2º GIE MODELIZACIÓN DE UN TRANSFORMADOR TRIFÁSICO
Contenido
o
o
Φ
ε1 = - N1 ·
(1)
u1 = - ε1 = N1 ·
(2)
ε2 = - N2 ·
(3)
u2 = - ε2 = N2 ·
(4)
rt =
rt =
P1 = P2
U1 · I1 · cos(φ1) = U2 · I2 · cos(φ2)
φ1 φ2
=
= rt
S1 = U1 · I1 = U2 · I2 = S2
U2' = U2 · rt
I2' =
Z2' =
=
·
· = Z2 · rt2
∆U = U1 - U2' = URcc + UXcc
Rcc = R1+R2'
Xcc = X1+X2'
η
=
C =
=
η · · · (
· · · ( · ,
Pcc = Rcc · I2n2
rt =
rt =·
·
rt
· (
I2n = I2
I2n = ·I2
I1n = I2n ·
Sn = 3 · U2 · I2n = · Us · I2n
Ucc = Uf
Ucc = · Uf
µ.
Tensión Bobinado U(V) I(A) P(W) Q(Var) cosϕ
190 Primario 191.100 0.036 8.900 8.300 0.736
Secundario 60.400
280 Primario 281.000 0.056 17.800 21.400 0.646
Secundario 91.000
380 Primario 380.800 0.116 32.000 71.300 0.417
Secundario 126.500
Mediciones experimentales:
Alimentación en el primario
Alimentación en el primario
Referidos al secundario
Tensión rt N1/N2 Rfe(Ω) Ife (A) Iμ (A) Xμ(Ω) Rfe*(Ω) Xμ*(Ω)
190 3.164 1.827 4103.282 0.027 0.024 4609.164 1229.717 1381.325
280 3.088 1.783 4436.011 0.037 0.042 3825.560 1395.674 1203.612
380 3.010 1.738 4531.520 0.049 0.105 2086.572 1500.211 690.783
Referidos al secundario
rt N1/N2 Rfe(Ω) Xμ(Ω) Rfe*(Ω) Xμ*(Ω)Media 3.087 1.782 4356.938 3507.099 1371.281 1103.807
Resultados globales:
Resultados finales
Po Io Rfe(Ω) Xμ(Ω) Rfe*(Ω) Xμ*(Ω)33.143 0.116 4356.938 2086.572 1371.281 690.783
Tensión rt190 3.164
280 3.088
380 3.010
U1 U1^2 Pfe k*1000191.1 36519.210 8.900 0.244
281 78961.000 17.800 0.225
380.8 145008.640 32.000 0.221
0.230 Km*1000
Comprobación de la relación Pfe=kU1^2
μ>>
Mediciones
Corriente Ucc1(V) Ucc2(V) I11(A) I12(A) P(W) Q(Var) cosϕ
2.27 23.100 23.300 2.238 2.175 87.000 21.000 0.973
(
·
Análisis
Corriente Zcc (Ω) Rcc (Ω) Xcc (Ω) Lcc (mH)
2.27 5.959 5.790 1.398 4.449
Corriente Pcc (W) εcc (%)
Zcc (Ω)
2.27 87.000 6.08%
5.790+1.398i
Referenciado al secundario
Corriente rtn R'cc (Ω) X'cc (Ω) 2.27 3.087 0.607 0.147
ε
Resultados finales
Corriente rtn Zcc (Ω) Rcc (Ω) Xcc (Ω) R*cc (Ω) X*cc (Ω) Pcc εcc
2.27 1103.807 5.959 5.790 1.398 0.607 0.147 87.000 6.08%
Rfe(Ω) Xμ(Ω) Rcc (Ω) Xcc (Ω)4356.938 2086.572 5.790 1.398
Rfe*(Ω) Xμ*(Ω) R*cc (Ω) X*cc (Ω)1371.281 690.783 0.607 0.147
cos cos
( ( · cos ·
Mediciones
Tensión1 U11 (V) U12(V) U2(V) I11(A) I12(A) P(W) Q(Var) cosϕ380 381.000 380.400 115.100 0.177 0.175 79.000 89.000 0.676
Tensión U1 (V) U2(V) I1(A) Pe(W) Qe(Var) cosϕ380 219.797 66.453 0.177 26.333 29.667 0.676
Tensión Ucc (V) U1* (V)380 0.875 218.922
·
·
Tensión Pfe (W) Pcu (W) Ppérd (W) Qfe (Var)380 11.000 0.181 11.182 22.969
Tensión Z' (Ω) Z (Ω) R' (Ω) R (Ω) X' (Ω) X (Ω) L (mH)380 7823.906 715.169 3163.117 289.135 7155.990 654.116 2082.116
(
∆ ( · cos ·
Re(I1) Im(I1)I1 (A) 0.177 0.000 0.177+0i
U1 (V) 148.583 161.969 148.582772+161.968948i
Tensión S (VA) P (W) Q (VAr) Sn (VA) C C (%)380 16.566 15.152 6.697 500.000 0.078 7.80%
Tensión ΔU (V) ΔU (%) η (%)380 0.875 0.996 57.54%
