兩電平和三電平逆變器的新模塊化似零電壓軟換流電路的分析和設(shè)計

兩電平和三電平逆變器的新模塊化似零電壓軟換流電路的分析和設(shè)計,平和,電平,逆變器,模塊化,電壓,換流,電路,分析,設(shè)計 2 0 0 5年1 0月 第 2 O卷第 1 O期 電 工 技 術(shù) 學(xué) 報 TRANS ACT1 0NS 0F CHI NA EL ECT R0T ECHNI CAL S OCI ET Y V0 1 2 O No 1 O 0c t 20 05 M o d u l a r App r o a c h o f S o f t S wi t c h i n g a t Re s i d u a l Vo l t a g e f o r Two Le v e l a n d Th r e e Le v e l I n v e r t e r s Ch a n g Ji e Hu d u n r 1 F l o r i d a A&M T a l l a h a s s e e F L 3 2 3 1 0 US A 2 F l o r i d a S t a t e U n i v e r s i t y F l o r i d a US A)Ab s t r a c t A n e g a t i v e b u s a u x i l i a r y r e s o n a n t c i r c u i t(NB AR C)and n o v e l mi rr o r s y mme t r i c a l p a i r o f r e s o nan t l i n k mo d ul e s f or s o ft c o mmu t a t i o n o f t wo l e ve l an d t h r e e l e ve l i n v e r t e r s i s p r e s e n t e dTh e NBARC t o p ol o g y r e d u c e s t h e p o we r d e v i c e c o u n t s a n d r e q u i r e s l o w d e v i c e p o we r r a t i n g s W h i l e t h e b a s i c NBARC r e s o n a n t c i r c u i t i s c on c e i v e d a n d a n a l yz e d f o r z e r o v ol t a ge s wi t c h i n g o f t wo l e ve l i n v e r t e r s，t h e t o p o l o g y an d mo d ul a r d e s i g n a p p r o a c h a r e e x t e n d e d t o for m a p i nc h e d l i n k r e s o n a n t s t a ge o f z e r o。v o l t a g e s wi t c hi n g for t h r e e l e ve l i n v e r t e r s u s i n g m i r r o r s y mme t r i c a l p a i r of r e s o n a n t mo d u l e s An an a l ys i s o f s wi t c hi n g l o s s e s v e r s u s t h e r e s i d u a l c o mmu t a t i o n v o l t a g e i s c o nd u c t e d Th e mo d u l a r a p p r o a c h a l l o ws t h e s o ft s wi t c h i n g c i r c ui t t o b e d e s i g ne d a s a n a dd o n o p t i o n a l mo d u l e t o a s t a n d ard i n v e r t e r,wh i c h c a n c o n v e rt a c o n v e n t i o n a l i n v e rte r i n t o a s o ft s wi t c h e d i n v e rte Ex p e r i me n t a l r e s u l t s v e r i f y ou r c i r c ui t an a l ys i s a n d i mp l e me n t a t i o n Ke ywo r ds：S oft s wi t c hi n g，r e s i d u a l c o mmu t a t i o n v ol t a ge a nd r e d uc e d s wi t c h i n g l o s s e s，ne ga t i v e b us a u xi l i a ry r e s o na n t c i r c ui t，mi r r o r s ymme t r i c a l pa i r of DC l i nk r e s on a n t c i r c u i t s，p i n c h e d 1 i nk r e s i d u a l vo l t a g e s wi t c hi ng 1 I nt r 0duc t i 0 n I n r e c e n t y e ars，s o ft s wi t c hi n g c i r c u i t s h a ve b e e n r e s e arc h e d【?！