Frequency Response Analysis by Prof Satish IISc

Prof. L. Satish
HV Lab, Dept. of Electrical Engineering
Indian Institute of Science, Bangalore
homepage: hve.iisc.ernet.in/~satish
Credits: Dr. Pritam Mukherjee
Localization of Incipient Mechanical Damage
– Frequency Response Analysis
Transformer Technology Symposium, 9th - 10th Aug 2016, BANGALORE

My Research Interests
 Signal processing of HV impulse test data
 Testing ADCs in waveform digitizers
 Basic study on transformer windings
 Indirect measurement of Series Capacitance
 FRA for diagnostics and interpretation
 Localization, severity assessment of radial &
axial displacements
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc

Outline
 Introduction
 FRA: State-of-the-art
 Longstanding issues in FRA
 Objectives
 Generalized Analytical Formulation
 Localization and Severity assessment
 Radial Displacement
 Axial Displacement
 Summary

Introduction
• Diagnostic Testing and Condition Monitoring
• Triggered by structural change in energy sector
• Power/Energy is now a marketable quantity
• DTCM is a necessity for power utilities to
 Optimise existing assets, Lower operating costs
 Prevent unscheduled outages
 Detect incipient fault, Track fault evolution
 Invaluable feedback to designer
Thereby, use HV power equipment efficiently

Monitoring and Diagnostics
 Monitoring
 Desirable qualities: On-line, On-site, Non-
destructive, Non-invasive
 Data acquisition and Noise suppression
 Includes sensor development
 Diagnostics
 Interpretation of monitored data
 Provide corrective/preventive action
 Strong mathematical basis

Insulation system Winding and Core
 Dissolved gas analysis
 Partial Discharge
 Top oil temperature
 Degree of polymerization
 Furan analysis
 Recovery voltage
 Insulation resistance
 Capacitance and tan
 IR Imaging, FO sensors
 Reactance
 Low voltage
impulse test
 HV dielectric test
and Transfer
function
 FRA/SFRA
DTCM methods for Transformers

Why Measure FRA?
 Functionally relates input and output
 Thus, allowing mathematical modeling
 FRA is very sensitive to changes in
the winding geometry
 Whenever L&C distribution is altered,
it leads to a deviation in FRA
 FRA mismatch IMPLIES winding damage
 FRA data contains hidden info about
fault, its location, etc….

 Cumulative effect of exposure to
abnormal conditions creates weak-
spots, incipient faults,…
 Weak-spot eventually leads to failure
 But, weak-spots are not immediately
found or perceivable
 Goal: Find such weak-spots by FRA

FRA: Longstanding Issues
 In existence for more than 25 years
 Is still a Monitoring Tool ONLY!!
 WHY?
 Lack of rigorous analysis
 Underlying phenomenon is intricate
 Capturing complex correlations between
FRA deviation and damage remains elusive
 A Cause-and-Effect rule for different faults,
based on indices, is difficult to generalize
HV Lab, Dept. of Electrical Engineering, IIScAugust 30, 2016

 An engineer expects FRA to provide
info on fault location, severity, etc.,
so that corrective action, if needed,
can be determined and initiated.
 On this count, sadly, FRA has failed
as a diagnostic
FRA: Longstanding Issues

FR Analysis Zones
Core and Magnetic Circuit (Low Freq)
•Freq < 10 kHz
Winding Geometry (Mid Freq)
•10 kHz < Freq < 600-800 kHz
Inter - Connections and Test System (High Freq)
•Freq > 1MHz
FRA Interpretation- Current Practice

International Standards and Status
 Stds recognize its inherent potential
 So, FRA is treated as an additional
source of valuable information
 But, NOT yet an Acceptance Test
 Guides/Stds issued by-
 IEC 60076-18 Ed. 1.0, 2012
 IEEE Std. C57.149™, 2012
 CIGRE Tech Brochure No. 342, 2008

Summary of Literature
F
R
A
1. Estd. in 1979, detect mechanical damage and establish
achievable level of sensitivity
2. Use of mathematical and statistical indices to connect
winding damage & frequency deviation. Is Not Universal!
3. Correlating a mechanical damage to an equivalent change
in ladder network
4. Rational function approximation of the measured FRA gain
and phase data
5. Synthesis of ladder-network corresponding to healthy and
faulty FRA, search/optimization and evolutionary algorithms

Ground Truth
1. No closed-form expression to
link damage location and its
severity to observed deviation
in FRA data
2. No generic method to locate
true mechanical damage in an
actual transformer winding
based on measured FRA data

Bottom-line
It appears that unless this
fundamental bottleneck is
overcome, it will be difficult to
foresee FRA attaining the status
of a true diagnostic tool.

Typical Failures: EXTREME EXAMPLES

Nominal Winding

Incipient Radial Displacement

FRA comparison: Healthy vs Faulty

The BIG QUESTION???
Given Healthy & Faulty FRA
data, is it POSSIBLE to work
BACKWARDS to Locate a
minor winding damage and
assess its severity??

