IEEE SENSORS JOURNAL, VOL. 15, NO. 3, MARCH 2015
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Core Saturation Detection and Calibration of a Current Probe for Fast Transient Currents Yi Liu, Member, IEEE, Tingzhi Zhao, Yibo Han, and Fuchang Lin, Member, IEEE
Abstract— Low-frequency distortion caused by core saturation has a great effect on the performance of magnetic core Rogowski coils (RCs). The maximum current-time product can be used to determine the reliable operating range of such a coil. This paper presents a core saturation detection and calibration method of RC with a Mn–Zn ferrite core for fast transient currents. To determine the maximum current-time product, the parameters of the core material are obtained from the dynamic initial B–H curves under fast current excitations, and the maximum current-time product of the probe is derived based on the magnetic path model. The low-frequency distortion phenomenon of core saturation and the calibration result of the maximum current-time product are analyzed and verified in the experiment. It shows that the probe has a good amplitude-frequency response in the range from 5 Hz to 2 MHz, with the sensitivity of 1.44 V/kA. Index Terms— Current measurements, current probe, Rogowski coil, magnetic materials, ferrite, magnetization curve.
I. I NTRODUCTION OGOWSKI coils (RCs) are widely used in those applications where isolation, robust, low cost, and easy to use are required [1]–[10]. Air core RCs with the appropriate active integrators or digital integrators can obtain good frequency characteristics [4], [5], [7]. However, the integrators are always together with external power supply, and the measurement systems are complexity and inconvenient. Magnetic core Rogowski coils (MRCs) can provide high accuracy and wide frequency bandwidths, but the saturation and hysteresis effects on the magnetization resulting in detection error should be considered while the primary current contains a very low frequency, direct-current component or is loaded with the fast transient current in a high frequency regime [10]–[12]. In the previous work, the design constraints and saturation limitations were introduced and analyzed. Hartmann et al. designed an alternating-current measurement system based on magnetic core current probe, and described the low-frequency and high-frequency behavior [10]. A wide bandwidth alternating-current monitoring system based on two-stage magnetic core current transformer for power electronics and EMI measurement was constructed and tested [3].
R
Manuscript received July 10, 2014; revised October 11, 2014; accepted October 12, 2014. Date of publication October 16, 2014; date of current version December 11, 2014. The associate editor coordinating the review of this paper and approving it for publication was Prof. Octavian Postolache. Y. Liu, Y. Han, and F. Lin are with the State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, China (e-mail:
[email protected];
[email protected];
[email protected]). T. Zhao is with the State Grid Shandong Electric Power Maintenance Company, Jinan 250021, China (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSEN.2014.2363497
Special attention was paid to direct-current and low frequency alternating-current signal saturation effects, with the aim of reducing distortion effect and low frequency variation. An air gap was set in the flux path of a MRC, and the linear region of the magnetic core was extended [2]. It should be noted that fast transient currents could also saturate the magnetic core, so it is necessary to indicate the reliable operating range [13]–[19]. In order to determine the performance, parameters identification and modeling of RCs were focused and presented [20]–[22]. The performance of a MRC is mainly determined by the coil construction and the characteristics of its magnetic core material. Since the core saturation has a great effect on the probe’s performance, there are two issues should be considered. One is how to analyze the core saturation causing a distortion on the output signal, and the other is how to determine the reliable operating range of the MRC. There is less related research work. It is necessary to propose a method to obtain the critical core saturation condition, and make it simple and practical in the design and calibration of such a probe. The low frequency distortion phenomenon can be explained when considering the effect of the magnetizing current based on magnetic path model of the MRC. For fast transient applications, current-time product (CTP) can be used to determine the reliable operating range of the MRC. The dynamic initial B-H curves of the core material under fast current excitations are measured, and key parameters are extracted. The maximum CTP of the probe is derived based on the parameters of the core material and the magnetic path model, and the calculated result is verified in the experiment. At last, the amplitude-frequency characteristics, linearity, and sensitivity of the probe are presented. II. F UNDAMENTALS ON S ELF -I NTEGRATING ROGOWSKI C OILS AND S ATURATION L IMITATIONS A. Lumped Element Model Fig. 1(a) shows the dimensions of the toroidal core RC with rectangular cross-section. D1 , D2 , and h are the inside diameter, outside diameter, and height of the core, respectively. The lumped element model of RC is shown in Fig. 1(b) [18]. M, L 0 , R0 , and C0 are the mutual inductance, lumped inductance, resistance, and capacitance of the coil, respectively. Rs is the integrating resistor terminating the coil. i 1 and i 2 are the measured transient current, and loop current respectively. Without consideration of the stray capacitance C0 , the loop-voltage equation is M
di 2 di 1 = i 2 (R0 + Rs ) + L 0 dt dt
1530-437X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
(1)
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Fig. 1. Dimensions and lumped element model of Rogowski coil. (a) Dimensions. (b) Lumped element model.
