Electric machinery fundamentals
5th Edition
ISBN: 9780073529547
Author: Chapman, Stephen J.
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 2, Problem 2.23P
A single-phase, 10-kVA, 480/120-V transformer is to be used as an autotransformer tying a 600-V distribution line to a 480-V load. When it is tested as a conventional transformer, the following values are measured on the primary (480-V) side of the transformer:
- Find the per-unit equivalent circuit of this transformer when it is connected in the conventional manner. What is the efficiency of the transformer at rated conditions and unity power factor? What is the voltage regulation at those conditions?
- Sketch the transformer connections when it is used as a 600/480-V step-down autotransformer.
- What is the kilovoltampere rating of this transformer when it is used in the autotransformer connection?
- Answer the questions in (a) for the autotransformer connection.
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b)
A 132 kV supply feeds a line of reactance 15 which is connected to a 100
MVA, 132/33 kV transformer of 0.08 p.u. reactance as shown in the
Figure 2. The transformer feeds a 33 kV line of reactance 8 Q, which, in
turn, is connected to a 75 MVA, 33/11 KV transformer of 0.12 p.u.
reactance. The transformer supplies an 11 KV substation from which a local
11 kV feeder of 4 Q reactance is supplied.
T1
T2
132 kV
33 kV
11 kV
Fault
X
CB
Relay
Figure 2. Network for Q4 b).
(i) Given the system base of 100 MVA, compute the total equivalent
reactance of the radial circuit in per unit (p.u.).
(ii) Determine the three-phase fault current at the load end of the 11 kV
feeder, assuming a fault impedance of 0.05 Q. Calculate the fault
current in Amperes.
(iii) The 11 kV feeder connects to a protective overcurrent relay via 200/5 A
current transformers. This relay has a standard normally inverse IDMT
characteristic, with a setting current of 3 A and a time multiplier setting
of 0.4. Calculate the…
Q2.
a) Two three-phase transformers, designated A and B, have the following
secondary equivalent circuit parameters per phase:
R₁ = 0.002 Q, XA = 0.03 Q, RB = 0.004 Q, X = 0.012 Q
Transformer A is 250 kVA and transformer B is 450 kVA. Calculate how
they share a load of 650 KVA when connected in parallel (assume the
voltage ratios are equal)
b) A step-up transformer is being specified for the beginning of a 3-phase, 4
wire high voltage transmission line. Discuss your recommendation for the
configuration of the transformer connections on both the primary and
secondary side of the transformer.
c)
Define power system protection and describe its fundamental purpose.
Discuss the following key concepts including discrimination, stability,
speed of operation, sensitivity, and reliability in the context of the power
system protection components and schemes.
Q3.
a) Given the unsymmetrical phasors for a three-phase system, they can be
represented in terms of their symmetrical components as follows:
[Fa]
[1 1
Fb = 1 a²
[Fc.
11[Fao]
a Fai
1 a a2F a2-
where F stands for any three-phase quantity. Conversely, the sequence
components can be derived from the unsymmetrical phasors as:
[11 1] [Fal
Faol
Fa1 =
1 a a² F
1 a²
a
a2.
Given the unbalanced three-phase voltages:
V₁ = 120/10° V, V₂ = 200/110° V, V = 240/200° V
Calculate in polar form the sequence components of the voltage.
Chapter 2 Solutions
Electric machinery fundamentals
Ch. 2 - Is the turns ratio of a transformer the same as...Ch. 2 - Why does the magnetization current impose an upper...Ch. 2 - What components compose the excitation current of...Ch. 2 - What is the leakage flux in a transformer? Why is...Ch. 2 - List and describe the types of losses that occur...Ch. 2 - Why does the power factor of a load affect the...Ch. 2 - Why does the short-circuit test essentially show...Ch. 2 - Why does the open-circuit test essentially show...Ch. 2 - How does the per-unit system of measurement...Ch. 2 - Why can autotransformers handle more power than...
Ch. 2 - What are transformer taps? Why are they used?Ch. 2 - What are the problems associated with the Y—Y...Ch. 2 - What is a TCUL transformer?Ch. 2 - How can three-phase transformation be accomplished...Ch. 2 - Prob. 2.15QCh. 2 - Can a 60-Hz transformer be operated on a 50-Hz...Ch. 2 - What happens to a transformer when it is first...Ch. 2 - What is a potential transform? How is it used?Ch. 2 - What is a current transformer? How is it used?Ch. 2 - A distribution transformer is rated at 18 kVA,...Ch. 2 - Why does one hear a hum when standing near a large...Ch. 2 - A 100-kVA, 8000/277-V distribution transformer has...Ch. 2 - A single-phase power system is shown in Figure...Ch. 2 - Consider a simple power system consisting of an...Ch. 2 - The secondary winding of a real transformer has a...Ch. 2 - When travelers from the USA and Canada visit...Ch. 2 - A 1000-VA, 230/115-V transformer has been tested...Ch. 2 - A 30-kVA, 8000/230-V distribution transformer has...Ch. 2 - A 150-MVA, 15/200-kV, single-phase power...Ch. 2 - A 5000-kVA, 230/13.8-kV, single-phase power...Ch. 2 - A three-phase transformer bank is to handle 500...Ch. 2 - A 100-MVA, 230/115-kV, Y three-phase power...Ch. 2 - Three 20-kVA, 24,000/277-V distribution...Ch. 2 - A 14,000/480-V, three-phase, Y-connected...Ch. 2 - A 13.8-kV, single-phase generator supplies power...Ch. 2 - An autotransformer is used to connect a 12.6-kV...Ch. 2 - Prove the following statement: If a transformer...Ch. 2 - A 10-kVA, 480/120-V conventional transformer is to...Ch. 2 - A 10-kVA, 480/120-V conventional transformer is to...Ch. 2 - Two phases of a 14.4-kV, three-phase distribution...Ch. 2 - A 50-kVA, 20,000/480-V, 60-Hz, single-phase...Ch. 2 - Prove that the three-phase system of voltages on...Ch. 2 - Prove that the three-phase system of voltages on...Ch. 2 - A single-phase, 10-kVA, 480/120-V transformer is...Ch. 2 - Figure P2-4 shows a one-line diagram of a power...
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