cz 6 pelna

background image

1

-$.2û(1(5*,,(/(.75<&=1(-

&=û±3URFHVáF]HQLDEDWHULLNRQGHQVDWRUyZ

Zbigniew Hanzelka

Akademia Górniczo-Hutnicza, 30-019 Kraków, Al. Mickiewicza 30

tel: (012) 617 28 78, tel/fax: (012) 633 22 84, e-mail:

hanzel@uci.agh.edu.pl

Konsultant techniczny Twelve Electric.

Streszczenie

:UD] ]H Z]URVWHP FHQ HQHUJLL HOHNWU\F]QHM VWDáD EDWHULD NRQGHQVDWRUyZ

SU]H]QDF]RQD GR NRPSHQVDFML Z SU]\SDGNX ]PLHQQHM PRF\ ELHUQHM MHVW MX* REHFQLH FRUD]

F]FLHM QLH DNFHSWRZDQ\P UR]ZL]DQLHP 3RWU]HEQH V EDWHULH SU]HáF]DOQH ]PLHQLDMFH

ZDUWRü PRF\ ELHUQHM Z ODG ]D ]PLDQDPL VWDQX NRPSHQVRZDQ\FK RGELRUQLNyZ 3RQLHZD*

ZDUWRüLFKPRF\RUD]ZDUXQNLSUDF\V\VWHPX]DVLODMFHJRSRGOHJDM]PLDQLHNRQGHQVDWRU\V

]DáF]DQH L Z\áF]DQH QLHNLHG\ EDUG]R F]VWR Z FHOX VSHáQLHQLD Z\PDJD UHJXODFML QDSLFLD

LNRUHNFMLZVSyáF]\QQLNDPRF\3URFHVáF]HQLDEDWHULLNRQGHQVDWRUyZWR(UyGáR]DEXU]HZVLHFL

]DVLODMFHM :D*QD MHVW ]QDMRPRü LVWRW\ W\FK SURFHVyZ ]ZL]DQ\FK ] QLPL ]DJUR*H RUD]
sposobów redukcji negatywnych skutków.

1.

:673

=DáF]DQLHEDWHULLNRQGHQVDWRUyZMHVWSURFHVHPEDUG]RF]VWRZ\VWSXMF\PZV\VWHPLH

]DVLODMF\P .RQGHQVDWRU\ VáX* ERZLHP GR UHDOL]DFML WU]HFK SRGVWDZRZ\FK FHOyZ

UyZQRF]HQLH EG( RGG]LHOQLH NRPSHQVDFML PRF\ ELHUQHM W\P VDP\P UHGXNFML PRF\

SR]RUQHM RGELRUQLND Z]URVWX SU]HV\áDQHM V\VWHPHP HOHNWURHQHUJHW\F]Q\P PRF\ F]\QQHM

UHGXNFML VWUDW SU]HV\áX HQHUJLL XQLNQLFLD HZHQWXDOQ\FK RSáDW NDUQ\FK SáDFRQ\FK SU]H]

RGELRUFGRVWDZF\HQHUJLLLWS±U\VXQHNILOWUDFMLZ\*V]\FKKDUPRQLF]Q\FKZK±U\VXQHN

RUD]VWDELOL]DFMLQDSLFLD±U\VXQHN

(a)

(b)

(c)

5\V=DVDGDVWRVRZDQLDEDWHULLNRQGHQVDWRUyZZXNáDGDFKNRPSHQVDFMLPRF\ELHUQHMP, Q, S – moc czynna,

bierna i pozorna, Q

C

– moc baterii kondensatorów): (a) wskazy mocy odbiornika; (b) wskazy mocy po

]DáF]HQLXEDWHULLNRQGHQVDWRUyZFZ]URVWPRF\F]\QQHMZOLQLL]DVLODMFHMSU]\QLH]PLHQLRQHMZDUWRFLPRF\

SR]RUQHMX]\VNDQ\ZHIHNFLHSU]\áF]HQLDEDWHULLNRQGHQVDWRUyZ

background image

2

(a)

(b)

(c)

5\VD8NáDGSDV\ZQ\FKILOWUyZZ\*V]\FKKDUPRQLF]Q\FKESUGRGELRUQLNDFSUGRGELRUQLNDSR

RGILOWURZDQLXSLWHMKDUPRQLF]QHMZILOWU]H)

(a)

(b)

5\V-HGQRID]RZ\VFKHPDW]DVWSF]\VLHFL]DVLODMFHMDRUD]EZ\NUHVZVND]RZ\GODRGELRUQLND

UH]\VWDQF\MQRSRMHPQRFLRZHJRSRGRáF]HQLXEDWHULLNRQGHQVDWRUyZ

0

U

U

S

àF]HQLHEDWHULLWRSURFHVZ\ZRáXMF\]DEXU]HQLHZ XNáDG]LH ]DVLODMF\P 6NXWNLHP V

VWDQ\ SU]HMFLRZH Z QDSLFLX NWyUH QDMF]FLHM QLH VWDQRZL SUREOHPX ] SXQNWX ZLG]HQLD

XU]G]H HOHNWURHQHUJHW\F]Q\FK OHF] NWyUH Z SHZQ\FK RNROLF]QRFLDFK PRJ QHJDW\ZQLH

I

0

.

U

0

U

S

X

S

I

0

R

S

I

0

8

…

Z

S

I

0

I

0

U

0

U

S

R

S

I

0

X

S

I

0

Z

S

background image

3

RGG]LDá\ZDüQDRGELRUFyZILQDOQ\FK=DLQVWDORZDQDXW\FKRVWDWQLFKRFKURQDSU]HSLFLRZD

RG ]DEXU]H Z\VRNLHM F]VWRWOLZRFL PR*H QLH E\ü SU]\VWRVRZDQD GR SU]HMFLD HQHUJLL

QLVNRF]VWRWOLZRFLRZ\FK SU]HELHJyZ WRZDU]\V]F\FK áF]HQLX NRQGHQVDWRUyZ :LHOH

XU]G]H HOHNWURQLF]Q\FK L HQHUJRHOHNWURQLF]Q\FK SRVLDGDMF\FK Z VZ\FK XNáDGDFK

]DVLODMF\FKNRQGHQVDWRU\VF]XáHQDWHQURG]DM]DEXU]HQLDQDZHWMH*HOLMHJRZDUWRüQLHMHVW

]E\WGX*D6NXWNLHPPRJE\üQLHSUDZLGáRZRFLZLFKG]LDáDQLXOXEQDZHWZNUDFRZ\FK

SU]\SDGNDFKWUZDáHXV]NRG]HQLD

2.

352&(6à&=(1,$%$7(5,,.21'(16$725Ï:

: SURFHVLH áF]HQLD PR*QD Z\Uy*QLü GZD SU]\SDGNL LVWRWQH ] SXQNWX ZLG]HQLD

Z\VWSXMF\FKSURFHVyZáF]HQLRZ\FK

áF]HQLHSRMHG\QF]HMEDWHULLNRQGHQVDWRUyZGRPLQXMSU]HSLFLD

SU]\áF]DQLH NROHMQHM EDWHULL GR V]\Q GR NWyU\FK V MX* GRáF]RQH LQQH

NRQGHQVDWRU\GRPLQXMSU]HW*HQLDRGX*HMF]VWRWOLZRFL

àF]HQLHSRMHG\QF]HMEDWHULLNRQGHQVDWRUyZ

1DU\VXQNXSU]HGVWDZLRQRXSURV]F]RQ\VFKHPDW]DVWSF]\REZRGXNWyU\SRVáX*\GR

DQDOL]\SURFHVXáF]HQLDSRMHG\QF]HMEDWHULLNRQGHQVDWRUyZRSRMHPQRFLC=DáR*RQREUDN

UH]\VWDQFML Z REZRG]LH RUD] EUDN QDSLFLRZHJR ZDUXQNX SRF]WNRZHJR QD NRQGHQVDWRU]H

ZFKZLOL]DPNQLFLDáF]QLND.

U

S

QDSLFLHVLHFL]DVLODMFHMZDUWRüVNXWHF]QD

L

S

LQGXNF\MQRüVLHFL]DVLODMFHM

L

B

LQGXNF\MQRü Z\VWSXMFD Z REZRG]LH

SU]\áF]DQHM

EDWHULL

NRQGHQVDWRUyZ

QS

LQGXNF\MQRüSU]HZRGyZáF]F\FK

C

SRMHPQRü]DáF]DQHMEDWHULLNRQGHQVDWRUyZ

5\V8SURV]F]RQ\VFKHPDW]DVWSF]\REZRGXZNWyU\PSU]\áF]DQDMHVWSRMHG\QF]DEDWHULDNRQGHQVDWRUyZ

&KZLOD ]DáF]HQLD NRQGHQVDWRUD WR PRPHQW ]ZDUFLD VLHFL ]DVLODMFHM Z PLHMVFX MHJR

SU]\áF]HQLDZ\QLNDMF\]IDNWX*HQDSLFLHQDNRQGHQVDWRU]HQLHPR*H]PLHQLüVLZVSRVyE

QDW\FKPLDVWRZ\ -H*HOL Z V]HUHJ ] NRQGHQVDWRUHP QLH PD GáDZLND ZyZF]DV QDSLFLH QD

V]\QDFK RVLJD Z SUDNW\FH ZDUWRü EOLVN ]HUR Z F]DVLH NLONX V 1LH QDáDGRZDQ\

NRQGHQVDWRU PR*H E\ü WUDNWRZDQ\ Z SRF]WNRZHM FKZLOL ]DáF]DQLD MDNR ]ZDUFLH

: PRPHQFLH ]DPNQLFLD áF]QLND SUG R Z\VRNLHM F]VWRWOLZRFL L GX*HM ZDUWRFL Sá\QLH

SRPLG]\ (UyGáHP ]DVLODQLD L NRQGHQVDWRUHP SRZRGXMF Z\UyZQDQLH QDSLü PLG]\ W\PL

GZRPD HOHPHQWDPL REZRGX -HJR ZDUWRü GHWHUPLQRZDQD MHVW QDSLFLHP (UyGáRZ\P

Z FKZLOL ]DP\NDQLD áF]QLND LQGXNF\MQRFL ]DVWSF] REZRGX RUD] SRMHPQRFL

SU]\áF]DQHJR NRQGHQVDWRUD SU]\ ]DáR*HQLX *H EDWHULD QLH E\áD ZVWSQLH QDáDGRZDQD

:DUWRüPDNV\PDOQDWHJRSUGXPR*HE\üRNUHORQD]ZL]NLHP

U

S

6

/

%

/

&

K

background image

4

CN

ZW

B

S

B

S

C

S

I

I

H

L

L

F

C

U

Z

U

I

.

.

max

2

)

)(

(

)

(

2

2

=

+

=

=

µ

µ

(1)

gdzie:

C

Z

- impedancja charakterystyczna analizowanego obwodu

.

ZW

I

SUG]ZDUFLDZPLHMVFXSU]\áF]DQLDEDWHULL

CN

I

]QDPLRQRZ\SUGEDWHULL

3RZ\*V]D ]DOH*QRü QLH XZ]JOGQLD WáXPLFHJR HIHNWX Z\VWSXMFHJR Z U]HF]\ZLVW\FK

XNáDGDFK : SUDNW\FH WáXPLHQLH UHGXNXMH SUG PDNV\PDOQ\ GR RNRáR ZDUWRFL

Z\]QDF]RQHM ] ]DOH*QRFL 3UG WHQ EG]LH ]DZV]H PQLHMV]\ QL* SUG ]ZDUFLD
analizowanego obwodu.