縯 o i mp r o v e e l e c t r o ma g n e t i c c o mp a t i b i l i t y o f t h e c o n v e rte rs a n d r e d u c e s wi t c h i n g l o s s e s Earl y p r o p o s e d r e s o n a n t typ e s o ft s wi t c h e d i n v e rte r L l,J u s e s p a s s i v e p o we r c o mpo ne n t s of i nd uc t o rs a nd c a p a c i t o rs o n DC l i n k I t s b e ne fit i s offs e t b y hi g h v o l t a g e s t r e s s e s o n i n v e rte r s s wi t c h i ng p o we r d e v i c e s a n d l i mi t e d c o n t r ol p e r f o r man c e o f AC c u rre n t s d u e t o i t s l a c ki ng s y nc h r o ni z a t i o n wi t h t i me v a ry i n g p u l s e wi d t h mo d u l a t i o n(P WM)Q u a s i r e s o n a n t c i r c u i t s 2-5 1，s u c h a s a c t i v e c l a mp e d r e s o n a n t(AC R 1 D C l i n k c i r c u i t，u s e a d d i t i o n a l a c t i ve c l a mp i n g s wi t c h e s a n d c a p a c i t o r s，t h u s b e i n g a bl e t o s y nc h r o ni z e DC l i n k r e s o n a n c e wi t h i n v e r t e r s PW M o p e r a t i o n a n d me e t i n g t he r e q u i r e me n t of s ys t e m s mod ul a t i o n Ho we ve r,t h e i r p e a k DC l i n k v ol t a ge i s s t i l l h i g h，i e 1 5-1 8 t i me s o f n o mi n a l b us v o l t a g e An a u x i l i a r y r e s o n a n t c o m mu t a t e d p o l e(A R C P)c i r c u i t J c a n mi ni m i z e t h e d e v i c e vo l t a g e s t r e s s e s t h r o u g h p l a c i n g t wo a u xi l i a ry s wi t c he s i n s e r i e s wi t h a r e s o na n t i nd u c t o r a t e a c h i n v e r t e r p h a s e p o l e Th e Re c e i v e d M a r c h 21，20 05；i n r e v i s e d f o r m M a y 1 1，2 0 0 5 d o wn s i de o f t hi s c i r c ui t i s i t r e q ui r e s s i x a u xi l i a r y p o we r s wi t c h e s fo r a t hr e e p ha s e i nv e r t e r b r i d ge a n d c o mp l i c a t e d c o n t r ol l o gi c I n t hi s p a p e r，we p r o po s e a n e g a t i v e b u s a u x i l i a r y r e s o n a n t c i r c u i t(NB AR C)a n d no v e l mi r r o r s y mme t r i c a l r e s o na nt c i r c ui t m o d ul e s f o r z e r o v ol t a g e s wi t c hi n g of i n v e r t e r s，i nc l u di ng b o t h t w0 一 l e ve 1 a n d t h r e e l e ve l i nv e r t e r s 9-1 1 M o r e o ve r,ne w r e s on a n t c i r c ui t s c a n b e d e s i gn e d a s o p t i o n a l mo d ul es fo r a s t a n d a r d i n ve r t e r pr od u c t u ni t By a t t a c hi ng s uc h a r e s o na n t m o d ul e o n t he DC l i nk，t he c o n v e n t i o n a l ha r d s wi t c h e d i n ve r t e r c a n b e c o n ve r t e d t o a z e r o v o l t a g e s w i t c h e d(z vs、i n v e r t e r 2 Ne g at i ve bus r e s o na nt modul e f or t wo 1 e ve l i n ve r t e r s Ou r p r o p os e d n e ga t i ve bu s a u xi l i a r y r e s o na n t c i r c ui t for z e r o v ol t a ge s wi t c hi ng i s s h o wn i n Fi g 1 a，wh e r e C1 a nd C2 a r e DC l i n k p owe r c a p a c i t o r s，a nd T1T6 a r e t h e mai n s wi t c h i n g d e vi c e s i n a c o n v e n t i o n a l i n v e r t e r b r i d g e(ma i n b r i d g e i n t h i s p a p e r)T h e DC l i n k p o we r c a p a c i t o r s n o r ma l l y h a v e l a r ge c a p a c i t a nc e v a l u e s，v a r yi n g f r o m t h ou s a n ds t o t e n s o f t h o u s a n d s o f mi c r o f a r a d s(k t F)i n p r o p o rt i o n