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Diagnostics of Stator Insulation by Dielectric Response andVariable Frequency Partial Discharge Measurements
A study of varied low frequencies in stator insulation, with particular
attention to end-winding stress-grading
Licentiate presentation by
Nathaniel Taylor
Division of Electromagnetic Engineering, KTH
Thursday 23rd November, 2006
10−3
10−2
10−1
100
101
102
103
10−13
10−12
10−11
frequency, Hz
C’,C
’’, F
0.1 kV pk
1.0 kV pk
10.0 kV pk
20.0 kV pk
phase, degrees
char
ge, C
90 180 270 360
−8
−6
−4
−2
0
2
4
6
8
x 10−9
00.060.120.170.230.290.350.40.460.520.580.630.690.750.810.860.92
0 0.01 0.02−2
0
2x 10
−4
time, s
curr
ent,
A
50.00Hz
0 0.1 0.2−2
0
2x 10
−5
time, s
curr
ent,
A
5.00Hz
0 1 2−2
0
2x 10
−6
time, s
curr
ent,
A
0.50Hz
0 10 20−2
0
2x 10
−7
time, s
curr
ent,
A
0.05Hz
PD x 13
PD x 7
PD x 20 PD x 51
1
1. Stator insulation
— Machine construction
— Stator insulation construction
— Stator insulation defects
— Current diagnostic practices
2. (HV) Dielectric spectroscopy
3. (VF) Partial discharge measurement
4. End-winding stress-grading
5. Examples on real stator insulation
6. Conclusions
2
Machine Construction
Stator insulation
slotend
Rotor insulation
Mechanical (bearings)
3
Stator Insulation
Un ' 1 kV =⇒ form-wound
Un ' 5 kV =⇒ ‘corona prevention’ (grading)
Un / 30 kV in spite of ratings ≈1—1500 MW!
turn insulation
main insulation
semicon layer
slot wedge
conductors
stator iron
Strand
Turn
Mainpicture: Siemens & vonRoll Isola
4
Relevant Constructional Variations
Insulation binding material
(between the mica pieces):
— bitumen high loss, migrates
— polyester resin
— epoxy resin
Hydro- or turbo-generator:
speed affects diameter/length,
which affects ratio of end-
length/slot-length and propaga-
tion of PD signals.
Cooling and coolant:
— indirect: heat comes out of
windings through the insulation
— direct: a coolant (typ. water) is
used within the windings
— air/hydrogen: air has lower
EBD and heat capacity, allows
O3 generation by PD, and assists
oxidation of organic insulation
‘Corona-prevention’ (semicon-
ductor layers) or not?
5
Stator Insulation Defects
Stress: Thermal, Electrical
‘Ambient’, Mechanical
Cause: primary, secondary?
Manifestation:
Delamination, cavities
Electrical Treeing
Worn slot semiconductor
Worn end semiconductor
Contamination on end-windings
6
Diagnostic Methods in Common Use
Many methods don’t depend on electrical connection to the windings,
e.g. detect PD by measuring RF emissions, chemicals, sound, light, or
use mechanical measurements and visual inspection, PD
measurement by couplers.
Others more relevant to this work: off-line, with galvanic connection.
Note that off-line usually implies significant differences from normal
stresses.
On-line—Off-line: expenses, realistic versus controlled conditions.
Measurement −→ (Physical State) −→ P(failure)
Complex system. Different phenomena can look similar in a
particular measurement. Cannot expect any method to give no false
positives or negatives.
7
Electrical Diagnostics in Common Use
Insulation ‘Resistance’ (IR): ‘DC’ with quite HV, i.e. a form of
time-domain spectroscopy with stepped voltage). This is also known as
‘megging’, and the derived quantity ‘Polarisation Index’ (PI) is popular.
Capacitance and Loss, possibly including ‘Tip-Up’: generally power
frequency (≈50 Hz), with several voltage steps typically up to the rated
line voltage per phase, i.e. overvoltage factor of√
3
Partial Discharge (PD) measurement: again, generally power
frequency, often as ‘phase resolved’ pattern.
8
1. Stator Insulation
2. (HV) Dielectric Spectroscopy
— Dielectric Materials and their Response
— Dielectric Spectroscopy (DS)
— Material Measurements and Disturbances
— Non-linearity
— High-Voltage (HV) DS, and Applications
— HV DS on Stator Insulation
3. (VF) Partial Discharge measurement
4. End-Winding Stress-Grading
5. Examples on Real Stator Insulation
6. Conclusions
9
Dielectric Materials
Polarisation:
— bounded movement of charge, changing charge-distribution
— increases supplied charge to electrodes (if fixed V)
— many mechanisms (e−, natural dipole, ionic . . . )
— some mechanisms very fast, lumped as ε∞, an increased ε0
— other mechanisms have considerable dynamics: represent as such
with polarisation function f(t) or susceptibility χ(ω):
P (t) = ε0
∫∞
0
f(τ)E(t − τ)dτ
P (ω) = ε0χ(ω)E(ω)
χ(ω) = χ′(ω) − iχ′′(ω) . . .