3RGF]DVSURFHVXáF]HQLRZHJRZ\VWSXM]QDF]FHVSDGNLQDSLFLDQDLPSHGDQFMDFKVLHFL

]DVLODMFHM FR PR*H XDNW\ZQLü XNáDG\ ]DEH]SLHF]H 1D U\VXQNX SU]HGVWDZLRQR W\SRZ\

SU]HELHJQDSLFLDZMHGQRVWNDFKZ]JOGQ\FK±MZSRGF]DVáF]HQLDEDWHULLNRQGHQVDWRUyZ

5\V7\SRZ\SU]HELHJQDSLFLD]DVLODMFHJRSRGF]DVSURFHVXáF]HQLDEDWHULL

1DJáH REQL*HQLH QDSLFLD QD V]\QDFK GR NWyU\FK SU]\áF]DQ\ MHVW NRQGHQVDWRU SRGF]DV

MHJR áDGRZDQLD Z\ZRáXMH EDUG]R GX* SRFKRGQ ]PLDQ\ QDSLFLD 0R*H WR VSRZRGRZDü

]QDF]FHSU]HSLFLDQDNRFDFK]ZRMyZX]ZRMHWUDQVIRUPDWRUyZ]HZ]JOGXQDSRMHPQRFL

PLG]\ ]ZRMRZH L PLG]\ X]ZRMHQLDPL :J >@ VSU]*HQLH SRMHPQRFLRZH SRPLG]\

X]ZRMHQLDPL PR*H VSRZRGRZDü ÄG\QDPLF]Q´ WUDQVIRUPDFM QDSLü LQQ QL* Z\QLND WR

] SU]HáR*HQLD ]ZRMRZHJR :J WHJR VDPHJR (UyGáD SU]\NáDGRZR GOD WUDQVIRUPDWRUD

RSU]HáR*HQLX]ZRMRZ\PSRMHPQRFLRZDWUDQVIRUPDFMDQDSLFLDPR*HSU]\MüZDUWRü

2]QDF]D WR *H Z]JOGQD ]PLDQD QDSLFLD R ZDUWRFL Z\VWSXMFD QD SLHUZRWQHM

VWURQLHWUDQVIRUPDWRUDZ\ZRáD]PLDQQDSLFLDRZDUWRFLGRZMHGQRVWNDFKZ]JOGQ\FK
na stronie wtórnej.

:Sá\Z VSU]*H SRMHPQRFLRZ\FK X]ZRMH WUDQVIRUPDWRUD ]Z\NOH QLH MHVW UR]ZD*DQ\

ERZLHP RGELRUQLN OXE GRGDWNRZD SRMHPQRü QD VWURQLH ZWyUQHM QS SRMHPQRü

SU]\áF]RQ\FK NDEOL VLOQLH UHGXNXMH WHQ HIHNW -HGQDN*H Z SU]\SDGNX EDUG]R VáDER

REFL*RQHJR WUDQVIRUPDWRUD LOXE NUyWNLFK NDEOL SU]HMFLRZH SU]HSLFLD PRJ SRZRGRZDü

XV]NRG]HQLH VSU]WX HOHNWURQLF]QHJR QS GLRG Z ZHMFLRZ\FK SURVWRZQLNDFK XU]G]H

HOHNWUR L HQHUJRHOHNWURQLF]Q\FK : JUDQLF]Q\FK SU]\SDGNDFK SU]HSLFLD WH PRJ Z\ZRáDü

WDN*HXV]NRG]HQLHL]RODFMLWUDQVIRUPDWRUD'ODLOXVWUDFML]MDZLVNDQDU\VXQNXSU]HGVWDZLRQR

background image

5

SU]HELHJ F]DVRZ\ QDSLFLD ZWyUQHJR VáDER REFL*RQHJR WUDQVIRUPDWRUD SRGF]DV ]DáF]DQLD
baterii kondensatorów na jego stronie pierwotnej.

=Z\NOH ZDUWRü HQHUJLL W\FK RVF\ODFML QLH MHVW GX*D L NRQZHQFMRQDOQH XNáDG\

SU]HSLFLRZHVWRVRZDQHZLQVWDODFMDFKX*\WNRZQLNDVWDQRZLZ\VWDUF]DMFH]DEH]SLHF]HQLH

5\V>@3U]HSLFLHQDZWyUQHMVWURQLHVáDERREFL*RQHJRWUDQVIRUPDWRUDVSRZRGRZDQHPLG]\]ZRMRZ\P

VSU]*HQLHPSRMHPQRFLRZ\PSRGF]DVV]\ENLHJRVWDQXSU]HMFLRZHJRZ\ZRáDQHJR]DáF]DQLHPEDWHULL

kondensatorów

1DJáH REQL*HQLH QDSLFLD SRGF]DV SURFHVX SU]\áF]DQLD EDWHULL Z\ZRáXMH V]F]HJyOQLH

Z VLHFLDFK Z\VRNLHJR QDSLFLD ]MDZLVNR IDO ZGUXMF\FK Z]GáX* ZV]\VWNLFK OLQLL

SU]\áF]RQ\FK GR V]\Q QD NWyU\FK RGE\ZD VL SURFHV áF]HQLD )DOH WH RGELMDMF VL RG

RWZDUW\FKNRFyZOLQLLRUD]UDGLDOQLHSUDFXMF\FKWUDQVIRUPDWRUyZSRZUDFDMSRQRZQLHGR

PLHMVFD SU]\áF]HQLD NRQGHQVDWRUD L Z SURFHVLH NROHMQ\FK RGELü XOHJDM Z]PRFQLHQLX

:GUXMFH IDOH XOHJDM ZLHORNURWQHPX RGELFLX ]DQLP ]RVWDQ RVWDWHF]QLH Z\WáXPLRQH

VWUDWDPL : HIHNFLH PRJ SRZVWDü SU]HSLFLD R EDUG]R GX*\FK ZDUWRFLDFK F]VWR JUR(QH
w skutkach.

: GUXJLP HWDSLH SURFHVX áF]HQLD QDSLFLH NRQGHQVDWRUD QDUDVWD RG ]HUD GR ZDUWRFL

PDNV\PDOQHM F]HPX WRZDU]\V]\ SU]HW*HQLH SUGRZH 5R]SRF]\QD VL RVF\ODF\MQ\ SURFHV

Z\PLDQ\HQHUJLL±SRPLG]\SRMHPQRFLNRQGHQVDWRUDLLQGXNF\MQRFLVLHFL]DVLODMFHM±

SRGF]DV NWyUHJR QDSLFLH RG]\VNXMH VZyM SLHUZRWQ\ SU]HELHJ F]DVRZ\ &]VWRWOLZRü W\FK
oscylacji (f

PR*HE\üV]DFRZDQDQDSRGVWDZLH]DVWSF]HMLQGXNF\MQRFLV\VWHPXZPLHMVFX

SU]\áF]HQLDEDWHULLLZDUWRFLMHMSRMHPQRFL

)

(

2

1

B

S

C

L

f

π

=

lub

CN

.

ZW

S

I

I

f

f

=

Hz

gdzie

Hz

f

S

50

=

=Z\NOH F]VWRWOLZRü WD Z\QRVL NLONDVHW Hz (typowo 300-600). W szczególnych

SU]\SDGNDFKPR*HRVLJQüZDUWRü+]LZLFHM

1DU\VXQNXSU]HGVWDZLRQRSU]HELHJLF]DVRZHQDSLFLDSRGF]DVáF]HQLDGZyFKEDWHULL

RUy*Q\FKPRFDFK3U]HELHJMDNQDU\VXQNXDGRW\F]\EDWHULLRGX*HMPRF\F]VWRWOLZRü

RVF\ODFML MHVW U]GX RNRáR Hz), natomiast na rysunku 7b baterii o mniejszej mocy

F]VWRWOLZRüRVF\ODFMLMHVWU]GXN+]

: SRF]WNRZ\P RNUHVLH RVF\ODFML FKZLORZH QDSLFLH Z ]DOH*QRFL RG ID]\ ]DáF]HQLD

PR*H RVLJQü Z QDMEDUG]LHM QLHNRU]\VWQ\P SU]\SDGNX ]DáF]HQLH QLH QDáDGRZDQHM EDWHULL

NRQGHQVDWRUyZ Z V]F]\FLH OXE EOLVNR V]F]\WX SU]HELHJX F]DVRZHJR QDSLFLD ]DVLODMFHJR

PDNV\PDOQ ZDUWRü UyZQ SRGZyMQHM DPSOLWXG]LH QLH ]DEXU]RQHJR SU]HELHJX 7áXPLHQLH

V\VWHPXUHGXNXMHWZDUWRüGRRNRáR&]DVWUZDQLD]MDZLVND]PLHQLDVLW\SRZR

background image

6

RG GR RNUHVyZ : SU]\SDGNX GRáF]RQ\FK UyZQROHJOH RGELRUQLNyZ LFK WáXPLF\

ZSá\ZVSUDZLD*HSURFHVSU]HMFLRZ\NRF]\VL]D]Z\F]DMSU]HGXSá\ZHPRNUHVXQDSLFLD

(a)

(b)

5\V>@3U]\NáDGRZHSU]HELHJLQDSLFLDSRGF]DVáF]HQLDEDWHULLNRQGHQVDWRUyZ3U]HELHJDGRW\F]\EDWHULL

GX*HMPRF\GODNWyUHMF]VWRWOLZRüRVF\ODFMLZ\QRVLRNRáR+]3U]HELHJEGRW\F]\PDáHMEDWHULLGOD

NWyUHMF]VWRWOLZRüRVF\ODFMLPLDáDZDUWRüRNRáRN+]

1D U\VXQNX SU]HGVWDZLRQR SU]\NáDGRZ\ SU]HELHJ F]DVRZ\ QDSLFLD ]DEXU]RQ\

SURFHVHP]DáF]DQLDEDWHULL3U]HGVWDZLRQRWDN*HSU]HELHJSUGXZOLQLLGRNWyUHMGRáF]RQR

NRQGHQVDWRU\ 3URFHV áF]HQLD EDWHULL WR UyZQLH* VWUHV GOD NRQGHQVDWRUyZ ]ZL]DQ\

]SU]HW*HQLHPSUGRZ\P

5\V>@3U]HELHJF]DVRZ\QDSLFLDDLSUGXESRGF]DVáF]HQLDEDWHULLNRQGHQVDWRUyZ

1D U\VXQNX SU]HGVWDZLRQR SURFHV áF]HQLD EDWHULL WUyMID]RZHM =DZV]H MHGQD ] ID]

Z\ND]XMHV]F]HJyOQLHGX*\Z]URVWSU]HMFLRZHJRQDSLFLD

5\V>@3URFHVáF]HQLDWUyMID]RZHMEDWHULLNRQGHQVDWRUyZ

background image

7

=DUyZQR SRF]WNRZD VNRNRZD ]PLDQD MDN L Sy(QLHMV]H RVF\ODFMH QDSLFLD V ZD*Q

F]FLáF]HQLRZ\FKVWDQyZSU]HMFLRZ\FK3RF]WNRZD]PLDQDMHVWLVWRWQD]HZ]JOGXQD

GX* SRFKRGQ Z\VWSXMFHM ZyZF]DV UHGXNFML QDSLFLD 1DVWSXMFH SR QLHM RVF\ODFMH

VWDQRZL ]QDF]QLH ZLNV]\ SUREOHP ,FK ZDUWRü QLH MHVW QLHEH]SLHF]QD ] SXQNWX ZLG]HQLD

V\VWHPX WUDQVPLVML L G\VWU\EXFML 6SU]W HOHNWURHQHUJHW\F]Q\ MHVW ERZLHP SURMHNWRZDQ\ GOD

SU]HSLüRZDUWRFLGRQDSLFLD]QDPLRQRZHJR-HGQDN*HRVF\ODFMHWH]HZ]JOGXQD

UHODW\ZQLH QLVN F]VWRWOLZRü SU]HQLNDM SU]H] WUDQVIRUPDWRU\ REQL*DMFH QDSLFLH

LXILQDOQHJRX*\WNRZQLNDPRJE\ü(UyGáHPHNVSORDWDF\MQ\FKNáRSRWyZ0R*QDZ\Uy*QLü
dwie kategorie problemów:
-

Z]PRFQLHQLH]DEXU]HQLD3URFHVáF]HQLRZ\Z\ZRáXMH]MDZLVNRZ]PRFQLHQLDRVF\ODFML

F]HJR VNXWNLHP PR*H E\ü PLG]\ LQQ\PL XV]NRG]HQLH QDSLFLRZH VSU]WX
elektronicznego, kondensatorów, przepalenie bezpieczników, uszkodzenie elementów

RFKURQ\SU]HSLFLRZHMLWS

-

DZDU\MQH Z\áF]HQLH F]Xá\FK RGELRUQLNyZ 1DZHW MH*HOL SU]HELHJL RVF\ODF\MQH QLH

SRGOHJDM Z]PRFQLHQLX SHZQH NDWHJRULH RGELRUQLNyZ PRJ E\ü F]XáH QD WHQ URG]DM

]DEXU]HQLD,FKZDUWRüMHVWZ\VWDUF]DMFDDE\VSRZRGRZDüDZDU\MQHZ\áF]HQLDQS

UHJXORZDQ\FK QDSGyZ L LQQ\FK RGELRUQLNyZ ] HOHNWURQLF]Q\PL ]DVLODF]DPL OXE

]QDSLFLRZV\QFKURQL]DFM

2.2

3URFHVZ]PDFQLDQLDRVF\ODFMLáF]HQLRZ\FK

:]PRFQLHQLHRVF\ODFMLZ\VWSXMHMDNRUH]XOWDWSREXG]HQLD±SURFHVHPáF]HQLDEDWHULL

± GUJD ZáDVQ\FK Z VáDER WáXPLRQ\P REZRG]LH

C

L

S

XWZRU]RQ\P ] ]DVWSF]\FK

LQGXNF\MQRFLV\VWHPX]DVLODMFHJRZVLHFLDFKUR]G]LHOF]\FKJáRZQLHWUDQVIRUPDWRUyZRUD]

