EE532 Power System Dynamics and Transients

1
EE532 Power System Dynamics and Transients
EUMP Distance Education Services

• Satish J Ranade
• Synchronous Generator Model
• Lecture 11

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Modeling of synchronous generators
Next More on steady state, round rotor
model Salient Pole Machine Transients and flux
freezing Coupled Circuit model
3
Modeling of synchronous generators
Fields -- Flux density due to field for rotor
position ?0
Field MMF and Flux Density(B) is a function Of
rotor position ? and observer position a. Flux
density is essentially radial through air gap.
Since field current If is dc , the peak
amplitudes are constant in time and proportional
to If MMFf(a,?) MMFfmax cos(a-?) Bf(a,?)
Bfmax cos(a-?) If rotor rotates at constant
speed ?r, then ? ?o ?r t t time Observer
at a sees a flux density that varies sinusoidally
in time Bf(a,t) Bfmax cos( ?r t- a ?o ) The
peak amplitude is independent of time. The phase
is a, the observers position
d
a
q
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Modeling of synchronous generators
Construction Terminology -- Flux density due
to stator phase a
Phase a MMF and Flux Density(B) is a function of
observer position a. Flux density is essentially
radial through air gap The current in phase a is
a sinusoid with frequency ? so are mmf and flux
density MMFa(a) MMFamax cos(a)cos(?t) Observer
at a sees a flux density that varies sinusoidally
in time Ba(a) Bamax cos(a) cos(?t) Ba(a) K
Iamax cos(a) cos(?t) Combined with the flux
density from phase b and c, the net stator flux
density will turn out to be a rotating field!
Stator phase a winding is also
actually Distributed across the Surface creates
a stepped mmf Waveform intended to approximate A
sinusoid
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Modeling of synchronous generators
Net Stator Field Rotating Magnetic
Field- balanced positive sequence operation
d
a
d
a
Schematic of Net Stator Field Phases a,b,and c At
t0
q
q
Ba(a) (3/2)K Iamax cos(a)
Schematic Representation Of Phase a flux
density Ba(a) K Iamax cos(a) cos(?t)
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Modeling of synchronous generators
d
d
d
a
a
a
q
q
q
ROTATING FIELD Bs(a,t) (3/2)K Iamax cos(?t-
a) Observer at a sees sinusoidal flux density in
time Frequency ? lags ia by a At any time
t flux density is sinusoidally distributed in
space Amplitude is time independent (3/2)K
Iamax Peak is at a ?/t
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Modeling of synchronous generators
d
a
Steady State Model from Fields Terminal voltage
under balance conditions
q

• The terminal voltage comprises of
• Voltage induced in phase ( a) by Field Flux
• Voltage induced by net stator flux
• Resistive voltage drop
• Inductive voltage drop in parts of the winding
  outside air gap (Overhang)
• Inductive voltage drop in individual phase from
  leakage flux

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Modeling of synchronous generators
Steady State Model from Fields-Terminal voltage
under balance conditions
a Vt - n
Ra
-Ear
Ll
Ia
Round Rotor
Ea -

• The terminal voltage comprises of
• Voltage induced in phase ( a) by Field Flux(Ea)
• Excitation, Induced Voltage, Generated Voltage,
  Open Circuit Voltage
• Voltage induced by net stator flux(Ear)
• -Armature Reaction
• Resistive voltage drop (Ra armature resistance)
• Inductive voltage drop in parts of the winding
  outside air gap (Overhang),Inductive voltage drop
  in individual phase from leakage flux (Ll leakage
  inductance)

