Sweep Frequency Response Analysis (SFRA)

Answers one question — has the geometry changed? — better than anything else.

A transformer can pass every dielectric test and still carry a silent mechanical deformation that will reduce its withstand capability at the next through fault. Frequency response analysis is the technique that sees that invisible dimension. It turns the internal geometry of the active part into an electrical signature — the fingerprint of the winding — and detects, by comparison, displacements and deformations that no routine test reveals.

Windings are electromechanical structures designed to withstand forces proportional to the square of current. A through fault with current 20% above the design value imposes roughly 44% more electromechanical stress. Every event consumes mechanical margin: turns shift, discs buckle, blocking loosens. The damage is rarely immediate. It degrades the capability to survive the next event, until an unremarkable fault becomes catastrophic. International reliability surveys consistently place the winding at the top of major failure contributions, and short-circuit test laboratories report that a substantial fraction of large transformers submitted to short-circuit testing fail, with winding deformation the most prominent failure mode. That is the dimension SFRA monitors.

What you will be able to do

• Explain the physical principle — the transformer as a distributed RLC network — and why the frequency signature works as an electromechanical fingerprint, including what the technique detects and what it does not.

• Perform repeatable measurements per IEC 60076-18 and IEEE C57.149-2024: coaxial cable management, grounding braids, tap changer position, core magnetic state, terminal condition, and complete setup documentation.

• Interpret signatures by frequency band — low for core and magnetisation, middle for winding structure, high for leads and connections — recognising that band boundaries are sensitivity maps rather than deterministic rules.

• Apply the comparative decision flow (baseline of the same unit, then phase to phase, then sister unit), use numerical indices with awareness of their limitations, and run the suspicious-signature protocol.

• Integrate FRA into the asset life cycle: factory baseline, transport monitoring with impact recorders, receipt, commissioning, post-fault and repairs.

The transformer as a distributed RLC network

At 50 or 60 Hz a transformer is described by a simple lumped circuit: winding resistance, leakage reactance, magnetising branch. For FRA that model is insufficient. As frequency rises, every construction element joins a distributed network: series resistance of conductors and connections; self inductances of each winding section and mutual inductances between sections and between windings; series capacitances between turns, discs and layers; capacitances to core, tank and grounded structures; capacitance between windings; and the contributions of bushings, taps and leads.

Each local resonance mode approximately obeys f_r ≈ 1/(2π√(LC)). The expression does not describe a real transformer on its own, but it reveals the principle: changing the geometry changes L, M and C, and therefore shifts poles, zeros, resonances and antiresonances. A radial deformation simultaneously alters the distance between discs, the effective area between conductors, the winding-to-core distance, the leakage flux path, and the capacitances to earth and between windings. Small geometric changes can produce large changes in high-Q resonances, which is the source of the technique's sensitivity. The reverse is also true and defines its principal limitation: the inverse solution is not unique, and similar signatures can result from different faults. FRA does not photograph the winding; it observes the electrical consequences of geometric change.

IEC 60076-18 defines the measurement technique, instrument requirements, connections and result recording, for both factory and field. Its minimum range requirements deserve attention: the lower frequency must not be higher than 20 Hz, and the upper must reach at least 1 MHz for equipment above 72.5 kV and 2 MHz at or below 72.5 kV, because smaller transformers show relevant resonances at higher frequencies. In practice, capability to at least 2 MHz is recommended for all classes. The standard is deliberately silent on universal pass/fail criteria: it guarantees that two signatures are comparable, and the comparative judgement belongs to the application guides and to engineering.

Four configurations, each illuminating a different angle

End-to-end open circuit applies the signal at one end of a winding and measures at the other, with the remaining windings floating or in the specified condition, always documented terminal by terminal. It is the most comprehensive configuration and normally the primary reference signature: sensitive to the magnetic state of the core at low frequency, to global winding integrity, to its own resonances, to radial and axial deformations, to leads and connections, to open circuits and to significant turn shorts. Its limitation is precisely the low-frequency region, which varies with magnetic remanence, the sequence of previous tests, and the natural differences between core limbs.

Inter-winding capacitive coupling applies the signal at a terminal of one winding and measures at a terminal of another, with the remaining ends floating, so transfer occurs predominantly by capacitive coupling. It is the most sensitive configuration to the capacitance between windings and therefore to the radial high-to-low distance and to relative displacements, including axial movements that alter the overlap between coils. The price is operational: attenuation can exceed 100 dB, demanding instruments with dynamic range above 120 to 140 dB, a low noise floor, impeccable grounding and redoubled rigour in repeatability.

Where comparisons die: setup and repeatability

The principle that should be posted on every laboratory wall: faced with an abnormal curve, the probability of a mounting error or configuration difference is frequently higher than the probability of a real transformer defect. The order of investigation is always instrument, then cables, then grounding, then connections, then transformer configuration, then ambient and magnetic conditions, and only then attribute the difference to the object.

