fink - insulation co-ordination and high voltage testing ... · pdf file2 | s. fink | itp...

1 | S. Fink | ITP |07.04.2009

KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)

Stefan Fink:

MATEFU – Insulation co-ordination and high voltage testing of fusion magnets

Le Chateau CEA Cadarache, FranceApril 7th, 2009

• Insulation co-ordination• Some principle considerations of HV testing• Testing of ITER TF Model Coil• ITER TF

2 | S. Fink | ITP |07.04.2009


Insulation co-ordination

Insulation co-ordination is the selection of test voltage(s) in relation to the operating voltages and overvoltages which can appear on the system.

System analysis

Representative voltages and overvoltages

Test voltages

Example in conventional HV engineering: waveform for a standard lightning impulseMultiplying with factors

Voltage value, waveform, test time

Voltage value, waveform

3 | S. Fink | ITP |07.04.2009


System analysis: RL discharge on a TF coilCurrent with initial value IL(t = 0) = I0 = 50 kA must be decreased to 0 A in case of a quench

0

2

4

6

8

10

0

10

20

30

40

50

0 10 20 30 40 50

U I

UkV

IkA

ts

1 2

L

1H

0

R

0.1

U = R * II = I0 * e-t / τ = I0 * e-t / (L / R)

=> U0 = 0.1 Ω * 50 kA = 5 kV High voltage (HV)!

Increase of the voltage is in range of few ms or faster=> TF coil is a high voltage impulse coil=> Testing of coil and coil components only with a DC test is not sufficient

4 | S. Fink | ITP |07.04.2009


Representative voltages for TF coil dischargeDifficult to make a single HV test which is relevant for all voltages (and overvoltages) which may appear on the coil

=> A set of tests with different waveform is used

• Most representative

• Stresses all types of insulation

• Non destructive insulation diagnostic possible (e. g. partial discharge (PD))

• Simple, cheap

• Low destructive

Representative for fast excitations (fast switching, faults)

Representative for increase if arc chute breakers are used

Representative for fall

ImpulseAlternating voltage ("AC")

Direct voltage ("DC")

1 2

Winding

Case

1 2

Winding

Case

1 2

Winding

Case

5 | S. Fink | ITP |07.04.2009


General aspects of HV testing of large devices

• Large devices may have internal overvoltages if they are subjected to “fast” excitations=> calculation of transient behaviour:Non linear voltage distribution?Oscillations?

• Non destructive test methods=> Partial discharge measurement

20 kV transformer of a 50 kA power supply

6 | S. Fink | ITP |07.04.2009


Special aspects of HV testing of “Paschen tight” apparatus• A “Paschen tight” device can be

operated independently of the surrounding dielectric properties (e. g. during vacuum breakdown).

• The ITER TFMC was designed with solid insulation covering completely the HV areas. The insulation is covered with conductive paint. This paint is grounded.

• Verification if a coil is “Paschen tight” is performed by HV DC testing with the transition of the Paschen curve of the surrounding air in the cryostat at room temperature.

Paschen tight apparatus

Current Lead

Insulated testsample coveredwith conductivepaint

Undefinedgas or vacuum

7 | S. Fink | ITP |07.04.2009


Some special aspects of HV testing of cryogenic apparatus

• Fault detection under cryogenic conditions is expensive and timeconsuming => make pre-tests at room temperature

• The dielectric strength of the cooling material may be a weak point under room temperature testing of cryogenic apparatus => increase the pressure or replace He by N2 or SF6 in cooling channels with insulation breaks

8 | S. Fink | ITP |07.04.2009


ITER Toroidal Field Model Coil (TFMC)

Coil parameters:Rated current 80 kARated voltage +5 kV / -5 kVDouble pancakes 5Turns per pancake 10 (or 9

for outermost)

Design of ITER TFMC

Coil Case Winding Pack

Cross Section

3 different insulation types:• Conductor insulation• Radial plate insulation• Ground insulation

9 | S. Fink | ITP |07.04.2009


FEM and network model for ITER TFMC

2D-FEM model of ITER TFMC as basis for calculation of the lumped elements of network model Network model of ITER TFMC

University KarlsruheUniversity Karlsruhe

10 | S. Fink | ITP |07.04.2009


Results of transient calculation for TFMC

First resonance frequency appears at 290 kHz for the relevant cases 2 and 3.(This was later conformed by low voltage / high frequency measurement on ITER TFMC.)

