JU MSŠ ŽIVINICE ELEKTROTEHNIČKA ŠKOLA
MATURSKI MATURSKI RAD ELEKTROENERGETSKE MREŽE
PRORAČUN ELEKTRIČNIH MREŽA
Mentor: Alji H!"i# Ži&ini'e( M!j( )*+,-
U$eni%: O#er.e/o&i S!#ir
Sadrzaj UVOD-------------------------------------UVOD---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0 -----0
+-1RORAČUN ELEKTRIČNIH MREŽA------------------------------------MREŽA-------------------------------------------------------------------------------------------------------2 ---------------------2 +-+-S&r3! 4ror!$5n!---------------------------------4ror!$5n!----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------22 +-)-6!/rij!&!nje &o7i$! i %!.lo&!------------------------------%!.lo&!---------------------------------------------------------------------------------------------------------------------------------------------------,, +-0-No#in!lne 8tr5je /oli3 &o7i$! i %!.lo&! 9t!.el!rni 4re/le7-------------------------------------------; 4re/le7-------------------------------------------; +-2-Do"&oljeni 4!7o&i n!4on!----------------------------n!4on!------------------------------------------------------------------------------------------------------------------------------------------++ -------------------++ +-,-I".or 4re8je%! &o7i$! i %!.lo&! 8 o."iro# n! "!/rij!&!nje-------------------------------------"!/rij!&!nje-------------------------------------------+) -----+) +-;-N!j#!nji 7o"&oljeni 4re8je'i &o7i$! n!7"e#ni3 &o7o&! 8 o."iro# n! #e3!ni$%5 8i/5rno8t &o7o&!-------------------------------&o7o&!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+0 -----+0 )-ELEKTRIČNI 1RORAČUN VODOVA VODOVA ISTOSMJERNE ISTOSMJERNE STRUJE------------------------------------+2 STRUJE---------------------------------- --+2 )-+-1ror!$5n je7no8tr!no n!4!j!no/ &o7! o4tereeno/ n! %r!j5----------------------------------------%r!j5-----------------------------------------+2 +2 )-)-1ror!$5n je7no8tr!no n!4!j!no/ n!4!j!no/ &o7! o4tereeno/ n! &ii&!nje 4!7! n!4on! 5 tro?!"no# &o75 8! o4tereenje# n! %r!j5-------------------------)) 0-)-O7re>i&!nje 4!7o&! n!4on! n!4on! 5 tro?!"no# &o75 o4tereeno# o4tereeno# n! &i
)
UVOD Ele%tri$no# #reo# n!"i&!#o 8i8te# &o7o&! i tr!n8?or#!tor8i3 8t!ni'! %oji 8l5e "! 4reno8 ele%tri$ne ener/ije o7 i"&or! 9ele%tr!n! 7o #je8t! 4otroe i"/r!7io 4r&5 ele%tr!n5 "! n!4!jenje ele%tri$ni3 8ij!li'! 8! 5/ljeno# niti- I8to8#jern! 8tr5j! i" /ener!tor! E7i8ono&e ele%rtr!ne n!4!j!l! je =*** 8ij!li'!( %oje 85 o7 ele%tr!ne .ile 57!ljene ne%oli%o 8totin! #et!r!-N!"i&ni n!4on /ener!tor! je .io +*0V(( ! n!"i&ni n!4on 8ij!li'! +**V +*0V +**V-- Ele%tri$n!#re! %oj! je e7i8ono&5 ele%tr!n5 4o&e"i&!l! 8 4otro5ti#( 4o&e!nje 4re8je%! &o7i! nije #o/lo ii 5 ne7o/le7( jer je to r!84o7jel5ele%tri$ne ener/ije $inilo nee%ono#i$no#- I"l!" je n!>en 5 4o&e!nj5 n!4on!-U#je8to n!4on!-U#je8to "! n!4on o7 +**V( 8ij!li'e 8e 4r!&e "! n!4on o7 ))*V( t!%o 7! 85 i 4otro
0
1.PRORAČUN ELEKTRIČNIH MREŽA 1.1.Svrha prorač!a Ele%tri'ne #ree #or!j5 .iti t!%o 4roje%to&!ne I i"/r!>ene 7! 5 4o/on5 "!7o&olj!&!j5 8lije7ee "!3tje&e: Te3ni$%5 i84r!&no8t e"o4!8no8t e"o4!8no8t 4o o%olin5 E%ono#i$no8tD! .i 8e o8t&!rili o&i "!3tje&i( #or!j5 8e %o7 4roje%to&!nj! ele%tri$ni3 #re! n!4r!&iti 8lije7ei 4ror!$5ni:
To4lotni Ele%tri$ni E%ono#8%i Me3!ni$%i R!"ni 7o45n8%i 4ror!$5ni
S&r3! to4lotno/ 4ror!$5n! je o7re>i&!nje j!$ine 8tr5je(o7no8no o7re>i&!nje 4re8je%! &o7i$! i %!.lo&! 4ri o7re7enoj j!$ini 8tr5je- To4lotni# 4ror!$5no# o7!.ir5 8e t!%&i 4re8je'i %oji 'e one#o/5iti 4re%o#jerno "!/rij!&!nje &o7i$!S&r3! ele%tri$no/ 4ror!$5n! je o7re7i&!nje 4!7o&! n!4on! 4ri 4o"n!ti# 4re8je'i#! &o7i$!( o7 o7no no8n 8noo o7 o7re re7i 7i&! &!nj njee 4re8 4re8je je%! %! &o &o7i 7i$! $! 4ri 4ri 4o 4o"n "n!t !ti# i# 4!7o 4!7o&i &i#! #! n!4o n!4on! n!-- Ele% Ele%tri tri$n $ni# i# 4ror!$5no# o7!.ri o7!.ri 8e t!%i 4re8je'i %oji %oji 'e o#o/5iti 7! 4otro
2
1.".#a$r%java!j& vod%ča % 'a()ova 1o"n!to n!# je 7! 8e &o7i$ "!/rij!&! !%o %ro" nje/! te$e 8tr5j!- A%o 8tr5j! tr!jno te$e( on7! 8e on tr!jno "!/rij!&!- Me>5ti# te#4er!t5re ne #o"e r!8ti neo/r!ni$>eno jer &o7i$ enj! &ienj! i#!#o i o7re7eno 4o&e!nje te#4er!t5reR!"5#lji&o je 7! 8e 4ri 8nienj5 te#4er!t5re o%oline &o7i$ #o"e o4teretiti &eo# 8tr5jo#1ror!$5no# e%etri$ni3 #re! 8#o 5t&r7ili 7! li 'e /oli nei"olir!ni &o7i$ ili %!.el .iti 5 nor#!lno# "!/rij!n n! te#4er!t5re %oj! je #!nj! o7 7o"&oljene te#4er!t5re Goli nei"olir!ni &o7i$i i'e i 5"!7 8#ij5 8e "!/rij!ti n!j&i
,
1.*.No+%!a)!& ,-rj& $o)%h vod%ča % 'a()ova -a(&)ar!% pr&$)&d/ Tablica 3.1- Trajna struja opterećenja homogenih zica i užadi u ! za izmjeni"nu struju #$%z I nadtemperaturu &$o'
1re8je% &o7i$! )
## ; +* +; ), 0, ,* =* B, +)* +,* +@, )2* 0**
Tr!jn! 8tr5j! !l5#inij A B) +)+ +2B +@= )); )@0 0)B 0@) 20, ,)* ,B@
.!%!r A ,) =2 ++, +,+ +=2 )02 )@) 0,= 2++ 2== ,22 ;0* =2=
!l7rej A @ ++, +2) +=@ )+, );B 0+0 ;0 2+2 2=B ,;@
Tablica 3.2 ( Trajna struja optererećenja alu"el"nih užadi u za izmjeni"nu struju #$%z I natemperaturu od &$ o'
1re8je% &o7i$! ##) +(;F)(, ),F2 0,F; ,*F@ =*F+) B,F+, +)*F)+ +,*F), +@,F0)
Tr!jn! 8tr5j! A B* +), +2, +=* )0, )B* 02, 2** 2,,
1re8je% &o7i$! ##) )+*F0; )2*F2* 0**F,* +),F)B +=*F2* )+*F,* 0+*F+** 02*F+**
Tr!jn! 8tr5j! A 2B* ,0* ;+, 0,, 22* ,*, ;0* ;@*
U o"n!'i 4re8je%! !l5$eli$no/ &o7i'! .roj 5 .rojni%5 o"n!'!&! n!"i&ni 4re8je% !l5#inij8%o/ 4l!
