IEEE SENSORS JOURNAL, VOL. 13, NO. 3, MARCH 2013 1081
Parameters Identification and Modeling ofHigh-Frequency Current Transducer for
Partial Discharge MeasurementsMuhammad Shafiq, Lauri Kütt, Matti Lehtonen, Tatu Nieminen, and Murtaza Hashmi
Abstract— Rogowski coil (RC) is a low-cost, air-cored, andflexible induction sensor for nonintrusive condition monitoringand thus can be used in a variety of applications. In this paper, alumped parameter model of RC is presented and an experiment-based methodology is developed to determine its parameters.The performance of the RC is analyzed for detection andmeasurement of high-frequency (pulsed) signals such as partialdischarge (PD) current pulses. A simple and efficient techniqueof numerical integration is adopted to avoid the conventionaltype of expensive and complex design analogue integrators. RCis modeled and simulated in the alternative transient program-electromagnetic transient program environment. The designedcoil is tested to measure PDs in the laboratory. Simulated andexperimental performance of RC is compared with a high-frequency current transformer. This comparison shows a goodmatch and, hence, validates the design of RC for PD applications.
Index Terms— Calibration, current sensor, damping, dataacquisition, Alternative Transient Program-ElectromagneticTransient Program (ATP-EMTP), integration, oscillations, partialdischarge, resonance, Rogowski coil.
I. INTRODUCTION
TODAY all industrially developed countries in the worldare depending on functioning and flawless power gen-
eration, transmission and distribution systems. A power sys-tem, equipped with best infrastructure of components andequipment is reliable if effective maintenance techniques areapplied for condition monitoring of its critical components.One effective method to observe the equipment state in anon-line mode (that is with all equipment operating) is partialdischarge (PD) sensing and monitoring, which provides earlyinformation of expected breakdown. Capabilities of currentsensing equipment are playing a key role in reliable detectionof PD. Today there is a variety of current sensing equip-ment available including shunts, current transformers (CT),
Manuscript received August 1, 2012; revised October 12, 2012; acceptedOctober 28, 2012. Date of publication November 15, 2012; date of currentversion February 4, 2013. This work was supported by Fortum Foundation,Finland. The associate editor coordinating the review of this paper andapproving it for publication was Dr. Kailash Thakur.
L. Kütt is with the Tallinn University of Technology, Tallinn 19086, Estonia(e-mail: [email protected]).
M. Hashmi is with the Department of Energy Systems, VTT TechnicalResearch Centre, Espoo 02044, Finland (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSEN.2012.2227712
Rogowski coils (RC), Hall effect sensors, magneto impedancesensors (MI), giant magneto resistive (GMR) sensors, pilotdevices in power semiconductors and optical current sen-sors [1]. For use with high voltage equipment, based on somecritical parameters of a sensor such as; cost, bandwidth, sen-sitivity, saturation, linearity, operating temperature, footprints,integratability, flexibility, isolation and material technology,RC has been considered as a favorite tool for PD currentsensing purposes [1].
Rogowski based current probes can be used for currentranging from few milliamperes to several thousand amperesand frequency from few hertz to several MHz, dependingupon the application and design of the RC [2]. There canbe different goals for designing a RC for current sensingapplications. Low- and medium-frequency current sensing inpower systems and power electronics applications focuseson the design of RC for few amperes to few hundredamperes with bandwidth reaching up to few MHz [3], [4].For applications like partial discharge (PD) detection andmeasurement, the design of RC is focused for high frequenciesup to tens to hundreds of MHz [5], [6].
RC is simple in construction and easy to use due to itsgalvanic isolation from the component under test. The authorsof this paper have been working with RC for PD monitor-ing purposes. In their previous work, RC was used withoutintegrator to detect, localize and characterize the propagationof PD signals in power distribution components. For effectivePD diagnostic purpose, RC should be able to measure the highfrequency PD signals in order to determine how far PD activityhas progressed and how fast it is progressing. In this paper,authors have extended their work to design RC for measuringthe original PD signals for which RC is needed to be designedalong with an efficient integrator. The challenge and goalis the accurate extraction of primary current (PD) signalfrom the output of RC. This needs the accurate modeling ofdesigned coil system to calibrate and validate the responseof prototype. For making a complete model circuit for RC,one would need to determine parameters of all electricalcomponents of RC system. Components Properties can be esti-mated based on different physical (geometrical) descriptionsand there is a variety of formulas to use [5], [7]. However,it turns out that the formulas are not very precise whenaccurate results are needed. Especially difficult are the coilcapacitance and inductance calculations. An overview aboutthe issues for calculating the inductance and capacitance of
1082 IEEE SENSORS JOURNAL, VOL. 13, NO. 3, MARCH 2013
induction sensors for high frequency signals is presented in [8].In this work measurement based parameters are proposed forreliable configuration of the model.
Integrator is a necessary part to accurately recreate theoriginal primary current from the output voltage of RC.Normally PD signals possess amplitude in few milliamperesand consist of wide band of frequencies. Close attentionis needed to design the integrator for such applications.Nowadays active, passive and numerical (digital) integrationtechniques are being used for this purpose. The first twotechniques have some serious limitations. Active integratorsconsisting of operational amplifier combined with RC-networkare only suitable for lower frequency range signal [9]. Passiveintegrators, generally RC-network and L/r (self-integration)are used for higher ranges of primary current frequencies(>100 kHz) [10]. In certain applications the properties of theanalogue and electronics integration can affect the capabilitiesof RC. Integration circuit using numerous high quality activeand passive components makes the circuits complex andexpensive. Moreover, it can experience temperature and ageingdrifts and may require periodic calibration [11]. Limitationsof amplitude, frequency and form of the signals (sinusoidal orpulsed) are also major concerns here [9]. In this paper digitalintegration technique is selected as a simple and efficientmethod. A method for selection of terminating resistanceis also presented to provide an oscillation free signal forintegration stage. The construction of the paper is describedas follows.
