high frequency model on an transformers

7/31/2019 High Frequency Model on an Transformers

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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 18, No. 2; April 2011 541

1070-9878/11/$25.00 2011 IEEE

Development of High Frequency Circuit Modelfor Oil-immersed Power Transformers and its Application

for Lightning Surge Analysis

Shigemitsu Okabe, Masanori Koto, Genyo UetaTokyo Electric Power Company

4-1, Egasaki-cho, Tsurumi-ku, Yokohama, Kanagawa, 230-8510, Japan

Toshiyuki Saida and Shin YamadaToshiba Corporation

1-1, Shibaura 1-chome, Minato-ku, Tokyo, 105-8001, Japan

ABSTRACTThe lightning impulse withstand voltage for an oil-immersed power transformer is

determined by the value of the lightning surge overvoltage generated at the

transformer terminal. This overvoltage value has been conventionally obtainedthrough lightning surge analysis using the electromagnetic transients program (EMTP),

where the transformer is often simulated by a single lumped capacitance. However,

since high frequency surge overvoltages ranging from several kHz to several MHz are

generated in an actual system, a transformer circuit model capable of simulating the

range up to this high frequency must be developed for further accurate analysis. In this

paper, a high frequency circuit model for an oil-immersed transformer was developed

and its validity was verified through comparison with the measurement results on the

model winding actually produced. Consequently, it emerged that a high frequency

model with three serially connected LC parallel circuits could adequately simulate the

impedance characteristics of the winding up to a high frequency range of several MHz.

Following lightning surge analysis for a 500 kV substation using this high frequency

model, the peak value of the waveform was evaluated as lower than that simulated by

conventional lumped capacitance even though the front rising was steeper. Thisphenomenon can be explained by the charging process of the capacitance circuit inside

the transformer. Furthermore, the waveform analyzed by each model was converted

into an equivalent standard lightning impulse waveform and the respective peak values

were compared. As a result, the peak value obtained by the lumped capacitance

simulation was evaluated as relatively higher under the present analysis conditions.

Index Terms Oil-immersed transformer, lightning surge, high frequency circuit

model, 500 kV substation, Electro-magnetic Transients Program.

1 INTRODUCTION

TO determine the lightning impulse withstand voltage for anoil-immersed power transformer, the value of the generated

overvoltage has been conventionally obtained through lightning

surge analysis using the Electro-magnetic Transients Program

(EMTP). In such cases, the transformer is often simulated by a

single lumped capacitance [1] called a surge intrusion

capacitance. However, the value to which this capacitance

should be set is not necessarily clear, nor is whether or not

surges ranging from several kHz to several MHz actually

generated can be simulated by a single capacitance.

On the other hand, amid ongoing trends, such as the

downsizing of substations and the direct connection to gas

insulated switchgears (GIS), overvoltages with frequencies

exceeding conventional ones are more likely to be generated.In addition, it is known that, with the introduction of, for

example, a winding with a large series capacitance, a

transformer itself exhibits resonance behavior at a high

frequency of around 1 MHz [2].

Under these circumstances, the development of a new

transformer model within the frequency range of lightning

surges is desirable. To precisely simulate the winding up to

the high frequency range, a detailed equivalent circuit is

required that provides the inductance and capacitance for each

turn of the conductor [3]. However, such a detailed model isManuscript received on 4 November 2010, in final form 18 January 2011.


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542 S. Okabe et al.: Development of High Frequency Circuit Model for Oil-immersed Power Transformers and its Applicationfar too complicated for the whole transformer if its purpose is

not to clarify the electric potential distribution within a

winding but to obtain the voltage generated at the transformer

terminal through surge analysis of the substation or overall

system. The authors previously proposed a relatively

simplified circuit model that could simulate a 275 kV gas

insulated shunt reactor up to the high frequency range [4].

In this paper, the above technique was applied to a 500 kV

oil-immersed transformer and a high frequency circuit model

for an oil-immersed transformer was developed, and its

validity was evaluated through comparison with the

measurement results of the actual model winding.

Subsequently, the new model was used to perform a lightning

surge analysis for a 500 kV substation. This result was

compared with the conventional case where a transformer was

simulated by an intrusion capacitance, and the level of the

lightning surge overvoltage generated at the transformer

terminal and its influence on the waveform were studied.

Furthermore, each overvoltage waveform was converted into

an equivalent standard lightning impulse waveform using the

waveform evaluation method [5] to evaluate from the

perspective of the severity for insulation.

2 CIRCUITMODELFORWINDING

As winding structures for a transformer, the present study

uses interleaved and continuous disk windings respectively,

for which circuit models are developed with the high

frequency range up to several MHz taken into consideration.

2.1 CIRCUIT MODEL FOR INTERLEAVED DISKWINDING

2.1.1 CIRCUIT MODEL IN THE LOW FREQUENCY

RANGE

An interleaved disk winding is a kind of disk winding used

for core type transformers and reactors. Since it has a large

series capacitance, it is used as a kind of lightning-surge-proof

winding mainly for high voltage winding. Figure 1 illustrates

the cross-sectional structure of an interleaved disk winding.

Two disks constitute a single structural unit, which comprise

the whole winding when collectively stacked. Assuming that

one disk is called a section, Figure 1 shows an example of a

winding with 8 turns per section. The numbers in the figure

indicate the order of winding. Assuming that the conductor of

the winding order numbers 1 to 8 is called Group A and that

of numbers 9 to 16 Group B, since the conductors of Groups

A and B lie adjacent, with potential difference equivalent to

that of the number of turns per section, the equivalent seriescapacitance of the winding is eventually large. The series

capacitance of an interleaved disk winding can be obtained

using what is called the stored energy method and given by

equation (1) [6]:

2)(n2

CC

r0 (1)

Cr: Turn-to-turn capacitance

n: Number of turns per section

In this equation, each turn within the two sections is

assumed to form a linear potential distribution, the

electrostatic energy stored between individual turns is totaled

and capacitance with electrostatic energy equal to this totaled

energy is regarded as the series capacitance C0 for two

sections. The value of n is about 5 to 30, while it varies

depending on the capacity and voltage class of the transformer.

