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Short Circuit Current Measurements Between Transformer Sheets Carl A. Schulz1;2 , Stéphane Duchesne1;2 , Daniel Roger1;2 , and Jean-Noël Vincent3 Université Lille Nord de France, 59000 Lille, France UA, LSEE, 62400 Béthune, France ThyssenKrupp Electrical Steel, 62330 Isbergues, France In large transformer cores, burr-induced insulation faults between laminations can result in short-circuit currents which may be high enough to damage the core. This study presents measurements of the actual worst-case short circuit currents encountered in artificial interlamination shorts. A procedure using an adapted miniaturized Rogowski coil is described. Results show that the maximum short circuit current is not proportional to the core width, but, except for extremely narrow cores, it increases with good approximation linearly with the core width. Peak currents can in large cores reach several amperes even when only two laminations are involved. Index Terms—Current measurement, short circuit currents, transformer cores.
I. INTRODUCTION
W
HEN interlamination shorts appear in a magnetic core, the benefits of the laminated core structure are partially undone. Eddy currents can circulate between the sheets, leading to elevated core loss. The short circuit currents involved can be substantial and may lead in unfavorable cases to local melting of the core [1]. The same phenomenon is known in the stator cores of large turbomachines. For this domain, different diagnosis procedures have been developed to detect the interlaminar shorts before they cause damage to the core [2], [3]. Interlaminar shorts arise principally from burr, which may remain from the mechanical cutting of the sheets. So far, measurements of local and global power loss have been presented, conducted on artificial short-circuits introduced over multiple sheets of a transformer core [4]. The importance of burr avoidance has been stressed repeatedly [5]. This work presents measurements of the actual short circuit current arising between two transformer sheets. For this purpose, pairs of artificial insulation faults have been introduced between conventional grain oriented (CGO) steel sheets. A custom-made miniaturized Rogowski coil has been employed to measure the current. II. EXPERIMENTAL SETUP
The current measurement procedure presented has been developed as a part of a project aiming to model interlaminar short circuits. A detailed explanation of the experimental setup is given in [6]. The important aspects concerning the current measurements are addressed in the following. The artificial short circuit was introduced between two transformer sheets by creating two contact points on opposite sides of the sheet. Thus, a closed path is introduced perpendicularly to the flux density vector , allowing eddy current circulation between the sheets. The placement of the contact points opposite each other constitutes the worst case, since their distance is Manuscript received June 19, 2009; revised August 27, 2009; accepted September 13, 2009. Current version published January 20, 2010. Corresponding author: C. A. Schulz (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/TMAG.2009.2032820
Fig. 1. Placement of the Rogowski coil around an artificial insulation fault.
shortest while maximum flux is enclosed in the resulting loop. In order to allow current measurement, some additional space was left between the sheets. The contacts were shaped as cones of solder, their height being chosen such as to leave 600 m distance between the sheets. This space is sufficient to place the very slim Rogowski coil around one of the contacts. Contact resistance can be considered negligible [6], the short circuit currents measured represent thus the worst case. Fig. 1 shows the placement of the coil between two CGO sheets of 300 m thickness. The additional air space between the two sheets does not influence the short circuit current: since the permeability of , the sheets is much bigger than that of the air space the additional electromotive force (EMF) induced due to the air space is negligible unless the steel is extremely saturated. III. ROGOWSKI COIL MANUFACTURE A. Principle of Operation A Rogowski coil is a sensor dedicated to measuring alternating currents. It consists of a wire wound around a nonmagnetic support, which is then bent around the conductor whose current is to be measured. The winding thus constitutes a mutual inductance coupled to the conductor; its output voltage is proportional to the variation of the current. For a circular coil with rectangular cross section, the relation is
0018-9464/$26.00 © 2010 IEEE
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SCHULZ et al.: SHORT CIRCUIT CURRENT MEASUREMENTS BETWEEN TRANSFORMER SHEETS
Fig. 2. Mechanisms of interference through stray fields. (a) Interference captured in the unwanted loop area. (b) Interference which cancels out due to symmetry.
where is the permeability of free space, is the number of turns, is the height of the rectangular turns, is the outer radius of the coil, is the inner radius of the coil, and is the current in the conductor enclosed. Integration of the output signal yields a voltage which is proportional to the current. A demonstration of (1) can be found in the literature [7].
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Fig. 3. Inhomogeneity of the flux interfering in the Rogowski coil.
