Low-Cost Power Meter for the Characterisation of ... - IEEE Xplore

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terisation of inverter-fed electrical machines. The power meter has been designed to perform a measurement of the electrical quantities associated to the first ...
IEEE Instrumentation and Measurement Technology Conference Ottawa, Canada, May 19-21, 1997

Low-cost power meter for the characterisation of inverter-fed electrical machines A. Carullo, M. Parvis and A. Vallan Dipartimento di Elettronica- Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino - Italy Phone +39-11-564-4114 Fax +39-11-564-4099 EMail [email protected] WWW: http://www.sermis.polito.it

Abstract: This paper describes a versatile though low cost power meter that was specifically conceived for the characterisation of inverter-fed electrical machines. The power meter has been designed to perform a measurement of the electrical quantities associated to the first harmonics that are obtained with an uncertainty of less than 0.7%. The power meter is simple and cheap thanks to the restriction of the measurement capabilities to the first harmonics, which allows low cost converters to be used. The wattmeter employs a Digital Signal Processor to obtain a measuring rate in excess of 2 Hz; a conventionalPersonal Computeris used for the graphical interface. The power meter characterisation is obtained by means of a special designed generator that allows distorted though known waveforms to be generated.

I. INTRODUCTION The wide diffusion of static power converters that work at frequencies of up to 100 kHz and which feed electrical motors, requires the development of special measuring instrumentation that is capable of handling highly distorted waveforms. Instrumentationwith this capability is currently available, but at a rather high cost. Such a high cost is justified by the versatility and complexity of the commercial instruments, which have several different features and are able to perform complete analyses of the involved electrical quantities. Fortunately, only a few parameters are actually required for the characterisation of static converters and therefore a great cost reduction can be obtained if the unnecessary features are not implemented. This paper firstly describes a power meter that is less expensive than many commercial instruments, but which provides a remarkable accuracy in the measurement of the basic quantities that are required for the electrical machine characterisation.

wattmeter are then described and the lack of standards and reference instruments are pointed out. II. IMPORTANCEOF FIRST HARMONIC COMPONENTS. The signals that inverters generate have a complex shape which prevents the conventional measuring procedures from being effective [l]. In the presence of such distorted waveforms, the simple measurement of root mean square (rms) values of voltage, current and active power leads to unreliable estimations of the parameters that characterize electrical machines, thus some form of spectral analysis must be performed. Such an analysis often need not be carried out for more than a few harmonics, since the energy that is actually converted from electricalinto mechanicalenergy is substantiallyrelated to the power associated to such harmonics [2]. Moreover, energy losses and magnetic stresses in magnetic materials usually depend on the first harmonic of the voltage that is used to feed the device [3- 41. In this scenario, the development of an instrument that is able to perform the measurement of quantities connected only to the first harmonics can be a cost effective solution. Ill. WATTMETER BLOCK DIAGRAM

The aim of the designed wattmeter is to reduce the cost without causing an excessive penalty to the overall accuracy of the important quantities. These constraints do not allow either high accuracy analog to digital converters (ADC) or floating point digital signal processors (DSP) to be used. A reasonable solution is shown in fig. 1: current and voltage signals are acquired by using low-costthough fast 8 bit ADCs and a fixed point TMS320C50 DSP is used for the first processing.

The problems related to the characterisation of such a

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Three Phase Electrical Machine

Fig. 1 Block diagram of the proposed wattmeter.

The ADCs have a signal bandwidth of 600 kHz and are capable of a sampling rate of up to 1 MHz; in the actual release such converters are used to sample the signals at a maximum sampling rates of 250 kHz. Such a high sampling rate is used to allow the processing to greatly reduce quantisation noise; traditional techniques are employed to get rid of the deterministic effects on the quantisation noise. Hall-effect transducers are used for the current channels and differential amplifiers are used for the voltage channels. An even cheaper solution is under investigation that uses two ADCs that are connected to the six input channels by means of analogue multiplexers. By employing these solutions monophase, Aron and complete three-phase system configurations are available though at different sampling rate. The converter outputs are connected to the DSP board via an optical barrier, which galvanically decouples the acquisition board from the computer circuits. The DSP and the relevant circuitry are located on a standard ISA board inserted into the personal computer: a commercial evaluation board, equipped with the TMS320-50 processor, has been used to build the prototype.

