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  • Chapter 3 SFRA Basics


    Chapter 3

    SFRA Basics

    3.1 Introduction

    Sweep Frequency Response Analysis (SFRA) testing has become a valuable tool for

    verifying the geometric integrity of transformers. SFRA provides internal diagnostic

    information using nonintrusive procedures. The SFRA test method has been proven to

    provide accurate and repeatable measurements.

    Power Transformers are specified to withstand the mechanical forces arising from

    both shipping and subsequent in-service events, such as faults and lightning.

    Transportation damage can occur if the clamping and restraints are inadequate; such

    damage may lead to core and winding movement. The most severe in-service forces

    arise from system faults and are axial and radial in nature. If the forces are excessive,

    radial buckling or axial deformation can occur. With a core form design, the principal

    forces are radially directed, whereas in a shell-form unit, they are axially directed.

    This difference is likely to influence the types of damage found.

    Once a transformer is damaged, even if only slightly, its ability to withstand further

    short circuits is reduced. Utility personnel need to effectively identify such damage. A

    visual inspection is costly and does not always produce the desired results or the

    correct conclusion. Since so little of the winding is visible, little damage can be seen,

    other than displaced support blocks. Often a complete teardown is required to

    identify the problem. An alternative method is to implement field-diagnostic

    techniques capable of detecting damage.

    Sweep Frequency Response Analysis (SFRA) is a tool that can give an indication of

    core or winding movement in transformers. The transformer is considered to be a

    complex network of RLC components as shown in Fig. 3.1

  • Chapter 3 SFRA Basics


    Fig. 3.1 Equivalent Geometry of Transformer

    Any form of physical damage to the transformer results in the changes of this RLC

    network. These changes are what we are looking for and employ frequency response

    to highlight these small changes in the RLC network within the transformer. For

    different frequencies the RLC network offers different impedance paths. Hence, the

    transfer function at each frequency is a measure of the effective impedance of the

    RLC network of the transformer. Any geometrical deformation changes the RLC

    network, which in turn changes the transfer function at different frequencies and

    hence highlights the area of concern [46]. The frequency response of such a network

    is unique and, therefore, it can be considered as a fingerprint as shown in Fig. 3.2

    Fig. 3.2 Principles of SFRA

  • Chapter 3 SFRA Basics


    3.2 SFRA Theory

    The primary objective of SFRA is to determine how the impedance of a test specimen

    behaves over a specified range of frequencies. The impedance is a distributive

    network of real and reactive electrical components. The components are passive and

    can be modeled by resistors, inductors and capacitors. The reactive properties of a

    given test specimen depend on, and are sensitive to, changes in frequency. The change

    in impedance versus frequency can be dramatic in many cases. This behavior

    becomes apparent when we model impedance as a function of frequency. The result is

    a transfer function representation of the RLC network in the frequency domain.

    When a transformer is subject to SFRA testing, the leads are configured to use four

    terminals. These four terminals can be divided into two unique pairs one pair each

    for the input and output. These terminals can be modeled in a two terminal pair or a

    two port network configuration as shown in Fig. 3.3.

    Fig. 3.3 Two Port Network

    Solving for the open-circuit impedance for each lumped element forms the

    impedances Z11, Z22, Z12 and Z21. It should be noted that the negative terminals are

    short circuited when transformers are tested. The transformer tank is common for both

    negative and lower terminals. The transformer tank and lead ground shields must be

    connected together to achieve a common mode measurement. This assures that no

    external impedance is measured. Applying the connection in this manner helps reduce

    the effects of noise. It is important to obtain a zero impedance between the lower or

    negative terminals to assure a repeatable measurement.

  • Chapter 3 SFRA Basics


    The transfer function of an RLC network is the ratio of the output and input frequency

    responses when the initial conditions of the network are zero. Both magnitude and

    phase relationship can be extracted from the transfer function.

    The transfer function is represented in the frequency domain and is denoted by

    Fourier variable H(j) where (j) denotes the presence of a frequency dependent

    function, and w=2f. The Fourier relationship for the input/output transfer function is

    given by :

    H(j) = Voutput (j)

    Vinput (j)

    When a transfer function is reduced to its simplest form, it generates a ratio of two

    polynomials. The main characteristics, such as half-power and resonance, of a transfer

    function occur at the roots of the polynomials.

