Algoritma Aliran Daya dengan Metode Back
ISSN: 2085-6350
Yogyakarta, 27 Juli 2017
CITEE 2017
$OJRULWPD$OLUDQ'D\DGHQJDQ0HWRGHBackward/Forward SweepSDGD
6LVWHP'LVWULEXVL5DGLDO
'LDQ%XGKL6DQWRVR6DUML\D6DVRQJNR3UDPRQR+DGL
'HSDUWHPHQ7HNQLN(OHNWURGDQ7HNQRORJL,QIRUPDVL)DNXOWDV7HNQLN8QLYHUVLWDV*DGMDK0DGD
-OQ*UDILND@3DGDbackwardsweepGLPXODL
78
GDULWLWLNXMXQJWHUMDXKGDULMDULQJDQDUXVEHEDQSDGDWLWLNEHEDQ
2OHK NDUHQD LWX DUXV \DQJ PHQJDOLU SDGD VDOXUDQ GLKLWXQJ
PHQXUXWDVXPVLDWDXKDVLONDONXODVLGDULWHJDQJDQSDGDLWHUDVL
VHEHOXPQ\D 6HWHODK PHQJKLWXQJ DUXV \DQJ PHQJDOLU SDGD
VDOXUDQSDGDforwardsweepGLPXODLGDULWLWLNVXPEHUWHJDQJDQ
GDULPDVLQJPDVLQJWLWLNEXVGLSHUEDUXL6HWHODKforwardsweep
NRPSHQVDVL DUXV LQMHNVL GLKLWXQJ /DOX NULWHULD NRQYHUJHQVL
GLXML $GD EHUEDJDL PDFDP NULWHULD NRQYHUJHQVL \DQJ
GLVHVXDLNDQGHQJDQWLWLNWHJDQJDQEHEDQDWDXDUXVVDOXUDQGDQ
PDVXNDQGD\DNHMDULQJDQ
%HUGDVDUNDQSHQMHODVDQGLDWDVGLNHPEDQJNDQPHWRGHDOLUDQ
GD\D GLVWULEXVL XQWXN MDULQJDQ GHQJDQ MXPODK VXPEHU \DQJ
EDQ\DN
B. Backward Sweep
3URVHGXU GDUL SHQ\HOHVDLDQ DOLUDQ GD\D GLPXODL GHQJDQ
backwardsweep3DGDLWHUDVLSHUWDPDWHJDQJDQGDULVHPXDWLWLN
GLDVXPVLNDQ VDPD GHQJDQ WHJDQJDQ SDGD VXPEHU XWDPD -LND
DGD EHEHUDSD VXPEHU SDGD MDULQJDQ DUXV LQMHNVL NRPSHQVDVL
SDGDVXPEHUWHUVHEXWEHUQLODLQROSDGDLWHUDVLSHUWDPD'LVLVL
ODLQ WHJDQJDQ SDGD PDVLQJPDVLQJ WLWLN GDQ DUXV LQMHNVL
NRPSHQVDVLGLKLWXQJSDGDLWHUDVLVHEHOXPQ\D.HWLNDWHJDQJDQ
SDGD PDVLQJPDVLQJ WLWLN GDQ DUXV LQMHNVL NRPSHQVDVL VXGDK
GLNHWDKXLDUXVEHEDQGDSDWGLFDULGHQJDQSHUVDPDDQEHULNXW
ାொ כ
ܫௗ ൌ ቂ
GHQJDQ
ቃ
ܫௗ $UXVEHEDQSDGDWLWLN݅
ܲ .HEXWXKDQGD\DDNWLISDGDWLWLN݅
ܳ .HEXWXKDQGD\DUHDNWLISDGDWLWLN݅
ܸ
7HJDQJDQSDGDWLWLN݅
C. Forward Sweep
3DGDforwardsweepGLPXODLGDULWLWLNVXPEHUXWDPDGLPDQD
QLODLWHJDQJDQQ\DGLNHWDKXLLPSHGDQVLGDQDUXV\DQJPHQJDOLU
SDGD PDVLQJPDVLQJ VDOXUDQVXGDK GLNHWDKXL VHPXDWHJDQJDQ
WLWLNGLSHUEDUXLPHQJDEDLNDQVXPEHUODLQQ\DMLNDDGD
ܸ ൌ ܸ െ ܼ ܫ
'LPDQD
ܸ
7HJDQJDQSDGDWLWLN݅