Compared with the series capacitance of a continuous disk

winding expressed by equation (8), which is described later,the series capacitance of an interleaved disk winding is

generally larger by approximately one digit.

Figure 2 presents the equivalent circuit for two sections of

an interleaved disk winding. Each turn is expressed by one

inductance element in Figure 2a, while two sections are

simulated by one inductance element in Figure 2b. The circuit

model for an interleaved disk winding that holds in the low

frequency range can be obtained if C0 in equation (1) is given

as the capacitance for two sections in Figure 2b to structure

the circuit of the whole winding. Here, L0 is the self-

inductance of the whole coil with 2n turns, which is about

(2n)2 times the value of the inductance per turn.

2.1.2 CIRCUIT MODEL WITH RANGES UP TO THE

HIGH FREQUENCY RANGE TAKEN INTO

CONSIDERATION

If the wavefront duration of the waveform applied to the

winding is shorter than the charging time (approximately 0.2

s to 0.5 s) for the turn-to-turn capacitance, the potential at

each turn within the section does not form a linear distribution.

Consequently, the capacitance in equation (1) obtained by the

stored energy method alone cannot obtain a circuit model

applicable to the high frequency range of several MHz.

In the circuit in Figure 2a, the capacitance seen from both

ends of the two sections at a high frequency (e.g. 10 MHz or

: Group A

: Group B

12

168157146135

192103114

Figure 1. Construction of an interleaved disk winding.

Figure 2. Equivalent circuit of an interleaved disk winding.

(a) Detailed circuit (b) Simplified circuit

L0 C0

CrCa/nEquipotential surface

between sections

Correspondingto the numberof the order ofwinding in Figure 1

Ca: Section-to-section capacitance

(1)(2)(3)(4)

(5) (6) (7) (8)

(9)(10)(11)(12)

(13) (14) (15) (16)


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more), where the inductance is negligible, is smaller than C0

obtained by equation (1). In this process of the change in

capacitance, a resonance phenomenon is observed within

section [2].

Pedersen assumed each section of an interleaved disk

winding to be a spirally wound parallel plane capacitor and

considered that the winding responded to steep front waves

like a transmission line of capacitance C and inductance L per

section [7]. Here, C is given by equation (2) because it

indicates the capacitance between conductors in Groups A and

B in Figure 1 and the number of locations where conductors

face each other is (n1) per section.

d/Db)1n(C 0 (2)

: Relative permittivity of the turn-to-turn insulation

0: Vacuum permittivity

D: Average winding diameter

b: Axial conductor width

d: Turn-to-turn insulation thickness

The value L is given by the inductance of the parallel

conductors consisting of the conductors in Groups A and B

and obtained in a simplified manner by equation (3) because

the length of the parallel conductor in one section is

equivalent to n/2 turns.

b/Dd)2/n(L 0 (3)

0: Vacuum magnetic permeability

Assuming that surges reflect at the point connected to the

next section on the inner periphery side of the section and thatthe oscillation is generated with the time of the round trip in

the section as their period, the oscillation period is given by

equation (4).

)n

11(

2nD2LC2T 00

(4)

In order to express an oscillation circuit of resonance

frequency f1 identical to this oscillation using the LC parallel

circuit with a lumped constant, its inductance L1 and

capacitance C1 can be replaced to equation (6) based on

equation (5).

11

1

CL2

1

LC2

1f

(5)

/CC,/LL 11 (6)

Consequently, the circuit displayed in Figure 3a was

devised in order to simulate, via a simplified circuit, the fact

that the value of the equivalent series capacitance of the

interleaved disk winding given by Figure 2b is small in the

high frequency range and that the resonance point is within

the section in the high frequency range. The L1C1 parallel

circuit, consisting of the inductance and capacitance obtained

by equation (6), is serially connected to the capacitance

branch of the L0C0 parallel circuit in Figure 2b. This circuit

has a parallel resonance point at frequency f1. At higher

frequencies, it is eventually expressed by the serially

connected capacitance with C0 and C1. If C1 is adequately

smaller than C0, the capacitance is almost determined by C1.

As subsequently described in Clause 3.2, since L1 is

adequately smaller than the inductance L0, which is for two

sections, the impedance characteristics of the circuit barely

changes, even if the L1C1 parallel circuit is serially connected

directly to the L0C0 parallel circuit in Figure 2b. Furthermore,

the oscillation caused by multiple reflections in the section

includes not only the fundamental oscillation frequency given

by equation (5) but also the higher order resonance

frequencies at its integral multiple frequencies. To simulate

higher order resonance frequencies up to the second order, the

L2C2 parallel circuit given by equation (7) is connected.

2/CC,2/LL 1212 (7)

Based on the above, a three-stage LC circuit shown in

Figure 3b is developed as a simplified circuit with ranges up

to the high frequency range taken into consideration. Parallel

resistors are connected in the second and third stage LC

circuits, which simulate the oscillation in the high frequency

range, and take the damping of high frequency oscillations

into consideration. The damping resistance of this high

frequency wave is expressed as k(L/C)1/2, and the value

k is obtained through comparison of the analysis waveform

of the equivalent circuit with the waveform actually measured.

2.2 CIRCUIT MODEL FOR CONTINUOUS DISKWINDING

A disk winding continuously wound without interleaving

conductors with the cross sectional structure as demonstrated

in Figure 4 is called a continuous disk winding and is used as

a low voltage winding that does not particularly require

lightning-surge-proof characteristics, as well as in the form of

a combined interleaved disk winding on the line terminal side

and a continuous disk winding on the neutral point side in the

same winding.

