DESIGN AND CALIBRATION OF ROGOWSKI COILS

TYPICAL CONSTRUCTION OF ROGOWSKI COILS

RECTANGULAR CROSS-SECTION

abhNM ln

2 20

21

abhNL ln

2

220

2

222

22 LRZ

CIRCULAR CROSS-SECTION

abbaNM 22

2021

abbaNL 22

220

2

OVAL CROSS-SECTION

abhabbaNM ln2

220

21

abhabbaNL ln2

2

220

2

THE UNCERTAINTY OF THE MUTUAL INDUCTANCE

22

uu

bbMa

aMMu

baabbabaNM

)uu)(2(2

u2b

2a20

ba

abbabaNM))(2(

2uu 20

Muba

bababau

)2(

DEPENDENCE OF THE UNCERTAINTY OF THE M ON THE UNCERTAINTY OF THE RC DIMENSIONS

0.920.0920.0092U2(a2,b2) (mm)

0.760.0760.0076U1(a1,b1) (mm)

1010.1u(M) (%)

Power and Energy Workshop22-23 March 2011, Noordwijk, The Netherlands

ROGOWSKI COIL DESIGN

ROGOWSKI COIL CALIBRATION USING A CURRENT LOOP

MAIN WINDOW OF THE SOFTWARE FOR ROGOWSKI COIL DESIGN

Current loop for RC calibration up to 30 kA

RC 340/310 mm RC 275/250 mm

RESULTRESULTS OF S OF MEASUREMENTSMEASUREMENTS

Rogowski coil with diameter 310/340 mm0,2000,2600,2300,02200,0210-----U(kS2) (mV/kA)999,776998,854998,84099,897099,9100-----kS2 1 turn (mV/kA)0,2200,2600,2300,02200,02100,02200,02990,02490,00280,0025U(kS1) (mV/kA)999,352999,158999,28699,890799,878499,880599,737399,75809,98749,9893kS1 10 turns (mV/kA)

1 0001 0001 0001001001001001001010integrator constant (mV/kA)

123451015251525Calibrated value (kA)

Rogowski coil with diameter 250/275 mm0,650,550,530,280,28--------U(kS2) (mV/kA)

1994,001995,501996,80998,1998,3--------kS2 1 turn (mV/kA)0,740,550,530,280,270,140,160,140,060,060,040,060,03U(kS1) (mV/kA)

1989,801989,701989,60995,40995,50497,80497,30497,60199,50199,20199,0199,299,80kS1 10 turns (mV/kA)

2 0002 0002 0001 0001000500500500200200200200100integrator const. (mV/kA)

12,5446,5913172022253030Calibrated value (kA)

YCURRENT

COMPARATOR

CURRENTREGULATOR

V2

INTEGRATOR

V1

U2RN

U1

SUPPLYTRANSFORMER

I´

EXTSYNCHRO

UiX Z

3x380 V 50 Hz

RC

CURRENT LOOPI2

OUTPUT VOLTAGE

IMjui IUkS 1

THE LAYOUT FOR ROGOWSKI COIL CALIBRATION AT 50 HZ

CURRENT PASSING THROUGH RC

NI RUpNINI 2

RELATIVE TYPE B UNCERTAINTY

222221 INS pRUUK uuuuBu

COMBINED UNCERTAINTY

22 BuAuCuSSkS kk

CONSTANT OF THE COMPLETE SYSTEM

I

NS pN

RUU

IUk

2

11

EXPANDED UNCERTAINTY

222 BuAuCuSSkS kk

USING 1 CONDUCTOR

Karel Draxler Czech Technical University Faculty of electrical engineeringTechnická 2166 27 Prague 6E-mail: draxler@fel.cvut.cz

Renata StyblíkováCzech Metrology Institute Laboratory of fundamental metrologyV Botanice 4150 72 Prague 5E-mail: rstyblikova@cmi.cz

CALIBRATION AT WIDER FREQUENCY RANGE

OUT

COAXIALSHUNT RB

U1

IN

LOCK-IN AMPLIFIER

POWERAMPLIFIER

SUPPLYTRANSFORMER

RC

V1

PC

V2 SWITCHVOLTAGE

FOLLOWER

IEEE/USBI

U2

1,82

1,84

1,86

1,88

1,90

1,92

1,94

1,96

10 100 1000 10000 100000

f [Hz]

KRC [mV/A]

Frequency dependence of the KRC constant

-20

0

20

40

60

80

100

10 100 1000 10000 100000

f [Hz]

F [ ° ]

Frequency dependence of phase displacement between measured current and induced voltage