SRMHPQRFL GRáF]DQHM L MX* SU]\áF]RQ\FK EDWHULL NRQGHQVDWRUyZ 5H]XOWDWHP MHVW PLG]\

LQQ\PL Z]URVW QDSLFLD QD V]\QDFK QLVNLHJR QDSLFLD nn). Rysunek 10 przedstawia taki
przypadek w typowej sieci rozdzielczej. Bateria C

MHVWSU]\áF]DQDGRUyZQROHJáHJRREZRGX

XWZRU]RQHJR SU]H] V]HUHJRZH SRáF]HQLH LPSHGDQFML ]DVWSF]HM WUDQVIRUPDWRUD L EDWHULL
kondensatorów nn przeznaczonej do kompensacji mocy biernej. Wzmocnienie oscylacji

Z\VWSXMHZSUDNW\FHMH*HOL
-

SRMHPQRü NRQGHQVDWRUD C MHVW GX*R ZLNV]D QL* SRMHPQRü NRQGHQVDWRUD C2, (co

QDMPQLHMUD]\QS09$ULN9$UZVSyáF]\QQLNMDNQDU\VXQNDFKL

-

F]VWRWOLZRüÄáF]HQLRZD´

C

ZW

Q

S

(S

ZW

±PRF]ZDUFLDZSXQNFLHSU]\áF]HQLDEDWHULL

Q

C

± PRF ]DáF]DQHM EDWHULL MHVW EOLVND F]VWRWOLZRFL V]HUHJRZHJR REZRGX

XWZRU]RQHJR SU]H] WUDQVIRUPDWRU REQL*DMF\ L EDWHUL C SU]H]QDF]RQ GR NRUHNFML

ZVSyáF]\QQLNDPRF\

-

QLHPDZ\VWDUF]DMFHMOLF]E\RGELRUQLNyZÄUH]\VWDQF\MQ\FK´ZVLHFLQQ,FKREHFQRü

JZDUDQWXMHWáXPLHQLHRVF\ODFML:ZLHOX]DNáDGDFKSU]HP\VáRZ\FKGRPLQXMMHGQDN*H

RGELRUQLNLVLOQLNRZHNWyUHQLH]DSHZQLDMZ\VWDUF]DMFHJRWáXPLHQLDLZLFKSU]\SDGNX

Z]PRFQLHQLH RVF\ODFML PR*H E\ü V]F]HJyOQLH SRZD*Q\P SUREOHPHP 3U]\SDGHN WDNL
przedstawiono na rysunku 11.

1DOH*\ ]DXZD*\ü *H WHQ URG]DM Z]PRFQLRQ\FK SU]HSLü PR*H Z\VWSLü GOD V]HURNLHJR

SU]HG]LDáXZDUWRFLPRF\EDWHULLNRQGHQVDWRUyZQLVNLHJRQDSLFLD5\VXQHNSU]HGVWDZLD

UH]XOWDW\REOLF]HGODXNáDGX]DVLODQLDMDNQDU\VXQNX3U]HGVWDZLRQ\SU]HELHJSRND]XMH

VWRSLH Z]PRFQLHQLD QDSLFLD QD V]\QDFK 9 VSRZRGRZDQ\ ]DáF]HQLHP EDWHULL
kondensatorów o mocy 3 MVAr (C

ZVLHFLUHGQLHJRQDSLFLD3U]HSLFLHX]DOH*QLRQHMHVW

od mocy baterii kondensatorów nn (C

]PLHQLDMFHM VL Z SU]HG]LDOH kVAr

background image

8

W\SRZHZDUWRFLPRF\EDWHULLGODWUDQVIRUPDWRUDREQL*DMFHJRRPRF\09$6WRSLH

Z]PRFQLHQLD SU]HNUDF]D Z MHGQRVWNDFK Z]JOGQ\FK %DGDQLD Z\ND]XM *H Z SUDNW\FH

ZDUWRüWD]DZLHUDVLZSU]HG]LDOH

5\V>@3U]\NáDGRZ\VFKHPDWXNáDGX]DVLODQLD]DNáDGXZNWyU\PPR*HZ\VWSLüSUREOHPSREXG]HQLD

RVF\ODFMLQDVNXWHNáF]HQLDEDWHULLNRQGHQVDWRUyZ

5\V>@3U]HELHJLLOXVWUXMFHZ]PRFQLHQLHRVF\ODFMLSRVWURQLHQLVNLHJRQDSLFLD

5\V>@:Sá\ZPRF\EDWHULLNRQGHQVDWRUyZQQCQDZ]PRFQLHQLHSU]HSLüáF]HQLRZ\FK0RF

SU]\áF]DQHMEDWHULLC1) wynosi 3 MVAr

background image

9

5\V>@:Sá\ZVNRQILJXURZDQLDEDWHULLCMDNRILOWUXKDUPRQLF]QHMQDZDUWRüSU]HSLFLDZVLHFLnn (C1 –

3MVAr)

2.3

'RáF]DQLHNROHMQHMEDWHULL

7HQ URG]DM áF]HQLD Z\ZRáXMH Z VLHFLDFK ]DVLODMF\FK SRJRUV]HQLH MDNRFL ]DVLODQLD

Z QDVWSVWZLH VWDQyZ SU]HMFLRZ\FK R GX*HM F]VWRWOLZRFL Z\VWSXMF\FK Z QDSLFLX

LZSUG]LH:DUWRüLF]VWRWOLZRüSUGXáF]HQLRZHJREDWHULL]DOH*RG

LPSHGDQFML FKDUDNWHU\VW\F]QHM REZRG\ ]DZLHUDMFHJR LQGXNF\MQRü (UyGáD ]DVLODQLD

LSRMHPQRüSU]\áF]DQHMEDWHULL

FKZLOL F]DVX Z]JOGHP SU]HELHJX F]DVRZHJR QDSLFLD ]DVLODMFHJR Z NWyUHM áF]QLN

zamknie obwód;

WáXPLHQLD]DáF]DQHJRREZRGX

1D U\VXQNX SU]HGVWDZLRQR SU]\NáDGRZ\ VFKHPDW LGHRZ\ D L ]DVWSF]\ E

VWRVRZDQ\GRDQDOL]\SURFHVXSU]\áF]DQLDUyZQROHJáHMEDWHULLNRQGHQVDWRUyZGREDWHULLMX*

SUDFXMFHM

(a)

(b)

5\VD6]\Q\]SU]\áF]RQ\PLGZRPDEDWHULDPLNRQGHQVDWRUyZEXSURV]F]RQ\VFKHPDW]DVWSF]\GR

DQDOL]\SURFHVX]DáF]DQLDNROHMQHMEDWHULLNRQGHQVDWRUyZL

zew.

±LQGXNF\MQRü]DVWSF]Doszynowania;

“

“

&

/

]DVWSF]DLQGXNF\MQRüLSRMHPQRüSU]\MWRL

1

=L

2

=L

3

; C

1

=C

2

=C

3

)

1D U\VXQNX E SRPLQLWR LQGXNF\MQRü L QDSLFLH (UyGáD ]DVLODQLD 8F]\QLRQR WDN

SRQLHZD*SRGF]DVNLONXSLHUZV]\FKPLOLVHNXQGSR]DPNQLFLXáF]QLNDGRPLQXMF\ZSá\Z

QDSURFHV\SU]HMFLRZHZ\ZLHUDMZDQDOL]RZDQ\PSU]\SDGNXMX*SU]\áF]RQHUyZQROHJáH

EDWHULH NRQGHQVDWRUyZ : W\P RNUHVLH ZSá\Z VLHFL ]DVLODMFHM MHVW SUDNW\F]QLH QLHZLHONL

6WG

“

/

/

/

/

/

“

&

&

&

U

S

S

L

1

L

1

C

2

L

3

L

2

C

3

C

3

L

Σ

L

Σ

C

3

C

.

zew

L

background image

10

3RGF]DVSU]\áF]DQLDWU]HFLHMEDWHULLMDNQDU\VXQNXZV]\VWNLHHOHPHQW\REZRGXV

SRáF]RQH V]HUHJRZR GDMF Z\SDGNRZ ZDUWRü LQGXNF\MQRFL L SRMHPQRFL ]DVWSF]HM
odpowiednio:

“

/

/

/

/

]HZ

“

“

&

&

&

&

&

-X* SU]\áF]RQH EDWHULH VWDQRZL (UyGáR QDSLFLD R PLQLPDOQHM LPSHGDQFML ]DVWSF]HM

'ODWHJR ZDUWRü PDNV\PDOQD SUGX áF]HQLRZHJR PR*H SU]HNURF]\ü SUG ]ZDUFLD

DQDOL]RZDQHJRREZRGXLZ\VWSXMHRQDWX*SR]DPNQLFLXáF]QLND0R*QDMV]DFRZDüQD

SRGVWDZLH]ZL]NXDQDORJLF]QHJRMDNGODSRMHG\QF]HMEDWHULLNRQGHQVDWRUyZ

)

(

2

2

2

2

1

.

2

1

.

max

CN

CN

zew

CN

CN

S

S

C

S

I

I

L

I

I

U

L

C

U

Z

U

I

+

=

=

=

ω

gdzie:

2

CN

1

CN

I

,

I

]QDPLRQRZHSUG\]DáF]RQHML]DáF]DQ\FKEDWHULL

7áXPLHQLH ]ZL]DQH ] Uy*Q RG ]HUD ]DVWSF] UH]\VWDQFM REZRGX SRZRGXMH UHGXNFM

ZDUWRFLPDNV\PDOQHMSUGXGRRNRáRZDUWRFLZ\]QDF]RQHM]SRZ\*V]HM]DOH*QRFL

'X*D MHVW QLH W\ONR ZDUWRü OHF] WDN*H F]VWRWOLZRü SUGX áF]HQLRZHJR RNUHORQD

]ZL]NLHP

LC

f

π

2

1

=

:DUWRü WHM F]VWRWOLZRFL ]DZDUWD MHVW W\SRZR Z SU]HG]LDOH kHz. Czas trwania

SURFHVX SU]HMFLRZHJR MHVW ]Z\NOH NUyWNL FR SU]HGVWDZLRQR SU]\NáDGRZR QD U\VXQNX

3U]\NáDGRZH SU]HELHJL SUGX EDWHULL NRQGHQVDWRUyZ GRáF]DQHM MDNR SLHUZV]D L NROHMQD

SU]HGVWDZLRQRWDN*HQDU\VXQNX

5\V3UGáF]HQLRZ\SRGF]DVSURFHVXSU]\áF]DQLDEDWHULLNRQGHQVDWRUyZGREDWHULLMX*SUDFXMFHM'OD

F]\WHOQRFLU\VXQNXQLHSU]HGVWDZLRQRVWDQXSU]HMFLRZHJRZQDSLFLX

background image

11

5\V>@D3UGSRGF]DVSURFHVX]DáF]DQLDSRMHG\QF]HMEDWHULLRUD]EDWHULLGRáF]DQHMGRMX*

SUDFXMFHME

6WDQ\ áF]HQLRZH Z QDSLFLX V UHGXNRZDQH SU]H] NRQGHQVDWRU\ MX* SU]\áF]RQH WDN

ZLF QDMEDUG]LHM QLHNRU]\VWQH ZDUXQNL ] SXQNWX ZLG]HQLD QDSLFLD GRW\F] áF]HQLD

SLHUZV]HJRVWRSQLD5HGXNFMDQDSLFLDQDV]\QDFKUR]G]LHOQLMHVWPQLHMV]DQL*ZSU]\SDGNX

áF]HQLD SRMHG\QF]HM EDWHULL ]H Z]JOGX QD áDGXQHN HOHNWU\F]Q\ Z NRQGHQVDWRUDFK MX*

SUDFXMF\FK3U]\NáDGRZRGODGZyFKEDWHULLRWDNLHMVDPHMPRF\PLQLPDOQDZDUWRüQDSLFLD

Z\QRVLRNRáRWHMNWyUDE\áDQD]DáF]RQHMEDWHULLWX*SU]HGFKZLOGRáF]HQLDNROHMQHM

1D U\VXQNX SU]HGVWDZLRQR RNUHVX SU]HELHJX F]DVRZHJR QDSLFLD GOD GZyFK

SU]\SDGNyZ ]DáF]DQLH SLHUZV]HM EDWHULL NRQGHQVDWRUyZ ZLGRF]QD VNáDGRZD RVF\ODF\MQD

SRMHG\QF]HM F]VWRWOLZRFL GRáF]DQLH GUXJLHM EDWHULL ZLGRF]QH VNáDGRZH RVF\ODF\MQH

RZLFHMQL*MHGQHMF]VWRWOLZRFL

5\V>@3RZLNV]RQ\SU]HELHJF]DVRZ\QDSLFLDSRGF]DV]DáF]DQLDEDWHULLNRQGHQVDWRUyZ3U]HELHJD

GRW\F]\]DáF]HQLDSLHUZV]HJRVWRSQLDEDWHULL:LGRF]QHVRVF\ODFMHRSRMHG\QF]HMF]VWRWOLZRFL3RWU]HFK

PLQXWDFK]RVWDá]DáF]RQ\GUXJLVWRSLH±SU]HELHJE:LGDüVNáDGRZHRVF\ODF\MQHRZLFHMQL*MHGQHM

F]VWRWOLZRFL

2.4

6]F]HJyOQHZDUXQNLáF]HQLDEDWHULL

:V]\VWNLH SRZ\*V]H UR]ZD*DQLD GRW\F]\á\ LGHDOQ\FK ZDUXQNyZ áF]HQLD ,VWQLHM

MHGQDN*H SHZQH V]F]HJyOQH SU]\SDGNL PDMFH ]DVDGQLF]\ ZSá\Z QD SU]HELHJ SURFHVyZ

áF]HQLRZ\FK6WR

]DáF]DQLHEDWHULLZVWSQLHQDáDGRZDQHM

]DSáRQáXNXSRGF]DVSURFHVXZ\áF]DQLDEDWHULL

background image

12

=DáF]DQLHEDWHULLZVWSQLHQDáDGRZDQHM

: QRUPDOQ\FK ZDUXQNDFK HNVSORDWDF\MQ\FK NRQGHQVDWRU SR Z\áF]HQLX SRZLQLHQ E\ü

UR]áDGRZDQ\ ZRNUHORQ\PF]DVLHGRRNUHORQHJR QDSLFLD QS PLQ 9 1DMEDUG]LHM

QLHNRU]\VWQH ZDUXQNL áF]HQLD Z\VWSL ZyZF]DV JG\ ]DPNQLFLH áF]QLND QDVWSL

ZV]F]\FLHQDSLFLD]DVLODMFHJRDNRQGHQVDWRUEG]LHQDáDGRZDQ\GRQDSLFLDRWDNLHMVDPHM

ZDUWRFLOHF]SU]HFLZQHMSRODU\]DFML0R*HQDVWSLüZyZF]DVSRGZRMHQLHSUGXZVWRVXQNX

GRMHJRZDUWRFLSU]\áF]HQLXUR]áDGRZDQHMEDWHULL

=DSáRQáXNXSRGF]DVSURFHVXZ\áF]DQLDEDWHULL

6NXWNLHP V VWDQ\ SU]HMFLRZH Z QDSLFLX ]DVLODMF\P MDNNROZLHN Z SU]\SDGNX

ZVSyáF]HVQ\FKNRQVWUXNFMLZ\áF]QLNyZUHDOQRüWHJR]DJUR*HQLDMHVWQLHZLHOND=MDZLVNRWR

PR*HZ\VWSLüZZ\áF]QLNDFKVWRVXMF\FKPDJQHW\F]QFHZNZ\GPXFKRZ*G\XVWDORQ\

SUGEDWHULLMHVW]QDF]FRPQLHMV]\RGSUGX]QDPLRQRZHJRZ\áF]QLNDZyZF]DVSRGF]DV

RWZLHUDQLD VWUXPLH PDJQHW\F]Q\ PDMF\ VSRZRGRZDü SU]HUZDQLH áXNX PR*H E\ü ]E\W

VáDE\E\VNXWHF]QLHSU]HUZDüREZyG

5\V>@3U]HELHJLSU]HMFLRZHQDSLFLDLSUGXZSU]\SDGNXZ\VWSLHQLDSU]HVNRNXáXNRZHJRZZ\áF]QLNX

SRGF]DVSU]HU\ZDQLDSUGXSRMHPQRFLRZHJR

background image

13

3URFHVRWZLHUDQLDZ\áF]QLNDZNWyU\PZ\VWSLá\SU]HVNRNLáXNRZHSU]HGVWDZLRQRQD

U\VXQNX*G\VW\NLáF]QLND]DF]\QDMVLRWZLHUDüSUGSRMHPQRFLRZ\SU]HVWDMHSá\Qü

SU]\SLHUZV]\PSU]HMFLXSU]H]ZDUWRü]HURZ3U]HUZDQLHSUGXSRMHPQRFLRZHJRQLHMHVW

WUXGQHV]F]HJyOQLHZSRUyZQDQLX]SUGHPLQGXNF\MQ\P1DSLFLHQDZ\áF]QLNXSRVWURQLH

]DVLODQLDLQDSLFLHQDNRQGHQVDWRU]HVZyZF]DVUyZQHDLFKZDUWRFLPDNV\PDOQH1DSLFLH

QD NRQGHQVDWRU]H ]DFKRZD W VWDá ZDUWRü 3yá RNUHVX Sy(QLHM QDSLFLH (UyGáD ]DVLODQLD

]PLHQLVLQDXMHPQHZVWRVXQNXGRQDSLFLDNRQGHQVDWRUD:yZF]DVUy*QLFDSRWHQFMDáyZ

PLG]\ VW\NDPL Z\áF]QLND RVLJQLH SRGZyMQ DPSOLWXG QDSLFLD ]DVLODMFHJR -H*HOL

WD ZDUWRü SU]HNURF]\ Z\WU]\PDáRü SU]HUZ\ PLG]\VW\NRZHM Z\áDGRZDQLH áXNRZH

SRPLG]\QLPLVSRZRGXMHJZDáWRZQ\Z]URVWSUGX(UyGáD]DVLODQLD1DSU]HFLZQ]PLHQLVL

SRODU\]DFMDQDSLFLDNRQGHQVDWRUD0R*HRQRRVLJQüZDUWRüUyZQSRWUyMQHMDPSOLWXG]LH

QDSLFLDVLHFL3URFHVWHQPR*HXOHFSRZLHOHQLXZGDOV]\FKFKZLODFKF]DVX

3.

63262%<5('8.&-,35=(3,û,35=(7)(à&=(1,2:<&+

=Z\NOHQLHPDSRWU]HE\NRQWURORZDQLD]DáF]DQLDEDWHULLMH*HOLSURFHVWHQQLHZ\VWSXMH

F]VWR,VWQLHMMHGQDN*HSU]\SDGNLZ\PDJDMFHWDNLFKG]LDáDV]F]HJyOQLHGODEDWHULLGX*HM

PRF\ SU]\áF]DQ\FK Z V\VWHPLH UR]G]LHOF]\P Z UR]G]LHOQLDFK RGELRUFyZ SU]HP\VáRZ\FK

OXEZV\VWHPLHWUDQVPLV\MQ\P0R*OLZHMHVWZyZF]DV

áF]HQLHEDWHULLZUD]]UH]\VWRUDPLZFHOX]ZLNV]HQLDWáXPLHQLDREZRGXLRJUDQLF]HQLD

SUGXáF]HQLRZHJR

ZáF]HQLHGáDZLNDZV]HUHJ]NRQGHQVDWRUDPL'áDZLNWHQPR*HRGVWURLüREZyGLZWHQ

VSRVyE SU]HFLZG]LDáDü Z]PRFQLHQLX GUJD W]Z GáDZLN RGVWUDMDMF\ 0R*H UyZQLH*

ZSRáF]HQLX]EDWHULNRQGHQVDWRUyZSHáQLüUROILOWUXGODZ\EUDQHMKDUPRQLF]QHMMH*HOL

QSRGELRUQLNLVQLHOLQLRZHLLVWQLHMHSRWU]HEDLFKILOWUDFML

UR]VWURMHQLH REZRGX SU]H] ]PLDQ PRF\ EDWHULL OXE MHM SU]\áF]HQLH GR LQQHJR SXQNWX

ZVLHFL]DVLODMFHMZFHOXUHGXNFMLHIHNWXZ]PRFQLHQLDRVF\ODFML

:áF]HQLH V]HUHJRZR ] ]DáF]DQ EDWHUL LPSHGDQFML GRGDWNRZHM UH]\VWDQFML OXE

UHDNWDQFML LQGXNF\MQHM ± MHVW MHGQ\P ]H VSRVREyZ RJUDQLF]HQLD SUGyZ L QDSLü

WRZDU]\V]F\FK ]Z\NOH SURFHVRZL áF]HQLD EDWHULL NRQGHQVDWRUyZ 3R ]DNRF]HQLX

SU]HELHJyZ SU]HMFLRZ\FK LPSHGDQFMD GRGDWNRZD PR*H E\ü HOLPLQRZDQD ] REZRGX

ERF]QLNRZDQD 7RZDU]\V]\ WHPX ]D]Z\F]DM VWDQ SU]HMFLRZ\ OHF] MHJR ZDUWRü L F]DV

WUZDQLD V ]QDF]FR ]UHGXNRZDQH :DUWRü GRGDWNRZHM LPSHGDQFML MHVW V]DFRZDQD

QD SRGVWDZLH SRF]WNRZHJR VWDQX áF]HQLRZHJR SU]HSLü L SU]HW*H WRZDU]\V]F\FK MHM

HOLPLQDFML ] REZRGX MDN UyZQLH* Z RSDUFLX R ]GROQRü GR G\V\SDFML HQHUJLL ]ZL]DQHM

] ]DEXU]HQLDPL L PR*OLZRFL UHJXODUQHJR SRZWDU]DQLD WHJR SURFHVX Z ]DOH*QRFL

RGELH*F\FKSRWU]HEHNVSORDWDF\MQ\FK

0RJWRE\üWDN*HG]LDáDQLDHOLPLQXMFHSU]\SDGNRZRüSURFHVXáF]HQLDQDU]HF]MHJR

VWHURZQLDDZLFV\QFKURQL]DFMDFKZLOL]DáF]DQLDWDNDE\QDVWSLáRRQRQS
-

SU]\SU]HMFLXQDSLFLDSU]H]ZDUWRü]HURZ

-

SU]\ SU]HMFLX QDSLFLD SU]H] ZDUWRü PDNV\PDOQ ] UyZQRF]HVQ\P ZF]HQLHMV]\P

QDáDGRZDQLHPZVWSQ\PNRQGHQVDWRUD7HQURG]DMáF]HQLDMHVWVWRVRZDQ\ZXNáDGDFK
kompensatorów statycznych TSC (Thyristor Switched Capacitors).

background image

14

5\V3URFHVáF]HQLDNRQGHQVDWRUD09$UDEH]UH]\VWRUDE]UH]\VWRUHPV]HUHJRZ\P

5\V>@3URFHVáF]HQLDEDWHULL]UH]\VWRUHPWáXPLF\P1DSU]HELHJDFKSLRQRZSU]HU\ZDQOLQL

]D]QDF]RQRPRPHQWZ\áF]HQLDUH]\VWRUD

background image

15

3.1. Szeregowa rezystancja

Jest jednym z najprostszych, a zarazem najskuteczniejszych sposobów kontrolowania

SRMHPQRFLRZ\FK VWDQyZ SU]HMFLRZ\FK U\V MDNNROZLHN Z]JOG\ QLH]DZRGQRFLRZH

XV]NRG]HQLDWHUPLF]QHLNRV]W\HNVSORDWDF\MQHSU]\]QDF]FHMF]VWRFLáF]HVSUDZLDM

*H X*\WNRZQLF\ F]VWR UH]\JQXM ] VWRVRZDQLD WHJR HOHPHQWX QD U]HF] GáDZLNyZ

V]HUHJRZ\FK 2SW\PDOQD ZDUWRü RSRUQRFL ]DOH*\ RG PRF\ ]DáF]DQHM EDWHULL

NRQGHQVDWRUyZ L RG PRF\ ]ZDUFLRZHM (UyGáD ]DVLODQLD :DUWRü V]HUHJRZHM UH]\VWDQFML R)

