IEC 60076 18 Edition 1 0 2012 07 INTERNATIONAL STANDARD NORME INTERNATIONALE Power transformers – Part 18 Measurement of frequency response Transformateurs de puissance – Partie 18 Mesure de la répons[.]
General
To conduct a frequency response measurement, a low voltage signal is applied to one terminal of the test object relative to the tank The voltage at this input terminal serves as the reference signal, while a second voltage signal, known as the response signal, is measured at another terminal with respect to the tank The frequency response amplitude, expressed in dB, represents the scalar ratio of the response signal (V out) to the reference voltage (V in) as a function of frequency Additionally, the phase of the frequency response indicates the phase difference between V in and V out, measured in degrees.
The response voltage is measured across a 50 Ω impedance, and any coaxial lead used between the test object and the voltage measuring instrument must have a matched impedance For precise ratio measurements, it is essential that the technical parameters of both the reference and response channels, as well as any measurement leads, are identical.
To minimize signal reflections and reduce the impact of coaxial leads on measurements, the characteristic impedance of the coaxial measuring leads is selected to match the input impedance of the measuring channel This ensures that the influence of the coaxial lead on the measurement is negligible within the specified frequency range.
With a matched impedance lead, the measuring impedance is effectively applied at the test object terminal
The output-to-input voltage ratio, expressed in decibels (dB), varies significantly The relative voltage response in dB is determined using the formula 20 × log₁₀(V out / V in), where V out / V in represents the scalar ratio.
An example of the general layout of the measurement method using coaxial measuring leads is shown in Figure 1
Figure 1 – Example schematic of the frequency response measurement circuit
Condition of the test object during measurement
For factory and site measurements, the test object must be fully assembled for service, including all bushings; however, coolers and related auxiliaries are not required to be assembled.
Liquid or gas filled transformers and reactors shall be filled with liquid or gas of the same type
For accurate testing, ensure that the relative permittivity matches the service requirements Remove all busbars and system connections, leaving only those necessary for the specific measurement If internal current transformers are present but not linked to a protection or measurement system, short and earth the secondary terminals Additionally, ensure that the core and frame connections to the tank are secure, and that the tank is properly earthed.
If a transformer is not assembled in the factory according to its service conditions, such as using oil/air bushings instead of oil/SF6 bushings, the Frequency Response Analysis (FRA) baseline measurement must be conducted on-site However, transport configuration measurements may still be feasible.
If the purchaser has specified special connections for the test object to facilitate frequency response measurements during transport, additional measurements must be conducted in the transport configuration, including draining if necessary, both before transport and upon delivery to the site, or as directed by the purchaser.
For site measurements, ensure the test object is safely disconnected from the electrical system at all winding terminals Disconnect line, neutral, and any tertiary line connections, while keeping the tank earth, auxiliary equipment, and current transformer service connections intact If two connections are made to one corner of a delta winding, conduct measurements with the delta closed.
In cases where a direct connection to the terminal is not feasible, it is essential to document the connection details alongside the measurement data, as the presence of additional bus bars linked to the terminals can influence the measurement outcomes.
Current transformers (CTs) may exhibit differences in connection between on-site measurements and factory tests However, the variation in frequency response between a transformer with shorted and earthed CTs and one connected to a low impedance protection system is typically minimal.
When a transformer is directly linked to SF6 insulated busbars, measurements can potentially be taken by connecting to the isolated earth connection of an earth switch In this scenario, it is essential to conduct measurements directly at the terminals prior to any further actions.
SF 6 busbar is assembled and using the earth switch
Measurements conducted in the factory should occur at approximately ambient temperature, avoiding immediate testing after a temperature rise It is essential to record the dielectric temperature of the test object, typically the top liquid temperature, during these measurements In contrast, on-site measurements are not temperature-controlled; however, while extreme temperatures may have a minor impact, this effect is generally not significant The influence of temperature on frequency response measurements is demonstrated in the results.
It is recommended that if possible measurements on-site are not made whilst the test object temperature is changing rapidly for example immediately following oil treatment.
Measurement connection and checks
Measurement connection and earthing
The methods of connection of the leads and lead earths to the test object are given in
Ensuring proper connections is crucial to avoid measurement errors, so it is essential to check the continuity of both the main and earth connections at the instrument end of the coaxial cable prior to taking measurements Special attention should be given to verifying connections to bolts or flanges to confirm a reliable connection to the winding or the test object tank.