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

0 100 200 300 400 500

Frequency [kHz]

|G(f

)|

Case 1

Case 2

Case 3

Transfer function at node 1 of the ITER TFMC network model with symmetric voltage excitation ±5 kV

The selected configuration with connection of the radial plate by 1.2 MΩ resistors and a symmetrical grounding gives no relevant overvoltages for rise times above 2 µs

=> No high overvoltages expected for all prepared HV tests

11 | S. Fink | ITP |07.04.2009


Typical HV tests for ITER TFMC

• DC test on ground insulation• Impulse test• DC test on ground insulation• DC and AC test on ground, radial plate

and conductor insulation without roomtemperature instrumentation cables

• DC test on ground insulation

• DC test voltage value for ground insulation was 10 kV (test voltages for other insulation types and waveforms had been lower)

• Tests were performed at room and cryogenic temperature• AC tests included partial discharge measurement

Groundedcase

Groundinsulation

Radial plateinsulationConductorinsulation

Conducto

Radial plate

12 | S. Fink | ITP |07.04.2009


Results of HV tests of ITER TFMC at room temperature

• All tests under ambient conditions were passed successfully

• During Paschen test it was found that TFMC is not Paschen tight

• 2 potential fault locations were found, Tedlar tapes were forgotten to remove during manufacturing at one location

Fault location at helium inlet tubes

13 | S. Fink | ITP |07.04.2009


Results of HV tests and HV discharge on ITER TFMC at cryogenic temperature

• Breakdown strength for AC and esp. impulse testing under cryogenic conditions does not fulfil the specification

• High current discharge withI = 80 kA and U < 1 kV was possible

• High voltage discharge was reduced from +5 kV / -5 kV to 0 / 4.4 kV

=> ITER TFMC does not fulfil the HV specification Breakdown during an impulse test

with 5 kV at the plus terminal

0

1

2

3

4

5

0 10 20 30

SC1116.QDA

Uplus terminal

UkV

tµs

14 | S. Fink | ITP |07.04.2009


ITER TF

ITER TF coils

Coil design parameters:Rated current 68 kAVoltage @ fast discharge 3.5 kVNumber of coils 18Double pancakes / coil 7Number of turns / pancake 11 (outer

DP: 3, 9)

Cross section of an ITER TF coil

15 | S. Fink | ITP |07.04.2009


Detailed network model of ITER TF

The mutual inductances are "invisible" included in:include Kopplungen_1kHz.txt

Network model of the ITER TF single coil for a frequency of 1 kHz (established by University of Karlsruhe, IEH)

C58

C72

L59

L78

R57

C57

R98

L86

C79

R94

L91

C92

R83

C84

L96

L79

L90

L83

C_P5_GE

22.5n

R92R81

C95

L85

C97

C93

L99

C88

L89

R82

L81

C87

C83

R86

C94

L98

R87

C91

L94

L87

C100

L92

C99

L82

C86

R93

R91

0

R80

R95

R96

L93

R90

L84

C81

L88

R97

R89

R79

L80

C82

C90

R85

L97

R99

R100

R88

C89

C98

C85

C80

R84

L95

C96

L100

R120

L108

C101

R116

L113

C114

R105

C106

L118

L101

L105

C_P6_GE

22.5n

R114R103

L112

C117

L107

C119

C115

L121

C110

L111

PARAMETERS:C_Lage1 = 80.9nFC_Lage2 = 81.8nFC_Lage3 = 82.7nFC_Lage4 = 83.6nFC_Lage5 = 84.5nFC_Lage6 = 85.3nFC_Lage7 = 86.2nFC_Lage8 = 87.0nFC_Lage9 = 87.9nFC_Lage10 = 88.8nFC_Lage11 = 89.6nF

R104

L103

C109

C105

R108

C116

L120

R109

C113

L116

L109

C122

L114

C121

L104

C108

R115

R113

0

R102

R117

R118

L115

L106

R112

C103

L110

R119

R111

R101

L102

C104

L119

R121

C112

R107

R122

R_Lage11

R110

C111

C120

C107

PARAMETERS:R_Lage1 = 797.04uR_Lage2 = 805.08uR_Lage3 = 814.32uR_Lage4 = 822.96uR_Lage5 = 831.60uR_Lage6 = 839.16uR_Lage7 = 847.80u