This paper presents all the stages of development of RCfrom construction to application for PD measurements. Work-ing principle and model representation of RC is given insection II. Section III discusses the construction featuresand building of hardware prototype of RC in laboratory.Section IV describes the parameter identification methodologyto determine the values of equivalent circuit components forcreating an accurate model of the RC. Behavior of the RC andselection criterion for external termination of RC is discussedin section V. In section VI, numerical integration techniqueis implemented on RC output in the view of final calibration.Finally, the RC is validated for operation by simulation of themodel in ATP-EMTP and actual testing in PD measurementapplication, in section VII. The results are compared with thereference measurements using a commercial HFCT. Validationfor transient current applications results show good correlation,thus RC is verified for PD monitoring operation.
II. WORKING AND DESIGN OF ROGOWSKI COIL (RC)
RC is an air-core induction type sensor with a certain num-ber of turns of wire wound in a toroidal form. RC is mountedaround the current carrying conductor for the detection ormeasurement of this current. RC with n number of evenlyspaced helical turns is shown in the Fig. 1(a) and Fig. 1(b).
When the RC having constant cross-section Ac of corewith coil/core length lc = πdm (dm is the mean diameter ofcoil) is mounted round the conductor or component carryingalternating or transient current iin(t), to be measured, thevoltage output Vrc(t) of the RC is directly proportional to
Hollow Inner forreturn conductor
dRC
dodi
dw
dm
T1 T2
r
a
Open ends of RC for
installing the coil around
conductors
Non-magnatic
coreiin(t)
dlc B
c
(a) (b)
Fig. 1. (a) Geometrical parameters of RC head. (b) RC around primarycurrent conductor.
Primary current
Vo(t)V
Vrc(t)= -Mc diin(t)/dtiin(t) Ccab Cp
RcLc
CcXc
Zcoil
XL
Rt
Rogowski coil
Terminating resistance
Connection cable
Measuringsystem
Fig. 2. Inverse-�-lumped parameters electrical equivalent model of coil.
the rate of change of magnetic flux φc as
Vrc (t) = −dφc
dt. (1)
Flux linking the coil, created by the current iin(t) can be foundby integrating the dφc = ndlc around the whole length of RCsensing the magnetic field strength H and is given as
φc =∫
dφc =∫
μo AcnH dlc cos α.
Ampere’s law evaluates the integral as given as∫H dl cos α = i in(t).
So (1) becomes
Vrc (t) = −μo Acndiin(t)
dt= −Mc
diin(t)
dt(2)
where μo Acn represents the constant of the above equationand by definition can be termed as mutual inductance Mc orsensitivity. Mutual inductance in Henries is the capability ofthe RC to induce the output voltage due to rate of changeof primary current while sensitivity in V/A for a specificfrequency is the voltage output Vo(t) of the RC as a resultof primary current.
At high frequencies RC can be best represented by twodifferent models developed [12], there are available transmis-sion line model and lumped parameters model. The lumpedparameters two-port network inverse- � model is used in thisresearch work to determine the voltage at the terminals of thecoil’s winding [13], [14] as shown in Fig. 2. RC system in thisfigure includes coil head, terminating resistance, coil cable,
SHAFIQ et al.: IDENTIFICATION AND MODELING OF CURRENT TRANSDUCER 1083
differential probe and oscilloscope. The model represents theinherent elementary properties of resistance Rc, inductanceLc and capacitance Cc of RC. Ccab and Cp are capacitancesof coil cable and differential probe respectively, used duringmeasurement.
The basic operation mentioned by (2), gives the under-standing about the emf induced in the RC for low frequencysinusoidal primary signals. Pulsed phenomena (with microor nanosecond pulse duration) consist of a wide band offrequencies. Interaction of this wide band of frequencies withelectrical components of RC in the form of 2nd order circuitmakes behavior of RC quite complex. This is analyzed in moredetail in chapter V.
III. CONSTRUCTION OF RC
In this section, the most important considerations duringconstruction of the coil are presented.
A. Geometry
Diameter of the core drc is selected so that coil should beable to fit into tight spaces. Moreover, suitable drc is importantfor stable design of RC. Large drc makes it difficult to bendand can cause deformation of the circular shape of the core intooval. Mean diameter dm (depending upon internal and externaldiameters) is selected so that it should be able to mount aroundcovered conductor (CC) lines or cables nicely. Smaller dm
means decreased distance between CC and winding of RC.This can be sensitive at higher operating voltage keepingin view the dielectric strength of air (3 MV/m). On theother hand, the larger dm can raise the issue of maintainingthe position of primary line at the central position insideRC. Keeping in view the above mentioned facts, selectedgeometrical parameters of the coil are given in Table I.