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Modeling of synchronous generators
Steady State Model from Fields-Terminal voltage
under balance conditions
Voltage induced in phase ( a) by Field Flux(Ea)
?
Ea?N? /?o
d
? rms value of flux , depends on field current
Ia
a
q
Ear?N(3K) Ia/-90 -j?LaIa
q
a
a
a
Vt Ea- j?LaIa- j?Ll Ia RaIa Vt Ea- -jXsIa-
RaIa
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Modeling of synchronous generators
Steady State Model from Fields-Terminal voltage
under balance conditions
a Vt - n
Ra
jXs
Ia
Round Rotor
Ea -
Ea open circuit voltage function of dc field
current If Ra Armature resistance Xs
Synchronous reactance Vt terminal voltage Ia
Armature Current
Ea
Open Circuit Curve
If
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Modeling of synchronous generators
Steady State Model from Fields-Terminal voltage
under balance conditions
Space Vectors and time phasors
From Field
Ea?N? /?o
?
d
a
From Stator
Ear?N(3K) Ia/-90 -j?LaIa
iaIam cos( ?tf)
q
IaIa/ f
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Modeling of synchronous generators
Steady State Model from Fields-Terminal voltage
under balance conditions
a Vt - n
Ra
jXs
Ia
Round Rotor
Ea -
?aaf
Ea
jXIa
Vt
Ia
?aas
Ear
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Modeling of synchronous generators
Fields -- Flux density due to stator phase a
Salient Rotor
Phase a MMF pattern is the same as
before MMFa(a,?) MMFamax cos(a)cos(?t) Resol
ve MMFa into space vectors MMFad and
MMFaq MMFadMMFa cos(?) MMFaq-MMFa sin(?)
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Modeling of synchronous generators
Steady State Model from Fields-Terminal voltage
under balance conditions
Salient Pole
x
?
a
?aaf
Bs
d
Bsq
Ea
Bsd
?aasq
Iaq
q
Earq
Ia
Eard
?aasd
Iad
Vt Ea Eard Earq RaIa -jXlIa
Earq -j Xd1 Iad Eard -j Xq1 Iaq
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Modeling of synchronous generators
Steady State Model from Fields-Terminal voltage
under balance conditions
Salient Pole
?aaf
Ea
?aasq
Iaq
Iaq
Ea
Earq
fd
Ia
Eard
?aasd
Ia
Iad
Iad
Ia Iad Iaq
Vt Ea Eard Earq RaIa jXl Ia
Earq -j Xd1 Iad Eard -j Xq1 Iaq
Vt Ea RaIa jXd Iad j Xq Iaq
XdXd1Xl Xq Xq1Xl
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Modeling of synchronous generators
Steady State Model from Fields-Terminal voltage
under balance conditions
Vt
Salient Pole
d
d
jXqIaq
jXdIad
fd
Iaq
Ea
f
RaIa
Iad
Ia
Vt Ea RaIa jXd Iad j Xq Iaq
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Modeling of synchronous generators
Steady State Model from Fields-Terminal voltage
under balance conditions
Vt
Salient Pole
d
d
jXqIaq
jXdIad
fd
Iaq
Ea
f
RaIa
Iad
Ia
Vt Ea RaIa jXd Iad j Xq Iaq
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Modeling of synchronous generators
Transients Fault Inductor Current does not
change instantaneously In coupled circuits
flux linkage does not change instantaneously
Field Flux linkages Remain constant
Fault
Stator Rotating Field
Normal
d
d
a
a
Stator flux due to fault current cannot penetrate
rotor
q
q
Stator field Appears stationary To rotor
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Modeling of synchronous generators
Transients Fault Inductor Current does not
change instantaneously In coupled circuits
flux linkage does not change instantaneously
Stator field diffuses Into rotor
Eventually staedy State Establishes
A little later
d
d
a
a
q
q
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Modeling of synchronous generators
Transients Fault Inductor Current does not
change instantaneously In coupled circuits
flux linkage does not change instantaneously
Stator field diffuses Into rotor
During fault
Stator Inductance flux linkage/amp
d
a
Since linkage is in air gt Inductance is low
Initially Subtransient Then Transient Finally
Steady state
q
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Modeling of synchronous generators
NEXT
Circuits approach
pd()/dt
? flux linkage ( Kundur Text)
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Modeling of synchronous generators
NEXT
Circuits approach
Develop R and L matrices Parks Transformation