LÝ THUYẾT CƠ BẢN VỀ ĐƯỜNG CONG ĐẶC TÍNH CÔNG SUẤT MÁY PHÁT (GENERATOR CAPABILITY CURVE )

GENERATOR
CAPABILITY CURVE
By
Prof. C. Radhakrishna
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CONTENTS
GENERATOR CAPABILITY CURVE
Reactive Capability Curves
Armature current limit
Field current limit
End region heating limit
Generator Characteristics
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GENERATOR CAPABILITY CURVE
Reactive Capability Curves
• Synchronous generators are rated in terms of the
maximum MVA output at a specified voltage and power
factor (usually 0.85 or 0.9 lagging) which they can carry
continuously without overheating.
• The active power output is limited by the prime mover
capability to a value within the MVA rating.
• The continuous reactive power output capability is limited
by three considerations: armature current limit, field
current limit, and end region heating limit.
Armature current limit
• One of the limitations on generator rating is the maximum
current that can be carried by the armature without
exceeding the heating limitations.
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Figure 1 Armature current heating limit
Armature current limit

The per unit complex output power is
where φ is the power factor angle.
Therefore, in the P-Q plane the armature current limit, as shown in
Figure 1, appears as a circle with centre at the origin and radius
equal to the MVA rating.
*
~
~
tt
IEjQPS 
)sin(cos

jIE
tt

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Because of the heat resulting from the power loss, the field
current imposes a second limit on the operation of the generator.
The constant field current locus may be developed by the steady-state
equivalent circuit developed earlier. With X
d
=X
q
=X
s
, the equivalent
circuit of Steady-state model gives the relationship between E
t
, I
t

and
E
q
(equal to X
ad
i
fd
). The corresponding phasor diagram, with R
a
neglected, is shown in Figure 2.
.
Field current limit
2
fdfd
iR
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Field current limit
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Field current limit
cos sin
ad
tt tfd i
s
X
PEI Ei
X



2

sin cos
ad t
tt tfd i
ss
X
E
QEI Ei
X
X

 
(1)
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The relationship between the active and reactive powers for a
given field current is a circle centred at ( ) on the Q-axis
and with as the radius. Therefore, the effect of the
maximum field current rating on the capability of the machine may
be illustrated on the P-Q plane as shown in Figure 3.
Field current limit
st
XE /
2

fdtsad
iEXX )/(
In any balanced design, the thermal limits for the field and armature
intersect at a point A, which represents the machine nameplate MVA and
power factor rating.
Figure 3 Field
current heating limit

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End region heating limit
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• The localized heating in the end region of the armature imposes a third
limit on the operation of a synchronous machine.
• This limit affects the capability of the machine in the under excited
condition.
• This is illustrated in Figure 4, which also includes the limit imposed by
the armature current heating effects.
• The field current and armature current heating limits when plotted on a
P-Q plane depend on the armature voltage.
End region heating limit
Figure 4 End region heating limit
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Generator Characteristics
The above limits on the operation of the generator are those
imposed by the capabilities of the machine itself and are determined
by the design of the machine. Additional limits may be imposed by
power system stability limits.
• During conditions of low-system voltages, the reactive power demand on
generators may exceed their field current and/or armature current limits.
• When the reactive power output is limited, the terminal voltage is no
longer maintained constant.
• On most generators, the armature current limit is realized manually by
operators responding to alarms.
• The operator reduces reactive and/or active power output to bring the

armature current within safe limits.
• On some generators, automatic armature current limiters with time delay
are used to limit reactive power output through the AVR.
REFERENCES :
[ 1 ] Prabha Kundur : “Power System Stability and control” , The EPRI
Power System Engineering Series, McGraw-Hill, Inc., 1994.
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CONCLUSIONS
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THANK
YOU