Realization and traceability of AC power standard at frequency of 50 Hz

Transcription

1 Realization and traceability of AC power standard at frequency of 50 Hz Ivan Leniček niversity of Zagreb, Faculty of Electrical Engineering and Computing, nska 3, 0000 Zagreb, Croatia, Abstract An AC power standard for traceable calibration of reference power and energy meters has been established in Primary electromagnetic laboratory PEL, the national calibration laboratory for electrical quantities in Croatia. The standard uses synchronous sampling technique for signal generation and measurement, driven by single digital voltmeter. Traceability of power to national standards has been achieved through validation of sampling-based AC voltage measurement with AC-DC voltage transfer method. The realized AC power standard is covered with expanded standard uncertainty of at frequency of 50 Hz. Index Terms AC power standard, traceability, digital sampling. digital voltmeter I. INTRODCTION Maintenance of standards and dissemination of units of electrical quantities in Croatia is a task of Primary electromagnetic laboratory (PEL), which acts as a designated institute of Croatian Metrology Institute (HMI). The national standards for DC voltage, resistance and capacitance serve as a traceability source in the field of electromagnetic measurements for other calibration laboratories and for the needs of industry in our country as well. Metrology infrastructure for power management requires primary power measurement standard to provide traceability of volt-ampere unit to the national standards. For that reason, PEL has put into operation an AC power standard for calibration of reference power and energy meters, primarily at frequency of 50 Hz. A number of approaches for establishment of power standard at national calibration laboratories have been extensively published [, 2]. All methods share universal principle of generation of phase-adjustable sinusoidal voltage and current sources, loading of sources with calibrated power meter and determination of applied power. Since test current is being transformed back to voltage by suitable current shunt, traceability of power relies on traceable measurements of AC voltage and shunt AC resistance. Several methods for accurate AC voltage measurement based on digital sampling techniques have been thoroughly investigated [3,4], achieving uncertainties of few parts of 0-6. II. WORKING PRINCIPLE OF AC POWER STANDARD The primary AC power standard implemented in PEL combines best outcomes of others' work (e.g. PTB improvements, [2]) with existing laboratory capabilities. The operating principle of the standard is the digital sampling system for synchronized generation and measurement of AC voltage. Comparing to non-synchronized sampling systems, this approach significantly reduces sampling errors and also simplifies evaluation of effective value (i.e. root-meansquare value, or RMS) and phase of sampled AC signal. To set fully synchronized two-channel system, the internal clock of single digital sampling voltmeter () is used as the sampling frequency reference for digital synthetization of the voltage and current test signals. Because of its basic accuracy on DC measuring range, outstanding linearity and versatility of sampling attributes as well, a reference is the laboratory standard 8½-digit voltmeter HP 3458A, which has been modified in a way that its internal clock was routed via digitally isolated circuitry to be accessible from the outside. As shown on block diagram in Fig., the 0 MHz clock derived from the synchronizes the 00 MHz time-base clock of the 6-bit dual-channel synthesizer (DS) of sinusoidal voltages u A and u B. In coherence with the sequence of signal cycles, the DS generates also the reference timing signal (RTS) which is routed back to the voltmeter to trigger the beginning of measurement. The initial phases ϕ A and ϕ B of respective voltage signals u A and u B are independently set in relation to RTS that allows adjustment of any phase angle between the signals in the range ±80. The signals u A and u B are further amplified by the voltage amplifier Fluke 5205A and the transconductance amplifier Fluke 5220A in order to reach voltage and current measuring levels P and I P, respectively. Current I P is sensed with the AC shunt R S, terminated by the voltage amplifier A (if used). Consequently, both AC voltages and 2 are measured alternately by the single on corresponding DC measuring ranges in combination with the signal switch SW. In addition, multiple range feature of the excludes a separate voltage divider within measurement chain of the voltage P. Fig.. Block scheme of AC power standard of PEL that utilizes generation of power, represented by voltage and current both applied to DT, and AC voltage measurement by means of single digital voltmeter.