݅ ൌ ܫǡ ǥ ǡ ܰ
ܸ 7HJDQJDQSDGDDWDVGDULWLWLN݅
Departemen Teknik Elektro dan Teknologi Informasi, FT UGM
CITEE 2017
ܼ
Yogyakarta, 27 Juli 2017
,PSHGDQVLVDOXUDQ݅
ISSN: 2085-6350
F. Matriks Branch Current to Bus Voltage (BCBV)
+XEXQJDQ DQWDUD DUXV FDEDQJ GDQ WHJDQJDQ EXV GDSDW
GHNVSUHVLNDQVHEDJDLEHULNXW
ܫ $UXV\DQJPHQJDOLUSDGDVDOXUDQ݅
D. Pemodelan Struktur Jaringan
%HUGDVDUNDQFRQWRKVLVWHPGLVWULEXVLUDGLDOSDGD)LJGDSDW
GLEXDWIRUPDVLGHQJDQPHQJJXQDNDQPDWULNV%%,&%&%9GDQ
'/)>@>@>@
ܸଶ ൌ ܸଵ െ ܤଵ ܼଵଶ
ܸଷ ൌ ܸଶ െ ܤଶ ܼଶଷ
ܸସ ൌ ܸଷ െ ܤଷ ܼଷସ
ܸହ ൌ ܸସ െ ܤସ ܼସହ
ܸ ൌ ܸଷ െ ܤହ ܼଷ
'HQJDQPHQVXEVWLWXVLSHUVDPDDQ GDQ NHSDGD
PDNDGLGDSDWNDQWHJDQJDQSDGDEXVVHEDJDLEHULNXW
ܸସ ൌ ܸଵ െ ܤଵ ܼଵଶ െ ܤଶ ܼଶଷ െ ܤଷ ܼଷସ
6DPD VHSHUWL QLODL WHJDQJDQ SDGD EXV ODLQ GDSDW GLWXOLV
VHEDJDLEHULNXW
ܸଷ ൌ ܸଵ െ ܤଵ ܼଵଶ െ ܤଶ ܼଶଷ
ܸହ ൌ ܸଵ െ ܤଵ ܼଵଶ െ ܤଶ ܼଶଷ െ ܤଷ ܼଷସ െ ܤସ ܼସହ
ܸ ൌ ܸଵ െ ܤଵ ܼଵଶ െ ܤଶ ܼଶଷ െ ܤଷ ܼଷସ െ ܤସ ܼସହ െ ܤହ ܼଷ
3HUVDPDDQ GDSDWGLVXVXQVHEDJDL
EHULNXW
)LJ 6DPSHO6LVWHP'LVWULEXVL5DGLDOEXV
E. Matriks Bus Injection to Branch Current (BBIC)
8QWXNVLVWHPGLVWULEXVLSDGDEXVNHEHEDQNRPSOHNVGDSDW
GLHNVSUHVLNDQ GHQJDQ SHUVDPDDQ GDQ QLODL HNXLYDOHQ DUXV
LQMHNVL \DQJ EHUVDQJNXWDQ GDSDW GLHNVSUHNVLNDQ GHQJDQ
SHUVDPDDQ
ܵ ൌ ሺܲ ݆ܳ ሻ ݅ ൌ ͳǡ ʹǡ ǥ ǡ ܰ
ܫ ൌ ሺܵ Ȁܸ ሻ כ
9HNWRULQMHNVLDUXVGDULVDPSHOVLVWHPGLDWDVGDSDWGLEXDW
SDGD7DEOH,VHEDJDLEHULNXW
7$%/(,
.(7(5$1*$19(.725$586,1-(.6,
%XV1R
$UXVLQMHNVL
ܫଶ
ܫଷ
ܫସ
ܫହ
ܫ
8QWXNVLVWHPSDGD)LJGLDSOLNDVLNDQKirchhoff’s Current
Law .&/ DUXVFDEDQJGDSDWGLHNVSUHVLNDQGHQJDQQLODLDUXV
LQMHNVLHNXLYDOHQVHEDJDLEHULNXW
ܼଵଶ ͲͲͲͲ ܤଵ
ܸଶ
ܸଵ
ې ܤۍ ې ͲͲͲ ܼ ܼ ۍ ې ܸۍ ې ܸۍ
ଷ
ଵ
ێ ۑଶۑ
ێ ۑ ێ ۑ ێଵଶ ଶଷ
ܸێଵ ۑെ ܸێସ ۑൌ ܼ ێଵଶ ܼଶଷ ܼଷସ ͲͲ ܤێ ۑଷ ۑ
ܸێଵ ܸێ ۑହ ܼ ێ ۑଵଶ ܼଶଷ ܼଷସ ܼସହ Ͳ ܤێ ۑସ ۑ
ܸۏଵ ܼۏ ے ܸۏ ےଵଶ ܼଶଷ ͲͲܼଷ ܤۏ ےହ ے
ሾοܸሿ ൌ ሾܸܤܥܤሿሾܤሿ
6HNDUDQJVXEVWLWXVLSHUVDPDDQ NHGDODP GDQKDVLO
SHUVDPDDQQ\DGDSDWGLHNVSUHVLNDQVHEDJDLEHULNXW
ሾοܸሿ ൌ ሾܸܤܥܤሿሾܥܤܫܤሿሾܫሿ
ሾοܸሿ ൌ ሾܨܮܦሿሾܫሿ
'HQJDQ'/)DGDODKPDWULNVDistribution Load Flow\DQJ
