Mfch chinh hru ban ky tai R

MACH CHINH LUU CO DIEU KHIEN

3.2 Mfch chinh hru co di~u khi~n mc)t pha

3.2.1 Mfch chinh hru ban ky tai R

C~u true cua m~ch chinh luu ban ky m(>t pha tai R duqc biSu di€n nhu hinh 3 .1.

Trong hinh 3.1: ~ + -

u2: la di?n ap tuc thoi ben thu R U d

dp bi~n ap dp cho m~ch chinh luu (con g9i la di?n ap ngu6n).

Ud, id: la tri di?n ap t(rc thoi tren Hinh 3.1 M9ch chinh luu c6 aiJu tai va dong di?n tuc thoi qua tai. khidn m{Jt pha ban kj; tai R Gia SU di?n ap hen thu dp cua bi~n ap dp cho m~ch chinh luu co d~ng

u2 = Um sin( mt) , SCR co goc kich la a. Goe kich a cua SCR duqc tinh t~i thoi diSm u2 >O.

+ Phan tich m9ch:

- Khi O < mt < a : thi m~c du UAK cua SCR la duong nhung do chua co tin hi?u kich vao SCR. Do do SCR ngiit, nen Ud=O, id=O va di?n ap tren hai dAu cua SCR la <pA -<pK = U2 -0 = U2.

- Khi a :::; OJt < tr : T~i thoi diSm wt=a ta cho xung kich vao chan kich cua SCR, luc nay SCR biit dAu dong. Khi SCR dong thi di?n th~ hai dAu cua SCR la bing nhau do do UsCR=O, Ud=u2 va id= Ud!R.

- Khi TC~ mt < 2TC : luc nay di~n ap ngu6n a nua am do do SCR bi phan

Cl,l'C nghich. Vi V?Y SCR bi ngiit, luc nay Ud=O, id=O va di~n ap tren hai d:lu cua SCR la <pA -<pK = U2 -0 = U2 (u2 luc nay co gia tri am).

Qua trinh cu nhu V?Y l~p l~i a cac chu ky ti~p theo.

- Can ct'.r vao USCR ta thfry di~n ap nguqc Cl,l'C d~i d~t len SCR la -Um.

Cac d~ng song minh h9a u2, Ud, id va USCR cua m~ch chinh ltru ban ky tai R duqc bi~u di€n a hinh 3.2.

-Um id

r ' - - - , - - - , - - - , - - - ,

1( 21r 4W1

Hinh 3.2 Cac dr;mg song cita mr;zch chinh luu c6 aiJu khidn m(>t pha ban ky tai R

Tir d~ng song tren hinh 3.2 ta suy ra duqc cac h~ qua sau:

- Tri trung binh di~n ap tren tai

I ~ U

ud =-f um sin(mt)d(mt) = __!!l_(l+cosa) (3.1)

2,r a 2,r

Nhuvay U • d max = Um

- Tri trung binh dong qua tai

u u

I = _E_ =-m-(1 +cos a)

d R 2trR - Tri hi~u di,mg di~n ap tai

U rms = ln 1 j" u2 ,,, Sill . 2 ( Wt )d( ) Wt = l u/11 (1-a)+-1-sin2a

1r 2n

- Trj hi~u di,mg dong di~n tai b~ng tri hi~u di,mg dong ngu6n

/ = U,ms

rms R

- Cong su~t tieu th1,1 boi di~n tr& tai

P= U,~n.,ã

R - H~ s6 cong su~t

p p

pf=s=u 1

2 _rms • 2 rms

Vi du 3.1

(3.2)

(3.3)

(3.4)

(3.5)

(3.6)

Cho m?ch chinh luu ban ky mc)t pha c6 di~u khi~n tai R nhu hinh 3.1.

Bi€t ngu6n c6 trj hi~u d1,1ng la 120V, f=50Hz. Tai R= 1 OOQ, di~n ap trung binh tren tai la 40V. Hay xac dinh cong su~t tieu th1,1 boi di~n tr& R va h~

s6 cong su~t cua m?ch.

Giai:

Oi~n ap trung binh tren tai

I " . U

U" =

21rfU111sin(cvt)d(cvt)=

2;(1+cosa)

Suy ra a= 61,25° = l ,07rad Trj hi~u d1,1ng di~n ap tai

u/'11/S = ~ 1/

Cong su~t tieu th1,1 tren tai

a) 1 . 2

(1-- +-sm a= 75,6V

1r 2n

P= U,2,ns =57 2W

R ,

Trj hi~u d1,1ng dong ngu6n bing tri hi~u d1,1ng dong tai

I = V,ms = 0.756A

2 _rm.,ã R

H~ s6 cong suit

if= 57,2 =0 63

P. 120.0, 756 ' 3.2.2 M~ch chinh hru ban ky tai RL

Ciu t~o m~ch chinh luu ban ky tai RL n6i ti~p duqc bi~u di~n nhu &

hinh 3.3.

