Me;1ch chinh luu du m<)t pha c6 di€u khiSn tai RL nhu a hinh 3.23.
SCR2
R
L
SCR4 SCR3
Hinh 3.23 Mr;zch chinh luu cdu m(jt pha c6 aiJu khiin tai RL Khi tai RL thi dong qua tai se ch~m pha sau di~n ap d~t len tai. Do d6 ta phai tim biSu thuc dong tuc thai qua tai tru6c. Bi~u thuc dong tuc thai qua tai duqc tinh gi6ng nhu me;1ch chinh luu ban ky m<)t pha c6 di€u khiSn tai RL.
{
um [ sin( wt - 0)-sin( a - 0)e(a-cv,)/o,r] a s OJ{ s /3 i(wt) = Z
0 wt~[a ,/3]
(3.65)
Tu d6 tim duqc /J va n6 se niim 6 hai tnrong hqp sau:
+ Truong h9p 1: /J<7r+a
Day la tnrong hqp dong qua tai gian do~n va c6 d~ng song nhu 6 hinh 3.24.
' I I
t = =
t" c:?-- I
E ããã~~ ãã ~ -":Ca
~ ~i2 () ---rr : ~ ã ã ããã _ : ~ - ;~ ããã ~ ã
2rr 3rr 4rr
Hinh 3.24 Cac dr:;mg song ciia mc;ich chi'nh luu cciu m(Jt pha c6 diiu khidn tai RL vcri /J<7r+a
+ Cac h~ qua suy ra tu hinh 3.24 nhu sau:
- Tri trung binh di~n ap ngu6n 1 /J
ud = - f viii sin(mt)d(mt)
1[ a
- Tri hi~u di.mg di~n ap ngu6n
, - - - -
1 /J ?
U,,,,, = - f (U111 sin(mt) f d(mt)
1[ a
- Tri trung binh dong qua tai l //
(, = - f i(cvt)d(mt)
1[ a
(3.66)
(3.67)
(3.68)
- Tri trung binh dong qua SCR l /3
lscR =
2n.J i(cvt)d(mt)
a
- Tri hi~u d1,mg dong tai
~ - - - - - 1 /i
!rm, = - f i2(cvt)d(cvt)
J[ a
- Tri hi~u di,mg dong ngu6n
, - - - - 2 /i
12 ,m.,ã =
21[ f i2(mt)d(cvt) - Cong su~t tieu th\l b6i tai
P=lrms 2 R
a
- Di~n ap nguqc ct,rc d~i d~t Jen SCR la U,n.
Vi du 3.7
(3.69)
(3.70)
(3.71)
(3.72)
Cho m~ch chinh luu du m(>t pha c6 di€u khi~n tai RL n6i ti~p. Bi~t R=I0Q, L=20mH, tri hi~u dl,lng di~n ap ngu6n la 100Y,.f=50Hz, g6c kich a=60°. Xac dinh
a) Bi~u thuc dong tuc thoi qua tai; b) Tri trung binh di~n ap tren tai;
c) Tri trung binh dong qua tiii;
d) Cong su~t tieu th\l tren di~n tr& tai.
Giai a) Bi~u thuc dong tuc thoi qua tai
Z = 11, 80; 0 = 0, 56rad; wr = 0, 63rad; a = 1, 04 7rad
i( wt)= 11,984 sin( mt -0, 56)- 29, 545e-w110•63 a ~ mt ~ f3
Thay mt=/3 choi(/3)=0suy ra /3=Jr+0=3,7rad. Yi n+a=4,187rad >
/3 nen dong qua tai la gian do~n.
Chit y: D~ tim /3 ta nen dung each b~m may tinh.
b) Di~n ap trung binh tren tai 1 //
ud = - f um sin(wt)d(wt) = 60,69V
J[ a
C) Dong trung binh qua tai 1 /J
Id= - f i(cvt)d(wt) = 6A
J[ a
137
d) Cong su~t tieu th\l b&i di~n tr& tai I /3
lrms = - f t2(cot)d(cot) = 7,27 A Jr a
P = J;m,R = 528, 5W + Tr,rirng h!J'P 2: fJ 2: n-+a
Truong hqp nay dong qua tai la lien t\lc va co d,;mg song nhu a hinh 3.25.
