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Effects of Turn to Turn Stator Winding Faults in

Synchronous Generators - A Numerical Study

Meinolf Klocke, Jens RosendahlUniversity of Dortmund

Chair of Electrical Drives and Mechatronics1

Emil-Figge-Str. 70, D-44221 Dortmund, Germany

 Abstract —  The effects of stator winding faults on the

behaviour of a synchronous generator are of interest for

predicting the severity of the occurring damage. The paper

in hand describes the numerical transient field and net-

work calculation for the sudden occurrence of stator wind-

ing turn to turn short circuits within coil groups and be-

tween different phases. For a 2-pole 775 MVA generator

six different locations of short circuits varying in the num-

ber of shorted turns and the position of the bypassed turns

in the winding are investigated. Transient currents in the

short-circuited windings as well as in the remaining stator

coils are calculated, taking saturation into account. Addi-

tionally, the unbalanced magnetic pull is determined and

output as a function of time. The results of the calculations

clarify the severity of such faults even if the machine is

disconnected from the grid and de-energized within a very

short period after the occurrence of the short-circuit.

 Index Terms— Electrical machine, stator winding fault,

numerical field computation, coupled problems.

I. I NTRODUCTION 

Stator winding faults are of great importance in large

synchronous generators as they not only damage the

stator winding of the machine severely, but can also

destroy the whole stator core. Common reasons for these

faults are material fatigue of the insulation conditioned

 by mechanical stress in the end winding zone as well as

thermal influences and moisture [1, 2 and 3].

The transient numerical field and network calcula-

tion appears to be an adequate and advantageous tool for

the quantitative prediction of effects of stator winding

faults since experimental studies are much too costly or

completely unfeasible. In opposition to a merely net-

work based analysis the transient variation of mutual

and self inductances caused by changes in the level of

iron saturation is implicitly taken into account since the

discretised model can be considered a representation of

the whole magnetic circuit.

The output quantities can be used for further evalua-

tions, e.g. the reconstruction of disturbances having

finally destroyed a generator. Forces having been ex-

erted on the end-winding zone of a destroyed generator

for instance can be calculated from the resulting coil

currents.

1  The Chair of Electrical Drives and Mechatronics, University ofDortmund, Germany, is held by Prof. Dr.-Ing. Dr.-Ing. S. Kulig.

This allows identifying the stator winding fault as

the primary cause of end-winding zone deformation of

the wrecked generator. In this study a finite difference

scheme coupled with an arbitrary circuit containing

windings and lumped elements is applied to a 2pole-775

MVA generator.

II. NUMERICAL TIME-STEPPING FIELD COMPUTATION

COUPLED TO STATOR NETWORK A NALYSIS 

In a strongly coupled numerical time-stepping com-

 putation for field and circuit quantities the governing

equations are solved simultaneously for each time-step.

The time-stepping results from replacing the time de-

rivatives by quotients of differences. In the program

used here this time discretisation is carried out accord-

ing to the θ-method as described in [4]. The spatialdiscretisation method for the magnetic field applied in

the program is a finite difference scheme. Since thesemethods are not novel, only a basic sketch of the result-

ing system of equations (1) for a given time-step is de-

scribed in the following [3, 4, 5, 6 and 7].

Like in the finite element method a reluctance matrix

(α) results from the spatial discretisation process, whichinterrelates the unknown nodal values of the magnetic

vector potential on the discretised machine cross-section

to each other. It should be noted that such a nodal ap-

 proach on a 2D cross-section can be considered equiva-

lent to a 3D edge approach applied to a cross-sectional

one-element-layer model. The inherent constraints are

given by edges in the front and back plane with a value

of zero whereas the unknown values occur for edges in

 perpendicular direction.

In massive conductive regions like the rotor core and

the damper bars eddy currents have to be taken into

account. They are assumed to close ideally, i.e. without

additional voltage drop in the machine end region. Their

current densities do not occur explicitly. Since they are

only determined by the time derivative of the vector

 potential and the material conductivity, their expressions

can immediately be inserted in the equations for the

vector potentials. Discretisation and rearrangement leads

to a diagonal matrix of nodal conductance coefficients

( F γ) with time step width h and the θ -method weightingfactor (1− θ) in the denominator.

