Chapter 5 Interpretation of SFRA 53 Chapter 5 Interpretation of SFRA 5.1 Introduction The Sweep frequency Response Analysis (SFRA) is an emerging method for investigation of transformer mechanical integrity after through fault in the system and its relocation. There are cases found, where SFRA has been a key tool in the decision making either to scrap, rewind or reenergize a transformer after an incident. Based on the practical experience with SFRA analysis, the frequency range from 10Hz to 2MHz is sufficient for the analysis and can be divided into three frequency band. These frequency bands are governed separately by the inductive effect of core, self and mutual inductance of the winding, series and shunt capacitance of the overall winding structures and the lead/tap connections. Interpretation of SFRA responses is crucial in order to assess the integrity of transformer windings. In order to achieve the correct interpretation of SFRA response, the effect of various circuit parameters of transformer winding on SFRA plot is studied in detail and discussed one of the major factors that influenced the SFRA responses, the winding structure itself in low, medium and high frequency range. [4] 5.2 Modeling of Transformer Winding for Interpretation of SFRA 5.2.1 Basic Circuit of Transformer SFRA normally measures the frequency response of a transformer from 10Hz to 2MHz. Circuit modeling thus needs to accurately represent the behavior of a transformer across this wide range of frequency. But, no such universal circuit model exists that can represent a transformer accurately over this entire range. Hence, modeling techniques for SFRA have been developed in several frequency regions, depending on the modeling accuracy required and the dominant components in each frequency region. The different type of circuit model in each frequency band, which is considered for the SFRA analysis are described below.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Chapter 5 Interpretation of SFRA
53
Chapter 5
Interpretation of SFRA
5.1 Introduction
The Sweep frequency Response Analysis (SFRA) is an emerging method for
investigation of transformer mechanical integrity after through fault in the system and
its relocation. There are cases found, where SFRA has been a key tool in the decision
making either to scrap, rewind or reenergize a transformer after an incident. Based on
the practical experience with SFRA analysis, the frequency range from 10Hz to
2MHz is sufficient for the analysis and can be divided into three frequency band.
These frequency bands are governed separately by the inductive effect of core, self
and mutual inductance of the winding, series and shunt capacitance of the overall
winding structures and the lead/tap connections.
Interpretation of SFRA responses is crucial in order to assess the integrity of
transformer windings. In order to achieve the correct interpretation of SFRA response,
the effect of various circuit parameters of transformer winding on SFRA plot is
studied in detail and discussed one of the major factors that influenced the SFRA
responses, the winding structure itself in low, medium and high frequency range. [4]
5.2 Modeling of Transformer Winding for Interpretation of SFRA
5.2.1 Basic Circuit of Transformer
SFRA normally measures the frequency response of a transformer from 10Hz to
2MHz. Circuit modeling thus needs to accurately represent the behavior of a
transformer across this wide range of frequency. But, no such universal circuit model
exists that can represent a transformer accurately over this entire range. Hence,
modeling techniques for SFRA have been developed in several frequency regions,
depending on the modeling accuracy required and the dominant components in each
frequency region. The different type of circuit model in each frequency band, which is
considered for the SFRA analysis are described below.
Chapter 5 Interpretation of SFRA
54
5.2.2 Low frequency model
The equivalent circuit of transformer winding at low frequency from 10 Hz. to 1000
Hz. is shown in Fig. 5.1
Fig. 5.1 Equivalent circuit of Transformer winding at Low frequency
The dominant features of low frequency plots are the first minima at low frequency
normally below 1000 Hz in all windings. This is the general feature of any winding
and is due to the fact that at the lowest frequencies windings behave as simple
inductances. This result in increasing attenuation of a transmitted signal with
frequency, until a frequency is reached when core capacitance start to become
significant and allow a recovery in transmitted voltage. The low frequency minimum
is determined by self inductance of winding, inductance and capacitance of core. The
position of minimum will vary somewhat depending on the remnant magnetism of
relevant core flux circuits, which is prominent in this case due to different magnetic
state of the winding. In low frequencies, a transformer winding behaves as an
inductive element, and the SFRA response follows a increasing negative magnitude
trend across the frequency range with a linear slope and this may not be exact linear
also due to core non-linearity with frequencies. As the inductance is increased, the
magnitude is increased. Power transformers with higher voltage and larger power
rating usually have larger negative response magnitudes. Effectively there are two
parts of inductance affecting the SFRA response the core magnetizing inductance and
the self inductance of the windings. Each affects the response in different frequency
ranges. The leakage inductance affects the SFRA response in lower frequencies of no
more than 100 Hz while the core magnetizing inductance influences the SFRA
response at high frequencies up to 1 kHz.
