modeling of generators for transient studies transients in power system may 2009

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


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


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


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.


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


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


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


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


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


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


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


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


Consequences of applying a step to 635 MVA/24 kV gen, through a 50 Ω bus

modeling of generators for transient studies transients in power system may 2009

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