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If a voltage source is applied to the primary while

If a voltage source is applied to the primary while

Power System Analysis and Design (MindTap Course List)
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter3: Power Transformers
Section: Chapter Questions
Problem 3.9P
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If a voltage source is applied to the primary while the secondary is left open-circuited (I2 = 0) the transformer equations reduce to: V, =(R,+jwL,)I, 200 If R, has been measured and we know the frequency ® , the measurements of V1, V20c, and I1, can be used to determine the values of L, and M. 20C, If a voltage source is now applied to the secondary while the primary is left open-circuited (i.e. I, = 0) the value of L2 can be determined in a similar fashion, V; =-(R,+jwL,)I,
Transcribed Image Text:If a voltage source is applied to the primary while the secondary is left open-circuited (I2 = 0) the transformer equations reduce to: V, =(R,+jwL,)I, 200 If R, has been measured and we know the frequency ® , the measurements of V1, V20c, and I1, can be used to determine the values of L, and M. 20C, If a voltage source is now applied to the secondary while the primary is left open-circuited (i.e. I, = 0) the value of L2 can be determined in a similar fashion, V; =-(R,+jwL,)I,
2. The parameters of a certain transformer are to be found. Following the procedure as outlined in the introduction under the first order low frequency model section: The resistance of the primary winding of a certain transformer is found to be R1 = 388 Q, while the resistance of the secondary winding is R, = 0.9 Q. A 200 Hz, 5 volt peak-to-peak sinusoid, V1, is applied to the primary while the secondary is left open-circuited. The primary current, I,, entering at the dot is measured to be 1.07 milliamps peak-to-peak, lagging the voltage by nearly 83°. The open circuit voltage across the secondary, V20c, is measured to be 0.155 volts peak-to-peak. The sinusoid driving the primary is removed and a 200 Hz, 5 volt peak-to-peak sinusoid, V2, is applied to the secondary while the primary is left open-circuited. The secondary current, I2, entering at the dot is measured to be 206 milliamps peak-to-peak, lagging the voltage by 87°. From these measurements, estimate the self-inductances, L, and L2, the mutual inductance, M, and the coupling coefficient, k, of the transformer.
Transcribed Image Text:2. The parameters of a certain transformer are to be found. Following the procedure as outlined in the introduction under the first order low frequency model section: The resistance of the primary winding of a certain transformer is found to be R1 = 388 Q, while the resistance of the secondary winding is R, = 0.9 Q. A 200 Hz, 5 volt peak-to-peak sinusoid, V1, is applied to the primary while the secondary is left open-circuited. The primary current, I,, entering at the dot is measured to be 1.07 milliamps peak-to-peak, lagging the voltage by nearly 83°. The open circuit voltage across the secondary, V20c, is measured to be 0.155 volts peak-to-peak. The sinusoid driving the primary is removed and a 200 Hz, 5 volt peak-to-peak sinusoid, V2, is applied to the secondary while the primary is left open-circuited. The secondary current, I2, entering at the dot is measured to be 206 milliamps peak-to-peak, lagging the voltage by 87°. From these measurements, estimate the self-inductances, L, and L2, the mutual inductance, M, and the coupling coefficient, k, of the transformer.
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