Lecture 19

GENERATOR  CAPABILITY CURVE By  Prof. C. Radhakrishna

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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Armature current limit The per unit complex output power is S



P 



 jQ



~ ~  E  t  I  t  *

 E t   I t  (cos    j sin  )

where φ is the power factor angle.

Figure 1 Armature current heating limit

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. 10/17/2010 10:20 AM

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Field current limit 2

Because of the heat resulting from the  R  fd  i  fd  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=Xq=Xs , the equivalent circuit of Steady-state model gives the relationship between Et, It and Eq (equal to Xadifd). The corresponding phasor diagram, with Ra neglected, is shown in Figure 2.

.

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Field current limit

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Field current limit (1)

P



E t I t cos 

Q  Et It sin  10/17/2010 10:20 AM



 X  ad   X  s

 Xad  Xs

E t i fd sin  i

Ei t fd cos i 

2 t 

E 

X s 7

Field current limit

The relationship between the active and reactive powers for a given field current is a circle centred at ( ) on the Q-axis 2   E t  /  X  sthe effect of the and with as the radius. Therefore, maximum( X  field current ad   /  X  s ) E t i  fd  rating on the capability of the machine may be illustrated on the P-Q plane as shown in Figure 3.

Figure 3 Field current heating limit 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. 10/17/2010 10:20 AM

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End region heating limit

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End region heating limit • 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.

Figure 4 End region heating limit 10/17/2010 10:20 AM

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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.

Generator Characteristics • 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. 10/17/2010 10:20 AM

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CONCLUSIONS

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THANK  YOU  10/17/2010 10:20 AM

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