R_Lage9 = 865.08u

R_Lage11 = 882.36u

R_Lage8 = 856.44u

R_Lage10 = 873.72u

C102

R106

L117

C118

L122

L130

C123

L133

C134

R127

L123

C128

C_P7_GE

132.97n

R134

R_Lage3

L127

L132

R125

L129

C_P3_P4

147.24n

S

Vterminal1

Implementation = Utf_L8_1

L125

R126

C131

C127

R130

R131

C133

L131

L134

L126

C130

R133

R_Lage2

0

R124

R132

R_Lage1

L128

R123

C126

C125

L124

C132

R129

C129

C124

R128

C_P4_P5

147.24n

R_P1_L R_P2_L

C_P5_P6

147.24n

R_P3_L R_P5_LR_P4_L R_P6_L R_P7_L

C_P6_P7

147.24n

PARAMETERS:R_Anbindung = 100k

C_P4_GE

22.5n

C_MessKable1 C_MessKable2 C_MessKable3 C_MessKable4 C_MessKable5 C_MessKable6

00

C_MessKable7

0 0000

PARAMETERS:L_Lage1 = 1.4485uHL_Lage2 = 1.5043uHL_Lage3 = 1.5527uHL_Lage4 = 1.6044uHL_Lage5 = 1.6513uHL_Lage6 = 1.6977uH

L_Lage8 = 1.7865uHL_Lage7 = 1.7421uH

L_Lage9 = 1.8247uHL_Lage10 = 1.8716uHL_Lage11 = 1.9140uH

0

R1

L1L_Lage1

R2

C1

L2L_Lage2

C2

R3

L3

L_Lage3

C3

c4

C6

C5

L5

R4

R5

L6

R6

C9

C_Lage6

R9

R_Lage6

C7

L9

L_Lage6

R7

R_Lage4

R8

R_Lage5

L8

L_Lage5

C8

L7

L_Lage4

C11

C_Lage8

R11

R_Lage8

C12

C_Lage9

L11

L_Lage8

L12

L_Lage9

R12

R_Lage9

R10

R_Lage7

L10

L_Lage7

C10

C_Lage7

0

C_P1_GE

132.97n

R31

C30

R26

L30

L25

L15

R15

L29

L13

R29

C28

C26

C32

L28

R30

R27

R13

L31

C31

R24

R25

C29

R14

C27

R32

L27

C25

C15

L14

R28

C24C13

C14

L26

PARAMETERS:C_Messkable = 24nF

L32

L4

C16

R17

C17

C18

L18

L17

L16

R16

R18

C19

R20

C20

C21

L20

L19

R19

L21

R21

C22

C_Lage10

C23

C_Lage11

L22

L_Lage10

R22R_Lage10

L23

L_Lage11

R23

L34

R33

L33

C34

C33

R34

0

C_P2_GE

22.5n

C_P1_P2

147.24n

L36

L42

C43

R53

L52

C46

L50

L44

R51

C_P3_GE

22.5n

C56

R38

L38

L46

C53

C_P2_P3

147.24n

L56

0L37

C42

L53

C55

L55

L54

L48

R40

R52

C49

R41

C45

C38

L45

R44

C39

R42

R55

C35

L47

L35

R35

L40

R39

0

R50

R49

R37

L49

C54

R36

R45

C37

R47

L51

L43

C36

R54

C51

C52

C48

C41

C44

C40

L39

L41

R56

R43

C47

R46

C50

R48

R62

R76

R71

R59

0

C74

R77

C62

L67

R75

C77

R67

R60

C61

R69

C75

L63

R64

C70

C66

L62

L58

R78

C68

R74

L60

C59

R72

R65

L61

L75

C63

C60

INCLUDE: Kopplungen_1kHz.txt

S

Vterminal2


L69

R63

L66

L71

R68

C73

R58

R73

R61

C78

R70

C64

L72

L77

L64

C69

L57

C67

L70

L65

L73

L68

C65

L74

R66

C76

L76

C71

• Lumped elements of the coil(s) are calculated with 2D-FEM for different frequencies

