2 Transformadores Problemas

��BLEMA� DE ��A��F��MAD��E�

ELEC��EC�IA � MA��I�A� ELEC��ICA� (2013) ��

�� 1: �� 1 = 40 �� 2 = 100 �� . C��: �. L� FEM �� 48 � (�� , �� ). �. E� �� 50 H�.



A� ��

 =  ⟹   =   =   ∙  = 48∙ 10840 = 129.6   = 4.44∙ ∙  ∙  ∙ 10     ∙ 10 48∙10   = 4.44∙ ∙  = 4.44∙40∙50 = 541.000 

D� �� : ��: � �� , ��:

�� 2:

�� 1000/120 �, �� 50 H�, �� 80 ��2 �� . D��: �. E� �� . �. E� �� . �. �� 1000 � �C�� ? � �C�� I��? � C�� .

L��:

 = 520000      =  ∙ = 6500  ∙80      ∙ 10 1000∙ 1 0   = 4.44∙ ∙ = 4.44∙50∙520000 = 866.2 ; =  =  = 1120000 = 8.33  =  = 8668.33 = 103.9 ≅ 104 

C�� 1000 �, ��:

2

ELEC��EC�IA � MA��I�A� ELEC��ICA� (2013)

 = 1 =  ⇒   =   ∙  = 1000∙8.33 = 8.333       ∙ 10 8 . 3 33  ∙10   = 4.44∙ ∙ = 4.44∙50∙866 = 4.351.250   =  = 4.351.80250  = 54.140 

C�� , �� , �� , �� /�� 10 � 12 �� , �� . �� 3: �� : S N = 333 KVA; U N : 6000/133 V; f = 50 Hz. �� , �� 133 � �� I 0 = 110 A � P0 = 1300 W . �� , �� 193, 5 � �� , �� 55.5 A � �� 2500 �.

C�� . D�� . L� �� :

 =  =  =  = 6133000 = 45.1  =  = 155.93.55 = 3.49 Ω  =  = 255.5005 = 0.81 Ω  =   −   =  3.49 − 0.81  = 3.39 Ω 3.419 = 0.001715 Ω;   =  = 45.0.811 = 0.000398 Ω;   =  = 45.3.319 = 0.00167 Ω  =  = 45.  =   ∙   ⇒   =  = 1100300 = 0.1074 Ω  =  = 111033 = 1.21 Ω  =   −   =  1.21− 0.1074  = 1.205 Ω    0. 1 074       =  +   = 0.1074 + 1.205  = 0.0734 ;   =  +   = 0.1 0741.2 +051.205  = 0.823 

L� �� :

D��:

�,

�� :

D�� R0 y Z 0, �� :

A�� :

A�� :

3


 = 1 (Siemens)    =  = 0.45.0734  1 =0.00003607 s;  =  = 0.45.8231 =0.0004044 s 1300110 =0.0889 ⇒ sin  = 0.996 cos =  ∙  = 133∙  =  ∙cos = 110∙0.0889 = 9.78 ; =∙sin =110 ∙ 0.996 =109.56 

�� G’0 y B’0 �� , �� .

�� , �� :

 =   = 9133.78 = 0.0734 ;   =  = 109.13356 = 0.823     =  = 0.45.0734  1 =0.00003607 s;  =  = 0.45.8231 =0.0004044 s

C�� :

�� 4: �� . E�� ; �� 33 � �� (�� ), �� CC = 85 �. �� 80% �� . E�� :

 =  = 5000380 = 13.16 ; =  = 13.3316  = 2.51 Ω 4


 =   ∙   ∙ cos  ⇒ cos  =  ∙  = 33 85∙13. 16  = 0.196 ⇒   = 78.7� A��:

cos = 0.8 ⇒   = 36.87�

D�� :

 ∙ cos( −  ) = 33∙cos(78.7−36.9) = 24.7 ;  ∙ sin ( −  ) = 33∙sin∙ (78.7−36.9) = 21.9   =   +   ∙ cos( −  ) +  ∙ sin ( −  ) 380 =   + 24.7  + 21.9 (*)

D�� ; �� :

′ + 49.4  − 143.312 = 0 A�� , �� :

� ��, �� (*):

 = −49.4 �  49.42 + 4∙143.312 = 354.7 

E� �� :

 =  380 − 21.9  − 24.7 = 354.67  7  (%) = 380−354. 380 ∙100 = 6.7%

5


�� 5: �� : S N = 100 KVA, U N = 3800/230 V y 50 Hz;

�� , �� , �� : U ecc = 7 V; I ecc = 435 A; Pecc = 1120 W

C��: �. L�� (�� ) �� , �� . �. E� �� . �. E� �� .