a l t o i nv e r t e r s po we r r a t i n g L 1，L2 a n d L3 r e p r e s e n t t o t a l 維普資訊 http:/ 1 4 電 工 技 術(shù) 學(xué) 報 2 0 0 5年 1 0月 i n d uc t a nc e a t t he i np u t l i n e s t h a t l i mi t t h e r a t e of c h a n ge of t h e l i n e c ur r e n t flowi ng i n t o t h e DC l i n k a n d t he i nv e r t e r Our pr op o s e d NBARC c i r c u i t i s p r e s e n t e d i n a s ha d e d b l o c k i n Fi g 1，whe r e t h e c o mp on e nt s o f Lr，Cr 1 a nd Cr 2 a r e s ma l l e n e r g y s t o r a g e de vi c e s，a n d S a a n d Sc a r e a u xi l i a r y s e mi c o nd u c t o r po we r s wi t c h e s Con n e c t e d wi t h t h e a ux i l i a r y s wi t c h e s，S a a nd S c，t h e L a n d C c o mp on e n t s f or m a n o n l i n e a r(o r p i e c e l i n e a r)s e c o n d o r d e r r e s o n a n t c i r c ui t a t t he DC l i n k I n t he c i r c u i t，t h e fir s t a u xi l i a r y s wi t c h Sc s e r v e s a s a vo l t a ge c l a mp i n g de vi c e i n r e f e r e nc e t o t h e ne g a t i v e DC l i nk b us，whi l e Sa i s t he s e c on d a u xi l i a ry s wi t c h t h a t a c t i va t e s o r d e a c t i v a t e s t h e s e c o n d o r d e r r e s on a n c e c i r c u i t by c o n t r ol l i n g t he s t a r t i n g a n d e n di n g t i me po i n t of t he r e s o na nc e I n a n or m a l s t e a d y s t a t e c o nd u c t i n g mod e o f t h e i n v e r t e r s ma i n b r i dg e，i e no n c o mmu t a t i o n s t a t us，Sc i s t ur ne d o n a nd Sa i s of f Th e vo l t a ge a t t he ne g a t i v e (mi n u s)一 b u s p o w e r t e r mi n a l，M，i s c l a mp e d b y S c t o t h e n e ga t i ve t e r mi n al of t h e DC l i n k c a p a c i t o r b a n k s o t ha t t he c a t i nv e r t e r s i np ut t e r mi na l s，P a nd M，e q ua l s t h e v ol t a ge o n t he DC l i n k c a p a c i t o r b a n kTh e vo l t a ge o n Cr 1 e q ua l s c，a nd t he v ol t a ge o n Cr 2 e q ua l s z e r oSi nc e t h e de vi c e Sa i s of f,t h e r e s o na n t c i r c u i t i s d i s c o n ne c t e d a n d t h e r e i s n o c u r r e n t flowi n g t hr o ug h t h e i n d uc t o r，Lr Th e r e s o n a n t mo d ul e a t t h e DC l i nk i s，t he r e f o r e，i n a do r ma n t o r s t a nd b y s t a t us T o s t a r t a v ol t a ge r e s o n a n ce a t t he i n pu t t e r m i na l s of t h e ma i n i n ve r t e r b r i d ge，S c i s t ur ne d o ff fir s t Thi s r e l e a s e s o r i s o l a t e s t h e n e g a t i v e t e r mi n a l o f t h e b u s f r o m t he DC l i nk c a pa c i t or C2，wh i c h fle e s t he vo l t a g e p o t e n t i a l o n M i n p ut t e r mi na l fo r a n i nc o m i n g r a pi d t r a ns i e n t c h a n g e As s o on a s S c t u r n s of f,t h e a ux i l i a r y s wi t c h S a i s t ur n e d o n Thi s ma ke s a n e nc i r c l e d c ur r e n t pa t h a s s h o wn i n Fi g 1 a a nd b s o t h a t a r e s on a n t c u r r e n t，i r，c a n be e s t a b l i s h e d Th e s e c o n d or de r r e s on a n t c i r c ui t i s t he n a c t i va t e d a nd i s d r i v e n b y t he v ol t a ge of 1 2 。