• Detailed network models in were established for different frequencies

16 | S. Fink | ITP |07.04.2009


Resonance frequencies of ITER TF

The resonance frequency of a single ITER TF coil is calculated to be 50 kHz

0

5

10

15

20

25

30

35

0 50000 100000 150000 200000

Uterminal2

UHeIn7

UHeIn6

UHeIn5

UHeIn4

UHeIn3

UHeIn2

UHeIn1

UR134:2 - RP7

UR131:2 - RP7

U = f(f) on the 50 kHz model for an excitation with 1 V. First resonance occurs at 50 kHz => natural frequency is calculated to be 50 kHz

17 | S. Fink | ITP |07.04.2009


ITER TF discharge circuit

• 18 TF coils

• 9 fast discharge units (FDUs)

• Soft grounding

TF discharge circuit (simplified)

FDUFDU FDU

FDU FDUFDU

TF Coil

Grounding resistor

Fast discharge unit

=> A model is required to calculate terminal voltages

18 | S. Fink | ITP |07.04.2009


Network model of 18 ITER TF coils

Output:• maximum terminal to ground

voltage• maximum terminal to terminal

voltage

ITER TF system with 18 simplified superconducting coils (established by University of Karlsruhe, IEH)

VV V-V+

R66

0

C51

R68

500

R69

0

C52

0

R71

C53

R73

0

C54

L19 L20 L21 L22 L23 L24

I1

+-

+

-

S3

S

V3

0

L25 L26 L27 L28 L29 L30

C7

C1C2

C3 C4 C5C6

C8C9 C10 C11 C12

C13C14 C15

C16 C17C18

C19C20

C21 C22C23

0

C24

C25 C26C27

0

0

0

0000

0

00 00 0

0

0

0 00 0

0

0

00

0 00

FDU1

TF_FDU

ein aus

L31 L32 L33 L34 L35 L36

L37 L39 L40 L41

L42L43

0

L44

C31

R27

0

R25

C30

R20

C28

R22

0

C29

0

L45

C32

R29

0

C33

0

R31

R32

C34

0

L1

0.349H

L2

0.349H

R1500

R2

500

R34

0

C35

L4

0.349H

FDU2

TF_FDU

ein aus

R36

L3

0.349H

R4

500

C36

0

R3

500

R6

500R7

500

L6

0.349H

L8

0.349H

R38

R8

500

FDU3

TF_FDU

ein aus

0

C37

L5

0.349H

FDU4

TF_FDU

ein aus

L7

0.349H

R5

500

R10

500

L14

0.349H

R11

500

R40

R13500

L10

0.349H

L16

0.349H

L13

0.349H

R14

500

FDU7

TF_FDU

ein aus

L12

0.349H

C38

0

R12

500

FDU5

TF_FDU

ein aus

R16

500

L9

0.349H

L11

0.349H

FDU6

TF_FDU

ein aus

R15500

L15

0.349H

FDU8

TF_FDU

ein aus

R9

500

R42

C39

0

R18

500

FDU9

TF_FDU

ein aus

L17

R17500

0

L18

R44

C40

0 0

R46

C41

R48

C42

0

R50

0

C43

R52

C44

0

R54

C45

0

R56

C46

0

R58

C47

0

R60

C48

0

R62

0

C49

R64

C50

0

19 | S. Fink | ITP |07.04.2009


Detailed network model of ITER TF

The mutual inductances are "invisible" included in:include Kopplungen_1kHz.txt

Network model of the ITER TF single coil for a frequency of 1 kHz (established by University of Karlsruhe, IEH)

C58

C72

L59

L78

R57

C57

R98

L86

C79

R94

L91

C92

R83

C84

L96

L79

L90

L83

C_P5_GE

22.5n

R92R81

C95

L85

C97

C93

L99

C88

L89

R82

L81

C87

C83

R86

C94

L98

R87

C91

L94

L87

C100

L92

C99

L82

C86

R93

R91

0

R80

R95

R96

L93

R90

L84

C81

L88

R97

R89

R79

L80

C82

C90

R85

L97

R99

R100

R88

C89

C98

C85

C80

R84

L95

C96

L100

R120

L108

C101

R116

L113

C114

R105

C106

L118

L101

L105

C_P6_GE

22.5n

R114R103

L112

C117

L107

C119

C115

L121

C110

L111

PARAMETERS:C_Lage1 = 80.9nFC_Lage2 = 81.8nFC_Lage3 = 82.7nFC_Lage4 = 83.6nFC_Lage5 = 84.5nFC_Lage6 = 85.3nFC_Lage7 = 86.2nFC_Lage8 = 87.0nFC_Lage9 = 87.9nFC_Lage10 = 88.8nFC_Lage11 = 89.6nF