0*
)*
+*
* ;
Kore%'ioni ?!'tor:
+(+)
+())
+(0*
+(0;
=
Tablica3.3. ( Trajna struja opterećenja u dožilnih! trožilni i ceterožilnih *abloa! nazinog napona 1 *+ I jednožilnih *abloa za istosmjernu struju ,a*arni odi"i!temperature o*oline 2$o'! poedina"no polaganje u zemlju
N!"i&ni 4re8je% &o7i$! ##) +(, )(, 2 ; +* +; ), 0, ,* =* B, +)* +,* +@, )2* 0** 2** ,** ;), @** +***
Je7noilni %!.lo&i
D&oilni %!.lo&i
A 0, ,* ;, @, ++* +,, )** ),* 0+* 0@* 2;* ,0, ;+* ;@, @** B+* +*@* +)0* +2)* +;2* +@@*
A 0* 2* ,* ;, B* +)* +,, +@, )0, )@* 00, 0@* 20, 2B* ,=* ;2* =;*
Troilni i 'et&eroilni %!.lo&i A ), 0, , ;* @* ++* +0, +;, )** )2, )B, 02* 0B* 22, ,+, ,B* =**
@
Tablica 3.&. ( Trajna struja opterećenja u trožilnih *abloa pojasnog tipa ba*arni odi"i temperature o*oline 2$o'! pojedina"no polaganje u zemlju
N!"i&ni 4re8je% &o7i$! ##) ; +* +; ), 0, ,* =* B, +)* +,* +@, )2* 0** 2**
0
;
N!"i&ni n!4on 5 %V +*
A ;* @* +*, +0, +;, )** )2, )B* 00, 0@* 20, ,*, ,=* ;;*
A ,, =, +** +0* +;* +B, )0, )@* 0), 0=* 2)* 2B* ,;* ;;*
A ;, @, ++* +0, +;, )** )2* )@* 0) 0;* 2)* 2=, ,;*
+,
)*
A @* +*, +0* +,, +B, )0* );, 0*, 0,* 2+* 2=*
A +*, +), +,* +@, )), );* 0** 02* 2**
Tablica 3.#. ( Trajna stuja opterećenja u trožilni *abloa trooloog tipa ba*reni odi"i! temperature o*oline 2$o'! pojedina"no polaganje u zemlju
N!"i&ni 4re8je% &o7i$! ##) ; +* +; ), 0, ,* =* B, +)* +,* +@, )2* 0** 2** ,**
N!"i&ni n!4on 5 %V 0 A ;, @, ++, +,* +@, ))* )=* 0+, 0=* 2)* 2=* ,2* ;+, =+* =B*
; A ;* @* ++* +2, +@* ))* );, 0+* 0;, 2+, 2;, ,0, ;+* =** =@*
+* A =* @, +), +,* +B* )0* )=* 0+* 0,* 0B, 2;* ,)* ;** ;=*
+, A B* +)* +2, +@* ))* ),, )B, 02* 0@* 22, ,** ,=, ;2*
)* A ++, +2* +=* )+* )2, )@, 0), 0;, 2), 2@* ,,* ;+,
0, A +0@ +;) +B, )0* );) 0** 00@ 0B* B
Tablica 3.. ( Trajna stuja opterećenja u trožilni *abloa aluminijs*i odi"i! temperature o*oline 2$o'
N!"i&ni 4re8je% &o7i$! ##) +* +; ), 0, ,* =* B, +)* +,* +@, )2* 0** 2**
N!"i&ni n!4on 5 %V 0 A =* B* +)* +,* +@* )+, ),, )B, 00, 0=, 20, 2B, ,=*
; A ;, @, ++, +2, +=, )+* ),* )B* 00* 0=* 20* 2B* ,;*
+* A ,, =, +** +)* +,* +@, )+, ),* )@* 0+, 0=* 2+, 2@*
+, A =* B, ++, +2, +=, )*, )2* )=* 0*, 0,, 2** 2;*
)* A B* ++* +0, +=* +B, )0* );* )B* 02* 0@, 22*
0, A +*, +0* +;* +@, )+, ),* )=, 0)* 0;* 2+,
J!$in! 8tr5je 5 t!.el!#! 90-0( 0-2-( 0-,- i 0-;- 4otre.no je %ori/ir!ti !%o je &ei .roj %!.lo&! 4oloen 5 ne4o8re7noj .li"ini t!%o 7! r!8toj!nje i"#e>5 nji3 i"no8i o7o = '#- Kori/or!nje tre.! i"&r8it 4re#! t!.li'i 90-=-Tablica 3./. ( 0a"ina struje u ) od strujnih opterećenja datih u tablicama 3.3! 3.&.! 3.#. i 3..)
roj %!.lo&! 5 ro&5 J!'in! 8tr5je 5
) B*
0 @*
2 =,
, =*
; ;,
@ ;)
+* ;*
J!$in! 8tr5je 5 t!.li'!#! 90-0( 0-2-( 0-,- i 0-;- &rije7e "! %!.lo&e 4oloene 5 "e#lj5- N!< 8t!n7!r7 JUS N C, ))*F+B;) %!"e 7! 8e %!.lo&i 4oloeni n! "!#lj5 #o/5 o4teretiti 8! @* 8tr5jni3 o4tereenj! 7!ti 5 o&i# t!.li'!#!-
+*
U%oli%o 8e 8tr5j! 5 t!.li!#! 90-0( 0-2-( 0-,- i 0-;- r!"li%5je o7 )* oC tre.! je 4o#noiti 8! %ore%'ioni# ?!%toro# 7!ti# 5 t!.li'i 90-@- Tablica 3.. - 4ore*cioni 5actor *ojim treba mnoćiti strujna opterećenja iz tablica 3.3! 3.&.! 3.#. i 3..)za temperature o*oline od 2$ o'
Te#4rer!t5r! o%oline 5 oC J!$in! 8tr5je "! %!.lo&e o7 + 7o ; %V o7 +* 7o )* %V o7 )* 7o 0* %V
,
+*
+,
)*
),
0*
0,
+(+, +()* +();
+(+* +(+0 +(+@
+(*, +(*= +(+*
+(** +(** +(**
*(B2 *(B0 *(B*
*(@@ *(@, *(=@
*(@) *(=; *(;0
K!o 8to &i7i#o %!.lo&i 8e 4ri te#4er!t5r!#! nii# o7 )* oC #o/5 o4teretiti &i
Vr8te tl!
