TheSociety PTB Primary for Electrical AC15-19 Power MAPAN - Journal of Metrology of India,Standard Vol. 24, No. 1, 2009; pp. REPORTS
The PTB Primary Standard for Electrical AC Power ENRICO MOHNS, GÜNTHER RAMM, W. G. KÜRTEN IHLENFELD, LUIS PALAFOX and HARALD MOSER PTB Braunschweig Germany, 38116 Braunschweig, Bundesallee 100 e-mail :
[email protected] [Received : 12.01.2009; Accepted 23.03.2009]
Abstract The present PTB primary standard allows power measurements with a measurement uncertainty of about 2.5 µW / VA (k = 2). It operates at voltages up to 240 V and currents up to 10 A in the frequency range from 16 Hz up to some kHz. This paper gives a short overview of the working principle of the standard and recent improvements.
1.
Basic Operating Principle
The scheme of the basic PTB ac power sampling standard [1] is shown in Fig. 1. The key to reach low uncertainties is due to the use of a single clock fClock, which is derived from a highly precise digital sampling voltmeter (DVM). It serves as master clock for the sampling process and for the generation of the test signals with a two-channel ac waveform synthesizer. This synthesizer generates two sinusoidal voltages U A and U B with very low distortion (< -100 dBc), high stability (< 10-6 / hour) and any phase angle γ within ± 180°. The very low distortion voltage and transconductance amplifiers generate the test signals U and I . These quantities are fed to the device / meter under test, to a calibrated voltage divider and a two-stage current transformer with its ac shunt, respectively. The output voltages U 1 and U 2 of the instrument transformers are voltages proportional to the test quantities U and I defining the power to be measured. The DVM samples the voltages U 1 and U 2 alternately via the signal switch. This fully synchronized operation eliminates sampling errors of the measurement process, as it © Metrology Society of India, All rights reserved.
allows to set the sampling frequency of the DVM equal to an exactly integer multiple of the signal frequency. Under the condition that the Nyquist theorem is fulfilled and an integer number of periods of the signals are measured, the complex voltages U 1 and U 2 of the fundamental signal frequency can exactly be reconstructed from the sampled dataset using the Discrete Fourier Transform (DFT). With the ratio of the voltage divider F u = U 1 / U and the ratio of the current-to-voltage transducer F i = U 2 / I , the power quantities P (active power), Q (reactive power) and S (apparent power) can be calculated according to: S = U ⋅ I* = U ⋅ I ⋅ e ( U I ) U ⋅U j ϕ −ϕ − arg( F u )+arg( Fi ) ) = 1 2 ⋅e ( 1 2 Fu ⋅ Fi U ⋅U S = Mod {S} = 1 2 Fu ⋅ Fi U1 ⋅ U 2 ⋅ P = Re {S} = Fu ⋅ Fi j ϕ −ϕ
cos ( ϕ1 − ϕ2 − arg(F u )+arg(Fi ))
Q = Im {S} =
U1 ⋅ U 2 ⋅ Fu ⋅ Fi
,
(1)
sin ( ϕ1 − ϕ2 − arg(F u )+arg(Fi ))
15
Enrico Mohns, Günther Ramm, W. G. Kürten Ihlenfeld, Luis Palafox and Harald Moser
Fig. 1. Principle of the PTB primary sampling standard for electrical AC power where I ∗ stands for the complex conjugate current I , and the arg expressions describe the phase displacements of the transducers. The very simplified calculation (i.e. without any correlation) of the Type B measurement uncertainty for this primary sampling standard at power frequencies and U = 120 V, I = 5 A and ϕUI = 0° is shown in Table 1 [2-3] for further details.
The relative measurement uncertainty including the Type A components of the active, reactive and apparent power of this sampling standard is calculated to 5 10-6 (k = 2, related to the apparent power) at U = 120 V, I = 5 A and any phase angle ϕUI. Although the working principle is explained under the assumption of pure sinusoidal signals, the system is also capable of generating and measuring distorted .
