Sampling primary power standard from DC up to 9 kHz using commercial off-the-shelf components

In the framework of the EMPIR project MyRails, METAS developed a primary standard for electrical power using commercial off-the-shelf components. Custom software controls the sampling system and determines amplitude and phase of the different frequency components of voltage and current. The system operates from DC up to 9kHz, even with distorted signals. The power uncertainty is 15 µW/VA at power frequencies and increases to 1.8 mW/VA at 9kHz. The voltage and current channels can also be used independently to calibrate power quality instruments. Thanks to a time-stamping system, the measurement is synchronised to UTC.


I. INTRODUCTION
In the framework of the EMPIR project MyRailS [1], calibration facilities for energy meters and power quality monitoring system are developed for railway applications.
As part of its contribution, METAS, the Swiss national metrology institute, developed a primary standard for electrical power using a power calibrator as voltage and current source, shunts, sampling voltmeters as well as a time-stamping system. All hardware is based on commercial off-the-shelf components to make the system easily reproducible and maintainable. Custom software controls the sampling system and determines amplitude and phase of the different frequency components of voltage and current [2]. The system operates from DC up to 9 kHz, both with pure and distorted signals. The active power uncertainty is 15 µW/VA at power frequencies and increases to 1.8 mW/VA at 9 kHz.
The voltage and current channels can also be used independently to calibrate power quality instruments [3]- [5]. A time-stamping system is used to synchronise the measurements to UTC [6]. This is particularly useful in power quality and phasor measurement unit applications, where the DUTs are also synchronised to UTC since in practical applications, their input signals are rapidly varying or the phasors at different locations need to be compared. Therefore, such instruments need to time-stamp their measurements to make measurements from different instruments comparable.
Metrological traceability is essential in science, since scientific results cannot be compared otherwise [7]. Compara-This research is being developed in the framework of the project 16ENG04 MyRailS. The latter has received funding from the EMPIR programme cofinanced by the Participating States and from the European Union's Horizon 2020 research and innovation programme. bility is essential to reproducibility and reproducibility is a fundamental principle of science. In industrial applications, traceability is a requirement for quality, since otherwise, the compliance with specifications cannot be shown. Consequently, traceability is a requirement of ISO/IEC 17025 [8].
The system was used in a comparison with PTB with pure sine signals at 52.63 Hz, where a maximum active power difference between METAS and PTB of 4 µW/VA was observed.

II. MEASUREMENT SET-UP AND CHARACTERISATION
The set-up is based on the following components: • One three-phase power calibrator Fluke 6105A/6135A or similar. In this set-up, the essential property is the stability of the outputs and the operating range (≤21 A, ≤9 kHz). • Three calibrated shunts Fluke A40B or similar. • Six calibrated sampling voltmeters Keysight 3458A or similar with trigger input and aperture waveform output. The 3458A is well documented, e.g. in [9]. It limits the maximum voltage to ≈700 V. • One UTC-synchronised six-channel time-to-digital converter (TDC), e.g. three NI PXI-6683. The system is easily scalable. It can be set up for any number of phases.

A. Characterisation of the shunts
Shunts are used to convert currents into voltages, which are sampled by the voltmeters. The power calculation is directly affected by the properties of the shunts. For the determination of power, the phase difference between voltage and current channels is required, but not the absolute phase with respect to UTC. Since shunts are only used in the current channels and there are no similar devices in the voltage channel, an absolute calibration is required for the phase of the shunt. The resistance of shunts can be calibrated at DC with standard uncertainties of ≤0.2 µΩ/Ω. The AC-DC difference and the phase were determined using multiple shunts of different resistance but similar geometry [10]. The resulting standard uncertainties are shown in tables I and II.