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The field excitations caused by stator and rotor

winding currents (iw) and (if ) are included by the matri-ces of turn density coefficients ( F  N,1)

T for the stator and

( F  N,2)T  for the rotor. The same matrices in transposed

form occur for the flux linkage calculation in the branch

voltage equations of stator and rotor windings. The

matrices ( Bw) and ( Bf ) contain the loop incidences ofstator and rotor winding branches in the overall net-

work. ( Dw) and ( Df ) are diagonal matrices for the wind-ing currents in the voltage equations. Their coefficients

are calculated from resistances and leakage inductances

directly associated with the windings. In the present case

the coefficients of ( Dw) are zero since the armaturewinding resistances and leakage inductances are mod-

elled as external network elements (see Fig. 1b).

 Network branch currents and voltages are embraced

in the vector ( x b). The coefficients in matrix ( M  b) on theone hand result from the dynamic current-voltage be-

haviour of the branches. On the other hand loop inci-

dences for voltages and node incidences for currents are

explicitly included there, too. The matrices (C w) and (C f ) provide these nodal incidences for the stator and rotor

winding currents (iw) and (if ) as they are not included in( x b).

( )  ( )

( )  ( )   ( ) ( )

( ) ( ) ( ) ( )

( )   ( ) ( ) ( ) ( )

( )   ( ) ( ) ( ) ( )

( )

( )

( )

( )

( )

( )

( )

( ) ⎟⎟⎟

⎟⎟⎟⎟⎟⎟⎟

 ⎠

 ⎞

⎜⎜⎜

⎜⎜⎜⎜⎜⎜⎜

⎝ 

⎛ 

=

⎟⎟⎟

⎟⎟⎟⎟⎟⎟⎟

 ⎠

 ⎞

⎜⎜⎜

⎜⎜⎜⎜⎜⎜⎜

⎝ 

⎛ 

⋅

⎟⎟⎟

⎟⎟⎟⎟⎟⎟⎟

 ⎠

 ⎞

⎜⎜⎜

⎜⎜⎜⎜⎜⎜⎜

⎝ 

⎛ 

−

−

−+

f 

w

 b

A

f 

w

 b

f f 

Fe

2, N

ww

Fe

1, N

f w b

T

2, N

T

1, N

01

01

0

01

r 

r 

r 

r 

i

i

 x

 A

 D Bl 

h F 

 D Bl 

h F 

C C  M 

 F  F h

 F 

θ 

θ 

θ α 

  γ 

  (1)

The right hand side of (1) is calculated from initial

values or the results of the previous time step. It is em-

 phasised that all network equations are explicitly taken

into account without the use of reductive methods like

node potential or loop current formulations. This ap-

 proach for network analysis is known as the “sparse

tableau approach” as referred to in [9].

The number of network equations appears to be neg-

ligible in the presence of thousands of field equations.Moreover, ill-conditioned systems, which would result

from practically cutting or short-circuiting branches by

extreme values of their resistances in reductive methods,

can be avoided by the sparse tableau approach.

The solution of the linear system of equations is car-

ried out directly, where a total pivot search is applied

during the elimination of the lower network matrices.

The nonlinear magnetic characteristic of stator and rotor

core material makes the reluctance matrix (α ) become

field dependent. This requires a few iterations per time

step, where the permeability is adapted by under-

relaxation.

In the program used here the stator was formerly re-

lated to fixed topologies and winding arrangements, i.e.

star and delta connection of an m-phase winding with allcoil groups of a phase connected in series or in parallel.

In contrast the stator coil groups are treated like inde-

 pendent branch elements in (1). This concept was al-

ready introduced in [8] for the rotor circuitry. It has

 been adapted for the stator without the need of changes

of the program source code. A virtual polyphase wind-ing is prescribed for the machine stator with a non regu-

lar winding scheme explicitly forced to be read in.

By neither specifying the star or delta connection of

 phases – an option previously implemented for consider-

ing grounded neutral points – the distinction between an

external supply network and the stator winding ar-

rangement vanishes. The former output line to ground

voltages of the network may be reinterpreted as inde-

 pendent winding branch voltages by a proper choice of

loop equations. This procedure allows modelling an

arbitrary stator network topology.