 =  = 1435120 = 0.006Ω; Z  = UI = 0.016Ω; X  =  Z − R  =  0.016 − 0.006  = 0.015Ω  =   +  0.006 = ( 0.006+0.015)Ω; cos =  = 0.016 = 0.375 ⇒   = 68�  =  = 0.230016Ω = 14380 

�� 6:

L� �� , �� : U N = 230 V; I 0 = 42 A; P 0 = 615 W.

�. D�� . �. C�� 3800 � � �� 300 A �� , �� 0.8 ��.

615 = 0.06366 ⇒   = 86.35�;sin   = 0.998 cos =  ∙  = 230∙42  =  ∙cos = 42∙0.0637 = 2.67 ;=∙sin =42 ∙ 0.998 =41.916   =   = 2230.67 = 0.0116 ;   =   = 41.230916 = 0.1822     =  = 0.16.0116   52=4.253∙10 s;  =  = 0.16.182252 =6.676∙10  s  = 3230800 = 16.52

D�� , �� :

6


 =   ∙   = 16.52  0=.016  ∙=4.3 =6716.Ω;52 =0.015 ∙ = 4. =09316.Ω52  0.006 = 1.637 Ω;

�� :

L� �� :

 =  + � =   ∙   ∙ cos  +  +   ∙    = 0.006  =Ω;0.cosφ  = 0.3676 ⇒   =68.43�;   =   ∙ tan68.43�  006∙2.528 = 0.015 Ω;   = ( 0.006+0.015)     ( ) (0.  =  cos − si n  = 300∙ 8 −06);  =  + 0       )∙(0.   =    +    ∙  ;   = (  + 0)+300∙(0. 8 −0. 6 0 06+0. 0 15)  =   + (3.9642+2.5272);  = (  +3.9642) +2.5272    =  230− 2.5272  −3.9642 =226   =   ∙   ∙ cos = = 226∙300∙0. 8 = 54240 ;   =   ∙   = 300 ∙ 0.006 = 540     +   +   = 54240+540+615 = 55395  4240 ∙100 = 97.9 % (%) =  ∙ 100 = 555395

�� (�IEM��E DE�DE EL LAD� DE BAJA �E��I��):

�� :

�� 7: �� , �� : E��

�� (�) C�� (A) �� (�) L��

��

240

8.75

480

B�

C��

600

��

1200

A�

C��: �. �. �. �.

�� 0.8 �� . �� . �� . �� 0.8 ��.

 =  =  =  = 12000 240 = 50

7


 6 00     =  =  = 10012 = 8. 3 3 ;  =   8.33  = 72.02 Ω  D��:

�,

 =  = 18.20033 = 17.29 Ω  =   −   =  72.02 − 17.29  = 69.914 Ω  =  = 72.5002 = 0.0288 Ω;   =  = 17.5029 = 0.006916 Ω;   =  = 69.50914 = 0.02796 Ω  =  ∙ = 50∙8. 3 3 = 416. 5     = (  ∙ cos  +   ∙  )+( ∙ sin   + ∙  )    = ( 240∙0.8+416. 5 ∙ 0 . 0 06916)+(240∙ 0 . 6 +416. 5 ∙ 0 . 0 2796) 8 7+155. 6 = 249. 3 7∠38. 6 �  = 194.  (   (%) =  − )= 249.32407−240 ∙100 = 3.9 %  ∙   ∙ cos  ∙ 100 = 240∙ 4 16. 5 ∙ 0 . 8 ∙100 = 97.94% % =  +  +  =  ∙   ∙ cos 240∙416.5∙0.8+480+1200  +   +   480 = 0.632 ⇒ % = 63.2%  ⇒  =  =   ∙   =   ∙  ∙  =   ∙  ∴  =   =  1200 0.63∙100000∙80+2∙480 .8 ∙100 = 98.14% % =  ∙ +∙2∙  ∙ 100 = 0. 63∙100000∙0.

