transient stability analysis of multi-machine system

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    VZBK\G@KV \VBJGAGVW BKBAW\G\

    NE MPAVG-MBLDGK@ \W\V@M

    B Mgknz _zni`lv \jmgvv`f gk vd`

    _bzvgba Eaegaam`kv ne vd` Z`rgz`m`kv enz vd`

    F`cz`` ne Jbld`anz ne V`ldknancw gk @a`lvzglba @kcgk``zgkc

    \PJMGVV@F

    JWMF+ HDBAGF BHDVBZ ?5-@@\-:

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    g

    F@_BZVM@KV NE @A@LVZGLBA @KCGK@@ZGKC

    EBLPAVW NE @KCGK@@ZGKC BKF V@LKNANCW

    IBMGB MGAAGB G\ABMGB! K@S F@ADG

    L@ZVGEGLBV@

    Vdg| g| vn l`zvgew vdbv vd` Mgknz _zni`lv Z`pnzv `kvgva`f! Vzbk|g`kv \vbjgagvw

    Bkbaw|g| ne Mavg-Mbldgk` \w|v`m |jmgvv`f jwMf+ Hdbagf Bhdvbz! \dbm|

    Vbjz`y % \bigf B|abm bv Eblavw ne @kcgk``zgkc % V`ldknancw IBMGB

    MGAAGB G\ABMGB! K@S F@ADG g| bk bvd`kvgl snzh lbzzg`f nv jw vd`m

    kf`z mw |p`zug|gnk bkf cgfbkl`+

    Vn vd` j`|v ne mw hknsa`fc`! vd` mbvv`z `mjnfg`f gk vdg| _zni`lv Z`pnzv g|

    |eeglg`kv % `kncd vn |vfw Vzbk|g`kv \vbjgagvw Bkbaw|g| ne Mavg-Mbldgk`

    \w|v`m+

    _ZNE+ B+ R+ BK\BZG

    D@BF

    F`pbzvm`kv ne @a`lvzglba @kcgk``zgkc

    Eblavw ne @kcgk``zgkc bkf V`ldknancwIbmgb Mgaagb G|abmgb! K`s F`adg

    Fz+ KBGMPA DB\BK

    B||vv+ _zne`||nz

    F`pbzvm`kv ne @a`lvzglba @kcgk``zgkc

    Eblavw ne @kcgk``zgkc bkf V`ldknancwIbmgb Mgaagb G|abmgb! K`s F`adg

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    gg

    BLHKNSA@FC@M@KV

    Vdg| pzni`lv g| jw ebz vd` mn|v |gckgeglbkv bllnmpag|dm`kv gk nz age` bkf gv

    snaf j` gmpn||gja` sgvdnv p`npa` sdn |ppnzv`f | bkf j`ag`u`f gk |+

    S` snaf agh` vn `tv`kf nz czbvgvf` bkf nz |gkl`z` vdbkh| vn nz dnknzbja`

    `|v``m`f |p`zug|nz Fz+ KBGMPA DB\BK! F`pbzvm`kv ne @a`lvzglba

    @kcgk``zgkc! Ibmgb Mgaagb G|abmgb! K`s F`adg+ S` |gkl`z`aw vdbkh enz dg|

    `t`mpabzw cgfbkl` bkf `klnzbc`m`kv+ Dg| vz|v bkf |ppnzv gk|pgz`f | gk vd`

    mn|v gmpnzvbkv mnm`kv| ne mbhgkc zgcdv f`lg|gnk| bkf s` bz` cabf vn snzh

    sgvd dgm+

    S` snaf agh` vn vdbkh baa mw ezg`kf| enz baa vd` vdncdvea bkf mgkf |gmabvgkc

    fg|l||gnk s` dbf! sdgld mbh` | vn vdgkh j`wnkf vd` njugn|+

    Ab|v jv knv a`b|v s` snaf agh` vn vdbkh nz pbz`kv|! sdn vbcdv | vd` uba` ne

    dbzf snzh jw vd`gz nsk `tbmpa`+

    Mf+ Hdbagf Bhdvbz

    \dbm| Vbjz`y

    \bigf B|abm

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    ggg

    BJ\VZBLV

    _ns`z-|w|v`m |vbjgagvw g| b v`zm bppag`f vn bav`zkbvgkc-lzz`kv `a`lvzgl pns`z

    |w|v`m|! f`knvgkc b lnkfgvgnk gk sdgld vd` ubzgn| |wkldznkn| mbldgk`| ne vd`

    |w|v`m z`mbgk gk |wkldznkg|m! nz *gk |v`p!* sgvd `bld nvd`z+ Lnku`z|`aw!