When i 2 · (R0 + Rs ) L 0 · di2 /dt, ignoring the voltage-drop of the resistance, equation (1) becomes L0 (2) = ni 2 M The coil is called self-integrating RC and it is suitable to measure fast transient currents [5], [7]. The output voltage across the integrating resistor is i1 ≈ i2
u s = Rs i 2 ≈
M Rs i1 L0
(3)
The transfer function relating the measured transient current i 1 to the voltage across the terminating resistor u s is given by equation (4). u s (s) = =
L 0 C0
s2
Mi 1 (s)s + (L 0 /Rs + R0 C0 )s + (R0 /Rs + 1)
Mi 1 (s)s L 0 C0 (s − s1 )(s − s2 )
(4)
where, s1,2 = −ω1 ±(ω12 −ω22 )0.5 are two poles of the system. Symbols ω1 and ω2 are respectively defined as L 0 + R0 C 0 Rs 2L 0 C0 Rs R0 + Rs ω2 = L 0 C 0 Rs
ω1 =
(5)
(6)
Under step current excitations, the output voltage can be expressed as u s (t) =
Mi 1 · (es1 t − es2 t ) L 0 C0 (s1 − s2 )
(7)
The rise time (from 10% to 90% transition) of the current probe can be calculated by tr ≈ 2.2Rs C0 .
(8)
B. Saturation Limitations The initial magnetization curve of magnetic material is shown in Fig.2. In curve oabc, as the current through the magnetic core increases, the magnetic field intensity (H ) increases from zero gradually, and the magnetic induction intensity (B) in the core increases. The permeability follows a U -shaped curve. In the initial segment, the permeability is low because of H is little. The permeability has a large value in the middle of
Fig. 2.
Initial B-H curve of the magnetic material.
the curve, and decreases at the end due to the core saturation. When the coil works along Oa segment orbc segment, the permeability is low, and the inductance L 0 in equation (1) may not satisfy the self-integrating condition. A distortion may appear in the measurement results. The analysis of the distortion caused by the core saturation is the key point of this paper. C. Frequency Behaviors When the RC is under the steady-state sinusoidal excitation, from equation (4), the lower cutoff frequency (LCF) f L and the higher cutoff frequency (HCF) f H can be derived as 1 fL ≈ (9) L0 2π( ) R0 + Rs 1 L0 2 fH ≈ = ω (10) 2π Rs C0 2π Rs 0 where, ω0 = (L 0 C0 )−0.5 . The LCF depends on its parameters (R0 , L 0 ) and the terminal resistor (Rs ), and the HCF is determined by the natural resonant frequency of the coil. It is noted that L 0 should be as large as possible to obtain a good low frequency behavior. It requires either a high permeability core or a large number of turns (n) to get a large L 0 . C0 is distributed, including the winding-to-winding and the coreto-winding capacitors. The HCF can be increased if C0 was minimized. Some methods, such as a single-layer winding strategy, and a minimum number of turns (n), are used to get the highest possible upper bandwidth. Unfortunately, the LCF would both be increased with the two methods, so a tradeoff should be found by considering the frequency characteristics of the measured current. As shown in Fig. 3, the current measuring system (MS) can be thought as a band-pass system, which predominantly is able to suppress the very high frequency component and the very low frequency component. The −3dB LCF and HCF are f L , and f H , respectively. For the measured current MC1, it has a lot of low frequency components beyond f L . There is low frequency distortion on the measured waveform when using the MS to detect the origin waveform. For the MRC, there are two possibilities to cause the low frequency distortion: one is the inherent LCF is high, and the bandwidth cannot cover the frequency components lower than the LCF; the other is the LCF will increase as the core get saturated gradually, causing low frequency components loss. For the measured
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Fig. 5. Typical voltage and current waveforms at the charging voltage of 500 V.