2 However, the measuring ranges higher than 0 V are not perfectly frequency compensated so their phase shift at frequency of 50 Hz must be determined separately. III. EVALATION OF RMS VALE AND PHASE OF VOLTAGE SIGNALS At the event of external trigger, initiated by the reference timing signal, the takes N samples on optimal DC measuring range over finite number of periods M, fulfilling condition for synchronous sampling: ( N ) T = M, () S f 0 where T S is the sampling time (i.e. the time interval between subsequent samples) and f 0 is the signal frequency. To keep the resolution of 7½ digits at the top of the measuring range as well as at least 2 bit of quantization [5], the integration time T i of the is optimized at first to satisfy condition T S>T i>500, μs. Then, two sampling setups are predefined; one setup used if the signal frequency is 50 Hz (defined with N = 32, T S = 625 μs, T i = 600 μs), and the second one utilized in a case of power lines interference to the measured signal, working at signal frequency of 62,5 Hz (N = 20, T s = 800 μs and T i = 775 μs). Furthermore, 0 subsequent signal cycles are subjected for RMS and phase calculation of the signal, hence the condition for integer multiple of power line periods for the second setup (i.e. 8 periods) is satisfied as well. After the voltage on Fig. have been measured repetitively specific number of times, the triggers the switch SW and begins the measurement of the voltage 2 in sequence. Generally, the RMS value of the sampled signal is calculated by equation:. (2) M = N i AV A M N i= 2 ( ) τ ( ε + ε + ε ) Here, AV is the average value of all M N samples, so it represents the DC component of the signal: AV = M N M N i= i DC S IN. (3) The factor τ A corrects the RMS calculation due to finite integration time T i, and is defined as follows: πt f i 0 τ A =. (4) sin( πti f0 ) The relative parts of the voltage (2) are expressed as quantities ε DC, ε S and ε IN. The quantity ε DC is error of the internal DC reference of the, relatively to external DC voltage standard. The value of ε S is related to imperfections of sampling process due to various limitations, so jointly includes gain error of the internal A/D converter, nonlinearity error, quantization error due to loss of resolution (related to full scale of measuring range) and error due to jitter of the sampling time. The error ε IN is associated to limited bandwidth of particular DC range, influenced by the input circuitry of the. Except ε DC, which can be nullified by external calibration, modeling and estimation of other errors is beyond the scope of this paper, but is well elaborated elsewhere [6-8]. Since external calibration of internal voltage reference determines absolute accuracy of taken samples, presented -method provides traceability of AC voltage to DC standard along with uncertainty budget given in Table I. Here, uncertainty contributions are specified for voltage of 80 V and frequency of 50 Hz, measured on 00 V range. Combined standard uncertainty of the voltage is estimated as: ( ) = k [ ciu( xi )] u, (5) and with coverage factor k = equals 367 μv, or relatively 4,6 μv/v. Correction factor τ A (4) is fairly reproducible [3,6], therefore contribution u(τ A) can be practically neglected. Initial phases ϕ and ϕ 2 (i.e. phase angles of the signals at the start of the sampling sequence) of respective voltages and 2 are calculated from taken samples with DFT (discrete Fourier transform) algorithm. The difference of initial phases, or simply phase ϕ 2, is obtained as: ( Δϕ + Δϕ ν ) ϕ 2 = ϕ ϕ , (6) where quantity Δϕ corrects the phase shift of input attenuator, Δϕ 2 corresponds to the phase angle of the current shunt, and ν represents deviation of the latency from external trigger to the start of sampling. Particularly for ranges of 00 V and 000 V, correction Δϕ is obtained from the difference of initial phases of the very same voltage measured on two adjacent ranges, starting with directly coupled 0 V range. TABLE I. NCERTAINTY BDGET OF AC VOLTAGE OF 80 V AND FREQENCY OF 50 HZ, MEASRED WITH -METHOD u() 2 ncert. u() τ A, ,2 0-6 normal 80 V 6 μv ε DC 0, after external calibration rectang. 80 V 60 μv ε S normal 80 V 320 μv ε IN rectang. 80 V 80 μv (2) ncertainty (k = ): u( ) = 367 μv (5)