and to the ADC quantisation can be expressed, for each phase, [5] as:

where I and V are the voltage and current rms values relevant to the selected harmonic; Ifsand V, are the rms full scale values and k is a coefficient which depends on the sampling rate, on the ADC resolution and on the equivalent input electrical noise. The algorithm is designed to be quite insensitive to the signal distortion and therefore the reportedfigures should be valid regardless of the signal shapes. Eqn. (1) is valid for input values above about 10% of both the voltage and current scales. Below these values an uncertainty increase is expected due to a less accurate frequency estimation, although a formula that expresses such an increase is not easily obtainable. The k value for a sampling rate of 250 kHz, ideal ADCs with 8 bit resolution and a negligible electrical noise is about 4.10-5.

The measurement software [5] is designed to extract the power associated to the fundamental component as well as to the first harmonics. The measurement is performed by using a time domain processing that is able to obtain a remarkable accuracy even though short observation time intervals are used. A brief description of such an algorithm is reported in the appendix. The DSP is used to filter and decimate the acquired samples that are eventually dispatched to the PC with a sampling rate of 2.5 kHz regardless of the actual input configuration.The PC is finally used to extract the harmonic amplitude and operates with floating point algorithms as described in the appendix.

The uncertainties connected to the ADC non linearities and to scale drifts of the input stages must be added to this value and appear as a local deviation of the computed power value with respect to the actual one. The maximum deviation, based on the ADC stated non linearities and on a separate characterisation of the input stages [6], can be expected to be below 0.1% of the apparent input range.

The expected wattmeter accuracy depends on both the algorithm performance and on the linearity and stability of the components that carry out the conversion and input stages. The power uncertainty connected to the algorithm

The metrologicalcharacterisation of a wattmeter designed to work with distorted signals cannot be performed in sinusoidal conditions only, since in such a situation all the phenomema connected to the harmonic presence are not taken into account.

IV. WATTMETER TESTING ISSUES

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Fig. 2 Test set for the wattmeter characterisation under distorted conditions

Unfortunately no power standards and widely accepted procedures are available when distorted signals are involved. For this reason, the authors are designing a test set that is able to create an arbitrary distorted environment and therefore to stimulate the instrument with distorted but known signals. The test set the authors are designing (Fig. 2) is composed of: 0

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A voltage and a current generator per phase. The generators are designed for “false power” measurements, so that the current generator is designed to produce values of up to 10 A, but with a compliance that is limited to a few volts, while the voltage generator is designed to produce hundreds of volts, but with a current that is limitedto a few milliamperes. This choice does not impair the generator utility for the characterisation, but greatly decreases both complexity and cost. Each generator contains two sections, based on separate digital to analog converters (DAC), which are optimised respectively for the first harmonic and for the higher harmonics. The fundamentalchannel has a high resolution though with a limited frequency response: the other channel has a lower resolution but a much wider frequency response. The two channel outputs are then physically summed to obtain the actual output. This is obtained, in the case of the current generator, by adding the currents in a low resistance line togheter and, in the case of the voltage generator, by serialising the two outputs that are galvanically isolated. All the DACs run from the same time base thus ensuring the required phase coherence; the

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samples corresponding to the required values of voltage and current are stored in a RAM, which is filled by the computer that controls the test set. In this way signals with well known characteristics are generated that can be used as standards during the characterisation. A preliminary version of the generator is currently available for a single phase system and without a complete metrological characterisation, so that it cannot be used as a standard. A reference top-class commercial wattmeter that is used as a standard until the generator is characterised. A computer that is used to program the signal generators and to record the different measured results. The computer is used to automatically span between different voltage and current amplitudes, phases and distortions so that a complete characterisation can be obtained without manual interventions. The proposed wattmeter plus any other wattmeter under test.

The signals that are used during the tests can be sinusoidal signals as well as signals that resembles the actual six-step and PWM generated output. Such signals have been obtained by acquiring the current and voltage outputs of PWM and six-step inverters with a 14 bit-48 kHz sampling system, computing the signal spectra and recreating a set of simulated signals that match the real ones, but with well defined and well completely known characteristics.

V. EXPERIMENTAL RESULTS Tests have been carried out both in sinusoidal and distorted conditions.The sinusoidal tests were carried out for

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Fig. 3 First harmonic local experimental standard deviation. The figure refers to measurements in sinusoidal conditions with unitary power factor.

