Explanation Given: Y- Δ connection is shown below- V a n , V b n and V c n are negative sequence set. The positive sequence for 3 - ϕ is a, b, c and the negative sequence is a, c, b. Diagram for negative sequence Δ connection is shown below- For delta connection, the relation between line and phase current is- I a n = ( 3 ) I a c where, I a n = Line voltage I a c = Phase voltage From above figure I a c = V a c Z Δ I a n = V a c Z Δ ( 3 ) ............. ( 1 ) Similarly, for star connection the relation between line and phase current is- I a ' = I a ' b ' Line current and phase current is same for star connection only. I a ' b ' = 3 V a ' b ' Z Y = I a ' ........... ( 2 ) As for 3 - ϕ circuit, the phase shift is 120 degree with each other in their respective sequence. Therefore, the phase shift for the voltages can be written as shown below- V a c = V b a ∠ − 240 o where, V b a ∠ − 240 o can be written as - V b a ∠ − 240 o = V a b * ∠ − 240 o Therefore, V a c = V a b * ∠ − 240 o .......... ( 3 ) Substituting the above equation in equation (1), I a n = V a c Z Δ ( 3 ) I a n = ( 3 V a b * Z Δ ) ∠ − 240 o Now comparing above equation with the equation (2)- I a n = ( 3 V a b * Z Δ ) ∠ − 240 o = ( 3 V a ' b ' Z Y ) V a ' b ' = ( V a b * ∠ − 240 o Z Δ ) Z Y Change the phase voltage to the line voltage- V a ' b ' = V a ' n 3 , V a n * = V a b * V a ' n = 3 ( V a n * ∠ − 240 o Z Δ ) Z Y ........ ( 4 ) In delta connection, V a c = V a n V a n = V a b * ∠ − 240 o V a n = I a n × Z Δ V a b = 1 I a n × Z Δ ∠ − 240 o ............ ( 5 ) Similarly, in star connection V a ' b ' = V a ' n 3 V a ' n = I a ' Z Y V a ' b ' = I a ' Z Y 3 ......... ( 6 ) Comparing equation (5) and equation (6), I a ' Z Y 3 = 1 I a n × Z Δ ∠ − 240 o I a ' = 3 I a n × Z Δ Z Y ∠ − 240 o

6th Edition

ISBN: 9781305886957

Author: Glover

Publisher: CENGAGE LEARNING - CONSIGNMENT

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Chapter 3, Problem 3.31P

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The gain for a negative sequence set.

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Chapter 3 Solutions

EBK POWER SYSTEM ANALYSIS AND DESIGN

Ch. 3 - The Ohms law for the magnetic circuit states that...Ch. 3 - For an ideal transformer, the efficiency is (a) 0...Ch. 3 - For an ideal 2-winding transformer, the...Ch. 3 - An ideal transformer has no real or reactive power...Ch. 3 - For an ideal 2-winding transformer, an impedance...Ch. 3 - Consider Figure 3.4. For an ideal phase-shifting...Ch. 3 - Consider Figure 3.5. Match the following, those on...Ch. 3 - The units of admittance, conductance, and...Ch. 3 - Match the following: (i) Hysteresis loss (a) Can...Ch. 3 - For large power transformers rated more than 500...