B. Number of Turns
The RC design often focuses on the sensitivity factor andaccording to (2) more turns in RC means more sensitivity.Higher number of turns provides increase in inductance, whichin turn will decrease the resonant frequency. Keeping inmind wide bandwidth for fast-pulse measurement applications,requirements for coil are higher resonant frequency for fasterresponse and acceptable output voltage signal level even forpulsed currents of smaller amplitude. Suitable number of turnsis selected to have a better trade-off between both quantities.An approach to selection of number of turns for an inductivesensor is presented in [15].
C. Core
A classical RC is composed of a single layer winding with acentral return-loop on a flexible circular toroidal core made ofdielectric (air-core) material. In this work, a plastic pipe withrough surface is used as former (core) of the coil. The pipe(core) has a hollow inner for return loop as shown in Fig. 1(a).The rough surface of the former helps the turns to remainfixed at their position during winding process and bendingwhile using for measurements. The hollow inner with smallerdiameter maintains the return loop at the central position ofthe core.
TABLE I
GEOMETRICAL PARAMETERS OF THE ANALYZED RC
Model Parameter Symbol Specification
Number of turns N 30
Outer diameter of coil do 16.08 cm
Inner diameter of coil di 14.12 cm
Core diameter drc 1.96 cm
Mean diameter of coil dm 15.1 cm
D. Winding
Suitable diameter of conductor should be used for windingto get better mechanical strength and lower electrical resis-tance. The winding turns should be evenly spaced to haveuniform turn density. During progression of the helical coilwinding, the incremental pitch between consecutive turns sumsup to create an additional undesirable circumferential turn-loop. The turn loop is normal to the axis of the coil andis sensitive to the magnetic fields other than the magneticfield of the enclosed targeted primary current. A return loopin opposite direction is added to cancel magnetically inducedeffect of this turn-loop.
E. Return Loop
Generally, the center of the core (center of the coil winding)is recommended for the return loop by most of the researchers.There are some reservations regarding radial position of thereturn loop in the center of the toroidal cross section whichcause error in compensation of external magnetic field [16].One option of developing a better compensation return loop isreturn winding provided that the forward and return windingsare identical regarding number of turns, turn spacing anduniformity. Drawback of using return winding is decrease ofresonant frequency due to additional inductance and capaci-tance of the turns. In this paper, high frequency operation istargeted and therefore, conventional return conductor throughthe center of winding is implemented to obtain return loop.
Additional advantage of this return loop is that both termi-nals T1 and T2 of the wire are available on the same end ofcore which makes it possible for coil with the flexible core toopen and close during installation on cable or conductor undertest as shown in Fig. 1(b).
Construction of the coil described above explains the designof coil head which senses the primary current as shown inFig. 1(b). There are two more external components whichcomplete the design of RC system as a current measuringdevice.
F. Terminating Resistance
Termination has very significant effects on response ofRC [17]. A terminating resistor Rt is connected across theterminals T1 and T2 of the coil for proper damping of theRC output signal. The resistance should necessarily be non-inductive and its value is determined based on the electricalparameters of RC. A method for the selection of terminatingresistance is also presented to provide an oscillation free
1084 IEEE SENSORS JOURNAL, VOL. 13, NO. 3, MARCH 2013
signal for integration stage. In section V, proper selection oftermination resistance is analyzed in detail.
G. Integrator
The output of RC is voltage proportional to the derivativeof the primary current signal. For our designed coil, a digitalintegrator is added at the output of a properly terminated RCto obtain the output of RC proportional to primary current.Different integration techniques are described in section I.
IV. PARAMETER IDENTIFICATION
Non-uniform turn density, imperfect central position ofthe return loop, non-uniformity of core or deformation of thecircular cross section into oval due to bend of flexible coilcan cause some geometrical deviation between a RC at man-ufacturing time and use. At high frequencies, the phenomenalike skin and proximity effect cause non-uniform distributionof current within the wires and hence cause the presenceof parasitic inductance and capacitance. Using simple math-ematical formulas can cause miscalculations for determiningthe inductance and capacitance of RC. Hence it is justifiedto consider these parameters as functions of coil geometryand frequency [8]. Furthermore, the RC behavior is alsodetermined by external physical components and devices.Identification measurements can be used to determine exactvalues for connecting wires, measurement device input charac-teristics etc. which can be very difficult to specify analytically.
Resonant frequency is a clear reflection of the electro-magnetic components of an induction sensor system [18].Here, a simple but useful technique of comparing the resonantfrequencies of RC is used for different known capacitorsconnected across.
The experimental setup made for identification of theparameters is shown in Fig. 3(a). Targeted parameters foridentification in the RC system are Lc, Cc, Cp and Ccab.A pulse is injected from the PD calibrator into the circuitand RC is connected around the conductor in the circuit.Output of RC is obtained by connecting coil terminal usinglow-capacitance active differential probe (ADP) to LeCroyWavesurfer 24Xs oscilloscope. Due to air core, RC has rela-tively low sensitivity and care must be taken to maintain theintegrity of measured signal. The use of ADP greatly reducesthe loop currents and common voltages at the terminals ofRC as it decouples the RC from ground. A commercialHFCT is used for reference measurements of primary currentpulses. This HFCT with the primary window of 15 mm has aspecified bandwidth from 0.5–80 MHz [19], which makes it anaccurate reference device for high frequency current waveformmeasurement.
In this double stage test reported below Cc and Cp aredetermined. Tests are carried out by observing the RC outputwaveforms and the oscillation frequency while different knowntesting capacitors CT are connected across the terminal of coilas shown in Fig. 3(b). Two sets of measurements are plannedto develop mathematical equations to determine two unknowncapacitances Cc and Cp as follows.