Table 1 Simplified calculation of the measurement uncertainty (Type B) for the PTB primary sampling standard at U=120 V, I=5A, power factor 1 and f = 50 to 60 Hz Contribution Xi rms voltage U1 rms voltage U2 voltage transformer Fu current transformer with ac shunt Fi
Value
Relative measurement uncertainty u(Xi) in 10-6
Sensitivity coefficient ci
Variance (ciu(Xi))2 in 10-12
Weight in %
6V 1V 6 V / 120 V = 0.05
0.6 1.8
1 1
0.36 3.24
8 72
0.5
1
0.25
6
1V/5A= 0.2 Ω
0.8
1
0.64
14
-12
active power P = 600 W 16
Σ (var) = 4.49·10 -6 relative uncertainty u (P ) = 2.1·10 (k = 1)
The PTB Primary Standard for Electrical AC Power waveforms with harmonic content up to a few kHz. The equations for the calculation of the results (i.e. voltage, current and power) are modified according to the definitions of these quantities under the presence of harmonic distortion. 2.
Recent Improvements
The obvious main components of the uncertainty budget are the rms voltages U1 and U2 determined from sampling (see Table 1). They represent about 80 % of the total uncertainty. The key factor to improve the accuracy is to determine rms values not from samples, but with the help of a thermal converter (TC), which allows measuring rms voltages at the 0.1 µV/V level [4]. As displayed in Fig. 2, a separate highly precise ac-dc transfer unit is used to measure the rms voltage of U 1 . In this case the ac-dc transfer unit determines the rms voltage U1,TC, while the ratio U2/U1 and the phase ϕUI is based on sampling as described before. The power quantities can now be calculated according to:
*
⎛ I ⎞ S = U ⋅ I* = U 2 ⋅ ⎜ ⎟ = U 2 ⋅ Y* ⎝U⎠ U 1 j( ϕ − ϕ − arg( F u )+arg( F i ) ) = U 12,TC ⋅ 2 ⋅ ⋅e 1 2 U 1 Fu ⋅ Fi U 1 S = U 2 ⋅ Mod Y * = U 12,TC ⋅ 2 ⋅ U 1 Fu ⋅ Fi 1 U P = U 2 ⋅ Re Y * = U 12,TC ⋅ 2 ⋅ ⋅ U 1 Fu ⋅ Fi
{ }
{ }
(2)
cos ( ϕ1 − ϕ2 − arg(F u )+arg(Fi ))
{ }
Q = U 2 ⋅ Im Y * = U 12,TC ⋅
U2 1 ⋅ ⋅ U 1 Fu ⋅ Fi
sin ( ϕ1 − ϕ2 − arg(F u )+arg(Fi ))
where Y * stands for the complex conjugate admittance Y = I / U . The simplified calculation of the Type B measurement uncertainty at power frequencies and U = 120 V, I = 5 A and ϕUI = 0° is shown in Table 2 (see [4] for further details). The combination of the sampling standard with
Fig. 2. PTB primary hybrid standard for electrical AC power 17
Enrico Mohns, Günther Ramm, W. G. Kürten Ihlenfeld, Luis Palafox and Harald Moser Table 2 Simplified calculation of the measurement uncertainty (Type B) for the PTB primary hybrid standard at U = 120 V, I = 5 A, power factor 1 and f = 50 to 60 Hz Contribution Xi
Value
Relative measurement uncertainty u(Xi) in 10-6
Sensitivity coefficient ci
Variance (ciu(Xi))2 in 10-12
Weight in %
6V
0.3
2
0.36
27
voltage ratio U2 / U1 (based on sampling)
1V/6V = 0.1666666
0.25
1
0.06
5
voltage transformer Fu
6 V / 120 V = 0.05
0.5
1
0.25
19
current transformer with ac shunt Fi
1V/5A = 0.2 Ω
0.8
1
0.64
49
rms voltage U1,TC (based on TC)
active power P = 600 W
Σ(var) = 1.31·10-12 relative uncertainty u (P ) = 1.1·10-6 (k = 1)
Fig. 3. PTB primary standard for AC electrical power incorporating a Josephson Waveform Synthesizer a PTB primary thermal converter allows therefore a reduction of the measurement uncertainty in ac power measurements by a factor of two to about 2.5 µW/VA (k = 2). 18
The accuracy of both these measurement principles depends in the same manner on the traceability to a dc voltage standard. For better traceability, current developments combine directly a programmable ac
