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Abstract—The continuous progress in magnetic sensor research provides increasing accuracy in measurement systems based on magnetic sensor arrays.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 50, NO. 5, OCTOBER 2001

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Processing Magnetic Sensor Array Data for AC Current Measurement in Multiconductor Systems Gabriele D’Antona, Luca Di Rienzo, Roberto Ottoboni, Senior Member, IEEE, and Angelo Manara

Abstract—The continuous progress in magnetic sensor research provides increasing accuracy in measurement systems based on magnetic sensor arrays. Many industrial applications in the field of protection for low-voltage electrical systems require novel technologies of ac current sensors characterized by lower costs and wider measuring range in amplitude and frequency. For this purpose, a promising solution is the utilization of sensor arrays provided with signal processing techniques. In the paper, we propose a new principle for simultaneous measurement of polyphase currents flowing in parallel conductors of arbitrary cross-sections based on processing magnetic sensor signals. After describing the analytical solution of the measurement problem, theoretical uncertainty analysis is carried out. Preliminary experimental results confirm the validity of the new approach.

TABLE I ACCURACY SPECIFICATIONS FOR PROTECTION APPLICATIONS IN RELATION TO THE RATED CURRENT

Index Terms—Current measurement, current transformers, Hall effect devices, multisensor systems, transducers.

Let us note here that the current error in percentage is defined as

I. INTRODUCTION

E

VEN in a classical technical field as that of low-voltage protection devices, the effort of reducing the size and cost of the devices is an actual trend. Significant improvements have been obtained in electric contacts, with new materials and shapes, in optimized kinematisms that make the switch fast, more reliable, and less expensive. Furthermore, data processing has been added in order to obtain sophisticated protection algorithms, as well as communication capability, allowing remote control, programming, and monitoring. For the purpose of current measuring, the use of current transformers seems unavoidable if the transformer has the duty both of measuring the current and supplying the electronic relay. Nevertheless, many industrial applications in the field of protection systems require novel ac non contact current sensors that shall be characterized by lower costs and a wider measuring range both in amplitude and frequency. Table I illustrates accuracy specifications for instrument transformers for protection applications [1]. To be of any practical interest, a novel current sensor must meet these specifications, which are defined at the nominal frequency of the instrument transformer.

Manuscript received October 20, 2000; revised July 31, 2001. G. D’Antona, L. Di Rienzo, and R. Ottoboni are with the Dipartimento di Elettrotecnica, Politecnico di Milano, Milano, Italy (e-mail: [email protected]). A. Manara is with ABB Ricerca S.p.A., Corporate Research Italy (ITCRC), Sesto S. Giovanni (MI), Italy (e-mail: [email protected]). Publisher Item Identifier S 0018-9456(01)09722-4.

(1) is the nominal transformation ratio, and where are the r.m.s. values of secondary and primary currents; the phase error is the phase difference between the phasors of the primary and secondary currents; while the composite error in percentage is defined as

(2) and are the instantaneous values of secondary where and primary currents. The rated accuracy limit is the maximum r.m.s. value of the primary current so that the composed error belongs to the required range. The rated accuracy limits are standardized to 5, 10, 15, 20, 30 times the primary nominal current. In this paper, we propose a new principle for simultaneous measurement of polyphase currents flowing in parallel cylindrical conductors of arbitrary cross-sections based on processing magnetic sensor signals. Advantages of this approach compared with traditional instrument transformers are a wider measuring range, low cost, and the capability to meet accuracy specifications not only at nominal frequency but also in a wide bandwidth. The principle has been applied to a three-phase bus-bar system, typical of low-voltage high current circuit breakers, employing an array of six Hall sensors (Melexis MLX90215, [2]) placed in the proximity of the bars. Fig. 1 shows the

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possible to demonstrate that the magnetic field in the space surrounding the conductors is linear with respect to the total current flowing in the conductors. Indicating with the characteristic function of the cross-section of -conductor (defined uniand zero outside), the field equation in terms of the tary over is given by [3] vector potential

Fig. 1. Three-phase conductor system and the proposed configuration of the Hall sensors array. Arrows indicate the sensitivity directions of the sensors.

geometry of the system designed for a rated current of 3200 A. Arrows indicate the sensitivity directions of the sensors. The magnetic sensors near the bus-bars no. 1 and no. 3 are not placed over the axis of symmetry of the bars, but nearer to the geometric center of the system. This condition has been realized for achieving a better robustness to cross-talk magnetic fields, as it is proved by numerical simulations. Hall effect sensors have been chosen for their extended measuring range. As a matter of fact, the multisensor system must be able to measure overcurrents of magnitude that might be ten times the nominal current.