= F f(t)
V free space
10
Dielectric Response: Exponential Model
Time
f(t) ∝ e−t/τ
10−1
100
101
10−5
10−4
10−3
10−2
10−1
100
time, s
Pol
aris
atio
n fu
nctio
n f(
t)Frequency
χ′(ω)− iχ′′(ω) ∝ 1
(1 + (iωτ)k1)k2
k1 = k2 = 1 in pure exponential case
10−2
10−1
100
101
10−4
10−3
10−2
10−1
100
frequency, Hz
Sus
cept
ibili
ty, R
e &
Im−2
−1
+1
0 imag
real
11
Dielectric Response: Power-Law Model
Time
f(t) ∝ t−n, 0 < n < 1
10−3
10−2
10−1
100
101
102
103
104
10−4
10−3
10−2
10−1
100
101
102
103
time, s
Pol
aris
atio
n fu
nctio
n f(
t)
n = 0.1n = 0.5n = 0.9
Frequency
χ′(ω) − iχ′′(ω) ∝ (iω)n−1
10−4
10−3
10−2
10−1
100
101
102
103
10−4
10−3
10−2
10−1
100
101
102
103
frequency, Hz
Sus
cept
ibili
ty, R
e &
Im
n = 0.1n = 0.5n = 0.9
imagreal
realimag
12
Power-Law Model with Two Parts
f(t) ∝ 1(tτ
)n1+(
tτ
)n2
0 < (n1, n2) < 1
10−4
10−2
100
102
104
10−2
10−1
100
101
time (t)
f(t)
n=0.1
n=0.9
13
Dielectric Spectroscopy
Dielectric Spectroscopy =⇒ Dielectric Response at varied t or ω.
Time-Domain (TD) measure f(t), (plus conduction and possibly prompt
response): e.g.
— Step-Response, e.g. Polarisation-Depolarisation Currents (PDC)
— Ramp-Response
— Return Voltage Measurement
Many frequencies are measured at once, but noise rejection is low.
Frequency-Domain (FD) measure χ(ω) (plus conduction and prompt
response), usually by applying a sinusoidal driving voltage V (ω) and
measuring the resultant current I(ω) for various ω.
C′(ω) − iC′′(ω) =I(ω)
iωV (ω)=
C0
ε0
“
ε′(ω) − iε′′(ω)”
ε′(ω) − iε′′(ω) =h
ε0χ′(ω) + (ε∞ − ε0) + ε0
i
− ih
ε0χ′′(ω) +
σ
ω
i
We favour FD: ease of PD measurement, form of non-linearity.
14
Practical DS Measurements
Basic Measurement sees:
— Free-space capacitance
— Polarisation current
— Bulk conduction
— Surface conduction
— (Fringing, material case)
A
σsurface
A
εmaterialσmaterial
h
Guarding: remove surface conduc-
tion and fringing.
Removal of conduction current
is harder: PDC time-domain
methods, or analysis of frequency-
domain results within assumptions
of linearity.
On actual equipment, one might be
less interested in the material pro-
perties than in the total current.
15
Non-linearity measured with FD-DS
Non-linearity: outin relation is dependent on amplitude.
Currents at frequencies other than the fundamental iff non-linear or
supply voltage not sinusoidal.
Frequency-representation allows even small non-linearity to be seen.
Frequency-representation still allows a lot of directly interpretable
information about the form of the time-domain distortion (odd/even,
sine/cosine).
C′ and C′′ are values calculated on the fundamental components: C′′
maintains its significance of power loss.
s(t) = Re
[K∑
n=0
|Sn|ei(nωt+∠Sn)
]=
K∑
n=0
(An cos(nωt) + Bn sin(nωt))
16
HV-(FD)DS System
FB(i)
FB(v)
Vref
Vmeas
Imeas
ADC, DSP,computer
v
i
HV amplifier30kV, ~50mA
divider MeasurementObject
guardelectrode
measurementelectrode
instrumentearth
Electrometers
A much simplified block diagram, showing the measurement and
guard electrodes.
17
Applications of HV-DS
Why HV?
— Non-linearity
— Higher current (SNR)
Development of HV-FDDS field-test system
Water-trees in XLPE cables (picture−→)
Machines: usually in time (TD)
Megging? (Qualifies? Inverse Step Response!)