GLWXQMXNDQGHQJDQPDWULNVEHULNXW>@
ܼଵଶ
ܼۍ
ێଵଶ
ܼێଵଶ
ܼێଵଶ
ܼۏଵଶ
ܼଵଶ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ
ܼଵଶ
ܼଵଶ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ ܼଷସ ܼଵଶ ܼଶଷ ܼଷସ
ܼଵଶ ܼଶଷ ܼଷସ ܼଵଶ ܼଶଷ ܼଷସ ܼସହ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ
ܼଵଶ
ܼଵଶ ܼଶଷ ې
ۑ
ܼଵଶ ܼଶଷ ۑ
ܼଵଶ ܼଶଷ ۑ
ܼଵଶ ܼଶଷ ܼଷ ے
/DQJNDKODQJNDK SHQ\HOHVDLDQ DOLUDQ GD\D PHQJJXQDNDQ
PHWRGHbackward and forwardGLMHODVNDQSDGD)LJ
ܤଵ ൌ ܫଶ ܫଷ ܫସ ܫହ ܫ
ܤଶ ൌ ܫଷ ܫସ ܫହ ܫ
ܤଷ ൌ ܫସ ܫହ
ܤସ ൌ ܫହ
ܤହ ൌ ܫ
ܤଵ
ͳͳͳͳͳ ܫଶ
ۍ ې ܤۍ
ې ܫۍ ې
ێଶ ێ ۑ ͳͳͳͳͲ ێ ۑଷ ۑ
ܤێଷ ۑൌ ܫێ ۑ ͲͳͳͲͲ ێସ ۑ
ܤێସ ܫێ ۑ ͲͳͲͲͲ ێ ۑହ ۑ
ܤۏହ ے ܫۏ ےͳͲͲͲͲۏ ے
3HUVDPDDQDUXVFDEDQJGLDWDVGDSDWGLVXVXQGHQJDQEHQWXN
XPXPVHEDJDLEHULNXW
ሾܤሿ ൌ ሾܥܤܫܤሿሾܫሿ
Departemen Teknik Elektro dan Teknologi Informasi, FT UGM
79
ISSN: 2085-6350
Yogyakarta, 27 Juli 2017
7$%/(,,
)LJ 'LDJUDP$OLU0HWRGH3HQ\HOHVDLDQ$OLUDQ'D\DGHQJDQBackward and
forward sweep
,,, +$6,/'$16,08/$6,
CITEE 2017
'$7$6$/85$1'$1%(%$16,67(07(6,(((%86
%UDQFK
1R
)URP
EXV
7R
EXV
;
/RDGDWWREXV
3
4
N:
N:
0HWRGH \DQJ GLXVXONDQ WHODK GLXML SDGD VLVWHP GLVWULEXVL
UDGLDO,(((EXV\DQJGLWXQMXNNDQSDGD)LJPHQJJXQDNDQ
0$7/$% 9HUVLRQ 5D GHQJDQ VSHVLILNDVL
ODSWRS3URFHVVRU,QWHO 5 &RUH 70 L8&38#*K]
&38V 5$0 *% GDQ VLVWHP RSHUDVL :LQGRZV
(GXFDWLRQELW (QJOLVK
1LODLDUXVGDQGURSWHJDQJDQ\DQJPHQJDOLUGLVHWLDSFDEDQJ
DNDQGLKLWXQJPHQJJXQDNDQHOHPHQGDULPDWULN.'HQJDQGDWD
VDOXUDQ GDUL WHV VLVWHP ,((( EXV SDGD 7DEOH ,, 7HJDQJDQ
GDVDUQ\DDGDODKN9GDQEDVLV09$DGDODK7ROHUDQVL
DGDODKSX+DVLOGLWXQMXNNDQSDGD7DEOH,,,GDQ7DEOH
,9%HVDUQ\DWHJDQJDQSDGDSXGDQVXGXWIDVDGDODPGHUDMDW
SDGDVHWLDSEXVGLWXQMXNNDQSDGD7DEOH,,,GDQUXJLUXJLGD\D
DNWLI GDQ UHDNWLI SDGD PDVLQJPDVLQJ FDEDQJ SDGD N: GDQ
N9$5 PDVLQJPDVLQJ GLWXQMXNNDQ SDGD 7DEOH ,9 3URILO
WHJDQJDQGDODPVLVWHPGLWXQMXNNDQSDGD)LJ
7$%/(,,,
0$*1,78'7(*$1*$1'$168'873+$6$
%XV
1XPEHU
)LJ 'LDJUDP6DWX*DULV6LVWHP7HV,(((EXV
'HQJDQGDWDVDOXUDQGDQEHEDQ\DQJWHUKXEXQJGLEXVWXMXDQ
