1. MODELING OF GENERATORS for Transient Studies Transients in Power System MAY 2009

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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.

10. MODELING OF GENERATORS  Figure: simple terminal model for a generator

11. 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

12. MODELING OF GENERATORS  Application of Model to a 270 MVA Gen.

13. 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 

14. 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

15. 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

16. MODELING OF GENERATORS  Terminal transient models for a generator including mutual phase coupling

17. 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

18. MODELING OF GENERATORS  Application of modified model to 270 MVA Gen.

19. 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

20. 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

21. 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 Z 0, low  however both increase with time as flux penetrates iron  surge impedance of end connections is higher since inductance is higher & capacitance lower

22. MODELING OF GENERATORS  Computation of inductance, based on geometry of the winding  Dick Formula for average surge impedance is:  Z 0 =(K s L’’ d /C d N p )^0.5  L’ ’ d =sub-transient inductance/phase  C d = capacitance/phase, N p =number of poles  K s is a geometrical factor typically about 0.6  Validity of formula for two machines in Ontario Hydro system, verified by comparison:  Machine Rating Z 0 measured Z 0  P: NGS 635 MVA/ 24 kV 28 Ω 27Ω  A:TGS 270 MVA/18 kV 20 Ω 21Ω

23. 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

24. MODELING OF GENERATORS  A distributed parameter model is also appropriate for studying transient in a generator  Figure below shows such a model

25. MODELING OF GENERATORS  Surge source shown by a thevenin equivalent, (V b, Z b )  Where V b twice incident wave (as discussed in chapter nine)  inductance L c typically a few micro-Henries, associated with unbonded enclosures in isolated phase bus, CTs, winding end ring & end winding preceding first winding slot  Z 1 & Z 2 represent surge impedances of slotted & end connection regions  Remaining coils of gen. winding modeled by a fixed Z 0  This model applied to the 635 MVA/24 kV gen. & results shown in next slide

26. MODELING OF GENERATORS  Consequences of applying a step to 635 MVA/24 kV gen, through a 50 Ω bus