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, 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


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


http://www.iec.ch/dyn/www/f?p=103:38:0::::FSP_ORG_ID,FSP_APEX_PAGE,FSP_LANG_ID,FSP_PROJECT:1224,23,25,IEC 60076-18 Ed. 1.0

http://www.iec.ch/dyn/www/f?p=103:38:0::::FSP_ORG_ID,FSP_APEX_PAGE,FSP_LANG_ID,FSP_PROJECT:1224,23,25,IEC 60076-18 Ed. 1.0

Summary of Literature


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


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: -ω2sci (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


Nominal Winding


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

Nominal Winding


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… ?