Chapter 5 Interpretation of SFRA
55
The magnetizing inductance of the core, Lm which decides the magnitude of Xm in
Fig. 5.1 is influenced by the winding number of turns, N and the reluctance, R which
is given by
Lm = N2 (5.1)
R
The magnetic path of the middle phase is different compared to the magnetic path of
the outer phases due to the symmetrical core construction of transformer in case of
middle phase and it is also affecting SFRA. This magnetic reluctance, R is analogous
to the resistance in the electrical circuit and thereby is influenced by the length of the
magnetic path, l and the area of the cross section of the core, A.
The inductance is divided in two groups self and mutual inductance of the winding as
shown in Fig. 5.2
Fig. 5.2 Winding self and mutual inductance
Because of such a coarse representation of the windings, localized winding movement
will not be reflected in this low frequency region unless the winding moves
significantly. The SFRA measurement in the low frequency region are primarily used
to detect problems related to the transformer core and major winding faults like
shorted turn, open circuit and high impedance fault in the early developing stage. [4]
5.2.3 Medium frequency model
The equivalent circuit of transformer winding at medium frequency from 1 kHz to
1000 kHz is shown in Fig. 5.3
Chapter 5 Interpretation of SFRA
56
Figure 5.3: n-stages lumped ladder network
In medium frequency range, as the frequency increases, the effect of core will become
less significant as the flux penetration depth in the core is frequency - dependent and
it is worst effected by DC voltage creating the core saturation problem after the DC
test like resistance measurement. Hence, in medium frequency range around 10 kHz,
core will behave as an earth plate. The winding structure, especially the winding
under test, becomes dominant factor of the frequency responses.
Therefore, it is necessary to use the multiple LC element equivalent network to model
the winding accurately in medium frequency range. However, in transformer winding,
the basic components are combined together and the transformer winding structure
becomes more complex than a simple LC element.
To represent a winding accurately in the medium frequency range, a detailed RLC
ladder network of the winding is required. Each winding is divided into cells. The cell
is represented as lumped - element unit, which consists of a series capacitance (Cs)
and a self inductance (L). The capacitive coupling between the cells and the tank wall
(Cg) for the outer winding cell and for the inner winding cell the shunt capacitance
are included between the cell and the core. This transformer model is considered to be
detailed enough to provide reasonably accurate SFRA results in the frequency range
governed by the main winding structure , which is normally from about 10 kHz to 500
kHz.
Chapter 5 Interpretation of SFRA
57
A uniformly structured winding can be represented by an n-stage ladder network, as
shown in Figure 5.3. The winding total leakage inductance L, the winding total series
capacitance Cs and the total shunt capacitance Cg are evenly distributed between the
n stages. The effect of dielectric losses or resistances connected either in series with
the inductance or connected in parallel with the capacitance on the SFRA response, is
to attenuate the sharpness of the resonances and the anti-resonances. The effect on the
sharpness of resonance of series RLC circuit due to change in the resistance is shown
in Fig. 5.4 and Fig. 5.5
Fig. 5.4 Series resonance of the RLC circuit having low R value
Fig. 5.5 Series resonance of the RLC circuit having high R value
Chapter 5 Interpretation of SFRA
58
The combination of winding inductance and winding series capacitance results in
parallel LC circuit and will produce parallel anti-resonance, consequently, blocking
the signal at that particular frequency. Also, the simplest representation of LC in
series is a T − connection where the shunt capacitance is connected in the middle of
the two halves of the winding inductance. The SFRA response of winding inductance
and shunt capacitance in the LC network shows a series resonance, amplifying the
signal at that particular frequency. In summary, the basic features of SFRA response
can be shown in Fig. 5.6
Fig. 5.6 Series and Parallel resonance of the winding
However, in transformer winding, these basic components are combined together and
the transformer winding structure becomes complex.