c r os s i n g C2 Th e r e s o n a n c e c ur r e n t，i r，di s c h a r ge s t h e vo l t a ge a c r os s Cr 1 r a pi dl y s i nc e i t ha s a ve r y s ma l l c a p a c i t a nc e，a n d m a t t he i np u t o f t he m a i n br i dg e i s d e s c e nd i n g r a p i dl y t o z e r o a c c o r di ng t o o u r d e s i g n Thi s c r e a t e s a z e r o v ol t a ge t r a n s i e n t fo r a s oft c o m mu t a t i o n of t h e ma i n s wi t c h i ng de vi c e s o f t he i n ve r t e r,T1 T6 Th e t i mi n g t o t r i g ge r t he c i r c ui t r e s on a n c e i s f ul l y c o n t r ol l e d b y t ur ni ng off Sc a n d g a t i n g o n Sa o nl y wh e n t h e r e i s a c h a n ge i n i n c o mi n g PW M c o nt r ol p a t t e r n，t h us a v oi d i n g a ny de t e r i o r a t i on of PW M c o nt r ol pe r f o r ma n c e I n ou r c i r c ui t d e s i gn，we u s e Cr 1 a nd Cr 1 t o b a l a n c e t h e c ha r ge of t he r e s o na n t e n e r g y e xc ha ng e s a n d p hy s i c a l l y pl a c e t h e m c l o s e t o e a c h ot he r t o r e du c e pa r a s i t i c e f f e c t De t a i l e d a na l ys i s wi l l b e g i ve n i n t he f o l l owi ng s e c t i o ns 厶。P C a+m 上+g I s。上 _ 一 M(a)NB AR C mo d u l e f o r z e r o v o l t a g e s wi t c h i n g P o s i t i v e DCb u s P t一厶。(b)Eq u i v a l e n t c i r c u i t for a n a l y s i s o f r e s o n a n t t r a n s i e n t St a g e：Ze r oVolt a g e I I：如 c 0 ：瓜一：r 2 T o J(c)Ne g a t i v e b u s v o l t a g e a n d r e s o n a n t c u r r e n t Fi g 1 NBARC ZVS c i r c u i t，e q u i t v a l e n t c i r c u i t a n d r es ona nt wav ef or m s 3 An a l y s i s o f n e g a t i v e-b u s a u x i l i a r y r e s o na nt c i r c ui t 3 1 Ope r a t i ng mo de s a nd e qu i va l e nt c i r c u i t a na l ys i s An e q ui va l e n t c i r c ui t of NBARC a nd i l l u s t r a t i ve wa v e f or m s of r e s o na n t vo l t a ge a n d c u r r e n t a r e s h o wn i n Fi g 1 b a n d Fi g 1 c r e s pe c t i ve l y W h e r e i n Fi g1 b，Cr 一O ，維普資訊 http:/ 第2 O 卷 第1 0 期 查 篁 塑 皇 三皇 器的 新模 塊化 似零電 壓軟 換流電 流電 路的分 析 和設(shè)計 1 5 Cr 1+Cr 2 Du r i ng a c o mmut a t i on i n t e r va l t ha t i s t y pi c a l l y a s h o r t pe r i od a nd l a s t s t e n s o r h u n dr e d s of m i c r o s e c on d s，t h e e q ui va l e nt c i r c u i t of t h e i nv e r t e r s ma i n b r i dg e r e l a t e d t o t he c o mmu t a t i on c a n b e s i mpl i fie d u s i ng a n o nl i ne a r c i r c u i t c o mp r i s i n g a d i o d e，D a n t i，(a n t i p a r a l l e l e d wi t h t h e I GB T d e v i c e s 1 a nd a c u r r e n t s o ur c e r e p r e s e n t i ng t he l o a d c u r r e nt Si nc e t h e c o mmut a t i on i nt e r v a l i s ve r y s ma l l i n c o mp a r i s o n wi