Applications of the Field Analysis During Design Process...

Department of Applied Electrical Engineering & Instrument TransformersTechnical University of Lodz

Applications of the Field Analysis During Design Process

of Instrument Transformers

Elzbieta LESNIEWSKA

Modern TransformersARWtr 2004 28 -30 October. Vigo – Spain http://webs.uvigo.es/arwtr04


ARWtr 2004 Lecture: APPLICATIONS OF THE FIELD ANALYSIS DURING DESIGN PROCESS OF IT by E. Lesniewska

Solution of Constructional ProblemsComputations of Electromagnetic and Magnetic Field Distributionsgives possibility of

1. Determining the Equivalent Circuit Parameters2. Choosing an Optimal Design Version3. Selection of Shields

The Field-and-Circuit Method is the most direct method of determining the Characteristics of Current Error and Phase Displacement

The Field-and-Circuit Method application also makes it possible to determine the Composite Error (the Instrument Security Factor KFS and the Accuracy Limit Factor KAF )


http://webs.uvigo.es/arwtr04/CV.htm#KRyen

http://webs.uvigo.es/arwtr04/CV.htm


Space-Time 2D analysis allows the computation of a break in the secondary circuit of a current transformer (Peak Values of the Secondary Voltage)

Joining the Field-and-Circuit Method and Space-Time Analysis permits the determination of the operation of protective current transformers during transient state(Instantaneous Error Current vs. Time )






1. Choosing the Design Version of an Insulation Systemof HV or Medium Voltage Instrument Transformers

2. Improvement of the Electric Strength of an Insulation System of HV or Medium Voltage Instrument Transformers

3. Selection of Electric Shields4. Design of an Insulation System with Capacitance

Control 5. Design of an Insulation System of the HV Combined

Instrument Transformers

Computation of Electric Fields Distributions gives the possibility of

Application of the Field Method permits the determination of thecoupling parameters of combined instrument transformer

(Mutual Reactance MUI and Mutual Capacitance CUI )(Inner Electromagnetic Compatibility)






In regions with currents of known and externally forced distribution, the harmonic electromagnetic field may be described, using the magnetic vector potential A (B = ∇×A), by an equation of Helmholtz type

with Neuman's and Dirichlet's boundary conditions.

wJAAA =j12 µ−ωµγ−×∇×⎟⎟⎠

⎞⎜⎜⎝

⎛µ

∇µ−∇

wzzz

zzz J)Vgradt

A()Arot(rot 1111=+

∂∂

γ+µ

Space-time 2D field-circuit analysis

A MATHEMATICAL MODEL

∫ ∫Ω Ω ∂

∂+

γ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

c c

dt

ASndi

Snu z

c

c

c

c vv2

2







Computations of Electromagnetic and Magnetic Field Distributionsgives possibility of

1. Determining the Equivalent Circuit Parameters

The Equivalent Circuits of Current and Voltage Transformers


http://webs.uvigo.es/arwtr04 http://webs.uvigo.es/arwtr04


http://webs.uvigo.es/arwtr04/home



.Magnetic flux density distribution of leakage flux of a voltage

transformer 100VA and ratio15: / 0.1: kV33

Consider this example where the value of total leakage reactance obtained based on field computation equals 0.187Ω and the value obtained by testing on a real life model is 0.190Ω.

mr z 2

2m

2 wX = L = I

ω ω dv 21=dv

21=w

V

B

0m ∫∫ ⋅⎮

⌡

⌠⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

VBHBH



http://webs.uvigo.es/arwtr04






2. Choosing an Optimal Design Version

protective coremodel 2model 1

measuring coremodel 1model 2

Distribution of magnetic flux density [T] along the axis passing through the centres of cores for both models






Distribution of magnetic flux density [T] of leakage flux at the surfaces passing through the centres of cores for two models of a current transformer 50A/5A/5Aa) model 1 b) model 2

a) b)



http://

webs.uvig

o.es/arwtr0

4

http://

webs.uvig

o.es/ar

wtr04

http://

webs.uvig

o.es/arwtr0

4

http://

webs.uvig

o.es/arwtr0

4




The best version is when the core with wound measuring winding is inside and the core with protective winding is outside, which shields the inner winding from the influence of the magnetic flux of the return conductor. Also the instrument security factor KFS is better in this version of the current transformer. The test results are a confirmation of the results of the numerical analysis.






