Lebanese University Faculty of Engineering – Branch 2 Chemical Department 4th year – Semester VII
Course: Electric Machinery Instructor : R. Mbayed, PhD Chapter 1: Three-phase systems Exercises
Exercise 1.1.
Prove the relation: Z Y
Z 3
Exercise 1.2.
For the 3-phase system in Figure 1, calculate the line-line voltage, real power and power factor at the load. Hint: first deal with a one-phase equivalent circuit.
. Figure 1 Exercise 1.3.
For the system in Figure 2, calculate the power factor and real power at the load as well as the phase voltage and current. The source voltage is 400 V line-line.
Figure 2 Exercise 1.4.
Two load are connected as shown in Figure 3. Load 1 draws from the system P L1 = 500kWat 0.8 pf 0.8 pf lagging lagging while the total load is S T = 1000 kVA at 0.95 pf 0.95 pf lagging. lagging. What is the pf the pf of load 2? T =
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Lebanese University Faculty of Engineering – Branch 2 Chemical Department 4th year – Semester VII
Course: Electric Machinery Instructor : R. Mbayed, PhD Chapter 1: Three-phase systems Exercises
Figure 3 Exercise 1.5.
A 208 V three-phase power system is shown in Figure 4. It consists of an ideal 208 V Y-connected three phase generator connected through a three-phase transmission line to a Y-connected load. The transmission line has an impedance of 0.06 + j0.12 Ω per phase, and the load has an impedance of 12 + j9 Ω per phase. For this simple power system, find:
Figure 4
1. 2. 3. 4. 5. 6. 7.
The magnitude of the line current I L The magnitude of the load's line and phase voltages V LL and V ϕ. The r eal, reactive, and a pparent power s consumed by the load. The power f actor of the load. The r eal, r eactive, and a pparent power s consumed by the tr ansmission line. The r eal, r eactive, and a pparent power s supplied by the gener ator. The generator 's power f actor. Exercise 1.6.
Repeat Exercise 1.5 for a ∆-connected load, with everything else unchanged. page 2
Lebanese University Faculty of Engineering – Branch 2 Chemical Department 4th year – Semester VII
Course: Electric Machinery Instructor : R. Mbayed, PhD Chapter 1: Three-phase systems Exercises
Exercise 1.7
Figure 5 shows one-line diagram of a simple power system containing one 480 V generator and two parallel loads. Assume that the transmission lines are lossless. Load 1 is Y connected, Load 2 is Δ connected. a.
Compute the phase voltage and phase current in Load 1 (RMS values).
b.
Compute the phase voltage and phase current in Load 2 (RMS values).
c.
Find the real, reactive and apparent power supplied by the generator when the switch connecting Load 3 is open. What is the total line current I L in this case.
The switch connecting Load 3 is now closed. d.
Find the new real, reactive and apparent power supplied by the generator. What is the total line current I L in this case.
e.
Deduce the overall PF of the distribution system.
f.
This overall PF shall be increased. Therefore a pure capacitive load, called capacitive bank, is mounted in parallel to the three existing loads. Find the real, reactive and apparent power of this capacitive load in order to obtain an overall PF of . I L1
G
Load 1
100 kW 0.9 PF lagging
Load 2
80 kVA 0.8 PF lagging
Load 3
80 kW 0.85 PF leading
I L I L2
480 V Y connected I L3
Figure 5
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Lebanese University Faculty of Engineering – Branch 2 Chemical Department 4th year – Semester VII
Course: Electric Machinery Instructor : R. Mbayed, PhD Chapter 3: Transformer Exercises
Exercise 3.1.
The equivalent circuit im pedances of a 20 kVA, 8000 V / 240 V, 60 Hz transformer are to be determined. The open-circuit test and the short-circuit test were performed on the primary side of the transformer, and the following data were taken: Open-circuit test (on primary)
Short-circuit test (on primary)
V oc = 8000 V
V sc = 489 V
I oc = 0.214 A
I sc = 2.5 A
Poc = 400 W
Psc = 240 W
Find the impedances of the approximate equivalent circuit ref erred to the primary side, and sk etch that circuit. Exercise 3.2.
A 60 Hz transformer is rated 30 kVA, 4000 V / 120 V. The open circuit test, performed with the high voltage side open, gives Poc = 100W, I oc = 1.1455A. The short circuit test, performed with the low voltage side shorted, gives Psc = 180 W, V sc = 129.79 V. Calculate the equivalent circuit of the transformer. Exercise 3.3.
A 60 Hz transformer is rated 30kVA. Its short-circuit impedance is 17.28 Ω and the open-circuit current is 0.0345 A. The rated iron losses are 100 W and the rated winding losses are 180 W. 1. Determine the equivalent circuit impedances. 2. Calculate the necessary primary voltage when the load at the secondary is at rated voltage, 20 kW at 0.8 pf lagging. 3. Calculate the transformer efficiency in this case. Exercise 3.4.
