One Machine

1
One Machine Infinite Bus

• EE341 Energy Conversion
• Ali Keyhani
• Synchronous Machines
• lecture 3

2
Infinite Bus

• Define of Infinite Bus infinite bus has the
  following properties
• Bus voltage will remain constant under any
  loading
• It has infinite capacity
• By definition, and infinite bus voltage is an
  ideal voltage source.

3
Infinite Bus
Problem 1
Power System
345/132 kV 10 100MVA T1
132/13.2 kV 10 50MVA T2
13.2kV/220V 5 10MVA T3
PL 500W lighting load rated at 220 volts

• For the load of 500W, which bus should be
  considered as an infinite bus?
• Assume load voltage is to be maintained at its
  rated value, which bus should be considered as
  infinite bus?
• Problem 2 Assume the load is equal to 500W at
  unity PF. Compute p.u equivalent circuit.
• Assume Sb100 MVA, Vb 345 kV at high side of T1

4
Infinite Bus
Assume Sb100 MVA, Vb 345 kV at high side of T1
345kV
j.10
j.20
j.50
220V
132kV
13.2kV
Sb 100 MVA
5
A Generator Power Flow
Assume Sb100 MVA, Vb 345 kV at high side of T1






1-? Eq. CKT
Assume
6
A Generator Power Flow
The complex power generated is
Note
7
Synchronous Machine On An Infinite Bus

• Synchronous Motor
• Electrical power supplied
• Tem produced to support
• mechanical load (Tmech)

• b) Synchronous Generator
• Mechanical power supplied
• to the shaft
• Electrical power supplied to
• The network

Assume
Note
8
Synchronous Machine On An Infinite Bus

• Synchronization Connecting
• A synchronous generator
• To a power system for
• synchronous operation. For
• synchronous operation, we
• Need to provide the following conditions

Circuit Breaker

1. Electrical speed of synchronous generator should
   be equal to the electrical speed of power system
   generators
2. The terminal voltage of generator should be equal
   to the V? bus and they must be in the same abc
   sequence

With above conditions satisfied, the C.B.
(circuit breaker) can be closed. Synchronous
operation means parallel operation of synchronous
generators.
9
?
Relationship Between and E
Consider a synchronous generator Assume
Pmech prime mover power
constant
Xs, E is determined by manufacturers
Adjust
(by changing Rf)
?
(this is called the excitation voltage)
10
?
Relationship Between and E
In general
when
is reduced
decrease
If
Keep Pmech constant
increase
therefore
Keep Pmech constant, and reduce If till ?
reaches 90o
This is called pull-out power
If we reduce If further, Pelec will decrease and
? will increase. The machine will lose
synchronization when ?gt90o It means power
cannot be injected, and the external power will
drive the machine
11
Operation of one machine - infinite bus
3

2
1

4

Pmech

5
6
Pelec

Computer control of generation is called
Automatic Generation Control (AGC)
12
Operation of one machine - infinite bus
Consider a generator supplying power at a lagging
power factor to an infinite bus
(Inductive load)
Pmech
Assume
(ie ?mconst, Ifconst)
Overexcited generator is
operating with lagging power factor
13
Operation of one machine - infinite bus
Overexcited Generator
Keep
?mconst
Reduce If to If, then EA will reduce to EA
That is the ? has to increase to ?
14
Operation of one machine - infinite bus
Note also
That is IL will reduce to IL , and ? will
reduce to ?
However,
Conclusions By reducing If, the reactive power
generated by synchronous generator will be
reduced. However, the active power generated by
the generator will remain the same (
). However, the balance of generations and
loads will be maintained
15
Operation of one machine - infinite bus
Suppose we reduce If such that ?0 (i.e. the
angle between V and I). That is,
dec
dec
dec
dec
Generator operation with unity power factor
Conclusions By reducing If, we can operate the
machine with unity power factor while generating
the same active power. However reactive power
generated by the machine will reduce to
zero. Note Computer control of generation will
control all generators such that
16
Operation of one machine - infinite bus
Underexcited Generator Operation Suppose we
reduce If such that ?gt0 (i.e. IL would lead V?)
dec
dec
inc
inc
Underexcited generator
Conclusions By reducing Ifsuch that ?gt0 leading,
we can operate the generator with leading power
factor while generating the same active power.
Note Computer control of generation will
control all generators such that
17
Problems

• Problem 1 A 13.8-kV 10-MVA 0.8-PF-lagging 60 Hz
  two-pole Y-connected steam turbine generator has
  a synchronous reactance of 18 ? per phase and an
  armature resistance of 2 ? per phase. This
  generator is operating in parallel with a large
  power system (infinite bus). Answer the following
  questions about this generator.
• What is the magnitude of EA at rated conditions?
• What is the torque angle of the generator at
  rated conditions?
• If the field current is constant, what is the
  maximum power possible out of this generator? How
  much reserve power or torque does this generator
  have at full load?
• At the absolute maximum power possible, how much
  reactive power will this generator be supplying
  or consuming? Sketch the corresponding phasor
  diagram. (Assume IF is still unchanged).

18
Problems
2j18
2j18
13.8-kV 10-MVA 0.8-PF-lagging P2
a)
b)
19
Problems
c) Ignoring RA, the maximum output power of the
generator is given by
d) The resulting reactive power produced by the
generator is
20
Problems

• Problem 2 A 100-MVA 11.8-kV 50-Hz two-pole
  Y-connected synchronous generator has a per-unit
  synchronous reactance of 0.8 and a per0unit
  armature resistance of 0.012. (pf0.85 lagging.)
• What is its synchronous reactance and armature
  resistance in ohms?
• What is the magnitude of the internal generated
  voltage EA at the rated conditions? What is its
  torque angle ? at these conditions?
• Ignoring losses in this generator, what torque
  must be applied to its shaft be the prime mover
  at full load?

21
Problems
a)
.012j.8
S1 pu pf .85 lagging
b)
In pu
or
22
Problems
c)
23
Problems

• Problem 3 A three-phase Y-connected synchronous
  generator is rated 120 MVA, 13.2 kV, 0.8 PF
  lagging, and 60 Hz. Its synchronous reactance is
  0.7 ?, and its resistance may be ignored.
• What is its voltage regulation?
• What would the voltage and apparent power rating
  of this generator be if it were operated at 50 Hz
  with the same armature and field losses as it had
  at 60 Hz?
• What would the voltage regulation of the
  generator be at 50 Hz?

24
Problems
a)
j.7
pf.8 lagging
25
Problems
b) Since the voltage produced by a generator is
directly proportional to speed, the voltage (and
hence the apparent power) rating of the generator
will be reduced by a factor of 5/6
c) At 50 Hz rated conditions, Note that the
synchronous reactance is also reduced by a factor
of 5/6, since reactance is a function of
frequency. The voltage regulation is