Ramp test
A little recent research interest, TD & FD
End-windings often guarded! (lab, not field)
ETKAesthetic
Obligation
18
1. Stator insulation
2. (HV) Dielectric spectroscopy
3. (VF) Partial discharge measurement
— Partial discharges (PDs)
— PD detection and analysis
— Effect of frequency on PDs
— PDs and PD measurement in stator insulation
4. End-winding stress-grading
5. Examples on real stator insulation
6. Conclusions
19
Partial Discharges (PDs)
A discharge that fails to bridge the space between the electrodes that
are applying the field; it therefore cannot develop into a disruptive
discharge. For example:
divergent field barrier
Presence of PD can suggest a problem in an insulation system;
detection methods may allow a distinction to be seen between
different sources of PD activity.
PD may cause insulation degradation by thermal, chemical, electrical
and radiation effects.
20
PD Detection
Many detectable consequences, for example . . .
— released chemicals, e.g. Ozone (O3)
— remnant chemical effects, e.g. powder on surfaces
— sound, ultrasound
— visible light, UV light
— RF emission
— HF and total (integrated) currents in supply ⇐=
Some give an averaged idea of PD activity, some give information
about each PD event (pulse).
Some localise the PD sources.
21
PD Charge & Calibration
PD charge > measured charge
V
Vcavity
measured PD charge, assumingSimplistic relation of actual and
cavity voltage not changed.
Qapparent =Vcavity
VQactual
Qactual
Qapparent < Qactual
Qapparent ∝ energy in PD
(fixed V)
Calibration: relate measured
Qapparent to a known injection
at the terminals.
Frequency-response (spect-
rum of pulse) can affect
measured charge. DS methods
can (but needn’t) capture the
whole measured charge.
22
VF-PRPD System
systemPR−PDPRP
sync
Vref
pre−amplifier
alternativeplacements
of measuringimpedance
DAP andcomputer
couplingcapacitor
Measurementobject200pF
HV amplifierfilter
Measuring impedance is typically in test-object earth for lab, or in
coupling capacitor earth for field tests of earthed objects.
Here, all but the PR-PD system is ‘home-brew’.
23
Phase-resolved PD: Simple Example
0 90 180 270 360−Qmax
0
Qmax
phase channels
char
ge c
hann
els
1
1
1
2
23
1
1
PD counts (#cycles)
For each cycle, for each phase-channel (x), any measured PD charge,
Q (y) increments the count in that phase-amplitude (x-y) point.
24
Phase-resolved PD: Typical Plot
phase, degrees
char
ge, C
90 180 270 360
−5
0
5
x 10−9
0
0.06
0.12
0.17
0.23
0.29
0.35
0.4
0.46
Intense cluster at bottom is typical for cavities; here there are also
many, widely distributed, large charges — delamination?
25
Phase-resolved PD: View as Current
phase, degrees
char
ge, C
90 180 270 360
−5
0
5
x 10−9
0
0.06
0.12
0.17
0.23
0.29
0.35
0.4
0.46
0 0.5 1 1.5 2 −1
−0.5
0
0.5
1x 10
−6 I(t)
time, s
curr
ent,
A
0 1 2 3 4 5 6 70
2
4
x 10−7
harmonic order, n
| I |,
A
I(f): Polar form
0 1 2 3 4 5 6 7−180−90
090
180
harmonic order, n
phas
e, d
egre
es
0 1 2 3 4 5 6 7−4−2
024
x 10−7 I(f): Rectangular form (sin/cos)
harmonic order, n
I sine
, A
0 1 2 3 4 5 6 7−4−2
024
x 10−7
harmonic order, n
I cosi
ne, A
26
PD with Variable Frequency Excitation
Sources of frequency-
dependence
εbulkσbulkv
Ah
σsurface
τcavity — relaxation of voltage across
the cavity due to conduction of current
through σsurface on the cavity’s walls.
τmaterial — relaxation of (space-charge)
field in material, due to εbulk and σbulk.
τstatistical — delay due to the (random)
occurence of a suitable initiating ioni-
sation in the cavity volume v.
Consider e.g. large and small σmaterial
and σsurface, or both = 0.
27
Example: PD Frequency-Dependence
Number of PD pulses from a single cylindrical cavity. Note the
greater distinction between different cavities when at low frequency.
0
2
4
6
8
10
10-2
10-1
100
101
102
10
7
1.5
p
f
0
2
4
6
8
10
10-2
10-1
100
101
102
p
f
28
PD Measurement on Stator Insulation
worn slot semicon
internal cavities/delaminations
end−windingsdischarge between
worn end−semicon
(slot)
(end)
Several very different sources: different
magnitude to fit between detection
threshold and full-scale
Large size: many ‘simultaneous’ PDs:
some lost in dead-time?