TABLE I SPECIFICATIONS OF THE MINIATURIZED ROGOWSKI COIL
B. Relevant Properties Two of the Rogowski coil’s fundamental properties merit some consideration, since these play an important role in the application. 1) Linearity: Since there is no ferromagnetic core inside the windings, there are no saturation effects. The mutual inductance does not depend on the current; the system is linear. For the custom-made coil this means that the calibration can be carried out at any convenient current level and will be valid over a theoretically infinite range. 2) Susceptibility to Interference: A Rogowski coil can be subjected to two principal types of interference. These are illustrated in Fig. 2. Since the coil forms a loop, it is sensitive to interference captured in the loop area [Fig. 2(a)]. The sensitivity to this kind of interference can only be minimized by reducing the loop area of the Rogowski coil. In the present application where the coil is placed between the transformer sheets, this kind of interference does not pose a problem, because the magnetic flux in normal direction to the sheets is negligible. A second type of interference may originate from magnetic flux in the plane of the coil [Fig. 2(b)]. In a circular coil, this interference conveniently cancels out if the interfering field is homogeneous: in this case, the voltages induced in the different parts of the coil have opposite signs due to symmetry. For perfect cancellation, it is crucial that the distance between the windings and the cross section remain constant all over the length of the coil. Unfortunately, the placement of the coil at the border of the sheets means that the leakage flux which is interfering cannot be considered homogeneous at all. As shown in Fig. 3, the coil protrudes from the iron core. Naturally, the leakage flux from the steel sheets decreases in the region outside the core. There is thus no cancellation of the interfering flux in the coil. As a remedy to this interference, a differential measurement procedure is adopted. It will be described in Section V. C. Specifications of the Miniaturized Rogowski Coil The custom-made coil was designed with the requirements that firstly, the system should be able to measure a current of 50 mA at 50 Hz and that secondly, the overall thickness must not exceed 600 m. Since the coil’s active cross section is very
Fig. 4. Full view of the fabricated Rogowski coil.
small, the number of turns has been increased as much as possible, in order to achieve sufficient self inductance. Table I lists the geometric and electric specifications, Fig. 4 presents a full view of the coil. The measurement coil was wound on a cardboard support with 300 m thickness. The whole sensor is sandwiched between two layers of adhesive tape, in order to protect the windings. The self inductance achieved leads to a sensitivity of the nV/(A Hz). current probe of IV. SIGNAL PROCESSING A low-noise amplification and integration circuit is needed to condition the extremely weak signals of the miniature Rogowski coil. The schematic is presented in Fig. 5. The first amplification stage consists in a low-noise, high-CMRR amplifier, set to a gain of 1000. The high CMRR (common-mode rejection ratio) serves to suppress any noise captured by capacitive coupling between the coil and the transformer sheets. The total gain of the two amplification stages equals 100 000. High-pass filters are inserted at different stages in the circuit in order to eliminate offset voltages. The sensitivity of the whole chain is mV/A. It is determined by averaging the sensitivities obtained
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Fig. 5. Amplification and integration circuit of the Rogowski coil.
Fig. 6. Phase and sensitivity response (20 Hz–30 kHz) of the measurement chain before correction.
Fig. 7. Phase and sensitivity response (20 Hz–30 kHz) of the measurement chain after correction.
for different currents of precisely known intensity. The overall measurement precision obtained is better than 3%. The circuitry contains a number of filters, which introduce a frequency-dependent phase lag. This phase lag must certainly be corrected, if the short circuit current is to be correlated to other quantities measured. Hence, additional signal processing is performed in the frequency domain in order to straighten out the phase lag of the measurement chain. This is done numerically after the acquisition of the measurement signals. Fig. 6 shows the system response of the chain before correction. The phase response shows considerable phase lag for low and very high frequencies. The gain response shows that the system sensitivity is approximately constant in the frequency range 60 Hz–8 kHz. The system response measured is saved as a reference in a . This table serves look-up table, in matrix form as the data base for correction. The correction procedure is implemented as to be executed automatically during current measurements. It comprises three steps. Firstly, the distorted measurement signal is transformed into the frequency domain using are converted to phase and FFT. Complex coefficients gain . Secondly, phase and gain are corrected for each harmonic frequency separately. Target values are zero for the phase and 0.260 V/A for the gain, respectively. The correction is thus
In order to remove the interference of the leakage flux on the sensing coil, a differential procedure is applied. A first measurement is conducted in open-circuit condition. The resulting is entirely due to leakage flux, since the output signal short circuit current is zero. A second synchronized measure. The ment in short circuit condition yields the signal signal sought-after which is due to the short-circuit current only is thus
(2)
(4)
(3) where the reference values are found by interpolation from the look-up table. It is sufficient to do the correction for the frequency range 40 Hz–20 kHz only. Thirdly and lastly, the corare reconverted to complex rected coefficients . These replace the old coefficients in the coefficients signal’s frequency domain vector. By applying the inverse transformation IFFT, the corrected signal is obtained. Fig. 7 presents the corrected system response, showing near-ideal behavior in the relevant frequency range. V. DIFFERENTIAL MEASUREMENT PROCEDURE
SCHULZ et al.: SHORT CIRCUIT CURRENT MEASUREMENTS BETWEEN TRANSFORMER SHEETS
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Fig. 8. Differential measurement technique. Left: weak excitation (0.15 T); right: strong excitation (1.70 T). Fig. 9. Phase relation of open-circuit voltage and short-circuit current at 51 Hz, 1.7 T. Measurement conducted on CGO 0.30 mm, core width 30 mm.