    The goal of SFRA is to measure the impedance model of the test specimen. When we

    measure the transfer function H(j), it does not isolate the true specimen impedance

    Z(j). The true specimen impedance Z(j) is the RLC network, which is positioned

    between the instrument leads, and it does not include any impedance supplied by the

    test instrument.

    It must be noted that when using the voltage relationship, H(j) is not always directly

    related to Z(j). For Z(j) to be directly related to H(j), a current must be

    substituted for the output voltage and then Ohms law can be realized. However,

    SFRA uses the voltage ratio relationship to determine H(j). Since SFRA uses a 50

    ohm impedance match measuring system, the 50 ohm impedance must be

    incorporated into H(j). The next equation shows the relationship of Z(j) to H(j) :

    H(jw) = 50___

    Z(jw) + 50

    It is often useful to plot the magnitude and phase relationship of the transfer function

    in logarithmic format. The units of magnitude and phase are in decibles (dB) and

    degrees, respectively. Magnitude and phase are represented as follows :

  • Chapter 3 SFRA Basics


    A(dB)=20 log10 (H(jw))

    A()= tan-1 (H(jw))

    This format takes advantage of the asymptotic symmetry by using a logarithmic scale

    for frequency. Plotting the phase relationship with the magnitude data helps determine

    whether the system is resistive, inductive or capacitive. It is often useful to compare

    resonance in the magnitude plots with the zero crossings in the phase relationship.


    3.3 SFRA History

    1960 Low Voltage Impulse Method (LVI) First proposed by W. Lech & L.

    Tyminski in Poland for detecting transformer winding deformation.

    1966 Result Published: W. Lech & L. Tyminski Detecting transformer winding

    damage the low voltage impulse method , Electric Review, no. 18, ERA, UK.

    The method was used by Dr. Alexandr Dobishevsky in former USSR and within

    Bonneville Power Administration, United States (Eldon Rogers)

    1976 Frequency Domain Analysis of Responses from L.V.I. Testing of Power

    Transformers Presented by A.G. Richenbacher at the 43rd Doble Intl Client


    1980 In the 1980s the Central Electricity Generating Board (CEGB) in the UK took

    up the measurement technique and applied it transmission transformers. The French

    also began to pursue measurements at the same time.

    1990 On the breakup of the CEGB in the early 1990s work in FRA was taken by

    National Grid in the UK and resulted in several papers at Doble Client Conferences.

    The technique has been spread further through Euro Doble Conferences and client

    meetings and several utilities took up the technique.[16]

    Many early practitioners tried impulse systems, and have continued to try them up to

    the 2003. Though appealing in terms of speed, they have never been able to match the

    range, resolution or repeatability of sweep methods and continue to reject such


    As the basic technique developed by early users required laboratory based equipment

    such as HP network analyzers, which were robust, but not field hardened and required

    specialist operators. Upon a successful program of product development and field

  • Chapter 3 SFRA Basics


    trials, Doble stepped in to provide field engineers and staff with a reliable and robust

    tool for transformer analysis the M5100. This outperforms the HP in terms of

    measurement characteristics and field usability. [9]

    3.4 SFRA Today

    SFRA is today an established technology to investigate the mechanical and electrical

    integrity of a transformer.

    Before the 1990s no designated SFRA equipment for transformer analysis existed.

    Since then several specialized products have been introduced.

    The value that SFRA provides to its users is quite easily established, by research of

    published material and customer experience.

    The international community, such as CIGRE, IEC and the IEEE has widely accepted

    its use and is now providing guide lines.

    CIGRE : CIGRE working group A2-26 Mechanical Condition Assessment of

    Transformer Windings created in 2004. The CIGRE WG A2-26 main objective is

    to develop a guide on the Mechanical Condition Assessment of Transformer

    Windings using the Frequency Response Analysis (FRA) method. The WG has

    delivered a final report end 2007 for a publication before the group session in

    August 2008. The WG is disbanded. UK will check with IEC TC 14 for a

    possibility to have a part of this document publish as an IEC document. [11]

    A new work item proposal 14/597/NP has been issued by IEC TC 14 on December

    2008 based on the work done within WG A2-26 Mechanical Condition Assessment

    of Transformer Windings and finalized with the publication of the TB 342 in April

    2008. [12]

    IEC : IEC published the FRA Standard, 60076-18, Power Transformers

    Part 18 : Measurement of Frequency Response in July, 2012.