B. Voltmeter triggering
Multiple solutions exist to trigger the sampling voltmeters. In principle, any source that can provide a TTL signal to the voltmeters can be used. It is also possible to operate the 3rd International Colloquium on Intelligent Grid Metrology (SMAGRIMET) online event, October 20-23, 2020.  3458As in a master-slave configuration where the master is triggered over the GPIB and all slaves are triggered in a daisy chain using the EXT OUT output of one voltmeter as the trigger signal for the next. Each voltmeter adds a delay of about 1 µs. This approach is convenient for a small number of phases. The EXT OUT output of the last slave in the chain is not used. Nevertheless, it should be connected to the TRIG IN input of the master, so that all EXT OUT output are loaded similarly.
Since the 3458A uses an easily accessible quartz oscillator as internal clock reference, it is fairly straight-forward to modify it so that an external clock can be used. In this case, the trigger source and all six voltmeters can run synchronously on the same clock. Another solution is to extract the internal clock of a 3458A and to use it in the trigger source. In this case, only one 3458A can be used since there cannot be more than one clock source; the voltmeter needs to be multiplexed to the different channels. If the trigger source and the voltmeter are synchronised in this way, the delay from the trigger edge leaving the trigger source to the voltmeter acquiring a signal can be known with sub-nanosecond uncertainty; the timing of each voltmeter sample can be predicted.
In general, the trigger source does not use the same internal 3rd International Colloquium on Intelligent Grid Metrology (SMAGRIMET) online event, October 20-23, 2020.
clock as the voltmeter that is triggered. As discussed in [6], this leads to a variable delay between the arrival of the trigger signal at the TRIG IN input and the trigger signal being used in the timing domain of the voltmeter. This delay can be as long as one internal clock period of the voltmeter. It is frequently called synchronisation jitter, even though it could be predicted with knowledge of the phase of the voltmeter's internal clock and therefore is not, strictly speaking, jitter.
The 3458A voltmeter can be configured to generate between 1 and 2 24 -1 samples for each trigger signal. It is convenient to trigger each sample individually. Unless the clocks of the voltmeters and the trigger generator are locked, each sample is subject to synchronisation jitter individually -the samples are not equally spaced. This can be a problem for some algorithms such as FFT, which assume equally spaced samples. However, the delay between corresponding samples of different channels does not change during the measurement. Another solution is to use a single trigger event per channel for all samples of a measurement together. In this case, only one trigger event from an external source is synchronised to each voltmeter's clock domain. This affects all samples of each channel equally, yielding an equal spacing between the samples. However, the delay between the samples depends on each voltmeter's internal clock frequency. Therefore, the delay between corresponding samples of different channels increases as the measurement progresses. In practice, additional knowledge about the input signal is always available -the frequency of the fundamental is identical for all channels. Otherwise, the phase between voltage and current would change with time in an uncontrolled way. Such a source could not be used as a power source. Knowing that the frequency is identical in all channels, an average timing can be calculated. The channel-dependent sampling frequency can be a problem for FFT based algorithms, since the two sampling frequencies are slightly different, in general not know a priori and cannot be an integer multiple of the signal frequency at the same time. Other algorithms which do not require synchonisation are more suitable [11]- [15]. Table III compares the different triggering modes.

C. Time-stamping voltmeter samples
The trigger events at the TRIG IN input can be time-stamped easily at the trigger generator. However, as discussed in the previous section, the delay between the trigger event reaching the TRIG IN input and the ADC starting the acquisition is subject to synchronisation jitter.
Another solution is to time-stamp the voltmeter's aperture waveform at the EXT OUT output. Since it originates in the clock domain of the voltmeter, it is not affected by synchronisation jitter. The time-stamping accuracy is limited by the performance of the time-stamping system. Even in FPGAs, TDCs can be implemented [16] with resolutions ≤20 ps; application-specific integrated circuits [17] can be avoided in most applications. Commercial solutions with resolutions of ≤1 ns are readily available. If synchronisation to UTC is required, time-stamping the aperture waveform at the EXT OUT output is the most practical solution. The delay between the aperture waveform used by the ADC and the aperture waveform reaching the EXT OUT output contributes to the time-stamping uncertainty. This delay is not part of the specifications, but it cannot be larger than the delay from TRIG IN to EXT OUT, which is easily accessible and about 1 µs. With some analysis of the circuit the part from TRIG IN input to the ADC can be separated from the part from the ADC to the EXT OUT output. This analysis requires the injection of a variable external clock and some temporary circuit modifications.

D. Latency of the voltmeter's analogue front-end
In practice, the dominant contribution to the time-stamping uncertainty is the delay of the analogue front-end of the voltmeter. It is easy to apply the same signal to multiple voltmeters and determine the relative differences with uncertainties of 3 ns (1 µrad at 50 Hz). As long as no synchronisation to external timing references is required, such as in power measurements, this is sufficient.
If the system is to be synchronised to UTC, the latency needs to be determined in absolute terms. Different methods for this have been proposed [18], [19]. The uncertainty of the latency is the dominant contribution to the absolute uncertainty of the time stamps. It amounts to 250 ns.
Often, the required uncertainty for power is such that the latency difference of the voltmeters' analogue front-ends needs to be determined with small uncertainties, e.g. ≤3 ns (1 µrad at 50 Hz). For the absolute latency of the voltmeters' analogue front-ends, the requirement is much less stringent -though not less challenging. For example, assume a total vector error uncertainty of 0.01 % is required to calibrate a class 0,1 PMU [20]. If this uncertainty is due to equal contributions of amplitude and phase uncertainties, this leaves 70 × 10 -6 for the amplitude and 70 µrad for the phase. At 50 Hz, 70 µrad correspond to 220 ns.