To4lotn! ot4orno8t K '#F ,,* 0+* +*, =, ,, B, ;* ;,
Kore%'ioni ?!%tori + 7o +* %V +, 7o 0, %V *(20 *(,* *(,= *(;0 *(@= *(B* *(B@ *(B@ +(*= +(*, *(B* *(B0 +(*, +(*0 +(*0 +(*)
A%o je %!.el 4oloen 5 &o75 9 n! 7n5 rije%e(je"er! ili 8l on7! %ore%'ioni ?!'tor i"no8i +(+,(
1.0.Dozvo)j&!% padov% !apo!a S&!%i ele#ent ili !4!r!t i 8&!%! ele%ti$n! #!eni 85 "! o7/o&!r!j5e n!4one-T!j n!4on 8e "o&e n!"i&ni n!4on- Sij!li'e 8e o.i$no /r!7e "! ))*V tro?!"ni !8i3roni #otori "! ))* i 0@* V(%5ni ter#i$%i !4!r!ti "! ))* i 0@* V-
A)$&(ar,'a raz)%'a %z+& ,-var!o$ !apo!a U % !az%v!o$ !apo!a U! !az%va ,& od,-pa!j& !apo!a - M!te#!ti$%i je o78t54!nje n!4on! 7!to i"r!"o#: m=U –Un ( V )
Ili 5 4ro'eneti#!: m=
U −Un 100 ( ) Un
N&po,r&d!% zroč!%' od,-pa!ja !apo!a j& raz)%'a !apo!a poj&d%!%+ &)&+&!-%+a +r&2&. T& raz)%'& !apo!a !z%vaj ,& padov% !apo!a. E)&'-r%č!% prorač! +r&2& ,& % za,!%va !a prorač! pada !apo!a. 1!7o&i n!4on! ne8#ij5 4rei 4ro4i8i#! o7re>ene &rije7no8ti-Mi 8e %ori8ti#o 8o&jet8%i# 8t!n7!r7i#! o8no&ne 8#jerni'e "! 4o%ret!nje /r!78%i3 ele%tri$ni3 #re!: ! Gr!78%e #ree ni8%o/ n!4on! O7 8!.irni'! ni8%o/ n!4on! tr!n8?or#!tor8%e 8t!ni'e 7o 5&o7! 5 %55 0(, 7o , . Gr!78%e #ree &i8o%o/ n!4on! K!.lo&8%e #ree 5 nor#!lno# 4o/on5 N!7e#ne #ree 5 nor#!lno# 4o/on5 K!.lo&8%e #ree %o7 4o/on! 5 8l5$!j5 %&!r! N!7"e#ne #ree %o7 4o/on! 5 8l5$!j5 %&!r! ' In758trij8%e #ree:
7o ; 7o @ 7o +* 7o +)
O7 8!.irni'! tr!n8?or#!tor8%e 8t!ni'e 7o "!7nji3 #otor!:
U nor#!lon 4o/on5 Ko7 4o/on! 5 8l5$!j5 %&!r! Ko7 n!4!j!nj! #otor! %oji 8e $e8to 4o%ree Ko7 n!4!j!nj! #otor! %oji 8e rijet%o 4o%ree
7o @ 7o +) 7o +* 7o +,
Ko7 n!8 je 5o.i$!jno 7! 7o"&oljeni 4!7o&i n!4on! ne 4rel!"e 8lije7ee &rije7no8ti: 6! #ree %oje n!4!j!j5 8!#o ele%tro#otore 6! #ree %oje n!4!j!j5 8!#o 8ij!li'e 6! #ree %oje n!4!j!j5 #je
7o ; o7 ) 7o 2(, 7o 0 +)
1.3.Iz(or pr&,j&'a vod%ča % 'a()ova , o(z%ro+ !a za$r%java!j& R!nije 8#o &i7jeli 7! n!j&e'! 7o"&oljen! te#4er!t5re /oli3 nei"lolo&!ni3 &o7i$! i"no8i @* oC ! "! %!.lo&e 2* 7o =, oCO8no&ni o.r!"!' "! i".or 4re8je%! &o7i$! 8 o."iro# n! "!/rij!&!nje %!e 7! tr!jno 7o"&oljen! 8tr5j! &o7i$! i %!l.! Id #or! .iti je7n!%! ili &e! o7 4o/on8%e 8tr5je I4: Id≥ Ip
9,-+
1o/on8%! 8tr5j! je o&7je n!j&e! 8tr5j! 5 nor#!lno# 4o/on5 te$e 5 .ilo %oje# 7ijel5 &o7i$! ! to nije ni8t! 7r5/o ne/o n!"i&n! 8tr5j!9no#in!ln! 8tr5j! 4otro
P=UI cosϕ ( W )
9,-)
9,-0
J!lo&!9 re!%ti&n! 8n!/!
Q =UI sinϕ ( VAr )
9,-2
1ri&i7n!95%54n! 8n!/!
S =UI ( VA )
9,-,
6! tro?!"n5 i"#jeni$ni 8tr5j5: Djel!tn! 8n!/! J!lo&! 8n!/! 1ri&i7n! 8n!/!
P=√ 3 UI cosϕ ( W )
9,-;
Q=√ 3 UI sinϕ ( VAr )
9,-=
S = √ 3 UI ( VA )
9,-@
N!4on je 5 V ! 8tr5j! 5 A- U ?or#5l!#! 9,-; 9,-= i 9,-@ n!4on i 8tr5j! 85 linij8%e &eli$ine-
+0
1.4.Naj+a!j% dozvo)j&!% pr&,j&5% vod%ča !adz&+!%h vodova , o(z%ro+ !a +&ha!%č' ,%$r!o,- vodova 1ri o7!.ir!nj5 4re8je%! &o7i$! 8 o."oro# n! "!/rij!&!nje i#!#o &rlo #!le 4re8je%e %oji ne #o/5 7! i"7re #e3!ni$%! n!4re"!nj!9&l!8tit! tein!( le7( inje( 8nije/( &jet!r ".o/ to/! 8e 4ro4i8i#! o7re>5j5 n!j#!nje 4re8je'i &o7i$! n!7"e#ni3 &o7o&! %oji 85 4ri%!"!ni 5 t!.eli ;-+ Tablica .1.- 7ajmanji dozoljeni presjeci odi"a nadzemnih odoa s obzirom na mehani"*u sigurnost odoa
Dio tr!8e &o7! Vo7o&i &i8o%o/ i ni8%o/ n!4on! n! nor#!lnoj tr!8i Vo7o&i &i8o%o/ i ni8%o/ n!4on! n! nor#!lnoj tr!8i 7o 2, # Vo7o&i &i8o%o/ i ni8%o/ n!4on! n! #je8ti#! %ri!nj! 8! elje"ni$%i# 4r5/!#! Vo7o&i &i8o%o/ n!4on! n! "&ije"7i
.!%!r
M!terij!l &o7i'! .ron'! !l5#inij !l7rej
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Vi7i#o 7! n!j#!nji 7o"&oljeni 4re8je'i &o7i$! i"no8e:
6! .!%!r ; ##) 6! .ron'o ; ##) 6! !l5#inij +; ##) 6! !l7er +* ##) 6! $eli% ; ## ) 6! !l5$el ;:+ +; ## )
+2
+,
".ELEKTRIČNI PRORAČUN VODOVA ISTOSM6ERNE STRU6E ".1.Prorač! j&d!o,-ra!o !apaja!o$ voda op-&r&7&!o$ !a 'raj N! 8li'i +-! <3e#!t8%i je 4ri%!"!no %olo i8to8#jerne 8tr5je 5 %o#e /ener!tor n!4!j! je7no/ 4otro
8li*a 1. 4olo istosmjerne struje a) I pojednostaljena 9ema *ola b)
U 7o&o7no# i o7&o7no# &o7i$5 te$e 8tr5j! I9A1!7 n!4on! 5 o.! &o7i$! i"no8i: Δu =U 1 – U 2 ( V ) U 1 9V n!4on n! 4o$et%5 &o7! 9 n! /ener!tor U 2 9V n!4on n! %r!j5 &o7! 9n! 4otro
1!7 n!4on! 8e #oe i"r!$5n!ti i 4o o#o&o# "!%on5: Δu = I ∗2 R=
I ∗2 pl I ∗2 l = ( V ) s ys
9=-)
G7je je 84e'i?$ni ot4or 5 ## )F# ! 84e'i?i'n! &o7lji&o8t 5 S#F## )- O&!j 4!7 n!4on! n!"&! 8e !48ol5tni 4!7 n!4on!-U 4re%8i 8e $e<e r!$5n! 4ro'ent5!lni 4!7 n!4on!:
+;
u=
Δu ∗100 ( ) U
9=-0
A%o 5#je8t !4ol5tno/ 4!7! n!4on! 5ne8e#o 5 o&!j o.r!"! nje/o&5 &rije7no8t 7!t5 o.r!8'e# 9=-) 7o.ije#o: u=
200 Il
ysU
()
9=-2
1re#! o.r!"'5 =-2 #o"e#o 4ro&jeriti 7! li 'e 4!7 n!4on! .iti &ei o7 7o"&loljeno/ n! o8no&5 4re8je%! %oje/ 8#o o7!.r!li1re8je% i"r!$5n!&!#o 4o ?or#5li: s=
200 Il
yuU
( mm2)
9=-,
U %oli%o je 4re8je% &o7i$! 7o.ijen 4o o.r!8'5 #!nji o7 ono/ %oje/ 8#o o7!.r!li 8 o."iro# n! nje/o&! "!/rij!&!nje( on7! e 4!7 n!4on! .iti #!nji o7 7o"&oljeno/-
U#je8t5 8tr5je I #o"e#o 4i8!ti o7no8 91FU 4! 7o.ije#o: 200 l
∗ P
yuU s= U
=
200 Pl
2 ( ) mm 2
yu U
1 je 8n!/! 5 - U %oli%o je 8n!/! 5 % on7! i"r!" 4rel!"i 5: s=
2∗10
5
Pl ( mm2) 2 yu U
Pr&,j&5% vod%ča , o(r!-o ,raz+j&r!% 'vadra-%+a !apo!a. s1 s2
=(
U 2 U 1
2
)
Pr%+j&r. s 2=(
U 2 U 1
2
) ∗s 1=(
110 220
2
) ∗240= 60 ( mm2 )
I" i"r!"! =-, i"r!$5n!#o 75"in5 l:
+=
l=
yuUs yuU = (m) I 200 I 200 s
yu l 200 s
= const
1! i"r!" #oe#o n!4i8!ti: l =cU ( m)
D5in! i"r!$5n!t! n!"i&! 8e 7o#!
