Minimization of Electrical Field in Stator Slot Groundwall Insulation of HV Generators

International Journal of Advanced Computer Science, Vol. 2, No. 11, Pp. 435-440, Nov., 2012.

Manuscript Received:

30,Jan., 2012

Revised:

15,Jun., 2012

Accepted:

19,Aug., 2012

Published: 15,Dec., 2012

Keywords

Electrical,

Generator,

Insulation,

Slot,

Stator,

Abstract It should be noted that most

important part of an electrical machine is the

Stator insulation. This fact reveals the

requirement for inspection of the electrical

machine insulation along with the electrical

tensions. Therefore with respect to insulation

system improvement of stator, the HV

generator can be optimized. Electrical

conductivity of groundwall insulation is

major design consideration for insulation

system of HV generator. A very powerful

method available to analyze electromagnetic

performance is Finite Element Method

(FEM) which is used in this paper. These

processes of optimization have been done

according the proposed optimization

algorithm. In this algorithm the technical

constraints have been considered. This paper

describes the process used to perform

classical design and improvement analysis of

stator slot’s insulation with respect to

objective function and constraints.

1. Introduction

Stator winding insulation is one of the most critical

components for reliable operation of ac electric machines of

all types and sizes. Since the stator insulation is

continuously exposed to an electrical stress, gradual

degradation of the insulation is inevitable [1]. Industrial

researches show that troubles initiated in the stator winding

insulation are one of the primary root causes of electric

machine failures [2, 3 and 4]. It is shown in [5, 6] that

30-40 % of ac machine failures are stator related and also

shown in [7] that 60-70 % high voltage machine failures result from stator insulation troubles. The winding and core

of stator integrity plays essential role in the reliability of the

alternator [8-12].

The electrical insulation system of high voltage

rotating machines is one of the most important parts with

respect to the manufacturing costs as well as to the

maintenance and life time aspects [13]. Almost one-third of

This work was supported by the Iran University of Science and

Technology.

Diako Azizi is with the University of Science and Technology, Tehran,

Iran (corresponding author to provide phone: +989128195358; e-mail:

[email protected]).

Dr. Ahmad Gholami is with University of Science and Technology,

Tehran, Iran. He is now with the Department of electrical engineering,

(e-mail:[email protected]).

the forced outages of large generators in generating stations

and industrial plants are caused by the failure of the

insulation system in the stator winding [14]. The stator

insulation system of generators consists of groundwall

insulation, phase-phase insulation as well as turn and the

strand insulation. The groundwall insulation is the main

insulation that separates the high voltage copper conductors from the grounded stator core, and the turn or strand

insulation prevents shorts between the turns or the strands in

a coil. Modern machines use mica flake or mica paper tapes

bonded with epoxy or polyester resin as groundwall

insulation [13, 15].

Thus, performing the optimal design consist of

electromagnetic study in core, winding and insulation of

stator slots is necessary. To attain an improved design,

electromagnetic analysis with observe to real condition is

performed which completes pervious researches.

The reason of applying the method is investigating the effects of electrical and magnetically stresses on insulation

parts. The main idea involves finding the optimum electrical

conductivity of stator slot’s groundwall insulation in order

to minimize the electrical stress. FEM analysis is used to

simulate the performance of generator. The main

supremacies of the simulations in comparison with other

researchers are:

• Simulating ordinary rotation of rotor.

• Considering magnetic saturation of core.

• Considering of technical constraints.

• Considering core losses.

• Considering insulation losses.

• Considering copper losses.

• Considering ambient conditions.

According to this method, electrical conductivity of

stator slot groundwall insulation is optimized to investigate

the possibility of improvement high voltage generator

characteristics.

2. Case study

To study a sample, it is required to determine or design

the sample first. Therefore, in order to do field analysis and

to study the generator insulation Status, a generator with a given profile has been selected. The selected generator is

synchronous, three phase, 4 poles that have 24 slots in

stator. Rated frequency, voltage and power are respectively

50Hz, 13.8 kV and 10 MVA. Wiring in this study is

form-wound multiturn type and has many layers insulation

with different specification (Fig. 1). In this study turn

Minimization of Electrical Field in Stator Slot

Groundwall Insulation of HV Generators Diako Azizi & Ahmad Gholami


International Journal Publishers Group (IJPG) ©

436

insulation and the strand insulation are the same, i.e. nylon

type. Ground wall insulation type is PMMA and semi

conductive coating is Si(c) with characters identified in

table 1.