Zero-check measurement
If specified, a zero-check measurement shall be carried out as an additional measurement
Before starting measurements, connect all measuring leads to the highest voltage terminal and ground them using the standard method This initial measurement will reveal the frequency response of the measurement circuit Additionally, if required, repeat the zero check measurement on other voltage terminals.
The zero-check measurement offers valuable insights into the maximum frequency that can be trusted for interpreting the results It is important to note that this measurement is not a calibration check, and any deviations observed in the zero-check measurement should not be adjusted or removed from the final results.
Repeatability check
On completion of the standard measurements the measurement leads and earth connections shall be disconnected and then the first measurement shall be repeated and recorded
This check is necessary to evaluate the repeatability and useable diagnostic frequency range under the specific conditions of the measurement.
Instrument performance check
To ensure the instrument's performance is reliable, it is essential to conduct one of three checks whenever there is uncertainty One method involves connecting the source, reference, and response channels with appropriate low-loss leads and verifying that the measured amplitude ratio remains at 0 dB ± 0.3 dB throughout the entire frequency range.
To ensure accurate measurements, connect the source and reference channels while keeping the response terminal open circuit, and verify that the measured amplitude ratio remains below -90 dB across the entire frequency range Additionally, assess the instrument's performance by measuring the response of a known test object, ensuring that the measured amplitude ratio aligns with the expected response within the specified requirements over the full frequency range The test object should exhibit a frequency response that spans the attenuation range of -10 dB to -80 dB Finally, confirm the instrument's proper operation by following the performance check procedure provided by the manufacturer, which will validate that the instrument functions within the specified parameters.
5.1.2 at least over an attenuation range of –10 dB to –80 dB over the whole frequency range.
Measurement configuration
General
For typical transformer and reactor winding configurations, a standard set of measurements is essential for establishing baseline data in most situations These measurements are mandatory in all instances, while additional measurements may be necessary to gather specific information or to align with prior measurements Standard measurements for other transformer and reactor types should adhere to these established principles.
Principles for choosing the measurement configuration
Standard measurements should consist of end-to-end assessments for each phase of every winding, ensuring that phases and windings are maximally separated while keeping all other terminals floating Additional specified measurements may encompass capacitive inter-winding, inductive inter-winding, and end-to-end short circuit evaluations.
For transformers and reactors equipped with an on-load tap-changer (OLTC), standard measurements on the tapped winding should be conducted at two specific positions: a) at the tap position with the maximum number of effective turns in the circuit, and b) at the tap position when the tap winding is out of the circuit.
For windings with a set number of turns, measurements should be taken at the tap position corresponding to the maximum number of effective turns Additional measurements may be required at other tap positions.
For auto-transformers with a line-end tap-changer, the standard measurements shall be:
• on the series winding with the minimum number of actual turns of the tap-winding in circuit
The tapping for the highest low voltage (LV) in a linear potentiometer type arrangement, the change-over position in a reversing type tapping arrangement, or the tapping for the lowest LV voltage in a linear separate winding tapping arrangement are crucial for optimizing performance and ensuring efficient operation.
• on the common winding with the maximum number of effective turns of the tap-winding in circuit (the tapping for the highest LV voltage), and
The common winding features the least number of actual turns in the tap-winding circuit, which is essential for achieving the lowest low-voltage (LV) output This can be accomplished through a linear potentiometer, a dedicated winding type tapping arrangement, or a change-over position in a reversing type tapping setup.
NOTE 1 The choice of tap-position is intended to provide at least one measurement with and one without the tap winding in circuit so that any damage can be more easily identified as being in the tap-winding or the main winding
For neutral or change-over positions, the tap-changer must move in the lowering voltage direction unless specified otherwise, and the direction of movement, whether raising or lowering, should be documented.
NOTE 2 The position of the change-over selector in reversing and coarse-fine arrangements has a profound effect on the measured frequency response
For transformers equipped with both an On-Load Tap Changer (OLTC) and a De-Energised Tap Changer (DETC), the DETC must be set to the service position if specified; otherwise, it should be positioned at the nominal setting for measurements at the OLTC positions outlined in section 4.4.2.2.