V]DFRZDQDMHVW]DSRPRF]DOH*QRFL

C

L

R

S

-HVWZLFRQDGRELHUDQDLQG\ZLGXDOQLHGOD

ND*GHJRSU]\SDGNXL]Z\NOH]DZLHUDVLZSU]HG]LDOH2PyZ

6WRVRZDQHE\ZDMXNáDG\ZNWyU\FKUH]\VWRUMHVWZáF]RQ\W\ONRQDNUyWNLRNUHVF]DVX

(10-15

PV =H Z]JOGX QD GRSXV]F]DOQ REFL*DOQRü SUGRZ VW\NyZ Z\áF]QLND NWyUH

UHDOL]XMSURFHVáF]HQLDUH]\VWRUyZ]Z\NOHLFKZDUWRü]DZLHUDVLZyZF]DVZSU]HG]LDOH

,P ZLNV]D UH]\VWDQFMD W\P EDUG]LHM HIHNW\ZQH MHVW WáXPLHQLH VWDQyZ

SU]HMFLRZ\FKZQDSLFLX-HGQDN*H]GUXJLHMVWURQ\ZUD]]HZ]URVWHPZDUWRFLUH]\VWDQFML

]ZLNV]DVLVWDQSU]HMFLRZ\WRZDU]\V]F\MHMZ\áF]DQLXERF]QLNRZDQLX±U\VXQHN

6]HUHJRZ\GáDZLN

-HVW]VXNFHVHPVWRVRZDQ\GRRJUDQLF]DQLDSUGXáF]HQLRZHJREDWHULL:SURZDG]DWDN*H

SHZLHQSR]LRPRJUDQLF]HQLDQDSLFLRZ\FKVWDQyZSU]HMFLRZ\FKMDNNROZLHNQLH]DZV]H:

ÄVáDE\FK´ VLHFLDFK ]DVLODMF\FK R PDáHM PRF\ ]ZDUFLRZHM Z SXQNFLH SU]\áF]HQLD EDWHULL

PR*H Z QLHNRU]\VWQ\FK ZDUXQNDFK Z\VWSLü Z]PRFQLHQLH ZDUWRFL FKZLORZ\FK QDSLFLD

SRGF]DVSURFHVX]DáF]DQLD=DOHWGáDZLNyZMHVWWR*HZSU]HFLZLHVWZLHGRUH]\VWRUyZV

EDUG]LHMQLH]DZRGQHPQLHMLVWRWQHZ]JOG\WHUPLF]QHLEDUG]LHMHNRQRPLF]QHZHNVSORDWDFML

PQLHMV]HVWUDW\PRF\'áDZLNLRJUDQLF]DMWDN*HSUGEDWHULLSRGF]DV]ZDUüZ\VWSXMF\FK

ZLFKSREOL*X

,VWQLHM XNáDG\ Z NWyU\FK GáDZLN MHVW ERF]QLNRZDQ\ SR ]DNRF]HQLX SURFHVX

áF]HQLRZHJR -HJR LPSHGDQFMD ]DOH*QD RG F]VWRWOLZRFL MHVW ZLNV]D Z SRF]WNRZ\P

RNUHVLH JG\ F]VWRWOLZRü SU]HELHJyZ MHVW GX*D 1DVWSQLH XOHJD ]PQLHMV]HQLX JG\ Sá\QLH

SUGRF]VWRWOLZRFLVLHFL]DVLODMFHM3RGREQLHMDNZSU]\SDGNXZ\áF]DQHJRUH]\VWRUDWX

UyZQLH* Z\VWSXMH GUXJL VWDQ SU]HMFLRZ\ SRGF]DV ERF]QLNRZDQLD GáDZLND :\VWSXMFH

ZyZF]DV SU]HSLFLD L SU]HW*HQLD V MHGQDN*H ]QDF]FR PQLHMV]H ]H Z]JOGX QD PQLHMV]

ZDUWRüUHDNWDQFMLGáDZLNDGODF]VWRWOLZRFLSRGVWDZRZHM

'áDZLNLV]HUHJRZHPRJE\üUyZQLH*áF]RQHSRVWURQLHRGELRUF\MDNPDWRPLHMVFHZ

SU]\SDGNXUHJXORZDQ\FKQDSGyZHOHNWU\F]Q\FKFKURQLFW\PVDP\PMHJRLQVWDODFMSU]HG

QHJDW\ZQ\PLVNXWNDPL]DáF]DQLDEDWHULLNRQGHQVDWRUyZ

$ZDU\MQHZ\áF]HQLDF]Xá\FKRGELRUQLNyZ

5\V6FKHPDWSRUHGQLHJRSU]HPLHQQLNDF]VWRWOLZRFLGR]DVLODQLDQDSGXHOHNWU\F]QHJR

background image

16

: LQVWDODFML NRFRZHJR X*\WNRZQLND Z\VWSXMH F]VWR VSU]W F]Xá\ QD ]DEXU]HQLD

WRZDU]\V]FH SURFHVRZL áF]HQLD NRQGHQVDWRUyZ 3U]\NáDGHP WDNLFK RGELRUQLNyZ

V UHJXORZDQH QDSG\ HOHNWU\F]QH NWyUH PRJ XOHF Z\áF]HQLX SRGF]DV SU]HELHJyZ

SU]HMFLRZ\FKQDZHWRPDáHMZDUWRFLWRZDU]\V]F\FKáF]HQLXNRQGHQVDWRUyZ

: SU]\SDGNX QDSGyZ SUGX SU]HPLHQQHJR U\V LFK RJUDQLF]RQD RGSRUQRü MHVW

VSRZRGRZDQD JáyZQLH ]PLDQ QDSLFLD Z REZRG]LH SRUHGQLF]F\P GOD QDSLFLRZ\FK

SU]HPLHQQLNyZF]VWRWOLZRFLLXDNW\ZQLHQLHP]DEH]SLHF]HNRQWUROXMF\FK QDSLFLH VWDáH

Z W\P REZRG]LH *UR(ED WDNLHJR Z\áF]HQLD ]DOH*\ RG ZLHOX F]\QQLNyZ ZUyG NWyU\FK

QDOH*\Z\PLHQLüZLHONRüEDWHULLNRQGHQVDWRUyZZREZRG]LHSUGXVWDáHJRSR]LRPQDVWDZ\

]DEH]SLHF]HQLD QDSLFLRZHJR

1

RUD] ZDUWRü ]DVWSF]HM LQGXNF\MQRFL SRPLG]\ GZRPD

NRQGHQVDWRUDPL]DáF]DQ\PZREZRG]LHacLLVWQLHMF\PZREZRG]LHdcQDSGX3U]\SDGHN
taki przedstawiono na rysunku 22.

5\V:Sá\ZSU]HSLüSRGF]DV]DáF]DQLDEDWHULLNRQGHQVDWRUyZQDSUGZHMFLRZ\QDSLFLRZHJR

SU]HPLHQQLNDF]VWRWOLZRFL

35=<.à$' 'OD QDSGX ]DVLODQHJR ] VLHFL 9 ZDUWRü QDSLFLD SREXG]DMFD ]DEH]SLHF]HQLH

QDGQDSLFLRZHZREZRG]LHdc przemiennika jest ustawiona na poziomie 760 V (rys. 23). W takim przypadku

PLG]\ID]RZH QDSLFLH PQLHMV]H RG ZDUWRFL ]QDPLRQRZHM Z SUDNW\FH SUDZLH ]DZV]H SU]HNURF]RQH

SRGF]DVáF]HQLDNRQGHQVDWRUyZPR*HVSRZRGRZDüZ\áF]HQLHQDSGX'RW\F]\WRUyZQLH*LQQ\FKXNáDGyZ
elektro- i energoelektronicznych z kondensatorami dc.

5\V>@:Sá\ZZHMFLRZ\FKGáDZLNyZQDZDUWRüQDSLFLDZREZRG]LHdcSU]HPLHQQLNDF]VWRWOLZRFL

SRGF]DV]DáF]DQLDEDWHULLNRQGHQVDWRUyZ2SLRQRZDMHVWZ\VNDORZDQDZZDUWRFLQDSLFLDNRQGHQVDWRUDdc

>9@DRSR]LRPDZms

3UREOHP WHQ GRZLDGF]D ZLHOX X*\WNRZQLNyZ .RU]\VWQ\P MHJR UR]ZL]DQLHP MHVW

]DVWRVRZDQLH QD ZHMFLX QDSGX GáDZLNyZ R RGSRZLHGQLR GREUDQHM LQGXNF\MQRFL WDN DE\

1

'OD ZLHOX QDSGyZ SUGX SU]HPLHQQHJR PDáHM L UHGQLHM PRF\ SR]LRP ]DEH]SLHF]HQLD Z REZRG]LH SUGX

VWDáHJR Z\QRVL F]VWR QDSLFLD ]QDPLRQRZHJR 7DND ZDUWRü PR*H E\ü RVLJQLWD QDZHW

Z SU]\SDGNX V\QFKURQLF]QHJR áF]HQLD EDWHULL MH*HOL EáG GHWHNFML SU]HMFLD QDSLFLD SU]H] ]HUR FR MHVW

SRGVWDZZ\ERUXFKZLOLáF]HQLDEDWHULLEG]LH]DZDUW\ZSU]HG]LDOH 1

±

ms [2, 3].

background image

17

MHJRLPSHGDQFMDSU]HFLZG]LDáDáDWDN*HSU]HW*HQLRPSUGRZ\PGRáDGRZXMF\PNRQGHQVDWRU
dc

MDNQDU\VXQNDFK-DNZLGDüSUGEH]GáDZLNyZZHMFLRZ\FKRVLJDZUR]ZD*DQ\P

SU]\SDGNX ZDUWRü V]F]\WRZ $ L FKDUDNWHU\]XMH VL GX* V]\ENRFL QDUDVWDQLD

3RZáF]HQLXGáDZLNDZHMFLRZHJRSUGMHVWEDUG]LHMÄUR]P\W\´LMHJRPDNV\PDOQDZDUWRü

QLH SU]HNUDF]D $ 5HGXNFML XOHJáD UyZQLH* ZDUWRü VNáDGRZHM ]PLHQQHM QDSLFLD
kondensatora dc.

2EHFQLHZZLNV]RFLSU]\SDGNyZSU]HPLHQQLNLF]VWRWOLZRFLVZ\SRVD*DQHZGáDZLNL

ZHMFLRZH OXE GáDZLNL SR VWURQLH SUGX VWDáHJR WHQ VDP FHO G]LDáDQLD 3R]ZDOD WR F]VWR

XQLNQü DZDU\MQ\FK Z\áF]H VSRZRGRZDQ\FK SURFHVHP áF]HQLD NRQGHQVDWRUyZ :\EyU

ZDUWRFL LQGXNF\MQRFL WDNLHJR GáDZLND QDOH*\ SU]HSURZDG]Dü Z RSDUFLX R XZD*Q DQDOL]

ZSá\ZX VSDGNX QDSLFLD QD GáDZLNX QD SUDF QDSGX 7\SRZH ZLHONRFL V]HUHJRZ\FK

GáDZLNyZLmax.)

5\V>@3U]HELHJLF]DVRZHQDSLFLDULSUGXIVLHFL]DVLODMFHMRUD]QDSLFLDU

dc

) w obwodzie

SRUHGQLF]F\PSU]HPLHQQLNDF]VWRWOLZRFLGODSU]\SDGNXDEH]GáDZLNDLE]GáDZLNLHPZHMFLRZ\P

2FKURQDSU]HSLFLRZD

=DEH]SLHF]D SU]HG Z]URVWHP ZDUWRFL QDSLFLD SRGF]DV SURFHVX áF]HQLRZHJR W\SRZR

QD SR]LRPLH QDSLFLD ]QDPLRQRZHJR .U\W\F]QH GOD SUDF\ ]DEH]SLHF]HQLD

V Z\áDGRZDQLD SRZWyUQH ]D ]DFLVNDFK Z\áF]QLND SRGF]DV SURFHVX áF]HQLD EDWHULL

: SU]\SDGNX LQVWDORZDQLD RFKURQ\ SU]HSLFLRZHM SR VWURQLH nn, podczas wzmocnienia

RVF\ODFML QDSLFLRZ\FK Z XNáDG]LH PR*H ]GDU]\ü VL *H HQHUJLD W\FK RVF\ODFML przekraczy

PR*OLZRFLDEVRUEFML]DEH]SLHF]HQLD]Z\NOHNLONDVHW-SRZRGXMFMHJRXV]NRG]HQLH

=DEH]SLHF]HQLD WH QLH UHGXNXM ZDUWRFL SUGyZ áF]HQLRZ\FK L VSDGNyZ QDSLFLD

SRGF]DVáF]HQLDNRQGHQVDWRUyZ

background image

18

3.4. Filtry wh

6 VWRVRZDQH JáyZQLH GR UHGXNFML ZDUWRü Z\*V]\FK KDUPRQLF]Q\FK : ZLNV]RFL

SU]\SDGNyZ]PQLHMV]DMWDN*HZDUWRüSU]HSLFLDERZLHP

GRGDQLH GáDZLND Z JDá]L ILOWUX PR*H ]PLHQLü NRU]\VWQLH FKDUDNWHU\VW\N

F]VWRWOLZRFLRZXNáDGX

QDZHW Z SU]\SDGNX Z]PRFQLHQLD RVF\ODFML ZLNV]Rü QDSLFLD RGáR*\ VL QD

NRQGHQVDWRU]HLGáDZLNXZPQLHMV]\PVWRSQLXQDV]\QDFK]DVLODMF\FK

Porównanie rysunków 12 i 13 uwidacznia korzystny efekt skonfigurowania baterii

kompensacyjnej nn jako filtru harmonicznego.

