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 QDSL FLD
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.
:67 3
=DáF]DQLHEDWHULLNRQGHQVDWRUyZMHVWSURFHVHPEDUG]RF] VWRZ\VW SXMF\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 XQLNQL FLD HZHQWXDOQ\FK RSáDW NDUQ\FK SáDFRQ\FK SU]H]
RGELRUF GRVWDZF\HQHUJLLLWS±U\VXQHNILOWUDFMLZ\*V]\FKKDUPRQLF]Q\FKZK±U\VXQHN
RUD]VWDELOL]DFMLQDSL FLD±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
2
(a)
(b)
(c)
5\VD8NáDGSDV\ZQ\FKILOWUyZZ\*V]\FKKDUPRQLF]Q\FKESUGRGELRUQLNDFSUGRGELRUQLNDSR
RGILOWURZDQLXSLWHMKDUPRQLF]QHMZILOWU]H)
(a)
(b)
5\V-HGQRID]RZ\VFKHPDW]DVW SF]\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 QDSL FLX 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
3
RGG]LDá\ZDüQDRGELRUFyZILQDOQ\FK=DLQVWDORZDQDXW\FKRVWDWQLFKRFKURQDSU]HSL FLRZD
RG ]DEXU]H Z\VRNLHM F] VWRWOLZRFL PR*H QLH E\ü SU]\VWRVRZDQD GR SU]HM FLD 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\VW SXMF\FKSURFHVyZáF]HQLRZ\FK
•
áF]HQLHSRMHG\QF]HMEDWHULLNRQGHQVDWRUyZGRPLQXMSU]HSL FLD
•
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]DVW SF]\REZRGXNWyU\SRVáX*\GR
DQDOL]\SURFHVXáF]HQLDSRMHG\QF]HMEDWHULLNRQGHQVDWRUyZRSRMHPQRFLC=DáR*RQREUDN
UH]\VWDQFML Z REZRG]LH RUD] EUDN QDSL FLRZHJR ZDUXQNX SRF]WNRZHJR QD NRQGHQVDWRU]H
ZFKZLOL]DPNQL FLDáF]QLND.
U
S
QDSL FLHVLHFL]DVLODMFHMZDUWRüVNXWHF]QD
L
S
LQGXNF\MQRüVLHFL]DVLODMFHM
L
B
LQGXNF\MQRü Z\VW SXMFD Z REZRG]LH
SU]\áF]DQHM
EDWHULL
NRQGHQVDWRUyZ
QS
LQGXNF\MQRüSU]HZRGyZáF]F\FK
C
SRMHPQRü]DáF]DQHMEDWHULLNRQGHQVDWRUyZ
5\V8SURV]F]RQ\VFKHPDW]DVW SF]\REZRGXZNWyU\PSU]\áF]DQDMHVWSRMHG\QF]DEDWHULDNRQGHQVDWRUyZ
&KZLOD ]DáF]HQLD NRQGHQVDWRUD WR PRPHQW ]ZDUFLD VLHFL ]DVLODMFHM Z PLHMVFX MHJR
SU]\áF]HQLDZ\QLNDMF\]IDNWX*HQDSL FLHQDNRQGHQVDWRU]HQLHPR*H]PLHQLüVL ZVSRVyE
QDW\FKPLDVWRZ\ -H*HOL Z V]HUHJ ] NRQGHQVDWRUHP QLH PD GáDZLND ZyZF]DV QDSL FLH 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 ]DPNQL FLD áF]QLND SUG R Z\VRNLHM F] VWRWOLZRFL L GX*HM ZDUWRFL Sá\QLH
SRPL G]\ (UyGáHP ]DVLODQLD L NRQGHQVDWRUHP SRZRGXMF Z\UyZQDQLH QDSL ü PL G]\ W\PL
GZRPD HOHPHQWDPL REZRGX -HJR ZDUWRü GHWHUPLQRZDQD MHVW QDSL FLHP (UyGáRZ\P
Z FKZLOL ]DP\NDQLD áF]QLND LQGXNF\MQRFL ]DVW SF] REZRGX RUD] SRMHPQRFL
SU]\áF]DQHJR NRQGHQVDWRUD SU]\ ]DáR*HQLX *H EDWHULD QLH E\áD ZVW SQLH QDáDGRZDQD
:DUWRüPDNV\PDOQDWHJRSUGXPR*HE\üRNUHORQD]ZL]NLHP
U
S
6
/
%
/
&
K
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]JO GQLD WáXPLFHJR HIHNWX Z\VW SXMFHJR Z U]HF]\ZLVW\FK
XNáDGDFK : SUDNW\FH WáXPLHQLH UHGXNXMH SUG PDNV\PDOQ\ GR RNRáR ZDUWRFL
Z\]QDF]RQHM ] ]DOH*QRFL 3UG WHQ E
G]LH ]DZV]H PQLHMV]\ QL* SUG ]ZDUFLD
analizowanego obwodu.