The general solution for voltage and current at any point x on the network shown in
Fig. 5.3 can be represented by Equation (5.2)
(5.2)
Chapter 5 Interpretation of SFRA
59
Where,
A and B are constants, x is the number of stages along the winding, starting from the
injecting end, Z is the characteristic impedance and γ is the propagation constant of
the winding.
SFRA response oscillate between capacitive and inductive and when multiple local
resonances are produced at the frequencies as
(5.3)
In terms of the structure of single windings, these can be categorized into windings
with either high- or low- series capacitance in proportion to the shunt capacitance.
Correspondingly, the SFRA responses of transformer windings of high series
capacitance exhibited the increasing trend of magnitude in the frequency range
between 10 kHz and 500 kHz while the windings of low series capacitance displayed
the steady magnitude trend with the resonances and anti-resonances (camel humps)
features in the frequency range between 10 kHz and 2MHz.
Fig. 5.7 illustrates the effect of having high or low series capacitance, Cs in the 8-
stage lumped network obtained from simulation. With low Cs, the response begins
with flat magnitude trend and resonances at intervals of frequencies determined by
Equation (5.3) and then followed by a decreasing inductive trend. In Fig. 5.7, it is
illustrated that as Cs is increased, some of the resonances diminish and the anti-
resonance appears at lower frequency.
Chapter 5 Interpretation of SFRA
60
Fig. 5.7 FRA response from 8-stage of lumped ladder network (L=800H) with
extreme cases of (a) Cs=0, Cg=480pF and (b) Cg=0, CsLOW=190pF, CsHIGH=3000
pF
The extreme cases of the 8-stage lumped network with negligible Cs or Cg are shown
in Figure 5.7. Fig. 5.7(a) depicts the features of winding with low Cs such as the
continuous disc while Fig. 5.7(b) depicts the features of winding with high Cs or
negligible Cg in comparison to Cs such as the interleaved winding.
Using the knowledge gained from the experimental studies during this research and
theoretical back-up, this factor is shown to dominate the SFRA responses of power
transformers in certain frequency ranges. In terms of the structure of single windings,
these can be categorized into windings with either high- or low- series capacitance in
proportion to the shunt capacitance. Correspondingly, the SFRA responses of
transformer windings of high series capacitance exhibited the increasing trend of
magnitude in the frequency range between 20kHz and 500kHz while the windings of
low series capacitance displayed the steady magnitude trend with the resonances and
anti-resonances (camel humps) features in the frequency range between 20kHz and
2MHz. [4]
Chapter 5 Interpretation of SFRA
61
5.2.4 High frequency model
In high frequencies, a transformer winding behaves as a capacitive element, and
power transformers having both higher voltage and larger power rating usually have
smaller negative response magnitudes in high frequency range as the capacitance is
high. At very high frequencies, the network can be represented as a capacitive ladder
network as shown in Fig. 5.8
Fig. 5.8 n-stage capacitive ladder network at high frequencies
The general solution of this equivalent circuit can be represented by Equation (5.4).
(5.4)
Where,
To be accurate in higher frequencies, a transformer winding would need to be
represented in more detail. A distributed parameter model using Multiple
Transmission line theory is then needed. This modeling technique treats each turn of
the winding as one transmission line. The parameters of the winding are calculated as
distributed capacitance per unit length and the high frequency signal travels through
the winding as transverse electromagnetic waves.
