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EE Publishers (https://www.ee.co.za)
Interpreting sweep frequency response analysis
measurements
141
Power transformers are critical components in an electrical power network. Testing, diagnostics and reliable
condition assessment of power transformers becomes increasingly relevant due to the ageing of transformer
fleets around the world. Transfer function measurements have been used as a diagnostic tool to detect
mechanical failures in power transformers.
Geometrical changes in the transformer windings and core due to mechanical stress can be reflected as a change in
the RLC parameters of the equivalent circuit of the power transformer. Such changes can be detected through the
change in the transfer function.
Sweep frequency response analysis (SFRA) proceeds by applying a sinusoidal signal of constant amplitude and
variable frequency to one end of the winding under test (U1(f)). The response is measured on the other end of the
winding (U2(f)). The response will vary in amplitude and phase. The transfer function (H(f)) is a comparison of the
applied signal and the response, see principle operation of SFRA in Fig. 1. As the SFRA method measures in
frequency domain there is no further signal processing by the mains of FFT required.
Fig. 1: Principle operation of SFRA.
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The measurement setup consists mainly in a network analyser and measurement cables. Given the fact that the cables
also a capacitance, these shall be grounded. Ideally, braids are used for grounding the shield of the measurement
cables. A braid has a lower inductivity compared to a single wire with the same cross-section. Furthermore, using
single braided wires will reduce the impact of the skin effect on the test results, especially at very high frequencies.
Usually, a measuring resistance is needed for producing the voltage drop U2(f). The wave impedance of the measuring
cables shall be the same as the resistance of the measurement input. Fig. 2 shows the test setup of the transfer
function in frequency domain.
The transfer function of a power transformer is measured according to:
H(f) = U2(f)/U1(f)
(1)
There are a number of possible methods of presenting the results of measurements made using the sweep frequency
response method. The most widespread is to plot a graph of the amplitude, as measured by the network analyser, over
frequency. Both linear and logarithmic scales are used [1].
The amplitude is defined by:
k(f) = 20log10(U2(f)/U1(f))
(2)
The phase, as measured by the network analyser, is defined by:
φ(f) = tan-1(∠U1(f)/∠U2(f)
(3)
This work will focus on the SFRA method only, since the SFRA method is superior to the IFRA method. The IFRA
method lacks reproducibility for in-site tests. Another major disadvantage is its low measurement resolution at very low
frequencies.
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Fig. 2: Transfer function measurement in frequency domain on a power transformer.
Type of measurements
The SFRA measurement is typically performed on all accessible windings. The transfer function of each test can be
compared to reference data.
The core and winding structure of a power transformer can be seen as a complex electrical network of resistances,
self-inductances, ground capacitances, coupling inductances and series capacitances as schematically shown in Fig.
3. The frequency response of such a network is unique and can therefore be considered as a fingerprint of the power
transformer under test.
Fig. 3: Simplified network behaviour and equivalent circuit diagram of a transformer’s active part.
For understanding the shape of the SFRA responses it is essential to have a clear idea about the behaviour of the
transfer function. The transfer function is dependent on the measurement resistance (Rm) which is usually 50 Ω and
the impedance of the power transformer under test (Ztransformer):
H(f) = U2(f)/U1(f) = Rm/(Rm + Ztransformer)
(5)
From an electrical point of view a power transformer is a combination of resistances, inductances and capacitances. A
first approach is necessary for distinguishing between the effects of the core and the windings in the transfer function.
The frequency response of the iron core is a result of the magnetising inductance (Lm), the core power losses (Rm) and
the parasitic capacitance coupled with the iron core (Cg1 and Cg2).
The response prevails at very low frequencies. The frequency response of the windings is a result of the copper losses
(R1 and R2), leakage inductances (L1 and L2) and other parasitic capacitances (Cs1, Cs2 and C12). The response of the
windings prevails as the test frequency is being increased. This is due to the fact that the inductance and parasitic
capacitance of the iron core is much greater than the leakage inductivity and parasitic capacitances of the windings.
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Fig. 4: Simplified network behaviour and equivalent circuit diagram of a transformer’s active part.
In Fig. 4 a typical FRA response is described with reference to the parameters of the equivalent circuit diagram of a
power transformer. At low frequencies, typically between 20 Hz and 1 kHz (frequency ranges are depending on the
transformer to be tested) the magnetising inductance dominates the response. The first parallel resonance frequency is
due to the resonance between the magnetising inductance of the iron core and the parallel, respectively parasitic
capacitance of the power transformer. It can be seen that for both phase A and phase C two parallel resonance points
take place, whereas for phase B only one parallel resonance takes place. This is due to the two magnetic paths in the
iron core when the test signal is injected at either phase A or phase C.
