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.