Fig. 1 Cross sections of stator slot insulation layers for form-wound

multiturn coils in selected HV generator

TABLE 1

ELECTRICAL AND THERMAL CHARACTERISTICS OF INSULATION LAYERS

Quantities Insulation layers

Nylon PMMA Si(c)

heat capacity [J/(kg*K)]

1700 1420 700

young’s modulus [Pa]

2e9 3e9 170e9

Thermal expansion coeff. [1/K]

280e-6 70e-6 2.6e-6

relative permittivity

4

3

11.7

thermal conductivity [W/(m*K)]

0.26 0.19 130

Density [kg/m^3]

1150

1190

2329

Electrical conductivity

[S] 0 0 0

3. Electromagnetic model

Ampere’s law is the main part to derive

electromagnetic system equation [13].

t

DJBvE

t

DJH e

(1)

Where:

E is the electric field intensity

D is the electric displacement or electric flux

density

H is the magnetic field intensity

B is the magnetic flux density

J is the current density

Je is the externally generated current

σ is the electrical conductivity

v is the velocity

Time variant-harmonic field’s effect can be introduced

by equations (2) and (3):

AB (2)

t

AVE

(3) Ampere’s law is rewritten by equations (2) and (3)

Combining with constitutive relationships B=μ0(H+M) and

D=ε0E+P , as:

PjJVjAv

MAAj

e

0

1

00

2

(4)

In which ω, ε0, μ0, M and P respectively refer to

Angular frequency, Relative permittivity, Relative

permeability, magnetization vector and electric polarization

vector.

In the case of 2-dimensional-plane, there are no

variations in z-direction, so the electric field is parallel to

z-axis. , therefore is written as −ΔV/L, where ΔV is the potential difference over the distance L. Now these

equations are simplified to:

z

e

z

zz

x

y

z

PjJL

V

AjAvM

MA

0

21

0 ..

(5)

In the ax-symmetric case, another form of the electric

potential gradient has been used (

) as the

electric field is only present in the azimuthally direction.

The above equation, in cylindrical coordinates, becomes:

PjJr

V

uVujr

zu

ru

vr

M

Mu

z

zu

ru

rzr

eloop

r

r

z

2

2.

0.

0

2

1

0

1

0

(6) The dependent variable u is the nonzero component of

the magnetic potential divided by the radial coordinate r, so

that:

rA

u (7)

The application mode performs this transformation to

avoid singularities on the symmetry axis.

Diako Azizi et al.: Minimization of Electrical Field in Stator Slot Groundwall Insulation of HV Generators.


437

4. Optimization algorithm

The optimization algorithm in this paper builds on the

proven SNOPT package developed by Prof. Philip Gill

(University of California, San Diego) along with Profs.

Walter Murray and Michael Saunders (Stanford University).

SNOPT is a general-purpose system for large-scale

nonlinearly constrained optimization. The optimization section builds on a flexible data

structure, the opt structure, which contains the entire

optimization problem within a single variable. The main

optimization function, selects the proper solver algorithm

depending on properties of the objective function and the

constraints. Linearity, for example, allows it to take

appropriate shortcuts.

For optimization involving fields of physics and

geometric properties, such as shape optimization, it can be

connected the optimization section to FEM to perform

optimization on a finite element model. Numerical optimization can be described as the art of

finding an optimum set of parameters or

optimization-variable values that minimize an objective

function subject to a number of constraints. The objective

function (also known under different names such as goal

function, cost function, or quantity of interest) can be an

explicit function of the optimization variables, or which is a

more interesting case an output quantity from a simulation

parameterized by the optimization variables.

While the optimization application mode can indeed

solve classical pure optimization problems, its real strength

is its ability to compute accurate gradients also when the objective function and constraints depend on the solution to

a multi physics model. This enables the use of an efficient

gradient-based optimization algorithm, reducing the number

of multi physics model evaluations required to find an

optimal solution.

To define and solve a complete optimization problem,

it will be needed to perform four tasks. In addition to those

that apply when solving a standard PDE problem:

•Define a scalar objective function

•Select optimization variables

•Set additional constraints •Compute optimal values of the optimization variables

The optimization application mode provides an

interface for handling all four tasks.