(a)
(b)
Fig. 3. (a) Test setup for identification of RC parameters. (b) Electricalequivalent circuit of test setup for identification of RC parameters.
First Set of Measurements: Two measurements are carriedout by first connecting capacitor CT 1 = 10.5 pF and on secondround CT 2 = 33.7 pF across RC. Response of RC system iscaptured using single ADP. Two resonance frequencies f11 =34.18 MHz and f12 = 22.61 MHz respectively are obtainedby performing fast Fourier transform (FFT) of the capturedresponse (see Fig. 4). Fig. 4(a) shows the current pulse injectedfrom a PD calibrator measured by a commercial HFCT whilethe output voltage measured by RC for CT 1 during first test isgiven in Fig. 4(b). The FFT given in Fig. 4(c) for the outputof RC is obtained in Matlab as 37.57 MHz. The resonancefrequency found by measurements can be expressed as
f11 = 1
2π√
L11(Cc + CT + Cp). (3)
Comparing the obtained resonance frequencies
f11
f12=
√Cc + Cp + CT 1
Cc + Cp + CT 2
Cc + Cp + CT 2 = (Cc + Cp + CT 1
) ·(
f11
f12
)2
.
This finally gives
Cc + Cp =CT 1
(f11f12
)2 − CT 2
1 −(
f11f12
)2 = 7.55 pF. (4)
Second Set of Measurements: Two similar measurementsare taken by connecting capacitor CT 1 and CT 2. In this test,response of RC system is captured using two identical ADPs in
SHAFIQ et al.: IDENTIFICATION AND MODELING OF CURRENT TRANSDUCER 1085
TABLE II
ELECTRICAL PARAMETERS OF RC
Parameter SymbolValue of theParameter
Self-resistance of coil Rc 0.71 �
Self-inductance of coil Lc 1.19 μH
Self-capacitance of coil Cc 5.16 pF
Probe capacitance C p 2.42 pF
Capacitance of coil cable Ccab 7.1 pF
Capacitance of coil system C = Cc + C p + Ccab 16.46 pF
Mutual inductance Mc 125.4 nH
Self resonant frequencyof coil
fc 64.6 MHz
Resonant frequency ofcoil with probe
fcp 53.2 MHz
Operating resonant frequencyof coil system
foc 37.6 MHz
Characteristic impedenceof coil system
Zc 360 �
parallel which provide resonant frequencies f21 = 32.10 MHzand f22 = 21.99 MHz respectively. These results provideessentially same formulas but now two probe capacitances Cp
are in parallel, thus
f21
f22=
√Cc + 2Cp + CT 1
Cc + Cp + CT 2⇒ Cc + 2Cp + CT 2
= (Cc + 2Cp + CT 1
) ·(
f21
f22
)2
Cc + 2Cp =CT 1
(f11f12
)2 − CT 2
1 −(
f21f22
)2 = 9.98 pF. (5)
From (4) and (5) values for Cc and Cp are calculated asCc = 5.16 pF and Cp = 2.42 pF. From (3) inductance valuescan be calculated as
L11 = 1
2π(Cc + Cp + CT 1) f 211
= 1.18 μH
L12 = 1
2π(Cc + Cp + CT 2) f 212
= 1.21 μH
where L11 and L12 are the effective inductance valuesin the first set of measurement. Negligible difference isseen calculating L21 and L22 using second set of measure-ment. Average of results can be used as coil inductanceLc = 1.91 μH.
In the next test, coil cable is attached and using samemethod capacitance of the coil cable Ccab is determinedas 7.1 pF.
The above set of measurements was repeated with anotherpair of capacitors using sinusoidal signal from a functiongenerator instead of pulsed signal. Varying the frequency ofsinusoidal signal indicates the resonant point at maximumamplitude of voltage output of RC. This has ensured thecorrect assessment of the values above determined with errorless than 2%.
0 0.2 0.4 0.6 0.8 1 1.2x 10-6
0
5
10
15x 10-3
Time (sec)
Am
plitu
de(A
mps
)
0 0.2 0.4 0.6 0.8 1 1.2x 10-6
-0.2
0
0.2
Time (sec)
Am
plitu
de(V
)
101
102
1030
1
2
3
Frequency (MHz)Am
plitu
de,F
FT(m
V)(c)
(a)
(b)
Fig. 4. (a) Input current pulse from PD calibrator measured by HFCT.(b) Output measured by RC along with measuring system configured for foc.(c) FFT of the measured response for CT 1.
The effective mutual inductance Mc of the coil is determinedin section VI using (24). The characteristic impedance Zc ofthe coil system can be calculated as
Zc =√
Lc
C. (6)
Finally the measured parameters are given in Table II.fc is self-resonant frequency (SRF) of the coil without anyadditional component connected to RC. It is impossible touse coil at its SRF as there are some components required tocarry the output of RC from its terminals to the oscilloscope orother recording instrument. This reduces the SRF to operatingresonant frequency (ORF) which is resonant frequency ofthe coil system along with the coil cable and probe and isdetermined as
foc = 1
2π√
LcC= 37.6 MHz (7)
where C = Cc + Cp + Ccab.In this work the RC along with measuring system is used atfoc (ORF) which is verified using the similar test as describedby Fig. 4 without any additional capacitance.