(3)

where unit vector; conductivity of conductor ; contour of its cross-section

.

Equation (3) is a linear integral–differential equation. Thus the superposition principle with respect to can be applied. Both the current and the sensor output voltage can be expressed as Fourier series

II. FORMULATION OF THE MEASUREMENT PROBLEM Let us consider a set of parallel conductors carrying ac . The r.m.s. values and relative currents phases we want to measure by processing magnetic field data magnetic sensors, whose sensitivity directions lie given by on planes that are perpendicular to the axis of the current conductors (Fig. 2). A magnetic field sensor can be characterized by a sensitivity vector whose amplitude is the sensitivity to the magnetic field and whose direction indicates the magnetic field component that it measures. In the following, we will suppose to know the positions of the conductors, the shapes of their cross-sections, and position and orientation of the sensors, defined after a design phase. We will also assume the magnetic sensors to be far enough from other current conductors and magnetized bodies. ), with Let us fix a rectangular coordinate system ( parallel to the axis of conductors. At a given time, a magnetic that is in position ( ) gives an sensor of sensitivity , , where output voltage signal equal to is the magnetic field. In the following, we will does not suppose to deal with linear magnetic sensors, i.e., dependent on . Since the currents under measurement are time-varying, mutual interactions between conductors must be taken into account. As a matter of fact, if current conductors are near enough to interact between each other, the time-varying magnetic field of every current induces eddy currents in near conductors. The appearance of eddy current phenomena (skin and proximity effects) modifies the magnetic field. By neglecting displacement currents (low-frequency approximation) from the set of Maxwell equations in free-space, it is

Re

(4)

,

with

Re

(5)

. with Linearity of eq. (3) and of the sensors response to the magnetic field allows writing the following relation between harmonic components in a matrix formulation

.. .

.. .

where the transimpedances

.. .

.. .

(6)

are given by

(7)

D’ANTONA et al.: PROCESSING MAGNETIC SENSOR ARRAY DATA

Fig. 2. System of

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P currents and N magnetic field sensors.

Equation (6) constitutes the measurement model. After algebraic calculations it can be factorized in terms of real and imaginary components .. .

.. .

.. .

.. .

.. .

.. .

Furthermore, under the hypothesis of negligible correlation between noise sequences of the sensor signals, the covariance matrix of the vector , of size , can be expressed as

.. . .. . .. .

..

.

.. .

(9)

According to estimation theory [5] and to statistical properties of the harmonic components, we can state that the least squares estimator is the minimum variance unbiased estimator of the vector . We can thus measure the th harmonic of the currents by applying the normal equaobtained by the DFT of the sensor signals tion to the vector

.. . (8)

(10) .. .

The estimated uncertainty of real and imaginary components of the currents is represented by the covariance matrix of the estimated quantities [6] and it is given by

III. MEASUREMENT ALGORITHM The harmonic component appearing in (6) can be calsamples taken from culated by the DFT of a sequence of the th sensor signal. It is proven in [4] that by imposing very weak assumptions on the noise in the time domain, the resulting noise of harmonic components can be modeled using a Gaussian distribution. In particular, if the noise sequence that is superimposed on the signal samples is white, with variance , then the are equal to variances of the two random variables for every and the covariance between them is zero.

var

(11) is not a diagIt must be noted here that in general onal matrix. The variance of the th harmonic component amplitude is related to the real and imaginary parts through (12), as shown at the bottom of the page. The expression for the variance of the th harmonic compois given by (13), as shown nent phase at the bottom of the page.

var

cov

var

var

(12)

var

var

cov

(13)

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IV. PROCEDURES FOR TRANSIMPEDANCE ESTIMATION The transimpedances also as

, defined by (7), can be expressed

(14) is the sensor sensitivity corresponding to the harwhere can be evalmonic order and the complex coefficients uated via 2D Finite Element Method (FEM) analysis. The two equations (7) and (14) indicate two ways for performing the calibration procedure, numerically applying (14) and experimentally applying (7). It is foreseeable that for a single prototype, the second approach is more accurate than the first based on a numerical modeling. On the other hand, it is important to underline the different cost of the two procedures and that the numerical approach is more flexible in the transducer design phase.