III. APPLICATION TO A SYNCHRONOUS GENERATOR  

A stator circuitry including three possible locations

for turn to turn short circuits within a given coil group

and three positions for short circuits between neighbour-

ing phases is set up according to Fig. 1a -c.

U

V

W

45678910

32

1234567

15161718192021

32142414039

17161514131211

32333435363738

42414039383736

293031333435

31302928272625

141312111098

18192021

28272625

upper 

layer 

lower layer 

upper 

layer 

lower 

layer 

 ps_II ps_III

 ps_I

ws_I

ws_II

ws_III

 positive

coil group

negative

coil group

slot numbers

 

Fig. 1a. Connectivity of the investigated windings.

The two parallel coil groups of each winding phase

are split into two partial windings, which in Fig. 1b are

denoted w1 – w7 and w10 – w4 for phase U, w2 – w8 andw11 – w5 for phase V as well as w3 – w9 and w6 – w12 for phase W. The RL-elements in series to the partial wind-ings represent the ohmic resistance of a partial winding

and its contribution to the end zone leakage inductance.

Both are assumed to be turn number proportional to the

total values of one coil group.

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 Fig. 1b. Network arrangement of stator windings with partial winding

coil groups w1…12 coupled directly to the field problem.

The resistive-inductive branches RL1…3 stand for theimpedance of the grid and the leakage inductance of the

machine transformer. The relative short circuit voltage is

set to 11 %. A capacitive-ohmic neutral to ground con-

nection of the winding star node with practically negli-gible admittance is inserted in order to allow for a sym-

metric arrangement of network loop equations.

TABLE 1: CHARACTERISTICS A ND ABBREVIATIONS

case phases coil group affected turns

ws_I U positive 2nd from terminal U

ws_II V positive 5th, 6th from terminal V

ws_III W negative 3rd, 4th, 5th (central turns)

 ps_I U / V neg. / neg. 1st / 1st, 2nd from neutral

 ps_II V / W neg. / pos.1st, 2nd from neutral

/ 1st-3rd from terminal W

 ps_III W / U pos. / neg.1st-3rd from terminal W

/ 1st from neutral

Furthermore, the voltage between the winding neu-

tral point and ground becomes an accessible output

quantity as the branch voltage of the related network

element. The partial windings w1, w2  and w3 with one,two and three turns can be shunted by a resistive branch

in parallel in order to simulate a turn to turn winding

fault within one coil group. The separating nodes be-tween the partial windings w10 – w4 and w11 – w5 as wellas w6  – w12  can be interconnected by correspondingresistive branches allowing for the simulation of wind-

ing faults between neighbouring phases. All cases are

listed in Table 1. The undisturbed operation is modelled

 by interconnecting resistances of 1012

 Ω.

Fig. 1d. Finite-difference polar grid of the machine cross-section Slot

numbering clockwise beginning with the first slot above the horizontal

line on the left side

Partial winding no.:+12 –5 –5 –11 … …–11 +7+1+7 … … …+7 –9 –9 –9 –3 …… –3 +8 … .. +8 +2+2 +8 -4–10 … … … .. -10+6 +6+6+12 ... 

Fig. 1c. Winding scheme with locations of short circuits within single coil groups ( ) and between different phases (). Shorted turns are marked by “×” for the shorts in a single coil group, and by “↑” for the shorts between different phases.

ws_I ws_IIws_III  ps_I ps_III ps_II

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At the instant of the short circuit (t sc = 3.5 s), thisvalue is reduced to 5 mΩ  for the winding fault underconsideration. The prescription of the complete topology

of the stator circuitry including all possible short-circuit

 branch elements artificially enlarges the network and

leads to additional computational cost. For a given fault

under investigation many obsolete network elementsappear and twelve stator voltage equations instead of

six, seven or eight have to be solved permanently. How-

ever, as an advantage only one time consuming calcula-

tion has to be carried out for reaching steady state opera-

tion of the machine.

The locations of the winding faults under considera-

tion are shown in Fig. 1c. Coil conductors on slot

ground are depicted thick on the left and upper layer

thin on the right. Short circuits at the marked crossing

 points in the end winding zone result in different num-

 bers of shorted turns and positions within the affected

coil groups. The cases also differ in the phases these coil

groups belong to as briefly characterised in Table 1. In

Fig. 1c the turns of these coil groups are also marked.

