformzyA vny “imulvtion vny zflpzrimzntvl rz“ult“ vt yifBfzrznt opzrvting xonyition“ fizrz proviyzy to vvliyvtz thz “tvwilit– vny pzrformvnxz of thzxlo“zyBloop “–“tzmCref v =20 Vref v =30 Vvo,iload = 7 Avo,iload = 3.5 Avo,iload = 1 Afs,iload = 7 Afs,iload = 3.5 Afs,iload = 1 A[igurz ICFGO Zflpzrimzntvl xvpturz rzfzrznxz “tzp from GE k to HE k for yiffzrznt lovy xurrznt“CXFO output voltvgz =isvak R L V)A XGO frzquznx– vvrivtion =L V)A bFO output voltvgz =isvak RF V)A bGO frzquznx– vvrivtion =F V)A bHO output voltvgz =isvak R H:J V)A bIO frzquznx–vvrivtion =H:J V)A XHO voltvgz rzfzrznxz “tzpCJI4BIB gummury(a)(b)Proposed  Dual-Loop ControllerProposed  Dual-Loop Controllerref v =18 Vref v =22 Vvoiavgireciload1.2 V2.2 ms1 ms1.5 V500 mV1.2 msvoiavgireciload1 ms600 mV6 A6 AThe response is consistent accros different condtions The response is consistent accros different condtions [igurz ICFHO Zflpzrimzntvl xvpturz xurrznt lovy “tzp from F V to L V for rzfzrznxz voltvgzFM kC XFO output voltvgzA XGO vvzrvgz xurrznt from thz mixroxontrollzrA XHO rzxtizyxurrzntA XIO lovy xurrzntCJJ4BIB gummury(a)(b)600 mV1.4 ms1 ms600 mV1.8 ms1 ms700 mVref v =26 Vvoiavgireciload 6 AThe response is consistent accros different condtions The response is consistent accros different condtions voiavgireciload 6 Aref v =32 VProposed  Dual-Loop ControllerProposed  Dual-Loop Controller[igurz ICFIO Zflpzrimzntvl xvpturz xurrznt lovy “tzp from F V to L V for rzfzrznxz voltvgzFM kC XFO output voltvgzA XGO vvzrvgz xurrznt from thz mixroxontrollzrA XHO rzxtizyxurrzntA XIO lovy xurrzntCJK4BIB gummury(a)(b)ref v =18 V2.6 ms2.3 VThe transient performance is impaired at differentconditions900 mV2.2 ms1.2 ms1 VThe transient performance is impaired at differentconditionsvoiavgireciload 6 Avoiavgireciload 6 A1.4 V1.8 msConventional Single-Loop ControllerConventional Single-Loop Controller[igurz ICFJO Zflpzrimzntvl xvpturz xurrznt lovy “tzp from F V to L V for rzfzrznxz voltvgzFM kC XFO output voltvgzA XGO vvzrvgz xurrznt from thz mixroxontrollzrA XHO rzxtizyxurrzntA XIO lovy xurrzntCJL4BIB gummury(a)(b)The transient performance is impaired at differentconditionsThe transient performance is impaired at differentconditionsref v =26 VConventional Single-Loop Controllervoiavgireciload 6 Aref v =30 Vvoireciload 6 A1.2 mV3 ms1.4 ms1.1 V1.4 V1.2 Viavg4.2 ms1.2 msConventional Single-Loop Controller[igurz ICFKO Zflpzrimzntvl xvpturz xurrznt lovy “tzp from F V to L V for rzfzrznxz voltvgzFM kC XFO output voltvgzA XGO vvzrvgz xurrznt from thz mixroxontrollzrA XHO rzxtizyxurrzntA XIO lovy xurrzntCJMWhuptyr IWonwlusionIBE gummuryihi“ fiork yzvzlopzy v “implz vny “trvightforfivry xompzn“vtor yz“ign mzthoyolog– for aaXrz“onvnt xonvzrtzr“C In thi“ vpprovxhA v numzrixvl vnvl–“i“ of thz xonvzrtzr'“ y–nvmix wzBhvvior fiv“ pzrformzyA