Fig. 3. Real parts of the coefficients normalized to their value at 50 Hz (o ). ,5 ,/ ,. ,

=_

_

=_

=_

=_

=

A. Procedure Based on FEM Analysis This approach has been carried out by means of a commercial FEM software, simulating the case of the three copper bus-bars depicted in Fig. 1. According to equation (14), three simulations for every frequency of interest are necessary, each one computing the magnetic field produced by a unitary current of zero phase, flowing in each bus-bar, when the other two bars are open circuits. must be calculated for each frequency in Coefficients the desired bandwidth. As a matter of fact, they depend on frequency, as well as the magnetic field, for the frequency dependence of skin and proximity effects in conductors. Figs. 3 and 4 represent their real and imaginary components (normalized to their values at 50 Hz) at different frequencies (only five of the eighteen quantities are reported, as the others can be obtained looking at the symmetry of the array). for different are relevant, the Since variations of multisensor system must be calibrated at different frequencies over the required bandwidth; otherwise, the uncertainty in measuring currents may be out of the required level. For example, if the array is calibrated only at 50 Hz, then the current errors would be those of Fig. 5 when measuring currents of higher frequencies (assuming sensor sensitivity constant with frequency and the current system to be balanced and of nominal amplitudes). In order to carry out the measurement uncertainty budget, let us consider its two main sources: sensor noise and transimpedance estimation accuracy. Expression (11) gives the contribution due to sensors noise. From expression (14), it can be are associated noted that the measurement uncertainties of (depending on mewith the measurement uncertainties of chanical tolerances in specimen realization) and with those of (due to dispersion of the sensors sensitivity). In the folwith respect lowing, we will neglect the uncertainty . to The difference between actual and nominal value (5 V/T is caused by their temperature @ 50 Hz) of sensitivities dependence and the temperature cross-sensitivity coefficients

Fig. 4. Imaginary parts of the coefficients normalized to their value at 50 Hz (o ,5 ,/ ,. , ).

=_

Fig. 5. only.

=_

=_

=_

=_

Current errors versus frequency with sensor system calibrated at 50 Hz

dispersions. With temperature coefficient variations between 0.01%/ C, and assuming an operating temperature range C– C [2] together with the hypothesis of a uniform is equal statistical distribution of the sensitivity errors, to 0.04 V/T.

D’ANTONA et al.: PROCESSING MAGNETIC SENSOR ARRAY DATA

Fig. 6. Estimated combined standard uncertainty of current amplitude versus the current amplitude (normalized to the nominal current) at 50 Hz. (a) Procedure based on FEM analysis. (b) Procedure based on direct calibration.

Fig. 7. Estimated combined standard uncertainty of current phase versus the current amplitude (normalized to the nominal current) at 50 Hz. (a) Procedure based on FEM analysis. (b) Procedure based on direct calibration.

The estimated combined uncertainties [6] of current amplitudes and phases versus the current amplitude obtained by Monte Carlo simulations are plotted in Figs. 6 and 7 (line a), respectively, at 50 Hz in the case of a three-phase balanced system (results corresponding to only a phase are reported, with those of the other two phases of the same entity). The linear growth of amplitude uncertainty limits the measuring range of the array (Fig. 6). Sensor noise contribution increases phase uncertainty at low amplitude current (Fig. 7). B. Procedure Based on Direct Calibration The transimpedances can be also indirectly measured as stated in (7). It has been performed by imposing a reference current (at different frequencies between 50 and 500 Hz) in every bus-bar and measuring the reference current and the instantaneous values of each sensor output voltage signal. Reference current measurement has been provided by a commercial closed-loop Hall effect current transducer. Its standard A uncertainty has been estimated as (0.015% ).

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Fig. 8. Mean value of composite error versus the current amplitude (normalized to the nominal current) at 50 Hz.