For transformers fitted with a DETC, baseline measurements shall also be made on each position of the DETC with the OLTC (if fitted) on the position for maximum effective turns
Changing the position of a DETC on a transformer during frequency response measurements is not advisable; measurements should be conducted at the 'as found' DETC tap position To ensure accurate assessments, it is essential to gather adequate baseline measurements for any potential service conditions of the DETC.
Star- and auto-connected windings with a neutral terminal
For standard measurements, the signal should be applied to the line connection or the higher voltage terminal for series windings If necessary for compatibility with previous measurements, an additional measurement can be taken with the signal applied to the neutral terminal A star-connected winding without a neutral terminal should be treated as a delta winding Table 1 provides the list of standard measurements for star-connected windings with taps.
Table 1 – Standard measurements for a star connected winding with taps
Measurement number Source and reference lead ( V in ) connected to Response lead ( V out ) connected to Tap position
1 Line terminal phase 1 Neutral Max effective turns
2 Line terminal phase 2 Neutral Max effective turns
3 Line terminal phase 3 Neutral Max effective turns
4 Line terminal phase 1 Neutral Tap winding out of circuit
5 Line terminal phase 2 Neutral Tap winding out of circuit
6 Line terminal phase 3 Neutral Tap winding out of circuit
Delta windings and other windings without an accessible neutral
If delta windings can be split into individual phases (six bushings brought out) then the standard measurement shall be made with the windings split
For large generator transformers, it is advisable to conduct baseline measurements at the factory and during commissioning with the delta connections both open and closed, especially when removing phase-to-phase connections in service is impractical.
Standard measurements should be conducted sequentially on each phase, starting with the terminal that has the lowest number or the letter closest to the beginning of the alphabet The response is then measured on the subsequent numbered or lettered terminal, continuing this process in a cyclic manner (refer to Table 2).
For delta tertiary or stabilising windings, the delta shall be closed
For delta tertiary or stabilising windings that are earthed at one corner in service, the earth shall be removed if possible without removing liquid or gas
Table 2 – Standard measurements for delta connected winding without tap
Measurement number Source and reference lead ( V in ) connected to Response lead ( V out ) connected to
Zig-zag connected windings
Zig-zag connected windings shall be measured as star windings with a neutral connection
The frequency responses of various phases in a zig-zag connected winding are not anticipated to align as closely as those in a star connected winding.
Two-winding three-phase transformers
For transformers without taps, standard measurements require one measurement for each phase of each winding, totaling six measurements In contrast, transformers equipped with an on-load tap-changer necessitate nine measurements.
Three-phase auto-transformers
For transformers, standard measurements include one measurement for each phase of the series winding and the common winding, totaling six measurements for transformers without taps and nine for those with an on-load tap changer Additionally, if a transformer features a tertiary winding connected to three line terminals, three extra measurements are necessary for this winding.
Phase shifting transformers
The standard measurement involves taking readings from the input terminal to the output terminal for each phase, as well as from the neutral of the shunt winding to the output terminal on each phase, including measurements on the neutral tap and each extreme tap, totaling 18 measurements If the phase-shifting transformer is a two-core type with removable external interconnections, it should be considered as two distinct transformers.
Reactors
For a three-phase reactor, series reactors require measurements from the input terminal to the output terminal for each phase, resulting in a total of three measurements In contrast, shunt reactors are treated as a star winding on a transformer, necessitating three measurements for a three-phase reactor without taps and six measurements for a reactor with taps.
Method for specifying additional measurements
For any necessary additional measurements, it is essential to specify the connection details for each test object terminal, including signal and reference, response, earthed, floating, or interconnected terminals Additionally, the tap-position and the previous tap-position for each measurement must be provided Please refer to the format outlined in Table 3 for guidance.
Table 3 – Format for specifying additional measurements
Measurement Tap Previous tap Source and reference ( V in )
Response ( V out ) Terminals earthed Terminals connected together
The terminal identification entered in the table shall be those permanently marked on the test object and shall be shown on a diagram included in the specification
Examples of particular measurement configurations using this format are given in Annex D.
Frequency range and measurement points for the measurement
The lowest frequency measurement shall be at or below 20 Hz
The minimum highest frequency measurement for test objects with highest voltage > 72,5 kV shall be 1 MHz
The minimum highest frequency measurement for test objects with highest voltage of
It is recommended that a highest measurement frequency of at least 2 MHz is used for compatibility and simplicity for all test objects
Reproducibility of measurements improves at frequencies above 1 MHz, particularly when utilizing shorter earth connections with smaller bushings Additionally, higher frequency data is crucial for diagnosing physically smaller windings.