p U2 I ~~- ~
Ud :
~
R=-E ~ '?=iS---
u.f":_cz ' -l Cd
i2 :
0 n ;r+a 2n 37t 4n
Hinh 3.25 Cac dgng song cita mgch chinh luu cdu c6 aiJu khi<2n tai RL v&i fJ 2: n+a
Phan tich Fourier cua d~ng song di~n ap tren tai ta duqc:
00
ud(OJt) =Uo + Lun cos(nav+</JJ (3.73)
n=l
- Tri trung binh di~n ap tren tai
1 ,r+a 2U
Uo = ud = - f um sin(OJt)d(OJt) = __ m cos a
Jr a Jr
(3.74)
- Trj hi~u d1,mg dong qua tai
Mu6n tinh trj hi~u d\mg dong qua tai ta phan tich tung thanh ph.1.n nhu sau:
Trong cong thi'.rc khai tri~n chu6i Fourier cua di~n ap tai, thanh ph.1.n Un dm;rc tinh:
Trong d6:
Vi du 3.8
Un = ✓a~ +b;
a = 2U m [ cos( n + l )a _ cos( n - l )a]
n tr n+l n-l
b = 2Um [sin(n+l)a _ sin(n-l)a]
n tr n+l n-l
n = 2;4;6; ...
I = Uo
o R
I = Un
n Z
n
(3.75) (3.76) (3.77)
(3.78)
Cho m<,1ch chinh luu du c6 di€u khi~n tai RL n6i ti~p .Hinh 3.23. Bi~t R=l0Q, L=20mH, trj hi~u di,mg di~n ap ngu6n la 100V,f=50Hz, g6c kich a=30°. Xac djnh
a) Bi~u thi'.rc dong ti'.rc thoi qua tai;
b) Trj trung binh di~n ap tren tai;
C) Trj trung binh dong qua tai;
d) Cong su§.t tieu thv tren di~n tra tai.
Giai
a) Tu cac s6 li~u d€ bai ta tinh duqc cac thong s6 sau:
Z = 11, 80; 0 = 0, 56rad; wr = 0, 63rad; a = 0, 52rad Thay vao bi~u thi'.rc dong di~n:
i( wt) = i [ sin( wt -0)- sin( a - 0)/a-wt)lwr] a s wt s /J
Taduqc:
i(wt) = 11, 98sin(wt-0,56) + l,0l6e-ax10•63 as wt s /J
Suy ra: /3 = 3, 7rad
Vi 7r+a=3,66rad < fJ nen dong qua tai la lien t\Jc.
b) Tri trung binh di~n ap tren tai
1 ,r+a 2U
u() = ud = - f um sin(wt)d(wt) =--"' cos a= 78V
ff a ff
C) Dong trung binh qua tai
1 = ud = 7 SA
" R ,
d) Cong suflt tieu th\l b&i di~n tr& tai Tri hiã d ~u \}Ilg ong ta1 d' ã, ã
n a,, bn u/1 z/1 Ill
0 (de) 78 10 7,8
2 -77,96 -15 79,39 16,05 4,95
4 -15,6 -21 26,16 27,04 0,97
6 4,45 -15,4 16,03 38,98 0,41
P = J ;,111R = 8,622. IO= 743, 044W
Chu y : Khi L co gia tri du Ion lam cho dong qua tai lien t1,1c va bling phimg thi chung ta khong dn phan tich Fourier. Luc do:
- Tri trung binh di~n ap tren tai
1 n+a 2U
ud = - f um sin(wt)d(wt) = __ m cos a
ff a ff
- Dong trung binh qua tai
1 = ud = 7 8A
" R ,
3.2.9 M~ch chinh hru c§u m{>t pha co di~u khi~n tai RLE
M~ch chinh luu du m(>t pha c6 di~u khi€n tai RLE duqc bi~u di~n nhu & hinh 3.26.
Chu y: di~u ki~n d€ cac SCR co kha nang kich dong duqc la a :2: a
111;
11 • Gia
tri Umin duqc xac djnh theo cong thtrc:
. - 1 ( E)
a min = Sill -
um
Trong d,;mg nay ta vi~t bi~u thuc dong tuc thc'Yi qua tai theo c6ng thuc (3.20) gi6ng nhu trnc'Yng hqp chinh luu ban ky c6 di~u khi~n m(>t pha tai RLE.