This method of detailed winding modeling ensures sufficient accuracy for the higher
frequency range, where effects such as the arrangement of tapping lead connections
are regarded as significant. However, representing all of the phase windings down to
the details of individual turns will result in a massive matrix size. This modeling
technique is only suitable to model a part of winding or the lead connections, whilst
the rest of the transformer is modeled simply as a ladder network. [4]
Chapter 5 Interpretation of SFRA
62
5.3 Basics of FRA Interpretation
5.3.1 Expected Resonance Frequency Range vs. Transformer Size and Winding
Type
Due to the typical range for natural frequencies, the interpretation methodology
should be adjusted according to the expected damage appearance. For investigating
winding displacements, FRA measurement and interpretation should then focus on the
natural frequency range of the respective windings.
For power transformer windings, there are various technical concepts. Even for
similar rated power, rated voltage and type of application, there could be very
different solutions. Details of technical solutions are defined by established design
concepts of manufacturers as well as technical boundaries in manufacturing and
transportation restrictions. Therefore, it is quite difficult to summarize general rules
for FRA patterns and the corresponding winding characteristics.
Natural frequencies are mainly defined by the absolute geometry of winding
assemblies. Based on the typical frequencies of large power transformers, smaller
transformers show similar frequency characteristics at systematically higher
frequencies.
Table 5.1 shows the expected resonance frequency range for windings of large power
transformer (above 100 MVA/limb) of different rated voltage. Table 5.2 shows
typical frequency ranges for windings of medium-power transformers (below 30
MVA/limb).
It is also to be noted that these tables represent calculation examples of the natural
resonance frequencies of separate windings. The interactions between components in
a real transformer could show different frequency characteristics. [15]
Chapter 5 Interpretation of SFRA
63
Table 5.1 Frequency range for natural frequencies of large transformer windings. [15]
Table 5.2 Frequency range for natural frequencies of medium transformer windings.
[15]
5.3.2 Typical FRA Responses
It is observed that although the detailed form of a frequency response depends on the
winding design used, usually the basic overall form of the response is surprisingly
similar for the same type of winding, even for significantly different winding
arrangements, and therefore is presumably determined by some essential
distinguishing property of the type of winding involved rather than by the details of its
construction. The method of interconnection used, e.g. LV delta connection, also
results in very characteristic forms.
In view of the above, it is useful to be able to recognize typical features when
interpreting responses. In the following, ‘typical’ responses for various winding types
are described:
• HV windings of transmission and generator transformers (core-form)
• LV windings of generator transformers and double-wound network
transformers (core -form)
Chapter 5 Interpretation of SFRA
64
• Shell-form transformers
Although specific examples are used to illustrate the typical responses, it is expected
that the general features described will be relevant to a wide range of transformers,
provided the windings involved are of an essentially similar type. [15]
5.3.2.1 HV windings of large power transformers
The essential features of the HV windings of large power transformers are that they
have large HV bushings, invariably have a large number of turns and for the highest
voltages are usually specially designed to spread out the distribution of high-
frequency impulses away from the line end terminals, usually by employing measures
to increase the series capacitance.
‘Typical’ HV responses exhibited by the series (HV to LV) windings of six three-
phase autotransformers (400/275 kV) with delta-connected tertiary windings are
shown in Fig. 5.9. Note that, although all six transformers are of the same type, they
feature a wide range of designs, built at various dates between 1967 and 2003 with
very different winding arrangements (multi-layer or inter-leaved disc): Despite the
large variation in age and design, there is a remarkable degree of similarity in the
general form of the responses.
Fig.5.9 HV winding response of large autotransformers
All show the usual open-circuit low-frequency (up to 2 kHz) response exhibited by all
transformer windings – an initially increasing attenuation with frequency (20 dB per
Chapter 5 Interpretation of SFRA
65
decade) due to the basic core-influenced inductance of the winding becoming much
larger than the input impedance of the measuring equipment until the first minimum
(or two minima if an outer phase of a three phase transformer is involved), followed
by a voltage recovery to the first maximum, presumably due to the effects of series
capacitance becoming significant.