Measurements below 100 Hz should be taken at intervals no greater than 10 Hz For frequencies above 100 Hz, a minimum of 200 measurements should be conducted, evenly spaced on either a linear or logarithmic scale within each frequency decade.
If the transformer operator does not need low frequency data for diagnosing core changes, a measurement frequency of at least 5 kHz can be specified.
Measuring instrument
Dynamic range
The measuring instrument must have a minimum dynamic range of +10 dB to -90 dB, ensuring a minimum signal-to-noise ratio of 6 dB across the entire frequency range, relative to the maximum output signal level of the voltage source.
Amplitude measurement accuracy
The measurement accuracy of the ratio between \$V_{in}\$ and \$V_{out}\$ must be within ±0.3 dB for all ratios from +10 dB to -40 dB, and within ±1 dB for ratios between -40 dB and -80 dB across the entire frequency range.
Phase measurement accuracy
The accuracy of the measurement of the phase difference between V in and V out shall be better than ± 1º at signal ratios between +10 dB and -40 dB, over the whole frequency range.
Frequency range
The minimum frequency range shall be 20 Hz to 2 MHz.
Frequency accuracy
The accuracy of the frequency (as reported in the measurement record) shall be better than ± 0,1 % over the whole frequency range.
Measurement resolution bandwidth
For measurements below 100 Hz, the maximum measurement resolution bandwidth (between
-3 dB points) shall be 10 Hz; above 100 Hz, it shall be less than 10 % of the measurement frequency or half the interval between adjacent measuring frequencies whichever is less.
Operating temperature range
The instrument shall operate within the accuracy and other requirements over a temperature range of 0 to +45 °C.
Smoothing of recorded data
Data recorded to meet this standard must not be smoothed using methods that rely on adjacent frequency measurements However, it is permissible to use averaging or other techniques to minimize noise by taking multiple measurements at a specific frequency or by utilizing measurements within the resolution bandwidth for that frequency.
The data displayed on a screen or any output data provided in addition to that required by
Clause 6 is not subject to the requirements of Clause 5, however it is recommended that the facility to view the data recorded in compliance with Clause 6 is provided.
Calibration
The instrument shall be calibrated to a traceable reference standard at regular intervals within a recognised quality system.
Measurement leads
For accurate measurements, it is essential to use separate measurement leads for the source, reference, and response connections Coaxial leads should be of equal lengths and maintain a characteristic impedance of 50 Ω Additionally, signal attenuation for each lead must not exceed 0.3 dB at 2 MHz A zero-check measurement conducted without a test object or earth leads should show an amplitude deviation of less than 0.6 dB at 2 MHz Furthermore, the maximum allowable length for a passive lead system is 30 m.
If an alternative measurement method is employed, such as using a measuring impedance, head amplifier, or active probe system near the test object terminal, the leads connecting the shunt, amplifier, or probe to other parts of the instrument are not considered 'used for the measurement' as per this Clause Therefore, these leads do not need to comply with this specification, provided they do not influence the measurement and all other requirements of Clause 5 are met.
Impedance
The measurement impedance for the response voltage measurement shall be 50 Ω ± 2 % over the full frequency range
If coaxial measurement leads are used, the input impedance of the reference and response voltage channels of the measuring instrument shall be 50 Ω ± 2 % over the full frequency range
Data to be recorded for each measurement
Data must be recorded as a single computer-readable file for each measurement in XML 1.0 format Each measurement should include the following information: a unique identifier for the test object, typically the customer serial number or location number; the measurement date in YYYY-MM-DD format; the completion time in HHhMM format using 24-hour notation; the manufacturer of the transformer or reactor; the manufacturer's unique serial number for the test object; identification details for the measuring equipment, including the manufacturer, model, and individual serial number; the peak voltage used during the measurement; the reference terminal identification for the connected leads; the response terminal identification; and a list of all connected test object terminals formatted as terminal identifier 1-terminal identifier 2-terminal identifier 3, and so on.