\DQJGLWXQMXNDQSDGD7DEOH,,VHEDJDLEHULNXW> @>@>@>@
80
5
9ROWDJH
0DJQLWXGH
3KDVH$QJOH
GHJUHH
Departemen Teknik Elektro dan Teknologi Informasi, FT UGM
CITEE 2017
Yogyakarta, 27 Juli 2017
(
ISSN: 2085-6350
)LJ 3URILO7HJDQJDQ6LVWHP7HV,(((EXV
7$%/(,9
58*,58*,'$@ $'5-%'DUMLDQG03DQG\D³%DFNZDUG)RUZDUG6ZHHS/RDG
)ORZ$OJRULWKPIRU5DGLDO'LVWULEXWLRQ6\VWHP´YROQRSS ±
>@ $KPDG 0HPDULSRXU ³3RZHU )ORZ LQ 'LVWULEXWLRQ 6\VWHP ZLWK
&RQVLGHUDWLRQRI'LVWULEXWHG*HQHUDWLRQ´
>@ 5:1RYLDOLILDK$6RHSULMDQWR56:LERZRDQG$.6'LVWULEXVL
³$OJRULWPD $OLUDQ 'D\D XQWXN 6LVWHP 'LVWULEXVL 5DGLDO GHQJDQ %HEDQ
6HQVLWLI7HJDQJDQ´YROQRSS± %,%&,QGRQHVLD
CITEE 2017
>@ 6KDWHUL + 6 ³/RDG )ORZ 0HWKRG IRU 'LVWULEXWLRQ 1HWZRUNV ZLWK
0XOWLSOH6RXUFHV1RGHV´,((((OHFWULFDO3RZHU (QHUJ\&RQIHUHQFH
>@ 7HQJ ³ -+ $ 'LUHFW $SSURDFK IRU 'LVWULEXWLRQ 6\VWHP /RDG )ORZ
6ROXWLRQV´,(((7UDQVDFWLRQVRQ3RZHU'HOLYHU\9RO1R
>@ $ * %KXWDG 0 6WDWH ( %RDUG $ .KDSDUGH DQG 6 9 .XONDUQL
³7KUHHSKDVH/RDG)ORZ0HWKRGVIRU5DGLDO'LVWULEXWLRQ1HWZRUNV´YRO
QRSS±
>@ 5:1RYLDOLILDK$6RHSULMDQWR56:LERZRDQG$.6'LVWULEXVL
³$OJRULWPD $OLUDQ 'D\D XQWXN 6LVWHP 'LVWULEXVL 5DGLDO GHQJDQ %HEDQ
6HQVLWLI7HJDQJDQ´YROQRSS±
>@ 3UDNDVK.0³7RSRORJLFDODQG3ULPLWLYH,PSHGDQFHEDVHG/RDG)ORZ
0HWKRG IRU 5DGLDO DQG :DHNO\ 0HVKHG 'LVWULEXWLRQ 6\VWHPV´ ,UDQLDQ
-RXUQDORI(OHFWULFDODQG&RPSXWHU(QJLQHHULQJ9RO1R
> @ ($I]DODQ0$7DJKLNKDQLDQG06HGLJKL]DGHK³2SWLPDO3ODFHPHQW
DQG6L]LQJRI'*LQ5DGLDO'LVWULEXWLRQ1HWZRUNV8VLQJ6)/$´YRO
QRSS±
>@ %DUDQ0(³1HWZRUN5HFRQILJXUDWLRQLQ'LVWULEXWLRQ6\VWHPVIRU/RVV
5HGXFWLRQDQGORDG%DODQFLQJ´,(((7UDQFVDFWLRQVRQ3RZHU'HOLYHU\
9RO1R
>@ $ :D]LU DQG 1 $UEDE ³$QDO\VLV DQG 2SWLPL]DWLRQ RI ,((( %XV
5DGLDO'LVWULEXWHG6\VWHP8VLQJ2SWLPL]DWLRQ$OJRULWKP´YROQR
>@ .6.XPDUDQG7-D\DEDUDWKL³(OHFWULFDO3RZHUDQG(QHUJ\6\VWHPV
3RZHUV\VWHPUHFRQILJXUDWLRQDQGORVVPLQLPL]DWLRQIRUDQGLVWULEXWLRQ
V\VWHPV XVLQJ EDFWHULDO IRUDJLQJ RSWLPL]DWLRQ DOJRULWKP´ ,QW- (OHFWU
3RZHU(QHUJ\6\VWYROQRSS±
82
