Implementation of a Rogowski coil for the measurement of partial discharges Marta Arg¨ ueso,∗ Guillermo Robles, and Javier Sanz Department of Electrical Engineering Universidad Carlos III. 28911 Madrid. Spain In order to obtain partial discharge (PD) measurements a PD measuring probe based on a Rogowski coil was constructed. Up to now, Rogowski coils had been used to measure high level currents. In this paper, the design of a Rogowski coil to measure very low currents, but with a very high frequency, such as partial dischages, is exposed. The Rogowski coil used as a PD transducer is very advantageous because it is inexpensive and easy to use. Besides, it provides the needed bandwidth for this application. PACS numbers: 07.07.-a Df, 07.50.-e Ls, 84.32.-y Hh, 84.37.+q
I.
INTRODUCTION
In the last decades, high-voltage and high-frequency power devices such as IGBTs (Insulated-Gate Bipolar Transistor) and MOSFETs (Metal-Oxide Field-Effect Transistor) have been developed and used in motor drives. Nowadays, they are already widely employed in the industry to energize low voltage induction motors. IGBT technology can provide very fast impulses, with a rise time as fast as 20-100 ns, with a switching frequency up to 20 KHz [1]. When this fast front waves travel from the inverter to the motor, a reflection wave appears because of the impedance mismatch between the cable and the motor. This reflection goes back to the inverter and induces a new reflection wave due to the impedance mismatch between the cable and the inverter. These are added to the original voltage wave, generating an overshoot at the front of the voltage wave in the motor terminals, [2]. The longer the cable, the stronger the overshoot will be, reaching magnitudes up to three times the nominal voltage. Thus, electrical insulation systems of inverter-fed motors are exposed to greater stresses than those powered by traditional fundamental sine-wave voltage. If the voltage in the motor terminals is above the PDIV (Partial Discharge Inception Voltage) of the insulation, PD in the insulation voids may occur. It is well known that PD can be one of the most influential phenomena in the ageing of electrical insulation systems. In order to ensure reliability in the operation of such equipment, the detection and interpretation of PD measurements is required to monitor the condition of insulation, [3]. PD are accompanied by a number of physical phenomena, which permits their detection and measurement. The associated visual and acoustical emissions are used to detect the presence of PD, though they do not permit quantitative measurements. When measuring PD in insulation voids, these emissions are not obtainable, so electrical measurement methods are used. These are based on the measurement of the charge displacement in the sample. As this is not accessible, the sample is connected to an external circuit, where an impedance is placed, so that the charge displacement is measured as a current. Being precise, this magnitude is not equal to the actual charge displacement in the void, but to the external charge displacement. Hence, calibration is needed to relate both magnitudes. According to the standard IEC 270-1981 [4], most circuits used to measure PD are based on one of the circuits shown in Figure 1. These circuits are composed by: • the sample under test, represented as a capacitance Ca . • a coupling capacitor, Ck . • the measurement impedance, Zm , the wire and the measurement device. • sometimes, a filter impedance, Z. The existing commercial equipments usually measure discharges as pulses localized in the fundamental 50 Hz cycle. With a high enough bandwidth, as the provided by the designed Rogowski coil, time-domain measurements can be achieved. This allows a deeper study of the mechanism of PD. In addition to that, commercial equipments need an integrator, that it is not necessary with the designed Rogowski coil.
∗ Electronic
address:
[email protected]
2
FIG. 1: Circuits for measuring PD.
The proposed measurement method is based on a Rogowski coil. Rogowski transducers have been used for the detection and measurement of electric currents since 1912 [5], particularly where large currents needed to be measured. Applications on measurement of pulsed currents of mega-amperes in plasma, electron beam, high radiation field environments and medium voltage cable networks can be found in [6], [7] and [8]. A Rogowski coil seems to be extremely adequate to measure PD because it has the following features: • Non-saturation, because it is air-cored. • Good linearity, due to the absence of magnetic materials. • Simple circuitry and low price. • Non-intrusive, i.e., the coil does not load the circuit carrying the current to be measured under certain conditions on impedance matching. The major aim when measuring PD with a Rogowski coil is to make its bandwidth wide enough. Though some authors expose very high bandwidth as a feature of a Rogowski coil, the highest frequency measured according to the references is around 10 MHz [9], which is low for the exposed purpose. In the following sections, the operating principle and the high frequency equivalent circuit of a Rogowski coil are exposed. Then, calibration of the coil and measurements made with the constructed one are shown. Finally, a discussion on the results is presented. II.