Fig. 3. Effects of low frequency distortion (left) and high frequency distortion (right). (MS: measuring system; MC: measured current).
Fig. 4. Equivalent circuit of the test stand for the toroidal magnetic core. (AC: alternating-current).
current MC2, it has a lot of high frequency beyond f H . The measured waveform shows slower rise edge when using the MS to detect the origin waveform. It is called high frequency distortion. For the MRC, it is important to calibrate the f L and f H , and determine the critical core saturation. III. DYNAMIC C HARACTERISTICS OF Mn-Zn F ERRITE C ORE The mutual inductance and self-inductance of the coil depend on the permeability and the dimensions of the core, and number of turns. Under fast transient current excitation, it is more appropriate to use the pulse permeability to calculate the inductance. The pulse permeability is defined as under pulse magnetization, the ratio of the maximum change Bm and the peak pulse magnetic field Hm , i.e. μr1 = Bm /(μ0 Hm ). The pulse width and incremental flux density have some influence on the pulse permeability, so the pulse permeability should be measured under a certain pulse width and incremental flux density. A. Test Stand The equivalent circuit of the test stand, which consists of the magnetization curve test circuit and the alternating-current demagnetization circuit, is shown in Fig. 4. C = 3.0 μF, R1 = 1 M, R2 = 300 , R = 2.5 , S is a thyristor. The ratio of the transformer T1 and T2 are 68.2 (220V/15kV), and 3 (220V/660V), respectively. The tested core with 6 turns
winding is connected to the switch K 2 . Prior to each shot, K 2 is connected to K 3 , and the demagnetization circuit producing an alternating current with a suitable amplitude is used to demagnetize the core to the initial point (H = 0 A/m, B = 0 T). The alternating current with a peak value of 2.5 A lasts for 1 min, and then goes to zero gradually. The Ferrite core with inner diameter of 55 mm, outer diameter of 100 mm, and height of 20 mm is tested, and the coercivity provided by the manufacturer is about 12 A/m. The demagnetizing field H Q satisfies H Q > (1 ∼ 2)Hc, the core can be demagnetized effectively [23]. After the core demagnetized, the capacitor C is charged to a set voltage, and then thyristor S is turn on. R is used to limit the peak value of the current after the core saturated. The voltage across the magnetic core u is measured by a Tektronix P6015A, and the current i flowing through the magnetic core is measured by a Pearson CT 110A. Typical waveforms of u and i are shown in Fig. 5. The saturation time tsat is shown in Fig. 5. tsat was defined to the time period from the commencement of presaturation leakage current to the time at which the voltage across the core decreasing rapidly. It is determined by the voltage-second product, which is defined as the time that the magnetic material can support a magnetic flux for a given time-dependent voltage. As shown in Fig. 4, the voltage-second product under the charging voltage of 500V and n = 6 is about 1.23 × 10−3 V· s. The magnetic induction B and magnetic field intensity H can be expressed as (11), (12) respectively. 1 B = udt (11) nA ni (12) H = l where, n is the number of turns; A is the effective crosssectional area of the core; l is the mean magnetic path length, l = π(D2 − D1 )/[ln(D2 /D1 )]; D1 and D2 are the inner diameter and the outer diameter respectively. B. Experimental Results and Analysis As shown in Fig. 6, the initial magnetization curves under different charging voltages across C are obtained based on equation (11) and (12). When H reaches approximately
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Fig. 6. Measured results of initial B-H curves under different charging voltages.