Fig. 4 First harmonic mean power difference between the proposed and reference wattmeter. The figure refers to measurements in sinusoidal conditions with unitary power factor.

all the triplets corresponding to currents and voltages between 10% and 80% of the full range in steps of 10% and for phases between 0" and 90" in steps of 30".

in sinusoidal conditions is therefore about O.O8%, confirming the initial preview.

Fig. 3 shows, in a gray scale, the power standard deviation for currents and voltages that span the input ranges. The standard deviation behaviour confirms the values expected by Eqn. (1) with a kvalue of about 1.2.iO-4. Such a value is about three times larger than that expected with ideal converters thus highlighting the influence of the electrical noise mainly due to electromagnetic compatibility phenomena. Fig. 4 shows the mean difference between the measurements of the proposed and reference wattmeters.The plot shows a maximum difference that occours for current and voltage values located at about 80% of the full scale. Such a difference, which is mainly due to the non linearities of the employed converters and of the input stages, is about 0.07% of the apparent power range. The total uncertainty 2j

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The plots of figs. 3 and 4 refer to a test at a frequency of 50 Hz and with a zero phase angle between the voltage and current, but similar or better results are obtained for frequencies in the range of 20 Hz to 100 Hz and for phase angles of up to 90". Tests in non sinusoidal conditions have been carried out by adding an increasing value of a 5th harmonic, up to an amplitude of 40% of the fundamental, to the sinusoidal signals. The relative phase of the 5th harmonic of voltage and current have been varied both with respect to the fundamental and between the current and voltage. Fig. 5 shows the performance obtained by the proposed wattmeter with the first harmonic phase set to 90" so that the nominal first harmonic power is zero while the apparent first harmonic power is about 260 VA.

Commercial wattmeter

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Apparent 5Ihharmonic power (VA) Fig. 5 Wattmeter performance in the presence of distorted waveforms. The plots refer to a test carried out with an apparent first harmonic power of 260VA and with increasing presence of fifth harmonic up to an apparent fifth harmonic power of 160VA. The first harmonic power factor is zero while the fifth harmonic power factor is unitary. The second plot refers to a commercial wattmeter.

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Phase (") Fig. 6 Example of signals that resemble the output of a PWM that feeds a saturated inductive load.

Fig. 7 Uncertaintyof both the proposed and commercial wattmeters in the presence of the signals shown in the previous figure and for the phase that varies in the range of 70" to 170"

The power standard deviation, in this conditions, is about 0.005% and the sensitivity of the computed power with respect to the harmonic amplitude is down to 0.05% W/VA therefore being negligible as expected.

terisation of inverter-fed electrical machines without the necessity of arranging a costly sinusoidal supply system with a variable frequency. The characterisation of the proposed wattmeters has been obtained by arranging a special test set that is able to generate voltages and currents with an arbitrary, but known distortion.

The figure also show the results obtained by using a recent commercial wattmeter that costs about 10000 $ and employs 12 bit ADCs. The standard deviation of such a wattmeter, at a fixed distortion level is 0.0050/), but the sensitivity, with respect to the distortion, reaches the not so negligible value of 0.7% W/VA. One should note that such a high value leads to uncertainties thtat are not greater than the wattmeter specifications, but nevertheless greatly impair the overall performance.

The power meter volume is about 1 dm3 and its cost, excluding the computer, is of the order of 200$ for the prototype, therefore enabling a really portable and low cost but useful instrument to be assembled. REFERENCES

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L. S. Czarneski and T. Swietlicki Powers in Nonsinusoidal Networks: Their interpretation, analysis and measurement. IEEE Tr. on IM voI39, no.2 apr. 1990, pp. 340-345. A.Boglietti, P.Ferraris, M.Lazzari, F.Profumo, "Energetic Behaviour of Induction Motors Fed by Inverter Supply", Proc. of IEEE-IAS Annual Meeting, 2-8 October 1993, Toronto, CANADA, pp. 331335. A.Boglietti, P.Ferraris, M.Lazzari, F.Profumo, "Energetic Behaviour of Soft magnetic Materials Fed by Inverter Supply", IEEE Transactions on Industry Applications, NovembedDecember 1994, V01.30, N.6, pp. 1580-1587. O.V. Thorsen, M. Dalva, " A comparative Investigation and evaluation of different methods for experimental determination of parameters for saturated induction machines with current displacement rotor", Proc. of 30th IAS Annual Meeting October 8- 12 1995 Orlando USA, pp.599-605. A. Carullo and M. Parvis Low cost Power meter for highlydistorted three-phase systems. IMTC96 Brussels 1996, pp. 939-944. A. Carullo, U. Grimaldi and M. Parvis Automatic characterisation of Hall-effect current sensors. 7th int. symp. on modern electrical and magnetic measurement, Prague, Sep. 13-14 1995, pp. 107111.

