Un iform energy conservation average models of sw itch ing converters

Transcription

1 EL ECTR ICMACH IN ESANCON TROL Vol3 No4 July 2009 ( 6023) : buck boost buck2boost :; ; ; : TM 3 : A : X (2009) U iform eergy coservatio average models of sw itch ig coverters Q IU Yig CHEN Xi2you (epartmet of Electrical ad Electroics Egieerig alia Uiversity of Techology alia 6023 Chia) Abstract: To cope w ith the p roblem of coversio betwee topology depedet models of differet co2 verters a uiform dc ad sm all2sigal models fo r both isolated ad o2isolated buck boost ad buck2 boost coverters ad its ope2loop trasfer fuctios i cotiuous coductio mode ( CCM ) are estab2 lished based o the eergy coservatio averagig p ricip le. B y trasferrig the parasitic param eters ad iductor equivaletly ito the brach i series coectio w ith output capacito r the models are ui2 fied ad the parasitic param eters are cotaied. The coversio betwee differet models ca be easily realized by simp ly chagig the topology factors. It ca be beeficial whe comparig differet covert2 ers. Models ad exp ressios ca be also app lied for sychroous rectifier mode. The p roposed model is validated by detailed sim ulatio ad is show to accurately p redict sm all2sigal frequecy dom ai char2 acteristics. Key words: sw itchig mode coverter; eergy coservatio; parasitic param eters; sm all2sigal model 0 [ - 3 ] [ 4 ] [ 5 ] : : (982) ; (962).

2 560 3 [ 6 ]buck2boost cuk sep iczeta buckboost buckboost [ 7 ] [ 8-3 ] buck boost buck2boost 3 R F U F ; R T R T2 ; R S ; R L R C ; I L I S ; : ; buck buck I L ; I SRM S T T 0 i 2 s dt I L () : T f P ST I 2 SRM S (R S + R T ) I2 L (R S + R T ) 2 (2) P ST R SAV I 2 L (3) R SAV (2)(3) R SAV (R S + R T ) 2 (4) R T2 R F R L R E

3 4 56 Table Equ iva le t param eters R E R E2 L E N ( s) buck R S + R T R C R 2 ( - ) 2 L 2 + R T2 + R F + R L 2 ( fl ) 2 boost buck2boost R S 2 ( - ) 2 + R L 2 ( - ) 2 + R T 2 ( - ) + R F + R T2 - (R S + R T ) R L 2 ( - ) ( - ) 2 + R F + R T2 - R C - R C - K 2 4 L K 2 4 L K L E R s - L E R s [ 8 ] I CRM S U O ( - ) (5) 2fL (5) R E2 R C R 2 ( - ) 2 2 ( fl ) 2 (6) (6) buck U T I I U T U I (7) I I I L (8) d + d^ d^ U T + ^u t + d^ I I + i^i + d^ (U I + ^u i ) U I + ^u i + U I d^ d^ + ^u i (9) ( I L + i^l ) I L + i^l + I L d^ + d^ i^l (0) (9) (0) buck 2boost 2 boostl L E L 2 ( - ) 2 () L E I L ( - ) I SRM S T T i 2 s d t 0 I L ( - ) (2) (2) R SAV (R S + R T ) 2 ( - ) 2 (3) R E ( ) boost buck I CRM S ( - ) I L (4) ( 4) R E2 R C (5) - U T + ^u t (U I + ^u i ) ( - - d^) U I ( - ) + ^u i ( - ) + d ^U I ( - ) 2 ( I L + ^ il ) I I + i^i ( - - I L d^) ( - ) + ^ il ^ d IL ( - ) + ( - ) 2 + d ^ ( ^ui + ^u t ) ( - ) + d ^ ( d^ l + ^ i ) ( - ) (6) (7) boost (6) (7) I O I O I L I O I O + i^o ( - - d^ ) ( I L + i^l ) - ^ i^ l d^ I L I L + i^l d (8) - (6) (7)(8) boost

4 buck2boost buck2boost buckboost [ 6 ] buck2boost L boost buck2boost boost buck2boost 2 3 ; ; ( 9 ) ( 0 ) ( 6 ) ( 7 ) (8) K 3 N ( s) Table 2Topology factor of coverter K K 2 K 3 K 4 buck boost buck - boost ( - ) ( - ) ( - ) 2 - ( - ) 2-0 ( - ) ( - ) ( - ) ( - ) 3 [ 8 ] P S fc O U 2 I fc O R P O (9) : C O P O U O I O U I I I + R E R K 2 + U F U O + fc O R K 2 (20) (20) ; boostbuck2boost M V ( s) ^u o ( s) ^u i ( s) K R C R L E (R + R C ) T P ( s) ^u o ( s) ^d ( s) Z O ( s) ^u o ( s) ^i o ( s) Z I ( s) ^u i ( s) ^i i ( s) K 2U I R C R L E (R + R C ) s + C + 2 r r s + 2 r (2) ( s + C ) N ( s) + 2 r r s + 2 r ( s + C ) ( s + L ) R C + 2 O Q s + L E K 2 2 O (22) (23) + 2 r r s + 2 r s + cr (24)

5 4 563 : Q 2 C ( R E + R E2 + R C ) C L E CR C L R E + R E2 r L E R + R E + R E2 L E C (R + R C ) O L E C r C [ R C R + R (R E + R E2 ) + R C (R E + R E2 ) ] +L E 2 L E C (R + R C ) (R + R E + R E2 ) cr (25) C (R + R C ) boostbuck2boost boostbuck2boost Z C ( s) Z O ( s) + T L ( s) (26) : Z C Z O T L Z C (s) + T L (s) Z O (s) - T L (s) + T L (s) K 2 (R +R E )N (s) - (27) R T R T2 0 buck U F R F - ; boostbuck2boost U F 0 R F R S R E ( 2) (24) 3 boost : R S 0 U F 0. 3 V R F 0 R T 02 R T2 0 C 00F R C 00 L 200H R L 0 R U I 2V f 00 khzmatlab Saber

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