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Two single phase, 11000/440 V transformers have kVA ratings of 200 kVA and 100 kVA respectively. The equivalent resistance and reactance of the 200 kVA transformer are respectively 1  and 5  when referred to 11000 V side. The equivalent reactance of 100 kVA transformer referred to the 11000 V side is 9  . (1) What should be the equivalent resistance of 100 kVA transformer if each transformer is to supply load in proportion to its kVA rating when operated in parallel?
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Two single phase, 11000/440 V transformers have kVA ratings of 200 kVA...
Solution:



Calculating the Total Load:

  • Two transformers are connected in parallel.

  • The total kVA rating of the two transformers is 200 kVA + 100 kVA = 300 kVA.

  • The load on each transformer should be in proportion to its kVA rating. Therefore, the 200 kVA transformer should supply twice the load of the 100 kVA transformer.

  • Let the load on the 200 kVA transformer be X and the load on the 100 kVA transformer be Y.

  • Then, X + Y = Total Load = 300 kVA.

  • Also, X = 2Y (since the 200 kVA transformer should supply twice the load of the 100 kVA transformer).

  • Substituting X = 2Y in the equation X + Y = 300 kVA, we get:

  • 2Y + Y = 300 kVA

  • 3Y = 300 kVA

  • Y = 100 kVA

  • Therefore, the load on the 100 kVA transformer should be 100 kVA.

  • The load on the 200 kVA transformer should be 2Y = 2(100 kVA) = 200 kVA.




Calculating the Equivalent Resistance of the 100 kVA Transformer:

  • Let the equivalent resistance of the 100 kVA transformer be R.

  • From the question, the equivalent reactance of the 100 kVA transformer referred to the 11000 V side is 9 .

  • Let the equivalent impedance of the 100 kVA transformer referred to the 11000 V side be Z.

  • Then, Z = R + jX, where X is the equivalent reactance of the 100 kVA transformer referred to the 11000 V side.

  • Therefore, Z = R + j9 .

  • The total impedance of the two transformers should be the same when they are connected in parallel.

  • Let the equivalent impedance of the 200 kVA transformer referred to the 11000 V side be Z1.

  • Then, Z1 = R1 + j5 , where R1 is the equivalent resistance of the 200 kVA transformer referred to the 11000 V side.

  • The total impedance ZT of the two transformers is given by:

  • ZT = (Z1Z)/(Z1 + Z).

  • Since the total impedance should be the same as the impedance of the 200 kVA transformer, we have:

  • ZT = Z1

  • Therefore, (Z1Z)/(Z1 + Z) = Z1

  • Simplifying this equation, we get:

  • Z = Z1(Z1 - Z)/(Z - Z1)

  • Substituting the values of Z1, X, and Z, we get:

  • R = 0.77  (approx.)

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Two single phase, 11000/440 V transformers have kVA ratings of 200 kVA and 100 kVA respectively. The equivalent resistance and reactance of the 200 kVA transformer are respectively 1  and 5  when referred to 11000 V side. The equivalent reactance of 100 kVA transformer referred to the 11000 V side is 9  . (1) What should be the equivalent resistance of 100 kVA transformer if each transformer is to supply load in proportion to its kVA rating when operated in parallel?
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Two single phase, 11000/440 V transformers have kVA ratings of 200 kVA and 100 kVA respectively. The equivalent resistance and reactance of the 200 kVA transformer are respectively 1  and 5  when referred to 11000 V side. The equivalent reactance of 100 kVA transformer referred to the 11000 V side is 9  . (1) What should be the equivalent resistance of 100 kVA transformer if each transformer is to supply load in proportion to its kVA rating when operated in parallel? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Two single phase, 11000/440 V transformers have kVA ratings of 200 kVA and 100 kVA respectively. The equivalent resistance and reactance of the 200 kVA transformer are respectively 1  and 5  when referred to 11000 V side. The equivalent reactance of 100 kVA transformer referred to the 11000 V side is 9  . (1) What should be the equivalent resistance of 100 kVA transformer if each transformer is to supply load in proportion to its kVA rating when operated in parallel? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two single phase, 11000/440 V transformers have kVA ratings of 200 kVA and 100 kVA respectively. The equivalent resistance and reactance of the 200 kVA transformer are respectively 1  and 5  when referred to 11000 V side. The equivalent reactance of 100 kVA transformer referred to the 11000 V side is 9  . (1) What should be the equivalent resistance of 100 kVA transformer if each transformer is to supply load in proportion to its kVA rating when operated in parallel?.
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