Figure 3. Equivalent circuit with ranges up to the high frequency range taken

into consideration. (a) Parallel resonance point at the frequency of f1considered (b) Resonance frequencies up to the second order considered.

(a) (b)

L0

C1L1

C0L0

L1

L2

C0

C1

C2

R1

R2


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544 S. Okabe et al.: Development of High Frequency Circuit Model for Oil-immersed Power Transformers and its ApplicationSimilarly to Figure 2a, an equivalent circuit with a lumped

constant for two sections with one turn expressed by one

inductance element is presented in Figure 5a. Here, consider

the capacitance value in the case where this circuit is

expressed by the LC parallel circuit in Figure 5b. Assuming

that each turn in the section has a linear potential distribution,

if the concept of the stored energy method is applied, the

series capacitance for two sections can be obtained by

equation (8) [8].

2

ra0

2n

C)1n(C

3

2C

(8)

Ca: Section-to-section capacitance

Next, obtain the series capacitance when steep front wave

surges are applied. Consider the circuit as given in Figure 6

consisting of only capacitances sandwiched by equipotential

surfaces between two sections. Here, the potential v(x) of each

turn is expressed by equation (9).

sinh

)x1(sinhxsinh12Ev(x) (9)

r

a

C

C)1n(4

E: Voltage distribution per section

The series capacitance C0' for two sections obtained by the

stored energy method based on equation (9) is expressed by

equation (10).

sinh

)cosh1(21

2

C'C

a0 (10)

The ratio of C0' to C0 with respect to Ca/Cr with n as a

parameter is exhibited in Figure 7. Since Ca/Cr is generally

about 1 to 2, C0' is only about 10% smaller than C0 in the

practical range. In other words, the series capacitance is

considered to barely vary within a low to high frequency

range covering several MHz. Consequently, in the case of a

continuous disk winding, the circuit in Figure 5b can be used

for the whole frequency range. For simulation up to the high

frequency range in detail, the present study uses the value C0'

based on equation (10).

3 EVALUATIONOFCIRCUITMODEL

3.1 MODEL WINDING AND MEASUREMENTMETHOD

To evaluate the validity of the circuit models devised inChapter 2, an interleaved disk winding with two sections

equivalent to those for a 500 kV actual transformer was

produced (To be more specific: In comparison with an actual

one, the axial conductor width b, the turn-to-turn insulation

thickness d, and the oil-gap length between the sections were

identical, and the average winding diameter D was scaled

down to 75%) and the impedance frequency characteristics were

measured. For measurement, a network analyzer (ANRITSU,

MS3401A) was used. Sine waves were applied to the winding

by sweeping the frequencies from 100 Hz to 10 MHz to

8

161514131211109

1234567

Figure 4. Construction of a continuous disk winding.

0.6

0.8

1

1.2

0.5 1 1.5 2Ca / Cr

C0'/C0

n=10

n=20

Figure 7. Series capacitances of a continuous disc winding.

Figure 5. Equivalent circuit of a continuous disk winding.

(a) Detailed circuit (b) Simplified circuit

Figure 6. Capacitance circuit of a continuous disc winding.

L0 C0

10x

Equipotential surface (v(1)=E)

Cr

2Ca/n

v(x)

Equipotential surface (v(0)=0)

CrCa/nEquipotential surface

between sections

Correspondingto the numberof the order of

winding in Figure 4

(1)(2)(3)(4)(5)(6)(7)(8)

(9) (10) (11) (12) (13) (14) (15) (16)


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measure the impedance at each frequency. Figure 8 shows the

appearance of a two section model. The measurement was

conducted in insulating oil. Furthermore, a ten section model

winding was produced to measure like frequency characteristics

as well as the response waveforms in various locations in the

winding, an overview of which is carried in Figure 9. Similarly

to the two-section model, this model was placed inside the

insulating oil to conduct measurement.

3.2 COMPARISON OF THE ANALYSIS RESULTSUSING CIRCUIT MODEL WITH ACTUAL

MEASUREMENT RESULTS OF MODEL WINDING

Using the size of the model winding with two sections

produced for the present study as well as the material constant,each parameter of the equivalent circuit in Figure 3b was

calculated as follows:

L0=4.76 mH, C0=5570 pF

L1=5.08 H, C1=1840 pF

L2=2.54 H, C2=920 pF

For the damping resistance of the high frequency wave

(R1=R2=k(L/C)1/2), the oscillation waveforms of the potential

to the ground inside the winding were observed when the

impulse waveform (0.24/50 s) was applied to the model

winding and the value k was determined so that the

damping rate of the high frequency oscillation component

coincided with the results of the analysis [4]. Meanwhile, the

impulse waveform of 0.24/50 s was used because the rising

frequency is approximately 1 MHz and this frequency

corresponds to the aim of present study, which develops the

circuit model in the high frequency range. Consequently, the

value was determined to be k=10, which led to R1=R2=526 .

Figure 10 represents the analysis results of the

impedance frequency characteristics using the equivalent

circuit with k=10 and the measurement results at the model

winding. For the analysis, EMTP was used. The results of

the comparison reveal that both the frequencies and values

of the impedance coincide well at the first, parallel

resonance as well as the second and third in the high

frequency range. Therefore, it is clarified that k=10 is

proper according to the frequency characteristics, as is the

circuit model in Chapter 2. A low level parallel resonance

can be observed at the series resonance point at around 700

kHz. This is considered attributable to the influence of the

stray capacitance of the model winding to the tank, which isnot taken into consideration in the circuit model in Figure

3b.