SCR2
f] I u, R L
SCR4 E
SCR3
Hinh 3.26 M{Jch chinh luu cciu m(Jt pha c6 diJu khidn tai RLE +TrU'ifng h(Yp 1: dong qua tai la lien ll:{C
D~u hi~u d~ nh~n bi~t dong qua tai la lien t\lc la /3 ~ ,r+a
- Khi L du l&n d~ dong qua tai la lien t\lc va bilng philng (L=oo ). d tr~mg thai xac l~p ta c6 d,;mg song nhu & hinh 3.27.
LI
5 f ~ ~ ~ f s d
id
' '
0 -ãã -------:-' - --:-' .. ----
I I j :
o~~ ~ iscRt
L
~ d
TT+U
Hinh 3.27 D9ng song m{Jch chinh luu cciu m(Jt pha c6 diJu khiin tai RLE khi L=oo
+ Cac h¢ qua suy ra tit hinh 3.27:
- Tri trung binh di~n ap tren tai
I ,r+a 2U
ud = - f um sin((l)t)dmt = __ m cos a
Jr Jr
(3.79)
(1
141
V, O< < l _a _1[ nen ___ ~ 2U m ~Ud ~ - - m 2U
TC TC
- Tri trung binh dong qua tai
I _ ud -E
d - R
- Di~n ap nguqc C\l'C d~i d~t len SCR la um
- Dong trung binh qua SCR la
(3.80)
(3.81) - Tri hi~u d\lng dong ngu6n bing tri hi~u d1,mg dong tai bing tri trung binh dong tai
I rm,ã nguon -- I d
- Cong sullt tieu th\l tren tai
P=Udld - H~ s6 c6ng sullt
pf= p = Udld = iJiurmJd = 0 9cosa
s urmslrms :rUrmsld '
Vi du 3.9
(3.82) (3.83)
(3.84)
Cho m~ch chinh luu du m(H pha c6 di~u khiSn tai RLE. Bi€t ngu6n c6 bien d(> 220V, f=50Hz. Tai c6 R=50., E=50V, L=oo. Goe kich cua cac SCR la 60°. Tinh:
a) Tri trung binh di~n ap tren tai;
b) Tri trung binh dong qua tai;
c) Dong trung binh qua T;
d) Tri hi~u d\lng dong ngu6n;
e) H~ s6 c6ng sullt.
Giai a) Tri trung binh di~n ap tren tai
ud = 2um cos a= 70V
TC
b) Tri trung binh dong qua tai
ld=Ud-E=4A R
c) Dong trung binh qua SCR la
ISCRI = ISCR2 = ISCR3 = ISCR4 = Id I 2 = 2A
d) Tri hi~u d\mg dong ngu6n
Jrm~_nguon = Jd = 4A e) H~ s6 cong su~t
p
nif=-=0 9cosa=O 45
r. s ' '
- Khi L c6 gici tri tuO'flg a6i /(rn ( dong qua tai la lien t'l:lc nhung chua bling ph&ng) thi c6 thd tinh gdn dung theo ccic cong thuc trong truimg h9]J L=oo.
+ Trll'img hf/P 2: (dong qua tai gicin iloc;m)
D~u hi?u d€ nh~n bi~t dong qua tai gian do~n la /J<Jr+a.
Truong hqp dong qua tai la gian do~n duqc th€ hi?n nhu a hinh 3.28.
opU2 . - - - ==±;;; -- --- ~ - - ==±;;; ... ;a
Ud
ol ~
iscR1 : 1 1
OE F=E:2E" : s:z
' '
0 a fl ,r+a s3
Hinh 3.28 Ccic dc;mg song cita mc;ich chinh luu cdu m(Jt pha c6 aiJu khidn tai RLE v&i /J<Jr+a
Khi O <wt< a thi SCR chua dong. Do do: UJ = E, id= 0, iscR1 = 0, uscR1
= u2 va i2 = 0.
Khi a < wt < /J thi SCR1+J dong. Khi do: UJ = u2, id = iJ(wt), iscR1 = id(Wt), USCRI = 0 VQ i2 = iJ(wt).
Khi /J < wt < Jr+a thi cac SCR d~u ng~t. Khi do: Ud = E, id = 0, iscR1 = 0, USCRJ = U2 Va i2 = 0.