The PTB Primary Standard for Electrical AC Power Josephson voltage source into this system [5, 6]. PTB has successfully manufactured a number of binary arrays with step widths suitable for generating waveforms with 10 V amplitudes recently [7]. These arrays operate in the microwave frequency range around 70 GHz and nominally include a total of 69 632 Superconductor - Insulator - Normal conductor Insulator - Superconductor (SINIS) Josephson junctions divided into 18 segments. The Josephson Waveform Synthesizer (JWS) can generate stepwise-approximated waveforms to any peak value between -10 V and +10V. As shown in Fig. 3, the underlying idea is to calibrate the DVM in-situ during the measurements, using a third input of the signal switch. The stepwise-generated waveform for calibrating the DVM consists typically on eight steps. The sampled dataset of the DVM is used to perform a linear least squares fit for each period of the input signal, relative to the Josephson voltages UJ = ± Ni f / KJ-90, where Ni is the number of junctions biased during the waveform step i, i = 1, 2,…, 8. The deviation of the resulting slope from unity represents the gain error for that period and can be used to correct the DVM readings for the signals U 1 and U 2 . This kind of calibration of the sampling DVM allows measuring its gain error with a very low uncertainty of 0.4 µV/V within a few seconds [8]. The gain error derived as described above has been compared with the results obtained using the highgrade ac-dc transfer switch as shown in Fig. 2. Sinusoidal waveforms at 62.5 Hz were used for these measurements. The agreement was better than 0.2 µV /V and thus clearly agrees within the combined 1σ-uncertainty bands of both measurement principles. References [1]
G. Ramm, H. Moser and A. Braun, A New
Scheme for Generating and Measuring Active, Reactive and Apparent Power at Power Frequencies with Uncertainties of 2,5 x 10-6, IEEE Trans. Instrum. Meas., IM-48 (1999). 422-426. [2]
W.G. Kürten Ihlenfeld, Maintenance and Traceability of AC Voltages by Synchronous Digital Synthesis and Sampling, PTB-Bericht, E-75 ( 2001)
.[3]
W.G. Kürten Ihlenfeld, Traceability of AC Voltage Ratios and AC Power by Synchronous Digital Synthesis and Sampling, PTB-Bericht, E76 ( 2001)
.[4]
W.G. Kürten Ihlenfeld, E. Mohns and K. Dauke, Classical Nonquantum AC Power Measurements With Uncertainties Approaching 1 µW/ VA, IEEE Trans. Instrum. Meas., IM-56 (2007) 410-413.
[5]
L. Palafox, G. Ramm, R. Behr, W.G. Kürten Ihlenfeld and H. Moser, Primary AC Power Standard Based on Programmable Josephson Junction Arrays, IEEE Trans. Instrum. Meas., IM-56 (2007) 534-537.
[6]
L. Palafox, G. Ramm, R. Behr, W.G. Kürten Ihlenfeld and H. Moser, Linking Primary Power Standards and Programmable Josephson Arrays, Measure 2 (2007) 70-75.
[7]
F. Müller, R. Behr, L. Palafox, J. Kohlmann, R. Wendisch and I. Krasnopolin, Improved 10 V SINIS Series Arrays for Applications in AC Voltage Metrology, IEEE Trans. Appl. Supercond., 17 (2007) 649-652.
[8]
L. Palafox, R. Behr, W.G. Kürten Ihlenfeld, F. Müller, E. Mohns, M. Seckelmann and F. Ahlers, The Josephson Effect based Primary AC Power Standard at PTB: Progress Report in IEEE Trans. Instrum. Meas. (accpted for Publication).
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