The article outlines key parameters for measuring test objects, including the identification of earthed terminals connected to the test object tank, the OLTC tap position during measurement, and the previous tap position from which adjustments were made It also specifies the DETC position, the test object's temperature in degrees Celsius, and whether the test object was fluid-filled Additionally, it allows for comments on the test object's condition, such as 'service' or 'transport.' The length of unshielded connections for each lead must be noted if coaxial leads are not directly connected to bushing terminals, along with any necessary information for repeating the measurement Finally, the measurement results should include frequency in Hz, amplitude in dB, and phase in degrees, formatted as a text string.
1.2345E+04 for frequency and -1.2345E+01 for amplitude and phase)
Each file shall be named identifier_reference terminal_response terminal_tap position_date_time.xml
Additional information to be recorded for each set of measurements
An additional computer readable file shall be supplied for each set of measurements
(measurements made on one test object on one occasion) This file shall include the following information a) Test object data
4) Highest continuous rated power of each winding
5) Rated voltage for each windings
6) Short circuit impedance between each pair of windings
8) Vector group, winding configuration / arrangement
9) Number of phases (single or three-phase)
10) Transformer or reactor type (e.g GSU, phase shifter, transmission, distribution, furnace, industrial, railway, shunt, series, etc.)
11) Transformer configuration (e.g auto, double wound, buried tertiary, etc.)
12) Transformer or reactor construction (e.g core form, shell form), number of legs (3 or
13) OLTC: number of taps, range and configuration (linear, reversing, coarse-fine, line- end, neutral-end, etc.)
14) DETC: number of positions, range, configuration, etc
15) Organisation owning the test object
16) Test object identification (as given by the owner if any)
17) Any other information that may influence the result of the measurement
It is recommended to include a drawing of the test object's nameplate along with the winding schematic If this information is provided, there is no need to repeat the data Additionally, location data should be included.
1) Location (e.g site name, test field, harbour, etc.)
2) Bay identification reference if applicable
3) Notable surrounding conditions (e.g live overhead line or energized busbars nearby)
4) Any other special features c) Measuring equipment data
1) Working principle of device (sweep or impulse)
2) Equipment name and model number
6) Any other special features of the equipment d) Test organization data
3) Any additional information e) Measurement set-up data
1) Remanence of the core: was the measurement carried out immediately following a resistance or switching impulse test, or was it deliberately demagnetised?
2) Whether the tank was earthed
3) Measurement type (e.g open circuit, short circuit, etc.)
4) Length of braids used to ground the cable shields
6) Reason for measurement (e.g routine, retest, troubleshooting, commissioning new transformer, commissioning used transformer, protection tripping, recommissioning, acceptance testing, warranty testing, bushing replacement, OLTC maintenance, fault operation, etc.)
7) Any additional information f) Photographs of the test object as measured showing the position of the bushings and connections
This annex contains requirements for the method of connection of the measurement leads to the test object Method 1 is the reference method preferred for repeatability beyond 1 MHz
Baseline measurements will typically utilize Method 1 unless an alternative is agreed upon Method 2, an alternative configuration for earth connections, can be employed at the request of the transformer user for convenience during measurements Additionally, Method 3 is available for use when the transformer user specifies it, particularly when compatibility with prior measurements conducted using Method 3 is necessary.
In general, the three methods are expected to yield similar results up to 500 kHz, while at frequencies up to 1 MHz, the results may differ but can still be utilized for diagnostic purposes.
A.2 Common requirements for all measurements
The details of the connections and connection method shall be given in the measurement record see Clause 6
The connections to the terminal and the transformer tank shall be made using a repeatable, reliable and low resistance method
Ensure that earth connections from the source and response leads are individually routed to the tank, while connections from the source and reference leads can be combined into a single conductor It is essential that the earth connection point is positioned as close as possible to the base of the bushing or terminal where the measurement lead is attached.
To ensure accurate measurements, connect the central conductor of the coaxial leads directly to the test object terminal with the shortest length of unshielded conductor Additionally, use braid to create the shortest possible connection between the measuring lead's screen and the flange at the base of the bushing A specific clamp arrangement or similar method is essential for minimizing the length of the earth connection.
NOTE In general this method may be expected to give repeatable measurements up to 2 MHz
B unshielded length to be made as short as possible
Method 2 mirrors Method 1, with the distinction that the earth connection from the measurement leads to the flange at the base of the bushing can utilize a fixed length wire or braid, allowing for a connection that is not necessarily the shortest possible.
