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(2) (z) Just to make sure as a preliminary question... if the base quantity is XB and the actual value of the quantity is X, write down the fundamental definition of Xpu- In a 3 phase balanced AC system, suppose that we have already chosen the 3 phase power base S and the line to line voltage base V. Now we choose the rest of the bases in a coordinated way. (a) What is the single phase power base SB that makes the 3 phase power and the single phase power numerically equal in per unit? (b) What is the line to neutral voltage base VB that makes the line to line voltage and the line to neutral voltage numerically equal in per unit? Show that it works. (c) What is the line current base IB that makes S = VI* work out in per unit? First give the answer expressing Ig in terms of SB and VB. Then express IB in terms of S and V. (d) What is the impedance base ZB that makes the V = ZI work out in per unit? First give the answer expressing ZB in terms of VB_and IB. Then express ZB in terms of VB and SB. Then express ZB in terms of S and V. (e) Now suppose that the per unit system above is relabeled as Sold, Vilold etc and that we also choose a new per unit system based on Sonew¸ vllnew Derive °B (B B B from first principles the formula expressing Znew in terms of Zold Soold, vlold B pu , PB s3ønew vllnew B (B

(2) (z) Just to make sure as a preliminary question... if the base quantity is XB and the actual value of the quantity is X, write down the fundamental definition of Xpu- In a 3 phase balanced AC system, suppose that we have already chosen the 3 phase power base S and the line to line voltage base V. Now we choose the rest of the bases in a coordinated way. (a) What is the single phase power base SB that makes the 3 phase power and the single phase power numerically equal in per unit? (b) What is the line to neutral voltage base VB that makes the line to line voltage and the line to neutral voltage numerically equal in per unit? Show that it works. (c) What is the line current base IB that makes S = VI* work out in per unit? First give the answer expressing Ig in terms of SB and VB. Then express IB in terms of S and V. (d) What is the impedance base ZB that makes the V = ZI work out in per unit? First give the answer expressing ZB in terms of VB_and IB. Then express ZB in terms of VB and SB. Then express ZB in terms of S and V. (e) Now suppose that the per unit system above is relabeled as Sold, Vilold etc and that we also choose a new per unit system based on Sonew¸ vllnew Derive °B (B B B from first principles the formula expressing Znew in terms of Zold Soold, vlold B pu , PB s3ønew vllnew B (B

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 3.29P: Consider three ideal single-phase transformers (with a voltage gain of ) put together as ...
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(2) (z) Just to make sure as a preliminary question... if the base quantity is XB and the actual value of the quantity is X, write down the fundamental definition of X,mu: In a 3 phase balanced AC system, suppose that we have already chosen the 3 phase power base S and the line to line voltage base V. Now we choose the rest of the bases in a coordinated way. (a) What is the single phase power base SB that makes the 3 phase power and the single phase power numerically equal in per unit? (b) What is the line to neutral voltage base VB that makes the line to line voltage and the line to neutral voltage numerically equal in per unit? Show that it works. (c) What is the line current base IB that makes S = VI* work out in per unit? First give the answer expressing IB in terms of SB and VB. Then express Ig in terms of S and V. (d) What is the impedance base ZB that makes the V = ZI work out in per unit? First give the answer expressing ZB in terms of VB_and IB. Then express ZB in terms of VB and SB. Then express ZB in terms of S and V. B (e) Now suppose that the per unit system above is relabeled as Sola, villold, etc and that we also choose a new per unit system based on Sonew, Vlnew. Derive from first principles the formula expressing Znew in terms of Zold Sold, vlold s3ónew vleneuw °B (B B B . nd, 'B (B 'B B
Transcribed Image Text:(2) (z) Just to make sure as a preliminary question... if the base quantity is XB and the actual value of the quantity is X, write down the fundamental definition of X,mu: In a 3 phase balanced AC system, suppose that we have already chosen the 3 phase power base S and the line to line voltage base V. Now we choose the rest of the bases in a coordinated way. (a) What is the single phase power base SB that makes the 3 phase power and the single phase power numerically equal in per unit? (b) What is the line to neutral voltage base VB that makes the line to line voltage and the line to neutral voltage numerically equal in per unit? Show that it works. (c) What is the line current base IB that makes S = VI* work out in per unit? First give the answer expressing IB in terms of SB and VB. Then express Ig in terms of S and V. (d) What is the impedance base ZB that makes the V = ZI work out in per unit? First give the answer expressing ZB in terms of VB_and IB. Then express ZB in terms of VB and SB. Then express ZB in terms of S and V. B (e) Now suppose that the per unit system above is relabeled as Sola, villold, etc and that we also choose a new per unit system based on Sonew, Vlnew. Derive from first principles the formula expressing Znew in terms of Zold Sold, vlold s3ónew vleneuw °B (B B B . nd, 'B (B 'B B
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