PD propagation: stator is large, con-
tains magnetic material but also the
unshielded end-windings; measuring
system frequency-response important.
29
Frequency-Dependence of Stator PD
All 3 general-case effects τmaterial, τcavity, τstatistical may be involved
in the many sizes and shapes of cavity and delamination that can all
be present together within the insulation.
Around the end-windings: PD on the surface, damaged
stress-grading, conductive contamination; PD between end-windings.
Spreading of earth potential increases the stress in the insulation
material under the stress-grading — more PD, from this part of
insulation too?
At extreme low frequency, end-winding stress-grading may have earth
potential up to its end — surface PD?
30
(end of SI, DS, PD overview)
31
Advantages: HV-FDDS or VF-PRPDA
FD-DS is here extended with the independent (controlled) variable of
voltage amplitude, V , and with the independent (measured) variable
of the low harmonic spectrum.
— excite non-linearities in the test-object
— distinguish non-linear components in the current
PRPDA is here extended with the independent variable frequency, f .
— get a better idea of location and type of PD sources
— reduce driving voltage source if able to stay ≪ fn
32
Simultaneous VF-PRPDA and HV-FDDS
Both methods require a quite expensive HV amplifier, driven by the
controlling computer.
Both methods may take a long time, when doing LF sweeps at
several voltages!
Both methods give complementary information, and it may even be
good to compare measurements from the same measurement time if
PD currents measured by the two systems are to be compared.
=⇒ combined system, measuring simultaneously, gets more
information, more directly comparable information, takes no more
time than using just one of the methods, and costs less than the sum
of the separate systems.
33
Simultaneous Measurement: Usefulness
Simultaneous Measurement even without a strong link between DS
and PD measurements may be useful in itself: more clues to the state
of the insulation, without extra measurement time.
If PD current seen by integrating charges measured by PD system is
very similar to the PD current measured in the DS system, the PD
part of the DS measurement could be removed. If not, then there are
two measures of PD, which may be a useful complement.
34
1. Stator insulation
2. (HV) Dielectric spectroscopy
3. (VF) Partial discharge measurement
4. End-winding stress-grading
— Purpose and methods
— Significance to HV-DS and VF-PD measurements
— Material properties, SiC paint and tape
— Physical test objects
— Numerical modelling
5. Examples on real stator insulation
6. Conclusions
35
End-Winding Stress-Grading
High surface field if slot semi-
conductor just ends.
(Why not continue the slot semi-
conductor at the ends?)
Must reduce the field to prevent
surface discharge.
‘Grading’ around the end:
– geometric, refractive, capacitive:
nice frequency-response, too much
space!
– resistive: frequency-dependence,
so only useful for a narrow fre-
quency band
– non-linear resistive: small space,
wide frequency range; but, wreaks
havoc on measurement of small V
and f dependencies in diagnostic
measurements!
36
Effect of Stress-Grading on DS & PD
PD
Very low frequency spreading of earth potential: surface PD?
Variable stress in insulation under the stress-grading: varied PD?
DS
Considerable (some %) increase in C′, much more in C′′
Large change with V (‘tip-up’) in C′ and C′′ (∆C′ ≈ ∆C′′)
Large change in C′ and C′′ with frequency
Non-linearity: harmonic currents from a source other than PD
Need to determine current into grading, in order to remove it from
DS measurement, if any more ‘material’ property is to be seen or if
PD current is to be seen from harmonics. This modelling is described
here . . .
37
Possibilities of Use of Model
Get some manufacturer data or do a brief measurement to determine
parameters. Then calculate and subtract the stress-grading current!
FAIL: hopelessly poorly defined parameters: material and geometry.
Measure DS, use V ,f dependence to determine parameters. Problem
of PD currents having also a non-linear source. Is DS of
stress-grading below the PD inception level sufficient?
38
Physical test-objects
PTFE tube (inner 20 mm, outer 31 mm), tightly around a metal
tube, with central external metallic electrode and stress-grading
material on either side. Low loss/dispersion apart from grading.
20 31
copper pipe250
PTFE
metallic coatinggrading material
dimensions in mm
gradingsheathbare
regionoverlap bare
insulation
39
SiC-based grading materials
50 100 30010
−11
10−9
10−7
10−5 SiC paint
mean electric field, V/mm
Cur
rent
, A
thicklypainted
moderatelypainted
thinlypainted
10 100 300
10−8
10−6
SiC B−stage tape
mean electric field, V/mm
Cur
rent
, A
SiC material around a 30 mm diameter insulating tube. The resistivity
spans several decades even just up to 300 V/mm. The measured results are
well fitted (the black circles) by:
Iaxial = EaxialG0 exp(n|Eaxial|2/3
)
Note the huge variation with the paint — a matter of thickness.