6\QFKURQLF]QHáF]HQLH

2]QDF]DNRQWURORZDQLHFKZLOL]DáF]HQLDOXEUR]áF]HQLDZ\áF]QLNDZ]JOGHPSU]HELHJX

F]DVRZHJR QDSLFLD OXE SUGX 5HDOL]XMH VL ZyZF]DV V\QFKURQLF]QH áF]HQLH QS SU]\

SU]HMFLX QDSLFLD SU]H] ZDUWRü ]HURZ ]D SRPRF Z\áF]QLNyZ 6) OXE SUy*QLRZ\FK

]QLH]DOH*QSUDFSRV]F]HJyOQ\FKVW\NyZID]RZ\FK:SUDNW\FHZ\PDJDWRDQDOL]RZDQLD

V\JQDáyZ QDSLFLD LOXE SUGX L HNVWUDSRODFM PR*OLZHM FKZLOL Z\NRQDQLD ]DGDQLD ±

SU]\FKRG]F\V\JQDá]DáF]HQLDOXEZ\áF]HQLDMHVWZyZF]DVRGSRZLHGQLRRSy(QLRQ\

%DWHULDSRáF]RQDZX]LHPLRQJZLD]G

=DáF]DQLHSROHJDQDQLH]DOH*Q\P]DP\NDQLXVW\NyZGODND*GHMID]\ZSREOL*XSU]HMFLD

QDSLFLDID]RZHJRSU]H]ZDUWRü]HURZMDNQDU\VXQNX2]QDF]DWR*HF]DVSRPLG]\

NROHMQ\PLáF]HQLDPLZ\QRVLPVms, 1/6 okresu, 1/3 okresu).

5\V.RQFHSFMDV\QFKURQLF]QHJRáF]HQLDEDWHULLNRQGHQVDWRUyZSRáF]RQHMZJZLD]GX]LHPLRQ

:FHOX]UHDOL]RZDQLD]DáF]HQLDZOXESREOL*XSU]HMFLDQDSLFLDSU]H]ZDUWRü]HURZ

QLH]EGQH MHVW ]DVWRVRZDQLH DSDUDWX áF]HQLRZHJR R Z\WU]\PDáRFL QDSLFLRZHM

Z\VWDUF]DMFHM GOD Z\HOLPLQRZDQLD Z\áDGRZD SRPLG]\ VW\NDPL SU]HG LFK IL]\F]Q\P

]HWNQLFLHP VL 3R*GDQH MHVW DE\ SUG ]DF]\QDá Sá\Qü GRSLHUR Z FKZLOL X]\VNDQLD

PHFKDQLF]QHJR NRQWDNWX VW\NyZ D QLH ZF]HQLHM Z HIHNFLH Z\áDGRZDQLD áXNRZHJR
To wymaganie zilustrowano na rysunku 26, gdzie u(t)

MHVW QDSLFLHP SRPLG]\ VW\NDPL

áF]QLND SyáSURVWH DG LOXVWUXM SR]LRP UHGXNFML Z\WU]\PDáRFL QDSLFLRZHM V]F]HOLQ\
powietrznej

PLG]\VW\NRZHM /LQLD D Z\ND]XMH UHGXNFM Z\WU]\PDáRFL QDSLFLRZHM

V]F]HOLQ\ XQLHPR*OLZLDMF V\QFKURQLF]QH áF]HQLH 3UG ]DF]QLH Sá\Qü ± Z HIHNFLH

background image

19

]DLQLFMRZDQHJRZ\áDGRZDQLDáXNRZHJRZyZF]DVJG\OLQLDDSU]HWQLHVL]SU]HELHJLHP
u(t).

: SU]\SDGNX OLQLL E Z\WU]\PDáRü QDSLFLRZD V]F]HOLQ\ PDOHMH V]\EFLHM FR F]\QL

PR*OLZ\P UHDOL]DFM V\QFKURQLF]QHJR áF]HQLD .RQWDNW VW\NyZ Z\VWSL Z QDMEDUG]LHM

SR*GDQHMFKZLOLF]\OLZ]HU]HQDSLFLD1DU\VXQNXSU]HGVWDZLRQRWDN*HOLQLHFLG

GRW\F]FHJUDQLF]Q\FKSU]\SDGNyZRSy(QLHQLDLZ\SU]HG]HQLDSU]HMFLDQDSLFLDSU]H]]HUR

.

1ms

±

:LGDüZ\UD(QLH*HNRU]\VWQLHMV]HZDUXQNLZ\VWSXMSU]\RSy(QLRQ\P]DáF]HQLX

FR SRZRGXMH Z SUDNW\FH ]DPLHU]RQH RSy(QLDQLH ]DáF]HQLD Z]JOGHP SU]HMFLD QDSLFLD

SU]H]]HURZJ>@RSy(QLHQLHWRZ\QRVLRNRáRms).

5\V:\WU]\PDáRüQDSLFLRZDV]F]HOLQ\PLG]\VW\NRZHMSRGF]DVV\QFKURQLF]QHJRáF]HQLDEDWHULL

REMDQLHQLDZWHNFLH

:SUDNW\FHPR*OLZHMHVWRVLJQLFLHSUHF\]MLáF]HQLD

5

,

0

±

PVZRNyáSU]HMFLDQDSLFLD

SU]H] ZDUWRü ]HURZ

2

%DGDQLD Z\ND]Dá\ *H GRNáDGQRü V\QFKURQL]DFML U]GX

0

,

1

±

ms

JZDUDQWXMH Z SUDNW\FH SR]LRP UHGXNFML SU]HSLü RVLJDQ\ Z SU]\SDGNX ]DVWRVRZDQLD

SUDZLGáRZR GREUDQHM UH]\VWDQFML V]HUHJRZHM

3

: W\P SURFHVLH LVWRWQD MHVW PR*OLZRü

]DVWRVRZDQLD WHM PHWRG\ Z Uy*Q\FK ]PLHQLDMF\FK VL ZDUXQNDFK ]DVLODQLD L ZDUXQNDFK

PHWURORJLF]Q\FK :\PDJD WR SUHF\]\MQHM SUHG\NFML FKZLOL áF]HQLD FR QLHNLHG\ QLH MHVW

]DGDQLHP WU\ZLDOQ\P =DOHW WHJR VSRVREX MHVW SRWU]HED MHG\QLH QLHZLHONLHM PRG\ILNDFML

NRQVWUXNF\MQHMW\SRZHJRáF]QLND±JáyZQLHLQVWDODFMDXNáDGXV\QFKURQL]DFML

5\V>@1DSLFLDLSUG\ID]RZHGODQLH

synchronic

]QHJRáF]HQLHSRMHG\QF]HMbaterii

kondensatorów

5\V>@1DSLFLDLSUG\ID]RZHGOD

synchronicznego

áF]HQLHSRMHG\QF]HMEDWHULL

kondensatorów

2

:>@SRGDQRMDNRJUDQLF]QHZDUWRFLEáGXV\QFKURQL]DFMLáF]HQLDVSRZRGRZDQHJáyZQLHWHPSHUDWXUL

F]DVHPHNVSORDWDFMLZ\áF]QLNDRGGRPVZRNyáSU]HMFLDQDSLFLDSU]H]ZDUWRü]HURZ

3

:J>@WHQSR]LRPWROHUDQFMLJZDUDQWXMHRNRáRUHGXNFMLSUGXáF]HQLRZHJR

background image

20

35=<.à$':DUW\NXOH>@RSLVDQRGRZLDGF]HQLDRPLROHWQLHMHNVSORDWDFMLGZyFKEDWHULLNRQGHQVDWRUyZ

[09$UN9Z.DQDG]LHZNWyU\FK]DVWRVRZDQRV\QFKURQLF]QHáF]HQLH1DU\VXQNXSU]HGVWDZLRQR

SURFHV áF]HQLD SRMHG\QF]HM EDWHULL EH] V\QFKURQL]DFML D QD U\VXQNX WHQ VDP SURFHV Z SU]\SDGNX

]DVWRVRZDQLD V\QFKURQLF]QHJR áF]HQLD :\UD(QLH ZLGDü UHGXNFM SU]HSLü L SU]HW*H WRZDU]\V]F\FK

]DáF]DQLXEDWHULL

%DWHULDSRáF]RQDZQLHX]LHPLRQJZLD]G

:SLHUZV]HMNROHMQRFL]DP\NDQHVVW\NLQDSLFLDPLG]\ID]RZHJRSU]\MHJRSU]HMFLX

SU]H]]HURDQDVWSQLH]DP\NDQHVVW\NLZ\áF]QLNDWU]HFLHMID]\]RSy(QLHQLHPms (90

0

)

– rysunek 29.

5\V>@6\QFKURQLF]QHáF]HQLHWUyMID]RZHMQLHX]LHPLRQHMJZLD]G\NRQGHQVDWRUyZ

=DáF]DQLHNRQGHQVDWRUyZ]DSRPRFáF]QLNyZW\U\VWRURZ\FK

: SU]HFLZLHVWZLH GR áF]QLNyZ PHFKDQLF]Q\FK áF]QLNL W\U\VWRURZH XPR*OLZLDM

EDUG]RSUHF\]\MQ\Z\EyUID]\]DáF]DQLDZWHQVSRVyEUHGXNXMFOXESUDNW\F]QLHHOLPLQXMF

áF]HQLRZHVWDQ\SU]HMFLRZH

1DU\VXQNXSU]HGVWDZLRQRUy*QHPR*OLZHNRQILJXUDFMHáF]HQLDEDWHULLNRQGHQVDWRUyZ

]D SRPRF áF]QLNyZ W\U\VWRURZ\FK Z VLHFLDFK WUyMID]RZ\FK QLVNLHJR QDSLFLD

.RQGHQVDWRU\LáF]QLNLPRJE\üSRáF]RQHZJZLD]GOXEZ WUyMNW MHGHQ ] W\U\VWRUyZ

áF]QLNDPR*HE\ü]DVWSLRQ\SU]H]GLRGPRJE\ü]DVWRVRZDQHW\ONRGZDáF]QLNLPR*H

E\üSU]HZyGQHXWUDOQ\OXEPR*HJRQLHE\üLWS:ND*G\PSU]\SDGNXRERZL]XMH]DVDGD

]JRGQLH ] NWyU áF]QLN PR*H E\ü ]DPNQLW\ JG\ MHJR QDSLFLH SU]HFKRG]L SU]H] ZDUWRü

]HURZ 1D U\VXQNX ]DVWRVRZDQR QDVWSXMF\ NRG R]QDF]H ]JRGQ\ ] ,((( 6WDQGDUG
428):

SLHUZV]D OLWHUD LGHQW\ILNXMH ]DVWRVRZDQ\ HOHPHQW SyáSU]HZRGQLNRZ\ U
pojedynczy tyrystor; V – jeden tyrystor i jedna dioda; W – dwa przeciw-równolegle