3 Phase shift of the is frequency dependant, so it is conveniently expressed as a linear regression over frequency range (40 70) Hz. The phase angle Δϕ 2 is inherent characteristics of the current shunt, discussed later in text. The latency of trigger is fairly high (about 400 ns, according to manufacturer's statement [5]) but persistent, thus deviation ν does not affect significantly the difference of initial phases measured in sequence. The DFT algorithm has been exhaustively validated by comparison of calculated phase with time interval measured by reference laboratory counter. Taking all corrections and into account, the method provides measurement of phase ϕ 2 with expanded uncertainty (k = 2) of,5 0-3 degrees. IV. TRACEABILITY OF AC POWER STANDARD For more than a decade PEL employs 0 V Josephson array voltage standard (JAVS) as a primary DC voltage standard. In April 2007 the JAVS of PEL has been bilaterally compared with the JAVS of PTB (Germany) in order to confirm its accuracy and automated operability. Direct comparison of two systems resulted with difference less than nv on 0 V level, as well as overall relative combined standard uncertainty better than part in 0 0. Besides regular calibration of solid-state (Zener reference) DC standards Fluke 732A and Fluke 732B, JAVS also made possible to perform direct external calibrations and linearity tests on top-end high resolution digital voltmeters in PEL. A. Traceability of AC voltage Although -method have ensured traceability of AC voltage to DC voltage standard by external calibration of the, its accuracy and associated uncertainty should be validated by another method. Common approach to establish traceability of AC voltage at frequencies up to MHz is based on comparison of RMS value with a reference DC voltage by means of thermal converter (TC), i.e. AC-DC voltage transfer method. As a component of all laboratory voltage transfer standards, TC is characterized with AC-DC voltage transfer difference δ, defined as: Fig. 2. Results of calibration of PEL voltage transfer standard, showing AC-DC voltage transfer difference δ measured at voltage of 00 V and at frequencies of 20 Hz, 40 Hz, khz and 20 khz. Associated relative uncertainites are expressed with coverage factor k = 2. For that reason PEL has developed the PC-controlled procedure for determination of both gain and reversal error of the TC employed in transfer standard. That way AC-DC voltage transfer is being performed by direct measurement of TC output voltage with the nanovoltmeter Keithley 82. The block scheme shown in Fig. 3 demonstrates traceability chain from the national standards of PEL to the components of the AC power standard. The self-calibrating Kelvin-Varley voltage divider Fluke 720A, in conjunction with the null-detector Fluke 845A, serves as a traceability linkage from the reference voltage of 0 V (provided by the secondary DC standard Fluke 732A), to the arbitrary DC voltage, generated by the calibrator Fluke 5440B within range (0,5 700) V. Both DC and AC voltage sources are connected to the transfer standard input over low-thermal switch SW. Besides calibration of -based AC voltage measurement system, the voltage transfer method is also employed for traceable calibration of AC working standard, namely multifunction calibrator Fluke 5700A. The AC voltage AC at particular frequency is derived using term: ( + Δ + ) = F. (8) AC DC0 ACDC δ ( f 0) 0 δ = /, (7) where f is the RMS value of the AC voltage and 0 is the DC voltage that causes the same output voltage on the TC. PEL uses commercial AC-DC transfer standard of Fluke 540B type, which AC-DC voltage transfer difference is determined by comparison against PTB equipment for voltage transfer. Calibration of δ has been performed three times in the past at voltages within range (0,5 000) V and frequencies up to MHz. Fig. partly illustrates calibration results of δ for voltage level of 00 V at low frequencies together with associated uncertainties. Since δ shows very good repeatability over time, PEL voltage transfer standard can be employed with significantly reduced measurement uncertainty than specified by the manufacturer. Fig. 3. Block diagram of PEL measuring setup for traceable calibration of AC power standard. National standards and relevant calibrated quantities are highlighted.