3RGF]DVSURFHVXáF]HQLRZHJRZ\VW SXM]QDF]FHVSDGNLQDSL FLDQDLPSHGDQFMDFKVLHFL
]DVLODMFHM FR PR*H XDNW\ZQLü XNáDG\ ]DEH]SLHF]H 1D U\VXQNX SU]HGVWDZLRQR W\SRZ\
SU]HELHJQDSL FLDZMHGQRVWNDFKZ]JO GQ\FK±MZSRGF]DVáF]HQLDEDWHULLNRQGHQVDWRUyZ
5\V7\SRZ\SU]HELHJQDSL FLD]DVLODMFHJRSRGF]DVSURFHVXáF]HQLDEDWHULL
1DJáH REQL*HQLH QDSL FLD QD V]\QDFK GR NWyU\FK SU]\áF]DQ\ MHVW NRQGHQVDWRU SRGF]DV
MHJR áDGRZDQLD Z\ZRáXMH EDUG]R GX* SRFKRGQ ]PLDQ\ QDSL FLD 0R*H WR VSRZRGRZDü
]QDF]FHSU]HSL FLDQDNRFDFK]ZRMyZX]ZRMHWUDQVIRUPDWRUyZ]HZ]JO GXQDSRMHPQRFL
PL G]\ ]ZRMRZH L PL G]\ X]ZRMHQLDPL :J >@ VSU] *HQLH SRMHPQRFLRZH SRPL G]\
X]ZRMHQLDPL PR*H VSRZRGRZDü ÄG\QDPLF]Q´ WUDQVIRUPDFM QDSL ü LQQ QL* Z\QLND WR
] SU]HáR*HQLD ]ZRMRZHJR :J WHJR VDPHJR (UyGáD SU]\NáDGRZR GOD WUDQVIRUPDWRUD
RSU]HáR*HQLX]ZRMRZ\PSRMHPQRFLRZDWUDQVIRUPDFMDQDSL FLDPR*HSU]\MüZDUWRü
2]QDF]D WR *H Z]JO GQD ]PLDQD QDSL FLD R ZDUWRFL Z\VW SXMFD QD SLHUZRWQHM
VWURQLHWUDQVIRUPDWRUDZ\ZRáD]PLDQ
QDSL
FLDRZDUWRFLGRZMHGQRVWNDFKZ]JO
GQ\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]HSL FLD 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]HSL FLD WH PRJ Z\ZRáDü
WDN*HXV]NRG]HQLHL]RODFMLWUDQVIRUPDWRUD'ODLOXVWUDFML]MDZLVNDQDU\VXQNXSU]HGVWDZLRQR
5
SU]HELHJ F]DVRZ\ QDSL
FLD 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]HSL FLRZHVWRVRZDQHZLQVWDODFMDFKX*\WNRZQLNDVWDQRZLZ\VWDUF]DMFH]DEH]SLHF]HQLH
5\V>@3U]HSL FLHQDZWyUQHMVWURQLHVáDERREFL*RQHJRWUDQVIRUPDWRUDVSRZRGRZDQHPL G]\]ZRMRZ\P
VSU] *HQLHPSRMHPQRFLRZ\PSRGF]DVV]\ENLHJRVWDQXSU]HMFLRZHJRZ\ZRáDQHJR]DáF]DQLHPEDWHULL
kondensatorów
1DJáH REQL*HQLH QDSL FLD SRGF]DV SURFHVX SU]\áF]DQLD EDWHULL Z\ZRáXMH V]F]HJyOQLH
Z VLHFLDFK Z\VRNLHJR QDSL FLD ]MDZLVNR IDO Z GUXMF\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]HSL
FLD R EDUG]R GX*\FK ZDUWRFLDFK F]
VWR JUR(QH
w skutkach.
: GUXJLP HWDSLH SURFHVX áF]HQLD QDSL FLH 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±SRPL G]\SRMHPQRFLNRQGHQVDWRUDLLQGXNF\MQRFLVLHFL]DVLODMFHM±
SRGF]DV NWyUHJR QDSL
FLH RG]\VNXMH VZyM SLHUZRWQ\ SU]HELHJ F]DVRZ\ &]
VWRWOLZRü W\FK
oscylacji (f
PR*HE\üV]DFRZDQDQDSRGVWDZLH]DVW SF]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+]LZL FHM
1DU\VXQNXSU]HGVWDZLRQRSU]HELHJLF]DVRZHQDSL FLDSRGF]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 QDSL FLH 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 QDSL FLD ]DVLODMFHJR
PDNV\PDOQ ZDUWRü UyZQ SRGZyMQHM DPSOLWXG]LH QLH ]DEXU]RQHJR SU]HELHJX 7áXPLHQLH
V\VWHPXUHGXNXMHW ZDUWRüGRRNRáR&]DVWUZDQLD]MDZLVND]PLHQLDVL W\SRZR
6
RG GR RNUHVyZ : SU]\SDGNX GRáF]RQ\FK UyZQROHJOH RGELRUQLNyZ LFK WáXPLF\
ZSá\ZVSUDZLD*HSURFHVSU]HMFLRZ\NRF]\VL ]D]Z\F]DMSU]HGXSá\ZHPRNUHVXQDSL FLD
(a)
(b)
5\V>@3U]\NáDGRZHSU]HELHJLQDSL FLDSRGF]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\ QDSL FLD ]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\QDSL FLDDLSUGXESRGF]DVáF]HQLDEDWHULLNRQGHQVDWRUyZ
1D U\VXQNX SU]HGVWDZLRQR SURFHV áF]HQLD EDWHULL WUyMID]RZHM =DZV]H MHGQD ] ID]
Z\ND]XMHV]F]HJyOQLHGX*\Z]URVWSU]HMFLRZHJRQDSL FLD
5\V>@3URFHVáF]HQLDWUyMID]RZHMEDWHULLNRQGHQVDWRUyZ
7
=DUyZQR SRF]WNRZD VNRNRZD ]PLDQD MDN L Sy(QLHMV]H RVF\ODFMH QDSL FLD V ZD*Q
F] FLáF]HQLRZ\FKVWDQyZSU]HMFLRZ\FK3RF]WNRZD]PLDQDMHVWLVWRWQD]HZ]JO GXQD