SRáF]RQHW\U\VWRU\

GZLHNROHMQHF\IU\LGHQW\ILNXMOLF]EID]RUD]OLF]EVWHURZDQ\FKáF]QLNyZ

GZLH RVWDWQLH OLWHU\ RNUHODM VSRVyE SRáF]HQLD áF]QLNyZ L NRQGHQVDWRUyZ ' ±

SRáF]HQLH Z WUyMNW < ± SRáF]HQLH Z JZLD]G 1 ± JZLD]GD ] SU]HZRGHP

]HURZ\P$±LQQHSRáF]HQLH

background image

21

5\V>@0R*OLZHNRQILJXUDFMHVFKHPDWyZáF]HQLRZ\FKEDWHULLNRQGHQVDWRUyZ]DSRPRFHOHPHQWyZ

SyáSU]HZRGQLNRZ\FK

3U]HGVWDZLRQHNRQILJXUDFMHREZRGXPR*QDSRG]LHOLüQDWU]\JUXS\

, JUXSD ± REZyG XWZRU]RQ\ MHVW SU]H] WU]\ MHGQRID]RZH JDá]LH : GZyFK SLHUZV]\FK

NRQILJXUDFMDFK :1$ L :$1 áF]QLNL L NRQGHQVDWRU\ SRáF]RQH V

V]HUHJRZR Z JZLD]G 3XQNW ]HURZ\ JZLD]G\ SRáF]RQ\ MHVW ] SXQNWHP

QHXWUDOQ\P V\VWHPX ]DVLODMFHJR : WU]HFLP SU]\SDGNX ± :$$ SRáF]RQH

V]HUHJRZR áF]QLNL L NRQGHQVDWRU\ WZRU] WUyMNW ,VWRWQ\ MHVW EUDN Z]DMHPQHM

LQWHUDNFMLSRPLG]\WU]HPDJDá]LDPL±MHGQRUyZQDQLHPR*HE\ü]DVWRVRZDQHGR

RSLVXSUDF\WU]HFKáF]QLNyZ

background image

22

,,JUXSD±FKDUDNWHU\]XMHVLLVWQLHQLHPLQWHUDNFMLSRPLG]\WU]HPDáF]QLNDPL]DPNQLFLH

L RWZDUFLH áF]QLNyZ ]DOH*\ RG DNWXDOQHJR VWDQX GZyFK LQQ\FK áF]QLNyZ
W pierwszej podgrupie – konfiguracje W33YA, W33AY i W33AD – zastosowano

WU]\ áF]QLNL W\U\VWRURZH : GUXJLHM SRGJUXSLH ± NRQILJXUDFMD 9<$ 9$<

L9$'±]DVWRVRZDQRáF]QLNLXWZRU]H]GLRG\LW\U\VWRUD:WU]HFLHMSRGJUXSLH

±:<$:'$:$<L:$'±]DVWRVRZDQRW\ONRáF]QLNLW\U\VWRURZH

.RQILJXUDFMH Z ND*GHM SRGJUXSLH Uy*QL VL SR]\FM W\U\VWRUyZ OXE SRáF]HQLHP

NRQGHQVDWRUyZ JZLD]GD OXE WUyMNW .RQILJXUDFMH :<$ L :'$ V

V]F]HJyOQH7HGZDREZRG\VHOHNWU\F]QLHMHGQDNRZHMHGQDN*HSLHUZV]\]QLFK

SRZVWDáMDNRPRG\ILNDFMDNRQILJXUDFML:<$DGUXJL]:'$

,,,JUXSD±:'$L8'$WZRU]REZRG\SRáF]RQ\FKZWUyMNWáF]QLNyZ:SU]\SDGNX

SLHUZV]HM NRQILJXUDFML UR]Sá\Z SUGyZ SRPLG]\ W\U\VWRUDPL ]DOH*\ RG

XVWDORQHJRVSDGNXQDSLFLDQDHOHPHQWDFKSyáSU]HZRGQLNRZ\FK'ODNRQILJXUDFML

8'$ W\U\VWRU\ QLH PRJ E\ü SRQRZQLH ]DáF]RQH ]DQLP QDSLFLH QD

NRQGHQVDWRUDFKQLH]PQLHMV]\VLSRQL*HMNU\W\F]Q\FKZDUWRFL

=DVDGQLF]D Uy*QLFD Z\VWSXMH SRPLG]\ NRQILJXUDFMDPL ÄMHGQRID]RZ\PL´ JUXSD ,

LSR]RVWDá\PL3RGF]DVJG\NRQILJXUDFMHÄMHGQRID]RZH´PRJE\üSRQRZQLH]DáF]DQHEH]

*DGQ\FKRJUDQLF]HSR]RVWDáHZ\PDJDMDE\áF]QLNLE\á\]DP\NDQHZFLOH]GHILQLRZDQHM

NROHMQRFL -H*HOL RNUHORQD VHNZHQFMD áF]HQLD QLH EG]LH VSHáQLRQD SR]RVWDMFH Z FKZLOL

]DQLNXSUGXQDSLFLDNRQGHQVDWRUyZVSUDZL*HQDSLFLHQDMHGQ\P]áF]QLNyZQLJG\QLH

RVLJQLH ZDUWRFL ]HURZHM XQLHPR*OLZLDMF W\P VDP\P MHJR ]DPNQLFLH EH] SU]HSLü
i

SU]HW*H

.RQILJXUDFMHSU]HGVWDZLRQHQDU\VXQNXUy*QLVLSRPLG]\VREQLHW\ONRZ\PLDUHP

SUGRZ\PáF]QLNyZOHF]WDN*HRSy(QLHQLDPLZZ\áF]DQLXL]DáF]DQLXEDWHULLQDSLFLHP

PDNV\PDOQ\P QD áF]QLNX L QD NRQGHQVDWRUDFK 1D U\VXQNX SRGDQR VNXWHF]QH ZDUWRFL

SUGyZ W\U\VWRUyZ L NRQGHQVDWRUyZ I

T

i I

C

LFK PDNV\PDOQH QDSLFLD U

T

i U

C

) oraz

VNáDGRZ VWDá QDSLFLD NRQGHQVDWRUD JG\ áF]QLNL V RWZDUWH U

dc

), maksymalny czas

RSy(QLHQLD ]DáF]DQLD Z SU]\SDGNX FDáNRZLWHJR UR]áDGRZDQLD NRQGHQVDWRUyZ T

on

),

PDNV\PDOQ\F]DVRSy(QLHQLDZ\áF]HQLDT

off

LPLQLPDOQHRSy(QLHQLHSRPLG]\FKZLOJG\

áF]QLNL ]DNRF] SU]HZRG]HQLH L FKZLO JG\ RQH PRJ E\ü SRQRZQLH ]DáF]RQH T

rec

).

1D W\P VDP\P U\VXQNX QDSLFLD L SUG\ ]RVWDá\ Z\UD*RQH Z MHGQRVWNDFK Z]JOGQ\FK

RGQLHVLRQ\FK GR VNXWHF]QHM ZDUWRFL QDSLFLD PLG]\ID]RZHJR U L VNXWHF]QHM ZDUWRFL

SUGXOLQLRZHJRIRSy(QLHQLDVZ\UD*RQHMDNRXáDPNLRNUHVXSRGVWDZRZHJRT).

5\V6FKHPDWNRPSHQVDWRUDVWDW\F]QHJR]EDWHULDPLNRPSHQVDWRUyZ]DáF]DQ\PLáF]QLNDPLW\U\VWRURZ\PLTSC )

background image

23

3.6.1. Konfiguracja W33AA (kompensator statyczny TSC)

: SU]\SDGNX NRPSHQVDWRUD 76& PLG]\ID]RZR áF]RQH V EDWHULH NRQGHQVDWRUyZ

SRG]LHORQH QD VHNFMH ] NWyU\FK ND*GD MHVW ]DáF]DQD OXE Z\áF]DQD LQG\ZLGXDOQLH

]D SRPRF áF]QLNyZ W\U\VWRURZ\FK SUGX SU]HPLHQQHJR U\V :DUWRFL susceptancji

NRPSHQVDF\MQ\FK ]PLHQLDM VL ZLF Z VSRVyE G\VNUHWQ\ Z ]DOH*QRFL RG OLF]E\

SU]HZRG]F\FKVHNFML3RSU]H]Z\EyURGSRZLHGQLRGX*HMLFKOLF]E\PR*QDX]\VNDüGRZROQLH

PDáZDUWRüPRF\ELHUQHMSRMHG\QF]HJRVWRSQLD

.D*G\ PLG]\ID]RZ\ REZyG Z ERNX SRMHG\QF]HJR WUyMNWD susceptancji zawiera trzy

JáyZQH HOHPHQW\ VNáDGRZH SRMHPQRü C (X

c

LQGXNF\MQRü L (X

L

QLH ]D]QDF]RQ QD

U\VXQNX RUD] áF]QLN W\U\VWRURZ\ SUGX SU]HPLHQQHJR 7 3U]HELHJ F]DVRZ\ SUGX

NRQGHQVDWRUDSR]DáF]HQLXáF]QLNDW\U\VWRURZHJRRSLVDQ\MHVW]DOH*QRFL

t

I

t

U

n

n

U

nB

t

I

t

i

m

Sm

C

C

m

0

0

2

2

0

cos

cos

sin

)

sin

1

(

)

cos(

)

(

ω

α

ω

α

α

ω

+

=

(2)

=

)

(t

i

.

ust

i

+

.

osc

i

gdzie:

α

ID]DSRF]WNRZDRNUHORQDFKZLO]DáF]DQLDW\U\VWRUD

ω

ω

n

LC

=

=

1

0

F]VWRWOLZRüZáDVQD]DáF]DQHJRREZRGX

ω

ω

0

=

=

L

C

X

X

n

Z]JOGQD F]VWRWOLZRü ZáDVQD ]DáF]DQHJR REZRGX

RGQLHVLRQDGRF]VWRWOLZRFLQDSLFLD]DVLODMFHJR

ω

.

B

C

=

ω

C

=DVDGQLF]\ ZSá\Z QD ZDUWRü QDSLü L SUGyZ SR ]DáF]HQLX W\U\VWRUyZ PD ZDUWRü

F]VWRWOLZRFL ZáDVQHM

0

ω

-HVW RQD WUXGQD GR SUHF\]\MQHJR RNUHOHQLD ERZLHP UHDNWDQFMD

LQGXNF\MQD VLHFL ]DVLODMFHM NWyUD VWDQRZL HOHPHQW VNáDGRZ\ ]DáF]DQHJR REZRGX MHVW

Z SUDNW\FH ]QDQD MHG\QLH ] SHZQ\P SU]\EOL*HQLHP =JRQLH ] ]DOH*QRFL Z SUG]LH

EDWHULLSR]DáF]HQLXPR*QDZ\Uy*QLüVNáDGRZSRGVWDZRZ

.

ust

i

NWyUDZ\SU]HG]DQDSLFLH

XRNW

2

π

$PSOLWXG

m

I

WHJRSUGXRNUHOD]DOH*QRü

1

2

2

=

n

n

B

U

I

C

Sm

m

(3)

'ZD RVWDWQLH VNáDGQLNL SUDZHM VWURQ\ ]DOH*QRFL UHSUH]HQWXM VNáDGRZ RVF\ODF\MQ

.

osc

i

,FKDQDOL]DZ\ND]XMHL*MHVWPR*OLZH]DáF]HQLHREZRGXLCEH]VWDQyZSU]HMFLRZ\FK

QDGRZROQFDáNRZLWLORüSyáRNUHVyZSU]HZRG]HQLD-HVWWRPR*OLZHSU]\VSHáQLHQLXGZyFK
warunków (4):

a)

0

cos

=

α

(4a)

b)

m

C

Sm

C

I

X

n

n

U

U

±

=

=

1

2

2

0

(4b)

background image

24

:DUXQHN SLHUZV]\ D R]QDF]D *H W\U\VWRU\ SRZLQQ\ E\ü ]DáF]DQH Z GRGDWQLP OXE

XMHPQ\PV]F]\FLHQDSLFLD]DVLODQLD

:DUXQHN GUXJL E R]QDF]D *H NRQGHQVDWRU ZLQLHQ E\ü XSU]HGQLR QDáDGRZDQ\

GR QDSLFLD

1

2

2

0

n

n

U

U

Sm

C

=

R WDNLHM VDPHM ELHJXQRZRFL MDN QDSLFLH ]DVLODQLD Z FKZLOL

]DáF]DQLD W\U\VWRUyZ 2EHFQRü LQGXNF\MQRFL Z REZRG]LH VSUDZLD *H NRQGHQVDWRU PXVL

E\ü QDáDGRZDQ\ GR QDSLFLD Z\*V]HJR RG DPSOLWXG\ QDSLFLD ]DVLODQLD U

Sm

0LDU

SU]HáDGRZDQLD NRQGHQVDWRUD MHVW ZVSyáF]\QQLN

1

2

2

n

n

*G\ ZDUWRü n MHVW PDáD

ZVSyáF]\QQLNWHQPR*HE\ü]QDF]F\

:ND*G\PNRPSHQVDWRU]H]HZ]JOGXQD]DVWRVRZDQHW\U\VWRU\V]HUHJRZR]áF]QLNLHP

7PXVLE\ü]DZV]HSRáF]RQDQLHZLHONDLQGXNF\MQRüZFHOXRJUDQLF]HQLDSRFKRGQHMSUGX
(di/dt

:ZLNV]RFLSU]\SDGNyZZDUWRüWHMLQGXNF\MQRFLMHVWZLNV]DQL*Z\QLNDáRE\WR

]SRZ\*V]HJRNU\WHULXP3HáQLRQDERZLHPUyZQLH*UROLQGXNF\MQRFLRGVWUDMDMFHMREZyG
szeregowy LC

RG KDUPRQLF]Q\FK Z\VWSXMF\FK Z QDSLFLX ]DVLODQLD LQGXNF\MQRü

SU]HFLZUH]RQDQVRZD 3U]\ SRPLQLFLX UH]\VWDQFML ]DáF]DQHJR REZRGX Z SUDNW\F]Q\FK

XNáDGDFKVáXV]QDMHVW]DOH*QRü

2

0

2

20

10

=

÷

=

=

ω

ω

L

C

X

X

n

(5)

8Z]JOGQLDMF ]PLDQ\ QDSLFLD ]DVLODQLD ZDUXQHN E EG]LH VSHáQLRQ\ MH*HOL

NRQGHQVDWRU QLH EG]LH UR]áDGRZDQ\ SRGF]DV VWDQyZ QLH SU]HZRG]HQLD áF]QLNyZ 7 OXE

MH*HOLZXNáDG]LHEGUHDOL]RZDQHMHJRGRáDGRZDQLDGRQDSLFLDUyZQHJR

1

2

2

n

n

U

Sm

.