Ch. 3 - For a short-circuit test on a 2-winding...Ch. 3 - The per-unit quantity is always dimensionless. (a)...Ch. 3 - Consider the adopted per-unit system for the...Ch. 3 - The ideal transformer windings are eliminated from...Ch. 3 - To convert a per-unit impedance from old to new...Ch. 3 - In developing per-unit circuits of systems such as...Ch. 3 - Prob. 3.17MCQ Ch. 3 - Prob. 3.18MCQ Ch. 3 - With the American Standard notation, in either a...Ch. 3 - Prob. 3.20MCQ Ch. 3 - In order to avoid difficulties with third-harmonic...Ch. 3 - Does an open connection permit balanced...Ch. 3 - Does an open- operation, the kVA rating compared...Ch. 3 - It is stated that (i) balanced three-phase...Ch. 3 - In developing per-unit equivalent circuits for...Ch. 3 - In per-unit equivalent circuits of practical...Ch. 3 - Prob. 3.27MCQ Ch. 3 - Prob. 3.28MCQ Ch. 3 - For developing per-unit equivalent circuits of...Ch. 3 - Prob. 3.30MCQ Ch. 3 - Prob. 3.31MCQ Ch. 3 - Prob. 3.32MCQ Ch. 3 - The direct electrical connection of the windings...Ch. 3 - Consider Figure 3.25 of the text for a transformer...Ch. 3 - (a) An ideal single-phase two-winding transformer...Ch. 3 - An ideal transformer with N1=1000andN2=250 is...Ch. 3 - Consider an ideal transformer with...Ch. 3 - A single-phase 100-kVA,2400/240-volt,60-Hz...Ch. 3 - Prob. 3.5P Ch. 3 - Prob. 3.6P Ch. 3 - Consider a source of voltage v(t)=102sin(2t)V,...Ch. 3 - Prob. 3.8P Ch. 3 - Prob. 3.9P Ch. 3 - A single-phase step-down transformer is rated...Ch. 3 - For the transformer in Problem 3.10. The...Ch. 3 - Prob. 3.12P Ch. 3 - A single-phase 50-kVA,2400/240-volt,60-Hz...Ch. 3 - A single-phase 50-kVA,2400/240-volt,60-Hz...Ch. 3 - Rework Problem 3.14 if the transformer is...Ch. 3 - A single-phase, 50-kVA,2400/240-V,60-Hz...Ch. 3 - The transformer of Problem 3.16 is supplying a...Ch. 3 - Using the transformer ratings as base quantities,...Ch. 3 - Using the transformer ratings as base quantities....Ch. 3 - Using base values of 20 kVA and 115 volts in zone...Ch. 3 - Prob. 3.21P Ch. 3 - A balanced Y-connected voltage source with...Ch. 3 - Figure 3.32 shows the oneline diagram of a...Ch. 3 - For Problem 3.18, the motor operates at full load,...Ch. 3 - Consider a single-phase electric system shown in...Ch. 3 - A bank of three single-phase transformers, each...Ch. 3 - A three-phase transformer is rated...Ch. 3 - For the system shown in Figure 3.34. draw an...Ch. 3 - Consider three ideal single-phase transformers...Ch. 3 - Reconsider Problem 3.29. If Va,VbandVc are a...Ch. 3 - Prob. 3.31P Ch. 3 - Determine the positive- and negative-sequence...Ch. 3 - Consider the three single-phase two-winding...Ch. 3 - Three single-phase, two-winding transformers, each...Ch. 3 - Consider a bank of this single-phase two-winding...Ch. 3 - Three single-phase two-winding transformers, each...Ch. 3 - Three single-phase two-winding transformers, each...Ch. 3 - Consider a three-phase generator rated...Ch. 3 - The leakage reactance of a three-phase,...Ch. 3 - Prob. 3.40P Ch. 3 - Consider the single-line diagram of the power...Ch. 3 - For the power system in Problem 3.41, the...Ch. 3 - Three single-phase transformers, each rated...Ch. 3 - A 130-MVA,13.2-kV three-phase generator, which has...Ch. 3 - Figure 3.39 shows a oneline diagram of a system in...Ch. 3 - The motors M1andM2 of Problem 3.45 have inputs of...Ch. 3 - Consider the oneline diagram shown in Figure 3.40....Ch. 3 - With the same transformer banks as in Problem...Ch. 3 - Consider the single-Line diagram of a power system...Ch. 3 - A single-phase three-winding transformer has the...Ch. 3 - The ratings of a three-phase three-winding...Ch. 3 - Prob. 3.52P Ch. 3 - The ratings of a three-phase, three-winding...Ch. 3 - An infinite bus, which is a constant voltage...Ch. 3 - A single-phase l0-kVA,2300/230-volt,60-Hz...Ch. 3 - Three single-phase two-winding transformers, each...Ch. 3 - A two-winding single-phase transformer rated...Ch. 3 - A single-phase two-winding transformer rated...Ch. 3 - Prob. 3.59P Ch. 3 - PowerWorid Simulator case Problem 3_60 duplicates...Ch. 3 - Rework Example 3.12 for a+10 tap, providing a 10...Ch. 3 - A 23/230-kV step-up transformer feeds a...Ch. 3 - The per-unit equivalent circuit of two...Ch. 3 - Reconsider Problem 3.64 with the change that now...Ch. 3 - What are the advantages of correctly specifying a...Ch. 3 - Why is it important to reduce the moisture within...Ch. 3 - What should be the focus of transformer preventive...

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