FEM1

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Insulation Design

Using

FEM Analysis

S V Kulkarni ([email protected])

Professor, Department of Electrical Engineering

Indian Institute of Technology Bombay, INDIA

IIT Bombay

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Need for Field Computation

Computation of fields is required in all low frequency and high frequency devices for:

Evaluation and improvement of performance parameters at the

design stage

Reliability enhancement

Investigative analysis

Field computation provides a non-destructive technique for testing and evaluation

In order to optimise material costs, in the present-day highly global market, an accurate analysis of the field distribution is essential

Prof. S.V. Kulkarni, EE Dept, IIT Bombay

IIT Bombay

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Methods for Computation of Fields

Analytical Methods:

Separation of Variables

Method of Images

Conformal Mapping

Schwartz-Christoffel Transformation

Analog Methods:

Conducting Paper and Electrolytic Tank Analysis

Disadvantages:

These methods cannot be applied for:

Complex Geometries

Non-uniformities, anisotropy and non-linearity in material properties


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Numerical Methods

Tremendous advances in the computational domain and improvements in algorithmic techniques have contributed to the success of numerical techniques

Analytical– Closed form solutions are

possible

– If solutions are available, they are exact

– Dependence of the field on various factors can be easily determined

– Applicable to 1-D and some 2-D problems

Numerical– Any complex geometry can be

handled

– Can be applied to even 3-D problems

– Non-uniformities, material discontinuities and material anisotropies can be taken into account

– Applicable for a wide range of problems

– The solutions are reasonably accurate for engineering purposes


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Numerical Techniques

Difference methods:

Finite difference method (FDM)

Finite-difference time-domain method (FDTD)

Variational / Weighted residual approach:

Finite element method (FEM)

Integral methods:

Method of moments (MoM)

Boundary element method (BEM)

Charge simulation method (CSM)

Other methods:

Reluctance network or magnetic equivalent circuit method (MEC)


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Numerical Methods

Boundary element method (BEM), charge simulation method (CSM) and method of moments (MoM):

The operator, in these cases, is an integral one

These methods are mathematically more intensive and lead to a

fully populated system matrix

However, in many cases, there is a reduction in the order of

magnitude of the problem

For example, in BEM, solution in a 3-D domain reduces to solving on

2-D boundaries. Similarly, a 2-D problem reduces to solution on a 1-

D domain.


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Illustration of BEM and CSM

Ω Γ

BEM: Reduction of Order from 2-D to 1-D

CSM: 11 Charges inside the conductor; 6 Potential

points on the conductor and 5 on the ground plane


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Finite Element Method

The method of finite element analysis has emerged as the forerunner among all the numerical techniques

Advantages:

The solution formulation is independent of the problem’s

geometrical complexity

Anisotropic, non-uniform and non-linear media can be

incorporated into the solution scheme

Availability of several commercial softwares makes applicability

to real-life problems easier

Finite element method can also be used in solving problems

involving coupling of electromagnetic fields with circuits and/or

other physical fields


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Classification of FEM Problems On the basis of application

Static problems

Example: Insulation design, inductance computation in electrical machines

Time-harmonic problems

Example: Computation of eddy current losses in conducting regions of electrical machines

Transient problems

Example: Analysis of dynamic behavior of machines under transient conditions

On the basis of material property

Linear problems

Non-linear problems


Insulation design in most of the cases can be classified as quasi-static linear problem

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Steps in FEM

1. Creation of geometry

2. Solution approximation (choice of type of finite element)

3. Meshing, definition of materials

4. Calculation of element coefficient matrices

5. Formation of global coefficient matrix

6. Imposition of boundary conditions

7. Solution of linear system of equations

8. Post-processing (getting desired performance parameters

from the obtained field solution)

Steps 4 & 5 are done internally by commercial FEM softwares


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Steps in FEM

For a typical 2-D insulation design problem, the governing partial differential equation is:

2 2

2 2

u u

x y

ρε

∂ ∂+ = −

∂ ∂

FEM discretization leads to the matrix equation:

[ ] K U = b

where, K is the global coefficient matrix and contains the geometry and material information, b is the force vector, which incorporates the boundary information / charge distribution, and U is the vector of unknown potentials

The solution obtained corresponds to minimum energy of the system


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Steps in FEM

The linear system of equations obtained is solved by direct or iterative methods


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Steps in FEM: An IllustrationPost-Processing:

Finally, the results obtained from the solution of the problem can be used for computing various useful quantities of interest in the electrical apparatus, such as,

o Voltage stress (electric field intensity)

o Eddy current losses

o Temperature rise

o Forces or torques

o Deformations

In insulation design application, we can calculate maximum stress, creep stress, stressed oil volume, cumulative stress values, etc.


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Insulation Design in Transformers

As voltage rating increases, insulation design becomes the most important aspect of transformer design

Comprehensive design verification is essential for reliability and optimization

Pressure on designers to reduce material content of which insulation is a major component

Margins between withstand levels and working stress levels are reducing

It is important to accurately estimate stress levels for various critical electrode configurations inside the transformer


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Factors Affecting Insulation Strength

Moisture and impurities

Temperature

Time and frequency parameters of high voltage surge

Thickness of insulation

Quality of insulation components

Quality of insulation processing / drying


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High Voltage Phenomena

Jump / bulk-oil breakdown

Creepage breakdown

Partial discharge

Corona

Withstand Theories

Stressed area / stressed volume theory

Cumulative stress computation


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Major insulation:

- Insulation between windings

- Insulation between winding and core (limb/yoke)

- Insulation between outer winding and tank

- Insulation between high voltage leads and earthed parts

Minor insulation :

- Insulation between turns / discs

Four types of tests :

- Lightning impulse test

- Switching impulse test

- Short duration power frequency test

- Long duration power frequency test with PD

measurement


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Conversion of test levels to one equivalent test level: generally

taken as short duration one-minute power frequency test

~ 1.25Long duration power frequency level

~ 0.55Switching impulse level

~ 0.44Lightning impulse level

Multiplication factorTest type

References:

1. Dahinden, V., Schultz, K., and Kuchler, A. “Function of solid insulation in transformers,” TRANSFORM 98, April 1998, Germany, pp. 41-54.

