Analysis of Simultaneous Faults by the Method of Symmetrical Comp
49
Scholars' Mine Masters eses Student Research & Creative Works 1948 Analysis of simultaneous faults by the method of symmetrical components Robert Marshall Montgomery Follow this and additional works at: hp://scholarsmine.mst.edu/masters_theses Department: is esis - Open Access is brought to you for free and open access by the Student Research & Creative Works at Scholars' Mine. It has been accepted for inclusion in Masters eses by an authorized administrator of Scholars' Mine. For more information, please contact [email protected]. Recommended Citation Montgomery, Robert Marshall, "Analysis of simultaneous faults by the method of symmetrical components" (1948). Masters eses. Paper 4915.
-
Upload
eduarzz-castillo-pizarro -
Category
Documents
-
view
23 -
download
0
description
Análisis de fallas simultaneas
Transcript of Analysis of Simultaneous Faults by the Method of Symmetrical Comp
Scholars' Mine
Masters Theses Student Research & Creative Works
1948
Analysis of simultaneous faults by the method ofsymmetrical componentsRobert Marshall Montgomery
Follow this and additional works at: http://scholarsmine.mst.edu/masters_thesesDepartment:
This Thesis - Open Access is brought to you for free and open access by the Student Research & Creative Works at Scholars' Mine. It has been acceptedfor inclusion in Masters Theses by an authorized administrator of Scholars' Mine. For more information, please contact [email protected].
Recommended CitationMontgomery, Robert Marshall, "Analysis of simultaneous faults by the method of symmetrical components" (1948). Masters Theses.Paper 4915.
o
o
•
o . 0 t
1 1 u t
o SC .......................,._ .......
o , au ·
9 8
T B o CO T T
Ll t of Illustrations .............................. a
i
1
:3
8
9
2
:3..•
......
..............
........
............................
Net ork
u t
..... ..........................
uano
8 ••••••••••••••••••••••••••• •• • ••
............................................................................
lterature
two
t on
to-
hort-C1rcults
o
r cal Components •.••.•.•.•••.•••.•
evle
T P 8 of
1st of Tabl s
Introduction
7
T
...
o
t -, d Z roof c ... ...... 9
on Thr... .....1 .. .....
q
2.
3.
1.
.......
• •
•
7.
• •
• •
o
t o... c ......
I T 0
1 1 1 t on0 ult eu - ..... 7
I , , 0,t It
1................ .... 8
c o
•
•
,
,
1
,
t
o c
to
c
•
o
•
.,( , )
(((
c
o OO...Y"Io·".... .£IIo....,,· ...
I
o
,
,
• •
....................... .-. .... .....1-..)
d
o
o
to 0
o
LI.&..LIi"",a.;;J·""~' 1 t
con 1
,
•
,
•
t
c
•••• ,un 1 y. b r pl c
1 t 0 ctor (po 1-
tlv - t ) h 1 h qU nc
t 0 1 n 1 u 1 ce ctors, (2) b d
( qu c t m)
to th
or 1 c or , (3 ) t
0 hr in 1 -p eto (z ro- qu nc t m)
lch r qu 1 tu n p
(6) c. ., Vol.3 ,918,
t
o o
o
2 o
o
•
o t t
• • c. • 11
1ho •
on
ch
t.
opt
(7)
c o
7
t
o
( )
o
•
10
o o c
t
C 0 ,
o
t
,0
o t
1
+ 2 +
+
zl +
+
+ z
)
)
• •
• ( ) ( )
o ( , ) , (
•
-1/ a+ + ) (7
- /3 ( + + ) (
2 I + + ) )
,
c
c
, ,c
c
c
t •
o
c •
,
t to b p 1
c ,
t,
o
o
•
o
,
,
olt
o ,
, ,,
( ,
,
,0
e
t 0 c
,
I ,
2' • 2
o
,I
, •
t
vol z 0 ,to 2' 0 c
n olt 0
on c
,
I
o t ,0 0 ,
)0)
u
( ) J
)
o J ,o
o
o
-"·""":a~-nt to
o ,
•
0- ........__
f h h
1 1 0 h o
) .1
o
hpp
d h
bo
n olt
po • o cu r t 0
o
z o
( ) , (
•
o
o
,
o t on (7 ) , 8 ) ,
() d ,
,
13 + 0+0) I
I (+0+0) I I
I (I + 0 + 0 I
2
(, ), ) ,
( ),
+h
{ , (
•
b t t
, ( 2),
( )
sto
,,
o o , ,
~- - -
~~
- - -
~~
- - -
~• 4. 31m It n 0 ults t 0 tr c 1
three-pha sy tem.