GX* SRFKRGQ Z\VW SXMFHM ZyZF]DV UHGXNFML QDSL FLD 1DVW SXMFH SR QLHM RVF\ODFMH
VWDQRZL ]QDF]QLH ZL NV]\ 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]HSL üRZDUWRFLGRQDSL FLD]QDPLRQRZHJR-HGQDN*HRVF\ODFMHWH]HZ]JO GXQD
UHODW\ZQLH QLVN F] VWRWOLZRü SU]HQLNDM SU]H] WUDQVIRUPDWRU\ REQL*DMFH QDSL FLH
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 PL
G]\ LQQ\PL XV]NRG]HQLH QDSL
FLRZH VSU]
WX
elektronicznego, kondensatorów, przepalenie bezpieczników, uszkodzenie elementów
RFKURQ\SU]HSL FLRZHMLWS
-
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 QDS GyZ L LQQ\FK RGELRUQLNyZ ] HOHNWURQLF]Q\PL ]DVLODF]DPL OXE
]QDSL FLRZV\QFKURQL]DFM
2.2
3URFHVZ]PDFQLDQLDRVF\ODFMLáF]HQLRZ\FK
:]PRFQLHQLHRVF\ODFMLZ\VW SXMHMDNRUH]XOWDWSREXG]HQLD±SURFHVHPáF]HQLDEDWHULL
± GUJD ZáDVQ\FK Z VáDER WáXPLRQ\P REZRG]LH
C
L
S
XWZRU]RQ\P ] ]DVW SF]\FK
LQGXNF\MQRFLV\VWHPX]DVLODMFHJRZVLHFLDFKUR]G]LHOF]\FKJáRZQLHWUDQVIRUPDWRUyZRUD]
SRMHPQRFL GRáF]DQHM L MX* SU]\áF]RQ\FK EDWHULL NRQGHQVDWRUyZ 5H]XOWDWHP MHVW PL G]\
LQQ\PL Z]URVW QDSL
FLD QD V]\QDFK QLVNLHJR QDSL
FLD nn). Rysunek 10 przedstawia taki
przypadek w typowej sieci rozdzielczej. Bateria C
MHVWSU]\áF]DQDGRUyZQROHJáHJRREZRGX
XWZRU]RQHJR SU]H] V]HUHJRZH SRáF]HQLH LPSHGDQFML ]DVW
SF]HM WUDQVIRUPDWRUD L EDWHULL
kondensatorów nn przeznaczonej do kompensacji mocy biernej. Wzmocnienie oscylacji
Z\VW
SXMHZSUDNW\FHMH*HOL
-
SRMHPQRü NRQGHQVDWRUD C MHVW GX*R ZL NV]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]HSL ü PR*H Z\VWSLü GOD V]HURNLHJR
SU]HG]LDáXZDUWRFLPRF\EDWHULLNRQGHQVDWRUyZQLVNLHJRQDSL FLD5\VXQHNSU]HGVWDZLD
UH]XOWDW\REOLF]HGODXNáDGX]DVLODQLDMDNQDU\VXQNX3U]HGVWDZLRQ\SU]HELHJSRND]XMH
VWRSLH Z]PRFQLHQLD QDSL
FLD QD V]\QDFK 9 VSRZRGRZDQ\ ]DáF]HQLHP EDWHULL
kondensatorów o mocy 3 MVAr (C
ZVLHFLUHGQLHJRQDSL FLD3U]HSL FLHX]DOH*QLRQHMHVW
od mocy baterii kondensatorów nn (C
]PLHQLDMFHM VL Z SU]HG]LDOH kVAr
8
W\SRZHZDUWRFLPRF\EDWHULLGODWUDQVIRUPDWRUDREQL*DMFHJRRPRF\09$6WRSLH
Z]PRFQLHQLD SU]HNUDF]D Z MHGQRVWNDFK Z]JO GQ\FK %DGDQLD Z\ND]XM *H Z SUDNW\FH
ZDUWRüWD]DZLHUDVL ZSU]HG]LDOH
5\V>@3U]\NáDGRZ\VFKHPDWXNáDGX]DVLODQLD]DNáDGXZNWyU\PPR*HZ\VWSLüSUREOHPSREXG]HQLD
RVF\ODFMLQDVNXWHNáF]HQLDEDWHULLNRQGHQVDWRUyZ
5\V>@3U]HELHJLLOXVWUXMFHZ]PRFQLHQLHRVF\ODFMLSRVWURQLHQLVNLHJRQDSL FLD
5\V>@:Sá\ZPRF\EDWHULLNRQGHQVDWRUyZQQCQDZ]PRFQLHQLHSU]HSL üáF]HQLRZ\FK0RF
SU]\áF]DQHMEDWHULLC1) wynosi 3 MVAr
9
5\V>@:Sá\ZVNRQILJXURZDQLDEDWHULLCMDNRILOWUXKDUPRQLF]QHMQDZDUWRüSU]HSL FLDZVLHFLnn (C1 –
3MVAr)
2.3
'RáF]DQLHNROHMQHMEDWHULL
7HQ URG]DM áF]HQLD Z\ZRáXMH Z VLHFLDFK ]DVLODMF\FK SRJRUV]HQLH MDNRFL ]DVLODQLD
Z QDVW SVWZLH VWDQyZ SU]HMFLRZ\FK R GX*HM F] VWRWOLZRFL Z\VW SXMF\FK Z QDSL FLX
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]JO GHP SU]HELHJX F]DVRZHJR QDSL FLD ]DVLODMFHJR Z NWyUHM áF]QLN
zamknie obwód;
WáXPLHQLD]DáF]DQHJRREZRGX
1D U\VXQNX SU]HGVWDZLRQR SU]\NáDGRZ\ VFKHPDW LGHRZ\ D L ]DVW SF]\ E
VWRVRZDQ\GRDQDOL]\SURFHVXSU]\áF]DQLDUyZQROHJáHMEDWHULLNRQGHQVDWRUyZGREDWHULLMX*
SUDFXMFHM
(a)
(b)
5\VD6]\Q\]SU]\áF]RQ\PLGZRPDEDWHULDPLNRQGHQVDWRUyZEXSURV]F]RQ\VFKHPDW]DVW SF]\GR
DQDOL]\SURFHVX]DáF]DQLDNROHMQHMEDWHULLNRQGHQVDWRUyZL
zew.