Cz Cz (%)0.033 3.31%
Análisis
Módulo Real Imaginaria Complejo
I1 (A) 0.1770 0.1777
Ucc (V) 1.0584 1.0289 0.2484 1.028883+0.2484246i
U1* (V) 218.9193 147.5539 161.7205 147.553889+161.7205234i
Io (A) 0.1163 0.1114 -0.0336 0.111371785674486-0.0335980016012871i
I1* (A) 0.0744 0.0663 0.0336 0.066328214325514+0.0335980016012871i
Z' (Ω) 2944.3538 2753.2132 1043.5689 2753.21324173988+1043.56888240112i
R' (Ω) 2753.2132
X' (Ω) 1043.5689
Z (Ω) 269.1379 251.6661 95.3907 251.666114055602+95.3906952798428i
R (Ω) 251.6661
X (Ω) 95.3907
L (mH) 303.6381
S (VA) 15.2205 15.2205 5.7691 15.2204723783093+5.76911773801137i
ϕ 0.3623
cosϕ 0.9351
Tensión S (VA) P (W) Q (VAr) Sn (VA) C C (%) Cz Cz (%) 380 15.220 14.232 5.395 500.000 0.078 7.80% 0.030 3.04%
Tensión ΔU (V) ΔU (%) ΔUt (V) ΔUt (%) Pfe (W) Pcu (W) Ppérd (W) η (%) 380 1.058 9.358 1.833 9.358 11.000 0.181 11.181 56.00%
Mediciones
Tensión1 U11 (V) U12(V) U2(V) I11(A) I12(A) P(W) Q(Var) cosϕ380 380.600 380.400 114.300 0.182 0.182 69.700 98.500 0.586
Tensión U1 (V) U2(V) I1(A) Pe(W) Qe(Var) cosϕ380 219.682 65.991 0.182 23.233 32.833 0.586
Análisis
Tensión Ucc (V) U1* (V)380 0.824 218.858
Tensión Z' (Ω) Z (Ω) R' (Ω) R (Ω) X' (Ω) X (Ω) L (mH)380 6270.707 565.848 3975.724 358.756 4849.267 437.582 1392.866
Tensión S (VA) P (W) Q (VAr) Sn (VA) C C (%) Cz Cz (%)380 15.579 12.048 9.878 500.000 0.080 8.02% 0.031 3.12%
Tensión ΔU (V) ΔU (%) η (%)380 0.824 0.996 51.86%
Tensión Pfe (W) Pcu (W) Ppérd (W) Qfe (Var)380 10.994 0.192 11.185 22.956
Análisis
Módulo Real Imaginaria Complejo
I1 (A) 0.1820 0.182
Ucc (V) 1.0841 1.0538 0.2544 1.05378+0.254436i
U1* (V) 218.8599 127.6802 177.7566 127.68022+177.756564i
Io (A) 0.1163 0.1145 -0.0204 0.114495753168393-0.0203928709560565i
I1* (A) 0.0705 0.0675 0.0204 0.067504246831607+0.0203928709560565i
Z' (Ω) 3103.6325 2462.2322 1889.4305 2462.23221992766+1889.43045899523i
R' (Ω) 2462.2322
X' (Ω) 1889.4305
Z (Ω) 280.0615 222.1837 170.4959 222.183676398699+170.49594359202i
R (Ω) 222.1837
X (Ω) 170.4959
L (mH) 542.7056
S (VA) 15.4334 12.2439 9.3956 12.2439237576379+9.39555672209342i
ϕ 0.6545
cosϕ 0.7933
Tensión S (VA) P (W) Q (VAr) Sn (VA) C C (%) Cz Cz (%)
380 15.433 12.244 9.396 500.000 0.08 8.02% 0.031 3.09%
Tensión ΔU (V) ΔU (%) ΔUt (V) ΔUt (%) Pfe (W) Pcu (W) Ppérd (W) η (%)
380 1.084 9.317 1.878 9.317 10.99 0.192 11.186 52.26%
Re(I1) Im(I1)
I1 (A) 0.182 0.000 0.000
U1 (V) 128.734 178.011 128.734+178.011i
Mediciones
Tensión1 U11 (V) U12(V) U2(V) I11(A) I12(A) P(W) Q(Var) cosϕ380 381.300 381.400 115.500 0.113 0.108 69.600 13.300 0.968
Tensión U1 (V) U2(V) I1(A) Pe(W) Qe(Var) cosϕ380 220.173 66.684 0.113 23.200 4.433 0.968
·
·
·
· ·
Análisis
Tensión Ucc (V) U1* (V)380 0.673 219.500
Tensión Z' (Ω) Z (Ω) R' (Ω) R (Ω) X' (Ω) X (Ω) C (μF)380 4754.815 436.164 3992.438 366.231 -2582.385 -236.885 1.573