t h t h e t i me c on s t a n t of t h e e l e c t r i c a l l o a d(e i t h e r AC ma c h i n e o r a R L l o a d)t h i s s i mpl i fic a t i o n s ho ul d n ot a f f e c t t he g e n e r a l i t y o f t h e c o mmu t a t i o n a na l ys i s o i s a n e q ui v a l e nt l o a d c ur r e nt a t t h e t i me of c o mmu t a t i o n T o a d d t o t h e c i r c u i t a na l y s i s，we f u r t h e r d e c o mp o s e t h e pi e c e l i n e a r c i r c ui t i n t o fiv e l i n e a r e qu i v a l e nt c i r c ui t s a n d d i s c u s s t h e o pe r a t i o n s s t a g e b y s t a g e The e q u i v a l e n t c i r c ui t i n e a c h s t a g e i s g i v e n i n Fi g 2F o r a c o n v e n i e n t c r o s s r e f e r e nc e o f t h e e q ui v a l e n t c i r c u i t s a n d t h e wa v e for m s，we h a v e a l s o hi g hl i g h t e d t h e t i me s e g me n t s a s s o c i a t e d wi t h t h e fiv e o pe r a t i o n a l s t a g e s of t h e r e s o n a n t o p e r a t i o n a n d g i v e n i n Fi g 1 c St a ge A：Th i s i s a n omi na l o p e r a t i n g s t a ge be f o r e a c t i va t i n g t h e s e c on d or de r r e s on a nt c i r c ui t The r e s on a nt c a p a c i t o r，Cr，h a s b e e n c h a r ge d u p t o 1 2 of t h e no r ma l b us v o l t a g e Th e c l a mpi ng s wi t c h，S c，i s o n，a n d t h e ne g a t i ve bus v ol t a ge i s c l ampe d t o t he (a)S t a g e A (b)S t a g e B (c)S t a g e C (d)S t a g e D 【e)S t a g eE F i g 2 Re s o n a n c e s t a g e s f o r s o f t c o mmu t a t i o n DC l i nk c a pa c i t or s v ol t a ge，wh i c h i s e qu a l t o一1 2 。C1 a n d C2 c a n b e r e pl a c e d b y v ol t a g e s o u r c e s E1 a n d E2 r e s p e c t i v e l y，E1=E2=1 2 。St a g e B：At t=0，a s s h o wn i n Fi g 1 c t he c l a mpi n g s wi t c h，Sc，t u r n s o f f Th e ne ga t i v e b us t e r mi n a l i s e l e c t r i c a l l y r e l e a s e d f r o m t he DC l i n k c a p a c i t o r C2 Fu r t h e r t u r n i n g o n Sa，a r e s on a n t c ur r e n t pa t h i s f or me d t h r o u gh Lr a nd Cr An e x pr e s s i o n o f t he r e s on a nt c u r r e nt，i r，i n t hi s s e c o n d o r d e r r e s o n a n t c i r c u i t c a n b e d e r i v e d a n d g i v e n i n E q (1)f ：，(赤 Th e e n e r g y s t o r e d i n Cr i s t r a ns f e r r e d t o t h e i nd u c t o r vi a t he DC l i n k c a p a c i t o r，a nd t he v ol t a ge c r o s s i n g Cr i s d e c r e a s i n g r a pi d l y t o z e r o f or 0 f T o a s s ho wn i n Fi g 1 c a n d Fi g 2 bTh e pe a k r e s o n a n t c u r r e nt i s gi ve n i n E q (2)V d c 2 (2)a n d To i s o n e h a l f o f t h e r e s o n a n t p e r i o d t h a t i s g i v e n b y =兀 C (3)wh e r e C r C r 1+C r 2 As s h o w n i n E q(2)，a p r o p e r s e l e c t i o n o f t h e va l u e s o f Lr a nd Cr wo u l d he l p t o l i mi t t h e pe a k va l ue of t h e r e s o na nt c u r r e nt r e s ul t i n g i n