The optimization application mode is built around a

general minimization problem formulation, where it will be

supplied an objective function to be minimized and

constraints on the optimization variables. On top of this, the

complete multi physics model and its constraints serve as an

additional condition on the optimization problem. For this

reason, the procedure is sometimes referred to as

PDE-constrained optimization. After it have been set up a complete optimization

model, the goal of the optimization process can be stated

roughly as “find the values of the optimization variables

that minimize the objective function under the condition

that u is a solution to the multi physics model and no

constraints are violated. More formally, this can be stated as

follows:

(8)

The objective function Q(u, ξ) is a function of the

optimization variables ξ ≡ { ξ i } both directly and indirectly

through u, which is the solution to the general multi physics

problem L(u, ξ) = 0. The objective function is defined as the

sum of integral contributions from all dimensions k in the

d-dimensional multi physics model. The optimization

procedure is presented in the Fig. 2.

Fig. 2 Flow chart of the optimization procedure

5. Simulation and results

Fig. 3 shows the primary generator. Fig. 4 shows this

structure at zoomed view. Voltage distribution along the

one of the stator slots for this 3 phase synchronous generator that has 24 slots in stator and 2 winding layers in

each slot has been presented at Fig. 5. Optimized electrical

conductivity for groundwall insulation layer has been

showed at Fig. 6. Electrical potential distribution for

optimized sketch at groundwall insulation layer has been

presented in Fig. 7. The optimization procedure leads to



438

plan which corresponding electrical field distribution

presented in Fig. 8. It can be seen that electrical field

distribution in groundwall insulation has been improved a

lot.

Fig. 3 Primary generator

Fig. 4 Typical stator slot of generator

Fig. 5 Electrical field distribution for primary sketch

Fig. 6 Optimized electrical conductivity for groundwall insulation layer

Diako Azizi et al.: Minimization of Electrical Field in Stator Slot Groundwall Insulation of HV Generators.


439

Fig. 7 Electrical potential distribution at groundwall insulation layer for

optimized sketch

Fig. 8 Electrical field distribution at groundwall insulation layer for

optimized sketch

6. Conclusion

Selection of proper insulation materials in several

layers of stator winding can decrease these stresses.

Different schemes with regard to different construction have different characters and specification. The SNOPT

optimization algorithms with respect to finite element

electromagnetic analyses are useful to improve the

insulation system of generator which conquests the previous

problems in classical design. In this paper, according to

optimization algorithm, optimized groundwall insulation

presented. According to optimized plan, maximum value of

electrical field decreases and electrical field distribution

becomes more uniform along the groundwall insulation

layer in stator slots compared to the primary mode. It should

be noted that additional costs due these changes in

insulation structure are negligible for manufactures.

References

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[3] Muhammad Arshad, Abdul Khaliq and Syed M. Islam, “Turbo generator stator winding condition assessment”,2004 international conference on power system technology, POWERCON 2004, Singapore, 21-24 November 2004.

[4] Sang Bin Lee, Jinkyu Yang, Karim Younsi and Raj Mohan

Bharadwaj, ‘‘An On-Line groundwall and phase to phase insulation quality assessment technique for AC machine stator winding,’’ IEEE Transactions on Industry Application, vol. 42 no.4, July/August 2006.

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235-238, 1996. [15] G.C. Stone, B.K. Gupta, J.F. Lyles and H.G. Sedding,

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Diako Azizi was born in 1985. He has received B.Sc. degree in Electrical Engineering from Tabriz University, Tabriz, Iran in 2007. And he received the Master degree in Electrical Power Engineering from the University of Science and Technology, Tehran, Iran in 2009. He is presently pursuing the Ph.D.

degree in Electrical Power Engineering, Iran University of Science and

Technology. His research interests are aging of insulations in electrical machines.

Ahmad Gholami has received his B.Sc. Degree in electrical engineering from IUST, Tehran, Iran, in 1975, the M.Sc.

and PhD. Degrees in electrical engineerin from UMIST, Manchester, England, in 1986 and 1989 respectively. He is currently an associate professor in the Electrical Engineering Department of Iran University of Science and

Technology. His main research activities are high voltage engineering, electrical insulation, insulation coordination,

transmission lines and substations planning.

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Minimization of Electrical Field in Stator Slot Groundwall Insulation of HV Generators