R104

L103

C109

C105

R108

C116

L120

R109

C113

L116

L109

C122

L114

C121

L104

C108

R115

R113

0

R102

R117

R118

L115

L106

R112

C103

L110

R119

R111

R101

L102

C104

L119

R121

C112

R107

R122

R_Lage11

R110

C111

C120

C107

PARAMETERS:R_Lage1 = 797.04uR_Lage2 = 805.08uR_Lage3 = 814.32uR_Lage4 = 822.96uR_Lage5 = 831.60uR_Lage6 = 839.16uR_Lage7 = 847.80u

R_Lage9 = 865.08u

R_Lage11 = 882.36u

R_Lage8 = 856.44u

R_Lage10 = 873.72u

C102

R106

L117

C118

L122

L130

C123

L133

C134

R127

L123

C128

C_P7_GE

132.97n

R134

R_Lage3

L127

L132

R125

L129

C_P3_P4

147.24n

S

Vterminal1


L125

R126

C131

C127

R130

R131

C133

L131

L134

L126

C130

R133

R_Lage2

0

R124

R132

R_Lage1

L128

R123

C126

C125

L124

C132

R129

C129

C124

R128

C_P4_P5

147.24n

R_P1_L R_P2_L

C_P5_P6

147.24n

R_P3_L R_P5_LR_P4_L R_P6_L R_P7_L

C_P6_P7

147.24n

PARAMETERS:R_Anbindung = 100k

C_P4_GE

22.5n

C_MessKable1 C_MessKable2 C_MessKable3 C_MessKable4 C_MessKable5 C_MessKable6

00

C_MessKable7

0 0000

PARAMETERS:L_Lage1 = 1.4485uHL_Lage2 = 1.5043uHL_Lage3 = 1.5527uHL_Lage4 = 1.6044uHL_Lage5 = 1.6513uHL_Lage6 = 1.6977uH

L_Lage8 = 1.7865uHL_Lage7 = 1.7421uH

L_Lage9 = 1.8247uHL_Lage10 = 1.8716uHL_Lage11 = 1.9140uH

0

R1

L1L_Lage1

R2

C1

L2L_Lage2

C2

R3

L3

L_Lage3

C3

c4

C6

C5

L5

R4

R5

L6

R6

C9

C_Lage6

R9

R_Lage6

C7

L9

L_Lage6

R7

R_Lage4

R8

R_Lage5

L8

L_Lage5

C8

L7

L_Lage4

C11

C_Lage8

R11

R_Lage8

C12

C_Lage9

L11

L_Lage8

L12

L_Lage9

R12

R_Lage9

R10

R_Lage7

L10

L_Lage7

C10

C_Lage7

0

C_P1_GE

132.97n

R31

C30

R26

L30

L25

L15

R15

L29

L13

R29

C28

C26

C32

L28

R30

R27

R13

L31

C31

R24

R25

C29

R14

C27

R32

L27

C25

C15

L14

R28

C24C13

C14

L26

PARAMETERS:C_Messkable = 24nF

L32

L4

C16

R17

C17

C18

L18

L17

L16

R16

R18

C19

R20

C20

C21

L20

L19

R19

L21

R21

C22

C_Lage10

C23

C_Lage11

L22

L_Lage10

R22R_Lage10

L23

L_Lage11

R23

L34

R33

L33

C34

C33

R34

0

C_P2_GE

22.5n

C_P1_P2

147.24n

L36

L42

C43

R53

L52

C46

L50

L44

R51

C_P3_GE

22.5n

C56

R38

L38

L46

C53

C_P2_P3

147.24n

L56

0L37

C42

L53

C55

L55

L54

L48

R40

R52

C49

R41

C45

C38

L45

R44

C39

R42

R55

C35

L47

L35

R35

L40

R39

0

R50

R49

R37

L49

C54

R36

R45

C37

R47

L51

L43

C36

R54

C51

C52

C48

C41

C44

C40

L39

L41

R56

R43

C47

R46

C50

R48

R62

R76

R71

R59

0

C74

R77

C62

L67

R75

C77

R67

R60

C61

R69

C75

L63

R64

C70

C66

L62

L58

R78

C68

R74

L60

C59

R72

R65

L61

L75

C63

C60

INCLUDE: Kopplungen_1kHz.txt

S

Vterminal2


L69

R63

L66

L71

R68

C73

R58

R73

R61

C78

R70

C64

L72

L77

L64

C69

L57

C67

L70

L65

L73

L68

C65

L74

R66

C76

L76

C71

• Maximum voltages (to ground or terminal to terminal) are used to excite two detailed models (1 kHz and 50 kHz). Maximum internal voltages are identified and located.