  • Chapter 3 SFRA Basics


    The Scope of the IEC 60076 series covers the measurement technique and measuring

    equipment to be used when a frequency response measurement is required either on-

    site or in the factory either when the test object is new or at a later stage.

    Interpretation of the result is not part of the normative text but some guidance is given

    in Annex B. This standard is applicable to power transformers, reactors, phase

    shifting transformers and similar equipment. [28]

    IEEE : IEEE C57.149 Working Group published the Guide for the Application

    and Interpretation of Frequency Response Analysis for Oil immersed

    Transformers in March 2013.

    IEEE C57.149 Working Group focused on the 3 failure modes, namely

    Radial Deformation

    Axial Deformation and

    Bulk Movement from Transportation.

    3.5 Purpose of FRA Measurements

    The main interest of FRA measurements on transformers is to detect winding

    deformations that may result from the very large electromagnetic forces arising from

    over-currents during through faults, tap-changer faults, faulty synchronization, etc.

    Winding deformation eventually results in a transformer failure by damaging the

    inter-turn insulation, resulting eventually in shorted turns, which means the immediate

    end of service life. Transformers are expected to survive a number of short circuits

    without failure but, once any significant winding deformation is produced, the

    likelihood of surviving further short circuits is greatly reduced because of locally

    increased electromagnetic stresses. Furthermore, any reduction in winding clamping

    due to insulation shrinkage caused by ageing will also increase the likelihood of

    failure by reducing the mechanical strength of the winding assemblies.

    In addition to diagnosing failures after a short-circuit event, there is increasing interest

    in detecting winding deformation damage prior to eventual failure during planned

    outages, i.e. mechanical-condition assessments to assess the expected reliability of

  • Chapter 3 SFRA Basics


    transformers in terms of any suspected increased susceptibility to failure under further

    short circuits.

    There is also an interest in using FRA measurements to detect any other problems that

    result in changes to the inductance or capacitance distribution in transformers, e.g.

    core faults or faulty grounding of cores or screens.

    Another application for FRA measurements is to check the mechanical integrity of a

    transformer after transportation, which usually means providing a reliable means of

    confirming that the core and winding assembly have not suffered any mechanical

    damage despite sustaining jolts during transportation. Note that for this application it

    may be necessary to have reference results without oil and bushings, if that is how the

    transformer is transported. Since transportation shocks are more likely to cause

    damage to the core structure than to the windings, there is a slightly different focus for

    this application. Because FRA measurements can provide information about the

    consistency of geometric structures of windings and core, such tests are increasingly

    being used as quality assurance checks. [15]

    3.6 Definitions

    Frequency Response Analysis (FRA)

    Any measurements of the frequency dependency (to high frequencies, e.g. MHz) of

    the electrical responses (transfer functions) of transformer windings to applied signals

    which are made with the primary intention of detecting winding deformation through

    the effects of resulting changes to capacitance or inductance distributions.

    Sweep Frequency Method

    A frequency response measured directly by injecting a signal of a variable frequency

    at one terminal and measuring the response at another.

    Impulse Voltage Method

    A frequency response measured indirectly by injecting an impulse signal of a

    particular shape at one terminal and measuring the response at another, and then

    transforming the time domain measurements into frequency domain results.

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    FRA Amplitude

    The magnitude of the response relative to that of the injected signal, usually expressed

    in dB calculated as 20*log 10(Vresponse/Vinjection).

    FRA Phase Angle

    The phase angle shift of the response relative to that of the injected signal.

    Resonance Frequency

    The frequencies corresponding to any local maxima or minima in the measured

    amplitude response. [15]

    3.7 Development and Variations in FRA Practices

    It is important to realize that a great variety of FRA measurement techniques are

    currently being used, not all of which have produced good results. Most of the

    variations in the FRA technique can be traced to how the technique developed from

