Frequency Response Analysis by Prof Satish IISc
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Transcript of 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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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, IISc August 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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
FRA: Longstanding Issues
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
HV Lab, Dept. of Electrical Engineering, IISc August 30, 2016
Summary of Literature
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
FRA
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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.
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
The BIG QUESTION???
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
HV Lab, Dept. of Electrical Engineering, IISc August 30, 2016
Ladder Network Model Used
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
DPI or
Z(s)
Each circuit element is DISTINCT
For an LTI system, DPI Peaks are the OCNFs, Troughs are the SCNFs
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
SCNFs/Zeros of DPI are eigenvalues of system matrix A, and can be determined for a 3-section ladder network
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Derivation: State Space Formulation
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Derivation: State Space Formulation
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….!!
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
New idea: Inverse square of SCNFs
Matrix A is 2Nx2N, Λ is NxN
Eigenvalues of A: ±jωsci (complex)
Eigenvalues of Λ: -ω2sci (real)
But, still inversion of L and C exists
This has to be avoided….
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
New idea: Inverse square of SCNFs
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
New idea: Inverse square of SCNFs
It is well-known from linear algebra:
Conjectured earlier, now proved !!!
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Eigenvalues of are
Inversion of symbolic L, C avoided
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Trace is sum of diagonal elements of
Computing it, and rearranging yields
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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.
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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.,
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Let,
Then,
Hence,
Thus, for a M0m, knowing M0i vs i, the location/position can be found
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Experiments on an Actual Winding
Requirements-
Measure SCNFs before and after RD
Measure Cg before and after RD
Variation of M0x vs x
Procedure-
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
CASE-A: RD of 1 disk-pair at
different positions
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Axial Displacement
Estimation of new L
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Disk-1
Disk-2
Disk-3
Disk-4
Disk-5
Disk-6
Estimation of new L
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Disk-1
Disk-2
Disk-3
Disk-4
Disk-5
Disk-6
Estimation of new L
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Disk-1
Disk-2
Disk-3
Disk-4
Disk-5
Disk-6
Inductance change for Disk-1
D1 D2 D3 D4 D5 D6
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Inductance change for Disk-1
D1 D2 D3 D4 D5 D6
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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-
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
Estimation of new L and new Cg
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
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
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc
1.
2.
3.
4.
5.
6.
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!!
HV Lab, Dept. of Electrical Engineering, IISc August 30, 2016
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!!
August 30, 2016 HV Lab, Dept. of Electrical Engineering, IISc