40
SiC-based Grading Materials
Iaxial = EaxialG0 exp(n|Eaxial|2/3
)
This equation is numerically friendly, e.g. the case E = 0.
With Iaxial in A, Eaxial in V/m, the parameters are:
Material G0 (Sm) n ρ(0)surface = 2πrG0
(Ω)
Paint(thin) 2.5 × 10−16 0.00114 3.9 × 1014
Paint(medium) 1.8 × 10−15 0.00115 5.4 × 1013
Paint(thick) 1.0 × 10−13 0.00110 9.7 × 1011
Tape 5.5 × 10−13 0.00115 1.7 × 1011
The “non-linearity” coefficient, n, is very similar in all cases.
It is small as E is in V/m.
41
Taped Bar: Pure Grading Response
Cplotted = Cmeasured − CLV,nograding
10−2
10−1
100
101
102
10−11
frequency, Hz
C’ a
nd C
’’, F
1.48 kVpk4.44 kVpk7.41 kVpk9.88 kVpk12.84 kVpk15.31 kVpk
C’’
C’
Nearly a plain f shift
in loss-peak with V
Low V case nearly
linear: C′ ≈ C′′ at HF
‘Full’ (whole grading
length) C′ at LF
C′′ at LF and HV (high
stress at grading end)
rises: surface leakage?
42
A general 1D Grading Model
Rs l/n Cp l/n Gp l/n
Cs n/l
Vsupply CendCp dx Gp dx Gend
Cs / dx
Rs dx
upper value: lumped (discrete) parameterslower value: distributed parameters
l (length)
dxn
Rs surely non-linear. End-leakage? Cs needed? Cs constant?
Assumes symmetry around axis. Rs,Cp alone popular even at HF.
43
Why consider simple cases
(Linear, Discrete)?
— The real case and the realistic 1D models have parts that resemble
simpler models, e.g. with low frequency or low voltage-amplitude.
— People often simplify the real case to a very primitive model for
quick qualitative discussion: how wrong is this?
Rs l/n Cp l/n Gp l/n
Cs n/l
Vsupply CendCp dx Gp dx Gend
Cs / dx
Rs dx
upper value: lumped (discrete) parameterslower value: distributed parameters
l (length)
dxn
44
Linear, Discrete: A simple RC-filter
10−4
10−2
100
102
10410
−20
10−18
10−16
10−14
10−12
10−10
frequency, Hz
C’,
C’’,
F C’, R/1C’, R/10C’, R/100C’’, R/1C’’, R/10C’’, R/100
RCC’, C’’
In the plot here (left), three
values of R are used, as
a crude approximation of
voltage-dependent grading.
This is the Debye response, seen earlier.
Slopes (log-log) of ±1 for C′′ away from loss peak, and −2 for C′ at
frequencies above loss-peak.
C′ − iC′′ =Cs
1 + ω2R2sC
2s
− iωRsC
2s
1 + ω2R2sC
2s
45
Linear, Distributed: A diffusive TL
The FD Transmission Line equations are not LC[RG] specific.
Using per-unit-length values of Rs and Cp, with l as TL length,
(characteristic impedance) Z0 =
r
Zseries
Yshunt
=
s
Rs
iωCp
(propagation constant) γ =√
ZseriesYshunt =p
iωCpRs
Zin =Z0
tanh(γl)(when Zend = ∞)
Zin = Z0
Zend + Z0 tanh(γl)
Z0 + Zend tanh(γl)(else)
Then, from Zin the complex capacitance seen at the start of the
grading is:
C′ − iC′′ =1
iωZin=
1 − i√
2
√Cp
ωRstanh
(l√
iωRsCp
)
if Zend=∞
46
The Linear Models Compared
10−4
10−2
100
102
10410
−20
10−18
10−16
10−14
10−12
10−10
frequency, Hz
C’,
C’’,
F C’, R/1C’, R/10C’, R/100C’’, R/1C’’, R/10C’’, R/100
10−4
10−2
100
102
10410
−20
10−18
10−16
10−14
10−12
10−10
frequency, Hz
C’,
C’’,
F C’, R/1C’, R/10C’, R/100C’’, R/1C’’, R/10C’’, R/100
— At high frequency, distributed case end is not ‘seen’, ∴ l = ∞ and
C′ = C′′ because C′ − iC′′ = 1iωZ0
=√
1i
√C
ωR = (1 − i)√
C2 ωR .
