Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN: 9781305632134
Author: J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher: Cengage Learning
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Chapter 3, Problem 3.25P
Consider a single-phase electric system shown in Figure 3.33. Transformers are rated as follows:
With the base in circuit Y chosen as
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Data from short-circuit and open-circuit tests of a 25-kVA, 6900-230 V, 60 Hz transformer are given in table below:
Sr No
Open circuit parameters
VOC = 230
IOC = 5.4 A
POC = 260 W
Short circuit parameters
VSC = 513
ISC = 3.6 A
PSC = 465 W
Determine:
(i) The magnetizing reactance referred to the high side
(ii) The per unit parameters
(iii) Efficiency
(iv) Voltage regulation at 0.65 per unit load and 85% power factor leading
(v) Low side voltage when the load is removed
(vi) Voltage that must be applied to the primary in order to obtain the low side voltage in the part (v)
SUBJECT: Elements of Electrical Machines DesignINSTRUCTIONS: - Please write clearly and understandable way. - Write all the corresponding Given with their corresponding symbols and units. - Draw/Illustrate the diagram/circuit or drawings that is related to the problem, IF POSSIBLE, which is HIGHLY REQUIRED. - Solve in step-by-step, no shortcut - Underline twice the Final Answer.PROBLEM: In connecting ideal single-phase transformers in parallel, how will the load be shared if the two transformers have different VA rating?
An electrical lineman is connecting three single-phase transformers in a Y(primary)-Y(secondary) configuration, for power service to a business. Draw the connecting wires necessary between the transformer windings, and between the transformer terminals and the lines:
Note: fuses have been omitted from this illustration, for simplicity.
Chapter 3 Solutions
Power System Analysis and Design (MindTap Course List)
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. 3.17MCQCh. 3 - Prob. 3.18MCQCh. 3 - With the American Standard notation, in either a...Ch. 3 - Prob. 3.20MCQCh. 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. 3.27MCQCh. 3 - Prob. 3.28MCQCh. 3 - For developing per-unit equivalent circuits of...Ch. 3 - Prob. 3.30MCQCh. 3 - Prob. 3.31MCQCh. 3 - Prob. 3.32MCQCh. 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. 3.5PCh. 3 - Prob. 3.6PCh. 3 - Consider a source of voltage v(t)=102sin(2t)V,...Ch. 3 - Prob. 3.8PCh. 3 - Prob. 3.9PCh. 3 - A single-phase step-down transformer is rated...Ch. 3 - For the transformer in Problem 3.10. The...Ch. 3 - Prob. 3.12PCh. 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. 3.21PCh. 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. 3.31PCh. 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. 3.40PCh. 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. 3.52PCh. 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. 3.59PCh. 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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- Consider the single-Line diagram of a power system shown in Figure 3.42 with equipment ratings given: Generator G1: 50MVA,13.2kV,x=0.15p.u. Generator G2: 20MVA,13.8kV,x=0.15p.u. Three-phase -Y transformer T1: 80MVA,13.2/165YkV,X=0.1p.u. Three-phase Y- transformer T2: 40MVA,165Y/13.8kV,X=0.1p.u. Load: 40MVA,0.8PFlagging,operatingat150kV Choose a base of 100 MVA for the system and 132-kV base in the transmission-line circuit. Let the load be modeled as a parallel combination of resistance and inductance. Neglect transformer phase shifts. Draw a per-phase equivalent circuit of the system showing all impedances in per unit.arrow_forwardConsider Figure 3.25 of the text for a transformer with off-nominal turns ratio. (i) The per-unit equivalent circuit shown in part (c) contains an ideal transformer which cannot be accommodated by some computer programs. (a) True (b) False (ii) In the - circuit representation for real c in part (d), the admittance parameters Y11 and Y12 would be unequal. (a) True (b) False (iii) For complex c, can the admittance parameters be synthesized with a passive RLC circuit? (a) Yes (b) Noarrow_forwardConsider the single-line diagram of the power system shown in Figure 3.38. Equipment ratings are Generator 1: 1000MVA,18kV,X=0.2perunit Generator 2: 1000MVA,18kV,X=0.2p.u. Synchronous motor 3: 1500MVA,20kV,X=0.2p.u. Three-phase -Y transformers T1,T2,T3,T4,: 1000MVA,500kV,Y/20kV,X=0.1p.u. Three-phase YY transformer T5: 1500MVA,500kV,Y/20kVY,X=0.1p.u. Neglecting resistance, transformer phase shift, and magnetizing reactance, draw the equivalent reactance diagram. Use a base of 100 MA and 500 kV for the 50-ohm line. Determine the per-unit reactances.arrow_forward