�� :

�� 8: A� �� S N = 250 KVA, �� 24.000/398 V , �� 960 V �� . �� 4.010 W , ��: �. �. �. �. �.

�� ; �� ; �� ; �� ; �� .

,   

M�� :

 =  = 25024 = 10.4   = 628   =  = 20.50398

8

ELEC��EC�IA � MA��I�A� ELEC��ICA� (2013) L�� :

 =  = 4.010 

�� :

401010.4 = 0.4;   = 66.3� cos =  ∙  = 960∙

L� �� Ucc:

960 100 = 4%  =  100 = 24000  = =  ∙ ∙cos  = 4∙cos66.3� = 1.6%   sin   = 4∙sin 66.3� = 3.7%  =  = 910.604 = 92.3 Ω   ==  ∙ sin ∙cos  = =92.92.33∙0.∙0.9164 ==36.84.95ΩΩ     =   ∙    =   ∙   = 5.2  ∙ 36.9 = 998   = 3.2 %;   = 2.4 %

L�� u Rcc � u Xcc �� :

D�� :

�� :

�� , �� , �� , �� , �� , �� : �� 9:

�� = 0,85. L�� : 10 KVA; 1000/398 V ; . A�� = 0,85 �� .

D�� , �� . C�� , �� , �� , �� . A �� (ε). 9


  −    (%) =  ∙100

�� (��) �� , �� :

  −    (%) =  ∙100 = − ∙100       −   =  − ≅  + =  ∙  ∙cos +  ∙   ∙sin     −   ∙  ∙cos + ∙  ∙ sin       (%) =  ∙100 = ∙100     ∙   ∙      (%) =  ∙100 ;  (%) =  ∙100 (%) =  (%)∙cos +(%)∙sin  = 3.2 ∙0.85+2.4 ∙0.53 = 4(%)

D�� : L��:

�� , �� ,

A�� , �� :

E��:

D�� : ϕ = 31.8º � sin ϕ = 0.53

E�� 4% � �� , �� :

 −   = 0.04∙1000 = 40   −   = 0.04∙398 = 15.9   =   − 15.9 = 398−15.9 = 382   =   − 15.29= 398−7.95 ≅ 390 

��, �� :

E� �� :

C�� , �� 50 % �� 50 % ��:

�� 10:

�� fp = 0,85. L�� 50 KVA � 1.000/230 V . E� �� : �� 90 W �� 10 V � �� 12,5 A. A�� : �. �� ; �. �� fp = 0,85 �� . L� �� :

 =  = 501  = 50 

10

ELEC��EC�IA � MA��I�A� ELEC��ICA� (2013) E�� (M�� ). E�� . �� , �� , �� :

 =  = 12.105 = 0.8 Ω  cos = ∙  = 10∙9012.5 = 0.72 ⇒   = 43.94�   =   ∙ cos  = 0.8 ∙0.72 = 0.58 Ω L�� :  =  ∙  = 0.58∙50  = 1450 

L� �� :

 =  ∙  = 0.8 ∙50 = 40     (%) =  ∙ 100 = 401000 ∙100 = 4 % (%) =  (%)∙cos = 4∙0.72 = 2.88 %;  (%) =  (%)∙sin = 4∙0.694 = 2.77 % (%) =  (%)∙cos +(%)∙sin  = 2.88∙0.85+2.77∙0.53 = 3.9 (%)  =   − 0.039∙  = 230−0.039∙230 = 221   =   − 0.0239∙  = 230− 0.0239∙230 = 225.5 

E� �� :

L��:

A�� :

L� �� U 2 �� U 2N : �� :

�� 11: �� , �� : E��

�� (�) C�� (A) �� (�) L��

��

250

80

4000

B�

C��

600

��

5000

A�

D��: �. �. �. �. �. �.