±LQGXNF\MQRü]DVW SF]Doszynowania;
&
/
]DVW SF]DLQGXNF\MQRüLSRMHPQRüSU]\M WRL
1
=L
2
=L
3
; C
1
=C
2
=C
3
)
1D U\VXQNX E SRPLQL WR LQGXNF\MQRü L QDSL FLH (UyGáD ]DVLODQLD 8F]\QLRQR WDN
SRQLHZD*SRGF]DVNLONXSLHUZV]\FKPLOLVHNXQGSR]DPNQL FLXáF]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
10
3RGF]DVSU]\áF]DQLDWU]HFLHMEDWHULLMDNQDU\VXQNXZV]\VWNLHHOHPHQW\REZRGXV
SRáF]RQH V]HUHJRZR GDMF Z\SDGNRZ ZDUWRü LQGXNF\MQRFL L SRMHPQRFL ]DVW
SF]HM
odpowiednio:
/
/
/
/
]HZ
&
&
&
&
&
-X* SU]\áF]RQH EDWHULH VWDQRZL (UyGáR QDSL FLD R PLQLPDOQHM LPSHGDQFML ]DVW SF]HM
'ODWHJR ZDUWRü PDNV\PDOQD SUGX áF]HQLRZHJR PR*H SU]HNURF]\ü SUG ]ZDUFLD
DQDOL]RZDQHJRREZRGXLZ\VW SXMHRQDWX*SR]DPNQL FLXáF]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 ]DVW SF] 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]HMFLRZHJRZQDSL FLX
11
5\V>@D3UGSRGF]DVSURFHVX]DáF]DQLDSRMHG\QF]HMEDWHULLRUD]EDWHULLGRáF]DQHMGRMX*
SUDFXMFHME
6WDQ\ áF]HQLRZH Z QDSL FLX V UHGXNRZDQH SU]H] NRQGHQVDWRU\ MX* SU]\áF]RQH WDN
ZL F QDMEDUG]LHM QLHNRU]\VWQH ZDUXQNL ] SXQNWX ZLG]HQLD QDSL FLD GRW\F] áF]HQLD
SLHUZV]HJRVWRSQLD5HGXNFMDQDSL FLDQDV]\QDFKUR]G]LHOQLMHVWPQLHMV]DQL*ZSU]\SDGNX
áF]HQLD SRMHG\QF]HM EDWHULL ]H Z]JO GX QD áDGXQHN HOHNWU\F]Q\ Z NRQGHQVDWRUDFK MX*
SUDFXMF\FK3U]\NáDGRZRGODGZyFKEDWHULLRWDNLHMVDPHMPRF\PLQLPDOQDZDUWRüQDSL FLD
Z\QRVLRNRáRWHMNWyUDE\áDQD]DáF]RQHMEDWHULLWX*SU]HGFKZLOGRáF]HQLDNROHMQHM
1D U\VXQNX SU]HGVWDZLRQR RNUHVX SU]HELHJX F]DVRZHJR QDSL FLD 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
RZL FHMQL*MHGQHMF] VWRWOLZRFL
5\V>@3RZL NV]RQ\SU]HELHJF]DVRZ\QDSL FLDSRGF]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\MQHRZL FHMQL*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]DQLHEDWHULLZVW SQLHQDáDGRZDQHM
•
]DSáRQáXNXSRGF]DVSURFHVXZ\áF]DQLDEDWHULL
12
=DáF]DQLHEDWHULLZVW SQLHQDáDGRZDQHM
: QRUPDOQ\FK ZDUXQNDFK HNVSORDWDF\MQ\FK NRQGHQVDWRU SR Z\áF]HQLX SRZLQLHQ E\ü
UR]áDGRZDQ\ ZRNUHORQ\PF]DVLHGRRNUHORQHJR QDSL FLD QS PLQ 9 1DMEDUG]LHM
QLHNRU]\VWQH ZDUXQNL áF]HQLD Z\VWSL ZyZF]DV JG\ ]DPNQL FLH áF]QLND QDVWSL
ZV]F]\FLHQDSL FLD]DVLODMFHJRDNRQGHQVDWRUE G]LHQDáDGRZDQ\GRQDSL FLDRWDNLHMVDPHM
ZDUWRFLOHF]SU]HFLZQHMSRODU\]DFML0R*HQDVWSLüZyZF]DVSRGZRMHQLHSUGXZVWRVXQNX
GRMHJRZDUWRFLSU]\áF]HQLXUR]áDGRZDQHMEDWHULL
=DSáRQáXNXSRGF]DVSURFHVXZ\áF]DQLDEDWHULL
6NXWNLHP V VWDQ\ SU]HMFLRZH Z QDSL FLX ]DVLODMF\P MDNNROZLHN Z SU]\SDGNX
ZVSyáF]HVQ\FKNRQVWUXNFMLZ\áF]QLNyZUHDOQRüWHJR]DJUR*HQLDMHVWQLHZLHOND=MDZLVNRWR
PR*HZ\VWSLüZZ\áF]QLNDFKVWRVXMF\FKPDJQHW\F]QFHZN Z\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]HMFLRZHQDSL FLDLSUGXZSU]\SDGNXZ\VWSLHQLDSU]HVNRNXáXNRZHJRZZ\áF]QLNX
SRGF]DVSU]HU\ZDQLDSUGXSRMHPQRFLRZHJR
13
3URFHVRWZLHUDQLDZ\áF]QLNDZNWyU\PZ\VWSLá\SU]HVNRNLáXNRZHSU]HGVWDZLRQRQD
U\VXQNX*G\VW\NLáF]QLND]DF]\QDMVL RWZLHUDüSUGSRMHPQRFLRZ\SU]HVWDMHSá\Qü
SU]\SLHUZV]\PSU]HMFLXSU]H]ZDUWRü]HURZ3U]HUZDQLHSUGXSRMHPQRFLRZHJRQLHMHVW
WUXGQHV]F]HJyOQLHZSRUyZQDQLX]SUGHPLQGXNF\MQ\P1DSL FLHQDZ\áF]QLNXSRVWURQLH
]DVLODQLDLQDSL FLHQDNRQGHQVDWRU]HVZyZF]DVUyZQHDLFKZDUWRFLPDNV\PDOQH1DSL FLH
QD NRQGHQVDWRU]H ]DFKRZD W VWDá ZDUWRü 3yá RNUHVX Sy(QLHM QDSL FLH (UyGáD ]DVLODQLD
]PLHQLVL QDXMHPQHZVWRVXQNXGRQDSL FLDNRQGHQVDWRUD:yZF]DVUy*QLFDSRWHQFMDáyZ
PL G]\ VW\NDPL Z\áF]QLND RVLJQLH SRGZyMQ DPSOLWXG QDSL FLD ]DVLODMFHJR -H*HOL
WD ZDUWRü SU]HNURF]\ Z\WU]\PDáRü SU]HUZ\ PL G]\VW\NRZHM Z\áDGRZDQLH áXNRZH
SRPL G]\QLPLVSRZRGXMHJZDáWRZQ\Z]URVWSUGX(UyGáD]DVLODQLD1DSU]HFLZQ]PLHQLVL
SRODU\]DFMDQDSL FLDNRQGHQVDWRUD0R*HRQRRVLJQüZDUWRüUyZQSRWUyMQHMDPSOLWXG]LH
QDSL FLDVLHFL3URFHVWHQPR*HXOHFSRZLHOHQLXZGDOV]\FKFKZLODFKF]DVX
3.