HV current transformer 2kA/1A1- primary winding type U, 2- cores with secondary windings, 3- housing,4- paper-oil insulation, 5-oil

A-A


3. Selection of ShieldsThe aim of using shields is elimination of

influence of the magnetic flux of the return conductor








Distribution of magnetic vector potential in A-A cross-section of HV current transformer with the application of:

b) the open copper electromagnetic shield(Amax=1,7510-3Wb/m, Amin= -1,3910-3Wb/m),

a) the closed magnetic shield (Amax=1,1810-2Wb/m,

Amin= -2,4310-3Wb/m),

c) the closed steel electromagnetic shield (Amax=2,0510-3Wb/m, Amin= -2,6610-3Wb/m)




http://webs.uvigo.es/arwtr04http://webs.uvigo.es/arwtr04




Distribution of the normal component of magnetic flux density along symmetry axis inside the housing of a HV current transformer with the application of: 1- the closed magnetic shield,2- the open copper electromagnetic shield,3- the closed electromagnetic shield made of constructional steel.

Finally an open electromagnetic shield, made from copper, was applied.Because electromagnetic steel shield caused larger power losses in the housing (489.4 W/m and 112.1W/m at the open copper electromagnetic shield)







The Field-and-Circuit Method is the most direct method of determining the Characteristics of Current Error and Phase Displacement

0 20 40 60 80 100 120I/In (%)

-0.40

-0.30

-0.20

-0.10

0.00

I (%)

1

2

3

4

∆

0 20 40 60 80 100 120I/In (%)

-0.40

-0.30

-0.20

-0.10

0.00

I (%)

1

2

3

4

∆

0 20 40 60 80 100 120I/In (%)

0.00

2.00

4.00

6.00

8.00

10.00

i (min)

1

2

3

4δ

a) b)

0 20 40 60 80 100 120I/In (%)

0.00

2.00

4.00

6.00

8.00

10.00

i (min)

1

2

3

4δ

Comparison of the current error and the phase displacement characteristics of a 5A/5A current transformer fora) S=Sn =10VA, cosϕ=0.8 b) S= 2.5VA, cos ϕ =0.8obtained using: 1– the field method to determine the parameters of the equivalent circuit of the current transformer and solving a non-linear circuit, 2– the analytic method, 3 – the measurement and 4– using the field-and-circuit method.










The Field-and-Circuit Method application also makes it possible to determine the Composite Error (Instrument Security Factor KFS and the Accuracy Limit Factor KAF )

( )2 02 1

1 10

I100% 1= = 100%I I

t

ni K i dtT

ε − ⋅∫

Distribution of magnetic vector potential A in a current transformer 5A/5Aa) at rated state I1 = I1n (Amax=2,010-3Wb/m, Amin= -1,710-3Wb/m)

b) at overcurrent state with rated burden I1 = 157A (ε=10) (Amax=6,010-3Wb/m, Amin= -3,810-2Wb/m)



htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04

htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04




0 50 100 150 200

I [A]

5

15

25

35

0

10

20

30

ε [%]

1I 1N10

.

The composite error vs. the primary current of a laboratory model 5A/5A current transformer, at an overcurrent state, obtained on the basis of field-

and-circuit calculations –determining the accuracy limit factor KAFL at composite error ε=10% (I1=157A therefore KAFL=31,4)







Space-Time 2D analysis allows the computation of a break in the secondary circuit of a current transformer (Peak Values of the Secondary Voltage)

2 6 10 140 4 8 12 16

t [ms]

-0.2

0.2

0.6

-0.4

0.0

0.4

0.8

[Wb]

-250

250

750

-500

0

500

1000

u [V]Ψ 2

2u

Flux and secondary voltage vs. time, at an open secondary circuit and rated primary current, calculated for a laboratory model 5A/5A current transformer (core losses taken into account)

tdd =u2Ψ








Peak values of the secondary voltage, determined on the basis of a field analysis and calculated using approximate formulas

based on the field analysis

V V V

918.0 2412.2 1414.2

u

1+

z2s max≈⎛

⎝⎜

⎞

⎠⎟

′′1 2

2 22

1ω

µ ωµL

R

Sl

I

Fe

Fe

Fe u 2s ≈ 2 100

2

SI kl

n

n .