Departemen Teknik Elektro dan Teknologi Informasi, FT UGM
Yogyakarta, 27 Juli 2017
CITEE 2017
$OJRULWPD$OLUDQ'D\DGHQJDQ0HWRGHBackward/Forward SweepSDGD
6LVWHP'LVWULEXVL5DGLDO
'LDQ%XGKL6DQWRVR6DUML\D6DVRQJNR3UDPRQR+DGL
'HSDUWHPHQ7HNQLN(OHNWURGDQ7HNQRORJL,QIRUPDVL)DNXOWDV7HNQLN8QLYHUVLWDV*DGMDK0DGD
-OQ*UDILND@3DGDbackwardsweepGLPXODL
78
GDULWLWLNXMXQJWHUMDXKGDULMDULQJDQDUXVEHEDQSDGDWLWLNEHEDQ
2OHK NDUHQD LWX DUXV \DQJ PHQJDOLU SDGD VDOXUDQ GLKLWXQJ
PHQXUXWDVXPVLDWDXKDVLONDONXODVLGDULWHJDQJDQSDGDLWHUDVL
VHEHOXPQ\D 6HWHODK PHQJKLWXQJ DUXV \DQJ PHQJDOLU SDGD
VDOXUDQSDGDforwardsweepGLPXODLGDULWLWLNVXPEHUWHJDQJDQ
GDULPDVLQJPDVLQJWLWLNEXVGLSHUEDUXL6HWHODKforwardsweep
NRPSHQVDVL DUXV LQMHNVL GLKLWXQJ /DOX NULWHULD NRQYHUJHQVL
GLXML $GD EHUEDJDL PDFDP NULWHULD NRQYHUJHQVL \DQJ
GLVHVXDLNDQGHQJDQWLWLNWHJDQJDQEHEDQDWDXDUXVVDOXUDQGDQ
PDVXNDQGD\DNHMDULQJDQ
%HUGDVDUNDQSHQMHODVDQGLDWDVGLNHPEDQJNDQPHWRGHDOLUDQ
GD\D GLVWULEXVL XQWXN MDULQJDQ GHQJDQ MXPODK VXPEHU \DQJ
EDQ\DN
B. Backward Sweep
3URVHGXU GDUL SHQ\HOHVDLDQ DOLUDQ GD\D GLPXODL GHQJDQ
backwardsweep3DGDLWHUDVLSHUWDPDWHJDQJDQGDULVHPXDWLWLN
GLDVXPVLNDQ VDPD GHQJDQ WHJDQJDQ SDGD VXPEHU XWDPD -LND
DGD EHEHUDSD VXPEHU SDGD MDULQJDQ DUXV LQMHNVL NRPSHQVDVL
SDGDVXPEHUWHUVHEXWEHUQLODLQROSDGDLWHUDVLSHUWDPD'LVLVL
ODLQ WHJDQJDQ SDGD PDVLQJPDVLQJ WLWLN GDQ DUXV LQMHNVL
NRPSHQVDVLGLKLWXQJSDGDLWHUDVLVHEHOXPQ\D.HWLNDWHJDQJDQ
SDGD PDVLQJPDVLQJ WLWLN GDQ DUXV LQMHNVL NRPSHQVDVL VXGDK
GLNHWDKXLDUXVEHEDQGDSDWGLFDULGHQJDQSHUVDPDDQEHULNXW
ାொ כ
ܫௗ ൌ ቂ
GHQJDQ
ቃ
ܫௗ $UXVEHEDQSDGDWLWLN݅
ܲ .HEXWXKDQGD\DDNWLISDGDWLWLN݅
ܳ .HEXWXKDQGD\DUHDNWLISDGDWLWLN݅
ܸ
7HJDQJDQSDGDWLWLN݅
C. Forward Sweep
3DGDforwardsweepGLPXODLGDULWLWLNVXPEHUXWDPDGLPDQD
QLODLWHJDQJDQQ\DGLNHWDKXLLPSHGDQVLGDQDUXV\DQJPHQJDOLU
SDGD PDVLQJPDVLQJ VDOXUDQVXGDK GLNHWDKXL VHPXDWHJDQJDQ
WLWLNGLSHUEDUXLPHQJDEDLNDQVXPEHUODLQQ\DMLNDDGD
ܸ ൌ ܸ െ ܼ ܫ
'LPDQD
ܸ
7HJDQJDQSDGDWLWLN݅