20 | S. Fink | ITP |07.04.2009


Calculated voltages in time domain

The calculated terminal voltages are in good agreement with some ITER DDDs.But non linear internal voltage distribution was found already during fast discharge without fault which was not in agreement with the simple calculations of the ITER DDDs (where only linear internal voltage distribution is assumed).

For an ideal fast discharge all coils have the same maximum voltage of 3.5 kV to ground and between both terminals of each coil.

=> HV tests are required to confirm proposed test voltages are compatible with ITER design

-2000

-1000

0

1000

2000

3000

4000

5.000 5.020 5.040 5.060 5.080 5.100

FD without fault - L8

UL8 terminal1

UL8 terminal2

21 | S. Fink | ITP |07.04.2009


Long term testing on ITER TFMC• Insulation: conductor and radial plate insulation

(ground insulation has fault)• Maximum voltage test value derived from

calculation of transient behaviour:11 kV peak (factor compared to TFMC acceptance tests: ≈4 for DC and ≈8 for AC)

• Voltage waveform: DC and AC• Duration of 3 voltage steps each: 10 h

• No voltage breakdown appeared during DC test (UDC, max = 11 kV)

• Breakdown appeared after 9 h 39 min of 7.78 kVrms on ground insulation during conductor insulation test on known fault location (increase of PD activity 15 min before breakdown)

ITER TFMC outside the cryostat=> Proposed test values for conductor and radial plate insulation would be OK

22 | S. Fink | ITP |07.04.2009


Burn out of fault location on ITER TFMC

• The burn out confirms the assumption of the fault location

Flashes around the helium tubes during burn out

23 | S. Fink | ITP |07.04.2009


Conclusion for ITER

• Calculation of terminal voltages and assuming only linear voltage distribution is not enough for prediction of internal voltages

• A Paschen Test is indispensable to prove high voltage strength during vacuum breakdown

• A cold test is recommended to verify reliable HV operation at cryogenic temperature

• Conductor and radial plate insulation can withstand the proposed test voltages derived from calculation of transient behaviour of ITER TF in special fault case for 10 h without breakdown.=> 1 working day (8 h) Paschen Test with permanently applied high voltage would be possible

24 | S. Fink | ITP |07.04.2009


End

25 | S. Fink | ITP |07.04.2009


3D FEM model for ITER TFMC

3D-FEM model of ITER TFMC for direct voltage calculation (University of Karlsruhe)

26 | S. Fink | ITP |07.04.2009


Terminal voltages in time domain (TF-7)

Maximum voltage to ground in fault case 2 is 16.35 kV (t = 5.0877 s,tr = 3.5 ms, terminal L8:2)

-5000

0

5000

10000

15000

20000

5.000 5.020 5.040 5.060 5.080 5.100

failure of FDU 2 and 3 + earth fault 3-1

Uterminal 2:1

Uterminal 2:2

Uterminal 8:1

Uterminal 8:2

-2000

-1000

0

1000

2000

3000

4000

5.000 5.020 5.040 5.060 5.080 5.100

FD without fault - L8

UL8 terminal1

UL8 terminal2

For an ideal fast discharge all coils have the same maximum voltage of 3.47 kV to ground and between both terminals of each coil.Rise time: tr = 1.6 ms.

27 | S. Fink | ITP |07.04.2009


Frequency measurements on ITER TFMC

Calculated (network) and measured resonance frequency show good agreement for the relevant cases

Damping directly in resonance case and above was calculated with poor accuracy sometimes too low and sometimes too high

Comparison of the transfer functions on outermost inner pancake joints for radial plates connected over resistors and symmetric excitation.

0

0,5

1

1,5

2

2,5

0 100 200 300 400 500

FRS.QDA

|G|FRS

calculated Case 2 ±5 kV

|G(f)|

fkHz

fink - insulation co-ordination and high voltage testing ... · pdf file2 | s. fink | itp...

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