Joining the Field-and-Circuit Method and Space -Time Analysis permits the determination of the operation of protective current transformers during transient state (Instantaneous Error Current vs. Time )

coreprimary bar

secondary windinggap

htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04

Distribution of magnetic vector potential A of toroidal protective current transformer 600A/1A at transient state for primary currenti1=8(cos314,16t-e-20t)kA and time t=5ms





-10

0

10

20

30

40

0 0,05 0,1 0,15 0,2

Instantaneous error current vs. time of toroidal protective current

transformer 600A/1A at saturation state

Primary and secondary currents vs. time of toroidal protective current

transformer 600A/1A at saturation state1- primary current

i1=8(cos314,16t-e-20t)kA in terms of secondary winding

2-secondary current-40

-30

-20

-10

0

10

20

0 0,05 0,1 0,15 0,2

1

2








A MATHEMATICAL MODEL

The electric field in an insulation system (after introducing the scalar electric potential

E = -∇V where E is the electric field strength) is described by the Laplace's equation

∇2 V = 0

with Neuman's and Dirichlet's boundary conditions.

The boundary conditions are: values of potential (Dirichlet's), and the condition of the

tangential electric field strength (Neuman's ) at the boundary of the whole system with

the surrounding air.






1. Choosing of Design Version of an Insulation Systemof HV Voltage Transformer

Computation of Electric Fields Distributions gives possibility of

Distribution of the electric potential [V] in the insulation

system of the HV voltage transformer 110: kV/100: V 3 3








. Distribution of the electric field strength [V/mm] in the core window of HV voltage transformer

In paper-oil nearby edge

of the primary coil

In paper-oil nearby edge of the secondary

coil

In transformer oil

Area where electric field

strength exceeded 5kV/mm

8,89kV/mm 6,70kV/mm 3,17kV/mm 42,5mm2

.Maximum values of the electric field strength in paper-oil and in oil insulation in considered voltage transformer







2. Improvement of the Electric Strength of an Insulation System of a Medium Voltage Instrument Transformer


epoxide resin

trivolton

core

secondary windings

bolt

A

A

A-A voltageterminal

The constructional variant of the voltage transformer 15kV/100VEvery construction improvement is carried out in order to obtain a better device. For the voltage transformer it means achieving a greater rated power at the same accuracy class and greater electric strength at the assumption of the same external dimensions.



http://webs.uvigo.es/arwtr04 htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04




under test conditions (38kV-1 minute) under operating conditions

Distribution of electric potential [V] at the surfaces passing through the centres of the voltage transformer after redesign







.Distribution of the electric field strength [V/mm] in the area of the voltage transformer after redesign under test conditions (38kV-1 minute)

Because of the definition of the picture, the field distribution ispresented at the assumption of the upper limit 8kV/mm.







Distribution of the electric field strength [V/mm] in the area of the voltage transformer after redesign under operating conditions

Because of the definition of the picture, the field distribution ispresented at the assumption of the upper limit 3kV/mm.








