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.
Analysis of Simultaneous Faults by the Method of Symmetrical Comp
Dec 14, 2015
Análisis de fallas simultaneas
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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 .""",,
,
Related Documents