400 A/m, the saturation induction Bs is 0.44 T. As the magnetization rate increases, due to the influence of magnetic viscosity and eddy current, the magnetization curve rises slowly [18]. To obtain a large inductance, the pulse permeability should be higher than a certain value under a certain pulse width and incremental flux density. It is assumed that the flux density swing B is aBs (0 < a < 1). Then the average permeability can be obtained by aBs μ0 H1
Structure schematic of the current probe. TABLE II PARAMETERS OF ROGOWSKI C OIL
TABLE I PARAMETERS OF Mn-Zn F ERRITE C ORE
μav =
Fig. 7.
(13)
where, H1 is the magnetic field corresponding to aBs . From Fig. 6, when H1 is 120 A/m, the average pulse permeability is about 2200. Table I shows the comparison of the parameters of Mn-Zn ferrite core obtained from pulse excitation and power frequency. The manufacturer always tests the cores under low magnetic field intensity, and the cores are not saturated completely. So there is a difference between the saturated magnetic induction. It should be noted there is a difference between the permeability, and it may cause an approximate 30% error when using the permeability provided by the manufacturer to calculate and analyze the inductance and CTP of the MRC. IV. D ESCRIPTION OF C URRENT P ROBE AND A NALYSIS OF C ORE S ATURATION A. Description of the Current Probe Based on the tested Mn-Zn Ferrite core, a MRC for measuring fast transient currents is design and constructed. The coil winding uses the varnished wire with the diameter of 0.58 mm, and has a single layer and a compensation turn.
The winding has 313 turns, and is kept uniform along the length of the coil. The construction of the current probe is shown in Fig. 7. The resistors are packaged in a separate shielding box. It can reduce the undesired signal. The parameters of the coil are listed in Table II. The electric parameters are measured by Agilent 4263B under 1kHz. B. Analysis of Core Saturation From Fig. 1(b), the MS can be thought to a transformer with one turn primary winding. A magnetic path model of the RC can be built to assist in analyzing the performance of the current probe. For a MRC without core saturation, the magnetic flux within the core should satisfy φ = i e · G m < φs = B s · A
(14)
where, G m is the permeance of the magnetic circuit; s is the saturation flux of the core; i e is the magnetizing current, and can be determined by i 1 , and i 2 . It should be noted that i e is approximately equivalent to zero in equation (2), and the core would never be saturated. i e can be expressed as ie = i1 − i2 · n
(15)
If the coil was worked without any core saturation, the relative permeability can be thought to be a constant. So G m depends on the dimensions of the core and relative permeability. When the core has the square cross-section
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shown in Fig.1, G m can be expressed as Gm =
μ0 μr h D2 ln 2π D1
(16)
where, μ0 is the vacuum permeability; μr is the relative permeability of the core material without saturation. Substituted equation (15) and (16) into equation (14), when the MRC works without any core saturation, it should satisfy ie
tm
Fig. 8.
Analysis flowchart of the current-time product.
