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GENERATORCAPABILITY CURVE

By

Prof. C. Radhakrishna

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CONTENTS

GENERATOR CAPABILITY CURVEReactive Capabil ity Curves

Armature current limit

Field current limitEnd 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 carrycontinuously without overheating.

The active power output is limited by the prime mover

capabili ty to a value within the MVA rating.

The continuous reactive power output capability is limited

by three considerations: armature current limit, fieldcurrent 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 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 fieldcurrent 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 Xd=Xq=Xs , the equivalentcircuit of Steady-state model gives the relationship between Et, It and

Eq (equal to Xadifd). The corresponding phasor diagram, with Raneglected, is shown in Figure 2.

.

Field current limit

2fdfdiR

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Field current limit

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Field current limit

cos sinad

t t t fd i

s

X

P E I E iX

2

sin cosad tt t t fd is s

X EQ E I EiX 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 themaximum field current rating on the capabil ity 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 Fieldcurrent 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 thirdl imit 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 plot ted 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 capabili ties of the machine itself and are determined

by the design of the machine. Additional limits may be imposed bypower system stability limits.

During conditions of low-system voltages, the reactive power demand ongenerators 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 l imit 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