    LVI. Differences in FRA practices arise from two main aspects:

    How the measurement is made

    Which measurement is made

    The main variation in how FRA measurements are made concerns whether a sweep

    frequency method (referred to as SFRA) or an impulse method (referred to as

    IFRA) is used. The first IFRA techniques used an impulse method with the same

    double exponential type of impulse signal as used by LVI, with appropriate rise and

    fall times to include components of the range of frequencies of interest. The impulse

    is applied to one terminal and the form of the applied and the transmitted signal at

    another terminal are recorded by a dual channel digital data acquisition system. One

    key development from time domain LVI is that the two measured impulses are then

    transformed into the frequency domain using the Fast Fourier Transform algorithm,

    and then the calculated amplitudes of frequency components of the transmitted signal

    are divided by the corresponding amplitudes of the applied signal to derive the

    frequency response indirectly. This frequency response has the advantage over the

    LVI time response that it is independent of the shape of the applied impulse, so that

    the result is more closely related to the test object and less to the test set-up, thereby

    simplifying interpretation and improving repeatability. The impulse method of

  • Chapter 3 SFRA Basics


    performing FRA measurements being a development of traditional high-voltage

    impulse testing, some transformer manufacturers use their modern digital impulse

    testing recorders to perform FRA measurements but recently purpose-built

    transformer test instruments have become available to perform IFRA measurements.

    Since the objective of FRA measurements is to obtain the frequency response of

    windings, an alternative technique was proposed [28] to measure this directly using a

    sweep frequency technique. A sine wave signal is applied to one terminal and the

    amplitude and phase of the transmitted signal at another terminal are measured

    relative to the applied signal for various frequencies over the frequency range of

    interest. Early practitioners had to use general-purpose laboratory Network/Spectrum

    Analyzer instruments, but more recently purpose-built transformer test instruments

    have become available to perform SFRA measurements.

    In principle, everything else being equal, the sweep frequency and impulse techniques

    should be capable of producing the same result, and this has been demonstrated on

    several occasions. For sweep frequency measurements, the accuracy depends on the

    ability of the equipment to perform over the frequency range of interest, and to reject

    noise at frequencies away from the measurement frequency. In order to obtain an

    accurate derivation of the frequency response using the impulse technique, the

    sampling frequency and record length of the digitizing equipment must be adequate to

    faithfully record all frequency components of interest in both input and output

    impulses, which must both return to zero at the end of the sampling period for the

    FFT algorithm to be valid (in case no window function is applied), and the applied

    impulse amplitude must be large enough to ensure that all noise components in the

    output frequency distribution are insignificant. The introduction of Spectral Density

    Estimates to the impulse technique helped to overcome the influence of noise in the

    output signal and the result of the FRA measurement.

    The other main way that variations in FRA results can be introduced by how the

    measurement is made concerns practices involving test leads. A three-lead system

    (separate leads for applying and measuring the signal at the input terminal) as shown

    in Fig. 3.4 is recommended to avoid including the input lead in the measurement.

  • Chapter 3 SFRA Basics


    Fig. 3.4 Color codes of leads at test set

    When making high-frequency measurements, it is good practice to use coaxial test

    leads with a good high-frequency bandwidth, and to ensure that the test leads are

    terminated in their characteristic impedance, usually 50 ohms, to avoid reflections.

    Good practice for grounding the shields of the coaxial cables is of primary importance

    to achieve good repeatability.

    The most basic and important variation in FRA results is introduced by which type of

    measurement is made. Most SFRA users perform an end-to-end measurement in

    which the input signal is applied to one end of every winding and the transmitted

    signal at the other end is measured, as for a simple resistance measurement. For some

    impulse users, following traditional impulse measurement practice, it is more usual to

    inject a voltage at one terminal (usually an HV terminal) and measure the transferred

    voltages to other windings, or currents in the injected winding (usually at the HV

    neutral) to derive self or transferred impedances (or admittances). Variation can also

    be introduced by different values of measuring impedances (50/10/1M etc.)

    and/or by the way other untested terminals are terminated. Some users prefer a

    practice of grounding untested windings while others prefer to leave all other

    terminals floating. Not surprisingly, these different measurements are not necessarily

    equally effective in detecting mechanical displacement. Some recent work has been

    done to compare the relative sensitivities of different connection techniques.

  • Chapter 3 SFRA Basics


    Lately, a technique has been demonstrated where a complete transformer fingerprint

    is measured such that subsequently any type of FRA curve can be calculated on

    demand. A device connects to all the transformer terminals at the same time and

    automatically measures all the linear properties of the transformer, i.e. the full

    admittance matrix, without requiring any reconnection. In addition, this technique

    allows the automated generation of high frequency terminal models of transformers

    for network simulation purposes.