4 Here, DC0 is the voltage of the secondary DC standard, estimated on the moment of measurement by extrapolation of past calibration results obtained by comparison with PEL- JAVS. Quantity F is voltage divider ratio and Δ ACDC is relative difference of compared AC and DC voltages. Table II contains contributions to the uncertainty budget of AC voltage of 00 V and frequency of 50 Hz measured by voltage transfer method with relative stamdard uncertainty of 8, μv/v. TABLE II. NCERTAINTY BDGET OF AC VOLTAGE OF 00 V AND FREQENCY OF 50 HZ, MEASRED BY VOLTAGE TRANSFER METHOD u() ncert. u() DC0 9, V V rectang μv F rectang. 0 V 50 μv Δ ACDC normal 00 V 400 μv δ rectang. 00 V 700 μv AC (8) ncertainty (k = ): u( AC) = 84 μv Validation of based measurement of AC voltage with the voltage transfer method has been carried out at the following voltages: 0,8 V; 80 V; 00 V and 500 V. It must be emphasized that voltages of 80 V and 00 V are being measured on adjacent ranges, namely 00 V and 000 V, testing this way full-scale and 0 %-scale accuracy of the, respectively. Since validation of the -method at voltages of 0,8 V and 80 V had to be done at 80 % level of the calibrated transfer standard ranges, it was justified to keep the calibration values of δ unchanged, but at expense of slightly higher uncertainty u(δ ACDC), in relation to the uncertainty obtained at full-scale comparison. Graph on Fig. 4 summarizes results of performed validation, where p is the relative error of voltage : p =. (9) The voltage AC, obtained by transfer method, is set as a zero reference voltage with uncertainty bars expressed with coverage factor k =. In addition, the error p is accompanied with the uncertainty of the -method, estimated from contributions listed in Table I. From Fig. 4 one can conclude that results of validation indicate good agreement between two approaches in establishment of AC voltage traceability. AC Fig. 4. Results of validation of the -based AC voltage measurement method with the AC-DC voltage transfer method which defines reference AC voltage traceable to national standards. Here, I f is the RMS value of the AC current and I 0 is the DC current which produces the same output voltage of the shunt as the AC current, i.e. δ I represents relative change of the shunt resistance over frequency range. The value of δ I has been calibrated at PTB twice regarding the following PEL shunts: two shunts of Fluke A40B type with nominal output voltage of 0,8 V at respective current of 00 ma and A, and one Fluke A40A shunt with nominal output voltage of 0,5 V at current of 20 A. Fig. 5 shows calibration results of the A shunt, indicating frequency independence of the AC shunt resistance practically up to 0 khz. Purposely for measuring currents of 5 A and 0 A at 50 Hz, the 20 A current shunt is used in combination with the additional voltage amplifier (marked as A on Fig. ) to extend the shunt voltage amplitude within V measuring range. The amplifier gain is precisely measured as output-toinput voltage ratio using the -method, resulting with relative gain error of 0-6 and phase error less than 0-4 degrees at 50 Hz. The phase angles of both A40B shunts have not been experimentally verified, but were calculated as less than degrees at low frequencies, based on their calibrated AC-DC current differences at higher frequencies. However, the phase angle of the low-ohm A40A shunt at 50 Hz is significantly higher. By measuring phase difference between A40A and A40B shunts at common current of A, the phase angle of the A40A shunt was determined with uncertainty of 0-3 degrees. B. Traceability of AC current AC current is traceably obtained by measuring AC output voltage of specially constructed AC current shunt which loads current source. AC current shunts are characterized by calibrated DC resistance as well as with AC-DC current transfer difference δ I, defined as: I ( I f I0) / I0 δ =. (0) Fig. 5. AC-DC current transfer difference of A current shunt in frequency domain, calibrated at PTB. The pointed uncertainties are stated for coverage factor k = 2.