 Derive expression to link change in
FRA data to change in winding L & C
 Employ this to
 Locate actual RD & AD in an actual winding
 Estimate its severity
 Given-
 Measurable inputs at terminals
 Winding data in its nominal state
HV Lab, Dept. of Electrical Engineering, IISc
Terms of Reference
August 30, 2016

Why Analytical Approach?
 Solutions are generic and applicable
to all types of uniform winding
 Removes empiricism that existed in
previous methods
 Establishes a theoretical basis for
FRA data interpretation

s
s
s
g
g
g
g
Origin of Equivalent Circuit
Core, winding and tank assembly of a transformer can be
visualized as a distributed parameter inductively coupled
ladder network of capacitances, inductances and resistors

Ladder Network Model Used
DPI
or
Z(s)
Each circuit element is DISTINCT

 For an LTI system,
DPI Peaks are the OCNFs, Troughs are the SCNFs
Choice of Network Function
 DPI was preferred to TF, as it
affords many advantages

Derivation: State Space Formulation
 Eigen values of system matrix A are
the natural frequencies of a system

 SCNFs/Zeros of DPI are eigenvalues of system matrix A,
and can be determined for a 3-section ladder network

 Substituting, system matrix A can be rewritten as
 Neglecting resistances leads to block anti-diagonal form of A

Difficulties
 Eigenvalues of A can be easily computed
when its entirely numeric
 But, when there are symbols, it is difficult,
especially, when N is large
 L, C are simple, have a systematic pattern
 Inversion destroys this, and leads to
higher-order and cross-terms
 Using A with symbols in its present form is
not suitable for an ANALYTICAL expression
 Hence, alternatives are needed….!!

Alternative- Use 1/ω2 instead of ω
 Avoid: Finding eigenvalues of A, in
its current form
 Avoid: Inversion of L and C
 Intuition: Resonance: series LC ckt
 Find: Matrix with 1/ω2 as its eigen
value, and expressible as product of
L and C matrices

 If jωsci is an eigenvalue of A, by def.
 Let,
 So, are the eigenvalues of Λ
New idea: Inverse square of SCNFs

 Matrix A is 2Nx2N, Λ is NxN
 Eigenvalues of A: ±jωsci (complex)
 Eigenvalues of Λ: -ω2
sci (real)
 But, still inversion of L and C exists
 This has to be avoided….

 It is well-known from linear algebra:

Compactly expressed as

Conjectured earlier, now proved !!!
 Eigenvalues of are
 Inversion of symbolic L, C avoided

Trace is sum of diagonal elements of
Computing it, and rearranging yields

Significance of M0i

Salient Features of Expression
 Monotonicity of M0i w.r.t index i
 M0i vs i needed for localization
 M0i can be computed for an actual
winding or estimated via FEM-based
 Generalized expression for N-sections

Analytical Expression
Therefore, for the first time, a
generalized expression
connecting SCNFs and the
parameters of a completely
inhomogeneous ladder network
having an arbitrary number of
sections has been derived.

Salient Features of the Expression
 Connects SCNFs & ladder network elements
 Valid for uniform, nonuniform & damaged wdg
 Contributions of Cg and Cs are decoupled
 Ψscnf proportional to amount of change, so is a
indicator of severity (qualitatively)
 Ψscnf contribution of lower frequency SCNFs are
more compared to the higher frequency
 Cg element contribution depends on its position
 This property is crucial in localization

Radial Displacement in Actual wdg
 RD causes significant change in Cg
alone
 The rest of distributions remain
more or less unaffected
 Minor/incipient RD can be modeled
as a change in Cg alone, viz.,

 Let,
 Then,
 Hence,
 Thus, for a M0m, knowing M0i vs i,
the location/position can be found

Experiments on an Actual Winding
 Requirements-
 Measure SCNFs before and after RD
 Measure Cg before and after RD
 Variation of M0x vs x
 Procedure-

 One healthy phase of a
discarded trfr taken
 Trfr rating-
 3-ph, 70 kVA, 2200/220 V,
25 Hz
 23 disk-pairs
 Cut out all disk-pairs
 13 identical disks pairs
selected and stacked
horizintally as shown
 FRA measurement
 Inner Dia = 240 mm
 Outer Dia = 290 mm

Experimental setup

M0x versus x

Radial Displacement: 11th disk-pair

FRA before Radial Displacement

FRA after Radial Displacement

Sample calculations

CASE-A: RD of 1 disk-pair at
different positions

CASE B: RD involving 2 disk-pairs

CASE C: Assessment of Severity
3mm

HV Lab, Dept. of Electrical Engineering, IISc
4mm
5mm
6mm

Axial Displacement

 Here, both Lii and Cg will change
 Philosophy of localization algorithm
1. Estimate changed Lii & Cg for an AD
2. Repeat step-1, for all positions of AD
3. Use equation and measurement to
locate AD and estimate its severity
Axial Displacement

Estimation of new L
Disk-1
Disk-2
Disk-3
Disk-4
Disk-5
Disk-6

Inductance change for Disk-1
D1 D2 D3 D4 D5 D6

Estimation of new L
 The new inductance matrix can
be estimated, for a given AD
location, if the quantum of
displacement can somehow be
worked out first.
 Three steps are involved-

Estimation of new L and new Cg
1.
2.
3.

Proposed Method- Steps
Measure before & after AD
For each AD location, find new L & C,
For each, compute
Plot versus ‘x’
Find ‘x’ corresponding to
1.
2.
3.
4.
5.
6.

Sample results: AD @ D-7 and D-8

8 7 6 5 4 3 2 1

Assessment of Severity of AD

Summary …
 Analytical expression derived to connect
radial/axial displacement and change in
natural frequencies
 Localization of actual radial and axial
displacement successfully demonstrated!!
 Assessment of severity is ALSO possible!!

 Takeaway- Innovative methods needed to
harness hidden information in FRA data, as
demonstrated by this work
 FR analysis is a very complex and teasingly
challenging task,
 But, solutions do exist and can be found!!

 Thanks for your kind attention
 Questions Please… ?

Frequency Response Analysis by Prof Satish IISc

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