143
Cac h~ qua suy ra tu hinh 3.28 nhu sau : - Tri trung binh di~n ap tren tai
1 [/i 1r+a ]
Uc1 = Jr [Um sin( cvt)d( cvt) + t Ed( cvt)
- Tri hi~u d1,mg di~n ap tren tai
~ - - - -
1 [fi 1r+a ]
Urm, = - f (Um sin(cvt))2 d(cvt) + f E2d(cvt)
J[ a fl
- Tri trung binh dong qua tai I P
Id= - f i(cvt)d(cvt)
J[
(1
- Tri hi~u d1,mg dong ngu6n bing tri hi~u di.mg dong tai 1 fi
I,.,,,, = - f i2 ( cvt)d( cvt)
J[ a
- Di~n ap nguc;rc qrc d?i d~t !en SCR la U111 - Dong trung binh qua SCR la :
Vi du 3.10
I.w_-R1 = lscR2 = lscR3 = 1scR4 = Id
2
(3.85)
(3.86)
(3.87)
(3.88)
(3.89)
Cho m?ch chinh luu du m()t pha c6 di~u khi~n tai RLE. Bi~t ngu6n c6 bien d() 220V,f=50Hz. Tai c6 R=l0Q, E=IO0V, L=50mH. G6c kich cua cac SCR la 60°. Tinh :
a) Tri trung binh di~n ap tren tai;
b) Tri hi~u di.mg di~n ap tren tai;
C) Tri trung binh dong qua tai;
d) Tri hi~u di.mg dong qua tai va tri hi~u di.mg dong ngu6n;
e) Dong trung binh qua SCR;
f) Ki~m tra l?i b~ng phin m~m Psim.
Giai
Can ct'r vao s6 li~u d~ bai ta c6 cac thong s6 sau:
Z = 18,620; 0 = 1; cv-r = 1,57; A= 18,4 Suy ra:
i( cut)= 11, 82 sin(cvt -1)-10 + I 8, 4e-"''11ã57
➔ p = 3, 41 <Jr+ a
a) Tri trung binh di~n ap tren tai
I [/3 1r+a ]
ud = 1r [ um sin(mt)d(mt) + ! Ed(mt) = 127,32V
b) Tri hi~u d1,mg di~n ap tren tai
1 [/3 ,r+a ]
Urms = 1r [ (Umsin(mt))2d(mt)+ ! E2d(mt) =148,48V
C) Dong trung binh qua tai 1 /3
Id= - f i(mt)d(mt) = 2, 71A
Jr a
d) Tri hi~u d1,mg dong tai bing tri hi~u d1,mg dong ngu6n 1 /3
Jrms = - I i2(mt)d(mt) = 3,47 A
Jr a
e) Tri trung binh dong qua SCR
ISCR = - = Id 1,36A 2
f) Sa d6 mo phong Psim th~ hi~n nhu hinh 3.29 va d~ng s6ng a hinh 3.30.
Gia tri trung binh va tri hi~u d1,mg duqc th~ hi~n a bang 3 .3.
iSCR1
(9
Hinh 3.29 Sad6 mo phong Psim cua vi d1;13.10
Uz --- _______ ;1
~ 1 f.-- --__;:::::==
0.01 0.02
Timc(s) 0.03
Hinh 3.30 Cac dc;mg song mo phong cua vi d11 3.10 Bang 3.3: Tri trung binh va tri hiiu d11ng
j
0.04
Average Value @ RMS Value
~---'==="""-"""---'-'---"'!::=:l
Tme From Tme To u2 . ud
2. O()()()O()()e..2
• 4. O()()()O()()e..2 . . •_-3,4 5 4 0 1 ~
! 1.2698662e+-002
' id _ _ _ _ _ _ _ _ _ _ _ !2.10168ne+-000 - iSCR1
: i2
i 1.3532282e+-OOO : -1.2308168e-003
,me From
Tme To u2 ud : id
; iSCR1
• i2
12. OOOOOOOe-002
I 4.0000000e-002 11 5552462~;- .
,1 4 8 3 1 ~ , J..4681507e+OOO
I 2. 4S20518e+-OOO
t"' -- -••• - .•• -- -., - ---
,3.-4681733e+-OOO
Nh~n xet: Ket qua ly thuyet va kJt qua mo ph6ng la gi6ng nhau.