    In view of the wide variety of FRA practices in use, there would obviously be benefit

    in carefully examining these with a view to standardizing those that have been shown

    to be most effective, while allowing variety where this does not impact on

    performance. [15]

    3.8 Measurements on Different Winding Types

    Most people immediately think of winding measurements as being only associated

    with the high-voltage and the low-voltage windings. When considering SFRA

    measurements, winding measurements realistically consist of five categories and not

    just two. The winding categories are high-voltage, low-voltage, inter, series, and


    Short circuit measurements made on one winding while short circuiting another

    winding are a variation on inter winding measurements.

    It should be noted that inter-winding measurement is not a true winding measurement,

    but rather the transfer impedance between two windings. The series and common

    winding measurements describe the SFRA application as it is applied to auto

    transformers. Regardless, certain expectations can be made for each.

    These measurement types produce some predictable characteristics and properties.

    Understanding these properties will minimize testing error and may help identify

    problems. The following expectations exist for each of the following categories. [39]

  • Chapter 3 SFRA Basics


    3.8.1 High-Voltage Winding

    High-voltage winding measurements have greatest attenuation as compared to low

    voltage and tertiary windings. Most traces start between 30 dB and 50 dB and are

    initially inductive. High-voltage windings are much larger in overall size, which

    contributes to greater complexity in its distributive network. High-voltage winding

    measurements generally produce steeper resonances and more of them as compared to

    its low-voltage counterpart. Fig. 3.5 illustrates these features.

    Fig. 3.5 High Voltage winding

    The traces shown in Fig. 3.5 are from different test specimens. Both traces are from

    230 kV core-forms transformers, however one trace is from a delta connected

    configuration and the other is from a wye connected configuration. [39]

    3.8.2 Low-Voltage Winding

    Low-voltage winding measurements have least attenuation as compared to the other

    categories. Most traces start between 5 dB and 15 dB and are also initially

    inductive This characteristic is due to the low impedance property of the high current

    side of the transformer. The first peak after the core resonance generally approaches

    5 dB to 0 dB and is concave and smooth. As compared to the high-voltage winding

    response, the low voltage winding fewer fluctuations and is slight smoother. Fig. 3.6

    illustrates these features. Again, both traces in this figure are from different

    transformers. [39]

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    Fig. 3.6 Low-Voltage Winding

    3.8.3 Inter-Winding

    Inter-winding measurements always start with high attenuation, between 60 dB and

    90 dB, and are capacitive. If electrostatic interference is present, it will show up at

    60 Hz and at the associated harmonics of 60 Hz during this measurement. Fig. 3.7

    illustrates these features. These traces are very common; most inter-winding traces

    adhere to one of the basic shapes shown below.

    Fig. 3.7 Inter-Winding

    Fig. 3.8 presents a high-voltage winding trace, a low-voltage winding trace, and an

    inter-winding trace together from a common test specimen. This illustrates their

    general relationship. It can be seen that the low-voltage winding has consistently

    lower attenuation then the high-voltage winding. Also, low-voltage winding is much

  • Chapter 3 SFRA Basics


    smoother at higher frequencies. This example was taken from a 10 MVA auxiliary

    transformer. [39]

    Fig. 3.8 Trace Relationship

    3.8.4 Series and Common Winding

    The series and common winding measurements are grouped together because of their

    similarities. These measurements are associated with auto transformer. The naturally

    low turns ratio of an auto transformer causes the series and common measurements to

    be similar. However, if an LTC is present on either winding, the similarities will be

    somewhat affected by the tap windings. Fig. 3.9 illustrate these features, and were

    obtained from a General Electric 440MVA 345 kV auto-transformer. Electrostatic

    interference was present during testing and is seen at 60 Hz. [39]

    Fig. 3.9 Series and Common Winding

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    3.9 Conclusion

    Sweep Frequency Response Analysis (SFRA) is a tool that can give an indication of

    core or winding movement in transformers. This is done by performing a

    measurement, a simple one, looking at how well a transformer winding transmits a

    low voltage signal that varies in frequency. Just how well a transformer does this is

    related to its impedance, the capacitive and inductive elements of which are intimately

    related to the physical construction of the transformer. Changes in frequency response

    as measured by SFRA techniques may indicate a physical change inside the

    transformer, the cause of which then needs to be identified and investigated.