R L

Hinh 3.3 Mqch chinh luu c6 aidu khiin m{jt pha ban ky tai RL

+ Phan tich mqch:

- Vi la tai mang tinh cam nen dong di~n qua tai se ch~m pha han so v&i

u2 m<;>t g6c 0

0 = tan-1 ( ~L)

D~ xac dinh dong di~n qua tai ta giai phuang trinh:

U sin(wt)= Ri(t) + L di(t)

"' dt

Nghi~m cua phuang trinh (3.8) co d~ng

i(t) = icb(t) +i,d(t) = ~sin(wt-0) u + Ae-llr

HO?C i(wt) = um sin(wt-0) + Ae-mtl,,,r

H~ s6 A duqc xac dinh tu di~u ki~n ban d~u: i(a) = o

i(a) = 0 = U,,, sin(a -0) + Ae-ai,,,r

⇒ A= [-i,' sin(a-0) ] e"1"'r

Thay A vao (3.9) ta duqc

i( wt) = i ' [ sin( wt - 0)- sin( a - 0)e<a-ml)!an] a ~ wt ~ /J

(3.7)

(3.8)

(3.9)

(3.10)

(3 .11)

Goe tit dong /J duqc xac dinh dva vao di~u ki~n t.;ti thai di~m wt=/J thi i(wt)=0, ta co:

i(/3) = ~ [ sin(/J-0)-sin(a-0)e(a-/JJ/wr] = 0 (3.12) Giai phuong trinh tren ta tim duqc goc /J

Goe (/J-a) duqc gQi la goc dftn dong

_ T.;ti thai di~m 0 < OJt <a: tuc la chua co tin hi~u kich cho SCR, do do SCR ngiit, dftn d~n:

{ :,==~-i, :O;u~ =O;u, =0

USCR - (f}A (f}K - U2

- T.;ti thai di~m mt = a : tin hi~u kich duqc dua vao chan kich cua SCR, k~t hqp v6-i USCR luc nay duong nen SCR dong.

- Khi a < mt < /J : SCR dong, dftn d~n:

{

id = i(OJt)

Ud = U2

UsCR = (f}A -rpK = 0

- T.;ti thai di~m mt = /3 : nang luqng tich h1y trong cu9n day giam xu6ng nho hon di~n ap ngu6n, do do SCR bi phan eve nghich -- SCR bi ngi1t.

- Khi /J <mt< 21[: khi SCR ngiit thi:

{

id= O; ud = 0

UsCR =rpA -rpK =U2 ,(u2 <0) - Qua trinh l~p l.;ti & cac chu ky ti~p theo

Cac d.;tng song cua m.;tch chinh luu ban ky m9t pha tai RL duqc bi~u di~n nhu & hinh 3.4.

Tit hinh 3.4, ta co cac hi qua sau:

- Tri trung binh di~n ap tren tai

1 /3 U

Ud =-f Um Sin(OJtyi(OJt) = __!!!...(COSa-COS/3)

21[a 21[

- Tri hi~u dvng di~n ap tren tai

. . - - - -

U,ms= -1 f[umsin(mt)]2d(mt) 2,r a

- Tri trung binh dong qua tai

(3.13)

(3.14)

1 /3

Id= -f i(wt)d(mt)

21r (3.15)

- Tri hi?u di.mg dong di?n qua tai bing tri hi?u di.mg dong qua ngu6n 1 /3

!,ms = -f i2(cot)d(cot) (3.16)

27r a

- Cong suit tieu thv b&i di?n tr& tai la I;msR

- Di?n ap nguqc ClJC d:;ii d~t len SCR c6 bien d(> la -Um

~~~ lld

t O Jr : ~---a 2Jr 3Jr 4Jr

Hinh 3.4 Cac dc;mg song cua mc;,ch chinh hru c6 aiJu khidn m9t pha ban ky tai RL

Vi du 3.2

Cho m:;ich chinh luu m(>t pha c6 di~u khi€n tai RL n6i ti~p nhu hinh 3.3, bi~t tri hi?u dvng di?n ap ngu6n la 120V, .f=50Hz, tai R=20Q, L=0,04H

va g6c kich a=45°.

a) Xac dinh bieu tht'.rc i(wt);

b) Dong trung binh qua tai;

C) Cong suit tieu thv b&i di?n tr& tai;

d) H? s6 cong suit.

Giai a) Ta c6:

Z = 23, 62.Q; 0 = 0, 56rad ; on = 0, 63 Thay vao phuang trinh (3.11 ), ta duqc:

i(wt) = {7,2[ sin(wt-0,56)-sin(0,22)e<0•785-r",l'0•63] a::; wt::; /J

0 wt~(a,/3)

Dung may tinh giai duqc /3 =3, 7rad.

b) Dong trung binh tren tai ] //

Id =-f i(mt'yl(mt) = 2,1 lA 2TC a

c) Tri hi~u d\mg dong di~n qua tai 1 /J

l,.111,. =

2n-f i2( wt)d( wt) = 3, 42A

Cong su~t tieu th1,1 b&i di~n tr& tai la 1,2,"'R = 234W d) H~ s6 cong su~t cua ngu6n

pf = P = I,2111, R = 234 = O 57 s u2 rmJ2 rms 120.3,42 '

M,ch chinh hru ban ky tai RL