L�� . E� �� . L�� : L�� : . L�� . L� �� (� �� ).

 ,      cos ,   cos,,   

11

ELEC��EC�IA � MA��I�A� ELEC��ICA� (2013) �. �. �. �.

L� �� 0.8 ��. I�� 50 %. �� 0.8 ��. �� .

E� �� , �� , �� :

 =  =  = 7120200 = 60 ⇒   =  ∙  = 60∙250 = 15000   =  = 25015  = 16.6  4000 = 0.2 ⇒   = 78.46� ⇒ sin  = 0.97979 cos =  ∙   = 250∙80  =   ∙   ⇒   =  = 480000 = 0.625Ω;   =  = 28050 = 3.125 Ω  =   −   =  3.125 − 0.625  = 3.062 Ω  =   ∙   = 60  ∙ 0.625 = 2250 Ω;  =   ∙   = 60   ∙ 3. =125 = ∙ 11250 Ω;    = 60  ∙ 3.062 = 11023.2 Ω

E� �� , ��:

E� �� :

�� (�� ) �� :





A�� , �� , �� :

 = 56250 Ω;  = 1 =  = 11250   2250 1250 2 = 11482 Ω   = 1  =   = 111023.  

�� :

 15000    =  ∙cos  = 1.315000 = 56250 Ω;  = =   ∙ sin   1.3 ∙0.97979 = 11482 Ω  ∙ 0.2 5000 6= 1 2 ⇒  = 60� ⇒ sin  =  32 cos =  ∙  = 600∙16.  =  ∙cos  = 60016.6 ∙ 0.5 = 18 Ω;   =  ∙sin  = 60016.6 ∙0.866 = 31.17 Ω

A��, �� :

L�� (�� ) �� :

12


  600 = 4%;  (%) =  (%)∙cos = 4∙0.5 = 2%;  (%) =  = 15000 (%) =  (%)∙sin = 4∙0.866 = 3.464%  ∙ 100 = 16.6 ∙100 = 416.5 ;  () =   ∙ 100 = 1000 ∙100 = 25000  () = (%) 4 (%) 4

D� �� , �� L� �� (�� /��) � �� .

�� :

(%)∙sin (%) =   (%)∙cos + = 2∙0. 8 +3. 4 64∙0. 6 = 3. 3 3 (%)    −  1 5000−    (%) =  ∙100 = 15000 = 3.33%; ⇒   = 14500      =  = 14500 60 = 241.67   ∙   ∙ cos  ∙ 100 % =  +  +  =  ∙   ∙ cos  +   +   0.8 ∙100 = 95.55% % = 241. 67∙241.1000∙67∙01.8000∙+4000+5000 % =   ∙ 100 =  45000000 ∙100 = 89.44% 250000∙ 0 . 8 % =  ∙ +∙2∙  ∙ 100 = 0.8 94∙0.8294∙50000∙ 0.8+2∙4000 ∙100 = 95.71%

�� :

A�� :

E� �� ( PFe = PCu), ��:

�� 12: E� �� S N = 100 KVA ��: η = 93.02% �� cos φ = 0.8 � η = 94.34% � �� (p = 0.5) � �� . C��: �. L�� . �. L�� . E� �� :

D�� “p” �� .

 ∙ + ∙ cos +   ∙   =  ∙ ∙ cos

D� �� :

1∙100000∙ 0 . 8 0. 5 ∙ 1 00000∙ 1 (1) 0.9302 = 1∙100000∙0. (2) , 0 . 9 434 = 8 + + 1  ∙  80000−74416 0. 5 ∙100000∙1+ + (0.5) (1):( + ) = 0.9302 = 6003  (3) , (2):( + 0.25) = 50000−47170 0.9434 = 3000  (4)

13

ELEC��EC�IA � MA��I�A� ELEC��ICA� (2013) �� (3) � (4), ��:

 +  = 6000 (3)    + −0.0.2525 = =30003000(4)   = 30.00075 = 4000   + 4000 = 6000  ⇒  = 2000 

L�� , �� :

�� (3)

AC��ALI�AD�: 29.03.2013

14

2 Transformadores Problemas

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