݅ ൌ ܫǡ ǥ ǡ ܰ
ܸ 7HJDQJDQSDGDDWDVGDULWLWLN݅
Departemen Teknik Elektro dan Teknologi Informasi, FT UGM
CITEE 2017
ܼ
Yogyakarta, 27 Juli 2017
,PSHGDQVLVDOXUDQ݅
ISSN: 2085-6350
F. Matriks Branch Current to Bus Voltage (BCBV)
+XEXQJDQ DQWDUD DUXV FDEDQJ GDQ WHJDQJDQ EXV GDSDW
GHNVSUHVLNDQVHEDJDLEHULNXW
ܫ $UXV\DQJPHQJDOLUSDGDVDOXUDQ݅
D. Pemodelan Struktur Jaringan
%HUGDVDUNDQFRQWRKVLVWHPGLVWULEXVLUDGLDOSDGD)LJGDSDW
GLEXDWIRUPDVLGHQJDQPHQJJXQDNDQPDWULNV%%,&%&%9GDQ
'/)>@>@>@
ܸଶ ൌ ܸଵ െ ܤଵ ܼଵଶ
ܸଷ ൌ ܸଶ െ ܤଶ ܼଶଷ
ܸସ ൌ ܸଷ െ ܤଷ ܼଷସ
ܸହ ൌ ܸସ െ ܤସ ܼସହ
ܸ ൌ ܸଷ െ ܤହ ܼଷ
'HQJDQPHQVXEVWLWXVLSHUVDPDDQ GDQ NHSDGD
PDNDGLGDSDWNDQWHJDQJDQSDGDEXVVHEDJDLEHULNXW
ܸସ ൌ ܸଵ െ ܤଵ ܼଵଶ െ ܤଶ ܼଶଷ െ ܤଷ ܼଷସ
6DPD VHSHUWL QLODL WHJDQJDQ SDGD EXV ODLQ GDSDW GLWXOLV
VHEDJDLEHULNXW
ܸଷ ൌ ܸଵ െ ܤଵ ܼଵଶ െ ܤଶ ܼଶଷ
ܸହ ൌ ܸଵ െ ܤଵ ܼଵଶ െ ܤଶ ܼଶଷ െ ܤଷ ܼଷସ െ ܤସ ܼସହ
ܸ ൌ ܸଵ െ ܤଵ ܼଵଶ െ ܤଶ ܼଶଷ െ ܤଷ ܼଷସ െ ܤସ ܼସହ െ ܤହ ܼଷ
3HUVDPDDQ GDSDWGLVXVXQVHEDJDL
EHULNXW
)LJ 6DPSHO6LVWHP'LVWULEXVL5DGLDOEXV
E. Matriks Bus Injection to Branch Current (BBIC)
8QWXNVLVWHPGLVWULEXVLSDGDEXVNHEHEDQNRPSOHNVGDSDW
GLHNVSUHVLNDQ GHQJDQ SHUVDPDDQ GDQ QLODL HNXLYDOHQ DUXV
LQMHNVL \DQJ EHUVDQJNXWDQ GDSDW GLHNVSUHNVLNDQ GHQJDQ
SHUVDPDDQ
ܵ ൌ ሺܲ ݆ܳ ሻ ݅ ൌ ͳǡ ʹǡ ǥ ǡ ܰ
ܫ ൌ ሺܵ Ȁܸ ሻ כ
9HNWRULQMHNVLDUXVGDULVDPSHOVLVWHPGLDWDVGDSDWGLEXDW
SDGD7DEOH,VHEDJDLEHULNXW
7$%/(,
.(7(5$1*$19(.725$586,1-(.6,
%XV1R
$UXVLQMHNVL
ܫଶ
ܫଷ
ܫସ
ܫହ
ܫ
8QWXNVLVWHPSDGD)LJGLDSOLNDVLNDQKirchhoff’s Current
Law .&/ DUXVFDEDQJGDSDWGLHNVSUHVLNDQGHQJDQQLODLDUXV
LQMHNVLHNXLYDOHQVHEDJDLEHULNXW
ܼଵଶ ͲͲͲͲ ܤଵ
ܸଶ
ܸଵ
ې ܤۍ ې ͲͲͲ ܼ ܼ ۍ ې ܸۍ ې ܸۍ
ଷ
ଵ
ێ ۑଶۑ
ێ ۑ ێ ۑ ێଵଶ ଶଷ
ܸێଵ ۑെ ܸێସ ۑൌ ܼ ێଵଶ ܼଶଷ ܼଷସ ͲͲ ܤێ ۑଷ ۑ
ܸێଵ ܸێ ۑହ ܼ ێ ۑଵଶ ܼଶଷ ܼଷସ ܼସହ Ͳ ܤێ ۑସ ۑ
ܸۏଵ ܼۏ ے ܸۏ ےଵଶ ܼଶଷ ͲͲܼଷ ܤۏ ےହ ے
ሾοܸሿ ൌ ሾܸܤܥܤሿሾܤሿ
6HNDUDQJVXEVWLWXVLSHUVDPDDQ NHGDODP GDQKDVLO
SHUVDPDDQQ\DGDSDWGLHNVSUHVLNDQVHEDJDLEHULNXW
ሾοܸሿ ൌ ሾܸܤܥܤሿሾܥܤܫܤሿሾܫሿ
ሾοܸሿ ൌ ሾܨܮܦሿሾܫሿ
'HQJDQ'/)DGDODKPDWULNVDistribution Load Flow\DQJ