63262%<5('8.&-,35=(3, û,35=(7 )(à&=(1,2:<&+
=Z\NOHQLHPDSRWU]HE\NRQWURORZDQLD]DáF]DQLDEDWHULLMH*HOLSURFHVWHQQLHZ\VW SXMH
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]ZL NV]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]EDWHULNRQGHQVDWRUyZSHáQLüURO ILOWUXGODZ\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 QDSL ü
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]HSL ü 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
VWHURZQLDDZL
FV\QFKURQL]DFMDFKZLOL]DáF]DQLDWDNDE\QDVWSLáRRQRQS
-
SU]\SU]HMFLXQDSL FLDSU]H]ZDUWRü]HURZ
-
SU]\ SU]HMFLX QDSL FLD SU]H] ZDUWRü PDNV\PDOQ ] UyZQRF]HVQ\P ZF]HQLHMV]\P
QDáDGRZDQLHPZVW
SQ\PNRQGHQVDWRUD7HQURG]DMáF]HQLDMHVWVWRVRZDQ\ZXNáDGDFK
kompensatorów statycznych TSC (Thyristor Switched Capacitors).
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
15
3.1. Szeregowa rezystancja
Jest jednym z najprostszych, a zarazem najskuteczniejszych sposobów kontrolowania
SRMHPQRFLRZ\FK VWDQyZ SU]HMFLRZ\FK U\V MDNNROZLHN Z]JO G\ 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
≈
-HVWZL FRQDGRELHUDQDLQG\ZLGXDOQLHGOD
ND*GHJRSU]\SDGNXL]Z\NOH]DZLHUDVL ZSU]HG]LDOH2PyZ
6WRVRZDQHE\ZDMXNáDG\ZNWyU\FKUH]\VWRUMHVWZáF]RQ\W\ONRQDNUyWNLRNUHVF]DVX
(10-15
PV =H Z]JO GX QD GRSXV]F]DOQ REFL*DOQRü SUGRZ VW\NyZ Z\áF]QLND NWyUH
UHDOL]XMSURFHVáF]HQLDUH]\VWRUyZ]Z\NOHLFKZDUWRü]DZLHUDVL ZyZF]DVZSU]HG]LDOH
,P ZL NV]D UH]\VWDQFMD W\P EDUG]LHM HIHNW\ZQH MHVW WáXPLHQLH VWDQyZ
SU]HMFLRZ\FKZQDSL FLX-HGQDN*H]GUXJLHMVWURQ\ZUD]]HZ]URVWHPZDUWRFLUH]\VWDQFML
]ZL NV]DVL VWDQSU]HMFLRZ\WRZDU]\V]F\MHMZ\áF]DQLXERF]QLNRZDQLX±U\VXQHN
6]HUHJRZ\GáDZLN
-HVW]VXNFHVHPVWRVRZDQ\GRRJUDQLF]DQLDSUGXáF]HQLRZHJREDWHULL:SURZDG]DWDN*H
SHZLHQSR]LRPRJUDQLF]HQLDQDSL FLRZ\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 QDSL FLD
SRGF]DVSURFHVX]DáF]DQLD=DOHWGáDZLNyZMHVWWR*HZSU]HFLZLHVWZLHGRUH]\VWRUyZV
EDUG]LHMQLH]DZRGQHPQLHMLVWRWQHZ]JO G\WHUPLF]QHLEDUG]LHMHNRQRPLF]QHZHNVSORDWDFML
PQLHMV]HVWUDW\PRF\'áDZLNLRJUDQLF]DMWDN*HSUGEDWHULLSRGF]DV]ZDUüZ\VW SXMF\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 ZL NV]D Z SRF]WNRZ\P
RNUHVLH JG\ F] VWRWOLZRü SU]HELHJyZ MHVW GX*D 1DVW SQLH XOHJD ]PQLHMV]HQLX JG\ Sá\QLH
SUGRF] VWRWOLZRFLVLHFL]DVLODMFHM3RGREQLHMDNZSU]\SDGNXZ\áF]DQHJRUH]\VWRUDWX
UyZQLH* Z\VW SXMH GUXJL VWDQ SU]HMFLRZ\ SRGF]DV ERF]QLNRZDQLD GáDZLND :\VW SXMFH
ZyZF]DV SU]HSL FLD L SU]HW *HQLD V MHGQDN*H ]QDF]FR PQLHMV]H ]H Z]JO GX QD PQLHMV]
ZDUWRüUHDNWDQFMLGáDZLNDGODF] VWRWOLZRFLSRGVWDZRZHM
'áDZLNLV]HUHJRZHPRJE\üUyZQLH*áF]RQHSRVWURQLHRGELRUF\MDNPDWRPLHMVFHZ
SU]\SDGNXUHJXORZDQ\FKQDS GyZHOHNWU\F]Q\FKFKURQLFW\PVDP\PMHJRLQVWDODFM SU]HG
QHJDW\ZQ\PLVNXWNDPL]DáF]DQLDEDWHULLNRQGHQVDWRUyZ
$ZDU\MQHZ\áF]HQLDF]Xá\FKRGELRUQLNyZ
5\V6FKHPDWSRUHGQLHJRSU]HPLHQQLNDF] VWRWOLZRFLGR]DVLODQLDQDS GXHOHNWU\F]QHJR
16
: LQVWDODFML NRFRZHJR X*\WNRZQLND Z\VW SXMH F] VWR VSU] W F]Xá\ QD ]DEXU]HQLD
WRZDU]\V]FH SURFHVRZL áF]HQLD NRQGHQVDWRUyZ 3U]\NáDGHP WDNLFK RGELRUQLNyZ
V UHJXORZDQH QDS G\ HOHNWU\F]QH NWyUH PRJ XOHF Z\áF]HQLX SRGF]DV SU]HELHJyZ
SU]HMFLRZ\FKQDZHWRPDáHMZDUWRFLWRZDU]\V]F\FKáF]HQLXNRQGHQVDWRUyZ
: SU]\SDGNX QDS GyZ SUGX SU]HPLHQQHJR U\V LFK RJUDQLF]RQD RGSRUQRü MHVW
VSRZRGRZDQD JáyZQLH ]PLDQ QDSL FLD Z REZRG]LH SRUHGQLF]F\P GOD QDSL FLRZ\FK
SU]HPLHQQLNyZF] VWRWOLZRFLLXDNW\ZQLHQLHP]DEH]SLHF]HNRQWUROXMF\FK QDSL FLH VWDáH
Z W\P REZRG]LH *UR(ED WDNLHJR Z\áF]HQLD ]DOH*\ RG ZLHOX F]\QQLNyZ ZUyG NWyU\FK
QDOH*\Z\PLHQLüZLHONRüEDWHULLNRQGHQVDWRUyZZREZRG]LHSUGXVWDáHJRSR]LRPQDVWDZ\
]DEH]SLHF]HQLD QDSL FLRZHJR
1
RUD] ZDUWRü ]DVW SF]HM LQGXNF\MQRFL SRPL G]\ GZRPD
NRQGHQVDWRUDPL]DáF]DQ\PZREZRG]LHacLLVWQLHMF\PZREZRG]LHdcQDS
GX3U]\SDGHN
taki przedstawiono na rysunku 22.