ROGOWSKI COIL DESIGN AND OPERATING PRINCIPLE
Rogowski coils are wound either on a rigid toroidal core form or on a flexible belt-like core form. Carefully manufactured coils with fixed, unopenable cores can provide better accuracy, because the openable ones are prone to change their characteristics when opened or closed due to the wire turns displacement. In the design developed in this paper an unopenable rectangular cross section core was utilized. The winding was returned in the opposite direction to that of the pitch-advancement turn along the central axis of the coil, in order to avoid the effect of a magnetic flux parallel to the conductor [10]. Some authors use multi-layer winding coils to increase sensitivity, but single-layer winding coils is more convenient since its lower inductance gives a higher bandwidth. The designed Rogowski coil is shown in Figure 2. The Rogowski coil operates on the basic principle of the Faraday Law. The air-cored coil is placed around the conductor where current pulses produced by PD are to be measured. This variable current produces a magnetic field.
3
FIG. 2: Rogowski coil.
The rate of change in current induces a voltage in the coil, given by vcoil = M ·
di dt
(1)
where vcoil is the voltage induced in the coil by the current i due to the mutual inductance M between the main current and the coil. To obtain a voltage signal proportional to the current waveform, integration of vcoil is required. Several options for integrating were considered: • mathematic integration, which consists in integrating the signal vcoil obtained with the oscilloscope or a data acquisition card. • electronic integration, which consists in integrating with passive integration networks. • self-integration, through the development of an self-integrating Rogowski coil, as it is explained below. The last option was chosen. Mathematic integration has the limitation of the capacitance added by the oscilloscope probe, which reduce the bandwidth. Electronic integration was not considered, to make the circuitry as simple as possible. III.
EQUIVALENT HIGH FREQUENCY CIRCUIT
The purpose of the constructed Rogowski coil is to measure partial discharges, which, typically, last some nanoseconds. So, high frequency behavior of the Rogowski coil has to be studied. Up to now, two different models have been developed ([8], [11]): the distributed parameter model and the lumped parameter model. In this section, both are exposed. The accordance between the experimental results and the models will be shown in the next section. A.
Distributed parameter model
Cooper [11] developed a model of distributed parameters to modelize the behavior of a Rogowski coil. The system is considered as a distributed line, with the following parameters: Cd = Capacitance per unit length Ld = Inductance per unit length Rd = Resistance per unit length
4 If a terminating impedance Z is connected to the coil, and assuming that the flow of current is symmetrical with respect to the coil, the transfer function that relates the induced voltage vcoil with the voltage per length voutl measured in the terminating impedance is given by the following equation, where l is the coil length and s is the Laplace variable:
voutl =
1+
Z sLd +Rd 1+e−2γl Z Z0 · 1−e−2γl
· vcoil
(2)
Z0 is an impedance that relates the parameters of the model and γ is a factor that indicates the transit time around the coil considered as a delay line [11]. Definitions of both are given by the following expressions: Z0 = γ =
p
p
(sLd + Rd )/sCd sCd (sLd + Rd )
In order to assure the symmetry of the flow of current with respect to the coil, the current carrying conductor must be centered and perpendicular to the plane of the coil. In the case of low-impedance termination, so that Z Z0 , the previous equation can be rewritten as: voutl =
Z · vcoil sLd + Rd
(3)
If the time constant of the coil, τ = Ld /Rd , is longer than the current pulse i to be measured, Rd can be neglected compared to sLd , and Equation (3) becomes:
voutl =
Z · vcoil sLd
(4)
For our convenience, the terminating impedance Z will be a resistance Rout , thus the output voltage vout can be expressed as:
voutl =
Rout · vcoil sLd
(5)
In this way, an integrating coil is obtained. The voltage induced in the coil, vcoil , was given by Equation (1). It can be seen in Equation (6) that voutl is related to the current i to be measured, by a constant of proportionality H = Rout M/Ld , called coil sensitivity per length from now on.
voutl =
B.
