Generator Capability Curve

In voltage stability and long torm stability studies, it is important to consider the reactive capability limits of synchronous machines. In this section, we will develop capability curve which identify these limit.

Synchronous generator are rated in term of the maximum MVA outpot 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 prime mover capability to a value within in MVA rating. The continuously reactive power output capability is limited by three consider; armature current limit, field current limit and region heating limit.

The armature cyrrent result in an RI2 power loss and the energy associated with this loss must be removed so as to limit the increase in temperature of the conductor and its immediate environment. Therefore, one of the limitations on generator rating is the maximum current that can be carried by the armature without exceeding the heating limitations.


The per unit ( PU ) complex output power is
S = P + jQ = Et.It
S = Et.It.( cosØ + j.sinØ ) where Ø is the power factor angle.

















Therefore, in the P-Q plane the armature current limit as shown in figure above which appears as a circle with centre at the origin and radius equal to the MVA rating.

Because of the heat resulting from the Rfd.i2fd power loss, the field current impose a second limit on the operation of generator.
The constant filed current locus may be developed by the steady state equivalent circuit developed and reproduce . Relationship between Et, It and Eq (equal to Xad.ifd).

The corresponding phasor diagram, with Ra negelcted is shown in figure below.

Eqiating the component along and perpendicular to the phasor Et we get

(Xad.Ifd)sinδi = Xs.It.cosφ

(Xad.Ifd)cosδi = Et + Xs.It.sinφ

Rearranging yield

It.cosφ = (Xad.Ifd.sinδi) / Xs

It.sinφ = (Xad.Ifd.cosδi - Et ) / Xs

















Therefore
P = Et.It.cosφ = (Xad/Xs).Et.ifd.sinδi

Q = Et.It.sinφ = (Xad/Xs).Et.ifd.cosδi – (Et2/Xs)

The relationship between the active and reactive power for a given field current is a circle centered at – (Et2/Xs) on the Q-axis and (Xad/Xs).Et.ifd as a radius. Therefore, the effect on the maximum field current rating on the capability of the machine may be illustrated on the P-Q plane as shown figure below.

















In any balanced design, the thermal limit for the yield and armature intersect at a point A, which represent the machine nameplate MVA and power factor rating.

The localized heating in the end region of the armature impose a third limit on the operation of a synchronous machine. As explained below, this limit affects the capability of the machine in underexcited condition.

Figure below is schematic of the end-turn region of generator. The end flux as shown in the figure, enetrs and leaves in a direction perpendicular (axial) to the stator laminations.

















This causes eddy currents in the laminations, resulting in localized heating in the end region. The high field currents corresponding to the overexcited condition keep the retaining ring saturated, so that end leakage flux is small.

However, in the underexcited region the field current is low and the retaining ring is not saturated, this permit an increase in armature end leakage flux. Also in the underexcited condition, the flux produced by the armature current adds to the flux produced by the field current, therefore the end-turn flux enhances the axial flux in the end region and the resulting heating effects may severely limit the generator output, particularly in the case of a round rotor machine.

This illustrated in figure below which also includes the limit imposed by the armature current heating effects.

















The field current and armature current heating limit when plotted on P-Q plane depend on the armature voltage. Figure below shows these limit for 588MVA, 22kV, 0.85power factor machine at two value of armature voltage, 1 PU and 0.95 PU.

















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 imposed by power system stability limit.

For detail information, click http://elektro.get.bme.hu/edu/subjects/BSc-EM/animations/www.machines.cg.ac.yu/syn_vectord.htm