V. ANALYSIS OF RC FOR TRANSIENT APPLICATIONS
The working principle described in section II reflects theoperation of RC which mainly deals with the physical featuresof the coil as an induction device. This is sufficient whenthe primary current signal is low frequency as inductanceand capacitance of the coil at low frequencies has insignif-icant effect. For high frequency or transient applications,
1086 IEEE SENSORS JOURNAL, VOL. 13, NO. 3, MARCH 2013
C
LcRC
Vo(t)Vrc(t)
i(t)
ic(t)
Primary current
Mc
iin(t)
iRt(t)
Rt
Fig. 5. Electrical equivalent circuit of RC with external terminatingresistance.
capacitance and inductance strongly interact with the signaland need in-depth investigation.
Vo(t) is the voltage measured across the terminal of RCterminated with resistance Rt . In the presence of terminatingimpedance, operation of RC (see Fig. 5) can be expressed bythe following set of equations as:
Vrc(t) = −Mcdiin(t)
dt(8)
Vrc(t) = Lcdi(t)
dt+ Rci(t) + Vo(t) (9)
i(t) = CdVo(t)
dt+ Vo(t)
Rt(10)
ic(t) = CdVo(t)
dt, iRt (t) = Vo(t)
Rt(11)
i(t) = ic(t) + iRt (t) (12)
where ic(t) and iRt(t) are the currents flowing in the capac-itive elements and terminating resistance of the coil systemrespectively. These currents cannot be observed by normalmeasuring methods but simulation of the valid model of coilhas made it possible to analyze the behavior of these currents.In s-domain, under zero initial conditions, the output of RCin terms of transfer function can be expressed as
Vo(s) =1
LcC
s2 + 1LcC
(LcRt
+ RcC)
s + 1LcC
(RcRt
+ 1) Mcs Iin (s)
(13)
where s Iin(s)L−1−→ diin (t)
dt .Equation (13) gives a complete representation of the opera-
tion involved between iin and Vo. It is worth to mention herethat (13) reveals more useful information about Mc than just asimple expression in (2). Effective value of Mc is significantlyinfluenced by RLC parameters and Rt of RC. Based on thisfact the effective value of Mc is measured at the final stage ofRC output in section VI.
This transfer function in (13) is a classical 2nd order systemwith characteristic equation written as [20]
s2 + 2ξωns + ω2n = 0 (14)
where ωn is the natural (resonant) angular frequency of the coilsystem depending upon its inductance and capacitance while ξis the damping coefficient which depends on Lc, C, Rc and Rt .Solution of this characteristic equation is mainly configured
Fig. 6. Effect of Rt to quantify the oscillations in term of poles location.
by ξ which is significantly influenced by Rt because its otherparameters are approximately fixed for a coil. Comparing (14)with the numerator of (13) provides
2ξωn = 1
LcC
(Lc
Rt+ RcC
)⇒ ξ ∝ 1
Rt. (15)
It has been observed during investigation that when outputof RC is measured without any terminating resistance (probeinput resistance as Rt = 1 M�), Rt >> ωn Lc and at the sametime
Rt >> (1/ωnC) ⇒ Rt >> Zc.
This shows that
iRt (t) << ic(t) ⇒ i(t) ≈ ic(t). (16)
In this condition ξ << 1 and the circuit in Fig. 5 behaves asa simple RLC series circuit. Charging and discharging of Lc
and C produces oscillations in the output, see Fig. 6 whichshows the complex poles in root locus plot. The location ofpoles is shown with respect to variation in Rt . The measuredoutput voltage of RC for calibrated PD current pulse usingdifferent values of Rt are shown in Fig. 7.
Oscillations introduced by the 2nd order circuit of the coilcan be eliminated by applying proper damping (ideally ξ = 1).The value of suitable terminating resistance for this purposecan be determined as
Rt = Lc
2ξωn LcC − RcC.
As RcC << 2ωn LcC => RcC ≈ 0 in above equation,
Rt = 1
2ξ
√Lc
C⇒ Rt = Zc
2for ξ = 1. (17)
For the design of the RC used in this work Rt = 175 �. Usingthis value of Rt it is observed clearly that
iRt (t) >> ic(t) ⇒ i(t) ≈ iR(t). (18)
For this value of Rt the coil circuit behaves as RL-seriescircuit with real poles. The output voltage of RC withoutoscillations can be seen in Fig. 7(d). This voltage output of RCis differential of primary pulse which needed to be integratedto obtain the current value in the wire.
SHAFIQ et al.: IDENTIFICATION AND MODELING OF CURRENT TRANSDUCER 1087
0 0.5 1
x 10-6
0
5
10
15x 10
-3
Time(sec)
Am
plitu
de(A
mps
)
0 0.5 1
x 10-6
-0.2
0
0.2
Time(sec)
Am
plitu
de(V
)
0 0.5 1
x 10-6
-0.05
0
0.05
0.1
0.15
0.2
Am
plitu
de( V
)
Time (sec)0 0.5 1
x 10-6
-0.05
0
0.05
0.1
0.15
0.2
Am
plitu
de( V
)
Time (sec)
(a) (b)
(c) (d)
Fig. 7. Effect of Rt to minimize the oscillations in the RC ouput. (a) Primarycurrent iin (t) measured by HFCT. (b) Voltage output of RC at Rt = 1 M�.(c) At Rt = Zc. (d) At Rt = Zc/2.