where, tm is the peak time; a1 , a2 , a3 , b1 , b2 , b3 are constants, which are determined by the circuit parameters. In the circuit, the main capacitance is 3275 μF, stray resistance is 10 m, and the inductance is 5 μH. The constants are calculated as a1 = 5040, a2 = 6148, a3 = 1132, b1 = 7072, b2 = 1500, b3 = 2335. The Laplace transform of equation (22) can be expressed as ⎧ ⎪ ⎪a1 b1 ⎨ s 2 + b12 (23) i L (s) = 1 1 ⎪ ⎪ − a3 e tm b3 ⎩a2 etm b2 s + b2 s + b3 The Laplace transform of i e can be obtained based on equation (20) and (23). ⎧ b1 β ⎪ ⎪ · ⎨a 1 s + β s 2 + b12 i e (s) = (24) 1 1 β β ⎪ ⎪ · · − a3 e tm b3 ⎩a 2 e t m b 2 s + β s + b2 s + β s + b3 where, β = (R0 + Rs )/L 0 . The expression of i e (t) can be obtained by inverse Laplace transform from equation (24). ⎧ ⎪ −βt − βa1 b1 cos(b t) − βa1 F sin(b t), ⎪ 1 1 ⎨ Xβa1 b1 e X X2 (25) i e (t) = 0 ≤ t ≤ tm ⎪ ⎪ ⎩ −βt −b t −b t (1 + 4 )e + 2 e 2 + 3 e 3 , t > tm where, X and F are variables. The parameters in equation (25) satisfy ⎧ 2 ⎪ ⎪ Xβ = F, Xb1 + Fβ = 1 ⎪ b t ⎪ m 2 ⎨ βa2 e βa2 eb2 tm , 2 = 1 = (26) b2 − β β − b2 ⎪ ⎪ b3 tm b3 tm ⎪ e e βa βa 3 3 ⎪ ⎩3 = , 4 = β − b3 b3 − β where, 1 , 2 , 3 , 4 are variables. When the charging voltage is 200 V, the discharge current is shown in Fig. 9. The core of the current probe is in critical saturation. The peak value of the current is 5.04 kA with a peak time of tm = 222 μs. Substituted the circuit parameters
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Fig. 11.
Schematic of current probe calibration at different frequency.
Substituted the relationship of i 2 = u s (t)/Rs into equation (27), i e can be deduced as
Fig. 9.
n(R0 + Rs ) i e = i 1 − ni 2 = L 0 Rs
Results of low frequency distortion displayed in the measurement.
t u s (t)dt
(28)
0
Substituted equation (16), (18), and (28) into equation (14), there is t u s (t) 2Bs n 2 A2 (29) n· dt < Rs (Rs + R0 ) · (D2 − D1 ) · h 0
The CTP of the measured current should satisfy t =
i 1 dt = 0
Fig. 10.
Measured waveforms from the pulsed power supply.
into equation (25) and (26), the value of i em corresponding to the critical core saturation in the measurement is about 96 A. The magnetic field intensity at the moment can be obtained as 391 A/m based on equation (12). From Fig. 6, the magnetic induction corresponding to 391 A/m is 0.44 T, and the core got saturated. Without consideration of the magnetizing current, if the core was not saturated before the peak value, the amplitude of the measured current decreases, and H would decrease. Then the core works along the dotted line in Fig. 2, and would not be saturated. However, the saturation was first appeared in the decline part of the measured current, as shown in Fig. 9. There is no core saturation occurred in Fig. 10, and the saturation effect begins to appear in Fig. 9 as the charging voltage increases. For a transient current measurement, the CTP will increase all the time if the polarity of the current did not reverse. It reaches the peak value at the end of the current. So the critical saturation point is always appearing at the last stages of the current firstly. It also can be called as low-frequency distortion, as shown in Fig. 3. B. Determination of Maximum Current-Time Product For a current probe, the maximum CTP can both be determined by calculation and experimental test. The theoretical maximum CTP is obtained based on the magnetic path model. Based on equation (1) and (15), i e can be expressed as 1 i e = i 1 − ni 2 = M
t i 2 (R0 + Rs )dt 0
(27)
t n 0
u s (t) dt < 4.07 A · s Rs
(30)
Theoretically, if the CTP of the measured current was not exceed 4.07 A · s, the core will not saturate, and the current probe can measure the current accurately. From Fig. 9, the critical saturation phenomenon is first appeared in the decline part of the measured current. The integral of the current times time before the saturation is obtained based on experimental waveform, and the measured maximum CTP is about 4.24 A · s. It is in agreement with the calculated value from equation (30). The saturation point can be represented in the experiment, and it is possible to verify the reasonability of the calculation method. VI. C ALIBRATION OF THE C URRENT P ROBE When the current probe is used to measure transient currents, not only the reliable operating range should be determined, but also other characteristics, such as amplitudefrequency characteristics, linearity, and sensitivity, etc. should be obtained. A practical method is used to determine the other characteristics of the current probe. A. Bandwidth A comparison method based on two current probes without invasive connection is used to determine the characteristics. Nearly sine current waveforms are produced by an L − C series resonance circuit. The two current probes are used to measure the current at the same time. The Pearson CT (model 110A) can be thought as a standard instrument. The scope is Tektronix TDS 3052C Digital Phosphor Oscilloscope. The comparison of the measured results can reflect the performance of constructed current probe. The test stand is shown in Fig. 11. The oscilloscope and the PC are communicated
LIU et al.: CORE SATURATION DETECTION AND CALIBRATION OF A CURRENT PROBE
Fig. 12.
