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Overview
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34-Synchronous Generator Control
Synchronization
Infinite Bus
Effects of Excitation
Mechanical Power
text: 7.13
ECEGR 450
Electromechanical Energy Conversion
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Synchronization
Synchronization
• Generators must be synchronized with the grid
before supplying power:
• Following conditions must be met
•
•
1. Generator frequency must equal grid frequency
2. Generator voltage must equal grid voltage (at
connection point)
3. Generator voltage must be in phase with grid
voltage (at connection point)
4. Generator phase sequence must match grid phase
sequence
Electric grid comprised of thousands of connected
generators
Single generator usually cannot significantly influence
system voltage or frequency
 J1 << J2 + … + JM
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Infinite Bus
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•
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Excitation Effects
• Assume a lossless cylindrical rotor synchronous
generator is connected to an infinite bus
• Assume Ea = Va (“floating”)
• Therefore:
Conceptual element representing a very large electric grid
Infinite bus properties:
 Constant voltage
 Constant current
 Sink or source infinite current (power) at any angle
Ia 
Ea  Va
 00A
jXs
Po  Re{VaI*a }  0W
Qo  Im{VaI*a }  0VAR
Infinite
bus
Infinite
bus
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Ia
  0
5
jXs
+
Ea
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Va
-
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Over-Excitation
Under-Excitation
What happens if if is increased?
What happens if if is decreased?
 |Ea| increases (> |Va|, overexcited)
 |Ia| non-zero
Ia 
 |Ea| decreases (<|Va|, under-excited)
 |Ia| non-zero
Ea  Va
| Ia |   90A
jXs
Ia 
Po  Re{VaI*a}  0W
Ea  Va
| Ia | 90A
jXs
Po  Re{VaI*a}  0W
Qo  Im{VaI*a}  0VAR (generator supplies reactive power)
Qo  Im{VaI*a}  0VAR (generator consumes reactive power)
  0
  0
Ia
Ea- Va
jXs
+
Ea
Va
Va
-
Qo
Ea
Ia
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Excitation Effects
Ea- Va
Ea
-
Qo
Va
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• How does varying the excitation affect , Ia, fp for
a constant real power and terminal voltage Va?
• To maintain constant power:
3 | Va || Ea | sin 
Po 
 |Ea|sin is constant
Xs
Po  3 | Va || Ia | cos fPF
 |Ia|cosfPF is constant
|Ea| = |Va|
P (W), Q(VAR)
Ia
Va
Excitation Effects
• Adjusting excitation alone does not influence real power
supplied to grid
• Similar results for non-zero power output
Q0
jXs
+
Ea
Dr. Louie
Ia
Supplying Q
P0 = 0
• Increasing |Ea| decreases power angle 
• Real part of Ia remains constant
Absorbing Q
induced voltage (V), field current (A)
Under-excited Over-excited
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Phasor Diagrams
|Ia|cosfPF
|Ea|sin
Va

fPF
Ea
jIaXs
Ea
jIaXs

Ia
jIaXs
fPF
Ia
Ia
• Two conventions for excitation
• Convention 1:Based on voltage magnitudes
|Ia|cosfPF
Ea

Va
Lagging PF
(over-excited)
Unity PF
P, Q
P
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Side Note
Each diagram has same real power output, differing excitation
|Ia|cosfPF
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Va
 |Va| > |Ea|: under-excited
 |Va| = |Ea|: normally excited
 |Va| < |Ea|: over-excited
• Convention 2: Based on PF
Leading PF
(under-excited)
P
 Leading PF: under-excited
 Unity PF: normally-excited
 Lagging PF: over-excited
Q
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Side Note
Excitation (infinite bus)
• For synchronous generators connected infinite
bus, adjusting excitation:
• Conventions not always compatible
• Example: for unity power factor, |Ea| > |Va| unless
Ea
armature current is 0
 Does not promote real power output if power angle
is zero, put reactive power will be affected
 Increases real power output if power angle is held
constant (non-zero)
 May not affect real power output if power angle is
adjusted such that |Ea|sin is constant, but reactive
power will be affected
jIaXs

Ia
Va
• Using the voltage magnitude convention:
 Over-excited generators tend to supply power to the grid at
lagging power factor (but could be unity power factor)
 Under-excited generators tend to supply power to the grid at
leading power factor
 Normally-excited generators supply power to the grid at nearly
unity power factor
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V-Curves
Power Effects
• How does varying the power output effect , Ia,
fp for a constant excitation |Ea| and terminal
voltage Va?
• To increase power:
3 | Va || Ea | sin 
Po 
 |Ea|sin increases
Xs
 |Ia|cosfPF increases
Po  3 | Va || Ia | cos fPF
armature current (A)
Increasing Po
Unity PF
Leading PF
(under-excited)
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• Increasing Po also increases power angle 
• Real part of Ia also increases
Lagging PF
(over-excited)
field current (A)
Increasing |Ea|
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Mechanical Power
Phasor Diagrams
Each diagram has same excitation, differing power
• How do we change the real power?
• Power output described by:
Po 
3 | Va || Ea | sin 
Xs
|Ia|cosfPF
|Ea|sin
Po  3 | Va || Ia | cos fPF
• If excitation and terminal voltage are held
constant, then increasing the mechanical power
into the generator results in:

Va
fPF
Ia
Lagging PF
(over-excited)
 Increase in power angle 
 Increase in |Ia|cosfPF (real part of armature
current)
Ea
Ea
Ea
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jIaXs
jIaXs


jIaXs
Ia
fPF
Ia
Va
Unity PF
Va
Leading PF
(under-excited)
Increasing Power
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Summary
• Generators must be properly synchronized to the
electric grid prior to connection
• Infinite bus concept: constant voltage and
frequency, capable of source or sinking any
amount of current
• Excitation affects reactive power
 Under-excited: generator absorbs reactive power
 Over-excited: generator supplies reactive power
• Increasing mechanical power increases power
angle, real part of armature current
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