Ko7 &o7! %oji je o4tereen 8n!/o# 1 i#!#o: l=
yus ∗U 2=c U 2 ( m) 200 P
O&7je &i7i#o 7! je 7o#!
Vo7i$i %oje 8#o 7o8!7 r!$5n!li 4r5!j5 4roti'!nj5 8tr5je ot4or R- U8lije7 to/! n!8t!je 4!7 n!4on! i /5.it!% 8n!/e Δp i"#e>5 %oji3 i#!#o o7no8: Δp = Δu ∗ I ( W )
O7no8no: Δp = I
2l
ys
∗ I = I 2
2 l
ys
( W )
1ro'ent5!lni /5.it!% 8n!/e:
+@
p=
Δp ∗100 ( ) p
1re#! to#e %o7 &o7o&! i8to8#jerne 8tr5je 4ro'ent5!lni /5.it!% 8n!/e je7n!% je 4ro'ent5!lno# 4!75 n!4on!: p=
Δu∗ I Δu 100= 100 =u P U s1 s2
=
u2 u1
I" i"r!"! =-+; &i7i#o 4ri o8t!li# i8ti# 4!r!#etri#! o7no8e o.rn5to 4ro4or'ion!lno 4ro'ent5!lni# 4!7o&i#! n!4on!-
+B
".".Prorač! j&d!o,-ra!o !apaja!o$ voda op-&r&7&!o$ !a v%8& +j&,-a N! 8li'i ) 4ri%!"!n je je7no8tr!no n!4!j!n &o7 i8to8#jerne 8tr5je o4tereen n! &i
8li*a 2. -jednostrano napajan od istosmjerne struje opterećen na i9e mjesta
1o7 58lo&o# 7! je 4re8je% %on8t!nt!n i 7! 85 &o7i$i i"r!7eni o7 i8to/ #!terij!l! 4!7o&i n!4on! n! 4oje7ini# 7ijoni'!# .i i"no8ili: Δu 1=
2 l1
ys
Δu 2=
( i1 + i2+ i3 + i4 )
2 l2
ys
Δu 3=
( i2 + i3 + i4 )
2 l3
ys
Δu 4=
( i3 + i4 )
2 l4
ys
i4
U&r8t!&!j5 &rije7no8t 5 je7n!$in5 i"n!7 7o.ije#o:
)*
l
[¿ ¿ 1 ( i1+ i2 + i3 + i 4 ) + l2 ( i2 + i3 +i 4 ) + l 3 ( i3 +i 4 ) + l 4 i 4 ] Δu=
2
ys
¿
U o4'enit 8l5$!j5 i"r!" 5 "!/r!7i #oe#o 8t!&iti 5 o.li%5 85#e: Δu =
2
ys
ƩIl
I 9A 8tr5j! n! 4oje7ini# 7ijoni'!#! l 9# 75in! 4oje7ini3 7ijoni'! Sre>i&!nje# i"r!"! 7o.ije#o: l
¿ l
(¿ ¿ 1 + l2+l 3 + l4 ) (¿ 1 +l 2¿ )+ i3 ( l1 +l2 + l 3 ) + i4 ¿ i 1 l 1+ i 2 ¿ Δu =
2
ys
¿
N! 8li'i )-. o"n!$ili 8#o 8!: L1=l 1 L2=l 1+ l 2 L3=( l 1 + l 2+ l3 ) L4= l1 + l 2 + l 3 + l 4
U&r8t!&!nje# o&i &rije7no8ti 5 je7n!$in5 i"n!7 7o.ije#o: Δu =
2
ys
( i 1 L1 +i 2 L2 + i3 L3 + i4 L4 )
Δu =
2
ys
ƩiL
i 9A 8tr5j! 4oje7ini3 4otro
L 9# 57!ljeno8t 4oje7ini3 4otro
200 ƩIl
yuU
=
200 ƩiL
yuU
(mm2 )
))
U%oli%o n!# je 7!t! 8n!/! 4otro
2∗10
5
Ʃ Pl
yuU
2
5
= s=
2∗10
Ʃ pL 2
yu U
( mm 2)
1 9% 8n!/! n! 4oje7inoj 7ijoni'i l 9# 75"in! 4oje7ine 7ijoni'e 4 9% 8n!/! 4oje7ini3 4otro
p ∗2 l 2 U 2 2 l = ( W ) Δp = ƩI ys ys
p=
Δp ∗100 () Ʃ P
)0
*.ELEKTRI9NI PRORAČUN VODOVA I#M6ENIČNE STRU6E R!nije 8#o o7r!7ili o8no&ne 4ror!$5ne #re! i8to8#jerne 8tr5je- T!%&e #ree 7!n!8 8e &eo#! rijet%o /r!7e- 6!%lj5$%e 7o %oji3 8#o 7oe #or!#o r!$5n!ti o8i# 8 o#8%i# i 8! in75%ti&ni# ot4ori#! i 4!7o&i#! n!4on!- S&e o&o %o#4li%5je 4ror!$5n &o7o&! i"#jeni$ne 8tr5je- 1ror!$5n 8e #o"e 4oje7no8t!&iti !%o 8e r!$5n! 8! %o#4le%8ni# .roje&i#!-O&!j r!$5n 8e "o&e %o#4le%8ni ili 8i#.oli$%i r!$5nKo#4le%8ne .roje&e 4re78t!&lj!#! 5 G!58o&oj r!&nini %!o 8to je 4ri%!"!no n! 8li'i 0-
8li*a 3. :ri*az *omple*snih brojea u ;ausooj rani
)2
N! !48i'in85 8e n!l!"e re!lne &rije7no8ti %o#4le%8ni3 .roje&! ! n! or7in!nt5 i#!/in!rne &rije7no8ti %o#4le%8ni3 .roje&!I#4en7!n8! 6 je 8!8t!&ljen! o7 o#8%o/ ot4or! R i in75%ti&no/ ot4or! P-Moe#o je n!4i8!ti %!o %o#4le%8!n .roj: Z = R + jX (Ω )
98li%! 0
I"r!'5n!&o je 4o 1it!/orinoj teore#i: Z =√ R + X ( Ω ) 2
2
I#4en7!n85 6 #oe#o i"r!"iti 5 e%84onen'ion!lno# o.li%5 4o#o5 #o75l! 6 5/l! 9!r/5#ent! Q: Z =Zcos φ + jZsin φ =Z ( cos φ + jsin φ ) =Z
j φ
9Sli%! 2
8li*a &.
