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Power and Energy Workshop 22-23 March 2011, Noordwijk, The Netherlands DESIGN AND CALIBRATION OF ROGOWSKI COILS Renata Styblíková Karel Draxler Czech Metrology Institute Czech Technical University Laboratory of fundamental metrology Faculty of electrical engineering V Botanice 4 Technická 2 150 72 Prague 5 166 27 Prague 6 E-mail: [email protected] E-mail: [email protected] TYPICAL CONSTRUCTION OF ROGOWSKI COILS RECTANGULAR CROSS-SECTION CIRCULAR CROSS-SECTION OVAL CROSS-SECTION   b  M  0 N h ln   N   21 2 2 a M  0 2 a  b  2 ab  N    h  b    21 M  0 2  a  b  2 ab   ln  2   21 2     a  2  N h b  N 2   L  0 2 ln L  0 2 a  b  2 ab  N 2    h  b  2 2 a 2 2 L  0 2  a b  2 ab   ln    2 2     a    2 2 Z  R  L 2 2 2 THE UNCERTAINTY OF THE MUTUAL INDUCTANCE ROGOWSKI COIL DESIGN 2 2  N (a  b  2 a b)(b u2  a u2 )  M   M  uM   ua   ub uM   0 2 a b MAIN WINDOW OF THE SOFTWARE FOR ROGOWSKI COIL DESIGN     a b 2 a b      N u (a  b  2 a b)(b  a) a b (a  b  2 a b) uM   0 2 u  uM  2 a b a  b DEPENDENCE OF THE UNCERTAINTY OF THE M ON THE UNCERTAINTY OF THE RC DIMENSIONS u(M) (%) 0.1 1 10 U (a ,b ) (mm) 0.0076 0.076 0.76 1 1 1 U (a ,b ) (mm) 0.0092 0.092 0.92 2 2 2 ROGOWSKI COIL CALIBRATION USING A CURRENT LOOP THE LAYOUT FOR ROGOWSKI COIL CALIBRATION AT 50 HZ CURRENT LOOP CONSTANT OF THE COMPLETE SYSTEM I 2 I´ U U R COMBINED UNCERTAINTY k  1  1 N S I U N p CURRENT 2 I REGULATOR RC RN U2 V2 uk C u A2 uk B2 S kS S CURRENT PASSING THROUGH RC U SUPPLY U CURRENT I  N I  N p 2 EXPANDED UNCERTAINTY i I X Y Z TRANSFORMER COMPARATOR R N 3x380 V50 Hz    2  2 INTEGRATOR RELATIVE TYPE B UNCERTAINTY u C 2 u A u B k k S kS S OUTPUT VOLTAGE U u B  u2 u2 u2 u2 1 EXT V KS U1 U2 RN pI 1 SYNCHRO U u  j M I k  1 i S I RC 340/310 mm RC 275/250 mm USING 1 CONDUCTOR Current loop for RC calibration up to 30 kA RREESSUULLTTSS OOFF MMEEAASSUURREEMMEENNTTSS Calibrated value (kA) 25 15 25 15 10 5 4 3 2 1 Calibrated value (kA) 30 30 25 22 20 17 13 9 6,5 4 4 2,5 1 integrator const. integrator constant 100 200 200 200 200 500 500 500 1000 1 000 2 000 2 000 2 000 10 10 100 100 100 100 100 1 000 1 000 1 000 (mV/kA) (mV/kA) k 10 turns (mV/kA) 9,9893 9,9874 99,7580 99,7373 99,8805 99,8784 99,8907 999,286 999,158 999,352 k 10 turns (mV/kA) 99,80 199,2 199,0 199,20 199,50 497,60 497,30 497,80 995,50 995,40 1989,60 1989,70 1989,80 S1 S1 U(k ) (mV/kA) 0,0025 0,0028 0,0249 0,0299 0,0220 0,0210 0,0220 0,230 0,260 0,220 U(k ) (mV/kA) 0,03 0,06 0,04 0,06 0,06 0,14 0,16 0,14 0,27 0,28 0,53 0,55 0,74 S1 S1 k 1 turn (mV/kA) - - - - - 99,9100 99,8970 998,840 998,854 999,776 k 1 turn (mV/kA) - - - - - - - - 998,3 998,1 1996,80 1995,50 1994,00 S2 S2 U(k ) (mV/kA) - - - - - - - - 0,28 0,28 0,53 0,55 0,65 U(k ) (mV/kA) - - - - - 0,0210 0,0220 0,230 0,260 0,200 S2 S2 Rogowski coil with diameter 310/340 mm Rogowski coil with diameter 250/275 mm CALIBRATION AT WIDER FREQUENCY RANGE RC 1,96 100 K [mV/A] RC F [ ° ] IEEE/USB 1,94 I 80 LOCK-IN POWER V OUT 1,92 1 AMPLIFIER AMPLIFIER 1,90 60 IN SUPPLY 1,88 40 TRANSFORMER COAXIAL PC 1,86 SHUNT R B 20 1,84 f [Hz] f [Hz] VOLTAGE 0 1,82 V U SWITCH 2 FOLLOWER 1 10 100 1000 10000 100000 10 100 1000 10000 100000 -20 U 2 Frequency dependence of the K constant Frequency dependence of phase displacement  RC between measured current and induced voltage