GLWXQMXNDQGHQJDQPDWULNVEHULNXW>@
ܼଵଶ
ܼۍ
ێଵଶ
ܼێଵଶ
ܼێଵଶ
ܼۏଵଶ
ܼଵଶ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ
ܼଵଶ
ܼଵଶ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ ܼଷସ ܼଵଶ ܼଶଷ ܼଷସ
ܼଵଶ ܼଶଷ ܼଷସ ܼଵଶ ܼଶଷ ܼଷସ ܼସହ
ܼଵଶ ܼଶଷ
ܼଵଶ ܼଶଷ
ܼଵଶ
ܼଵଶ ܼଶଷ ې
ۑ
ܼଵଶ ܼଶଷ ۑ
ܼଵଶ ܼଶଷ ۑ
ܼଵଶ ܼଶଷ ܼଷ ے
/DQJNDKODQJNDK SHQ\HOHVDLDQ DOLUDQ GD\D PHQJJXQDNDQ
PHWRGHbackward and forwardGLMHODVNDQSDGD)LJ
ܤଵ ൌ ܫଶ ܫଷ ܫସ ܫହ ܫ
ܤଶ ൌ ܫଷ ܫସ ܫହ ܫ
ܤଷ ൌ ܫସ ܫହ
ܤସ ൌ ܫହ
ܤହ ൌ ܫ
ܤଵ
ͳͳͳͳͳ ܫଶ
ۍ ې ܤۍ
ې ܫۍ ې
ێଶ ێ ۑ ͳͳͳͳͲ ێ ۑଷ ۑ
ܤێଷ ۑൌ ܫێ ۑ ͲͳͳͲͲ ێସ ۑ
ܤێସ ܫێ ۑ ͲͳͲͲͲ ێ ۑହ ۑ
ܤۏହ ے ܫۏ ےͳͲͲͲͲۏ ے
3HUVDPDDQDUXVFDEDQJGLDWDVGDSDWGLVXVXQGHQJDQEHQWXN
XPXPVHEDJDLEHULNXW
ሾܤሿ ൌ ሾܥܤܫܤሿሾܫሿ
Departemen Teknik Elektro dan Teknologi Informasi, FT UGM
79
ISSN: 2085-6350
Yogyakarta, 27 Juli 2017
7$%/(,,
)LJ 'LDJUDP$OLU0HWRGH3HQ\HOHVDLDQ$OLUDQ'D\DGHQJDQBackward and
forward sweep
,,, +$6,/'$16,08/$6,
CITEE 2017
'$7$6$/85$1'$1%(%$16,67(07(6,(((%86
%UDQFK
1R
)URP
EXV
7R
EXV
;
/RDGDWWREXV
3
4
N:
N:
0HWRGH \DQJ GLXVXONDQ WHODK GLXML SDGD VLVWHP GLVWULEXVL
UDGLDO,(((EXV\DQJGLWXQMXNNDQSDGD)LJPHQJJXQDNDQ
0$7/$% 9HUVLRQ 5D GHQJDQ VSHVLILNDVL
ODSWRS3URFHVVRU,QWHO 5 &RUH 70 L8&38#*K]
&38V 5$0 *% GDQ VLVWHP RSHUDVL :LQGRZV
(GXFDWLRQELW (QJOLVK
1LODLDUXVGDQGURSWHJDQJDQ\DQJPHQJDOLUGLVHWLDSFDEDQJ
DNDQGLKLWXQJPHQJJXQDNDQHOHPHQGDULPDWULN.'HQJDQGDWD
VDOXUDQ GDUL WHV VLVWHP ,((( EXV SDGD 7DEOH ,, 7HJDQJDQ
GDVDUQ\DDGDODKN9GDQEDVLV09$DGDODK7ROHUDQVL
DGDODKSX+DVLOGLWXQMXNNDQSDGD7DEOH,,,GDQ7DEOH
,9%HVDUQ\DWHJDQJDQSDGDSXGDQVXGXWIDVDGDODPGHUDMDW
SDGDVHWLDSEXVGLWXQMXNNDQSDGD7DEOH,,,GDQUXJLUXJLGD\D
DNWLI GDQ UHDNWLI SDGD PDVLQJPDVLQJ FDEDQJ SDGD N: GDQ
N9$5 PDVLQJPDVLQJ GLWXQMXNNDQ SDGD 7DEOH ,9 3URILO
WHJDQJDQGDODPVLVWHPGLWXQMXNNDQSDGD)LJ
7$%/(,,,
0$*1,78'7(*$1*$1'$168'873+$6$
%XV
1XPEHU
)LJ 'LDJUDP6DWX*DULV6LVWHP7HV,(((EXV
'HQJDQGDWDVDOXUDQGDQEHEDQ\DQJWHUKXEXQJGLEXVWXMXDQ
\DQJGLWXQMXNDQSDGD7DEOH,,VHEDJDLEHULNXW> @>@>@>@
80
5
9ROWDJH
0DJQLWXGH