Results of frequency characteristics of the current probe.
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Fig. 13. Typical measured waveforms in the frequency characteristic test with the frequency of 0.56 MHz.
through a network cable, and the data is extracted by the software of e-Scope. The circuit is worked under damped conditions, and the discharge current can be expressed as R R2 1 − i (t) = a4 · e− 2L t sin t (31) LC 4L 2 where, a4 is a constant, and R is the stray resistance. When i (0+ ) = 0, (di /dt)t=0+ = U1 /L, it can be obtained that a4 =
U1 L C
−
R2 4
(32)
where, U1 is initial voltage across C. A series of nearly sine currents with different frequency are produced by adjusting the value of L and C. The equivalent frequency is calculated by 0.35 f = tr
(33)
where, tr is the rise time. The gain of the current probe is calculated based on the experimental results. Gain(dB) = 20 log10
Us Up · Sp
(34)
where, Us is the first peak value of the voltage across the terminal resistor Rs ; U p is the corresponding peak value of the voltage obtained by the Pearson CT; S p is the sensitivity of the Pearson CT. As shown in Fig. 12, the gain is in the range of −56 dB ± 1 dB. The gain approximately was a flat line in the measured range from 5 Hz to 2 MHz. Some typical waveforms in the frequency characteristic tests are shown in Fig. 13. The higher frequency response test is completed when there is a high frequency distortion appeared. There is a high frequency distortion appeared when the rise time (10% to 90% peak value) is 110 ns, as shown in Fig. 14. B. Linearity and Sensitivity In order to determine the linearity under different current waveforms, two types of current pulses are applied to check the amplitude response. The comparison system is similar to the circuit shown in Fig. 11. The two current probes are both connected in a pulsed power supply and a lightning current generator. The front time (10% to 90% peak value) of the
Fig. 14. High frequency distortion displayed in the frequency characteristic test results.
pulse current in the pulsed power supply is 160 μs, and the half peak value width is 0.63 ms. The lighting current generator is shown in Fig. 15(a). The typical output current pulse of the lighting current generator is shown in Fig. 15(b). The front time (10% to 90% peak value) is 6.8 μs, and the half peak value width is 20μs. The peak values of the measured signals are obtained by the Pearson CT and self-made current probe. The results are shown in Fig.16, and very good linearity is confirmed under different pulse shapes. The sensitivity of the probe is 1.44 V/kA. In order to determine the overall approximation uncertainty to the Pearson CT, the fitting uncertainty e% as the percentage of the peak current of fitting error over the entire linearity test range can be estimated by. 25 [v (j) − v (j)]2
w d v (j) d j =1 (35) e% = 25 where, vw ( j ) is the measured peak value corresponding to the test number of j . vd ( j ) is the voltage related to the ideal straight line with a slope of 1.44 V/kA. The effective test shot is 25, and the calculated uncertainty is about 0.2%. Table III shows the comparison of the calculated and measured parameters of the current probe. It is obvious that the LCF and sensitivity are consistent between calculated and measured values. The magnetic path model, which is used to determine the reliable operating ranging of the current probe,
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of magnetic materials under similar operating conditions can be used to determine the current-time product of such a current probe based on magnetic path model. The amplitudefrequency characteristics, linearity, and sensitivity of the probe are determined by experimental calibration, and the calibration method is simple and practical. R EFERENCES
Fig. 15. Amplitude response test in the lightning current pulse generator. (a) Picture of the lightning current pulse generator. (b) Measured current waveforms in the lightning current pulse generator.