5 In accordance with presented laboratory capabilities, AC current is generally calculated by expression: I, () ( + ) AC AC = δ I A RS where AC is the measured shunt voltage, A stands for the amplifier gain (unity, if amplifier is not used) while R S is the DC shunt resistance. Besides foregoing uncertainty contributions of shunt AC-DC current difference, amplifier gain and output shunt voltage, uncertainty budget of AC current includes as well a contribution of DC shunt resistance calibration with DC resistance standard. PEL has well established DC resistance traceability for the group of standard resistors ranging from mω to 0 MΩ, having two primary reference standards of Ω and 0 kω regularly calibrated at PTB. sing quantities depicted on Fig., the apparent power S applied to DT is given by expression: S = I. (2) P P Herein, voltage P and current I P are respectively substituted with (8) and (), resulting with: F F S =, (3) ( + Δ + Δ + δ + δ + ) 2 2 DC0 2 2 δ I A RS where quantities indexed with and 2 belong to respective AC voltages and 2, both traceable to DC standard by voltage transfer method. Table III recapitulates uncertainty parts for apparent power of 00 VA, obtained at P = 00 V, I P = A and frequency of 50 Hz, measured in November 207. The relative expanded standard uncertainty of the apparent power, (S) = k u(s), with the coverage factor k = 2 equals TABLE III. NCRETAINTY BDGET FOR APPARENT POWER OF 00 VA, REALIZED WITH AC POWER STANDARD AT FREQENCY OF 50 HZ u() ncert. u() DC0 9, V V rectang. 20 A 200 μva F rectang. 0 VA 50 μva F 2 0, rectang. 250 VA 50 μva Δ (at 00 V) normal 00 VA 400 μva Δ (at 0,8 V) normal 00 VA 600 μva δ (at 00 V) rectang. 00 VA 700 μva δ (at V) rectang. 00 VA 700 μva δ I 0 (at A) rectang. 00 VA 200 μva A (not used) 0 rectang. 00 VA 0 μva R S 0, Ω Ω rectang. 80 A 2 60 μva S (3) ncertainty (k = ): u(s) = 269 μva V. CONCLSION The AC power standard of PEL is capable to calibrate reference power meters with uncertainty of few tens of 0-6 at voltages up to 700 V and currents up to 0 A, thus providing satisfactory metrological reference for power management in Croatia. Validation of the incorporated digital sampling method for AC voltage measurement with the voltage transfer method has confirmed convenience of use of the single digital sampling voltmeter in establishment of power traceability towards national standards. Moreover, the principle of digital synchronization between signal generating and sampling greatly improves accuracy of measurement of effective values and phases of calibration voltage and current. It must be emphasized that repeatability of power measurement mainly depends on stability of voltage and current sources, that is satisfactory met with running laboratory equipment. Further efforts will be aimed to reduction of prevailing uncertainty of AC-DC voltage transfer by incorporating more accurate multijunction thermocouple converter, that will provide better validation of digital sampling method for AC voltage measurement. REFERENCES [] L. Jol, G. Rietveld, "Improved sampling watmetter for low frequencies (45Hz 55Hz)", Conference on Precision Electromagnetic Measurements, CPEM 2004 Digest, London, K, June 27- July 2, 2004, pp [2] G. Ramm, H. Moser, A. Braun, "A new scheme for generating and measuring active, reactive and apparent power at power frequencies with uncertainties of 2,5 0 6 ", IEEE Transaction on Instrumentation and Measurement, Vol. 48, No. 2, April 999, pp [3] M. Kampik, H. Laiz, M. Klonz, "Comparison of three accurate methods to measure AC voltage at low frequencies", IEEE Transaction on Instrumentation and Measurement, Vol. 49, No. 2, April 2000, pp [4] G.A. Kyriazis, R. Swerlein, "Evaluation of uncertainty in AC voltage measurement using a digital voltmeter and Swerlein's algorithm", Conference on Precision Electromagnetic Measurements, CPEM 2002 Digest, Ottawa, Ontario, Canada, June 6-2, 2002, pp [5] "Component level information packet for HP 3458A digital multimeter", Hewlett Packard document part No , SA, 989 [6] R. Lapuh, B. Voljč, M. Lindič, "Accurate measurement of AC voltage in audio band using Agilent 3458A sampling capability", Conference on Precision Electromagnetic Measurements, CPEM 204 Digest, Rio de Janeiro, Brazil, August 24-29, 204, pp [7] K.B. Ellingsberg, T. SØrsdal, "Method for computing the effective aperture time in the HP3458" Conference on Precision Electromagnetic Measurements, CPEM 2008 Digest, Broomfield CO, SA, June 8-3, 2008, pp [8] W.G. Kürten Ihlenfeld, W. Guilherme, "Measurement uncertainties of digital sampling and Fourier analysis (ntersuchungen zur Messunsicherheit bei Abtastverfahren mit Fourieranalyse)", unpublished