3KDVH$QJOH
GHJUHH
Departemen Teknik Elektro dan Teknologi Informasi, FT UGM
CITEE 2017
Yogyakarta, 27 Juli 2017
(
ISSN: 2085-6350
)LJ 3URILO7HJDQJDQ6LVWHP7HV,(((EXV
7$%/(,9
58*,58*,'$@ $'5-%'DUMLDQG03DQG\D³%DFNZDUG)RUZDUG6ZHHS/RDG
)ORZ$OJRULWKPIRU5DGLDO'LVWULEXWLRQ6\VWHP´YROQRSS ±
>@ $KPDG 0HPDULSRXU ³3RZHU )ORZ LQ 'LVWULEXWLRQ 6\VWHP ZLWK
&RQVLGHUDWLRQRI'LVWULEXWHG*HQHUDWLRQ´
>@ 5:1RYLDOLILDK$6RHSULMDQWR56:LERZRDQG$.6'LVWULEXVL
³$OJRULWPD $OLUDQ 'D\D XQWXN 6LVWHP 'LVWULEXVL 5DGLDO GHQJDQ %HEDQ
6HQVLWLI7HJDQJDQ´YROQRSS± %,%&,QGRQHVLD
CITEE 2017
>@ 6KDWHUL + 6 ³/RDG )ORZ 0HWKRG IRU 'LVWULEXWLRQ 1HWZRUNV ZLWK
0XOWLSOH6RXUFHV1RGHV´,((((OHFWULFDO3RZHU (QHUJ\&RQIHUHQFH
>@ 7HQJ ³ -+ $ 'LUHFW $SSURDFK IRU 'LVWULEXWLRQ 6\VWHP /RDG )ORZ
6ROXWLRQV´,(((7UDQVDFWLRQVRQ3RZHU'HOLYHU\9RO1R
>@ $ * %KXWDG 0 6WDWH ( %RDUG $ .KDSDUGH DQG 6 9 .XONDUQL
³7KUHHSKDVH/RDG)ORZ0HWKRGVIRU5DGLDO'LVWULEXWLRQ1HWZRUNV´YRO
QRSS±
>@ 5:1RYLDOLILDK$6RHSULMDQWR56:LERZRDQG$.6'LVWULEXVL
³$OJRULWPD $OLUDQ 'D\D XQWXN 6LVWHP 'LVWULEXVL 5DGLDO GHQJDQ %HEDQ
6HQVLWLI7HJDQJDQ´YROQRSS±
>@ 3UDNDVK.0³7RSRORJLFDODQG3ULPLWLYH,PSHGDQFHEDVHG/RDG)ORZ
0HWKRG IRU 5DGLDO DQG :DHNO\ 0HVKHG 'LVWULEXWLRQ 6\VWHPV´ ,UDQLDQ
-RXUQDORI(OHFWULFDODQG&RPSXWHU(QJLQHHULQJ9RO1R
> @ ($I]DODQ0$7DJKLNKDQLDQG06HGLJKL]DGHK³2SWLPDO3ODFHPHQW
DQG6L]LQJRI'*LQ5DGLDO'LVWULEXWLRQ1HWZRUNV8VLQJ6)/$´YRO
QRSS±
>@ %DUDQ0(³1HWZRUN5HFRQILJXUDWLRQLQ'LVWULEXWLRQ6\VWHPVIRU/RVV
5HGXFWLRQDQGORDG%DODQFLQJ´,(((7UDQFVDFWLRQVRQ3RZHU'HOLYHU\
9RO1R
>@ $ :D]LU DQG 1 $UEDE ³$QDO\VLV DQG 2SWLPL]DWLRQ RI ,((( %XV
5DGLDO'LVWULEXWHG6\VWHP8VLQJ2SWLPL]DWLRQ$OJRULWKP´YROQR
>@ .6.XPDUDQG7-D\DEDUDWKL³(OHFWULFDO3RZHUDQG(QHUJ\6\VWHPV
3RZHUV\VWHPUHFRQILJXUDWLRQDQGORVVPLQLPL]DWLRQIRUDQGLVWULEXWLRQ
V\VWHPV XVLQJ EDFWHULDO IRUDJLQJ RSWLPL]DWLRQ DOJRULWKP´ ,QW- (OHFWU
3RZHU(QHUJ\6\VWYROQRSS±
82
Departemen Teknik Elektro dan Teknologi Informasi, FT UGM