Fig. 16.
Results of linearity test under different current pulses.
TABLE III C OMPARISON OF C ALCULATED AND M EASURED PARAMETERS OF C URRENT P ROBE
is practical. However, the HCF has a large difference. It is much better to use the distributed element model of the current probe to analyze the high frequency characteristics. VII. C ONCLUSION The core saturation of magnetic core Rogowski coil has an effect on the measurement results, and it can be detected by calibrating the current-time product. The characteristics
[1] C. Qing, L. Hong-Bin, H. Ben-Xiong, and D. Qiao-Qi, “Rogowski sensor for plasma current measurement in J-TEXT,” IEEE Sensors J., vol. 9, no. 3, pp. 293–296, Mar. 2009. [2] L. Du, C. Wang, X. Li, L. Yang, Y. Mi, and C. Sun, “A novel power supply of online monitoring systems for power transmission lines,” IEEE Trans. Ind. Electron., vol. 57, no. 8, pp. 2889–2895, Aug. 2010. [3] F. Costa, E. Labouré, F. Forest, and C. Gautier, “Wide bandwidth, large AC current probe for power electronics and EMI measurements,” IEEE Trans. Ind. Electron., vol. 44, no. 4, pp. 502–511, Aug. 1997. [4] C. R. Hewson, W. F. Ray, and R. M. Davis, “Verification of Rogowski current transducer’s ability to measure fast switching transients,” in Proc. 21st IEEE APEC, Mar. 2006, pp. 573–579. [5] W. Li, C. Mao, and J. Lu, “Study of the virtual instrumentation applied to measure pulsed heavy currents,” IEEE Trans. Instrum. Meas., vol. 54, no. 1, pp. 284–288, Feb. 2005. [6] C. Qing, L. Hong-Bin, Z. Ming-Ming, and L. Yan-Bin, “Design and characteristics of two Rogowski coils based on printed circuit board,” IEEE Trans. Instrum. Meas., vol. 55, no. 3, pp. 939–943, Jun. 2006. [7] Y. Liu, F. Lin, Q. Zhang, and H. Zhong, “Design and construction of a Rogowski coil for measuring wide pulsed current,” IEEE Sensors J., vol. 11, no. 1, pp. 123–130, Jan. 2011. [8] R. Romary, C. Demian, and P. Schlupp, and J.-Y. Roger, “Offline and online methods for stator core fault detection in large generators,” IEEE Trans. Ind. Electron., vol. 60, no. 9, pp. 4084–4092, Sep. 2013. [9] P. Orr, P. Niewczas, C. Booth, G. Fusiek, A. Dysko, F. Kawano, T. Nishida, and P. Beaunont, “An optically-interrogated Rogowski coil for passive, multiplexable current measurement,” IEEE Sensors J., vol. 13, no. 6, pp. 2053–2054, Jun. 2013. [10] M. Hartmann, J. Biela, H. Ertl, and J. W. Kolar, “Wideband current transducer for measuring AC signals with limited DC offset,” IEEE Trans. Power Electron., vol. 24, no. 7, pp. 1776–1781, Jul. 2009. [11] I. A. Metwally, “Design of different self-integrating and differentiating Rogowski coils for measuring large-magnitude fast impulse currents,” IEEE Trans. Instrum. Meas., vol. 62, no. 8, pp. 2303–2313, Aug. 2013. [12] S. K. Mishra, S. Nigam, K. Aneesh, C. P. Navathe, and P. D. Gupta, “Measurement of EMI in a capillary discharge plasma system and its application as a diagnostic tool,” in Proc. 10th IEEE INCEMIC, Bangalore, India, Nov. 2008, pp. 211–215. [13] J. D. Ramboz, “Machinable Rogowski coil, design, and calibration,” IEEE Trans. Instrum. Meas., vol. 45, no. 2, pp. 511–515, Apr. 1996. [14] E. Abdi-Jalebi and R. McMahon, “High-performance low-cost Rogowski transducers and accompanying circuitry,” IEEE Trans. Instrum. Meas., vol. 56, no. 3, pp. 753–759, Jun. 2007. [15] W. F. Ray and C. R. Hewson, “High performance Rogowski current transducers,” in Proc. IEEE IAS, vol. 5. Rome, Italy, Oct. 2000, pp. 