VI. RC FOR MEASUREMENT OF HIGH-FREQUENCY
CURRENT PULSES
Time domain parameters like rise time, zero-to-peak time,fall time and pulse duration, apparent charge and PD energyare frequently used for estimation of intensity, size, shape,location and type of PD defects within the insulation [21], [22].This concerns with the wave shape of the PD pulses whichcan be retrieved by obtaining integrated output Vo(t) of coilto get the signal proportional to primary current iin(t) as
iin(t) = − 1
Mc
∫Vo(t)dt . (19)
Apparent charge of PD q(t) can be determined as
q(t ′) = − 1
Mc
t ′∫
0
(∫Vo(t)dt
)dt ′. (20)
Here t ′ is the time for single discharge. The PD energy Et
delivered by the PD source when discharges occur over theapplied voltage for time interval T is given as [23];
ET =w∑
r=1
[K ′ × qr (t
′) × Vr]
(21)
where qr (t ′) is the apparent charge of r th discharge, Vr is thevalue of the voltage across test object at the moment of r th
discharge inception and w is the total number of dischargesoccurring during the time interval T .
Fig. 8 shows four stages of RC system to represent theoverall current measuring process. The first stage refers tothe sensing of primary current by RC head, second stagedamps the oscillations introduced by RC head, the third stagetransforms the obtained voltage signal into digitalized formand fourth stage implements the digital integration techniqueto get the primary current signal. Digital integration makesthe design of RC system simple and provides stability to
Fig. 8. Stages of proposed RC system for current measurement.
integration process for reconstruction of current waveform.The third stage of applying this technique is analogue todigital conversion of output the signal of RC, with the helpof a data acquisition system (DAS). Generally there are twomajor concerns for this process: vertical resolution, expressedin m-bits of DAS and horizontal resolution, expressed insamples/second (S/s).
LeCroy Wavesurfer 24Xs oscilloscope is used for thispurpose where 8-bit built-in DAS is used with a samplingrate of 2.5 GS/s. Here 8-bit resolution provides (2m = 28)256 quantization levels of the observed signal which meanseach level gives 0.4% of full scale. The maximum errorduring digitalization of the signal with 8-bit DAS is less than± 0.2% which is clearly negligible. Moreover, to maximize theaccuracy it is advised to keep volt/division (vertical axis) sothat the measured signal should fill the full screen of display.After analogue to digital conversion, data signal is saved onoscilloscope and processed on personal computer (PC).
There is a broad family of numerical algorithms to computethe definite integral. Method known as trapezoidal rule whichin general is considered as having faster convergence inparticular cases of rougher signals is chosen in this work. Thisis calculated as [24]
i (N) = i (N − 1) + 1
2 fs[Vo (N − 1) + Vo (N)] N > 0
(22)where fs is sampling frequency and N is the order number ofsample. During successive process of integral evaluation forVo[N] at the given samples, presence of noise in the signal hasdiverged the integration output. This problem can be solvedby either by removing the input signal average value beforeintegration or by using first order low pass circuit working asintegrator in the required frequency range [11]. Here, the firstoption is used to eliminate the problem.
Integration results of the RC output while applying differentvalues of terminating resistance Rt are presented as outputcurrent io(t) in Fig. 9(b), (c) and (d). Integration result shouldprovide the waveform proportional to the primary currentiin(t) measured by HFCT in Fig. 9(a). Comparison of thewave shapes of reconstructed current waveforms measured byRC and HFCT shows that io(t) in Fig. 9(c) (for ξ ≈ 1) has anice match with iin(t). This confirms the design of RC to beused for measurement of a fast current pulse.
It can be observed from Fig. 9(d) that as ξ is increased, theslower response makes it difficult for obtaining the accuratewaveform, but also signal to noise ratio will become unaccept-ably small.
1088 IEEE SENSORS JOURNAL, VOL. 13, NO. 3, MARCH 2013
0 0.5 1
x 10-6
0
5
10
15x 10
-3
Time (sec)
Am
plitu
de(A
mps
)
0 0.5 1
x 10-6
0
1
2
3
4
x 10-9
Time (sec)
Mea
sure
dC
urr e
n t(A
mps
)
0 0.5 1
x 10-6
-0.5
0
0.5
1
1.5
2
x 10-9
Time (sec)
Mea
sure
dC
urre
nt(A
mps
)
0 0.5 1
x 10-6
-5
0
5
10
15
20x 10
-10
Time (sec)
Mea
sure
dC
urre
nt(A
mps
)Output of RC Output of RC
Output of RCPrimarycurrentby HFCT
(a) (b)
(c) (d)
Fig. 9. (a) Primary current iin (t) measured by HFCT. (b), (c), and (d) io(t)measured by numerically integrated RC for ξ << 1, ξ ≈ 1, and ξ > 1,respectively.
Fig. 9(c) shows the measured current io(t) obtained byintegrating the Vo(t) of RC as∫
Vo(t)dt → io(t).
Substituting the value in (19) the expression can be written as
iin(t) = − 1
Mc
(∫Vo(t)
). (23)
The measured current in this case is directly proportional to theprimary current and constant of proportionality (Mc) can bedetermined by comparing io(t) and iin(t) magnitudes [shownin Fig. 9(a) and 9(d) respectively], which provides a calibrationfactor as
Mc = io(t)
iin(t)= 125 nH. (24)
Value of Mc determines the sensitivity calibration factor forthe designed RC. Multiplying the resultant signal from RCintegration by this calibration factor (K = 1/Mc) providescorrect amplitude of the primary current to be measuredcurrent.
