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lecture3

# lecture3 - EE 740 Professor Ali Keyhani Lecture#3 Ideal...

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EE 740 Professor Ali Keyhani Lecture #3 Ideal Transformers

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I 1 I 2 I 1 I 2 V 1 V 2 V 1 V 2 N 1 N 2 IT + + - - I 1 I 2 Z 2 V 1 V 2 N 1 N 2 The ideal transformer: V 1 /N 1 = V 2 /N 2 N 1 I 1 = N 2 I 2 S 1 = V 1 I 1 * S 2 = V 2 I 2 * S 1 = S 2 a = V 1 /V 2 = N 1 /N 2 V 1 = aV 2 I 1 = I 2 /a Z 2 = V 2 /I 2 Z 2 ’ = V 1 /I 1 = (aV 2 ) / (I 2 /a) = a 2 Z 2 Real transformer: I 2 I 1 N 2 N 1 R 1 jX 1 R 2 jX 2 Load V 1 V 2 I c R c jX m I m V 1 I 2 /a
N 2 N 1 I 1 I 2 IT V 1 V 2 + - + - V 2 V 1 I 2 I 1 V 2 V 1 N 2 N 1 a = = V 1 I 1 I 2 R 1 jX 1 I c R c jX m R 2 jX 2 Load I m N 1 N 2 I 1 R 1 jX 1 I c R c jX m R 2 jX 2 I m N 1 N 2 V 1 I 2 Load I 2 /a R 2 ’ = a 2 R 2 X 2 ’ = a 2 X 2

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I 1 I 2 I 1 I 2 V 1 V 2 V 1 V 2 N 1 N 2 IT + + - - I 2 I 1 N 2 N 1 R 1 jX 1 R 2 jX 2 Load V 1 V 2 I c R c jX m I m V 1 I 2 /a N 2 N 1 V 2 V 1 a = = I 1 R 1 jX 1 I c R c jX m R 2 jX 2 I m N 1 N 2 V 1 I 2 Load R 2 & X 2 are referred to winding 1
I 1 R eq jX eq I 2 V 1 N 1 N 2 Load R eq = R 1 + R 2 X eq = X 1 + X 2 Neglecting excitation current N 1 N 2 I 2 jX eq I 1 V 1 Load V 2 V 2

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Determination of Req and Xeq from short-circuit test.
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