GENERATOR CAPABILITY CURVE

ByProf. C. Radhakrishna

10/17/2010 10:20 AM 2

CONTENTSGENERATOR CAPABILITY CURVE

Reactive Capability Curves

Armature current limit

Field current limit

End region heating limit

Generator Characteristics

10/17/2010 10:20 AM 3

GENERATOR CAPABILITY CURVEReactive 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.

10/17/2010 10:20 AM 4

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 inFigure 1, appears as a circle with centre at the origin and radiusequal to the MVA rating.

*~~tt IEjQPS

)sin(cos jIE tt

10/17/2010 10:20 AM 5

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 Xd=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 Raneglected, is shown in Figure 2.

.

Field current limit

2fdfd iR

10/17/2010 10:20 AM 6

Field current limit

10/17/2010 10:20 AM 7

Field current limit

cos sinadt t t fd i

s

XP E I E iX

2

sin cosad tt t t fd i

s s

X EQ EI EiX X

(1)

10/17/2010 10:20 AM 8

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

10/17/2010 10:20 AM 9

End region heating limit

10/17/2010 10:20 AM 10

• The localized heating in the end region of the armature imposes a thirdlimit on the operation of a synchronous machine.• This limit affects the capability of the machine in the under excitedcondition.• This is illustrated in Figure 4, which also includes the limit imposed bythe armature current heating effects.• The field current and armature current heating limits when plotted on aP-Q plane depend on the armature voltage.

End region heating limit

Figure 4 End region heating limit

10/17/2010 10:20 AM 11

10/17/2010 10:20 AM 12

10/17/2010 10:20 AM 13

10/17/2010 10:20 AM 14

10/17/2010 10:20 AM 15

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.

10/17/2010 10:20 AM 16

CONCLUSIONS

10/17/2010 10:20 AM 17

THANK YOU