E. Frequency response of the voltmeter
The 3458A's ADC is an integrating ADC with a configurable aperture time t aperture . This leads to a low-pass behaviour. It can be corrected for by multiplying the amplitude of a frequency component at f signal by sin(π·f signal ·taperture) π·f signal ·taperture [21]. The analogue front-end of the 3458A is known to show a low-pass behaviour, too [9].
Once these well-known effects are corrected for, the uncertainty of the voltage measurement is much smaller than the uncertainties specified for the ACV mode. Below 100 Hz, the uncertainty is ≤5 µV/V in the DCV mode. Between 100 Hz and 400 Hz, the uncertainty increases to 10 µV/V. Between 400 Hz and 1000 Hz, the uncertainty reaches to 100 µV/V. The uncertainty in the DSDC mode is 150 µV/V from DC up to 9 kHz. Above 1 kHz, the uncertainty in the DCV mode exceeds that of the DSDC mode. Therefore, the DCV mode is used up to 1 kHz and the DSDC mode above 1 kHz.
These uncertainties were validated in a comparison of a 3458A with a Fluke 5790A voltmeter. The Fluke 5790A uses a solid-state thermal RMS sensor and is known to have a flat frequency response above 100 Hz.

III. UNCERTAINTY BUDGET
The uncertainty budget for the apparent power |S| and the displacement angle ϕ is shown in tables IV and V. The relative uncertainty does not decrease significantly with the number of phases since the dominating uncertainty contributions are correlated. Therefore, both the absolute uncertainties as well as the apparent, active and reactive power of all phases are to be added arithmetically. Their ratios, the relative uncertainties, are independent of the number of phases.
The voltmeters for voltage and current are used in different ranges with different frequency responses and their calibration uses different set-ups. Therefore, their uncertainties can be considered uncorrelated. In the current circuit, the shunt of the reference and the current circuit of the DUT are connected in series. If possible, the link between the shunt of the reference and the current circuit of the DUT should be connected to a virtual ground using a Wagner earth circuit. Otherwise, the common mode voltage at this link is non-zero and leads to a capacitive leakage current, which strongly affects the phase measurement. In some applications, namely with some DUTs, this is not possible. Table V shows the uncertainty for this case since we are not aware of any suitable commercial offthe-shelf Wagner earth circuit. Connecting the link to a virtual ground will remove this dominant contribution. For each frequency component of an AC signal, the uncertainties of the active power P and the reactive power Q are a function of the displacement angle ϕ and the uncertainty of the apparent power |S|. It is convenient to normalise these uncertainties to the apparent power |S|, which yields finite values for all ϕ. Due to the tan ϕ term, this is not the case for u(P)/P and u(Q)/Q.  Active energy is defined as "electrical energy transformable into some other form of energy" [22], [23]. Therefore, at DC, there is active energy with P = |S| and u (P) = u |S| ; there is no reactive energy at DC.

IV. COMPARISON
This system was compared with PTB using a Radian Research RD-22 transfer standard at 52.63 Hz. Since the RD-22 is a single phase device, all three phases of the primary power standard were compared individually. This is a valid approach since all three phases of the primary power standard contribute to the three-phase power independently without impacting the other phases.
As an example, table VII shows the differences between the measurements at METAS and PTB for one phase at 240 V and 5 A. While the stability of the phase difference across different phases could be shown by calibrating the RD-22 with the voltage from one phase and the current from another phase, it is much simpler to adjust the phase of the measuring system. All voltage measurement channels are connected to one voltage channel of the source. The phase difference is zero by definition. Any non-zero phase difference measurement is due to imperfections in the measurement channels and can be safely adjusted. Afterwards, all source channels are connected to one measurement channel each. The measurements show the differences between the channels. The same procedure is repeated for the current measurement channels. Care needs to be taken to avoid common mode effects. The phase stability of the Fluke 6105A across different channels is below 2 × 10 -6 = 2 µrad ≈ 0.0001°at power frequencies. The resulting unbalance is negligible in usual power and power quality calibrations.

V. CONCLUSION
In this paper, a primary power standard using only commercial off-the-shelf components was presented. The system uses two sampling voltmeters and one shunt per phase. It is easily scalable to, e.g., three phases. Since it does not use inductive devices, it operates also at DC. The maximum frequency, 9 kHz, is limited by the source.
At DC and power frequencies, the uncertainty is as low as 15 µW/VA. Without using a custom-design Wagner earth circuit, it increases to 1.8 mW/VA at 9 kHz.
The performance of the system was confirmed at power frequencies by a comparison with PTB.