Tap changer position is documented for both the de-energised and the on-load changer, and — a detail frequently ignored — so is the direction from which the on-load changer arrived at the position. Steps of only 2.5% on a de-energised changer are distinguishable in the curves, and two measurements at the same neutral position have been documented to differ because the changer reached neutral from opposite directions. Temperature alters conductor resistance, resonance damping and the permittivity of the oil-paper system, with a difference of 40 K visibly shifting resonance frequencies downward on heating; there is no universal correction as there is for tan delta, so it is recorded and considered in interpretation. Oil matters too: without oil the capacitances decrease and resonances rise in frequency, while esters of higher permittivity push them down. A factory curve taken without oil is not directly comparable to a field curve with oil.

Reading the signature, and knowing what FRA cannot answer

Radial deformation, or hoop buckling, comes from short-circuit radial forces that compress the inner winding, which can buckle against the core or against the blocking, and expand the outer one. The probable signature is resonance shifts typically between 20 and 400 kHz, new peaks or valleys, altered antiresonance amplitude, and differences between phases, often more evident in the shorted configuration. Axial displacement, or telescoping, comes from axial forces that shift a disc pack or the whole winding, opening spaces, tilting conductors and moving clamping rings. The probable signature is displacement of the first winding resonances and changes in inter-winding coupling between tens of kilohertz and 1 MHz, with divergence between the open and shorted measurements. A sensitive limitation: small displacements escape the numerical indices, with documented studies showing correlation coefficients failing to detect axial displacements below 1% of winding height, and one methodology failing to detect displacements smaller than 1 cm.

Numerical indices deserve critical use. Correlation calculated per band is the most widespread, but it is weakly sensitive to constant vertical offsets, can stay high despite localised differences, and a single number hides where the divergence occurred. The relative factor derived from correlation and computed in three fixed bands has been evaluated and documented to fail: two 100 MVA transformers with confirmed evident deformation were classified as normal, axial displacements under 1 cm went unnoticed, and the fixed bands do not adapt to every design. It is a triage tool, not a protective relay. The absolute sum of logarithmic error, the mean of the absolute magnitude differences in decibels, responds to amplitude shifts the correlation ignores and is intuitive in decibels, but its value depends on band and point distribution, its thresholds are not universal, and implementations diverge, so the report must declare the formula the software uses. Generic thresholds must not be adopted without validation by transformer family.

Honesty closes the differential diagnosis. FRA is not the test for chemical ageing of paper, moisture content, acidity, dissolved gas, incipient partial discharge, hot spots, tap changer contact resistance, dielectric losses, or thermal faults without geometric change. On its own it also does not give absolute mechanical severity, future short-circuit capability, residual life, root cause, or a universal energisation criterion. FRA answers one question — has the geometry changed? — and answers it better than any other test.

Syllabus

• Why the mechanical dimension matters: forces proportional to I², cumulative margin consumption

• Standards status: IEC 60076-18 and the current IEEE C57.149 edition

• Minimum measurement range: lower frequency no higher than 20 Hz, upper at least 1 or 2 MHz depending on class

• From the 60 Hz lumped model to the broadband distributed model

• Transfer function and decibel scale; why dynamic range is a critical specification

• The role of the 50 Ω reference impedance, and a conceptual error to avoid

• The four measurement configurations and what each one illuminates

• Frequency band reading as a sensitivity map, not a rule

• The low-frequency remanence trap and the sequencing of DC tests

• Setup and repeatability: cables, braids, tap position, temperature, oil, bushings, core grounding, neutral, test voltage

• The comparison validity checklist

• Failure modes and signatures: radial buckling, axial displacement, turn short, collapse and spiralling, clamping loss, leads, core, open circuit

• What FRA does not detect

• Comparison hierarchy: baseline, phase to phase, sister unit

• Numerical indices: correlation, the relative factor of the Chinese method, absolute sum of logarithmic error

• The suspicious-signature protocol in seven steps

• FRA in the asset life cycle, including transport and post-fault sequences

Laboratory work

A blind classification exercise. The student receives a library of five curve pairs (reference plus current measurement) from real anonymised transformers, all in end-to-end open circuit and, where available, shorted. The task: classify each case as normal, radial deformation, axial displacement, turn short or measurement error, and defend the classification in writing, band by band. The required analysis routine for each case: (1) verify comparison validity against the checklist, since setup metadata accompanies every pair; (2) overlay the curves on a log scale and locate the divergent bands; (3) confront the result with the sensitivity map; (4) compute correlation per band and the relative factor, and confront the numerical result with the visual analysis; (5) issue an opinion with a confidence level and the recommended next action — release, repeat the measurement, run complementary tests, or open for internal inspection. The pedagogical traps include a defect that is actually an over-long grounding braid, showing a deviation only at high frequency and not repeatable between phases, and a turn short whose curve realigns above 10 kHz, which the student who memorised middle band equals winding will classify wrongly. Pass criterion: 4 of 5 correct with coherent justification.

Key takeaway

Before you blame the transformer, audit the setup — the cause is usually outside the tank. And when you do have a valid comparison, remember that FRA answers one question only. Cross it with turns ratio, resistance, excitation current, short-circuit impedance, dissolved gas analysis and tan delta before deciding to open a unit or to energise a deformed one.

Module 21 of the Atlas Energy Academy · Diagnostic Methods · about 5 hours · Video series (7 × 10–15 min) plus signature analysis · Prerequisites: Part IV completed (Modules 18–20)