, , OJ , , ,
It , I 2' ,
o •
•
t
lb1··· .....".... -"III""'lII ••
t to
o
,
, , 1 +
•
•
o
o
o
o c
(
•
tot
of t
an t t
o I t o t o
o
+ ) (2 )
t Y 1
+ ) ( 22)
18)~, ( ) ,
22 0(
o
o t
(
( .
t
• o
ou
to t g
,t b
e It
z
,
• •
b h z ro po
t t , , b t
2
z 2
z
p
,, ,
, , p •
nd
I
-~
, , , t
,
•
t
I
•
, ,
2',
o 10
2 2 2 2 22
2 2
2
o
), (27 ), ( 8 ), ( ) ,
C1L..l~l.£IJ~"'.L~.L""
h
•
, ,I
2
( )
( ( )-( )
)
co
( )-( ),
It tot , ,
zo (
,
+++
+++
,i. I , ,
v -1 -- V
.x2 - 2 - z2
( 9)
(70)
c - V - V nd inc I l' I l' and I Z11 - 1 zlt q I to z ro, t i a 1 e n from equ t10n ( 2) ,
(33) , d (34) that k, 1, m, n, 0, p, q, r, nd
11 qu 1 to z rOe The result r ch g d r 0 , 0,
0 0 the thr a-phase f It e 0 d.
L ne-to- ound Fau t at Y on
t 1 , h a n -to ult t
C • t f 1 oint
0 1
I 2 I 7
2
dd eq • (27) d (30) nd au t t n
tl - nd z o s uence co po ant
( 2+ )1 +{ 2+ )I 1+ I (8 )0 0 z2 z
. (28) nd (31) n ubstitutln fo th n
n z 0 uenc component
z2 +D zo)I & ( z2 +D zo) 1 +D zz2 z(8 )
ts k, 1, m, n, 0, p, q, r, pr
(80) , (81) , (82) •
0 0 t t h
0
CI , C v 1 0 T b I 0
I 0 I 1 (8 )
2
0
o )
I 2
(
), ( ) ,
•
u It co t ,,"' ... .u........... ...,."t 0
...u....,""......" .....t
t 0 ( )
+ )I +( +) +( z + ) z )
c
7)
+ (
) , ) , ( 00)
, I J
) )
)
) )
) ) (
) ) (-
, ) )
+ ( + + +)
( 1 + ) Q} 1 +1)( z +} - (
( +)[I 1+)( z+
+} z +.~
(D z +)( 1+~o 1 11
...... __...- ( )
, ( ( ) .
,
,
o.
c
o
c
10.
p
----- + +
____......... + + --_....0.-.
+ + ............._-
), 7)
) , (
, Co po.......... _........ wo_, 2
II
, , m, n, 0, p, q,t Thr e 0 nt onh se , , and A' a e •
C S n 1e Lin to Ground a lt t Thr e 01 t •
( ) h se , A, nd (b) h s , nd Bt
k (D 2t- D 0) k (D 2 +D 0)
1 (D 2 +Dx 0) 1 ( 2+ 0
m (Dxz2 +D zo) ( z2 + 2 zo)
n (D 2~ yo) ( 2 +D
o - ( 2 +D 0) 0 (D 2+
P ( z2 + zo) p ( z2 + z
( 2+ D 0) ( z2 4-
1- +--+ )
( , ( )
( + ) +( 2-+ 0) (
( ) ( zo)
( ) (
0 ( ) 0
( ) )z( +( ) 0
+ z zz2 -+ Z 0
T B E II co tid
C n -to L n t t Thr e o n( ) band c, B (b) he. s a and c, an
Bt and C t a. d , and ct.k Dxx.2 k xx2
2 1 2D 2x
= Dxz2 m 8.2 2
n D 2 n D 2
0 2 0 2
P z2 P 2
z2 2
z2 z2
z zz2
z
o
+
T II cont'd
Case • Lin -to-Line Fault at t 0 points and a Lin -toGround F ult at one point.
( ) hase a, B & 0, Bt & C' ( ) h b & c, I B' C
k = ( xx2 +Dxxo )k _ D
2
1 -Dx 2 2
m xz2 m z2
n - - n 22
0 2 0 ( 2+P z2 z2
q z2 z2
z2 z2
olt
tho 0 th t
s on tel m
It
t
t
f ct d
o on , too
Th f It 1
1 n s.
o c ( ,
,
00
•
,
3 d ns d s
46-49.
I
,o•
0 .""",,
,