HV voltage transformer 110: kV/100: V 1- core, 2-grounded shield 3- HV shield 4-foil 5-secondary coil 6-housing 7-cover

3 3

3. Selection of Electric Shields



htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04

htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04




. Distribution of electric potential [V] in insulation of HV voltage transformer when grounded shield has radius a) 190mm, b) 147mm, c) without shield


htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04

htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04

htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04





Distribution of electric potential [V] in insulation of the last design version of HV voltage transformer

Radius of grounded shield Area where electric field strength exceeded 8kV/mm

Maximum values of the electric field strength

190mm 79,6mm2 15,8kV/mm

147mm 23,3mm2 15,2kV/mm

0mm 11,4mm2 14,5kV/mm

Table III. Maximum values

of the electric field strength in

insulation of voltage

transformer


htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04






4. Design of an Insulation System with Capacitance Control Computation of Electric Fields Distributions gives possibility of

main shields

intermediate shields

FIELD DISTRIBUTIONS

SHIELDSOPERA3D

capacitance

potentialsThe commercial software OPERA3Dwas used to compute field distribution and the author’s software SHIELDSwas used to optimise the number, dimensions and position of each electrostatic control shields in the insulation. Both programs interact with each other.

∫⋅

=v

e dvW2

ED2

2UWC e=


htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04





Distribution of the electric potential along the height of the ceramic insulator

of the ceramic insulator of the combined instrument transformer

with capacitance control of the current and voltage parts in the axis direction and in the radius direction

Distribution of the electric field strength [V/mm] in the insulation system



htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04










5. Design of an Insulation System of the HV Combined Instrument Transformers


Computing the electric strength of this insulation system of combined instrument transformers creates many problems. All these problems are connected and one modification in the design produces, out of necessity, other modifications. The results of mutual interaction are field distributions in the whole insulation system of the combined instrument transformer computed for the final version of design.





of the casing with cores

Distribution of the electric field strength [V/mm] in the insulation systemof the current part of the combined transformer

of the pipe with the endings of the secondary windings in the place where the shields begin








of the HV voltage coil

Distribution of the electric field strength [V/mm] in the insulation systemof the voltage part of the combined transformer

of the of lead conductor of HV coil in the place where the shields begin

The designed prototype of the combined transformer successfully passed all HV tests.




htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04




Application of the Field Method permits the determination of thecoupling parameters (Mutual Reactance MUI and Mutual Capacitance CUI (Inner Electromagnetic Compatibility)

Circuit model of couplings in a combined transformer

Where: CUI - mutual capacitance (coupled by the electric field), MUI -mutual reactance (coupled by the electromagnetic field), ZU, ZI- the burdens of the secondary windings of the voltage and current transformer

UI 22 eW

CU

= IUm UI

ψX = ωM = ω 2 I


htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04





The location of the endings of the secondary windings of the current transformer nearby the voltage transformer core in the bottom part of the housing



htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04

http://webs.uvigo.es/arw

tr04





Distribution of the magnetic flux density [T] in the core of voltage part of the combined instrument transformer caused by secondary currents of the current parts.







Distribution of the electric field strength [V/mm] in the area of the ceramic insulator, where the electric shields end


htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04





The variation of current error

±εi

The variation of voltage error

±ε v

results of computing 0.033 % 0.004%

test results 0.034% 0.02%

Prevention of possible couplings before making the prototype is simpler and less expensive than the elimination of interference during the operation of individual instrument transformers caused by placing them in the same case.

The mutual inductance MIU and the mutual capacitance CUI are very small for the final construction of the combined instrument transformer after limited mutual influences and equal to 0.12µH and 1.95pF respectively.







Analysis of physical field distribution using accurate numerical methods gives wide possibilities especially for constructors of precision electrical devices, which require very high accuracy. By applying the field method, the constructor is able to predict all steady state and transient parameters of the designed device before making a real life prototype. In the case of instrument transformers, it is very important to accurately compute the field distribution.

The tests on the real-life model are very expensive so it is vitally important to carry out careful experimentation using computer software first to perfect the design prior to building and testing real-life models.






HV Combined Instrument Transformer

HV SF6 Voltage Transformer

Medium Voltage Voltage Transformer


htt

p:/

/web

s.uvi

go.e

s/ar

wtr

04









Date post:	06-Mar-2018
Category:	Documents
Upload:	lyhuong
View:	215 times
Download:	2 times

Applications of the Field Analysis During Design Process...

Documents