),
*.1.Odr&%va!j& pada !apo!a -ro:az!o+ vod ,a op-&r&7&!j&+ !a 'raj U 4ror!$5ni#! #re"e i &o7o&! i"#jeni$ne(je7no?!"ne i tro?!"ne 8tr5je 4o8toje tri %!r!%teri8ti$n! 8l5$!j! 8 o."iro# n! 4!r!#eter &o7! i &r8te o4tereenj! n! %r!j5 ili 75 &o7!: R!$5n!#o 8!#o 8! o#8%i# ot4oro# &o7! i o4tereenje# n! %r!j5 ili 75" &o7!(%oje i#!j5 r!7n! 8n!/5 9'o8Q+ R!$5n!#o 8!#o 8! o#8%i# ot4oro# &o7! i o4tereenje# n! %r!j5 ili 75" &o7! %oje i#! r!7n5 i j!lo&5 8n!/5 R!$5n!#o 8! in75%ti&ni# i o#8%i# ot4oro# &o7! i o4tereenje# n! %r!j5 ili 75" &o7!( %oje i#! r!7n5 i j!lo&5 8n!/51r&i 8l5$!j 8e &eo#! rijet%o 4oj!&lj5je jer 8e rijet%o 4oj!&lj5j5 5re>!j5 8! 9'o8Q+- A%o 8e t!%!& 8l5$!j 4oj!&i on7! 8e 4ri#jenj5j5 8&! 4r!&il! "! 4ror!$5n &o7o&! i8to8#jerne 8tr5je "! 4ror!$5n t!%&o/ &o7! i"#jeni$ne 8tr5jeDr5/i 8l5$!j je &e re!lniji i 4ot45no o7/o&!r! 8t&!rni# &o7o&i#! i"#jeni$ne 8tr5je9 8 o."iro# 7! "!ne#!ri#o 4o8toj!nje %!4!'itet!-1o8#!tr!#o tro?!"ni &o7 o4tereen n! %r!j5 neo&i8no o7 84oj! 4otroe je7n!%- N! 8li'i , 4ri%!"!n je &o7 i"#jeni'e 8tr5je 8! o#8%i# ot4oro# &o7!- 6.o/ 8i#etri'no o4tere'eni3 ?!"ni3 &o7i'! 4o8#!tr!#o 8!#o je7!n &o7i'- S&e ele%tri'ne &eli'ine n! %r!j5 &o7! o"n!'!&!#o 8! ) ! 8&e ele%tri'ne &eli'ine n! 4o'et%5 &o7! 8! + N! 8li'i , 4ri%!"!n je i &e%tor8%i 7i!/r!# ele%tri$ni3 &eli$in! n! %r!j5 i n! 4o$et%5 &o7! 5
G!58o&oj r!&ni- Str5j! I
8t&!r! n! &o75 4!7 n!4on! I R %oji je n! 7i!/r!#5 n!'rt!n
%!o );
8li*a #- a)+od tro5azne struje samo sa oms*im opterecenjem odica) b) e*tors*i diagram ele*tricnih elicina
&e%tor 8 i83o7i
A%o "!ne#!ri#o in7e%8 ) jer je ?!"ni 4o#!% n! 4o'et%5 i n! %r!j5 &o7! je7n!% 95" "ene#!ri&!nje 5/l! 7o.ije#o: Δu ! = IR cos φ ( V )
G7je je I'o8 φ = Id r!7n! %o#4onent! 8tr5je 5 &o751re#! to#e 5%54!n 4!7 n!4on! n! &o7o&i#! i"#jeni'ne 8tr5je i"no8i N! je7no?!"no# &o75
Δu =2 IR cos φ
N! tro?!"no# &o75
Δu =" 3 IR c os φ 2
G5.it!% 8n!/e n! tro?!"no# &o7i'5 je 4re#! D5lo&o# "!%on5 Δp = I R 1re#! to#e ( 5%54!n /5.it!% 8n!/e n! &o7o&i#! i"#jeni'ne 8tr5je i"no8i: 2
N! je7no?!"no# &o75
Δp=2 I R
N! tro?!"no# &o75
Δp =3 I R
2
Tre'i 8l5'!j 4ror!'5n! ele%tri'ni3 &o7o&! 5 %oje# r!'5n!#o o#8%i i in75%ti&ni ot4or &o7i'! i 8! r!7no# i j!lo&o# 8n!/o# o4tere'enje( o7no8no 8! r!7no# i j!lo&o# 8tr5jo# o4tere'enj!- O4et 4o8#!tr!#o tro?!"ni( 8i#etri'no o4tere'eni &o7- U t!%&o# 8l5'!j5 n!# nije 4otre.!n n5l &o7i'9!li je i4!% n!'rt!n ".o/ l!%8e/ o"n!'!&!nj! ?!"ni3 n!4on!-
)=
8li*a +od tro5azne struje s oms*im i indu*tonim otporom odi"a)
S&e ele%tri'ne &eli'ine n! %r!j5 &o7! o"n!'!&!#o 8! ) ! 8&e ele%tri'ne &eli'ine n! 4o'et%5 &o7! 8! +- !"ni n!4on n! 4o'et%5 &o7! 7o.ije#o !%o ?!"no# n!4on5 n! %r!j5 7o7!#o 9&e%tro8%i 8!.ere#o 4!7 n!4on! n! &o7i'5: U ! 1 =U ! 2 + IZ
G7je je I6 4!7 n!4on!U#je8to &e%tor! I i 6 #o"e##5 5 i"r!" 5nijeti nji3o&e %o#4onenete: I = I #+ jI j
Z = R + jX
1! 7o.ije#o: U ! 1 =U ! 2 + ( I # + jI j ) ( R + jX )=U ! 2 =( I # R + I j X ) + j ( I # X − I j R )
N! 8li'i , o"n!'ili 8#o 8!: $ u! = I # R + I j X
5"75"n! %o#4onent! 4!7! n!4on!(
%u! = I # X − I j R
4o4re'n! %o#4onent! 4!7! n!4on!-
)@
8li*a /-+e*tors*i diagram ele*tri"nih eli"ina na odu pri*azanom na slici .
A48ol5tn! &rije7no8t n!4on! n! 4o'et%5 &o7! je: U ! 1 =√ ( U ! 2 + $u! ) + %u! (V ) 2
2
U/!o % i"#e75 &e%tor!n!4on! n! 4o$et%5 i n! %r!j5 &o7! o7re75je#o i" i"r!"!: % =arctan
%u ! U ! 2 + $ u!
