design and calibration of rogowski coilsprojects.npl.co.uk/power_energy/docs/7 design and...
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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: [email protected]
Renata StyblíkováCzech Metrology Institute Laboratory of fundamental metrologyV Botanice 4150 72 Prague 5E-mail: [email protected]
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