Also in the case of the ten section model winding, the

analysis results with k=10 were compared with the

measurement results for the impedance frequency

characteristics. The analysis model consisted of five of the

models for two sections (Figure 3b) serially connected. In this

analysis model, the inductances in the low frequency range

were based on the calculation of self and mutual inductances

for five coils with two sections, with their values as given in

Table 1. Figure 11 shows the comparison results. Similarly to

the results for two sections, analysis using the equivalent

circuit was almost able to adequately express the resonance

points within the high frequency range. Meanwhile, a little

deviation was seen in the frequency range exceeding several

MHz. This is considered attributable to the fact that the circuit

model was constructed to simulate resonance frequencies up

to the second order. Also, the effect of the measurement lead

inductance was presumable.

Figure 8. Overview of the two-section model winding.

Figure 9. Overview of the ten-section model winding.

100

101

102

103

104

105

103

104

105 106 107

Frequency (Hz)

Impedance()

Calculation resultsMeasurement results

Figure 10. Comparison in the impedance frequency characteristics between

the analysis results using the circuit model and the measurement results of the

model winding (two-section model).


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546 S. Okabe et al.: Development of High Frequency Circuit Model for Oil-immersed Power Transformers and its Application

Table 2 summarizes the parallel and series resonance

frequencies of the two- and ten-section winding models

obtained from Figures 10 and 11. The fundamental resonance

frequency for ten sections is about 15 kHz, which is half that

for two sections, or about 30 kHz. This is considered

attributable to the fact that the inductance L is about 20 times

and the capacitance C about a fifth of the time for ten sections

compared with two sections, which leads to LC being about

four times (or 1/(LC)1/2=1/2). Conversely, there is no

significant difference between the parallel and series

resonance frequencies. Following detailed comparisonbetween the analysis values and the actual measurement

values, it emerges that they coincide relatively well for both

the fundamental resonance frequency and those in the high

frequency range.

3.3 RESPONSE CHARACTERISTICS WITHIN THEWINDING OF TEN SECTION WINDING MODEL TO

IMPULSE VOLTAGE

To investigate the potential distribution in the winding in

response to the high frequency surges, the voltage response

characteristics against a steep front voltage in various

locations in the winding were obtained using the ten-section

winding model. The applied voltage waveforms used included

a standard lightning impulse waveform (1.2/50 s) and step

waveforms (wavefront duration: 240 ns, 64 ns, and 32 ns)

with a steeper wavefront. Measurement was conducted using

the terminals (1 to 6, and E) displayed in Figure 12 for the

turn-to-turn voltage (1-2) and the section-to-section voltage

(1-3, 3-4, 4-5, 5-6, 6-E).

Turn-to-turn and section-to-section voltages measured

under the above conditions are normalized with respect to the

applied voltage (ratio to the peak values: measured

voltage/applied voltage 100 (%)) and summarized in Table 3.

Figure 13 shows the turn-to-turn (1-2) and section-to-section

(1-3) voltage at the terminal where the voltage is applied with

the wavefront duration as a parameter. Figure 14 indicates the

relationship of the location in the section-to-section direction

with the voltage generated. According to the figures and table,

the turn-to-turn and section-to-section voltages at the terminal

where the voltage is applied intensively increase when the

wavefront duration of the applied voltage is less than 0.1 s. It

also emerges that, if the wavefront duration is 1.2 s or 240 ns,

the section-to-section voltage is almost constant regardless of

location. Conversely, if the wavefront duration is 64 ns or 32ns, the section-to-section voltage increases; not only at the

terminal where the voltage is applied but also at the earth

terminal. Based on these findings, it was confirmed that

the potential distribution in the winding is not linear in the high

L0_1 L0_2 L0_3 L0_4 L0_5

L0_1 4.76

L0_2 4.21 4.76

L0_3 3.66 4.21 4.76

L0_4 3.18 3.66 4.21 4.76

L0_5 2.78 3.18 3.66 4.21 4.76

Table 1. Matrix of inductances (self and mutual inductances) in the low

frequency range of the analysis model winding; Unit: mH.

Figure 11. Comparison in the impedance frequency characteristics between

the analysis results using the circuit model and the measurement results of the

model winding (ten-section model).

Parallel resonancefrequency

f0 - f1 - f2

Series resonancefrequency

- f1' - f2' -

Two sections30.9 kHz 708 kHz 1.65 MHz 2.38 MHz 3.31 MHz

30.1 kHz 618 kHz 1.83 MHz 2.46 MHz 3.53 MHz

Ten sections14.9 kHz 708 kHz 1.53 MHz 2.38 MHz 2.97 MHz

13.5 kHz 795 kHz 1.31 MHz 2.48 MHz 3.24 MHz

Table 2. Comparison of the parallel and series resonance frequencies of the

two- and ten-section winding models (Upper row: Analysis results; Lower

row: Measurement results).

Frequency (Hz)

Impedance()

101

102

103 104

105

103

104

105

106

102 106 107

Calculation resultsMeasurement results

Figure 12. Locations of the connection of lead wires for measurement of the

voltage of the winding model with ten sections.

Wavefront duration of theapplied voltage

1.2 s 240 ns 64 ns 32 ns

Turn-to-turn voltage 1-2 9.85 10.4 19.6 34.4

Section-to-sectionvoltage

1-318.9

(20.6)20.1

(21.8)27.8 34.5

3-420.5

(20.2)21.1

(20.5)23.4 27.0

4-522.2

(19.9)24.4

(20.1)28.2 30.7

5-620.5

(19.8)24.0

(20.2)23.6 25.4

6-E18.9

(19.7)27.1

(20.3)35.7 57.7

Table 3. Measurement results of the potential distribution of the ten-section

winding model represented by % of the applied voltage (Calculation results

for wavefront duration of 1.2 s and 240 ns are shown in parentheses).

