The document discusses the implications of load angle and excitation on generator stability. It explains that the load angle is the angle between the generator induced EMF and terminal voltage. It increases as the generator transfers power from no load to load conditions. The generator operates stably when the derivative of power with respect to load angle is positive, up to a load angle of 90 degrees. Boosting excitation can reduce the load angle and increase power output at a given load angle, as long as excitation limits are respected. The generator capability curve depicts the stability limits imposed by the load angle, rotor current, and stator current limiters.

1. IMPLICATIONS OF LOAD ANGLE &
EXCITATION ON GENERATOR STABILITY,
SIGNIFICANCE OF GENERATOR
CAPABILITY CURVE
PREPARED BY: -
KUNAL GUPTA
DGM(EMD)

2. WHAT IS LOAD ANGLE ?
• Load Angle δ is the angle between the Generator induced
E.M.F & Generator terminal voltage.
• Physically, this is the angle by which the reference line
made on the Generator shaft front deviates from no load-
to-load condition.

3. D
EG IXS φ
δ V
A B C
φ
I
FIG – (I)
Vector Diagram of Generator
parameters with lagging
power factor

4. GENERATOR PARAMETER DETAILS AS
DEPICTED IN FIG (I)
• AD = EG = Generator Induced E.M.F.
• I = Generator Stator Current.
• AB = V = Generator Terminal Voltage.
• XS = Generator Synchronous Reactance.
• φ = Angle between Generator Terminal Voltage V &
Stator Current I. (COS φ = p.f).
• δ = Load Angle.

5. EQUATION OF POWER CURVE
• CD = IX S COS φ = E G SIN δ -------(i)
• Active Power P = VI COS φ = VE G SIN δ (From i
above) XS
• From above, it becomes clear that the power curve
with reference to excitation shall be a sinusoidal one
as EG is proportional to Generator Excitation.
• BC = IX S SIN φ = E G COS δ __ V -------(ii)
• Reactive Power Q = VI SIN φ = VE G COS δ / XS
__ V 2 / XS (From ii above)
• It is apparent that Reactive Power Q shall be equal to
( __ V 2 / XS ) when EG = 0.

6. P max at load
angle δ = 90
P (Power ) P2 Degree.
P1
δ1 δ2
Load Angle δ
FIG – (II)
Power Curve

7. POWER CURVE CHARACTERISTICS
• From FIG (II), it becomes evident that with constant
Excitation, maximum power would be generated at
δ=900 .
• As the power increases from P1 to P2, the reference
load angle increases from δ1 to δ2.
• The Generator operates on stable zone up to the
time dP/dδ is positive, i.e., up to δ=900.
• This is the reason to operate the Generator with load
angle limiter control, which limits the load in case the
load angle tends to cross the design value.

8. P (Power ) P2
P1
δ1 δ2
Load Angle δ
FIG – (III)
Power Curve

9. POWER CURVE CHARACTERISTICS
• From FIG (III), it is quite clear that with constant
power generation P1, if the excitation is boosted up,
then load angle shall reduce from δ2 to δ1.
• Also, with same load angle δ2, power generation
increment is possible from P1 to P2 with boosting up
of excitation.
• As changing Generator Excitation is done primarily
by A.V.R, the load angle at which the Generator is
safe to operate is determined by the A.V.R response.
• With fast acting A.V.R, Generator can be operated at
higher load angle & vice versa.
• However, boosting up of excitation shall be limited to
the design value only.

10. D
φ
EG I IXS
δ
φ V
A B
C
FIG – (IV)
Vector Diagram of Generator
parameters with leading power
factor

11. EFFECT OF NEGATIVE REACTIVE POWER
ON GENERATOR
• From FIG (IV), it is evident that EG reduces when
stator current I leads the terminal voltage V. This is
the situation when the Generator is subjected to
negative reactive MVAR.
• In such case, Grid no longer require MVAR from
Generator, rather it exports MVAR to the connected
machines, causing reduction of Generator excitation.
• As it is shown in FIG (III) that for constant power,
reduction of EG means increase in load angle δ, the
capability of the Generator to absorb reactive MVAR
at a particular load is subjected to load angle
limitation.

12. MW
C
F
VI
EGV / XS
φ
A δ G MVAR
V 2 / XS E B
FIG – (V)
Generator
Capability Curve

13. GENERATOR CAPABILITY CURVE
• By multiplying FIG (I) by V / XS, we do arrive at FIG (V).
• EFCG depicts the Generator capability curve.
• Load angle limiter limits the negative reactive MVAR as
shown by the line EF.
• Rotor current limiter limits the rotor current & is
depicted by CG which is the arc of AC with A as center
& is proportional to Generator excitation as well as the
rotor current.
• Stator current limiter limits the stator current as shown
by FC, which is the arc of BC with B as center & is
proportional to stator current.
• All these limiters ensure that the Generator, at any
point of time, operates within the framework EFCG for
electrical as well as thermal stability of the machine.