The length of the excess earth conductor in relation to the bushing can influence amplitude measurements above 500 kHz and resonant frequencies exceeding 1 MHz It is essential to consider this factor when comparing baseline measurements with subsequent ones.
When an alternative connection point is used instead of the flange at the base of the bushing, measurements may be impacted at frequencies exceeding 500 kHz It is crucial to carefully document the connection setup and consistently use the same connection point to achieve repeatable measurements, as this scenario deviates from standard measurement practices.
In a method 3 connection, the coaxial measurement lead's screen is directly linked to the test object tank at the bushing's base, while an unshielded conductor connects the central conductor to the terminal at the top of the bushing.
Using a method 3 connection solely for the response lead yields results comparable to method 1, making it a practical choice when an external shunt for measuring impedance is employed However, if a common conductor is utilized for both signal and reference connections, the measurement will differ from that of method 1 due to the inclusion of the conductor in the measurement.
Frequency response and factors that influence the measurement
In frequency response measurements, both amplitude and phase of the voltage ratio are recorded, but typically only amplitude data is utilized for visual interpretation However, incorporating both amplitude and phase information is essential for parameterizing frequency response data in automated systems, such as those using pole-zero representations Frequency response can be displayed on logarithmic or linear scales; logarithmic scale plots facilitate overall trend analysis, while linear scale plots are advantageous for examining discrete frequency bands and comparing minor differences at specific frequencies.
Figure B.1 – Presentation of frequency response measurements
In order to interpret a measured frequency response, a comparison is made between the measured response and a previous baseline measurement (if available), as shown in
In the absence of baseline measurements, comparisons can be made using the response from a twin transformer, which is manufactured to the same specifications as shown in Figure B.3 However, caution is necessary when using data from sister transformers, as variations in winding configurations may lead to discrepancies in frequency responses, potentially resulting in incorrect diagnoses of winding damage Additionally, for three-phase transformers, it is possible to compare the responses of individual phases, as illustrated in Figure B.5.
Figure B.2 – Comparison with a baseline measurement
Figure B.3 – Comparison of the frequency responses of twin transformers
1 Figures in square brackets refer to the Bibliography
Figure B.4 – Comparison of the frequency responses from sister transformers
Figure B.5 – Comparison of the frequency responses of three phases of a winding
The comparison of frequency response measurements is used to identify the possibility of problems in the transformer Problems are indicated by the following criteria [4]:
• changes in the overall shape of the frequency response;
• changes in the number of resonances (maxima) and anti-resonances (minima);
• shifts in the position of the resonant frequencies
Confidence in diagnosing transformer issues relies on the magnitude of observed changes relative to expected variations based on the type of comparison (baseline, twin, sister, or phase) It's essential to consider that discrepancies may arise from different measurement setups or other variations Notably, when comparing phases within the same transformer, significant differences can be deemed "normal" due to factors such as varying internal lead lengths, winding interconnections, and the proximity of phases to the tank and each other Additionally, the grounding of windings and measurement leads, along with the position of the tap changer, can significantly influence measurement outcomes.
It is important to be able to determine or eliminate the variations caused by these factors to avoid a misleading diagnosis when interpreting frequency response measurement results
Effective frequency response measurement is essential for accurate diagnostics, necessitating an understanding of transformer structure and high-frequency behavior This article outlines key features of frequency response and factors that affect it, while providing guidelines to emphasize the significance of proper measurement practices and how to identify unreliable measurements.
Information is also provided to help to distinguish the differences that may be caused by problems in the winding from the “normal” differences caused by transformer construction variations
B.3 Fundamental understanding of frequency response characteristics
The frequency response characteristics of transformers vary significantly due to their core and winding structures This response can be categorized into three regions: the lower frequency region, influenced by the core; the middle frequency region, shaped by the interactions between windings; and the higher frequency region, determined by the winding structure and internal connections An example of this is illustrated in Figure B.6, which highlights that the frequency limits for each region are not universally applicable, as they depend on the transformer's size and winding ratings In the core influence region (up to approximately 2 kHz), the response is primarily governed by the core's magnetizing inductances and the transformer's bulk capacitances For three-phase three-limb core-form power transformers, the middle phase exhibits a single anti-resonance due to symmetrical magnetic reluctance paths, while the outer phases show two anti-resonances from different magnetic reluctance paths Additionally, the core's residual magnetization affects the frequency response in this region, and five-limb cores display a distinct response.