3083–3090. [16] O. Poncelas, J. A. Rosero, J. Cusido, J. A. Ortega, and L. Romeral, “Motor fault detection using a Rogowski sensor without an integrator,” IEEE Trans. Ind. Electron., vol. 56, no. 10, pp. 4062–4070, Oct. 2009. [17] G. D’Antona, M. Lazzaroni, R. Ottoboni, and C. Svelto, “AC current-tovoltage transducer for industrial application,” in Proc. 20th IEEE IMTC, vol. 2. Vail, CO, USA, May 2003, pp. 1185–1190. [18] B. Jie, Heavy Current Measurement. China, Beijing: Mechanical Industry Press, 1987, pp. 181–210. [19] X. Wang, M. Han, X. Wang, and J. Feng, “Study of the core saturation in a Rogowski coil,” J. Elect. Technol., no. 2, pp. 34–38, May 1994. [20] I. A. Metwally, “Performance improvement of slow-wave Rogowski coils for high impulse current measurement,” IEEE Sensors J., vol. 13, no. 2, pp. 538–547, Feb. 2013. [21] I. A. Metwally, “Coaxial-cable wound Rogowski coils for measuring large-magnitude short-duration current pulses,” IEEE Trans. Instrum. Meas., vol. 62, no. 1, pp. 119–128, Jan. 2013. [22] M. Shafiq, L. Kutt, M. Lehtonen, T. Nieminen, and M. Hashmi, “Parameters identification and modeling of high-frequency current transducer for partial discharge measurements,” IEEE Sensors J., vol. 13, no. 3, pp. 1081–1091, Mar. 2013.
LIU et al.: CORE SATURATION DETECTION AND CALIBRATION OF A CURRENT PROBE
[23] R. H. Wang, Design of Pulse Transformers. Beijing, China: Science Press, 1996, pp. 204–208. [24] Y. Liu, F. Lin, L. Dai, Q. Zhang, L. Li, Y. Han, W. Li, and W. Lu, “Development of a compact 450-kJ pulsed-power-supply system for electromagnetic launcher,” IEEE Trans. Plasma Sci., vol. 39, no. 1, pp. 304–309, Jan. 2011.
Yi Liu (S’10–M’14) was born in Hunan, China, in 1985. He received the B.S. degree in electrical engineering from Wuhan University, Wuhan, China, in 2008, and the Ph.D. degree in electrical and electronic engineering from the Huazhong University of Science and Technology (HUST), Wuhan, in 2013. He is currently a Lecturer with the School of Electrical and Electronic Engineering, HUST, where he has been working on high-voltage engineering and pulsed-power technology.
Tingzhi Zhao was born in Shandong, China, in 1989. He received the B.S. degree in electrical engineering from the Shandong University of Science and Technology, China, in 2011, and the M.S. degree in electrical engineering from the School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China, in 2014. He is currently an Engineer with State Grid Shandong Electric Power Maintenance Company, Jinan, China.
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Yibo Han was born in Hubei, China, in 1991. He received the B.S. degree in electrical engineering and automation from Xi’an Jiaotong University, Xi’an, China, in 2013. He is currently pursuing the M.S. degree in electrical engineering at the School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, where he has been working on high-voltage engineering and pulsed-power technology.
Fuchang Lin (M’10) was born in Zhejiang, China, in 1969. He received the Ph.D. degree in electrical and electronic engineering from the Huazhong University of Science and Technology (HUST), Wuhan, China, in 1996. He is currently a Professor with the School of Electrical and Electronic Engineering, HUST, where he has been working on pulsed-power technology and high-voltage engineering. Dr. Lin is a Member of the Chinese Society for Electrical Engineering.