— At low frequency, the discrete and distributed cases are very
similar; the effective length is short.
— The loss peak, C′′, is independent of resistance: this is seen for the
discrete case from ω = 1RC , and C′′ = C (ωRC)
1+(ωRC)2 .
47
Non-linear, Discrete
10−3
10−2
10−1
100
101
102
103
10−13
10−12
10−11
frequency, Hz
C’,C
’’, F
0.100 kVpk
1.000 kVpk
10.000 kVpk
20.000 kVpk
C’
C’’
– Even C′′ is similar for all
V at LF (low stress, so small
effect of non-linearity)
– Effect of V on loss peaks
almost as effect of scaling Rs
– Very fast HF fall-off of C′
& C′′, at different rates
VNL = Vsupply − Vcapacitor
CdVcapacitor
dt= VNLG0 exp
(n |VNL|2/3
)
48
Non-linear, Distributed
10−3
10−2
10−1
100
101
102
103
10−13
10−12
10−11
frequency, Hz
C’,C
’’, F
0.1 kV pk
1.0 kV pk
10.0 kV pk
20.0 kV pk
C’
C’’
– Low f → C′′ similar ∀V
(low stress, so G ≈ G0)
– Low V → ≈ linear
(low stress, so G ≈ G0)
– Increased V : n ↑ in t−n,
i.e. (1 − n) ↓ in (iω)1−n,
so gradient shallower and
C′/C′′ exceeds 1.
C∂V
∂t=
∂
∂x
(∂V
∂xG0 exp
(n
∣∣∣∣∂V
∂x
∣∣∣∣2/3))
49
Comparison: Models of Varied Degree
10−3
10−2
10−1
100
101
102
103
10−13
10−12
10−11
frequency, Hz
C’,
C’’,
F
R/1
R/10
R/100
10−3
10−2
10−1
100
101
102
103
10−13
10−12
10−11
frequency, Hz
C’,
C’’,
F
R/1
R/10
R/100
10−3
10−2
10−1
100
101
102
103
10−13
10−12
10−11
frequency, Hz
C’,C
’’, F
0.100 kVpk
1.000 kVpk
10.000 kVpk
20.000 kVpk
C’
C’’
10−3
10−2
10−1
100
101
102
103
10−13
10−12
10−11
frequency, Hz
C’,C
’’, F
0.1 kV pk
1.0 kV pk
10.0 kV pk
20.0 kV pk
C’
C’’
50
Comparison: Model and Measurement
10−2
10−1
100
101
102
10−12
10−11
frequency, Hz
C’,
F
1.5 kV pk − measured
7.4 kV pk − measured
15.3 kV pk − measured
1.5 kV pk − simulated
7.4 kV pk − simulated
15.3 kV pk − simulated
10−2
10−1
100
101
102
10−12
10−11
frequency, Hz
C’’,
F 1.5 kV pk − measured
7.4 kV pk − measured
15.3 kV pk − measured
1.5 kV pk − simulated
7.4 kV pk − simulated
15.3 kV pk − simulated
Correct Parameters? Rs (G0), n, Cp
Sufficient Model? Any need for Cs, Gend, etc.?
The Physical Measurement: correct subtraction of bulk current?
51
Harmonic Content in Grading Current
1 Hz time-domain currents.
0 90 180 270 360 450 540 630 720−4
−3
−2
−1
0
1
2
3
4x 10
−6
phase, degrees
I(t)
, A
15.3 kV pk
7.5 kV pk
1.5 kV pk
voltage Solid lines: physical
Dashed lines: simulation
Quite good correspondence
(but this was close to the loss
peak, where the model fitted
well).
52
Potential-Distributions in the Grading
0 90 180 270 360−20
−10
0
10
20kV
End potential, 15.3 kV
0 90 180 270 360−1
−0.5
0
0.5
1
V /
Vap
plie
d
End potential, 1 Hz
0 10 20 30 40 50 60 70 800
0.5
1
distance from fixed potential, mm
V /
Vap
plie
d
Maximum potential along length
0 90 180 270 360−20
−10
0
10
20
kVphase
Waveform, by length, 50 Hz 15 kV
100 Hz
10 mHz
1.5 kV
15.3 kV
1.5 kV (green), 15.3 kV (red)10 mHz
100 Hz
end
electrode
53
Improvement of Modelling
Extra components in model not very helpful.
Variation of Rs (G0) allows much improved fitting.
n (non-linearity) is largely constant between the materials used.
Cp maybe not so easy in real, aged insulation.