The cross-section of the machine is discretised by a grid

with about 19,000 nodes as shown in Fig. 1d, which also

shows the positions of coil cross-sections of w1, w2 andw3, the partial windings to be shunted. Fig. 1d addition-ally contains the rotor reference frame axes d and q.

This coordinate system is used as a frame of reference

for the magnetic pull on the rotor later on. The simula-

tions start with short-circuiting the connection under

investigation. A period of time later (0.2 s) the machine

is disconnected from the power grid as a result of pro-

tection equipment interaction and de-excitation is initi-ated by immediately reducing the exciter voltage to

zero.

IV. R ESULTS 

 A. Currents

In all investigated cases high short circuit currents

occur as listed in Table 2.

Fig. 2. Current in short-circuit resistance for three-turn winding faultin phase W (case ws_III) from FD calculation.

In general their characteristics qualitatively are quite

similar to the one depicted in Fig. 2 showing one ex-

treme case ws_III. The time-course is characterised by a

quickly vanishing asymmetric part at the very begin-

ning, the intensity of which strongly depends on the

 phase condition at the instant of time before the fault

occurs.The effective value of the uninterrupted short-circuit

current  I sc, eff   is reached within about 0.15 s. It is notmuch reduced after de-excitation and disconnection of

the machine from the power grid.  I sc, eff, disc  is at mostonly about 20 % less than  I sc, eff , as shown in Table 2.Even 1.8 s after disconnection there is still a high level

of short-circuit current up to about a half of the value at

the instant of disconnection and start of de-excitation.

TABLE 2: CHARACTERISTICSHORT-CIRCUIT CURRENT VALUESFor comparison: rated value per coil group I eff, group = 8.6 kA.

|isc, peak |  I sc, eff   I sc, eff, disc  I sc, eff, 1.8 sCase kA kA kA kA

ws_I 215.2 107.8 107.9 59.96

ws_II 207.9 118.7 105.5 51.14

ws_III 307.4 128.2 104.8 45.48

 ps_I 139.4 96.6 87.8 41.25

 ps_II 250.1 113.5 79.72 29.89

 ps_III 259.2 103.5 79.56 34.87

The process of de-excitation is shown in Fig. 3.

Right after the short-circuit the contribution of the

shorted windings to the overall fundamental MMF is

reduced to zero. This loss of MMF is partly compen-

sated by the field winding hence its current is raised.

The excitation if   is superposed by a grid frequencyalternating current which is induced by the asymmetric

field distribution of the armature winding. After discon-

nection it drops off sharply until it reaches a more flat

course later on. The transient characteristic of whole

 process is rather double exponential than single expo-

nential, due to the inductive interaction between the

massive iron and the damper bars on the one hand and

the field winding on the other hand

Fig 3. Excitation Current for case ws_III with de-excitation starting at3.7 s.

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 Fig. 4a. Line currents in case ws_I (Phase U) from FD calculation

Fig. 4b. Line currents in case ws_II (Phase V) from FD calculation

Fig. 4c. Line currents in case ws_III (Phase W)

In contrary to the fast reduction of if , the short circuitcurrent isc is decaying slowly. The degressive course ofinduction due to nonlinearity and iron saturation pre-

vents a fast drop down of isc. In addition the massiveiron and the damper winding are taking over the amper-

age of the exciter due to induction; this also is a reason

for the rather single exponential decay of current ampli-

tude in Fig. 2.

The line currents at the terminals iline in the Figures 4and 5 show a strong asymmetric behaviour, which fi-

nally triggers protection equipment for all investigated

cases.

Fig. 5a. Line currents in case ps_I (between Phase U and V)

Fig. 5b. Line currents in case ps_II (between Phase V and W)

Fig. 5c. Line currents in case ps_III (between Phase W and U)

Obviously the transient behaviour after the occur-

rence of the short circuit is stronger the more windings

are shorted, as shown in Fig. 4c for case ws_III with

three shorted windings. The maximum effective value

occurs in the phase following the one with the shorted

turns, whereas the line current in the phase before is

decreased in cases ws_II and ws_III.

Winding faults between different phases are of much

higher effect regarding the terminal currents, as shown

in Fig. 5 a-c. The current peaks are much higher and a

stronger asymmetry occurs.