The seven signals have been simultaneously sampled and acquired by a 12 bit @ 12.8 ksamples/sec data acquisition system. and At each frequency, the voltage and current phasors have been obtained by FFT analysis of 1024 samples. Measurement uncertainty of sensor output voltages has been estimated combining the contribution from the sensor mV) and the ADC (1 LSB noise ( mV) through the FFT algorithm [6], [7] and obtaining mV. The quantization effect in reference current measurement has been neglected. In order to evaluate the current measurement uncertainty of the sensor array up to 10 , a Monte Carlo simulation method has been applied. Figs. 6 and 7 (line b) show that the procedure based on direct calibration guarantees lower uncertainty than the procedure based on numerical computations. In order to demonstrate that accuracy of current measurement matches when current amplitude is several times its nominal value, the mean value of the composite error defined by (2) has been also estimated by Monte Carlo computations, thus allowing a comparison with the specifications reported in Table I. Fig. 8 shows that the accuracy limit is fulfilled up to ten times the nominal current amplitude. V. EXPERIMENTAL RESULTS The array configuration of Fig. 1 was fabricated by mounting six programmable Hall sensors on three boards with two sensors for each board. The boards were mechanically fixed perpendicularly to the bars. The commercial sensors have been programmed with 5 mV/mT sensitivity. They are characterized by 180 mT maximum detectable field, 130–1300 Hz bandwidth to C operating temperature range. Their cost and is approximately $2. Testing of the novel current measurement technique has been performed in two laboratories. at 50 Hz It has been tested in a range between 0 and 6 in ABB Italian laboratories. The ac current flowed in one bar and returned in another of the three bars, while the third bus-bar was an open circuit. Reference current measurement was performed by a standard shunt. Only measurements referred to one phase have been reported. Figs. 9 and 10 show measurement

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Fig. 9. Current error versus reference current (o have been obtained following procedure based on FEM analysis while points and uncertainty bars correspond to the procedure based on direct calibration). The return cable flowed in bus-bar number 2.

Fig. 10. Phase error versus reference current (marks have the same meaning of Fig. 9). The return current flowed in bus-bar number 2.

errors of current of bus-bar number three when the return current flowed in bus-bar number two. The graphs report the mean values and the standard deviation bars of current and phase errors obtained by the statistical analysis of ten repeated measurements applying the procedure based on direct calibration. The same graphs report also the current errors obtained by applying the procedure based on FEM analysis. Taking into account standard shunt uncertainty of 0.05% , it can be concluded that experimental results reported in Figs. 9 and 10 are in accordance with the numerical uncertainty analysis reported in Figs. 6 and 7. In the laboratory of Politecnico di Milano, due to the limitations of the available current generator, preliminary tests have been specifically aimed at investigating current measurement accuracy when current amplitude is lower than 15% the nominal one. That is a critical condition since signal-to-noise ratios of magnetic sensors are very low. The three bus-bars have been connected in series and fed by a single-phase ac current source. Reference current measurement has been performed as described in Section IV-B.

Fig. 11. Current error versus reference current at 50 Hz (o have been obtained following procedure based on FEM analysis while have been obtained following the procedure based on direct calibration).

Fig. 12. Phase error versus reference current at 50 Hz (marks have the same meaning of Fig. 11).

Figs. 11 and 12 show current and phase errors versus reference current, obtained by following both the numerical procedure of Section IV-A and the experimental procedure of Section IV-B. Those experimental tests show the limitations of the former procedure. The reported errors are only those of one of the three currents, since the other two phases show a similar behavior. In the same laboratory, the current sensor has been also tested at different frequencies between 50 and 500 Hz. Figs. 13 and 14 show current and phase errors in the range 50–500 Hz (at 400 A) after estimating transimpedances by direct calibration at the corresponding frequencies and those obtained calibrating the array at 50 Hz only. As it can be noted, the calibration at all the frequencies of interest is mandatory, especially for amplitude current measurement. From the preliminary experimental tests, it can be concluded that the novel three-phase current sensor meets accuracy requirements defined for a 5P current transformer (reported in Table I) in a 0–20 kA amplitude range and in a 50–500 Hz frequency range.

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REFERENCES

Fig. 13. Current error versus frequency (/ have been obtained calibrating the array at 50 Hz only while have been obtained following the procedure based on direct calibration at all frequencies).