Rout Rout · sM i = · M i = Hi sLd Ld
(6)
Lumped parameters model
In order to simplify the study, the behavior of the Rogowski coil with a terminating impedance Z can be represented by the equivalent circuit of lumped parameters represented in Figure 3, [12]. The transfer function for this model is given by Equation (7).
vout =
Ll ZCl
s2
Z · vcoil + (Ll + Rl ZCl )s + Rl + Z
(7)
Poles of this transfer function are expressed by Equation (8), that has been arranged to show the influence of the terminating impedance, Z:
5
FIG. 3: Equivalent circuit.
s=
−(1 +
Rl Z Ze2 )
±
q
1+
Rl2 Z 2 Ze4
2Ll
−
2Rl Z Ze2
2
2 − 4Z Ze2 Ze Z
(8)
p where Ze = Ll /Cl . As long as the terminating impedance is low enough (Z Ze ), poles of the transfer function move along the real axis, so that the system does not oscillate (Figure 4). Besides, the Rogowski coil behaves like an integrator in the frequencies between both poles, as it is shown in the Bode plot (Figure 6). From equation (8) and under the hypothesis Z Ze , poles can be calculated as: s=
−1 ± 1 Ze2 = 2Ll Z
→0 → −∞
The lower the terminating impedance, the larger the separation between poles, so that the frequency band where the coil is self-integrating will be wider. IV.
CALIBRATION AND MODEL VERIFICATION A.
Calibration
When designing a Rogowski coil, maximization of its sensitivity is sought. The coil sensitivity is the parameter that relates the current i to be measured, with the voltage in the terminating impedance, Z. According to Equation (5), with the hypothesis assumed above, the coil sensitivity per length at high frequencies is given by the following expression: H=
Rout M Ld
(9)
The geometric characteristics of the constructed rectangular cross section coil are shown in Figure 5 and Table I. For toroidal coils having a rectangular cross section, the lumped parameters of the second model exposed above can be calculated as follows: l πd2 µ0 N 2 W b Ll = log 2π a 4π 2 0 R Cl = log Rr µ0 b M = N W log 2π a Rl = ρ ·
(10) (11) (12) (13)
6
FIG. 4: Coil dimensions.
where d is the wire diameter, R = (b + a)/2 and r = (b − a)/2. For the first model, it was assumed that the parameters are the same as in the lumped parameters but distributed along the length of the coil. So, the following expressions were considered: Rl l Ll = l Cl = l
Rd =
(14)
Ld
(15)
Cd
(16)
In Table II, the calculated parameters are shown. The bandwidth where the coil behaves as self-integrating, according to the lumped parameters model, depends on the terminating impedance, as it was seen in Equation (8) and Figure 7. The smallest the terminating impedance, the wider the bandwidth. The coil poles for a terminating impedance of Rout = 1 Ω are at 0.1 MHz and 7.7 GHz, so the coil will be self-integrating in the frequency band between 1.0 MHz and 770 MHz. This can be verified also in Figure 6. On the other hand, Rout should be as high as possible to make the coil sensitivity high enough. As it is seen in Figure 8, a termination resistance of Rout = 0.5 Ω for the constructed coil provides a sensitivity good enough for our purpose, while a zero dephase is achieved for the frequencies of interest in PD measurement. B.
Model validation
Equivalence between both models is demonstrated through their frequency response. That can be seen in Figure 6, where a Bode plot is shown for a terminating resistance of Rout = 1 Ω.
For the experimental validation of the models exposed above, measurement of sinusoidal currents were taken at several frequencies. As an example, the measurement of 10 MHz waves is shown in Figure 8, for two different terminating impedances. Here, it can be observed that, while the voltage in the 10 Ω resistance is dephased from the current through the 1 KΩ, the voltage through the 0.5 Ω resistance is in phase, as it could be deduced from Figure 7.
7
FIG. 5: The output of the Rogowski coil, was measured as the voltage in Rout . Ch1, Ch2, Ch3 are three input channels of the oscilloscope.
V.
MEASUREMENT OF CALIBRATOR PULSES
The constructed coil with the terminating resistance of 1 Ω and 10 Ω were used to measure pulses with a rise time of 50 ns provided by a commercial calibrator. A metallic box was used in order to filter external high frequency noise. The measurements were made as indicated in Figure 9. Ray [13] pointed out that ringings at the coil resonant frequency results from any asymmetry or discontinuity in the current waveform such as a step or ramp. This is the case when measuring pulses. For the designed coil, the resonant frequency occurs at: 1 = 105 MHz fres = √ 2 LC
(17)
A mathematic filter was designed, so that this frequency were eliminated from the output signal. Results for both terminating resistances are shown in Figures 10 and 11. VI.
PARTIAL DISCHARGES MEASUREMENT
After testing the designed probe to measure high rise time pulses from a calibrator, an actual partial discharge was measured in the laboratory. The experimental setup was based on the circuits for measuring PD shown in Figure 1 from the standard IEC 270-1981 [4]. The measurements were made using the Rogowski coil as well as measuring the voltage in the impedance Zm , so that the current could be obtained, to compare both results. Despite that measuring
Excitation Current (A)
0.08 0.06 0.04 0.02 0 −0.02 −0.04 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 −6
x 10 −3
Output Voltage (V)
3
x 10
2 1 0 −1 −2 −3 0
0.1
0.2
0.3
0.4
0.5 Time (s)
0.6
0.7
0.8
FIG. 6: Pulse measured with a Rout = 1 Ω.