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 Fig. 6a. Winding currents in phase U (case ps_III)

Fig. 6b. Winding currents in phase V (case ps_III)

Fig. 6c. Winding currents in phase W (case ps_III)

Strong circulating currents in the parallel coil groupsof the affected as well as the undisturbed phases arise

during the fault and after disconnecting the machine

from the grid. The currents in the winding partitions for

case ps_II are displayed in Fig. 6 a-c, where the wind-

ings w12 and w4 form a shorted loop through the neutral

 point. Hence strong currents can be observed in the two

windings (see Fig. 6a and c).

After disconnection (t=3.7s) still serious circulatingcurrents are induced in those windings, which are only

little lower than before and decreasing slowly.

On the other hand, the undamaged coil groups in

 phase V (Fig. 6b) carry much lower currents, as ex- pected. However, it is not the rule that undamaged coil

groups are little affected by short-circuits, by reason of

inductive coupling between all windings of the machine,

e.g. in Fig. 6c. The first peak of the current in the undis-

turbed coil group w3 and w9 is about 4 times of its rated

value. After disconnection it is even rising to about 3

times the rated value.

All those currents do not disappear before total de-excitation of the machine.

 B. Unbalanced magnetic pull

Another phenomenon, which was already discussed

in context with the rotor short-circuits [8], is the unbal-

anced magnetic pull generated by the asymmetric field.

The forces in the rotor d-, q- coordinates follow a char-

acteristic similar to the time-function of the short-circuit

currents since they are strongly related to each other.

Hence the resulting force magnitude is displayed in

Table 2 for 4 characteristic values (in similar manner as

for the currents in Table 2).As expected the highest peak occurs instantly after

the short circuit. The magnitude is decreasing exponen-

tially during the transient phase of 0.2-0.3 s. In the case

of ps_II a very high peak value acts on the rotor, which

is equivalent to a weight of 736000 kg.

TABLE 3: FORCE MAGNITUDES OF U NBALANCED MAGNETIC PULL 

 peak  F 

max F 

 discmax,

 F 

 

s1.8max, F 

Case MN MN MN MN

ws_I 1.076 0.741 0.750 0.257

ws_II 2.206 1.718 1.604 0.388ws_III 1.267 0.582 0.502 0.0847

 ps_I 1.980 1.894 1.850 0.496

 ps_II 7.361 4.157 3.541 0.525

 ps_III 6.364 3.275 2.753 0.558

The transients level of to a steady state value | F 

| max 

until the machine is disconnected from the power grid.

Thereafter the force magnitudes decay like the short-

circuit currents. Case ws_I shows the lowest values in

Table 3, but is still more critical than rotor winding

splay the time after

disconnection during de-excitation.

shorts.

Figures 7 and 8 display the trajectories of the magneticforce exerted on the rotor in the d-, q- reference frame.

Since all cases generate a similar pattern, only the least

and most critical cases are included here, namely ws_I

on the left side and ps_II on the right. The upper trajec-

tories are shown during 0.2 s after the instant of the

short circuit and the lower ones di

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 Fig. 7a. Trajectory of force vector on rotor in rotor reference frame for

a period of 0.2 s after winding fault in phase U (case ws_I).

Fig. 7b. Trajectory of force vector on rotor in rotor reference frame

after disconnection (case ws_I).

The orbit of the force vector follows an epicyclical

curve getting smaller during the transient process and

stabilizing after a few turns of the rotor. During the

steady state process the force vector can be separated

into of a fundamental frequency and a triple frequency

 part of the same magnitude. In stator related coordinates

this corresponds with the sum of a constant and a double

frequency part, whereas the rotation is oriented in theopposite direction. The shorted windings create a con-

stant pressure on the rotor as well as an alternating part

every time a pole passes the axis of the coils.

In the Figures 7 and 8 a continuous change of the

angle between the long axis of the epicycle and the d-

axis of the rotor after disconnection can be observed.

This result in a slow variation of the direction of the

magnetic pull related to the stators reference frame.

Fig. 8a. Trajectory of force vector on rotor in rotor reference frame for

a period of 0.2 s after the fault between V and W (case ps_II).

Fig. 8b. Trajectory of force vector on rotor in rotor reference frame

after disconnection (case ps_II).