It is worth noting that the error signal comprises all interference on coil or circuitry which is synchronized to the excitation frequency. The differential technique eliminates thus all the modes of interference discussed in Section III-B. Further averaging is used to filter the remaining noise and any interference not synchronized to the excitation frequency. The latter is set to 51 Hz, to allow elimination of 50 Hz components. VI. RESULTS Fig. 8 presents the differential signals for weak and strong excitation. One can see that the error signal is in the same order of magnitude as the resulting signal. This illustrates that the differential approach is indispensable for measuring in an environment with strong inhomogeneous leakage flux. Numeric precision does not constitute a problem, since the instantaneous and are sufficiently different. Quantities are values of only sinusoidal at low flux densities: the magnetic circuit exhibits increased leakage flux, because it was primarily optimized for easy modification of the core width. Thanks to the phase correction, the short-circuit current can be correlated to other measurement quantities, such as, e.g., the EMF measured in open-circuit condition. This is done in Fig. 9, comparing the waveforms of open-circuit voltage and short-circuit current at 1.7 T. The normalized waveforms reveal that, neglecting the small difference between the curves, the behavior of an interlaminar short can be considered purely resistive. This means that results obtained at low flux densities can be extrapolated to higher flux densities, up to 1.7 T. Fig. 10 presents the short-circuit current and power dissipation as a function of core width. The diagram shows that, for extremely narrow cores, the short circuit current is certainly a nonlinear function of the core width. This is probably due to the fanning-out of the current between the contacts. However, for cores which are not extremely narrow, the function can with good precision be approximated by a linear law. Extrapolation of the experimental results permits an estimation of the short circuit current in a large transformer core. For
Fig. 10. Interlaminar short circuit current as a function of core width. Peak induction 0.4 T.
example, for a very large core of 60 cm width at 50 Hz, 1.7 T, the peak short circuit current can reach 9.8 A. ACKNOWLEDGMENT The authors gratefully acknowledge support from the European Union (European Regional Development Fund), the Nord-Pas de Calais region, and the French Ministry (FRT). REFERENCES [1] P. Beckley, European Electrical Steels, Electrical Steels—A Handbook for Producers and Users, 2000. [2] P. Tavner and A. Anderson, “Core faults in large generators,” IEE Proc. Elect. Power Appl., vol. 152, no. 6, pp. 1427–1439, 2005. [3] Z. Posedel, “Inspection of stator cores in large machines with a low yoke induction method—Measurement and analysis of interlamination short circuits,” IEEE Trans. Energy Convers., vol. 16, no. 1, pp. 81–86, 2001. [4] A. J. Moses and M. Aimoniotis, “Effects of artificial edge burrs on the properties of a model transformer core,” Physica Scripta, vol. 39, pp. 391–393, 1989. [5] P. Beckley, N. J. Layland, E. Hopper, and D. Power, “Impact of surface coating insulation on small motor performance,” IEE Proc. Elect. Power Appl., vol. 145, no. 5, pp. 409–413, 1998. [6] C. A. Schulz, D. Roger, S. Duchesne, and J.-N. Vincent, “Experimental characterization of interlamination shorts in transformer cores,” IEEE Trans. Magn., submitted for publication. [7] W. Koon, “Current sensing for energy metering,” in IIC-China/ESCChina Conf. Proc., 2002, pp. 321–324.