vny thz rz“onvnt frzquznx– opzrvtion fiv“ iyzntizy v“ thz mo“t xhvlBlznging xonyition from v xontrol yz“ign point of vizfiC Vn vxxurvtz lvrgzB“ignvl vvzrvgz moyzlvny v “implizy linzvrizzy moyzl of thz xonvzrtzr opzrvting vt rz“onvnt frzquznx– fizrz proBpo“zyC Vn zffzxtivz yuvlBloop “xhzmz fiith innzr xurrznt loop vny outzr voltvgz loop fiv“implzmzntzy zmplo–ing thz output voltvgz vny output rzxtizr xurrznt v“ fzzywvxk “ignvl“Cihi“ yuvlBloop “xhzmz znvwlzy numzrou“ vyvvntvgz“A “uxh v“A tight xurrznt rzgulvtion vnyovzrBxurrznt protzxtionC ihz implzmzntvtion of vn innzr xurrznt loop minimizz“ thz vvrivBtion“ of thz “mvllB“ignvl xhvrvxtzri“tix“ of thz xonvzrtzr vt yiffzrznt opzrvting point“A thu“vxhizving “imilvr trvn“iznt rz“pon“z“ ovzr v fiiyz rvngz of frzquznxiz“Cihz zffzxtivznz““ of thz propo“zy yuvlBloop “xhzmz fiv“ vzrizy w– “imulvtion vny zflpzrBimzntvl rz“ult“ w– u“ing v FJE l fullBwriygz aaX rz“onvnt xonvzrtzrC ihz owtvinzy rz“ult““hofi thvt thz implzmzntvtion of v yuvlBloop xongurvtion proviyz“ thz yz“irzy xlo“zyBlooppzrformvnxz for thz zntirz opzrvtionvl rvngzC [invll–A thi“ fiork introyuxz“ v u“zful tool thvtznvwlz“ v “implz vny “trvightforfivry proxzyurz for yz“igning linzvr xontrollzr“ for v xomplzfltopolog–O thz aaX rz“onvnt xonvzrtzrCJNIBFB Futury korkIBF Futury korkihz xonxzpt yzvzlopzy in thi“ fiork proviyz“ vn originvl xontriwution to thz yz“ign of xonBtrollzr“ for aaX rz“onvnt xonvzrtzr“C ihi“ fiork xouly wz zfltznyzy to yzvzlop moyzl“ ofthz xonvzrtzr vt yiffzrznt opzrvting point“A inxluying vyyitionvl zffzxt“ “uxh v“ pvrv“itix zlzBmznt“ vny inyu“tr– “tvnyvry ltzr“A vny yz“igning vny implzmznting vyvptivz xontrollzr“ toimprovz thz pzrformvnxz of thz “–“tzmCihz “implizy xontrollzr yz“ign mzthoyolog– xouly wz zfltrvpolvtzy to othzr topologiz“Cihz implzmzntvtion of v yuvlBloop “xhzmz opzn“ thz po““iwilit– of zfltznying thz xontrol“trvtzg– to “zvzrvl xonvzrtzr“ fiorking in pvrvllzlC ihz fiholz “–“tzm xouly wz xontrollzy w–implzmznting vn inyiviyuvl innzr xurrznt loop in zvxh xonvzrtzr vny v mvin voltvgz loop toproviyz thz xurrznt rzfzrznxz of zvxh inyiviyuvl “tvgzCKEVivliogruphypFr [C YzgiovnniA IC GC ourwriggznA vny bC dryonzzA qYuvlBloop xontrollzr for aaX rz“oBnvnt xonvzrtzr“ u“ing vn vvzrvgz zquivvlznt xirxuitA7 in FDE7 IEEE Enyrgy ConvyrsionCongryss unx Efiposition (ECCE)A dxt GEFLA ppC GHE{GHKCpGr [C YzgiovnniA IC GC ourwriggznA vny bC dryonzzA qYuvlBloop xontrollzr for aaX rz“onvntxonvzrtzr“ u“ing vn vvzrvgz zquivvlznt moyzlA7 IEEE hrunsuwtions on dowyr ElywtroniwsAvolC eeA noC NNA ppC F{FA GEFLCpHr ]C KvkigvnoA nC biurvA vny iC I“zA qaofiBvoltvgz wipolvrBt–pz YX mixrogriy for “upzrhigh quvlit– yi“triwutionA7 IEEE hrunsuwtions on dowyr ElywtroniwsA volC GJA noC FGA ppCHEKK{HELJA Yzx GEFECpIr eC iC KrzinA qYvtv xzntzr xhvllzngz“ vny thzir