Transformadores principios
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Transcript of Transformadores principios
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7/23/2019 Transformadores principios
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v= L di
dt
i= VZ
R= 10
L= 100mH
V1= 12
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7/23/2019 Transformadores principios
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V1=Ri+Ldi
dt
Ldidt
=V1 Ri
di
dt
= 1
L
(V1 Ri)
dt
(V1 Ri)
di
V1 Ri=
dt
L
di
V1 Ri=
ln(V1 Ri)
R
dt
L =
t
L+c1
ln(V1 Ri)
R =
t
L+c1
t= 0
i= 0A
c1
c1= ln(V1)
R
ln(V1 Ri)
R =
t
L
ln(V1)
R
ln(V1)
R +
ln(V1 Ri)
R =
t
L
ln(V1) +ln(V1 Ri) = R
Lt
ln(V1 Ri
V1) =
R
Lt
e
i
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7/23/2019 Transformadores principios
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e(ln(V1 Ri
V1)) =e(
R
Lt)
V1 Ri
V1=e
R
Lt
1 Ri
V1=e
R
Lt
Ri
V1=1 e
R
Lt
i=V1
R(1 e
R
Lt)
i=V1
R
V1
Re
R
Lt
V1R
V1R
eR
Lt
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v = 12sin(wt)
w = 260
vL= Ldidt
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l1 m1
m2
l1
m1
l2
m2
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l1 m1
m2
1 = l1+m1+m2
2 = l2+m2+m1
L =
i
v = Ri+d
dt
1 = N11
2 = N22
= l
A
l1 = N1i1
l1
l2 = N2i2
l2
m1 = N1i1
m
m2 = N2i2
m
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1 = N1
l1i1+
N1
mi1+
N2
mi2
2 = N2
l2i1+
N2
mi2+
N1
mi1
1= N11=N1( N1
l1i1+
N1
mi1+
N2
mi2) =
N21
l1i1+
N21
mi1+
N1N2
mi2)
2= N22=N2( N2
l2i2+
N2
mi2+
N1
mi1) =
N22
l2i2+
N22
mi2+
N2N1
mi2)
L11 = N2
1
l1+
N21
m=Ll1+Lm1
L22 = N2
2
l2+
N22
m=Ll2+Lm2
L12 = N1N2
m
L21 = N2N1
m
Lm1 Lm2 m1
m = N2
1
Lm1
m = N2
2
Lm2
N21
Lm1=
N22
Lm2
Lm2
N22
= Lm1
N21
L12 L21
Lm1
L12 = N1N2Lm1
N21
= N2
N1Lm1
L21 =
N2N1Lm2
N22 =
N1
N2 Lm2
1 = Ll1i1+Lm1i1+L12i2= Ll1i1+Lm1i1+N2
N1Lm1i2= Ll1i1+Lm1(i1+
N2
N1i2)
2 = Ll2i2+Lm2i2+L21i1= Ll2i2+Lm2i2+N1
N2Lm2i1= Ll2i2+Lm2(
N1
N2i1+i2)
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i
1 =
N1
N2i1
i1 = N2
N1i
1
i
2 =
N2
N1i2
i2 = N1
N2i
2
2= N1
N22 v
2= N1
N2v2
2=
N1
N2Ll2
N1
N2i
2+
N1
N2Lm2
N1
N2i1+
N1
N2Lm2
N1
N2i
2=
N21
N22
Ll2i
2+
N21
N22
Lm2i1+N2
1
N22
Lm2i
2
L
l2= N2
1
N22
Ll2 Lm1= N2
1
N22
Lm2
2= L
l2i
2+Lm1i1+Lm1i
2
1=Ll1i1+Lm1(i1+i
2)
2= L
l2i
2+Lm1(i1+i
2)
r
2=
N21
N22 r2
v1=r1i1+d1
dt v
2=r
2i
2+
d
2
dt
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P1= |V1||
I1|cos()
= cos1 P
|V1||I1|=cos1
12
110 1= 83.70
V1 I1 V1
Z=V1
I1=
11000
1 83.70= 12 +j109.3
r1 = 12 L11 = Ll1+ Lm1
X11=Xl1+Xm1= 109.3
i1 = i
2
Lm1 |r
2+L
l2| Xm1 |r
2+jX
l2|
= cos1 22
30 1= 42.800
(r1+r
2) + (Ll1+L
l2)
(r1+r
2) +j(Xl1+X
l2)
Z= 3000
1 42.80= 22 +j20.4
r1+r
2 = 22
r1 = 12 r
2 = 22 12 = 10
Ll1=L
l2 Xl1=X
l2 Xl1=Xl2= 20.4
2 = 10.2
Xm1= 109.3 10.2 = 99.1
r1= 12 Ll1= 10.2260
= 27X103H
r
2= 10
Ll2= 27X103H
Lm1= 99.1260 = 262.9X10
3
H
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1 = Ll1i1+Lm1(i1+i
2)
2
= L
l2i
2+Lm1(i1+i
2)
v1 = r1i1+d1
dt
v2
= r
2i
2+
d
2
dt
1
2
=
Ll1+Lm1 Lm1
Lm1 Ll2+Lm2
i1
i
2
v1
v
2
=
r1 0
0 r
2
i1
i
2
+
d
dt
1
2
ddt
1
2
=
Ll1+Lm1 Lm1
Lm1 Ll2+Lm2
ddt
i1
i
2
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v1
v
2
=
r1 0
0 r
2
i1
i
2
+
Ll1+Lm1 Lm1
Lm1 Ll2+Lm2
d
dt
i1
i
2
didt
Ll1+Lm1 Lm1
Lm1 L
l2
+L
m2
d
dt i1
i
2=
v1
v
2
r1 0
0 r2
i1
i2
d
dt
i1
i
2
=
Ll1+Lm1 Lm1
Lm1 Ll2+Lm2
1
(
v1
v
2
r1 0
0 r2
i1
i2
)
N1 = 50 N2 = 100 r = 4000
Lm1 Lm2 L12 r1= 2 r2= 4 v1= 127cos(377t)
v2
i2= 0
1 = Ll1i1+Lm1i1= (Ll1+Lm1)i1
2
= Lm1i1
v1 = r1i1+d1
dt
v2
= d
2
dt
Ll1
Ll1
=
N21
l1
l1 = l
r0A=
0.25
4x107 4000 0.0025= 19894.368
Ll1 = N2
1
l1=
502
19894.368= 0.1256637H
l = 0.25
A= 0.05x0.05 = 0.0025 m2
Lm1
Lm1= N2
1
m
Lm1= 0.75 A= 0.0025 m2
l1 = l
r0A=
0.75
4x107 4000 0.0025= 59683.104
Lm1 = 502
59683.104= 0.0418879H
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L12=N1N2
m=
50 100
59683.104= 0.0837758H
d
dt1 = (Ll1+Lm1)
di1
dt
v1 = r1i1+ (Ll1+Lm1)di1
dt
di1
dt = (
1
Ll1+Lm1)(v1 r1i1)
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7/23/2019 Transformadores principios
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r = 2500
i1= 1cos(wt) w= 260
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7/23/2019 Transformadores principios
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