VII. VALIDATION OF THE DESIGN
The performance of the RC for pulse measurement applica-tion has been compared with the HFCT for calibrated PD pulsein Fig. 9. In this section two entirely independent environmentsare briefly described to assess the performance of modeled RCfor PD measurement. Firstly, the designed RC is simulated inATP-EMTP and secondly, RC is used to measure the PDs ina practical laboratory setup.
A. ATP Simulation of RC
RC is simulated in ATP-EMTP. The ATP program isconsidered to be one of the most widely used digital simulation
4.5 5 5.5 6 6.5 7 7.5 8x 10-7
0
0.005
0.01
0.015
Time(sec)C
urre
nt(A
mps
)
HFCTSimulated Rogowski coilReal Rogowski coil
(a)
(b)
Fig. 10. (a) ATPDraw simulation circuit of RC along with digital integrator.(b) Comparison of primary current measured by HFCT, simulated RC andreal RC.
software for electromagnetic transients, as well as electro-mechanical transients in electric power systems.
The ATPD raw circuit diagram for RC measuring theprimary pulse current iin(t) is given in Fig. 10(a). Electricalparameters of the RC identified previously are used in thesimulation. Block B1 in diagram is the primary current iin(t)source. To make the simulation close to real experimentalconditions, digital data of iin(t) measured by HFCT is savedby the DAS of oscilloscope. This current signal is transportedto ATPD raw to be measured by RC model set up as in Fig. 5.B2 senses the current iin(t) of the test circuit and voltagesource of the RC consists of B3. Mc represents the mutualinductance in differential block B3 and output of this block isVrc(t). B4 implements the transfer function to encapsulate thetime and frequency dependent response of RC on Vrc(t) toget Vo(t). Transfer function is implemented for ξ = 1 to get anon-oscillating response of RC. B5 is the numerical integrationof the Vo(t) obtained from B4 calibrated by K = 1/Mc . Dueto not having any source of noise in the simulation, there isno need for signal processing for removing the noise as doneduring practical measurements.
A comparison of the measured and simulated responsescaptured by the RC for pulses is presented in Fig. 10(b).The comparison is carried out considering the time domainperformance and FFT analysis. Resonant frequencies of coilgiven in Table II are verified. iin(t) measured by HFCT,io(t).1/Mc (measured by real RC) and io(t) · K (the simu-lated calibrated output of RC) are compared in Fig. 10(b).
SHAFIQ et al.: IDENTIFICATION AND MODELING OF CURRENT TRANSDUCER 1089
(a)
(b)
(c)
2 3 4 5 6 7x 10-7
-0.1
0
0.1
Cur
rent
(Am
ps)
2 3 4 5 6 7x 10-7
-0.1
0
0.1
Time (sec)
Cur
rent
(Am
ps)
Fig. 11. (a) Laboratory experimental setup for PD measurements. (b) Snapshot of the waveforms captured by DSO, showing applied voltage andmeasured PD signals. (c) PD signal measured. Top: by HFCT. Bottom:by designed model of RC.
The comparison shows a close match regarding wave shapeand amplitude of captured pulse which ensures that themeasured parameters and calculated mutual inductance aredetermined reliably for the designed RC.
Apart from the iin(t) waveform presented in this paper,good performance of RC model has been observed for varioussimulated pulses of different pulse duration and amplitude.
B. Measurement of PDs
An experimental setup was assembled in the laboratory asshown in Fig. 11(a). Voltage of 50 Hz is applied from aregulator (0–230 V) for ac supply voltage to a HV powertransformer 230 V/100 kV. Test object used in the experimentconsists of two plate-plate electrodes assembly inside a cubicalsolid epoxy resins insulation material. The distance betweenelectrodes is 0.5 cm while there are few voids to cause thePDs due to high voltage across the electrodes. The voltageis increased gradually and PD activity is initiated at 5.2 kV
while the PD data is recorded at 6.5 kV. C1 = 100 pF andC2 = 0.3 pF makes a voltage divider to measure the appliedvoltage on oscilloscope. Electromagnetic current sensors usedto capture this PD activity were the designed RC and HFCT.Both sensors were installed suitably close to each other tomaintain the similarity in measurement regarding location ofsensors. Unprocessed PD data captured during positive halfcycle of applied voltage is shown in Fig. 11(b). The recordeddata is processed to mitigate the noise.
The circled pulse is zoomed in for closer view at thebottom of Fig. 11(b). PD signal captured by RC is integratedand multiplied with the calibration factor to get the PDcurrent waveform. The PD signal measured by RC and HFCTis compared in Fig. 11(c). The close match between bothmeasured waveforms verifies the designed prototype of RCfor accurate PD measurements.
VIII. DISCUSSION AND CONCLUSION
Prior to building a RC, some estimation can be given forthe self-inductance and self-capacitance values to adjust thenumber of turns and geometrical dimensions. Several mathe-matical expressions are given in [5] and [25] for calculating theself-inductance and self-capacitance of RCs. These formulaeare based on the geometrical parameters of the RCs. Duringthe design of RC, accuracy of knowing the parameters of RCis very important for creating correct model of the RC, tocalculate Zc for determining its proper Rt and to calibrate itssensitivity. In this paper, a rather direct approach was takento identify the RC parameters. The advantage of presentedmethodology of parameters identification is that the coil mea-suring system is exposed to the measurement environment andhigh frequency components of measured signals which providemore reliable parameters of the coil.