pofizr zlzxtronix“A7 Cdgg hrunsuwtionson dowyr Elywtroniws unx UppliwutionsA volC GA noC FA ppC HN{IKA GEFLCpJr YC YongA IC XvztkovixA YC Woro–zvixhA lC ohvngA gC lvngA vny eC bvttvvzlliA qGriyBintzrfvxz wiyirzxtionvl xonvzrtzr for rz“iyzntivl YX yi“triwution “–“tzm“ B pvrt onzO ]ighByzn“it– tfioB“tvgz topolog–A7 IEEE hrunsuwtions on dowyr ElywtroniwsA volC GMA noC IAppC FKJJ{FKKKA Vpril GEFHCpKr XC WuxxzllvA XC XzxvtiA ]C avtvfvtA vny KC gvziA qXompvrvtivz trvn“iznt rz“pon“z vnvlB–“i“ of aaX rz“onvnt xonvzrtzr xontrollzy w– vyvptivz piy vny fuzz– logix xontrollzr“A7in IECcN FDEF A 3Lth Unnuul Confyrynwy on IEEE Inxustriul Elywtroniws gowiytyA dxtGEFGA ppC ILGN{ILHICKFVivliogruphypLr ]C eC evrk vny JC ]C JungA qeofizr “tvgz vny fzzywvxk loop yz“ign for aaX rz“onvnt xonBvzrtzr in highB“fiitxhingBfrzquznx– opzrvtionA7 IEEE hrunsuwtions on dowyr ElywtroniwsAvolC HGA noC FEA ppC LLLE{LLMGA dxt GEFLCpMr aC ]uwzrA aC GvngA vny bC bC JovvnovixA qYz“ignBorizntzy vnvl–“i“ vny pzrformvnxzzvvluvtion of wuxk pfx front znyA7 IEEE hrunsuwtions on dowyr ElywtroniwsA volC GJAnoC FA ppC MJ{NIA Jvn GEFECpNr XC bvthnvA cC lvngA hC KulkvrniA vny hC go–A qgzvizfi of intzgrvtzy mvgnztix“ for pofizr“uppl– on xhip =pfir“ox)A7 IEEE hrunsuwtions on dowyr ElywtroniwsA volC GLA noC FFA ppCILNN{IMFKA cov GEFGCpFEr WC XC KimA KC WC evrkA XC ZC KimA WC ]C azzA vny GC lC boonA qaaX rz“onvnt xonvzrtzrfiith vyvptivz linkBvoltvgz vvrivtion for v highBpofizrByzn“it– vyvptzrA7 IEEE hrunsuwAtions on dowyr ElywtroniwsA volC GJA noC NA ppC GGIM{GGJGA hzpt GEFECpFFr JC Xvo vny VC ZmvyiA qV nzfi wvttzr–DultrvBxvpvxitor h–wriy znzrg– “torvgz “–“tzm forzlzxtrixA h–wriy vny plugBin h–wriy zlzxtrix vzhixlz“A7 in FDDM IEEE Vyhiwly dowyr unxdropulsion ConfyrynwyA hzpt GEENA ppC NIF{NIKCpFGr lC ai vny mC ]zA qgzvizfi of noni“olvtzy highB“tzpBup YXDYX xonvzrtzr“ in photovoltvixgriyBxonnzxtzy vpplixvtion“A7 IEEE hrunsuwtions on Inxustriul ElywtroniwsA volC JMA noC IAppC FGHN{FGJEA Vpril GEFFCpFHr oC fivnA dC VwyzlBgvhmvnA ]C VlBVtrv“hA vny IC Wvtvr“zhA qboyzling vny xontrol ofthrzzBport YXDYX xonvzrtzr intzrfvxz for “vtzllitz vpplixvtion“A7 IEEE hrunsuwtions ondowyr ElywtroniwsA volC GJA noC HA ppC KHL{KINA bvrxh GEFECKGVivliogruphypFIr VC Kfiv“in“ki vny XC cC dnfiuxhzkfivA qY–nvmix wzhvvior vny “tvwilizvtion of YX miBxrogriy“ fiith in“tvntvnzou“ xon“tvntBpofizr lovy“A7 IEEE hrunsuwtions on dowyr ElywAtroniwsA volC GKA noC HA ppC MGG{MHIA bvrxh GEFFCpFJr [C bu“vviA bC XrvxiunA YC hC GvutvmA vny lC ZwzrlzA qXontrol “trvtzgiz“ for fiiyz outBput voltvgz rvngz aaX rz“onvnt YXBYX xonvzrtzr“ in wvttzr– xhvrgzr“A7 IEEE hrunsAuwtions on Vyhiwulur hywhnologyA volC KHA noC HA ppC FFFL{FFGJA bvrxh GEFICpFKr ]C yz GrootA ZC Jvn““znA gC evgvnoA vny KC hxhzttzr“A qYz“ign of v FBmhz aaX rz“onvntxonvzrtzr wv“zy on v y“pByrivzn “oi hvlfBwriygz pofizr mo“ moyulzA7 IEEE hrunsuwtionson dowyr ElywtroniwsA volC GGA noC KA ppC GHEL{GHGEA cov GEELCpFLr WC auA lC aiuA nC aivngA [C XC azzA vny JC YC vvn l–kA qdptimvl yz“ign mzthoyolog–for aaX rz“onvnt xonvzrtzrA7 in hwyntyAFirst Unnuul IEEE Uppliyx dowyr ElywtroniwsConfyrynwy unx Efiposition, FDD6B UdEC 'D6BA bvrxh GEEKA ppC K ppC{CpFMr gC lC Zrixk“on vny YC bvk“imovixA Funxumyntuls of powyr ylywtroniwsC hpringzr hxiBznxz ; Wu“inz““ bzyivA GEELCpFNr gC aC htzigzrfivlyA qV xompvri“on of hvlfBwriygz rz“onvnt xonvzrtzr topologiz“A7 IEEEhrunsuwtions on dowyr ElywtroniwsA volC HA noC GA ppC FLI{FMGA Vpr FNMMCpGEr JC YzngA hC aiA hC ]uA XC XC biA vny gC bvA qYz“ign mzthoyolog– of aaX rz“onvntxonvzrtzr“ for zlzxtrix vzhixlz wvttzr– xhvrgzr“A7 IEEE hrunsuwtions on Vyhiwulur hywhAnologyA volC KHA noC IA ppC FJMF{FJNGA bv– GEFICpGFr lC XhznA eC gongA vny oC auA qhnuwwzrlz““ wiyirzxtionvl YXBYX xonvzrtzr fiith nzfiXaaX rz“onvnt tvnk fzvturing minimizzy “fiitxhing lo““A7 IEEE hrunsuwtions on InxusAtriul ElywtroniwsA volC JLA noC NA ppC HELJ{HEMKA hzpt GEFECKHVivliogruphypGGr gC WzirvnvvnyA WC gv“hiyivnA bC gC oolghvyriA vny hC bC ]C VlvviA qV yz“ign proxzyurzfor optimizing thz aaX rz“onvnt xonvzrtzr v“ v fiiyz output rvngz voltvgz “ourxzA7 IEEEhrunsuwtions on dowyr ElywtroniwsA volC GLA noC MA ppC HLIN{HLKHA Vug GEFGCpGHr WC nvngA qiopolog– invz“tigvtion of front zny YXDYX xonvzrtzr for yi“triwutzy pofizr“–“tzmA7 ehCYC yi““zrtvtionA kirginiv izxhA GEEHCpGIr bC Kvzimizrxzuk vny iC cvnyvkumvrA qXlv““ y voltvgzB“fiitxhing invzrtzr fiith tvppzyrz“onvnt inyuxtorA7 in IEE drowyyxings V (Elywtriw dowyr Uppliwutions)A volC FIEA noC HCIZiA FNNHA ppC FLL{FMKCpGJr YC Xzvrkofi“ki vny bC KC KvzimizrxzukA qehv“zBxontrollzy xll rz“onvnt xonvzrtzrA7 inUppliyx dowyr Elywtroniws Confyrynwy unx Efiposition, EMM3B UdEC'M3B Confyrynwy droAwyyxings EMM3B, Eighth UnnuulC IZZZA FNNHA ppC IHG{IHMCpGKr bC KC Kvzimizrxzuk vny YC Xzvrkofi“kiA fysonunt powyr wonvyrtyrsC John lilz– ;hon“A GEFGCpGLr XC XC ]uvA nC ]C [vngA vny XC lC ainA qaaX rz“onvnt xonvzrtzr for zlzxtrix vzhixlzwvttzr– xhvrgzr“A7 IEh dowyr ElywtroniwsA volC NA noC FGA ppC GHKN{GHLKA GEFKCpGMr ]C lvngA hC Yu“mzzA vny VC KhvlighA qYz“ign vny vnvl–“i“ of v fullBwriygz aaXBwv“zypzv xhvrgzr optimizzy for fiiyz wvttzr– voltvgz rvngzA7 IEEE hrunsuwtions on VyhiwulurhywhnologyA volC KHA noC IA ppC FKEH{FKFHA bv– GEFICpGNr ]C ]uA mC [vngA [C XhznA oC JC hhznA vny IC Wvtvr“zhA qV moyizy highBzffixiznx–aaX xonvzrtzr fiith tfio trvn“formzr“ for fiiyz inputBvoltvgz rvngz vpplixvtion“A7 IEEEhrunsuwtions on dowyr ElywtroniwsA volC GMA noC IA ppC FNIK{FNKEA Vpril GEFHCpHEr fC ohvngA XC ]uA aC XhznA VC VmirvhmvyiA cC KutkutA oC JC hhznA vny IC Wvtvr“zhA qVxzntzr point itzrvtion mppt mzthoy fiith vpplixvtion on thz frzquznx–Bmoyulvtzy