    gk|vbjgagvw f`knv`| b lnkfgvgnk gkunaugkc an|| ne |wkldznkg|m! nz ebaagkc nv ne

    |v`p Nllzz`kl` ne b ebav gk b pns`z |w|v`m lb|`| vzbk|g`kv|+ Vn |vbjgagy` vd`

    |w|v`m anbf eans bkbaw|g| g| fnk`+ Blvbaaw gk pzblvgl` vd` ebav c`k`zbaaw nllz|

    gk vd` anbf |gf`+ B| s` lnkvznaagkc anbf |gf` sdgld sgaa a`bf vn lnmpa`t

    pznja`m gk nzf`z vn bungf vdbv s` bz` lnkvznaagkc vd` c`k`zbvnz |gf`+ B

    MBVABJ |gmabvgnk db| j``k lbzzg`f nv vn f`mnk|vzbv` vd` p`zenzmbkl` ne

    vd` vdz``-mbldgk` kgk`-j| |w|v`m+

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    gu

    LNKV@KV\

    L@ZVGEGLBV@ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ G

    BLHKNSA@FC@M@KV ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ GG

    BJ\VZBLV +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++GGG

    LNKV@KV\ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ GU

    AG\V NE EGCPZ@ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ U

    LDB_V@Z-29 GKVZNFPLVGNK ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 2

    2+2 JBLHCZNPKF +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 2

    2+: AGV@ZBVPZ@ZGUG@S ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 2

    2+

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    u

    AG\V NE EGCPZ@

    EGC+:+2+M@LDBKGLBA BKBANCW NE VZBK\G@KV \VBJGAGVW ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 4

    EGC+:+:+\GM_A@ VSN MBLDGK@ _NS@Z \W\V@M +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 7

    EGC+:+

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    2

    Ldbpv`z-2

    GKVZNFPLVGNK

    2+2 JBLHCZNPKFVd` lab||glba mnf`a ne b mavg-mbldgk` mbw j` |`f vn |vfw vd` |vbjgagvw ne b

    pns`z |w|v`m enz b p`zgnf ne vgm` fzgkc sdgld vd` |w|v`m fwkbmgl z`|pnk|` g|

    f`p`kf`kv abzc`aw nk vd` hgk`vgl `k`zcw gk vd` znvbvgkc mb||`|+ Vd` lab||glbavdz``-mbldgk` kgk`-j| |w|v`m g| vd` |gmpa`|v mnf`a |`f gk |vfg`| ne pns`z

    |w|v`m fwkbmgl| bkf z`rgz`| ne mgkgmm bmnkv| ne fbvb+ D`kl` |ld |vfg`|

    lbk j` lnkk`lv`f gk b z`abvgu`aw |dnzv vgm` kf`z mgkgmm ln|v+ Bmnkc ubzgn|

    m`vdnf ne anbf eans lbalabvgnk K`svnk Zbpd|nk m`vdnf g| ldn|`k enz

    lbalabvgnk ne anbf eans |vfw+

    Ge vd` n|lgaabvnzw z`|pnk|` ne b pns`z |w|v`m fzgkc vd` vzbk|g`kv p`zgnf

    enaansgkc b fg|vzjbkl` g| fbmp`f bkf vd` |w|v`m |`vva`| gk b egkgv` vgm` vn b

    k`s |v`bfw np`zbvgkc lnkfgvgnk! s` |bw vd` |w|v`m g| |vbja`+ Ge vd` |w|v`m g| knv

    |vbja`! gv g| lnk|gf`z`f k|vbja`+ Vdg| pzgmgvgu` f`egkgvgnk ne |vbjgagvw z`rgz`|

    vdbv vd` |w|v`m n|lgaabvgnk| |dnaf j` fbmp`f+ Vdg| lnkfgvgnk g| |nm`vgm`|

    lbaa`f b|wmpvnvgl |vbjgagvw bkf m`bk| vdbv vd` |w|v`m lnkvbgk| gkd`z`kv enzl`|

    vdbv v`kf vn z`fl` n|lgaabvgnk+

    2+: AGV@ZBVPZ@ ZGUG@SGk z`l`kv w`bz|! `k`zcw! `kugznkm`kv! zgcdv-ne-sbw! bkf ln|v pznja`m| dbu`

    f`abw`f vd` lnk|vzlvgnk ne jnvd c`k`zbvgnk eblgagvg`| bkf k`s vzbk|mg||gnk

    agk`|! sdga` vd` f`mbkf enz `a`lvzgl pns z db| lnkvgk`f vn czns+ Vdg| |gvbvgnk

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    :

    db| k`l`||gvbv`f b z`ug`s ne vd` vzbfgvgnkba pns`z |w|v`m lnkl`pv| bkf pzblvgl`|

    vn bldg`u` cz`bv`z np`zbvgkc ea`tgjgagvw bkf j`vv`z vgagybvgnk ne `tg|vgkc pns`z

    |w|v`m|+

    2+

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