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MODELING OF GENERATORS
for Transient Studies
Transients in Power System
MAY 2009
MODELING OF GENERATORS
 Model of a device is very dependent on its
physical attributes
 A generator model would be quite different
from a transformer model
 A generator has more coils than a
transformer, however they are connected in
parallel
 Generator coils on the other hand have
relatively few turns
MODELING OF GENERATORS
 A turn has these parts: straight sections in
slots, with significant capacitance to
grounded slot walls & to other conductors
in the slot , but negligible capacitance to
conductors elsewhere
 There are end connections with less
capacitance to frame & more mutual
capacitance with other conductors in end or
overhang region
 The inductances, magnetic flux linkages per
unit current are likewise different
MODELING OF GENERATORS
 How different depends on speed of
transient event
 Eddy currents prevent immediate
penetration of flux into stator iron and into
adjacent turns for very fast transients
 Hydro generators are different from turbo
generators in that slots are shorter & the
end sections longer
 Hydro generators have more turns per coil
than turbo generators
MODELING OF GENERATORS
 Picture just presented advises that a good
model for generator may comprise :
- a number of short transmission lines
of alternatively low & high surge
impedances (corresponding to slot & end
regions) connected in series or multiple π
sections to represent winding fractions
 Experience shows such an elaborate
portrayal is rarely justified
MODELING OF GENERATORS
 The form of a model depends on how it is
to be used
 A popular way of connecting generators is
the unit scheme




G: generator
GB: generator bus
GSUT: generator step-up transformer
AT: auxiliary transformer
MODELING OF GENERATORS
 In some stations, specially nuclear stations, a
generator circuit breaker is connected in main bus
between generator and auxiliary tap so that
auxiliaries can be supplied from system when
generator is out of service
 need to be concerned with transients caused: by
lightning and switching surges on power
system which reach generator through GSUT, & by
faults , cct. B. operations on generator bus
 Models used should be appropriate to source &
nature of stimulus
MODELING OF GENERATORS
 Response of a 270 MVA, 18 kV, turbo
generator to a step of voltage shown below
 test made at low voltage by applying 12 V
from a stiff source , between phase &
ground, & measuring transient on terminal
of a second phase
MODELING OF GENERATORS
 Remarkable feature of last oscillogram: is
its near single frequency appearance
 there is clearly at least one other
frequency initially, however it dies out
quickly
 This evidence suggests generator can be
represented by a relatively simple model at
least as far as this particular event concern
 An equivalent cct. Shown in next slide, in
which each phase represented by a π cct.
MODELING OF GENERATORS
 Figure: simple terminal model for a
generator
MODELING OF GENERATORS
 In this figure R and L represents resistance
and leakage inductance of each phase and
C is phase capacitance
 Result of applying this model for 270 MVA
generator is illustrated in next slide
 Where for this machine L=540 μH &
C=0.38 μF, the resistance selected is
discussed later
 Correspondence to measured result
reasonable, however initial minor loop is
missing
MODELING OF GENERATORS
 Application of Model to a 270 MVA Gen.
MODELING OF GENERATORS
 This is attributed to omission of mutual
coupling between phase which must surely
exist
 A simple way of including such coupling
proposed by Lauber as illustrated in figure
below

MODELING OF GENERATORS
 In this figure each phase of winding
concentrated & produces uniform flux
density in air gap
 Outcome is a mutual phase inductance
which is 1/3 of phase self-inductance
 Note: normal convention of currents 
negative flux linkage
 in general this coupling factor designated
by K will not be 1/3 due to distributed
nature of winding
MODELING OF GENERATORS
 To include mutuals in equivalent transient
model of this generator, L must be
increased by 1+K & a mutual of K must be
introduced between each pair of phases
 Alternatively, L can be left intact & an
additional inductance –KL inserted in
neutral
 these modified models shown in next slide
MODELING OF GENERATORS
 Terminal transient models for a generator
including mutual phase coupling
MODELING OF GENERATORS
 Using this corrected model, the voltage shown in
next slide will be observed at terminals B & C
when generator is energized on phase A
 question of damping to include in generator model
is of some concern
 figure of last slide is matched with the measured
result by arbitrarily choosing value of resistance ,
chosen value is 5 Ω
 if assume x/R=7  R=0.029 Ω
 This indicate damping arises mostly due to eddy
current losses
MODELING OF GENERATORS
 Application of modified model to 270 MVA
Gen.
MODELING OF GENERATORS
 This result suggest that ωL/R should be
considered constant
 At principal frequency of the response (6.9
kHz) resistance would be 115 times the 60
Hz value
 model just described is suitable where an
oscillatory disturbance created
 Examples: disconnecting of generator by its
breaker or disconnection of entire
generator / transformer unit by opening
H.V. breaker
MODELING OF GENERATORS
 fast rising transients, such as those created
by a reignition in a disconnect switch in
generator bus, or a fast rising surge
coupled capacitively through GSUT, need
different model
 in these circumstances generator might be
represented by a distributed parameter
model which appears on entry as a surge
impedance, while choice of value depend
on circumstances
MODELING OF GENERATORS
 As mentioned, conductor in slot behaves
like a short transmission line
 Initially, magnetic flux is confined within the
slot, screened from stator iron by eddy
currents
 These effects maintain L & consequently
surge impedance Z0 , low
 however both increase with time as flux
penetrates iron
 surge impedance of end connections is higher
since inductance is higher & capacitance lower
MODELING OF GENERATORS
 Computation of inductance, based on geometry of
the winding
 Dick Formula for average surge impedance is:

Z0=(Ks L’’d/CdNp)^0.5
 L’’d=sub-transient inductance/phase
 Cd= capacitance/phase , Np=number of poles
 Ks is a geometrical factor typically about 0.6
 Validity of formula for two machines in Ontario Hydro
system, verified by comparison:
 Machine
Rating
Z0 measured Z0
 P: NGS
635 MVA/ 24 kV
28 Ω
27Ω
 A:TGS
270 MVA/18 kV
20 Ω
21Ω
MODELING OF GENERATORS
 Surge impedances are relatively low, lower
than surge impedance of isolated phase bus
 Which is around 50 Ω
 And it means surge arriving on the bus to
generator face a reduction due to a
refraction coefficient of less than one
 However it is expected that these values
will increase as flux penetrates core steel
 Abetti et. al. indicate a change from 50 Ω at
1 μs to 80 Ω at 10 μs for a 13.8 kV, 100
MVA generator
MODELING OF GENERATORS
 A distributed parameter model is also
appropriate for studying transient in a
generator
 Figure below shows such a model
MODELING OF GENERATORS
 Surge source shown by a thevenin equivalent, (Vb,
Zb)
 Where Vb twice incident wave (as discussed in chapter
nine)
 inductance Lc typically a few micro-Henries,
associated with unbonded enclosures in isolated phase
bus, CTs, winding end ring & end winding preceding
first winding slot
 Z1 & Z2 represent surge impedances of slotted & end
connection regions
 Remaining coils of gen. winding modeled by a fixed Z0
 This model applied to the 635 MVA/24 kV gen. &
results shown in next slide
MODELING OF GENERATORS
 Consequences of applying a step to 635
MVA/24 kV gen, through a 50 Ω bus