1!7 n!4on! n! &o7i'5 je7n!% je &e%tor8%oj r!"li'i n!4on! n! 4o'et%5 i %r!j5 &o7!- K!%o je %5t % &eo#! #!li 5 ni8%on!4on8%i# #re"!#! #o"e#o 8#!tr!ti 7! je % =0 o7no8no 7! 85 &e%tori ?!"ni3 n!4on! n! 4o'et%5 i n! %r!j5 &o7! 5 ?!"i- Ti#e 7! je o#o/5'eno 7! 4!7 n!4on! i"r!'5n!#o %!o !rit#eti'%5 r!"li%5 ?!"ni3 n!4on! n! 4o'et%5 i n! %r!j5 &o7!: $ u! = U ! 1 −U ! 2 = I # R + I j X = I ( Rcosφ 2 + Xsinφ2 )
A%o lije&5 i 7e8n5 8tr!no 4o#no"i#o 8! √ 3 7o.it 'e#o r!"li%5 linij8i3 n!4on! n! 4o'et%5 i n! %r!j5 &o7!: $ u =U 1−U 2= √ 3 I ( Rcos φ2+ Xsin φ 2 ) ( V )
G7je je
cos φ 2
?!%tor o4tere'enj! 8n!/e n! %r!j5 &o7!-
K!%o je 4ri&i7n! 8n!/! n! 4oet%i i n! %r!j5 &o7! 7!t! i"r!"o#: )B
S 2=√ 3 U 2 I
Mo"e#o 8tr5j5 I je7n!'ini "!#ijeniti 8!: I =
S2 √ 3 U 2
1! 7o.ije#o: $ u =U 1−U 2= √ 3
S2
√ 3 U 2
1 ( Rcosφ + Xsin φ )= U ( R S 2
2
2
cos φ2 + X S2 sin φ2 )
2
K!%o je S 2 cos φ2= P2 i S 2 sin φ2=Q2 7o.ije#o %on!'no: P2 R + Q 2 X ( V ) $ u= U 2
G7je je: 1) 9 7jel!tn! 8n!/! o4tere'enj! n! %r!j5 &o7!( ) 9V!r j!lo&! 8n!/! o4tere'enj! n! %r!j5 &o7! R 9 o#8%i ot4or &o7! P 9 in75%ti&ni ot4or &o7! U) 9V linij8%i n!4on n! %r!j5 &o7!-
0*
A%o n! 7!8n5 8tr!n5 je7n!'ine i"&5'e#o i"r!" R S 2 cos φ2 i !%o n!4on U ) "!#jeni# 8! n!"i&ni# n!4ono# #re"e U( 7o.ije#o:
(
)
R S2 cos φ2 P2 R X 1 + tan φ2 = $ u= & U R U
G7je je % ?!%tor %oji# 5"i#!#o 5 o."ir ?!%tor 8n!/e 4otro8!'! i in75%ti&ni 4!7 n!4on! n! &o75: & =1+
X tan φ 2 R
U#je8to !48ol5tno/ 4!7! n!4on! $ u #o"e#o 4i8!ti: $ u=
uU 100
( V ) u
G7je je
4ro'ent5!l!n 4!7 linij8%o/ n!4on! %!7! to 5&r8ti#o 5 r!nij5 je7n!'in5
7o.ije#o: uU 100
=
P2 l ysU
&
O7!%le n!# je 4ro'ent5!lni 4!7 linij8%o/ n!4on!: u=
100 & P2 l 2
ys U
()
Vi7i#o 7! 85 i"r!"i "! 4ro'ent5!l!n 4!7 n!4on! i %o7 i"#jeni'no/ i i8to8#jerno/ 4ror!'5n! /oto&o i7eni'ni-R!"li%! je 8to 5 .rojni%5 %o7 i8to8#jerno/ 4ror!'5n! i#!#o .roj ) ! %o7 i"#jen'no/ 4ror!'n! ?!%tor %- rojn! &rije7no8t ?!%tor! % o&i8i o7 &eli'ine 4re8je%! &o7i'!( 8re7nje /eo#etrij8%e 57!ljeno8ti i"#e75 ?!"ni3 &o7i'!97 i ?!%tor! 8n!/e 8n!/e
cos φ 2=0,8 i cos φ2=0,9
cos φ 2 '
6! ?!%tor
7!te 85 5 t!.li'i 0-+ .rojne &rije7no8ti ?!%tor! % "! .!%!rne
i !l5#inij8%e &o7i'e-
0+
Tablica 3.1.- +rijednost 5a*tora *
1re8je% &o7i$! ##) ; +* +; ), 0, ,* =* B, +)* +,*
R!"#!% i"#e75 ?!"ni3 &o7i$! 9# *(,* *(=, +(** +(,* 'o8*(B +(*; +(*= +(*@ +(*B +(+* +(++ +(++ +(+) +(+, +(+; +(+= +(+@ +(*B +(+* +(++ +(+) +()) +()0 +(), +(); +(+2 +(+, +(+, +(+= +()B +(0) +(00 +(0; +(+@ +()* +()+ +()) +(2) +(2, +(2@ +(,+ +(); +()@ +(0* +(0) +(,2 +(,B +(;) +(;; +(02 +(0= +(0B +(2) +(=2 +(@* +(@, +(B+ +(2; +(,* +(,0 +(,= +(B) )(** )(*, )(+0 +(,= +(;) +(;= +(=+ )(+* )()+ )()@ )(0B +(;B +(=; +(@* +(@=
R!"#!% i"#e75 ?!"ni3 &o7i$! 9# *(,* *(=, +(** +(,* 'o8*(@ +(+* +(++ +(+) +(+0 +(+, +(+; +(+= +(+@ +()0 +(), +(); +()@ +(+, +(+; +(+; +(+= +(02 +(0; +(0; +(0@ +()+ +()0 +()2 +(); +(2; +(,* +(,) +(,; +()B +(0+ +(0) +(0, +(;, +(=* +(=2 +(@* +(2* +(22 +(2; +(,* +(@2 +(B+ +(B; )(*0 +(,) +(,; +(;* +(;, )(+, )(), )(0) )(2+ +(=) +(=@ +(@0 +(@@ )(2) )(,2 )(;0 )(=; +(@B +(B; )(*) )(+* )(=* )(@= )(B@ 0(+; )(*= )(+@ )()2 )(0;
Gornje &rije7no8ti 5 t!.li'i 90-+ &rije7e "! .!%!r ! 7onje "! !l5#inij- I" t!.li'e &i7i#o 7! je &rije7no8t ?!%tor! % rel!ti&o #!l! "! #!le 4re8je%e i &e'e ?!%tore 8n!/e- !%tor % #o"e#o i"r!'5n! i" ?or#5le
& =1+
X tan φ 2 R
4ri 'e#5 #or!#o &o7iti r!'5n! 8! 4ro.li"no#
&rije7no8'5 in75%to&no/ ot4or! %oji 4o %ilo#etr5 &o7i'! ni8%on!4o8n%o/ n!4on! i" no8i 4ri.li"no *(0; F%#- !%or % #o"e#o i"r!'5n!ti i ! ni8%on!4on8%e %!.lo&e- 1ri.li"n! &rije7no8t in75%to&no/ o4tor! ni8%on!4on8%i3 %!.lo&! i"no8i o7 *(*= 7o *(*B F%#-
0)