Other tests have been carried out in situations that resemble those that are likely to be encountered in inverter-fedelectrical machines. Fig. 6 shows an example of signals that describe a situation where a PWM inverter feeds a saturated inductive load. The uncertainty of both the proposed and commercial wattmeter with these signals and for a phase that is artificially changed in the range of 70" to 170" is reported in fig. 7. The uncertainty of the proposedwattmeter is lower than 0.04% regardless of the phase while the commercial wattmeter shows a performance reduction for phases that approach 90".

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VI. CONCLUSIONS The measurement of the power associated to the first harmonics in heavily distorted conditions does not require costly instruments to be employed. A low cost wattmeter, based on a PC that embeds a cheap fixed point DSP and low cost 8 bit converters, is able to measure such a power with an uncertainty of below 0.1% of the apparent power range. Such an accuracy level is maintained regardless of the signal distortions thus enabling an accurate charac-

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APPENDIX: ALGORITHMS The power associated to the required harmonics is obtained by determining the modulus and phase of the relevant harmonic of voltage and current.

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Firstly, the acquired samples are filtered and decimated by means of a cascade of two finite impulse response (FIR) low pass filters, in order to reduce the pass-band to 1 kHz and the sampling rate to 2.5 kHz by means of a decimation process. The first FIR is composed of a rectangular window of five or ten taps of unitary amplitude, depending on the measurement configuration (three or four wire operations). The unitary tap amplitude, though non-optimal, is used to allow the processor to avoid performing multiplications.The second FIR has 101 taps and a low pass frequency of 1 kHz. The filter is designed using an optimal window approach.

squared difference R between the original samples and the equivalent samples obtained by applying the model:

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R= U . S o , A c , A , -S;

[ [

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U.

The estimation is repeated by adjusting the fundamental frequency Ff until a minimum of R is found. The initial frequency value is determined by using a simple threshold detector and is performed only the first time the instrument detects a valid signal or when the minimisation process fails to converge.

The decimated samples S i , of both current and voltage, are used to determine a four parameter sine model in the form:

The average signal value So is removed from the signals and then the samples corresponding to an integral multiple of the signal period are used to compute cosine and sine amplitudes:

where f , is the fundamental frequency and F, is the sampling frequency.

where: w,sin( k ) w,sin ( 2 k )

wpos ( k ) w2cos( 2 k )

w,,,sin ( N k )

wfios ( N k )

(8)

The model is linear in three (offset So, cosine amplitude A, and sine amplitude A,) of the four parameters. The identification is performed by means of an iterative least square estimation that employs a time weighting window. Such a weighting window is required to reduce the effect of the non-synchronous sampling, which othemise would not allow a meaningful estimation to be obtained.

The power pl associated to the first harmonic is readily available as:

The three linear parameters are estimated for a defined fundamental frequency value f,as:

f ,=

(3)

[ S O , A c , A . ] t = ( U ' U Y U'S,

where:

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where Vc, V, , I C , I, are the cosine and sine amplitudes of the voltage and current. The sample values S, corresponding to the first harmonic are then computed as:

w,cos ( 2 k )

w,,, wgin ( N k ) w,+os ( N k )

and subtracted from the original signal.

(5) The process is repeated for the subsequent harmonics whose amplitude has to be computed, by changing the matrix U ' each time. where wl, w2,. .. ,wN are weighting coefficients that implement a Hanning window on the estimation interval One should note that the computation of and N is the number of the samples in the observation does not actually require three matrix interval. matrix inversion due to the matrix symmetries that greatly the processing. simplifies The estimated parameters are used to compute the t

S, =[w1 Si 1~2S29.. .

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