5\V:Sá\ZSU]HSL üSRGF]DV]DáF]DQLDEDWHULLNRQGHQVDWRUyZQDSUGZHMFLRZ\QDSL FLRZHJR
SU]HPLHQQLNDF] VWRWOLZRFL
35=<.à$' 'OD QDS GX ]DVLODQHJR ] VLHFL 9 ZDUWRü QDSL FLD SREXG]DMFD ]DEH]SLHF]HQLH
QDGQDSL FLRZHZREZRG]LHdc przemiennika jest ustawiona na poziomie 760 V (rys. 23). W takim przypadku
PL G]\ID]RZH QDSL FLH PQLHMV]H RG ZDUWRFL ]QDPLRQRZHM Z SUDNW\FH SUDZLH ]DZV]H SU]HNURF]RQH
SRGF]DVáF]HQLDNRQGHQVDWRUyZPR*HVSRZRGRZDüZ\áF]HQLHQDS
GX'RW\F]\WRUyZQLH*LQQ\FKXNáDGyZ
elektro- i energoelektronicznych z kondensatorami dc.
5\V>@:Sá\ZZHMFLRZ\FKGáDZLNyZQDZDUWRüQDSL FLDZREZRG]LHdcSU]HPLHQQLNDF] VWRWOLZRFL
SRGF]DV]DáF]DQLDEDWHULLNRQGHQVDWRUyZ2SLRQRZDMHVWZ\VNDORZDQDZZDUWRFLQDSL FLDNRQGHQVDWRUDdc
>9@DRSR]LRPDZms
3UREOHP WHQ GRZLDGF]D ZLHOX X*\WNRZQLNyZ .RU]\VWQ\P MHJR UR]ZL]DQLHP MHVW
]DVWRVRZDQLH QD ZHMFLX QDS GX GáDZLNyZ R RGSRZLHGQLR GREUDQHM LQGXNF\MQRFL WDN DE\
1
'OD ZLHOX QDS GyZ SUGX SU]HPLHQQHJR PDáHM L UHGQLHM PRF\ SR]LRP ]DEH]SLHF]HQLD Z REZRG]LH SUGX
VWDáHJR Z\QRVL F] VWR QDSL FLD ]QDPLRQRZHJR 7DND ZDUWRü PR*H E\ü RVLJQL WD QDZHW
Z SU]\SDGNX V\QFKURQLF]QHJR áF]HQLD EDWHULL MH*HOL EáG GHWHNFML SU]HMFLD QDSL FLD SU]H] ]HUR FR MHVW
SRGVWDZZ\ERUXFKZLOLáF]HQLDEDWHULLE G]LH]DZDUW\ZSU]HG]LDOH 1
±
ms [2, 3].
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 QDSL
FLD
kondensatora dc.
2EHFQLHZZL NV]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 QDSL FLD QD GáDZLNX QD SUDF QDS GX 7\SRZH ZLHONRFL V]HUHJRZ\FK
GáDZLNyZLmax.)
5\V>@3U]HELHJLF]DVRZHQDSL FLDULSUGXIVLHFL]DVLODMFHMRUD]QDSL FLDU
dc
) w obwodzie
SRUHGQLF]F\PSU]HPLHQQLNDF] VWRWOLZRFLGODSU]\SDGNXDEH]GáDZLNDLE]GáDZLNLHPZHMFLRZ\P
2FKURQDSU]HSL FLRZD
=DEH]SLHF]D SU]HG Z]URVWHP ZDUWRFL QDSL FLD SRGF]DV SURFHVX áF]HQLRZHJR W\SRZR
QD SR]LRPLH QDSL FLD ]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]HSL FLRZHM SR VWURQLH nn, podczas wzmocnienia
RVF\ODFML QDSL FLRZ\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 QDSL FLD
SRGF]DVáF]HQLDNRQGHQVDWRUyZ
18
3.4. Filtry wh
6 VWRVRZDQH JáyZQLH GR UHGXNFML ZDUWRü Z\*V]\FK KDUPRQLF]Q\FK : ZL NV]RFL
SU]\SDGNyZ]PQLHMV]DMWDN*HZDUWRüSU]HSL FLDERZLHP
−
GRGDQLH GáDZLND Z JDá ]L ILOWUX PR*H ]PLHQLü NRU]\VWQLH FKDUDNWHU\VW\N
F] VWRWOLZRFLRZXNáDGX
−
QDZHW Z SU]\SDGNX Z]PRFQLHQLD RVF\ODFML ZL NV]Rü QDSL FLD 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]JO GHPSU]HELHJX
F]DVRZHJR QDSL FLD OXE SUGX 5HDOL]XMH VL ZyZF]DV V\QFKURQLF]QH áF]HQLH QS SU]\
SU]HMFLX QDSL FLD 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 QDSL FLD 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
QDSL FLDID]RZHJRSU]H]ZDUWRü]HURZMDNQDU\VXQNX2]QDF]DWR*HF]DVSRPL G]\
NROHMQ\PLáF]HQLDPLZ\QRVLPVms, 1/6 okresu, 1/3 okresu).
5\V.RQFHSFMDV\QFKURQLF]QHJRáF]HQLDEDWHULLNRQGHQVDWRUyZSRáF]RQHMZJZLD]G X]LHPLRQ
:FHOX]UHDOL]RZDQLD]DáF]HQLDZOXESREOL*XSU]HMFLDQDSL FLDSU]H]ZDUWRü]HURZ
QLH]E GQH MHVW ]DVWRVRZDQLH DSDUDWX áF]HQLRZHJR R Z\WU]\PDáRFL QDSL FLRZHM
Z\VWDUF]DMFHM GOD Z\HOLPLQRZDQLD Z\áDGRZD SRPL G]\ VW\NDPL SU]HG LFK IL]\F]Q\P
]HWNQL FLHP 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 QDSL FLHP SRPL G]\ VW\NDPL
áF]QLND SyáSURVWH DG LOXVWUXM SR]LRP UHGXNFML Z\WU]\PDáRFL QDSL
FLRZHM V]F]HOLQ\
powietrznej
PL G]\VW\NRZHM /LQLD D Z\ND]XMH UHGXNFM Z\WU]\PDáRFL QDSL FLRZHM
V]F]HOLQ\ XQLHPR*OLZLDMF V\QFKURQLF]QH áF]HQLH 3UG ]DF]QLH Sá\Qü ± Z HIHNFLH
19
]DLQLFMRZDQHJRZ\áDGRZDQLDáXNRZHJRZyZF]DVJG\OLQLDDSU]HWQLHVL
]SU]HELHJLHP
u(t).