10−2
10−1
100
101
102
10−12
10−11
frequency, Hz
C’’,
F
15 kV1.5 kV1*Rs
2*Rs
2*Rs
1*Rs
10−2
10−1
100
101
102
10−11
frequency, HzC
’, F
15 kV
1.5 kV
1*Rs
1*Rs
2*Rs
2*Rs
Suggestion: assume SG and PD is the only non-linearity; get SG
parameters from sub-PD-inception voltages.
54
Differences between Physical Models
and Real Stator Insulation
Geometry: not circular.
Isolation: surrounded by others, not in open space.
C0 typically larger (thinner insulation) in the real case.
Permittivity is greater for stator insulation than for PTFE.
So, Cp is larger in real case, and loss-peak at much lower frequency.
— unfounded worries about PD at end at practical LF
— HF part of model (l → ∞) is of most interest
55
1. Stator Insulation
2. (HV) Dielectric spectroscopy
3. (VF) Partial discharge measurement
4. End-winding stress-grading
5. Examples on real stator insulation
— Measurements on a coil, new and aged
Accelerated thermal aging, Practical stress-grading parameters, PD current by
PD and DS methods, Frequency-dependence of PD
— Field measurement on whole windingsConstraints on frequency, Variability of different measurement methods
6. Conclusions
56
Real Stator Coils: A1 & A2
Newly made stator coils. Accelerated thermal aging.
le
ls
lw
transition from slot to
guard−break in slotsemicon screen
end grading material
lc
crosssection
w1
w2
end−windingslot part
end−winding
Slot length between guards ls = 1553 mm
External slot cross-section w1 × w2 = 11.5 mm × 33.0 mm.
Insulation thickness ≈ 1.9 mm.
Rated r.m.s. line voltage, Un = 7.2 kV.
57
Slot semiconductor resistivity
0 100 200 300 400 5000
1
2
3
4
5
6
7x 104
mean field, V/m
per−
leng
th r
esis
tanc
e, O
hm/m
1.0m, new0.5m, new1.0m, new0.5m, aged0.5m, aged1.0m, aged
10−2
100
102
10410
−11
10−10
10−9
10−8
frequency, Hz
Cp,
Cb
(C
’,C’’,
Far
ads)
12.5 Vpk50 Vpk200 Vpk
loss, Cb
capacitance, Cp
three electrodes andsparsely wrapped wire
one, centralelectrode
— Surface resistivity ≈ 5kΩ(/sq) before, ≈ 2kΩ(/sq) after aging.
— With Al foil taped around slot-section, very small loss tip-up.
— Slight voltage-dependence — blame this on the very low voltages
(contact?), not important for our usual voltage levels.
58
Guarded DS on New Coil (A1)
10−4
10−2
100
102
4.8
5
5.2
5.4
5.6x 10
−9
frequency, Hz
C’,
F
1 kVpk
3 kVpk
6 kVpk
10−4
10−2
100
102
10−10
frequency, Hz
C’’,
F
1 kVpk
3 kVpk
6 kVpk
Largely linear.
≈ 10% increase in C′, 50 Hz → 0.0001 Hz
≈ 5× increase in C′′ in same range.
59
Unguarded DS on New Coil (A1)
10−4
10−2
100
102
5
5.5
6
6.5x 10
−9
frequency, Hz
C’,
F
1 kVpk
4 kVpk
7 kVpk
10 kVpk
10−4
10−2
100
102
10−10
frequency, Hz
C’’,
F
1 kVpk
4 kVpk
7 kVpk
10 kVpk
Not linear.
Extra ≈ 10% increase in C′, 50 Hz → 0.0001 Hz
Now ≈ 10× (previously 5×) increase in C′′ in same range.
60
Guarded DS on Aged Coil (A1)
10−2
100
102
4.45
4.5
4.55
4.6
4.65
4.7x 10
−9
frequency, Hz
Cp
(
C’,
Far
ads)
1kVpk
3 kVpk
5 kVpk
7 kVpk
9 kVpk
10−2
100
102
2
4
6
8
10
12
14x 10
−11
frequency, Hz
Cb
(
C’’,
Far
ads)
1 kVpk
3 kVpk
5 kVpk
7 kVpk
9 kVpk
— Amplitude-dependent increase in C′ and C′′ is very similar,
reflecting the ≈ 45 phase of the non-linearity (PD).
— Amplitude-dependent increase is greater at lower frequency,
suggesting greater PD charge, implying (on average) long τcavity or
some external PD.
61
DS and PD Measurement of PD Current
Accelerated thermally aged stator coil. PD and guarded DS.