aaXKIVivliogruphymixroinvzrtzrA7 IEEE hrunsuwtions on dowyr ElywtroniwsA volC GNA noC HA ppC FGKG{FGLIAbvrxh GEFICpHFr JC nC azzA nC hC JzongA vny WC bC ]vnA qVn i“olvtzy YXDYX xonvzrtzr u“ing highBfrzquznx– unrzgulvtzy LLS rz“onvnt xonvzrtzr for fuzl xzll vpplixvtion“A7 IEEE hrunsAuwtions on Inxustriul ElywtroniwsA volC JMA noC LA ppC GNGK{GNHIA Jul– GEFFCpHGr gC WzirvnvvnyA WC gv“hiyivnA bC gC oolghvyriA vny hC bC ]C VlvviA qYz“igning vn vyBju“tvwlz fiiyz rvngz rzgulvtzy xurrznt “ourxzA7 IEEE hrunsuwtions on dowyr ElywtroniwsAvolC GJA noC FA ppC FNL{GEMA Jvn GEFECpHHr XC XzxvtiA ]C VC KhvliyA bC iinvriA GC VyinolA vny GC GrvyitiA qYx nvnogriy forrznzfivwlz “ourxz“ fiith moyulvr YXDYX aaX xonvzrtzr wuilying wloxkA7 IEh dowyrElywtroniwsA volC FEA noC JA ppC JHK{JIIA GEFLCpHIr WC XC KimA KC WC evrkA XC ZC KimA WC ]C azzA vny GC lC boonA qalx rz“onvnt xonvzrtzrfiith vyvptivz linkBvoltvgz vvrivtion for v highBpofizrByzn“it– vyvptzrA7 IEEE hrunsuwAtions on dowyr ElywtroniwsA volC GJA noC NA ppC GGIM{GGJGA hzpt GEFECpHJr bC GC aC goz“A JC aC YuvrtzA vny bC VC bC ]znyriflA qYi“turwvnxz ow“zrvzrBwv“zy xontrolof v yuvlBoutput aaX xonvzrtzr for “oliyB“tvtz lighting vpplixvtion“A7 IEEE hrunsuwtionson dowyr ElywtroniwsA volC GKA noC LA ppC GEFM{GEGLA Jul– GEFFCpHKr iC JivngA JC ohvngA mC luA KC hhzngA vny nC lvngA qV wiyirzxtionvl aaX rz“onvntxonvzrtzr fiith vutomvtix forfivry vny wvxkfivry moyz trvn“itionA7 IEEE hrunsuwtionson dowyr ElywtroniwsA volC HEA noC GA ppC LJL{LLEA [zw GEFJCpHLr WC nvngA [C XC azzA VC JC ohvngA vny GC ]uvngA qalx rz“onvnt xonvzrtzr for front znyYXDYX xonvzr“ionA7 in UdECB gyvyntyynth Unnuul IEEE Uppliyx dowyr ElywtroniwsConfyrynwy unx Efiposition (CutB NoBDFCH3733I)A volC GA GEEGA ppC FFEM{FFFG volCGCKJVivliogruphypHMr hC YC himonzA XC VyrvgnvA XC hpiniA vny GC GvttvvvriA qYz“ignBorizntzy “tzvy–B“tvtzvnvl–“i“ of aaX rz“onvnt xonvzrtzr“ wv“zy on fhvA7 in Intyrnutionul gymposium on dowyrElywtroniws, Elywtriwul Drivys, Uutomution unx aotion, FDD6B gdEEDUa FDD6BA bv–GEEKA ppC GEE{GELCpHNr hC VwyzlBgvhmvnA qgz“onvnt aaX xonvzrtzrO dpzrvtion vny yz“ignA7 Innyon hywhAnologiys North Umyriwu (IFNU) CorpBA GEFGCpIEr JC ]oon Jung vny JC Gi KfionA qihzorztixvl vnvl–“i“ vny optimvl yz“ign of aaX rz“onvntxonvzrtzrA7 in FDD7 Europyun Confyrynwy on dowyr Elywtroniws unx UppliwutionsA hzptGEELA ppC F{FECpIFr ]C ]uvngA q[hvBwv“zy voltvgz gvin funxtion fiith hvrmonix xompzn“vtion for aaX rz“Bonvnt xonvzrtzrA7 in FDED hwyntyAFifth Unnuul IEEE Uppliyx dowyr Elywtroniws ConAfyrynwy unx Efiposition (UdEC)A [zw GEFEA ppC FLLE{FLLLCpIGr WC gC ainA JC JC XhznA vny XC aC nvngA qVnvl–“i“ vny implzmzntvtion of yuvlBoutput aaXrz“onvnt xonvzrtzrA7 in FDDL IEEE Intyrnutionul Confyrynwy on Inxustriul hywhnologyAVpril GEEMA ppC F{KCpIHr GC lC lz“tzr vny gC YC biyylzwrookA