a n e c on o mi c d e s i gn fo r t he c u r r e nt r a t i n g o f t h e a ux i l i a r y s wi t c he s St a ge C：At t he e n d of fir s t h a l f r e s o n a n t p e r i o d 戶To，t h e v o l t a g e a c r o s s Cr h a s b e e n d i s c h a r g e d t o n e a r l y z e r o o r ZO F，wh i c h i s e qui va l e n t t o a f o r wa r d 一，Y 維普資訊 http:/ 1 6 電 工 技 術(shù) 學(xué) 報 2 0 0 5年 1 0月 v ol t a ge d r o p o f p o we r di od e An y e x c e s s c ur r e n t i n t h e i n d u c t o r p a t h wi l l f l o w t hr o u g h t he a n t i p a r a l l e l d i o de，Da n t i，o f t h e i n ve rte r a n d VPM r e a c he s z e r o，a s s h o wn i n Fi g 1 b a n d c At t h i s t i me，a l l p o we r s wi t c he s o f t h e ma i n i n ve rte r b r i d ge，T1 T6，s e e n e a r l y z e r o v o l t a ge，e0 Th e r e f o r e，i t c r e a t e s z e r o v ol t a ge s wi t c h i n g c o n di t i o n f o r s o f t c o mmu t a t i o nTh e i n v e r t e r b r i d g e c o mmu t a t i o n s h a l l c o mpl e t e s ho rtl y a fte r f=T o b y a p p l y i n g n e w i n c o mi n g P WM p a t t e rn t o t h e ma i n b r i d g e St a g e D：As t h e r e s o na n t c u r r e n t i r，c on t i n ue s flo wi n g i n t o i t s n e g a t i v e ha l f c y c l e s h o wn i n Fi g 1 c，t h e a nt i pa r a l l e l d i o de，Da，s t a r t s t o c on d uc t a nd p r o v i de s a p a t h t o c h a r g e ba c k Cr As a r e s ul t，t h e r e s on a n t e ne r g y i s b e i n g t r a n s f e r r e d b a c k t o Cr b y i r i n a r e v e r s e d i r e c t i o n for Tot Th e s e c o n d i s t h e l o a d c u r r e n t a nd l i n e i n p u t c u rre n t a r e c o n s t a n t d u r i n g t h e t r a n s i e n t d u e t o l o a d an d l i n e s i d e i n d u c t a n c e Th o s e a p p r o x i ma t i o n s a l e v a l i d fo r a c o mmu t a t i o n a n a l y s i s o f p r a c t i c a l i n v e rte r s y s t e ms 3 2 Ke y f e a t ur e s o f NBARC c i r c u i t As s h o wn i n F i g 1 a a n d f r o m t h e a b o v e a n a l y s i s，o ur p r op o s e d NBARC c i r c u i t us e s o nl y t wo a u xi l i a r y p owe r s wi t c h e s i n t he ZVS l i n k s t a g e for a t h r e e p ha s e i nv e r t e r A b r i e f c o mpa r i s o n o f t he p r o p os e d ZVS c i r c ui t a n d o t he r a u xi l i a r y r e s on a nt c i r c u i t s i s gi v e n i n Ta b 1 The NBARC ha s t he l o we s t n umb e r of a u xi l i a r y s wi t c he s a n d l o we s t vo l t a g e r a t i ng s fo r bo t h ma i n p o we r d e vi c e s a nd a u xi l i a r y s wi t c he s The NBARC t o p ol og y a r r a n g e s t h e s a me v ol t a g e po t e n t i a l fo r t h e e mi t t e r s of t he c l a mpi ng d e vi c e，S c a nd t h e I GBT fo r a DC l i n k b r a k i n g c i r c ui t t h a t i s ne c e s s a r y fo r s u c h a n i n ve r t e r，a l t h o ug h n o t s h o wn i n t he c i r c ui t d i a gr a m，t h us s a v i ng a s e p a r a t e d flo a t i n g p o we r s up pl y Ta b 1 Co m p a r i s on wi t h p o pu l a r s o f t s wi t c hi n g t o p o l o g y Ke y f e a t u r e s of t he NBARC c i r c ui t t o p ol o g y a r e s umma r i z e d a s fo l l o ws：。