*.".Odr&%va!j& padova !apo!a -ro:az!o+ vod op-&r&7&!o+ !a v%8& +j&,-a N! 8li'i @- 4ri%!"!n je tro?!"ni &o7 8i#etri$no o4tereen 5 t!$%!#! + i )- Str5j! o4tereenj! 4ri%lj5$eno/ 5 t!'%i + o"n!'en! je 8! I +( ! 8tr5j! 5 t!$%i ) 8! I )- !'tor 8n!/e o4tereenj! 5 t!$%i + o"n!$en je 8! 'o8Q + ! ?!'tor 8n!/e o4tereenj! 5 t!$%i ) 8! 'o8Q )- N! 7ioni'i A+ o#8%i ot4or &o7! je R + ! in75%ti&itet P+( n! 7ioni'i +) o#8%i ot4or je R ) ! in75%ti&itet P)-
8li*a . 8imetri"no opterećen tro5azni od
N! 8li' B- n!'rt!n je &e%tor8%i 7i!/r!# ele%tri$ni3 &eli$in! n! o&o# &o75- N! 7ioni'i A+ te$e ".ir /eo#etrij8%i3 8tr5j! I + i I) tj I+ I) I+) N! 7ioni'i te$e 8!#o 8tr5j! I )-
8li*a 6. +e*tors*i diagram ele*tri"nih eli"ina na odu pri*azanom na slici
6!ne#!r5j5i %5to&e + i ) "!ne#!rili 8#o i 4o4re$ne %o#4onente 4!7o&! n!4on! t!%o 7! 4!7o&i n!4on! o8t!j5 8!#o 5"75ne %o#4onenteU%5ni !48ol5tni 4!7 linij8%o/ n!4on! i"no8i:
00
Δu =√ 3 ƩIZ = √ 3 ( ƩId − j Ʃ I 1 ) ( R + jX )= √ 3 ( ƩIdR + Ʃ I 1 X ) + j ( ƩIdX − Ʃ I 1 R )
6!ne#!ri&!nje# 4o4re$ne %o#4onente 4!7! n!4on! 7o.ije#o: IdR + I 1 X Ʃ
(¿)=√ 3 Ʃ ( IRcosφ + IXsinφ ) Δu =√ 3 ¿
A%o 4re74o8t!&i#o 7! 85 &o7i$i n! 8&i# 7ijoni'!#! i"&e7eni o7 i8to/ #!terij!l! i 7! 8i i8to/ 4re8je%!( #oe#o 5#je8to o#8%o/ ot4or! R i in75%ti&no/ ot4or! P 4i8!ti: RR +l i PP+l G7je 85 R+ i P+ ot4ori 4o je7no# %ilo#etr5 &o7i$! Δu =√ 3 ( R 1 ƩIdl + X 1 ƩI 1 l )
6! i8te ?!%tore 8n!/e 8lije7i: Δu =√ 3 ( R1 cosφ + I X 1 sinφ ) ƩIl I =
S √ 3 U
Δu =√ 3 ( R1 cosφ + I X 1 sinφ ) Ʃ (
S l) U 3 √
1ro'ent5!l!n 4!7 linij8%o n!4on! 4i
100 & ƩPl 2
ysU
()
02
*.*.Prorač! dvo,-ra!o !apaja!o$ -ro:az!o$ voda Go&orei o je7no8t!&no n!4!j!ni# &o7o&i#! i8to8#jerne 8tr5je re%li 8#o 7! oni ne o.e".je>5j5 4o/on8%5 8i/5rno8t- S&!%i %&!r 5 ne4o8re7noj .li"ini i"&or! one#o/5!&! n!4!j!nje 4otro
8li*a 1$. <ostrano napajani tro5azni od
1ri 4ror!$5n5 &o7! 4ol!"i#o o7 8lije7ei3 4re74o8t!&%i:
N!4oni 5 i"&ori#! A i ni85 je7n!%i 9UAWU I#4en7!ntni ot4ori 6 4oje7ini3 7ijoni'! 85 r!"li$iti !%tori 8n!/e 'o8 φ 4oje7ini3 4otro
1re#! 7r5/o# %ir3o?o&o# "!%on5 #oe#o r!"li%5 linij8%i n!4on! 5 t!$%!#! A i i"r!$5n!ti i" i"r!"!: I A Z 1+ ( I A − I 1 ) Z 2− I ( Z 3 U A − U (= √ 3 ¿
Str5je
I A
( I A − I 1 ( I (
te%5 n! 7ijoni'!#! $iji ot4ori i"no8e Z 1 ) Z 2 ) Z 3 -
1ri#jenj5j5i + %ir3o?o& "!%on n! t!$%5 ) #oe#o 4i8!ti: ( I (= I 2 + I 1 − I A ( U&r8t!&!j5i + %ir3o?o& "!%on 5 /ornji i"r!" 7o.ije#o: 0,
I A Z 1+ ( I A − I 1 ) Z 2−( I 2+ I 1− I A ) Z 3=¿ U A −U (
√ 3
=¿
Z Z I 1 (¿ ¿ 2 + Z 3 )− I 2 Z 3 I A (¿ ¿ 1 + Z 2 + Z 3)−¿
¿
O7!%le "! 8tr5j5 I A i#!#o: Z Z I 1 (¿ ¿ 2 + Z 3)+ I 2 Z 3 Z 1+ Z 2+ Z 3 √ 3 (¿ ¿ 1 +Z 2 + Z 3)+¿ U A−U ( I A =
¿
An!lo/no 6! 8tr5j5 I: Z Z I 1 (¿ ¿ 2 + Z 3)+ I 2 Z 3 Z 1+ Z 2+ Z 3 √ 3 (¿ ¿ 1 +Z 2 + Z 3)+¿ −(U A −U ( ) I ( = ¿
1r&i $l!n 5 je7n!$in!#! je 8tr5j! i"je7n!$enj! i on! te$e 5 &o7i$i#! ".o/ r!"li$iti3 n!4on! 5 i"&ori#! A i - Dr5/i $l!n je 8tr5j! %oj! .i te%l! %!7! .i n!4oni .ili je7n!%i9&e%tor8%i je7n!%i( 1re#! to#e !%o 85 n!4oni 5 i"&ori#! A i je7n!%i on7! je7n!$ine 4rel!"e 5 no&e o.li%e:
0;
I A =
I (=
Ʃ
( IZ ) ( ƩZ
Ʃ ( IZ ) A ƩZ
U%oli%o je &o7 i"#e75 t!$!%! A i i"&e7en 8! &o7i$i#! i8to/ 4re8je%! i i8to/ #!terij! i 8! i8ti# r!"#!'i#! i"#e>5 ?!"ni3 &o7i$! on7! tre.! r!$5n!ti 8!#o 75ine 8! o8toj!nji#! 4oje7ini3 o4tereenj!-
0=
*.0.Prorač! -ro:az!& &)&'-r%č!& zvj&zda,-& +r&2& Tri ili &i
8li*a 11. Tro5azna zjezdasta mreža
O4tereenje 5 $&ori8t5 K n!4!j! 8e i" tri i"&or! A((CKoli%o je 8tr5jno o4tereenje 4oje7ini3 i"&or! D! .i 8#o 7o.ili o7/o&or n! o&o 4it!nje 4oi e#o o7 8lije7ei3 4re74o8t!&%i: 1re8je% &o7i$! 8&i3 &o7o&! je i8ti M!teri!l &o7i$! 8&i3 &o7o&! je i8ti N!4oni n! n!4ojni# t!$%!#! 85 je7n!%iKori8tei 8e o&i# 4re74o8t!&%!#! 4ol!"ei o7 $injeni'e 7! 4!7o&i n!4on! n! 4oje7ini# &o7o&i#! #or!j5 .iti je7n!%i #oe#o n!4i8!ti 8lije7ee je7n!$ine: Δu A* =√ 3 I A
Δu (* = √ 3 I (
I A* cos φ * ys
I (* ys
cos φ *
I (* cos φ * Δu +* =√ 3 I + ys Δu A* = √ 3 I A
I A* ys
cos φ * = Δu (* = √ 3 I (
I (* ys
I (*
cos φ * = Δu +* = √ 3 I +
ys
cos φ *
0@
Ili !%o i"r!" 4o7jeli# 8!