qaofiBfrzquznx– xhvrvxtzrizvtion of “fiitxhzy YXBYX xonvzrtzr“A7 IEEE hrunsuwtions on Uyrospuwy unx Elywtroniw gystymsA volC VZhBNAnoC HA ppC HLK{HMJA bv– FNLHCpIIr gC YC biyylzwrook vny hC XukA qV gznzrvl unizy vpprovxh to moyzlling “fiitxhingBxonvzrtzr pofizr “tvgz“A7 in EM76 IEEE dowyr Elywtroniws gpywiulists ConfyrynwyA JunzFNLKA ppC FM{HICpIJr hC XukA qboyzllingA vnvl–“i“A vny yz“ign of “fiitxhing xonvzrtzr“A7 ehCYC yi““zrtvtionAXvliforniv In“titutz of izxhnolog–A FNLLCKKVivliogruphypIKr lC bC eolivkvA eC gC KC Xhztt–A vny gC YC biyylzwrookA qhtvtzB“pvxz vvzrvgz moyBzlling of xonvzrtzr“ fiith pvrv“itix“ vny “torvgzBtimz moyulvtionA7 in EMLD IEEE dowyrElywtroniws gpywiulists ConfyrynwyA Junz FNMEA ppC FFN{FIHCpILr gC YC biyylzwrookA qboyzling xurrzntBprogrvmmzy wuxk vny woo“t rzgulvtor“A7 IEEEhrunsuwtions on dowyr ElywtroniwsA volC IA noC FA ppC HK{JGA Jvn FNMNCpIMr kC korpzrivnA qVpproflimvtz “mvllB“ignvl vnvl–“i“ of thz “zriz“ vny thz pvrvllzl rz“onvntxonvzrtzr“A7 IEEE hrunsuwtions on dowyr ElywtroniwsA volC IA noC FA ppC FJ{GIA Jvn FNMNCpINr gC JC King vny iC VC htuvrtA qhmvllB“ignvl moyzl for thz “zriz“ rz“onvnt xonvzrtzrA7IEEE hrunsuwtions on Uyrospuwy unx Elywtroniw gystymsA volC VZhBGFA noC HA ppC HEF{HFNA bv– FNMJCpJEr bC GC Kim vny bC JC nounA qV yi“xrztz timz yomvin moyzling vny vnvl–“i“ of xontrollzy“zriz“ rz“onvnt xonvzrtzrA7 IEEE hrunsuwtions on Inxustriul ElywtroniwsA volC HMA noC FAppC HG{IEA [zw FNNFCpJFr GC XC kzrghz“zA bC ZC ZlwulukA vny JC GC Kv““vkivnA qV gznzrvl vpprovxh to “vmplzyByvtv moyzling for pofizr zlzxtronix xirxuit“A7 IEEE hrunsuwtions on dowyr ElywtroniwsAvolC eZBFA noC GA ppC LK{MNA Vpril FNMKCpJGr hC gC hvnyzr“A JC bC cofiorol“kiA mC oC aiuA vny GC XC kzrghz“zA qGznzrvlizzy vvzrvgingmzthoy for pofizr xonvzr“ion xirxuit“A7 IEEE hrunsuwtions on dowyr ElywtroniwsA volC KAnoC GA ppC GJF{GJNA Vpr FNNFCpJHr JC Grovz“A qhmvllB“ignvl vnvl–“i“ u“ing hvrmonix wvlvnxz mzthoy“A7 in dowyr Elywtroniwsgpywiulists Confyrynwy, EMMEB dEgC'ME fyworxB, FFnx Unnuul IEEEC IZZZA FNNFA ppCLI{LNCKLVivliogruphypJIr JC hun vny ]C Grot“tollznA qVvzrvgzy moyzling vny vnvl–“i“ of rz“onvnt xonvzrtzr“A7 indowyr Elywtroniws gpywiulists Confyrynwy, EMM3B dEgC 'M3 fyworxB, FHth Unnuul IEEEAJun FNNHA ppC LEL{LFHCpJJr GC JC JC vvn o–lA qV novzl frzquznx–Byomvin “mvllB“ignvl vnvl–“i“ of rz“onvnt pofizrxonvzrtzr“A7 IEEE hrunsuwtions on Cirwuits unx gystyms IN fygulur dupyrsA volC JFAnoC LA ppC FHLN{FHMIA Jul– GEEICpJKr WC XhzngA [C bu“vviA vny lC GC YunforyA qcovzl “mvll “ignvl moyzling vny xontrol ofvn aaX rz“onvnt xonvzrtzrA7 in FDEH IEEE Uppliyx dowyr Elywtroniws Confyrynwy unxEfiposition A UdEC FDEHA bvrxh GEFIA ppC GMGM{GMHICpJLr ZC mCBfC nvngA qZfltznyzy yz“xriwing funxtion mzthoy for “mvllB“ignvl moyzling of rz“Bonvnt vny multiBrz“onvnt xonvzrtzr“A7 ehCYC