No ma i n p owe r flo ws t h r o ug h t he a u xi l i a r y r e s o na n t d e vi c e s i n c o n t r a r y wi t h t he ACR t o po l o gy，t h u s r e q ui r i n g l e s s c ur r e n t r a t i n g s a n d t h e r ma l ma na g e m e n t Us e t wo a u xi l i a r y s wi t c he s a nd o ne s e t o f LC c o m p o ne n t s i ns t e a d o f s i x a ux i l i a r y s wi t c he s a nd t h r e e s e t s o f LC c o mpo ne n t s c o mp a r e d wi t h t he ARCP t o pol og y Vol t a ge r a t i n g o f t h e c l a mp i n g s wi t c h，S。，i s t h e s a me a s t h e DC 1 i n k vo l t a g e Vol t a ge s t r e s s of t h e a u xi l i a r y s wi t c h，Sa，i s r a t e d o ne h a l f of t he DC 1 i nk v ol t a g e Cu r r e n t r a t i n g c a n be pr o g r a mme d t o a l ow l e v e l b y E q (2)Ze r o v ol t a ge t u r n on for t h e i n ve rte r s wi t c h e s a nd c l a mpi n g s wi t c h，S。Ze r o c ur r e n t t ur n of f fo r t he a u xi l i a r y s wi t c h，S 維普資訊 http:/ 第 2 0卷第 l 0期 張 杰等 兩電平和三 電平逆變器的新模塊化似零電壓軟換流電流電路的分析和設(shè)計 l 7 No r e q ui r e me n t f o r i n c r e a s i n g t he v ol t a ge a n d c u r r e n t r a t i n g s of i n v e r t e r s ma i n p o we r d e vi c e s Ci r c u i t c a n be a p pl i e d t o a n e xi s t i n g h a r d-s wi t c he d i n ve r t e r a s a n op t i on a l a d d-on mod ul e 3 3 Br i e f d i s c us s i on o f l o a d c ur r e nt e f f e c t I n t h e a b o v e di s c u s s i o n，we pe r f or me d a de t a i l e d a n a l ys i s o f t h e b a s i c op e r a t i o n o f ou r NBARC r e s o n a n t c i r c ui t No w l e t s t a k e a l oo k on t h e l o a d c u r r e n t o t ha t s o me h ow p a r t i c i p a t e s i n t h e c o mmu t a t i on p r o c e s s I n a pr a c t i c a l s ys t e m，t h e l o a d c u r r e n t a s s i s t s t h e c ha r gi n g a n d d i s c h a r gi ng o f t h e e ne r g y s t o r a ge c o mpo n e n t s Cr a n d Lr Thi s c o ul d a f f e c t o u r i ni t i a l t he or e t i c a l e s t i ma t i on，b y u s i n g e q u a t i o n(3)，o f t h e z e r o c r o s s i n g p o i n t o f I r a t w h i c h VPM r e a c h e s t he mi n i mu m Ho we ve r，t h i s t u r ns ou t n o t t o be a pr o bl e m s i n c e we c a n u s e a v ol t a ge s e ns o r t o de t e c t t he l o we s t po i n t o f M S u c h a vo l t a g e s e ns o r i s n or ma l l y a v a i l a b l e i n a s t a nd a r d pr o du c t o f a n i n d us t r i a l i n ve r t e r for o ve r v ol t a g e p r o t e c t i on，t h us n o t i n c r e a s i n g t h e c os t o f ou r ZVS c i r c ui t A f ur t he r a s s e s s me n t of no n i d e a l s i t u a t i o ns of t h e ZVS c i r c ui t op e r a t i o n wi l l be gi ve n i