0.9
1 −6
x 10
8
the pulse in Zm is accurate enough, it is worth pointing out that this could be dangerous for the oscilloscope if a specimen breakdown occurred. This is solved by means of a Rogowski coil because it provides galvanic isolation. The layout of this experiment can be seen in Figure 12.
FIG. 7: Experimental setup for the measurement of PD using the Rogowski coil based probe. Two signals were obtained: one measuring the voltage in the impedance Zm , the other measuring the output voltage from the Rogowski coil.
The specimen where the PD occurred was a needle-plate electrode configuration. It consisted of a vessel which was covered on the upper side with a plate in the middle of which a needle electrode was placed. The plane electrode was fixed to the lower plate of the vessel. The gap distance was adjusted to 1 cm. A schematic diagram of the vessel is shown in Figure 13.
FIG. 8: Schematic diagram of the vessel with a needle-plate electrode configuration.
The results are exposed in Figure 14. The voltage signal obtained with the Rogowski coil is compared with the current measured in the impedance Zm , which was obtained from the measured voltage signal. Both were mathematically processed in order to eliminate a noise band of frequencies around 100 MHz. The measured PD pulse has a fundamental frequency of about 20 MHz, so it is in the range of frequencies that can be detected with the designed Rogowski coil. Therefore, it is verified that the Rogowski coil based probe obtains an accurate measurement of the PD pulse. VII.
DISCUSSION
A new PD measuring probe was constructed and calibrated. The Rogowski coil described in this paper provides an exceptionally valuable method to detect PD in insulation voids at extremely low price. It achieves the required
9
Current in Zm (A)
0.15 0.1 0.05 0 −0.05 −0.1 0
1
2
3
4
time (s)
5 −7
x 10
Output Voltage (V)
0.02 0.01 0 −0.01 −0.02
0
1
2
3 time (s)
4
5 −7
x 10
FIG. 9: PD measured with the Rogowski coil based probe.
bandwidth to measure PD. With the developed probe, PD pulses shape can be recorded in an oscilloscope, so that changes in PD pulses as insulation ages can be studied in future research. Acknowledgments
The authors would like to thank to the student Daniel Gallardo his valuable contribution to the development of the Rogowski coil and his deep study in its behavior in both time and frequency.
10
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
W. Yin, IEEE Electrical Insulation Magazine 13, 18 (Nov-Dec 1997). E. Persson, IEEE Transactions on Industry Applications 28, 1095 (Sep.-Oct. 1992). B. Fruth and L. Nemeyer, IEEE Transactions on Electrical Insulation 27, 60 (Feb. 1992). IEC 270-1981. Partial discharges measurements (IEC, 1981). W. Rogowski and W. Steinhaus, Arch Electrotech 1, 141 (1912). P. Nevalainen and K. Nousiainen, Nordic Insulation Symposium (June 2003). M. S. D. Capua and D. G. Pellinen, Proceedings of the International School of Plasma Physics Course on Diagnostics for Fusion Experiments (Sept. 1978). D. G. Pellinen, M. S. D. Capua, S. E. Sampayan, H. Gerbracht, and M. Wang, Rev. Sci. Instrum. 51, 1535 (Nov. 1980). W. F. Ray and C. R. Hewson, IEEE - IAS Conf. Proc. (Sept. 2000). J. D. Ramboz, IEEE Transactions on Instrumentation and Measurement 45, 511 (April 1996). J. Cooper, Plasma Physics (Journal of Nuclear Energy. Part C) 5, 285 (1963). D. A. Ward and J. L. T. Exon, Engineering Science and Education Journal pp. 105–113 (June 1993). W. F. Ray and R. M. Davis, EPE’99-Lausanne (1999).
11 TABLE I: Parameters of the coil. Coil Parameter Outside diameter, b Inside diameter, a Thickness, W Number of Turns, N
Specification 50 mm 13 mm 50 mm 12
12 TABLE II: Calculated parameters of the coil for both models. Model Parameter M Rl Ll Cl Rd Ld Cd
Specification 0.16 µH 0.23 Ω 1.94 µH 15 pF 0.12 Ω 1.06 µH 11.3 pF