C. Field map

The field map in Fig. 9 on the cross-section of the

investigated machine at an instant of time with maxi-

mum rotor forces at 3.693 s (case ps_II) shows obvious

irregularities. It illustrates the influence of the asymmet-

ric field distribution on the unbalanced magnetic pull on

the rotor. The shorted coils are marked with the refer-ence direction of the short-circuited loop.

Obviously the current in this loop strongly disturbs

the field. Knowing that normal components contribute

tensile stress to the fictitious Maxwell stress tensor,

whereas the tangential components result in compres-

sive stress, the extreme high forces may be explained.

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The tangential field lines are pushing mainly on the

left side of the rotor, whereas much more normal flux is

 pulling on the right than on the left. A flux density of 1

Tesla creates a tensile stress of about 400 kN per square

meter. With diameter of 1 m and a length of 7 m of the

rotor, the calculated values in Table 3 appear plausibly.

A more distinct asymmetry leads to stronger forces.

Fig. 9. Field map 3.693 s after occurrence of sudden short circuit in

 phase W (case ps_II).

V. CONCLUSION

Six different stator winding faults differing in the

number of shorted turns and affected phases have beeninvestigated by means of a combined transient network-

field computation. In all cases a strong impact on the

machine arises while the machine is still connected to

the power-grid. But even immediately disconnecting the

machine from the grid cannot be considered an effective

measure for reducing the occurring damage unless a

quick de-excitation is provided. The turn currents re-

main at a high level of about six to nine times their rated

values in the short circuit loop and also winding parts

not included in the short circuit path are exposed to

inadmissibly high currents, if the excitation remains at

its previous level.

As for the rotor, attention has been paid to the unbal-anced magnetic pull which besides the damper currents

and eddy current losses not dealt with here appears to be

a quantity with problematic values. Further investiga-

tions concerning the mechanical consequences of such

strong impacts on the mechanical properties of bearings

and the shaft train seem to be indicated. However, prac-

tical observations of bearing damages or permanent

 bending deformation of rotor shafts caused by stator

winding faults are not known to the authors.

R EFERENCES 

[1] T. S. Kulig,  Die innere Unsymmetrie vonSynchronmaschinen, PhD thesis AGH, Krakau1974.

[2] T. S. Kulig, Über die Beeinflussung der Ströme und

des Elektromagnetischen Drehmoments vonTurbogeneratoren durch Windungs- und

 Phasenschlüsse, PhD thesis, Hannover 1979.[3] M. Daneshnejad,  Erfassung von Windungs-

 schlüssen in der Erregerwicklung einesTurbogenerators, PhD thesis, University ofDortmund, Institute of Electrical Machines, Drives

and Power Electronics, 2001.

[4] M. Klocke, Zur Berechnung dynamischer Vorgängebei von einem Drehstromsteller gespeisten

 Antrieben mit Asynchronmaschinen und mehreren gekoppelten Massen mittels Finite-Differenzen- Zeitschrittrechnung , PhD thesis, University ofDortmund, Institute of Electrical Machines, Drivesand Power Electronics, 1999.

[5] R. Gottkehaskamp,  Nichtlineare Berechnung von Asynchronmaschinen mit massiveisenem Rotor und zusätzlichem Dämpferkäfig im transienten Zustandmittels Finiter Differenzen und Zeitschrittrechnung ,PhD thesis, University of Dortmund, Institute of

Theoretical Electrical Engineering and Electrical

Machines, 1992.

[6] A. Krawczyk, J. A. Tegopoulos,  Numerical Model-ling of Eddy Currents, Oxford: Clarendon Press,1993.

[7] T. S. Kulig “Anwendung der numerischen

Feldberechnung zur Modellierung elektrischer

Drehstrom-Maschinen mit inneren Fehlern” Bulletin

SEV/VSE(1990)7.

[8] M. Klocke, M. Daneschnejad: “New Aspects of

Winding Faults in the Rotor of a Large

Synchronous Generator”, Record of the 2001 IEEE

International Symposium on Diagnostics for

Electrical Machines, Power Electronics and Drives

(SDEMPED 2001), p. 161-166. Grado, Italy,

September 1-3, 2001.

[9] W. Mathis: Theorie nichtlinearer Netzwerke,Springer-Verlag, Berlin, Heidelberg, New York,

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