For measurements across the series or common windings of auto-transformers, there
is a characteristic second maximum in the intermediate frequency range (2 to 20 kHz),
which is known to be dependent on the shunt capacitance of the winding and affected
by bulk movement of the winding or bushing capacitances, among other factors. It is
not known for certain what causes this feature, but the most likely explanation is some
resonance between series and common windings.
In the high-frequency range (20 kHz to 2 MHz), all these transformers exhibit
essentially the same response: a generally rising response (roughly 20dB per decade),
starting from about 50 dB at around 20 kHz, until a maximum at or slightly above 0
dB, which invariably occurs at about 1 MHz Within this high-frequency range, there
may be evidence of ‘ripples’ (part-winding resonances) superimposed on the overall
generic rising trend, more marked for some transformers than others.
Since essentially very similar responses have been obtained from very different
winding arrangements (multi-layer and interleaved disc), it would appear that the
general form of the response is determined by some basic global property of such
arrangements, probably high-series capacitance, rather than the detailed geometry.
Although the HV responses shown in Fig. 5.9 are entirely typical, they are also
somewhat ideal: not all auto-transformers exhibit such smooth responses.
The LV (common) windings of auto-transformers tend to show the same basic
response as in Fig. 5.10, particularly if they are also of a layer construction, but can
also show very marked resonances, particularly if plain disc windings are used.
HV winding responses of three generator transformers from different manufacturers
are shown in Fig. 5.10. The characteristics of the transformers are:
Chapter 5 Interpretation of SFRA
66
TA → 430/23.5 kV, 800 MVA, single-phase unit
TB → 300/23 kV, 735 MVA, three-phase unit
TC → 290/16 kV, 190 MVA, three-phase unit
Up to 20 kHz, the response of these three differ because of different core and LV
winding arrangement : a single-phase core (A), a three-phase core with separate LV
phases (B) and a three-phase core with LV phases connected in delta (C).
Above 20 kHz, the responses of all three exhibit the same general form as those for
transmission
transformer series windings.
Fig. 5.10 HV winding responses of large generator transformers
To conclude, the ‘typical’ response for an HV winding is considered to be essentially
that shown in Fig. 5.9 and Fig. 5.10, although there may be more evidence of
resonances in the high frequency region, depending on the detailed winding
arrangement used. [15]
5.3.2.2 LV windings of large power transformers
The essential features of the LV windings of large power transformers are that they
have relatively small LV bushings and invariably have a relatively small number of
turns. LV windings are usually the innermost windings, and may be connected in star
Chapter 5 Interpretation of SFRA
67
or delta arrangement. For the low-voltage/high-current LV windings of generator
transformers, relatively large conductors are used and therefore tend to be of a
particularly simple winding arrangement, often a simple spiral winding, although
sometimes with two (go and return) layers.
The simplest type of LV response is that shown in Fig. 5.11: this is obtained for large
generator transformers with single layer LV windings where the LV phases are
brought out separately to six LV bushings, the LV delta connection being made
externally by connecting together the relevant pairs of bushings (a2-c1, b2-a1 and c2-
b1 for the usual YNd1 vector grouping).
At low frequencies, there is the usual first core-related minimum at around 400 Hz,
although with significantly less attenuation than for HV windings, followed by a
maximum at about 8 kHz, with an intermediate maximum and minimum if the
transformer is three-phase rather than single phase.
Fig. 5.11 Generator transformer LV winding responses (3 phases of a transformer)
The characteristic high-frequency LV response is a sequence of four or five ‘U’
shaped resonances in the 2-MHz band starting with a first maximum at around 200
kHz, sometimes with occasional ‘notches’, as shown in Fig. 5.12 for three different
transformers from different manufacturers. This type of response is what is expected
from simple standing-wave resonances in a single-layer coil.