1

2

3

4

5

6

Impulse voltage

E


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frequency range as described in Clause 2.1.2. Consequently,

in order to analyze overvoltages generated in the transformer

by steep-front lightning surges, it will be necessary to develop

a circuit model capable of simulation up to a high frequency

range of several MHz. Meanwhile, the calculation results for

wavefront duration of 1.2 s and 240 ns using the circuit

model of Figure 3b were also shown in Table 3. Although a

little deviation was seen at the earth terminal side, when

comparison was made between the measurement and

calculation results, they agreed generally well. The deviation

is considered attributable to the influences of the simulated

method of the capacitance to the tank under the calculation

and the inductance of the lead wire under the measurement.

4 CIRCUITMODELFOR500KVOIL-IMMERSEDPOWERTRANSFORMER

4.1 DEVELOPMENT OF CIRCUIT MODEL

Figure 15 illustrates a circuit model for a 500 kV oil-

immersed power transformer developed based on an

assumption that it is a core type transformer with a high-

voltage winding comprising interleaved disk windings and its

medium-voltage winding and tertiary winding comprising

continuous disk windings, respectively. Partial models, each

with two sections, are produced using the method in Clause

2.1 for an interleaved disk winding and that in Clause 2.2 for a

continuous disk winding and the whole model is produced

with a combination of both. The figure is simplified, with each

of the one-stage LC parallel circuits of the high-voltage

winding (interleaved disk winding) actually replaced with a

three-stage LC parallel circuit in Figure 3b. In addition, whilethe inductance for the low frequency waves is omitted in the

figure, it is actually expressed by the inductance matrix,

including the winding-to-winding mutual inductance. The

winding-to-winding electrostatic coupling and the earth

capacity are also provided.

4.2 IMPEDANCE FREQUENCY CHARACTERISTICS

Figure 16 demonstrates the impedance frequency

characteristics for one phase seen from the high-voltageterminal for the circuit model illustrated in Figure 15;

developed by assuming a 500 kV core type transformer. The

characteristics are based on circumstances whereby the

medium-voltage and tertiary windings are grounded, and the

damping resistance of the three-stage LC parallel circuit is

calculated by k=10. The following characteristics are observed

from the figure:

(1) The fundamental resonance frequency f0 is 6.2 kHz.

(2) The impedance at f0 or less exhibits inductivity.

Figure 13. Relationship of the wavefront duration of the applied voltage with

the turn-to-turn (1-2) and section-to-section (1-3) voltage at the terminal

where the voltage is applied.

0

10

20

30

40

0.01 0.1 1 10

Turn-to-turn voltage: 1-2

Section-to-section voltage: 1-3

Wavefront duration (s)

Voltagegenerated(%)

Figure 14. Relationship of the location in the section-to-section direction with

the section-to-section voltage.

0

10

20

30

40

50

60

0 2 4 6 8 10

1.2 s 240 ns

64 ns 32 ns

Location in the section-to-section direction

Voltagegenerated(%

)

Figure 15. Circuit model of 500 kV power transformer.

Neutralpoint

Core

Tank

Side leg

High-voltageterminal

Medium-voltageterminal

High-voltagewinding

Medium-voltagewindingTertiary

winding


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548 S. Okabe et al.: Development of High Frequency Circuit Model for Oil-immersed Power Transformers and its Application(3) There are four resonance points above f0 between 5

kHz and 50 kHz, and capacitive impedance is exhibited

at higher frequencies. At f=100 kHz, the capacitance is

C=4080 pF.

(4) In the high frequency range of f=300 kHz or more,

there are three parallel resonance and series resonance

frequency points, respectively.

(5)

In the high frequency range of f=2 MHz or more, thecapacitance is about 1500 pF.

The earth capacitance of the high-voltage winding (sum of

the capacitance to the medium-voltage winding and the

capacitance to the tank) is 10410 pF.

As mentioned above, the analysis results of the transformer

model in Figure 15 correlate well to the characteristics of the

actual measurement results in Figures 10 and 11 in that

several resonance points emerge in the high frequency range

of 500 kHz or more and the capacitance in the MHz range is

smaller than that in the 100 kHz range.

5 LIGHTNINGSURGEANALYSISOF500KV

SUBSTATION

A lightning surge analysis is performed using the model

proposed in the present study (hereinafter the high frequency

model) and various others, including conventional, to

investigate the influence on the results.

5.1 SUBSTATION CIRCUIT TO BE ANALYZED ANDVARIOUS CONDITIONS

With reference to [9], the substation circuit to be analyzed

was determined as the three-phase-in-one-tank GIS substation

in the 500 kV system sketched in Figure 17. The main

analysis conditions are listed as follows. The substation

simulation method in (4) pertains to the content of the present

study:

(1) Lightning stroke conditions

Lightning stroke current: 150 kA, 1/70 s ramp wave

Point struck by lightning: Top of the first tower

ac superposition: Crest value in reverse polarity

(2) Power transmission facilities

Transmission line: Multi-phase transmission line

simulation (J. Marti model)

Tower: Four-section tower

(3) Substation facilities

Circuit conditions: Consisting of two banks with four lines

led in; One bank is in operation with one line led in (Figure

17)

Three-phase GIS: Multi phase simulation (K. C. Lee

model)

Surge arrester: 870 kV (10 kA)Figure 16. Impedance frequency characteristics of the circuit model of 500

kV power transformer.