√ 3 cosφ ys
)
7o.ije#o
IAlAK IlK IClCK 6! t!$%5 K %!o $&orn5 t!$%5 7jel5je + %ir3o?o& "!%on: I * = I A + I ( + I +
I" je7n!$ine i"n!7 7o.ije#o i"r!"e "! 8tr5je &o7o&!: I (= I A
I + = I A
I i I$ 4o#o5 8tr5je IA i 75ine 4oje7ini3
I A* I (* I A* I +*
U&r
I A =
I A * I (*
+ I A
l * l A* l A* 1+ + l (* l +*
I A* I +*
= I A ( 1 +
l A* l A*
+
l (* l +*
)
( A )
I" 'e/! #oe#o 4i8!ti i"r!" "! 8tr5je I i IC: I (=
I + =
l * l (* l (* + 1+ l A* l+* l * l +* l +* 1+ + l A* l (*
( A )
( A )
N!%on r!84o7jele o4tereenj!( #oe#o "&ije"7!8t5 #re5 r!8t!&iti n! tri je7no8t!&no n!4!j!n! tro?!"n! &o7! %!o 8to je 4ri%!"!no n! 8li'i-
0B
6! i".or 4re8je%! 8 o."iro# n! "!/rij!&!nje 58&!j!#o on!j &o7 $ije je 8tr5jno o4tereenje n!j&ee- O&! #re! je &eo#! rijet%! #no/o je $e<! #re! /7je 85 o4tereenj! o8t!&ljen! 75 &o7o&! %!o n! 8li'i +)-
8li*a 12. Tro5azna zjezdasta mreža sa opterećenem duž oda b)rastaljena tro5azna zjezdasta mreža
1ri 7i#en"ioni8!nj5 o&e #ree 4ol!"i#o i" i8ti3 58lo&! %!o i #ree n! 8li'i ++- Do7!t 'e#o 7! 85 ?!%tori 8n!/e 8&i3 o4terenj! je7n!%i- N!j4rije e#o o4tereenje n! &o7o&i#!AK( K( CK 4re.!'iti 5 $&or K- t!%o 7o.i&en! o4tereenj! 85 re75'ir!n! o4tereenj!- 1ri to#e 8e ele%tri$ne 4rili%e n! &o7o&i#! ne 8#ij5 #ijenj!ti9#onenti 8tr5j! i 8n!/e o8t!j5 i8ti: I 1 l 1= I 1r l A* I 2 l 2= I 2r l (*
I 3 l 3= I 3 r l+*
O7!%le 7o.ije#o:
2*
I 1 r = I 1
I 2 r = I 2
I 3 r = I 3
l1 l A* l2 l (* l3 l +*
6.ir re75'ir!ni3 8tr5j! 5 $&or5 K i o4tereenj! I % ( %oji 5 $&or5 &e 4o8toji 7!je 5%54no o4tereenje I5: I u = I 1 r + I 2 r + I 3 r + I *
N! t!j n!'in #re5 4ri%!"!n5 n! 8li'i 8&o7i#o n! #re5 4ri%!"!n5 n! 8li'i- Kori8tei 8e r!niji# ?or#5l!#! #oe#o n!4i8!ti i"r!"e "! 8tr5jn! otereenj! 4oje7ini3 i"&or!: I !A=
I !(=
I !+ =
l * l A* l A* 1+ + l (* l +* l * l (* l (* + 1+ l A* l +* l * l +* l +* + 1+ l A* l (*
( A )
( A )
( A )
St&!rn! o4tereenj! 7o.ije#o !%o o7 ?i%ti&ni3 o75"#e#o re75'ir!n! o4tereenj!: I A* = I !A− I 1 r
I (* = I !( − I 2 r I +* = I !+ − I 3 r
2+
U%oli%o 85 o4treenj! 4o"iti&n! on7! to "n!'i 7! te 8r5je te%5 4re#! $&or5 ! !%o 85 ne/!ti&n! on7! 8tr5je te%5 o7 $&or! 4re#! i"&ori#!- 6!3&!lj5j5i r!84o7jeli o4tereenj!( 4ron!l!"i#o n! #rei 858retn5 t!$%5 i n! t!j n!$in "&ije"7!8t5 tro?!"n5 #re5 r!"7&oji#o n! tri je7no8t!&no n!4!j!n! &o7!- U#je8to 8! 8tr5j!#! #oe#o 5 o&i# i"r!"i#! r!$5n!ti 8! 8n!/!#! 5 ili %-
2)
0.#ADATAK 6!7!t!%: Di#en"ioni8!ti tro?!"n5 "&ije"7!8t5 #re5 8 o."iro# n! tr!jne 8tr5je in! 7o"&oljeni 4!7 n!4on!( %oj! je i"&e7en! 8! Al 5eto#( !%o 85 n!4oni i"&or! je7n!%i 4o inten"itet5 i ?!"i9 U A =U ( =U + =U , - N!"i&ni n!4on #ree jeU 0X0@*F))* V- 1ro8je$!n ?!%tor 8n!/e tro
+- 1re.!'i#o9re75%5je#o o4tere'enj! 5 C&orn5 t!'%5 K-
Vo7 AK I 1 r = I 1
I 3 r = I 3
l1 l A*
=30
l3 l A*
=90
70 310
280 310
=6,77 A
I 2 r = I 2
l2 l A*
= 80
180 310
= 46,45 A
= 81,29 A
Vo7 K I 4 r= I 4
l4 290 = 40 = 28,29 A 410 l (*
I 5 r = I 5
l5 l (*
=20
140 410
=6,83 A
20
I 6 r = I 6
l6 l (*
=100
80 410
=19,91 A
Vo7 CK I 7 r = I 7
l7 900 =130 =22,94 A 510 l+*
I 8 r = I 8
l8 l +*
=70
310 510
=42,55 A
Vo7 DK I 9r = I 9
l9 l ,*
= 30
300 480
= 18,75 A
I 10 r = I 10
l10 160 =150 =50 A l ,* 480
)- U%54no re75%o&!no o4tere'enje 5 t!'%i K I u = I 1 r + I 2 r + I 3 r + I 4 r + I 5 r + I 6 r + I 7 r + I 8 r + I 9 r + I 10 r + I * =353,38
0-I"r!'5n!ti ?i%ti&n! o4tere'enj! i"&or! I !A=
I !(=
I !+ =
I !,=
l * 353,38 = =117,79 A 310 310 310 l A* l A* l A* + + 1+ + + 1+ 410 510 480 l (* l +* l ,* l * 353,38 = =88,78 A 410 410 410 l (* l (* l (* 1+ + + + + 1+ 310 510 480 l A* l +* l ,* l * 353,38 = =71,37 A 510 510 510 l +* l +* l +* + + 1+ 1+ + + 310 410 480 l A* l (* l ,* l * 353,38 = =75,83 A 480 480 480 l ,* l ,* l ,* + + 1+ + + 1+ 310 410 510 l A* l (* l +*
2-I"r!'5n!#o 8t&!rn! o4tere'enj! %oj! i"&ori 7!j5 I '&orn5 t!'%5 K I A* = I !A− I 1 r− I 2 r− I 3 r =−16,72 A
22
I (* = I !(− I 4 r − I 5 r− I 6 r =34,15 A I +* = I !+ − I 7 r − I 8 r =5,88 A I ,* = I !+ − I 9 r − I 10 r =7,08 A
Kontrol! I A* = I A* + I (* + I +* + I ,* =30,39 - 30 A
,- N!'rt!#o r!84o7jel5 o4tere'enj! 5 #re"i i o7re7i#o 858retn5 t!'%5
;- R!8t!&i#o #re"5 5 858retnoj t!'%i 0 n! 'etiri je7no8tr!no n!4!j!n! &o7!
! #!%8i#!ln! 8tr5j! te'e i" i"&or! C I i"no8i : I')*,(@@ A N!o8no&5 te 8tr5je o7!.ire#o 4re8je% 0X=* =* ##) 2,
=- 1ro&jeri#o 4re8je%e 4ro&o7ni%! 8 o."iro# n! 7o"&oljeni 4!7 n!4on! s=
100 & ƩIl
yu U
=71,52 mm 2
@-St&!rni 4!7 n!4on! n! /l!&no# &o75 i"no8i ust. =u
s1 s2
=3,76
3.#AKL6UČAK D! .i8#o 5 4r!%8i 4o&e!li 4o/on8%5 &rije7no8t &o7o&! "! 7i8tri.5'ij5 el- ener/ije #i ?or#ir!#o "&je"7!8t5 #re5 %oj5 n!4!j!#o i" &i5 i"&or!- 1ri rje
2;