0 0.01 0.02−2
0
2x 10
−4
time, s
curr
ent,
A
50.00Hz
0 0.1 0.2−2
0
2x 10
−5
time, s
curr
ent,
A
5.00Hz
0 1 2−2
0
2x 10
−6
time, s
curr
ent,
A
0.50Hz
0 10 20−2
0
2x 10
−7
time, s
curr
ent,
A0.05Hz
PD x 13
PD x 7
PD x 20 PD x 51
Waveform fits well
between DS and
PD measurements.
Magnitude doesn’t!
See scaling factors
for PD.
Very heavy PD:
— dead-time
— attenutation
— spectrum
62
New and Aged Coils: Lessons
Much lower frequency of the loss-peak of stress-grading than in the
laboratory models.
Obvious large influence of stress-grading on insulation and PD
currents.
The thermal aging at 180C for about 1 week left a large number of
PD sources throughout the previously PD-free (as much as
detectable) insulation.
Even without very long windings and ferrous surroundings, DS
apparently measures much higher total PD current than is seen from
the calibrated PD pulse measurement.
63
Field-Test: DS on Whole Windings
Large-diameter hydro-generator.
Sn = 10 MVA, Un = 6.3 kV
About 30 years old.
Diagnostic testing before and after some maintenance work.
64
Whole Winding: Insulation ‘Resistance’
IR (‘megging’) at 5 kV.
3 occasions. Measure u, v, w, uvw.
0 100 200 300 400 500 6000
500
1000
1500
time, s
"r
esis
tanc
e", M
Ohm
−x− : 1a −+− : 1b −o− : 2
uv w
uvw
Expect ≈ 5000 MΩ
at 600 s
Large difference
between phases
uvw value tracks
worst of u, v, w
Large difference
between the three
measurement occa-
sions 1a,1b,2!
65
Whole Windings: DS with LV & LF
10−2
10−1
100
101
102
10−9
10−8
10−7
10−6
10−5
frequency, Hz
capa
cita
nce,
F
C’ uvw
C’ u, v, w
C’’ uvw
C’’ u, v, w
w rising
Occasion ‘1b’.
Measurement: 50 V
peak
C′ similar for u,v,w
LF C′′ w rises
LF C′′ uvw rises too
66
Whole Windings: DS with HV
0 2 4 65.71
5.72
5.73
5.74
5.75x 10
−7
applied peak voltage, kV
C’ (
0.31
6 H
z), F
u
v
w
0 2 4 61.8
2
2.2
2.4
2.6
2.8x 10
−8
applied peak voltage, kV
C’’
(0.3
16 H
z), F
u
v
w
(Note: a different occasion (2) from the LV&LF measurement (1b) ).
Too little time or current to go much lower or higher in f .
A large difference in loss is seen in u, with HV.
67
Whole Windings: Lessons
Time is very limited during outage: cannot do large number of V
values or very low f . Need a well-planned V ,f sequence. Particular
advantage of simultaneous measurements if doing DS & PD.
Winding capacitance is of the order of 1 µF (at 50 Hz). Maximum
frequency is therefore around 1–2 Hz for 5 kV test with our amplifier.
The above points restrict the usable range of frequencies! One
consequence is a reduced bandwidth requirement for the
stress-grading model.
Varied V and f may have a large effect on the measurement in the
presence of insulation problems.
68
1. Stator Insulation
2. (HV) Dielectric spectroscopy
3. (VF) Partial discharge measurement
4. End-winding stress-grading
5. Examples on real stator insulation
6. Conclusions
69
Conclusions
• Stress-grading model presented seems good for fundamental and harmonic
components away from the extremes of frequency; components other than
Rs (NONLINEAR)and Cp
• Stress-grading model needs good parameters: the most variable is G0, within
the expression for Rs. Infeasible in real machines to calculate parameters a
priori; try fitting from sub-PD measurements?
• Stress-grading C′ and C′′ strongly disturb insulation DR and PD harmonics.
Different V dependence: insulation DR generally quite linear, PD doesn’t
occur below some inception voltage.
• PD measurement with varied V and f is distinctly interesting!
• Whole PD current may be measured with (suitable) DS system; this may be
a lot more than measured with a PD pulse detector (is this useful?).
Consequently, removal of PD from DS given a PR-PDP is not feasible.
• Use of harmonic spectrum in DS is a good way to consider just the
phenomena beyond the (largely linear) bulk material.
70
Continuation
• Equipment for simultaneous measurement
• More comparison of DS and PD measurement of PD current
• Approximate removal of SG harmonics to leave PD harmonics,
using sub-inception sweep to determine parameters of SG
• Further investigation of frequency-dependence of PD in stator
insulation
• What is a good ‘index’ for PD and non-linear DS measurements?
For example, C′&C′′ ignores substantial and interesting currents.
• Some more thorough field tests on various machines.
71
