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