yi““zrtvtionA kirginiv izxhA FNNICpJMr XC WuxxzllvA XC XzxvtiA ]C avtvfvtA eC ezpzA vny KC gvziA qdw“zrvzrBwv“zy xontrol of aaXYXDYX rz“onvnt xonvzrtzr u“ing zfltznyzy yz“xriwing funxtion“A7 IEEE hrunsuwtions ondowyr ElywtroniwsA volC HEA noC FEA ppC JMMF{JMNFA dxt GEFJCpJNr WC XC ]–zon vny WC ]C XhoA qVnvl–“i“ vny yz“ign of thz lms rz“onvnt xonvzrtzr for lofioutput xurrznt ripplzA7 IEEE hrunsuwtions on Inxustriul ElywtroniwsA volC JNA noC LA ppCGLLG{GLMEA Jul– GEFGCpKEr oC [vngA JC lvngA hC YuvnA kC liuA vny iC XviA qXontrol of vn aaX rz“onvnt xonvzrtzru“ing lovy fzzywvxk linzvrizvtionA7 IEEE hrunsuwtions on dowyr ElywtroniwsA volC HHAnoC FA ppC MML{MNMA GEFLCpKFr ZC mC nvngA [C XC azzA vny bC bC JovvnovixA qhmvllB“ignvl moyzling of “zriz“ vnypvrvllzl rz“onvnt xonvzrtzr“A7 in Uppliyx dowyr Elywtroniws Confyrynwy unx Efiposition,EMMFB UdEC 'MFB Confyrynwy drowyyxings EMMFB, gyvynth UnnuulA [zw FNNGA ppC LMJ{LNGCKMVivliogruphypKGr hC iivnA [C XC azzA vny fC aiA qV “implizy zquivvlznt xirxuit moyzl of “zriz“ rz“onvntxonvzrtzrA7 IEEE hrunsuwtions on dowyr ElywtroniwsA volC HFA noC JA ppC HNGG{HNHFA bv–GEFKCpKHr hC iivnA [C XC azzA vny fC aiA qZquivvlznt xirxuit moyzling of aaX rz“onvnt xonvzrtzrA7in FDE6 IEEE Uppliyx dowyr Elywtroniws Confyrynwy unx Efiposition (UdEC)A bvrxhGEFKA ppC FKEM{FKFJCpKIr WC nvngA [C XC azzA vny bC JovvnovixA qhmvllB“ignvl vnvl–“i“ for aaX rz“onvnt xonBvzrtzrA7 in CdEg gyminurA volC LA noC HA GEEHA ppC FII{FINCpKJr ]C ]uvngA q[zzywvxk loop yz“ign of vn aaX rz“onvnt pofizr xonvzrtzrA7 Uppliwutionfyport, gLiUILFUA GEFECpKKr hC Xhvttopvyh–v– vny hC Yv“A qV yigitvl xurrznt moyz xontrol tzxhniquz for YXBYXxonvzrtzr“A7 in hwyntiyth Unnuul IEEE Uppliyx dowyr Elywtroniws Confyrynwy unx EfiAposition, FDDIB UdEC FDDIBA volC GA bvrxh GEEJA ppC MMJ{MNF kolC GCpKLr nC fiuA ]C aiuA vny mC XhznA qYigitvl vvzrvgz xurrzntBmoyz xontrol of elb YXflGEFHPYX xonvzrtzr“ fiithout xurrznt “zn“or“A7 IEEE hrunsuwtions on Inxustriul ElywAtroniwsA volC JLA noC JA ppC FKLE{FKLLA bv– GEFECpKMr WC Wr–vnt vny bC KC KvzimizrxzukA qkoltvgz loop of woo“t elb YXBYX xonvzrtzr“fiith pzvk xurrzntBmoyz xontrolA7 IEEE hrunsuwtions on Cirwuits unx gystyms IN fygulurdupyrsA volC JHA noC FA ppC NN{FEJA Jvn GEEKCpKNr YC KC hviniA VC gzvttiA vny bC KC KvzimizrxzukA qVvzrvgz xurrzntBmoyz xontrol of wuxkYXBYX xonvzrtzr fiith rzyuxzy xontrol voltvgz ripplzA7 in Inxustriul Elywtroniws gowiyty,IECcN FDE6AHFnx Unnuul Confyrynwy of thy IEEEC IZZZA GEFKA ppC HGLE{HGLJCKNpLEr JC JvngA eC hC KumvrA YC KimA vny WC XhoiA qVvzrvgz xurrzntBmoyz xontrol for aaX“zriz“ rz“onvnt YXBtoBYX xonvzrtzr“A7 in drowyyxings of hhy 7th Intyrnutionul dowyrElywtroniws unx aotion Control ConfyrynwyA volC GA Junz GEFGA ppC NGH{NHECpLFr JC JvngA bC JoungA hC XhoiA nC XhoiA vny WC XhoiA qXurrznt moyz xontrol for aaX “zriz“rz“onvnt YXBtoBYX xonvzrtzr“A7 in FDEE hwyntyAgifith Unnuul IEEE Uppliyx dowyrElywtroniws Confyrynwy unx Efiposition (UdEC)A bvrxh GEFFA ppC GF{GLCLEUppynxifi UEfitynxyx Dyswriving Funwtionautriwysihz Jvxowivn mvtrixz“ =GCGM) vny =GCGN) vrz xvlxulvtzy from zquvtion“ =GCGF)B =GCGL)C [or“implixvtionA thz zquvtion“ hvvz wzzn rzyznzy v“ v); v2; v+; v4; v5; v6 vny v7 rz“pzxtivzl–Cihz mvtrifl V i“ formzy w– thz follofiing zlzmznt“a)) R@v)=x; t)@iysR − InLyfv(Fip− =iys − ims)2i+p)=VCF)a)2 R@v)=x; t)@iyjR −!s − InLyfv(=ims − iys)=imj − ipyj)i+p)=VCG)a)+ R@v)=x; t)@vjsR − FLy; a)4 R@v)=x; t)@vjjR E =VCH)a)5 R@v)=x; t)@imsRInfvLy(Fip− =ims − iys)2i+p)=VCI)a)6 R@v)=x; t)@imjRInfvLy(=ims − iys)=imj − iyj)i+p)=VCJ)a)7 R@v)=x; t)@fvRInfvLy=ims − iys)ip=VCK)a2) R@v2=x; t)@iysR !s +InfvLy(=imj − iyj)=ims − iys)i2p)=VCL)a22 R@v2=x; t)@iyjR −InfvLy(Fip+=imj − iyj)2i+p)=VCM)LFAppynxifi AB Efitynxyx Dyswriving Funwtion autriwysa2+ R@v2=x; t)@vjsR E; a24 R@v2=x; t)@vjjR − FLy=VCN)a25 R@v2=x; t)@imsR −InfvLy(=imj − iyj)=ims − iys)i+p)=VCFE)a26 R@v2=x; t)@imjRInfvLy(Fi2p+=imj − iyj)2i+p)=VCFF)a27 R@v2=x; t)@fvRInfvLy(=imj − iyj)ip)=VCFG)a+) R@v+=x; t)@iysRFSs; a+2 R@v+=x; t)@iyjR E; a++ R@v+=x; t)@vjsR E =VCFH)a+4 R@v+=x; t)@vjjR −!s; a+5 R @v+=x; t)@imsR E; a+6 R@v+=x; t)@imjR E; a+7 R@v+=x; t)@fvR E=VCFI)a4) R@v4=x; t)@iysR E; a42 R@v4=x; t)@iyjRFSs; a4+ R@v4=x; t)@vjsR !s =VCFJ)a44 R@v4=x; t)@vjjR E; a45 R@v4=x; t)@imsR E; a46 R@v4=x; t)@imjRFSs; a47 R@v4=x; t)@fvR E =VCFK)a5) R@v5=x; t)@iysRInfvLy(Fip− =ims − iys)2i+p)=VCFL)a52 R@v5=x; t)@iyjRInfvLy(=ims − iys)=imj − iyj)i+p)=VCFM)a5+ R@v5=x; t)@vjsR E; a54 R@v5=x; t)@vjjR E =VCFN)a55 R@v5=x; t)@imsR −InfvLy(Fip− =ims − iys)2i+p)=VCGE)a56 R@v5=x; t)@imjR −!s + InfvLy(=ims − iys)=imj − iyj)i+p)=VCGF)a57 R@v5=x; t)@fvR −InfvLy(=ims − iys)ip)=VCGG)a6) R@v6=x; t)@iysR −InfvLy(=imj − iyj)=ims − iys)i+p)=VCGH)LGAppynxifi AB Efitynxyx Dyswriving Funwtion autriwysa62 R@v6=x; t)@iyjR vrasInfvLy(Fip− =imj − iyj)2i+p)=VCGI)a6+ R@v6=x; t)@vjsR E; a64 R@v6=x; t)@vjjR E =VCGJ)a65 R@v6=x; t)@imsR !s +InfvLy(=imj − iyj)=ims − iys)i+p)=VCGK)a66 R@v6=x; t)@imjRInfvLy(Fip− =imj − iyj)2i+p)=VCGL)a67 R@v6=x; t)@fvR −InfvLy(=imj − iyj)ip)=VCGM)a7) R@v7=x; t)@iysR − GnSv=ims − iys)ip=VCGN)a72 R@v7=x; t)@iyjRGnSv=imj − iyj)ip=VCHE)a7+ R@v7=x; t)@vjsR E; a74 R@v7=x; t)@vjjR E =VCHF)a75 R@v7=x; t)@imsRGnSv=ims − iys)ip=VCHG)a76 R@v7=x; t)@imjR − GnSv=imj − iyj)ip=VCHH)a77 R@v7=x; t)@fvR − nSvbL=VCHI)ihz mvtrifl W i“ xompounyzy w– thz follofiing zlzmznt“r)) R@v)=x; t)@!sR −iyj; r)) R @v2=x; t)@!sR iys =VCHJ)r+) R@v+=x; t)@!sR −vjj; r4) R @v4=x; t)@!sR vjs =VCHK)r5) R@v)=x; t)@!sR −imj; r6) R @v6=x; t)@!sR ims =VCHL)LHAppynxifi AB Efitynxyx Dyswriving Funwtion autriwysr7) R@v7=x; t)@!sR E =VCHM)LI

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