[1] IEC 44-1 International Standard, “Instrument trasformers: Part 1: Current transformers,” Dec. 1996. [2] Precision Programmable Linear Hall-Effect Sensor MLX90215 [Online]. Available: www.melexis.com. [3] M. Chiampi, D. Chiarabaglio, and M. Tartaglia, “FEM analysis and modeling of busbar systems under AC conditions,” in Proc. Int. Conf. Comput. Electromagn., London, U.K., Nov. 1991, pp. 252–255. [4] J. Shoukens and J. Renneboog, “Modeling the noise influence on the fourier coefficients after a discrete Fourier transform,” IEEE Trans. Instrum. Meas., vol. IM-35, pp. 278–286, June 1986. [5] J. V. Beck, Parameter Estimation in Engineering and Science. New York: Wiley, 1977. [6] ISO, IEC, BIPM, OIML, “Guide to the expression of uncertainty in measurement,” 1995. [7] M. F. Wagdy, “Effect of ADC quantization errors on some periodic signal measurements,” IEEE Trans. Instrum. Meas., vol. IM-36, pp. 983–989, Aug. 1987.

Gabriele D’Antona was born in Milan, Italy, in June 1964. He received the electrical engineering degree from the Politecnico di Milano, Milan, in 1990 and the Ph.D. degree in electrical engineering in 1994. In 1991, he served for four years at Joint European Torus (JET), Abingdon, U.K., where he worked in the Plasma Configuration Group of the Operations Division on the definition of a method for the stabilization of magnetic perturbation in thermonuclear plasmas and for the realization of an experiment for the control of magnetic rotating islands. Since 1995, he has been working with the Electrical Department of the Politecnico di Milano. His research interests deal with megnetohydrodynamic modelization of thermonuclear plasmas, inverse problems related to electromagnetic measurements, and the application of digital parallel systems for real-time measurement and control of fast processes in nuclear plasma physics.

Fig. 14. Phase error versus frequency (marks have the same meaning of Fig. 13).

Luca Di Rienzo was born in Italy in 1971. He received the Laurea degree in electrical engineering in 1996 and the Ph.D. degree in electrical engineering in 2001, both from the Politecnico di Milano, Milan, Italy. Currently, he is Research Assistant at the Dipartimento di Elettrotecnica, Politecnico di Milano. His research interests include current sensors for industrial applications, estimation of linear continuous-time systems transfer functions, statistical models for electromagnetic compatibility, and boundary element method formulations for eddy current problems.

VI. CONCLUSION The novel current sensing technique has been analytically formulated for a general system of many conductors of arbitrary cross-sections. Then, it has been applied to a three-phase bus-bar system, and uncertainty propagation in the measurement algorithm has been analyzed. Accuracy specifications for protective current transformers are fulfilled not only at the nominal frequency, but in the whole bandwidth. Preliminary experimental results are promising. The measurement model has been verified, and the experimental results are in accordance with numerical simulations. The calibration procedure based on FEM analysis is the starting point for undertaking the optimization of sensor positions. A more complete metrological characterization is now under development. In particular, environmental effects, such as those due to temperature changes and to cross-talk magnetic field, are under experimental investigation. Furthermore, the transient behavior of the current sensor must be analyzed, both from a theoretical and an experimental point of view.

Roberto Ottoboni (M’90–SM’01) was born in Milan, Italy, on April 1, 1961. In 1988, he received his M.Sc. degree in electronic engineering at the Polytechnic University of Milan, Milan, and in 1992 he received his Ph.D. degree in electrical engineering at the same university. From 1992 to 1998, he was Assistant Professor of electrical measurements at the Polytechnic University of Milan. Since 1998, he has been Associate Professor of electrical and electronic measurements at the same department. His scientific activity deals with the digital signal processing techniques applied to the electrical measurements. In particular, he is concerned with the application of DSP techniques to the experimental analysis of the electric systems under distorted conditions. He is also involved in a research activity for the development of industrial sensors and tactile sensors for robots. His scientific activity is summarized in over 50 papers published in national and international journals and presented in international conferences.

Angelo Manara received the degree of Doctor in electronic engineering at Politecnico di Milano, Milan, Italy, in 1980, and a M.Sc. degree in EMC at Hull/York University, York, U.K., in 1995. He worked as electronic designer in aerospace, electro-medical, and defense industries. Then, he worked for ten years in the largest EMC Lab, Milan, Italy, and he is now with ABB Corporate Research as EMC expert. He is also a NARTE Certified EMC Engineer. At ABB, his main research fields are current sensing technologies and RF communication/identification.