: SU]\SDGNX OLQLL E Z\WU]\PDáRü QDSL FLRZD 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]HQDSL FLD1DU\VXQNXSU]HGVWDZLRQRWDN*HOLQLHFLG
GRW\F]FHJUDQLF]Q\FKSU]\SDGNyZRSy(QLHQLDLZ\SU]HG]HQLDSU]HMFLDQDSL FLDSU]H]]HUR
.
1ms
±
:LGDüZ\UD(QLH*HNRU]\VWQLHMV]HZDUXQNLZ\VW SXMSU]\RSy(QLRQ\P]DáF]HQLX
FR SRZRGXMH Z SUDNW\FH ]DPLHU]RQH RSy(QLDQLH ]DáF]HQLD Z]JO GHP SU]HMFLD QDSL FLD
SU]H]]HURZJ>@RSy(QLHQLHWRZ\QRVLRNRáRms).
5\V:\WU]\PDáRüQDSL FLRZDV]F]HOLQ\PL G]\VW\NRZHMSRGF]DVV\QFKURQLF]QHJRáF]HQLDEDWHULL
REMDQLHQLDZWHNFLH
:SUDNW\FHPR*OLZHMHVWRVLJQL FLHSUHF\]MLáF]HQLD
5
,
0
±
PVZRNyáSU]HMFLDQDSL FLD
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]HSL ü 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>@1DSL FLDLSUG\ID]RZHGODQLH
synchronic
]QHJRáF]HQLHSRMHG\QF]HMbaterii
kondensatorów
5\V>@1DSL FLDLSUG\ID]RZHGOD
synchronicznego
áF]HQLHSRMHG\QF]HMEDWHULL
kondensatorów
2
:>@SRGDQRMDNRJUDQLF]QHZDUWRFLEá GXV\QFKURQL]DFMLáF]HQLDVSRZRGRZDQHJáyZQLHWHPSHUDWXUL
F]DVHPHNVSORDWDFMLZ\áF]QLNDRGGRPVZRNyáSU]HMFLDQDSL FLDSU]H]ZDUWRü]HURZ
3
:J>@WHQSR]LRPWROHUDQFMLJZDUDQWXMHRNRáRUHGXNFMLSUGXáF]HQLRZHJR
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]HSL ü L SU]HW *H WRZDU]\V]F\FK
]DáF]DQLXEDWHULL
%DWHULDSRáF]RQDZQLHX]LHPLRQJZLD]G
:SLHUZV]HMNROHMQRFL]DP\NDQHVVW\NLQDSL FLDPL G]\ID]RZHJRSU]\MHJRSU]HMFLX
SU]H]]HURDQDVW SQLH]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 QDSL FLD
.RQGHQVDWRU\LáF]QLNLPRJE\üSRáF]RQHZJZLD]G OXEZ WUyMNW MHGHQ ] W\U\VWRUyZ
áF]QLNDPR*HE\ü]DVWSLRQ\SU]H]GLRG PRJE\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 ]DPNQL W\ JG\ MHJR QDSL FLH SU]HFKRG]L SU]H] ZDUWRü
]HURZ 1D U\VXQNX ]DVWRVRZDQR QDVW
SXMF\ 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]E ID]RUD]OLF]E VWHURZDQ\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$±LQQHSRáF]HQLH
21
5\V>@0R*OLZHNRQILJXUDFMHVFKHPDWyZáF]HQLRZ\FKEDWHULLNRQGHQVDWRUyZ]DSRPRFHOHPHQWyZ
SyáSU]HZRGQLNRZ\FK
3U]HGVWDZLRQHNRQILJXUDFMHREZRGXPR*QDSRG]LHOLüQDWU]\JUXS\
, JUXSD ± REZyG XWZRU]RQ\ MHVW SU]H] WU]\ MHGQRID]RZH JDá ]LH : GZyFK SLHUZV]\FK
NRQILJXUDFMDFK :1$ 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
LQWHUDNFMLSRPL G]\WU]HPDJDá ]LDPL±MHGQRUyZQDQLHPR*HE\ü]DVWRVRZDQHGR
RSLVXSUDF\WU]HFKáF]QLNyZ
22
,,JUXSD±FKDUDNWHU\]XMHVL LVWQLHQLHPLQWHUDNFMLSRPL G]\WU]HPDáF]QLNDPL]DPNQL FLH
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 SRPL G]\ W\U\VWRUDPL ]DOH*\ RG
XVWDORQHJRVSDGNXQDSL FLDQDHOHPHQWDFKSyáSU]HZRGQLNRZ\FK'ODNRQILJXUDFML
8'$ W\U\VWRU\ QLH PRJ E\ü SRQRZQLH ]DáF]RQH ]DQLP QDSL FLH QD
NRQGHQVDWRUDFKQLH]PQLHMV]\VL SRQL*HMNU\W\F]Q\FKZDUWRFL
=DVDGQLF]D Uy*QLFD Z\VW SXMH SRPL G]\ 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 E G]LH VSHáQLRQD SR]RVWDMFH Z FKZLOL
]DQLNXSUGXQDSL FLDNRQGHQVDWRUyZVSUDZL*HQDSL FLHQDMHGQ\P]áF]QLNyZQLJG\QLH
RVLJQLH ZDUWRFL ]HURZHM XQLHPR*OLZLDMF W\P VDP\P MHJR ]DPNQL
FLH EH] SU]HSL
ü
i
SU]HW *H
.RQILJXUDFMHSU]HGVWDZLRQHQDU\VXQNXUy*QLVL SRPL G]\VREQLHW\ONRZ\PLDUHP
SUGRZ\PáF]QLNyZOHF]WDN*HRSy(QLHQLDPLZZ\áF]DQLXL]DáF]DQLXEDWHULLQDSL FLHP
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 QDSL FLD U
T
i U
C
) oraz
VNáDGRZ VWDá QDSL FLD 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(QLHQLHSRPL G]\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 QDSL FLD L SUG\ ]RVWDá\ Z\UD*RQH Z MHGQRVWNDFK Z]JO GQ\FK
RGQLHVLRQ\FK GR VNXWHF]QHM ZDUWRFL QDSL FLD PL G]\ID]RZHJR U L VNXWHF]QHM ZDUWRFL
SUGXOLQLRZHJRIRSy(QLHQLDVZ\UD*RQHMDNRXáDPNLRNUHVXSRGVWDZRZHJRT).