2. V. K. Lakhiani and S. V. Kulkarni, “Insulation design of EHV transformers – a review,” International Insulation Conference, INSUCON 2002, Berlin, Germany, 18-20 June, 2002, pp. 283-287.

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• Sub-division of oil ducts increases kV/mm withstand stress

• Propagation of discharge streamer in oil is countered

• Electric stress is inversely proportional to permittivity

- Barriers should be as thin as mechanically possible, otherwise

there will be more stress in oil

• First duct should be as small as possible with due considerations to

adequate cooling requirements

LV HV

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FEM Analysis of Hi-Lo Gap

• Accurate representation of

conductor with its paper covering is

essential

• Mostly 2-D FEM analysis is done

• Winding diameter effect should

be accounted separately if x-y

system is used


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• It is important to know contribution and significance of various

factors affecting stress levels

• It is essential to do a detailed FEM analysis while doing optimization

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(Reference: D. A. Koppikar, S. V. Kulkarni, A. K. Dubey, "Optimization of EHV

Transformer Insulation by Statistical Analysis", ISH'97, International Symposium

on High Voltage Engineering, Montreal, 25 - 29 August 1997, Vol. 6, pp. 289-292)

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Optimization through Design of Experiments + FEM approach


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End insulation Design

• Oil ducts should be designed so that

margin in each of the resulting oil ducts

is approximately same

• Use of contoured angle rings along

equipotential lines is required to

minimize creep stress (refer page 357,

Fig. 8.18 of the book: S.V. Kulkarni and

S.A. Khaparde - Transformer

engineering: design and practice -

Marcel Dekker, New York, May 2004)

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• Select a contour as shown

in the earlier figure

• Find cumulative stress

values in each oil duct and

compare them with the

reference withstand

equation:

kV/cm38.0

175−

= dEoil

References:

1. Nelson, J. K. “An assessment of physical basis for the application of design criteria for dielectric

structures,” IEEE Transactions on Electrical Insulation, Vol. 24, No. 5, October 1989, pp. 835-847)

2. Kulkarni, S. V. and Khaparde, S. A. - Transformer engineering: design and practice - Marcel

Dekker, Taylor and Francis Group, New York, May 2004

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Higher end

insulation

Optimized end insulation

- Angle ring in first duct

- Angle ring with higher

corner radius

Reduced end insulation with same

margin

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IIT Bombay Cumulative creep stress calculation

(Reference: Nelson, J. K. “Some steps toward automation of the design of composite dielectric structures,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 1, No. 4, August 1994, pp. 663-671)

(i) Note down the voltage values along the pressboard at the different points

(e.g., at every 1 or 2 mm steps).

(ii) Note down the highest stress point, i.e., the point along the pressboard at

which the stress is highest.

(iii) Determine on which side of the highest stress point the field is higher and

extend the path by one spatial step in that direction.

(iv) Find out the cumulative stress when the path is extended in either direction

and choose a path extension in the direction yielding the higher cumulative

stress.

(v) Repeat the above step number (iv) until the complete creepage path along

the angle ring is encompassed.

(vi) Withstand for each of these creepage distances is calculated by,

kV/mm

Reference: Derler, F., Kirch, H. J., Krause, C., and Schneider, E. “Development of a

design method for insulating structures exposed to electric stress in long oil gaps

and along oil / transformerboard surfaces,” International Symposium on High

Voltage Engineering, ISH'91, Dresden, Germany, August 1991

37.0

215−

∗= dEcr

25Prof. S.V. Kulkarni, EE Dept, IIT Bombay

IIT Bombay

High voltage lead clearances

- Oil and paper stresses can be calculated by analytical formulae or

FEM analysis

- Stressed oil volume (between max. stress and 90% of max. stress) is

calculated by approximate formula

lr

SOV18

2π=

(Kawaguchi, Y., Murata, H., and Ikeda, M. “Breakdown of transformer oil,” IEEE Transactions

on Power Apparatus and Systems, Vol. PAS-91, January-February 1972, pp. 09-19)

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-The 50 % power frequency breakdown probability stress is determined by

kV/mm

where SOV is in cm3

( ) 5.25.11 5.91

50 +=−

SOVE

- The safe withstand value is considerably lower than E50 value

- Different manufacturers will generally have different safety margins

- Barriers are generally put between lead and earth, close to lead. Extra

advantage due to barrier should not be considered if they are not along

equipotential lines; in such cases, in fact, barriers could be counterproductive

- When there are rows of tap leads, due to wall effect, stress is lower as

compared to isolated lead

Reference: Ikeda, M., Teranishi, T., Honda, M., and Yanari, T. “Breakdown

characteristics of moving transformer oil,” IEEE Transaction on Power Apparatus

and Systems, Vol. PAS-100, No. 2, February 1981, pp. 921-928.

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Conclusions

Insulation design for EHV/UHV transformers is a very challenging task

FEM technique is now widely accepted as a standard tool for insulation design

Techniques such as Design of Experiments can be used in conjunction of FEM analysis for optimization

Cumulative stress / SOV concepts are used to find withstand

Breakdown phenomenon is a statistical process and a proper value of factor of safety needs to be determined and used

Integral numerical methods are also being used for finding field distribution

3-D analysis is essential for some electrode configurations


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Thank You !

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