FAKULTEIT INGENIEURSWESE
FACULTY OF ENGINEERING
Elektriese Aandryfstelsels 324 / Electrical Drive Systems 324
Tutoriaal 6 / Tutorial 6
13 en 14 Maart 2014 / 13 and 14 Maart 2014
Die volgende probleme uit Chapman 5uit moet gedoen word en aan die dosent aan diens gewys word voor
16:00 om vir die Tutoriaal afgemerk te word.
The following problems from Chapman 5ed shall be done and shown to the lecturer on duty before 16:00
in order to be signed off for the Tutorial.
P5-6 If a 60 Hz synchronous motor is to be operated at 50 Hz, will its synchronous reactance be the same as at
60 Hz, or will it change? (Hint: Think about the derivation of XS .)
P5-7’ A 208 V Y-connected synchronous motor is drawing 50 A at unity power factor from a 208- V power
system. The field current flowing under these conditions is 2,7 A. Its synchronous reactance is 1,6 Ω.
Assume a linear open-circuit characteristic (i.e. EA ∝ IF ).
(a) Find Vφ and EA for these conditions.
(b) Find the torque angle δ .
(c) Sketch the phasor diagram under these circumstances.
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(d) How much field current would be required to make the motor operate at 0,80 PF leading?
(e) What is the new torque angle in part (d)?
P4-8’ A 200 MVA, 12 kV, 0,9 PF-lagging, 50 Hz, 20-pole, Y-connected water turbine generator has a per-unit
synchronous reactance of 0,9 and a per-unit armature resistance of 0,1. This generator is operating in
parallel with a large power system (infinite bus).
(a) What is the speed of rotation of this generator’s shaft?
(b) What is the magnitude of the internal generated voltage EA at rated conditions?
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(c) What is the torque angle of the generator at rated conditions?
(d) What are the values of the generator’s synchronous reactance and armature resistance in ohms?
(e) If the field current is held constant and the armature resistance were to be ignored, what is the
theoretical maximum power possible out of this generator? (i.e. at δ = 90◦ ) How much reserve
power (or torque) does this generator have at full load?
(f) At the absolute theoretical maximum power possible, how much reactive power will this generator
be supplying or consuming? Sketch the corresponding phasor diagram. (Assume IF and hence EA is
still unchanged.)
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P4-29’ A 100 MVA, 14,4 kV 0,8 PF-lagging, Y-connected synchronous generator has a negligible armature
resistance and a synchronous reactance of 1,0 per-unit. The generator is connected in parallel with a
60 Hz, 14,4 kV infinite bus that is capable of supplying or consuming any amount of real or reactive
power with no change in frequency or terminal voltage.
(a) What is the synchronous reactance of the generator in ohms?
(b) What is the internal generated voltage EA of this generator under rated conditions?
(c) What is the armature current IA in this machine at rated conditions?
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(d) Suppose that the generator is initially operating at rated conditions. If field current, IF and hence the
internal generated voltage, EA , is decreased by 5 percent, what will the new armature current IA be?
P5-12’ Figure P5-3 shows a small industrial plant supplied by an external 480 V three-phase power supply.
The plant includes three main loads as shown in the figure. Answer the following questions about the
plant. The Y-connected synchronous motor is rated at 75 kW, 480 V and 0,8 PF-leading. The synchronous
reactance is 1,1 pu and armature resistance can be ignored. The field current value that corresponds to
the rated open circuit line-to-line terminal voltage of 480 V is equal to 1,5 A.
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(a) If the switch on the synchronous motor is open, how much real, reactive, and apparent power is being
supplied to the plant? What is the line current, IL , in the transmission line?
The switch is now closed and the synchronous motor is supplying rated power at rated power factor.
(b) What is the field current in the motor? (If the terminal voltage of the motor, Vφ , remains constant, we
can assume that IF ∝ EA .)
P
75 000
=
= 93,75 kVA
PF
0,8
VL,base = 480 V
VL,base 480
Vφ ,base = √ = √ = 277,13 V
3
3
93,75
Sbase
=
= 112,76 A
Iφ ,base =
3Vφ ,base 3 · 277,13
Vφ ,base 277,13
Zφ ,base =
=
= 2,458 Ω
Iφ ,base
112,76
Sbase =
θ = cos−1 (0,8) = 36,87◦
EA = Vφ − jXS IA
= 277,13 0◦ − j1,1 · 2,458 · 112,76 36,87◦
= 520,714 −27,93◦ V
∴
IF =
520,714
× 1,5 = 2,818 A
277,13
(c) What is the torque angle of the motor?
δ = 27,93◦
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(d) How much real, reactive, and apparent power is being supplied to the plant now? What is the line
current IL in the transmission line?
Pmotor = 75 kW
Qmotor = −Pmotor tan θ = 75 000 tan 36,87◦ = −56,25 kvar
Ptotal = P1 + P2 + Pmotor = 100 × 103 + 64 × 103 + 75 × 103 = 239 kW
Qtotal = Q1 + Q2 + Qmotor = 48,4 × 103 + 48 × 103 − 56,25 × 103 = 40,15 kvar
q
q
2 + Q2
Stotal = Ptotal
=
(239 × 103 )2 + (40,15 × 103 )2 = 242,34 kVA
total
IL = Iφ =
S
242,34 × 103
=
= 291,5 A
3Vφ
3 × 277,13
(e) If the motor is only drawing 50 kW, what must the value of the field current, IF , be in order to improve
the power factor of the plant to unity.
0
Pmotor
= 50 kW
Q0motor = −(Q1 + Q2 ) = −(48,4 × 103 + 48 × 103 ) = −96,4 kvar
q
q
0
2
Smotor
= Pmotor
+ Q2motor = (50 × 103 )2 + (96,4 × 103 )2 = 108,6 kVA
0
108,6 × 103
Smotor
=
= 130,6 A
3Vφ
3 × 277,13
0
50
0
−1 Pmotor
θ = cos
=
= 62,58◦
0
Smotor
108,6
IA0 =
E0A = Vφ − jXS I0A
= 277,13 0◦ − j1,1 · 2,458 · 130,6 62,58◦
= 612,55 −27,93◦ V
∴
IF =
612,55
× 1,5 = 3,315 A
277,13
P5-17’ A 440 V, 60 Hz, three-phase Y-connected synchronous motor has a synchronous reactance of 1,5 Ω per
phase. The field current has been adjusted so that the torque angle δ is 25◦ when the power supplied by
the generator is 80 kW.
(a) What is the magnitude of the internal generated voltage EA in this machine?
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(b) What are the magnitude and angle of the armature current in the machine? What is the motor’s power
factor?
(c) If the field current remains constant, what is the absolute maximum power this motor could supply?
P5-18 A 460 V 200 kVA 0,85 PF-leading 400 Hz four-pole Y-connected synchronous motor has negligible armature resistance and a synchronous reactance of 0.90 per unit. Ignore all losses.
(a) What is the speed of rotation of this motor?
(b) What is the output torque of this motor at the rated conditions?
(c) What is the internal generated voltage of this motor at the rated conditions?
(d) With the field current remaining at the value present in the motor in part (c), what is the maximum
possible output power from the machine?
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