3 3

3 5.5 3 5.53 333 33 1.5 31.5 1.531.5 1.531.55.5

G2-7R G2-7S G2-7T

BA-3 BA-2 BA-1

BU-1

BU-2

BU-3

BU-4

BU-5

BU-6

BU-7 BU-8 BU-9 BU-10 BU-11

BU-12

BU-13 BU-14

BU-15

BU-16 BU-17

BU-18 BU-19

G3-7R G3-7S G3-7T

2.5

2.5

2.5

2.52.52.52.52.52.52.52.52.5

BU-PDTBU-PDSBU-PDR

PD200pF

PD200pF

PD200pF

T1-7R T1-7S T1-7T B2-7R

G1-1T

G1-2T

G1-LAT

G1-8T

G1-3TG1-4T

G1-5T

G1-6TG1-7TG1-7SG1-7R

G1-1SG1-1R

B1-7R B1-7S B1-7T

B g200pF

PD200pF

B1-1R B1-1S

B1-6T

B1-5T

B1-8TB1-4T

B1-3T

B1-2T

B1-1T B1-LAT

60

3.7

7.8

1.5

2.5

5

1.5

6.5

7.8

4.7

1.53

0

B2-7S B2-7T

Transmission line

Transformer (Simulated by the high-frequency model or the lumped C)

Surge arrester

The numbers indicate length.

1 GIS

3 GIS

Figure 17. Substation analysis circuit.

Impedance()

101

102

105

103

104

Frequency (Hz)

103102 105 106 107104


9/12


(4) Transformer simulation

Assuming a single-phase three-coil transformer typical for

a 500 kV class, the following five cases were considered as

simulation methods of a transformer:

Case 1: High frequency model (Figure 15)

Case 2: Lumped capacitance C=10730 pF (Windings earth

capacitance 10410 pF + Bushing capacitance 320 pF)For the windings earth capacitance, the collective

value of three coils is used.

Case 3: Lumped capacitance C=3790 pF (Windings earth

capacitance 10410 pF/3 + Bushing capacitance 320 pF),

Conventional method

For the windings earth capacitance, the value of one

coil is used. Here, the collective windings earth

capacitance for three coils is divided by three to obtain

the equivalent capacitance for a single coil, assuming

the potential of the winding to be linearly distributed.

Case 4: Lumped capacitance C=4080 pF (Calculated based

on the impedance of the high frequency model at f=100

kHz)

Case 5: Lumped capacitance C=1500 pF (Calculated based

on the impedance of the high frequency model at f=2 MHz

or more)

5.2 ANALYSIS RESULTS

Figure 18 summarizes the lightning surge waveforms at the

transformer terminal corresponding to the above five cases of

transformer simulation. The peak value of the generated

voltage and dV/dt differ according to the difference in thesimulation method. Figure 19 highlights the front rising for

Cases 1 and 3 with an enlarged time axis. For the analysis

waveform in each case, the maximum potential gradient at the

front rising of voltage is obtained as dV/dt and summarized in

Table 4 together with the peak voltage value.

In the case where the high frequency model (Case 1) is

connected, the peak voltage value decreases to 84% but the

voltage build-up rate increases up to 128% compared with that

in which the lumped capacitance equivalent to 1/3 of the earth

capacitance is connected in the conventional simulation

method (Case 3).

For simulation by the lumped capacitance, the voltage

build-up rate increases in inverse proportion to capacitance;however, the peak voltage value does not monotonously

increase or decrease with respect to the capacitance. Figure 20

evaluates the relationship between the lumped capacitance

value simulating the transformer and the peak voltage value

generated. As the capacitance falls, the peak voltage reaches a

local maximum value at 3000 pF, followed by a local

minimum value at 1200 pF, subsequently peaking at 300 pF.

In the surge waveform, with 1200 pF as a boundary, the peak

value emerges in the first and second peaks with lower and

higher capacitance respectively.

(a) Case 1: High frequency model

(d) Case 4: Lumped capacitance C=4080 pF

(e) Case 5: Lumped capacitance C=1500 pF

(b) Case 2: Lumped capacitance C=10730 pF

(c) Case 3: Lumped capacitance C=3790 pF

Figure 18. Lightning surge analysis waveform at the transformer terminal

using each of the transformer simulation methods.

Time (s)

Voltage(kV)

Time (s)

Voltage(kV)

Time (s)

Voltage(kV)

Time (s)

Voltage(kV)

Time (s)

Voltage(kV)


10/12

550 S. Okabe et al.: Development of High Frequency Circuit Model for Oil-immersed Power Transformers and its Application

The frequency of the oscillation component that emerges at

the front rising of the voltage waveform at the transformer

terminal is determined by the oscillation of the capacitance of

the GIS from the location of the surge arrester to the

transformer and the transformer itself. Consequently, the

oscillation frequency decreases as the value of the capacitance

simulating the transformer increases. This frequency ranges

from several hundred kHz to about 1 MHz. Since multiple

reflections of surges elsewhere in the substation possibly

cause oscillations in this frequency range, the peak value of

the voltage waveform at the transformer terminal is

considered to be influenced by the mutual interference with

such oscillations.

6 EVALUATIONOF

LIGHTNING

SURGE

ANALYSISRESULTS

A study is conducted on the influence of the transformer

model and the configuration of the substation on the lightning

surge analysis results. Furthermore, each overvoltage

waveform is converted into an equivalent standard lightning

impulse waveform using the waveform evaluation method [5]

to perform an evaluation from the perspective of the severity

for insulation.

6.1 INFLUENCE OF TRANSFORMER MODEL

As described before, if the high frequency model was used

as a transformer model for lightning surge analysis, the

voltage generated at the transformer terminal had a steeperfront rising but a lower peak value compared with when the

conventional model was used. This difference is due to the

capacitance charging process inside the transformer and can

be explained as follows [4]:

The conventional model is charged exponentially with the

time constant of the product of the surge impedance of the line

and the earth capacitance. In contrast, the high frequency model

behaves in the same manner as the stage zero (parallel circuit of

L0 and C0 in Figure 3b) that corresponds to the conventional

model; however, it oscillates at about 700 kHz in the first stage

(parallel circuit of L1 and C1 in Figure 3b) and at about 1.4 MHz

in the second stage (parallel circuit of L2 and C2 in Figure 3b) of

the high frequency. Consequently, the high frequency elemententers the discharge phase even when the stage zero is being

charged, and the crest value is reduced. Since a small

capacitance corresponding to the high frequency element is

initially charged, the rising is sharp. This high frequency model

was developed based on measurement, as described before,

hence the surge waveform is influenced due to the fact that the

capacitance seen from the transformer terminal in the high

frequency range is small. Consequently, the analysis result in

Case 1 is considered to be close to the actual lightning surge.