6SHáQLHQLH ZDUXQNyZ áF]HQLRZ\FK Z\PDJD RG XNáDGX VWHURZDQLD V\QFKURQL]DFML

PRPHQWX ]DáF]DQLD W\U\VWRUyZ ,VWQLHM MHGQDN*H SHZQH V]F]HJyOQH VWDQ\ SUDF\ XNáDGX

ZNWyU\FKZDUXQNLáF]HQLRZHVGDOHNLHRGVSHáQLHQLD

-HGQ\P ] QLFK MHVW FKZLOD XUXFKDPLDQLD XNáDGX Z NWyUHM NRQGHQVDWRU MHVW FDáNRZLFLH

UR]áDGRZDQ\W]Q

0

0

=

C

U

. W bardziej ogólnym przypadku

0

C

U

PR*HPLHüGRZROQZDUWRü

Z ]DOH*QRFL RG ZDUXQNyZ Z NWyU\FK ]DNRF]\áR VL RVWDWQLH SU]HZRG]HQLH W\U\VWRUyZ

,VWRWQH V ZyZF]DV RGSRZLHG]L QD S\WDQLD MDN DPSOLWXGD VNáDGRZHM RVF\ODF\MQHM SUGX

]DOH*\ RG

0

C

U

Z FKZLOL ]DáF]DQLD" -DN QDOH*\ Z\EUDü FKZLO ]DáF]DQLD W\U\VWRUyZ DE\

]PLQLPDOL]RZDü ZDUWRü VNáDGRZHM RVF\ODF\MQHM GOD ]DGDQHJR QDSLFLRZHJR ZDUXQNX

SRF]WNRZHJRNRQGHQVDWRUD":SUDNW\FHPR*OLZHVGZLHVWUDWHJLH]DáF]DQLDW\U\VWRUyZ

a) w chwili gdy

m

C

C

U

U

U

u

0

0

sin

=

=

α

(5a)

b) w chwili gdy

0

cos

0

=

=

α

dt

du

(5b)

: SLHUZV]\P SU]\SDGNX D LVWQLHMH JUR(ED XWUDW\ VWHURZDOQRFL XNáDGX MH*HOL

Sm

C

U

U

0

-H*HOL

Sm

C

U

U

=

0

ZyZF]DVQLH]HURZDVNáDGRZD RVF\ODF\MQDSUGXPD WDN VDP

ZDUWRüGODRE\GZXVWUDWHJLL]DáF]DQLDW\U\VWRUyZEH]Z]JOGX QD ZDUWRü F]VWRWOLZRFL

background image

25

Z]JOGQHMn'ODND*GHMZDUWRFL

Sm

C

U

U

0

]DáF]DQLH]JRGQLH]ZDUXQNLHPDGDMH]DZV]H

SHZQZDUWRüVNáDGRZHMRVF\ODF\MQHM

*G\ QDSLFLRZ\ ZDUXQHN SRF]WNRZ\

0

C

U

MHVW UyZQ\ DPSOLWXG]LH QDSLFLD VLHFL

]DVLODMFHM

Sm

U

ZyZF]DV SU]\ ]DáF]DQLX W\U\VWRUyZ Z V]F]\FLH QDSLFLD DPSOLWXGD

VNáDGRZHMRVF\ODF\MQHM

.

osc

I

PDZDUWRü

n

X

X

I

I

C

L

m

osc

1

.

=

=

(6)

,P ZLNV]D EG]LH ZDUWRü UHDNWDQFML

L

X

W\P ZLNV]D EG]LH NURWQRü WHM VNáDGRZHM

Z RGQLHVLHQLX GR ZDUWRFL XVWDORQHM -HGQDN*H ZH ZV]\VWNLFK SU]\SDGNDFK JG\

C

L

X

X

〈〈

VNáDGRZDRVF\ODF\MQDSUGXQLHSU]HNUDF]DDPSOLWXGSUGXXVWDORQHJR

1DU\VXQNXSU]HGVWDZLRQRSU]\NáDGRZRZ\EUDQHSU]HELHJLF]DVRZHSUGXLQDSLFLD

Z]DOH*QRFLRGZ]DMHPQHMUHODFMLQDSLFLRZHJRZDUXQNXSRF]WNRZHJRLDPSOLWXG\QDSLFLD

]DVLODMFHJR

0

L

X

).

5\V6\QFKURQLF]QHáF]HQLHEDWHULLNRQGHQVDWRUyZVWRVRZDQHZNRPSHQVDWRUDFK76&U

C0

±QDSLFLRZ\

ZDUXQHNSRF]WNRZ\NRQGHQVDWRUD

background image

26

5\VXQHN E SU]HGVWDZLD SURFHV ]DáF]DQLD ZHGáXJ ZDUXQNX D W]Q JG\ QDSLFLH

]DVLODQLDPDSR]LRPQDSLFLDNRQGHQVDWRUDSU]HGRVLJQLFLHPVZHMZDUWRFLPDNV\PDOQHM

.RQGHQVDWRU MHVW ZyZF]DV ]DáF]DQ\ ] SHZQ\P VWDQHP SU]HMFLRZ\P R FKDUDNWHU]H

RVF\ODF\MQRWáXPLRQ\P SU]\ F]\P VWRSLH WáXPLHQLD ]DOH*Q\ MHVW ]DUyZQR RG GREURFL

GáDZLND L NRQGHQVDWRUD MDN UyZQLH* RG UH]\VWDQFML VLHFL ]DVLODMFHM L UyZQROHJOH

SU]\áF]RQ\FK RGELRUQLNyZ 'UXJL SU]\SDGHN U\VXQHN F WR ]DáF]HQLH Z FKZLOL JG\

QDSLFLH RVLJD ZDUWRü PDNV\PDOQ NWyUD MHVW PQLHMV]D RG QDSLFLRZHJR ZDUXQNX

SRF]WNRZHJR NRQGHQVDWRUD

0

C

U

]DáF]DQLH ZHGáXJ VWUDWHJLL E ,GHDOQH ]DáF]DQLH

SU]HGVWDZLRQRQDU\VXQNXDR]QDF]DVSHáQLHQLHRE\GZXZDUXQNyZDLE

4.

WNIOSKI

3URFHV áF]HQLD EDWHULL NRQGHQVDWRUyZ WR (UyGáR ZLHOX ]DEXU]H Z VLHFL ]DVLODMFHM

:D*QDMHVWZLF]QDMRPRüLVWRW\W\FKSURFHVyZ]ZL]DQ\FK]QLPL]DJUR*HRUD]VSRVREyZ

UHGXNFMLQHJDW\ZQ\FKLFKVNXWNyZ:SU]\SDGNXLQVWDODFMLNRQGHQVDWRUyZZD*QHMHVWDE\
1.

Z\NRU]\VWDü LVWQLHMFH PR*OLZRFL UHGXNFML QHJDW\ZQ\FK HIHNWyZ SURFHVX áF]HQLD

EDWHULLV]F]HJyOQLHZSU]\SDGNXRGELRUFyZSU]HP\VáRZ\FKSRVLDGDMF\FKGX*OLF]E

UHJXORZDQ\FKQDSGyZOXELQQHJRVSU]WXHQHUJRHOHNWURQLF]QHJR

2.

HQHUJHW\ND ]DZRGRZD SRVLDGDáD LQIRUPDFMH RUD] LQIRUPRZDáD VZRLFK JáyZQ\FK

SU]HP\VáRZ\FK RGELRUFyZ RGQRQLH ORNDOL]DFML L SURFHGXU\ áF]HQLD F]DVX VSRVREX

áF]HQLDLWSGX*\FKEDWHULLNRQGHQVDWRUyZ

3.

QLH ]DSRPLQDü *H LQVWDORZDQLH ZHMFLRZ\FK GáDZLNyZ GOD XU]G]H

HQHUJRHOHNWURQLF]Q\FKV]F]HJyOQLHUHJXORZDQ\FKQDSGyZSRGZ\*V]DLFKRGSRUQRü

QDSU]HELHJLáF]HQLRZHEDWHULLNRQGHQVDWRUyZUyZQLH*]PQLHMV]DRGNV]WDáFHQLHSUGX

ZHMFLRZHJR

4.

EDWHULH NRQGHQVDWRUyZ V]F]HJyOQLH Z VVLHG]WZLH RGELRUQLNyZ QLHOLQLRZ\FK

Z\SRVD*\üZGáDZLNLRGVWUDMDMFHOXELQVWDORZDüMDNRILOWU\KDUPRQLF]Q\FK

background image

27

LITERATURA:

1.

Dugan R.C., McGranaghan M.F. Wayne B.H.: Electrical power systems quality. McGraw-Hill, 1996

2.

Grebe T.E.: CIGRE 36.05/CIGRE CC02/9925: Capacitor switching and its impact on power quality

3.

Grebe T.E.: Application of distribution system capacitor banks and their impact on power quality. IEEE
Trans. IA, 3, 32, 1996

4.

Hanzelka Z., Piekarz A.:

=DáF]DQLH EDWHULL NRQGHQVDWRUyZ Z VLHFLDFK QLVNLHJR L UHGQLHJR QDSLFLD

Seminarium JUEE, AGH-Kraków, 2000.

5.

Handbook of power signatures. Dranetz BMI 1997

6.

McCoy C.H., Floryancic B.L.: Characteristics and measurement of capacitor switching at medium voltage
distribution level
. IEEE Trans. on Ind. Appl. 6, 30, 1994

7.

Miller D.F.: Application guide for shunt capacitors on industrial distribution systems at medium voltage
levels
. IEEE PCIM-75-26

8.

Nandi S., Biswas P., Nandakumar V.N., Hegde R.K.: Two novel schemes suitable for static switching
of three-phase delta-connected capacitor banks with minimum surge current
. IEEE Trans. on Ind. Appl., 5,
33, 1997

9.

Olivier G., Mougharbel I., Dobson-Mack G.: Minimal transient switching of capacitors. IEEE Trans. on
Power Delivery, 4, 8, 1993

10.

Raport EPRI: Analyzing and solving power quality problems.

11.

Sapiejewski M.:

7HFKQLF]QH DVSHNW\ VWRVRZDQLD SU]HPLHQQLNyZ F]VWRWOLZRFL L XNáDGyZ áDJRGQHJR

rozruchu silników. Seminarium Naukowo-Techniczne pt. Zastosowanie nowoczesnej aparatury Groupe

6FKQHLGHUZXU]G]HQLDFKLLQVWDODFMDFKHOHNWURHQHUJHW\F]Q\FKQLVNLHJRQDSLFLD3ROLWHFKQLND%LDáRVWRFND

%LDá\VWRN

12.

Shunt capacitor bank switching stresses and test methods. 1

st

part – Electra, 182, Feb. 1999; 2

nd

part –

Electra, 183, April, 1999

13.

Söderström R.: Synchronized switching of MV-circiut breaker for MV-capacitor banks.

PDWHULDá\

otrzymane od autora).

14.

Stanek M., Carvalho A.C., Rahmani M., Alatalo P., Sawada J.H., Peelo D.F., Bergman W.J., Bowden G.T.:
Experiences with improving power quality by controlled switching. CIGRE Session-2000, 13/14/36-01


Wyszukiwarka

Podobne podstrony:
cz 5 pelna
cz 1 pelna id 127130 Nieznany
cz 6 pelna
cz 4 pelna
cz 2 pelna
cz 5 pelna
cz 4 pelna
cz 2 pelna
cz 5 pelna
cz 1 pelna
7 RGK cz 2 Metoda pełna wyłączenia
Biol kom cz 1
Systemy Baz Danych (cz 1 2)
cukry cz 2 st
wykłady NA TRD (7) 2013 F cz`

więcej podobnych podstron