Self-integrating technique is often implemented by using asmall resistance for the termination resistor Rt . This decreasesthe sensitivity of RC and hence amplification is needed toincrease the signal strength especially in the noisy environ-ment. To avoid additional amplifier circuit, the terminatingresistance was used here only to damp the oscillations anddigital integration method has used for performing actualintegration.
Generally PD signal is considered as more like a pulseshaped as shown in Fig. 10(b) while the captured PD signal inFig. 11(c) represents the PD pulse propagating thorough theline added with certain oscillations (14.3 MHz). This is due toinherited RLC properties of the line and capacitors connectedin the measurement setup. Similar phenomenon is observed indifferent articles for measuring PDs in real cables. Possiblenoise is another factor added to the capture signal. A pulseshaped PD signal can be measured if the cables are terminatedwith matched impedances. This is only possible while makingoff-line measurements. In case of online measurements, loadimpedance determines the terminating impedance which ismostly different from the impedance of the cable.
During both tests given in Fig. 3 and Fig. 11(a), RC is usedin noise-free environment. High frequency PD pulses gener-ated shown in Fig. 11(a) during the test, are naturally sources
1090 IEEE SENSORS JOURNAL, VOL. 13, NO. 3, MARCH 2013
of electromagnetic interference (EMI). However, nicely com-parable output of RC and HFCT shows that due to less numberof turns of RC, its output is not significantly responsive tothe EMI. Still, there is a need for further tests verifying theoperation capability of RC in the presence of real EM-noisyenvironment, in real online system. Extraction of measured PDsignal captured by RC in the noisy environment is efficientlyaddressed in [26].
A new method of correct identification of the parametersof RC for partial discharge measurements was described andverified. ATP-EMTP simulation of the RC model presented inthis paper can be used to fine-tune the response of coil and tomodify the model before implementing a new or improveddesign. Although HFCT used in this work is excellent inperformance for PD measurements, RC is yet more attractivedue to low cost, light weight and flexibility of installation.
ACKNOWLEDGMENT
Tests were done in Power Systems and High Voltage (HV)Laboratory, Aalto University, Espoo, Finland. The authorsappreciate the valuable and interesting discussions withDr. P. Hyvönen and Dr. J. Klüss from the Department ofElectrical Engineering, Aalto University.
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Muhammad Shafiq received the B.Sc. and M.Sc.degree in electrical engineering from the Universityof Engineering and Technology, Lahore, Pakistan, in2001 and 2007, respectively.
He joined the Department of Electronics Engi-neering, Islamia University, Bahawalpur, Pakistan,as a Faculty Member, in 2002. He had been work-ing there at positions of Lecturer and an AssistantProfessor. He joined the Department of ElectricalEngineering, Aalto University, Espoo, Finland, in2009, as a Doctoral Researcher. His current research
interests include design and implementation of induction sensors for pulsed(high frequency) current measurement and on-line condition monitoring ofpower distribution system components based on partial discharge measure-ments.
Lauri Kütt received the B.Sc. degree in computerand automation technology and the M.Sc. degree inelectrical power engineering from the Tallinn Uni-versity of Technology, Tallinn, Estonia, in 2002 and2004, respectively, and the Doctoral degree from theDepartment of Energy and Geotechnology, TallinnUniversity of Technology, in 2012.
He has been with the Tallinn University of Tech-nology as a Researcher since 2007. His currentresearch interests include fast transients on electricpower lines, power line diagnostics, power quality,
and electromagnetic compatibility.
SHAFIQ et al.: IDENTIFICATION AND MODELING OF CURRENT TRANSDUCER 1091
Matti Lehtonen received the Masters and Licentiatedegrees in electrical engineering from the HelsinkiUniversity of Technology, Espoo, Finland, in 1984and 1989, respectively, and the Doctor of Technol-ogy degree from the Tampere University of Tech-nology, Tampere, Finland, in 1992.
He was with VTT Energy, Espoo, Finland, from1987 to 2003, and since 1999, has been a Professorwith the Helsinki University of Technology, wherehe is currently the Head of Power Systems and HighVoltage Engineering. His current research interests
include power system planning and asset management, power system protec-tion including earth fault problems, harmonic related issues, and applicationsof information technology in distribution systems.
Tatu Nieminen received the M.Sc. degree in elec-trical engineering from Aalto University, Espoo,Finland, in 2010.
He has been with the Power Systems and HighVoltage Engineering, Helsinki University of Tech-nology, Espoo, since 2005, as a Research Assistantand since 2010, he has been with the Departmentof Electrical Engineering, Aalto University, as anOperations Engineer. His current research interestsinclude electronics design of wireless sensors, highvoltage testing, and installations.
Murtaza Hashmi received the B.Sc. degree inelectrical engineering from the University of Engi-neering and Technology, Lahore, Pakistan, in 1994,the Masters degree in electric power engineeringfrom the Royal Institute of Technology, Stockholm,Sweden, in 2001, and the Ph.D. degree in partialdischarge detection in distribution networks from theHelsinki University of Technology (TKK), Espoo,Finland, in 2008.
He is currently a Senior Scientist with the Depart-ment of Energy Systems, VTT Technical Research
Centre, Espoo. His current research interests include asset management ofdistribution networks, ICT applications for smart grids, renewable energysources and their integration, demand response, and energy efficiency.