6.2 APPLICATION OF WAVEFORM EVALUATIONMETHOD

The authors have developed a method to convert anovervoltage waveform (non-standard lightning impulse

waveform) in various lightning surge ranges to the equivalent

standard lightning impulse waveform (1.2/50 s) in terms of

insulation in the previous study [5], the details of which are

not described in the present paper. The results of the

application of this waveform evaluation method to the

lightning surge analysis waveform in the present study are

summarized in Table 5. Here, the result obtained by dividing

the peak value of the analysis waveform by the conversion

ratio is the equivalent standard lightning impulse voltage.

Time (s)

Voltage(kV)


CaseTransformer simulation

methodPeak voltage

(kV)Voltage build-up rate

dV/dt (kV/s)

1 High frequency model 968 1474

2 Lumped C (10730 pF) 910 562

3 Lumped C (3790 pF) 1149 1156

4 Lumped C (4080 pF) 1133 1127

5 Lumped C (1500 pF) 1097 1950

Table 4. Peak voltages and voltage build-up rates of the lightning surge

analysis waveforms.

Figure 19. Front rising of the lightning surge analysis waveforms.

Figure 20. Relationship between the capacitance simulating the transformer

and the peak value of the lightning surge analysis waveform.

Time (s)

Voltage(kV)


Capacitance (pF)

Peakvalueofthegeneratedvoltage(kV)

Maximum value at

the second peak

Maximum value

at the first peak


11/12


First, following comparison of the peak values of the

analysis waveforms, the value in Case 3 is evaluated to be

about 19% higher than Case 1, and the peak values of Cases 4

and 5, where the capacitance is small, are also computed to be

relatively high. Conversely, the values after waveform

evaluation differ relatively little between transformer models.

This is because, while the peak value is large, for example, in

the waveform in Case 3, the conversion ratio to the standard

lightning waveform is also large since the waveform isoscillatory. As in this case, due to the application of the

waveform evaluation method and comparison from the

perspective of the insulation severity, the difference was

lessened. However, the value in Case 3, where the

conventional simulation method is applied, is still evaluated at

about 7% higher and hence as relatively severer (on the safety

side), which will mean, conversely, that some potentiality

remains for rationalization. To evaluate the overvoltage value

more accurately within the frequency range handled in the

lightning surge evaluation, a model must be developed in

which the high frequency characteristics are taken into

consideration in accordance with the winding structure.

6.3 INFLUENCE OF SUBSTATION CIRCUIT

As indicated in Figure 17, the substation circuit used in the

present lightning surge analysis includes GIS with 30 m long

from the surge arrester location to the transformer terminal.

The 500 kV three-phase bus bar spreads 35 m on the right

hand side of the BU-2, BU-4, and BU-6 nodes connected to

the G1 lines, from which lightning surges are assumed to

occur. Consequently, to clarify the influence of the lightning

surge waves, which have intruded from the G1 lines, branched

into the bus bar and reflected at its terminal on the voltage

waveform at the transformer terminal, the lightning surge

analysis was performed on the condition that the bus bar was

separated at the BU-6 node in the circuit in Figure 17.

The results when Cases 1 and 3 are used as the transformer

simulation methods are compared in Figures 21a and 21b,

respectively. The peak values of the generated voltage are

1117 kV and 1270 kV, increases of 15% and 11%,

respectively, compared with the results in Figure 18. As for

the shape of the waveforms, the first peak is higher, which

reveals that the phenomenon of the higher second peak as

indicated in Figure 18 is due to the influence of the waves

branched into and reflected at the bus bar. As in this case, if

the transformer is far from the surge arrester location, the

voltage generated at the transformer terminal exceeds the

surge arrester residual voltage based on distance, and the

voltage build-up rate is significantly influenced by the

substation configuration.

Attention needs to be paid when studying the lightning

surge waveform at the transformer terminal because the

waveform not only influences the development of the

transformer model but is also dependent on the substation

configuration.

Following the application of the waveform evaluation to

Figure 21, the voltages were 1013 kV and 1017 kV in Cases 1

and 3, respectively, meaning minimal difference from the

perspective of insulation severity.

7 SUMMARY

A relatively simplified circuit model was developed; capable

of simulating the winding at frequencies up to the high

frequency range of several MHz for a 500 kV oil-immersed

transformer, and its validity was evaluated by comparison with

the measurement results of the model winding. In addition,analysis of lightning surges to a 500 kV substation was

performed using the new model to study its influence on the

lightning surges generated at the transformer terminal in

comparison with the conventional simulation method.

The examination results are summarized as follows:

(1) For the interleaved disk winding of an oil-immersed

transformer, a simplified model with three serially connected

LC parallel circuits can adequately simulate the impedance

characteristics of the winding at frequencies up to the high

frequency range.

CasePeak voltage

(Relative value on thebasis of case 1)

Conversion ratioEquivalent standard-LI(Relative value on the

basis of case 1)

1 968 kV (1.00) 1.04 931 kV (1.00)

2 910 kV (0.94) 0.98 929 kV (1.00)

3 1149 kV (1.19) 1.16 993 kV (1.07)

4 1133 kV (1.17) 1.15 986 kV (1.06)

5 1097 kV (1.13) 1.14 959 kV (1.03)

Table 5. Peak value of the lightning surge analysis waveform and equivalent

standard lightning impulse through the application of the waveform

evaluation method.