- PowerWorid Simulator case Problem 3_60 duplicates Example 3.13 except that a resistance term of 0.06 per unit has been added to the transformer and 0.05 per unit to the transmission line. Since the system is no longer lossless, a field showing the real power losses has also been added to the oneline. With the LTC tap fixed at 1.05, plot the real power losses as the phase shift angle is varied from 10 to +10 degrees. What value of phase shift minimizes the system losses?arrow_forwardConsider the three single-phase two-winding transformers shown in Figure 3.37. The high-voltage windings are connected in Y. (a) For the low-voltage side, connect the windings in , place the polarity marks, and label the terminals a, b, and c in accordance with the American standard. (b) Relabel the terminals a, b, and c such that VAN is 90 out of phase with Va for positive sequence.arrow_forwardConsider three ideal single-phase transformers (with a voltage gain of ) put together as three-phase bank as shown in Figure 3.35. Assuming positive-sequence voltages for Va,Vb, and Vc find Va,Vb, and VC. in terms of Va,Vb, and Vc, respectively. (a) Would such relationships hold for the line voltages as well? (b) Looking into the current relationships, express IaIb and Ic in terms of IaIb and Ic respectively. (C) Let S and S be the per-phase complex power output and input. respectively. Find S in terms of S.arrow_forward
- In developing per-unit equivalent circuits for three-phase transformers. under balanced three-phase operation. (i) A common Sbase is selected for both the H and X terminals. (ii) The ratio of the voltage bases Vbase/VbaseX is selected to be equal to the ratio of the rated line-to-line voltages VratedHLL/VratedXLL. (a) Only one of the above is true. (b) Neither is true. (C) Both statements are true.arrow_forwardConsider Figure 3.4. For an ideal phase-shifting transformer, the imda nce is unchanged when it is referred from one side to the other. (a) True (b) Falsearrow_forwardConsider the oneline diagram shown in Figure 3.40. The three-phase transformer bank is made up of three identical single-phase transformers, each specified by X1=0.24 (on the low-voltage side), negligible resistance and magnetizing current, and turns ratio =N2/N1=10. The transformer bank is delivering 100 MW at 0.8 p.f. lagging to a substation bus whose voltage is 230 kV. (a) Determine the primary current magnitude, primary voltage (line-to-line) magnitude, and the three-phase complex power supplied by the generator. Choose the line-to-neutral voltage at the bus, Va as the reference Account for the phase shift, and assume positive-sequence operation. (b) Find the phase shift between the primary and secondary voltages.arrow_forward
- In developing per-unit circuits of systems such as the one shown in Figure 3.10. when moving across a transformer, the voltage base is changed in proportion to the transformer voltage ratings. (a) True (b) Falsearrow_forwardFigure 3.39 shows a oneline diagram of a system in which the three-phase generator is rated 300 MVA, 20 kV with a subtransient reactance of 0.2 per unit and with its neutral grounded through a 0.4- reactor. The transmission line is 64km long with a cries reactance of 0.5-/km. The three-phase transformer T1 is rated 350MVA.230/20kV with a leakage reactance of 0.1 per unit. Transformer T2 is composed of three single-phase transformers, each rated 100 MVA, 127/13.2kV with a leakage reactance of 0.1 per unit. Two 13.2kV motors M1 and M2 with a subtransient reactance of 0.2 per unit for each motor represent the load. M1 has a rated input of 200 MVA with its neutral grounded through a 0.4- current-limiting reactor, M2 has a rated input of 100 MVA with its neutral not connected to ground. Neglect phase shifts associated with the transformers. Choose the generator rating as base in the generator circuit and draw the positive-sequence reactance diagram showing all reactances in per unit.arrow_forwardReconsider Problem 3.64 with the change that now Tb includes both a transformer of the same turns ratio as Ta and a regulating transformer with a 4 phase shift. On the base of Ta, the impedance of the two comp onents of Tb is jO.1 per unit. Determine the complex power in per unit transmitted to the load through each transformer. Comment on how the transformers share the real and reactive pors.arrow_forward
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