A 250kVA transformer has an efficiency of 0.98 when absorbing 250kVA under unity power factor. 1. Compute the transformer total losses. 2. Derive the losses at no load and the copper losses given that the iron losses ar e the fifth of the total losses. 3. Under which load condition, the efficiency is maximum? Compute the efficiency in this case.
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Lebanese University Faculty of Engineering – Branch 2 Chemical Department 4th year – Semester VII
Course: Electric Machinery Instructor : R. Mbayed, PhD Chapter 5: Synchronous machine Exercises
Exercise 5.1.
A 480V, 60Hz, ∆-connected, 2-pole synchronous generator has the open-circuit characteristic shown in the figure below.
This generator has a synchronous reactance of 0.1Ω and an armature resistance of 0.015Ω. At full load, the machine supplies 1200A at 0.8 PF lagging. Under full-load conditions, the friction and windage losses are 40 kW and the core losses are 30 kW. Ignore any field circuit losses. 1. What is the speed of rotation of this generator? 2. How much field current must be supplied to the generator to make the terminal voltage 480 V at no load? 3. If the generator is now connected to a load and the load draws 1200 A at 0.8 PF lagging, how much field current will be required to keep the terminal voltage equal to 480 V? 4. How much power is the generator now supplying? How much power is supplied to the generator by the prime mover? What is this machine's overall efficiency?
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Lebanese University Faculty of Engineering – Branch 2 Chemical Department 4th year – Semester VII
Course: Electric Machinery Instructor : R. Mbayed, PhD Chapter 5: Synchronous machine Exercises
5. If the generator's load were suddenly disconnected from the line, what would happen to its terminal voltage? 6. Suppose that the generator is connected to a load drawing 1200 A at 0.8 PF leading . How much field current would be required to keep the line-to-line voltage at 480 V? Exercise 5.3.
(Final 2014-2015)
A 2300 V, 1000 kVA, 0.8 PF lagging, 60 Hz, Y-connected synchronous generator has a synchronous reactance of 1.1 Ω and an armature resistance of 0.15Ω. At 60 Hz, its friction and windage losses are 24 kW and its core losses are 18 kW. The field circuit has a DC voltage of 200 V and the maximum field current I f is 10 A. The resistance of the field circuit is adjustable over the range from 20 to 200 Ω. The Open-circuit Characteristic of this generator is shown in the figure below (Terminal open-circuit voltage v/s field current).
1. How much field current is required to make the terminal voltage equal to 2300 V when the generator is running at no load? 2. What shall be the value of the field circuit resistance in this case? 3. What is the armature current magnitude in the machine at rated conditions (2300 V, 1000 kVA, 0.8 PF lagging)? 4. What is the internal generated voltage of this machine at rated conditions? 5. How much field current is required to make maintain the terminal voltage equal to 2300 V when the generator is running at rated conditions? page 2
Lebanese University Faculty of Engineering – Branch 2 Chemical Department 4th year – Semester VII
Course: Electric Machinery Instructor : R. Mbayed, PhD Chapter 5: Synchronous machine Exercises
6. What is the power drawn from the generator prime mover under rated conditions? 7. What is the generator efficiency? Exercise 5.2.
A 480V, 50Hz, Y-connected, two-pole synchronous generator has a per-phase synchronous reactance of 1.0Ω. Its full-load armature current is 60 A at 0.8 PF lagging. This generator has friction and windage losses of 1.5 kW and core losses of 1.0 kW at 60 Hz at full load. Since the armature resistance is being ignored, assume that the copper losses are negligible. The field current has been adjusted so that the terminal voltage is 480 V at no load. 1. What is the speed of rotation of this generator? 2. What is the terminal voltage of this generator if the following are true? a. It is loaded with the rated current at 0.8 PF lagging. b. It is loaded with the rated current at 1.0 PF. c. It is loaded with the rated current at 0.8 PF leading. 3. What is the efficiency of this generator (ignoring the unknown electrical losses) when it is operating at the rated current and 0.8 PF lagging? 4. How much shaft torque must be applied by the prime mover at full load? 5. How large is the induced counter-torque?
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Lebanese University Faculty of Engineering – Branch 2 Chemical Department 4th year – Semester VII
Course: Electric Machinery Instructor : R. Mbayed, PhD Chapter 6: Induction machine Exercises
Exercise 6.1.
A 380 V, two-pole, 50 Hz induction motor draws 29 A at 0.85 PF lagging. It supplies 15 kW to a load at a speed of 2950 r/min. Neglect any mechanical losses. 1.
What is the motor's slip?
2.
What is the induced torque in the motor in N.m under these conditions?
3.
What is the motor efficiency?
4.
What will the operating speed of the motor be if its torque is doubled?
5.
How much power will be supplied by the motor when the torque is doubled?
Exercise 6.2
An induction machine is used in a winch in order to lift a solid of 10 T. The lifting speed should not exceed 1 m/s. The winch has a diameter of 50 cm. The motor shaft and the winch are connected through of a gearing of a ratio 45. 1. Choose the adequate motor from the attached catalog table. 2. Calculate the following quantities: a. The nominal slip b. The nominal current c. The nominal mechanical torque
d. The motor speed and the lifting speed
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