Figure 21. Influence of the substation circuit.



Time (s)

Voltage(kV)

Time (s)

Voltage(kV)


12/12

552 S. Okabe et al.: Development of High Frequency Circuit Model for Oil-immersed Power Transformers and its Application(2) In the lightning surge analysis at a three-phase-in-one-

tank GIS substation in a 500 kV system, if the high frequency

model is connected, the peak voltage value decreases while

the voltage build-up rate increases compared with the

conventional simulation model. This phenomenon can be

explained with the capacitance charging process inside the

transformer taken into consideration. This is based on the

transformer simulation method and considered generally

applicable regardless of the substation configuration.

(3) When the lightning surge analysis waveform by each

transformer model is converted into the equivalent standard

lightning impulse waveform and analyzed, the difference in

the peak value decreases from that in the original waveform.

This is because, if a transformer is simulated by a lumped

capacitance, the conversion ratio to the standard lightning

impulse waveform increases with the increase of the

oscillatory component even though the waveform becomes

more oscillatory and the peak value increases.

(4) In the lightning surge analysis, the results obtained

differ due to the change in conditions, such as branched waves

and reflections, depending on the substation circuit including

the bus bar length and connected lines. The waveform shape

and the crest value vary due to the interference of these

conditions with the transformer simulation method. Therefore,

to accurately obtain the lightning surge waveform at the

transformer terminal, it is effective to use a transformer

simulation method that takes the characteristics in the high

frequency range into consideration.

The high frequency model developed in the present study is

expected to be applied, not only to the lightning surge analysis

but also widely to others such as that of the propagation

characteristics of relatively high frequency partial discharge

signals generated inside the transformer.

REFERENCES

[1] IEC60071-4, Insulation co-ordination Part 4: Computational guide to

insulation co-ordination and modeling of electrical networks, 2004.

[2] T. Terahishi, M. Ikeda, M. Honda, and T. Yanari, Local Voltage

Oscillation in Interleaved Transformer Windigns, IEEE, Trans. Power

Apparatus Syst., Vol. 100, pp. 873-881, 1981.

[3] K. Cornick, B. Filliat, C. Kieny, and W. Muller, Distribution of Very

Fast Transient Overvoltages in Transformer Windings, CIGRE, Report

12-204, 1992.

[4] S. Okabe, M. Koto, T. Teranishi, M. Ishikawa, and T. Saida, An

Electric Model of Gas-Insulated Shunt Reactor and Analysis of Re-

Ignition Surge Voltages, IEEE, Trans. Power Delivery, Vol. 14, pp.

378-386, 1999.

[5] S. Okabe and J. Takami, Evaluation of Breakdown Characteristics of

Oil-immersed Transformers under Non-standard Lightning ImpulseWaveforms - Method for Converting Non-standard Lightning Impulse

Waveforms into Standard Lightning Impulse Waveforms, IEEE, Trans.

Dielectr. Electr. Insul., Vol. 15, pp. 1288-1296, 2008.

[6] Y. Kawaguchi, Calculation of Circuit Constants for the Computation of

Internal Oscillating Voltage in Transformer Windings, IEEJ Trans., Vol.

89, pp. 115-124, 1969.

[7] A. Pedersen, On the Response of Interleaved Transformer Windings to

Surge Voltages, IEEE, Trans. Power Apparatus Syst. Vol. 66, pp. 349-

356, 1963.

[8] A. Schleich, Behaviour of Partially Interleaved Transformer Winding

Subject to Impulse Voltages, Bulletin Oerikon, No.389/390, 41, 1958.

[9] Central Research Institute of Electric Power Industry Report, The

Suggestion of the Useful way to Analysis of Lightning Overvoltages and

Application, T90068, 1991.

Shigemitsu Okabe (M98) received B. Eng., M.Eng.and Dr. degrees in electrical engineering from the

University of Tokyo in 1981, 1983 and 1986,

respectively. He has been with Tokyo Electric Power

Company since 1986, and presently is a group

manager of the High Voltage & Insulation Group at

the R & D center. He was a visiting scientist at the

Technical University of Munich in 1992. He has been

a guest professor at the Doshisha University since

2005, at the Nagoya University since 2006, and a

visiting lecturer at the Tokyo University. He works as a secretary/member at

several WG/MT in CIGRE and IEC. He is an Associate Editor of the IEEE

Dielectrics and Electrical Insulation.

Masanori Koto received the B.Eng., M.Eng. degrees

in electrical engineering from Kanazawa University in1987 and 1989. He has been with the Tokyo Electric

Power Company since 1989, and was engaged in

diagnosing deterioration in oil-immersed transformers

when attached to the High Voltage & Insulation

Group. Currently, He is a Senior Engineer of the

Substation Engineering Group of Transmission

Department.

Genyo Ueta received the B.S. and M.S. degrees from

Doshisha University in 2000 and 2002, respectively.

He joined Tokyo Electric Power Company in 2002.

Currently, He is a researcher at the High Voltage &

Insulation Group of R & D Center and mainly

engaged in research on insulation characteristics of

GIS.

Toshiyuki Saida received the B.S. and M.S. degrees

in electrical engineering from Nagoya University in

1989 and 1991, respectively. In 1991, he joined

Toshiba Corporation, and has been engaged in

substation engineering in the Power transmission &

Substation Department.

Shin Yamada received the B.Eng. and M.Eng.

degrees in electrical engineering from Waseda

University in 1988 and 1990, respectively. In 1990,

he joined Power Industrial and Systems Research and

Development Center of Toshiba Corporation. In 1997,

he changed to the Transformer Department at

Hamakawasaki Works, and has been engaged in the

designing of power transformers.

high frequency model on an transformers

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