At medium frequencies, typically between 1 and 10 kHz, the parallel capacitance and the mutual inductances are
dominating the response. The mutual inductances are due to the mutual coupling effect between the high voltage (HV)
and low voltage (LV) winding of a power transformer. Hence, this frequency range is often referred to as the mutual
coupling frequency range.
At high frequencies, typically between 10 kHz and 1 MHz, the response is dominated by the winding capacitances and
inductances. Any mechanical change within the winding structure would affect this frequency range. At frequencies of 1
MHz and beyond, the effect of the actual measurement setup will have a great impact the response. Therefore, it is not
standard practice to analyse traces at frequencies beyond 1 MHz.
The upper frequency limit for analysing purposes depends very much on the physical size of the power transformer and
is lower the bigger the transformer. Typically, for a large power transformer (> 500 MVA, > 400 kV) the upper frequency
limit is approximately 0,5 MHz. For a small distribution transformers (<5 MVA) the upper frequency limit is about 4
MHz).
There are different types of FRA measurements. In the existing recommended practices [2, 3] different types of
measurements have been standardised. According to the Cigré terminology these measurements can be subdivided
into four groups:
End to end open-circuit test
End to end short-circuit test
Capacitive inter-winding test
Inductive inter-winding test
The most common type is the end to end open-circuit test. This type of test provides information about both the winding
and the core. The end to end short-circuit test is normally performed for on-site measurements in which only problems
in the winding structure have to be identified. Inter-winding tests have recently been introduced.
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Capacitive inter-winding measurement seems to be a potential type of FRA measurement due to its higher sensitivity in
the detection of radial deformations.
Fig. 5: Typical response of an end to end open circuit test (left)
and connection diagram (right).
Fig. 5 shows the typical response of an end to end open-circuit test on a YN connected power transformer. The source
(yellow) and the reference input (red) are connected to one phase. The response (blue) is measured on the neutral as
per the IEC 60076-18 standard [4].
Fig. 6: Typical response of an end to end short circuit test (left)
and connection diagram (right).
Fig. 6 shows the typical response of an end to end short circuit test on a YN connected power transformer. A
comparison between the response of an end to end open-circuit test and an end to end short-circuit test is shown on
the left hand side.
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At low frequencies the differences between the two measurement methods is caused by the short circuit of the
magnetic core. At higher frequencies the response of both methods line up as the actual winding structure is
dominating the response at high frequencies. The end to end short-circuit test is very sensitive to any change in the
leakage channels. Therefore, it is the preferred method for detecting any axial or radial movements of the windings.
Fig. 7: Typical response of a capacitive inter winding test (left)
and connection diagram right.
Fig. 7 shows the typical response of the capacitive inter-winding test. The capacitive inter-winding test has proven to be
sensitive for detecting any radial deformations within the power transformer active part. The test signal is applied to one
phase on the high voltage winding. The response is measured on the low voltage winding which corresponds to the
high voltage winding according to the power transformer vector group.
Fig. 8: Typical response of an inductive inter winding test (left)
and connection diagram (right).
Fig. 8 shows the typical response of the inductive inter-winding test. This is the least common test method. The
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measurement is carried out on two adjacent coils in order to measure the transfer admittance of the power transformer.
The test signal is applied to one end of the high voltage winding. The other end of the high voltage winding has to be
connected to ground in order to allow for a magnetic flux to build up. The response is measured on the corresponding
low voltage winding. The other end of the corresponding low voltage winding has to be grounded as well to be able to
pick up the induced voltage.
Interpretation of test results
SFRA is a comparative measurement method. This implies that any sort of reference data has to be available in order
to analyse the test results. This means results of an actual test, which is usually a certain set of curves, are compared
to reference baseline data.
Three methods are commonly used to assess the measured traces:
Time-based comparison: Current SFRA results are compared to previous results on the same power transformer under
test.
Type-based comparison: Current SFRA results are compared to another power transformer of the same design (sister
unit).
Phase-based comparison: Current SFRA results of one phase are compared to the results of the other phases of the
same power transformer under test.
Acknowledgement
This article is an abridged version of a paper which was presented at TECHCON Asia-Pacific 2016. It was published in
APT’s Purchasing Directory April – May 2016, and is republished here with permission. The full paper can be
downloaded here: www.omicronenergy.com/sfrapaper
References
[1]
S Ryder, S Tenbohlen: “A comparison of the swept frequency and impulse response methods for making
frequency response analysis measurements”, Doble Conference, 2003.
[2]
Cigré WG A2.26: “Mechanical condition assessment of transformer windings: guidance, FRA standardization,
further improvements“, 2008.
[3]
IEEE C57.149-2012: “IEEE Guide for the Application and Interpretation of Frequency Response Analysis for
Oil-Immersed Transformers”.
[4]
IEC 60076-18 Edition 1.0 2012-07 Power transformers – Part 18: “Measurement of frequency response”.
Contact Florian Predl, Omicron, info@omicronenergy.com (mailto:info@omicronenergy.com)
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