5\V6FKHPDWNRPSHQVDWRUDVWDW\F]QHJR]EDWHULDPLNRPSHQVDWRUyZ]DáF]DQ\PLáF]QLNDPLW\U\VWRURZ\PLTSC )
23
3.6.1. Konfiguracja W33AA (kompensator statyczny TSC)
: SU]\SDGNX NRPSHQVDWRUD 76& PL G]\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 ZL F 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\ PL G]\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]JO GQD F] VWRWOLZRü ZáDVQD ]DáF]DQHJR REZRGX
RGQLHVLRQDGRF] VWRWOLZRFLQDSL FLD]DVLODMFHJR
ω
.
B
C
=
ω
C
=DVDGQLF]\ ZSá\Z QD ZDUWRü QDSL ü 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]DQDSL FLH
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)
24
:DUXQHN SLHUZV]\ D R]QDF]D *H W\U\VWRU\ SRZLQQ\ E\ü ]DáF]DQH Z GRGDWQLP OXE
XMHPQ\PV]F]\FLHQDSL FLD]DVLODQLD
:DUXQHN GUXJL E R]QDF]D *H NRQGHQVDWRU ZLQLHQ E\ü XSU]HGQLR QDáDGRZDQ\
GR QDSL FLD
1
2
2
0
n
n
U
U
Sm
C
=
R WDNLHM VDPHM ELHJXQRZRFL MDN QDSL FLH ]DVLODQLD Z FKZLOL
]DáF]DQLD W\U\VWRUyZ 2EHFQRü LQGXNF\MQRFL Z REZRG]LH VSUDZLD *H NRQGHQVDWRU PXVL
E\ü QDáDGRZDQ\ GR QDSL FLD Z\*V]HJR RG DPSOLWXG\ QDSL FLD ]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]JO GXQD]DVWRVRZDQHW\U\VWRU\V]HUHJRZR]áF]QLNLHP
7PXVLE\ü]DZV]HSRáF]RQDQLHZLHONDLQGXNF\MQRüZFHOXRJUDQLF]HQLDSRFKRGQHMSUGX
(di/dt
:ZL NV]RFLSU]\SDGNyZZDUWRüWHMLQGXNF\MQRFLMHVWZL NV]DQL*Z\QLNDáRE\WR
]SRZ\*V]HJRNU\WHULXP3HáQLRQDERZLHPUyZQLH*URO
LQGXNF\MQRFLRGVWUDMDMFHMREZyG
szeregowy LC
RG KDUPRQLF]Q\FK Z\VW SXMF\FK Z QDSL FLX ]DVLODQLD LQGXNF\MQRü
SU]HFLZUH]RQDQVRZD 3U]\ SRPLQL FLX 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]JO GQLDMF ]PLDQ\ QDSL FLD ]DVLODQLD ZDUXQHN E E G]LH VSHáQLRQ\ MH*HOL
NRQGHQVDWRU QLH E G]LH UR]áDGRZDQ\ SRGF]DV VWDQyZ QLH SU]HZRG]HQLD áF]QLNyZ 7 OXE
MH*HOLZXNáDG]LHE GUHDOL]RZDQHMHJRGRáDGRZDQLDGRQDSL FLDUyZQHJR
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 QDSL FLRZHJR 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]JO GX QD ZDUWRü F] VWRWOLZRFL
25
Z]JO GQHMn'ODND*GHMZDUWRFL
Sm
C
U
U
〈
0
]DáF]DQLH]JRGQLH]ZDUXQNLHPDGDMH]DZV]H
SHZQZDUWRüVNáDGRZHMRVF\ODF\MQHM
*G\ QDSL FLRZ\ ZDUXQHN SRF]WNRZ\
0
C
U
MHVW UyZQ\ DPSOLWXG]LH QDSL FLD VLHFL
]DVLODMFHM
Sm
U
ZyZF]DV SU]\ ]DáF]DQLX W\U\VWRUyZ Z V]F]\FLH QDSL FLD DPSOLWXGD
VNáDGRZHMRVF\ODF\MQHM
.
osc
I
PDZDUWRü
n
X
X
I
I
C
L
m
osc
1
.
=
=
(6)
,P ZL NV]D E G]LH ZDUWRü UHDNWDQFML
L
X
W\P ZL NV]D E G]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]DVRZHSUGXLQDSL FLD
Z]DOH*QRFLRGZ]DMHPQHMUHODFMLQDSL FLRZHJRZDUXQNXSRF]WNRZHJRLDPSOLWXG\QDSL FLD
]DVLODMFHJR
0
≈
L
X
).
5\V6\QFKURQLF]QHáF]HQLHEDWHULLNRQGHQVDWRUyZVWRVRZDQHZNRPSHQVDWRUDFK76&U
C0
±QDSL FLRZ\
ZDUXQHNSRF]WNRZ\NRQGHQVDWRUD
26
5\VXQHN E SU]HGVWDZLD SURFHV ]DáF]DQLD ZHGáXJ ZDUXQNX D W]Q JG\ QDSL FLH
]DVLODQLDPDSR]LRPQDSL FLDNRQGHQVDWRUDSU]HGRVLJQL FLHPVZHMZDUWRFLPDNV\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\
QDSL FLH RVLJD ZDUWRü PDNV\PDOQ NWyUD MHVW PQLHMV]D RG QDSL FLRZHJR 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*QDMHVWZL F]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\FKQDS GyZOXELQQHJRVSU] 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\FKQDS GyZSRGZ\*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
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 QDSL FLD
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\FKQLVNLHJRQDSL FLD3ROLWHFKQLND%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