Tensión S (VA) P (W) Q (VAr) Sn (VA) C C (%) Cz Cz (%)380 22.220 12.068 -18.657 500.000 0.050 4.98% 0.044 4.44%
Tensión ΔU (V) ΔU (%) η (%)380 0.673 0.997 52.02%
Tensión Pfe (W) Pcu (W) Ppérd (W) Qfe (Var)380 11.058 0.074 11.132 23.091
Análisis
Módulo Real Imaginaria Complejo
I1 (A) 0.1130 0.113
Ucc (V) 0.6731 0.6543 0.1580 0.65427+0.157974i
U1* (V) 219.4995 212.4727 55.0940 212.47273+55.094026i
Io (A) 0.1166 0.0752 -0.0892 0.0751706144521603-0.0891834859104001i
I1* (A) 0.0969 0.0378 0.0892 0.0378293855478397+0.0891834859104001i
Z' (Ω) 2265.8020 1380.0241 -1797.0509 1380.02408655025-1797.050935255i
R' (Ω) 1380.0241
X' (Ω) -1797.0509
Z (Ω) 207.8444 126.5911 -164.8454 126.591088308442-164.845408030747i
R (Ω) 126.5911
X (Ω) -164.8454
Z1 (Ω) 280.0615 222.1837 170.4959 222.1837+170.4959i
R1 (Ω) 222.1837
X1 (Ω) 170.4959
Zce (Ω) 166.9321 2.7216 -166.9099 2.7215596355636-166.909892269806i
Rce (Ω) 2.7216
Xce (Ω) -166.9099
Xc (Ω) -500.7297
C (μF) 6.3569
S (VA) 12.9512 12.9512 -1.5470 12.9511901130903-1.54703402606039i
ϕ -0.1189
cosϕ 0.9929
Tensión S (VA) P (W) Q (VAr) Sn (VA) C C (%) Cz Cz (%)
380 21.264 21.114 -1.547 500.000 0.05 4.98% 0.043 4.25%
Tensión ΔU (V) ΔU (%) ΔUt (V) ΔUt (%) Pfe (W) Pcu (W) Ppérd (W) η (%)
380 0.673 9.317 1.166 9.317 11.058 0.074 11.132 65.48%
M1 M2 M3
P (W) 79.000 69.700 69.600
Q (Var) 89.000 98.500 13.300
S (VA) 119.004 120.666 70.859
cosϕ 0.676 0.586 0.968
ηp (%) 57.54% 51.86% 52.02%
ηi (%) 56.00% 52.26% 65.48%
119.004 120.666
70.859
0.000
20.000
40.000
60.000
80.000
100.000
120.000
140.000
0 1 2 3
Un
idad
es
de
po
ten
cia
Montaje
Comparación de potencias
P (W)
Q (Var)
S (VA)
0.676 0.586
0.968
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
1.100
0 1 2 3
cosϕ
cosϕ
57.54%
51.86%
52.02%
56.00%
52.26%
65.48%
50.00% 55.00% 60.00% 65.00%
M1
M2
M3
Rendimientos del trafo
ηp (%)
ηi (%)
M1 M2 M3
Pfep(W) 11.00014 10.99371 11.05824
Pfei(W) 10.99985 10.99388 11.05823
Pcup(W) 0.18139 0.19179 0.07393
Pcui(W) 0.18139 0.19179 0.07393
Pperdp(W) 11.18153 11.18549 11.13217
Pperdi(W) 11.18125 11.18566 11.13216
Cp (%) 7.80% 8.02% 4.98%
Ci (%) 7.80% 8.02% 4.98%
ΔUp (V) 0.87507 0.82362 0.67296
ΔUi (V) 1.05845 1.08406 0.67307
10.99985 10.99388
11.05823
0.18139 0.19179
0.07393
10.85000
10.90000
10.95000
11.00000
11.05000
11.10000
11.15000
11.20000
11.25000
M1 M2 M3
Pé
rdid
a d
e p
ote
nci
a (W
)
Potencias de pérdidas (i)
Pcui(W)
Pfei(W) 11.00014 10.99371
11.05824
0.18139 0.19179
0.07393
10.85000
10.90000
10.95000
11.00000
11.05000
11.10000
11.15000
11.20000
M1 M2 M3
Pé
rdid
a d
e p
ote
nci
a (W
)
Potencia de pérdidas (p)
Pcup(W)
Pfep(W)
0.87507
0.82362
0.67296
1.05845 1.08406
0.67307
0.60000
0.70000
0.80000
0.90000
1.00000
1.10000
M1 M2 M3
Caí
da
de
te
nsi
ón
(V
)
Caídas de tensión en el trafo.
ΔUp (V)
ΔUi (V)
7.80% 8.02%
4.98%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
M1 M2 M3
Índice de carga (p)
Cp (%)
o
o
o
o
o
o