Jianting Zhao

The presence of interharmonics in power systems can lead to asynchronous sampling, a phenomenon further aggravated by shifts in the fundamental frequency, which significantly degrades the accuracy of power measurements. Under such asynchronous conditions, interharmonics lose orthogonality with the fundamental and harmonic components, giving rise to additional power components. To address these challenges, this paper introduces a linearization algorithm based on DFT spectrum analysis for precise power measurement in systems containing interharmonics. The proposed approach constructs a system of linear equations from the DFT spectrum and solves it through efficient matrix operations, enabling accurate extraction of interharmonic components near the fundamental and harmonic frequencies (with a frequency interval ≥1 Hz). This allows for precise measurement of power across the fundamental, harmonic, interharmonic, and cross-power bands, as well as total power. Test results demonstrate that the proposed method accurately computes various power components under diverse conditions— including varying interharmonic/fundamental/harmonic intervals, fundamental frequency deviations, and noise. Compared to existing methods such as fast Fourier transform (FFT), Windowed interpolation FFT, and Matrix pencil-Singular value decomposition, the proposed technique reduces estimation error by several times to multiple folds and exhibits improved robustness, while maintaining a computational time of only 7 ms for processing 10-power-line-cycle (200 ms) data.

The presence of interharmonics in power systems can lead to asynchronous sampling, a phenomenon further aggravated by shifts in the fundamental frequency, which significantly degrades the accuracy of power measurements. Under such asynchronous conditions, interharmonics lose orthogonality with the fundamental and harmonic components, giving rise to additional power components. To address these challenges, this paper introduces a linearization algorithm based on DFT spectrum analysis for precise power measurement in systems containing interharmonics. The proposed approach constructs a system of linear equations from the DFT spectrum and solves it through efficient matrix operations, enabling accurate extraction of interharmonic components near the fundamental and harmonic frequencies (with a frequency interval $\geq$1 Hz). This allows for precise measurement of power across the fundamental, harmonic, interharmonic, and cross-power bands, as well as total power. Test results demonstrate that the proposed method accurately computes various power components under diverse conditions--including varying interharmonic/fundamental/harmonic intervals, fundamental frequency deviations, and noise. Compared to existing methods such as fast Fourier transform (FFT), Windowed interpolation FFT, and Matrix pencil-Singular value decomposition, the proposed technique reduces estimation error by several times to multiple folds and exhibits improved robustness, while maintaining a computational time of only 7 ms for processing 10-power-line-cycle (200 ms) data.

To meet the growing demand for high-precision DC power measurement and calibration, this paper presents a quantum-based DC power standard developed with a “standard source” architecture. This system integrates a compact heliumfree dual-channel programmable Josephson voltage standard, a three-stage cascaded high-voltage amplifier with low common-mode rejection ratio error, a large-current transconductance amplifier based on DC current transformer, voltage/current ratio self-calibration device, and other essential components. The design principles and key performance metrics of these core components are thoroughly described. Test results indicate that the system achieves a combined uncertainty of 1.5 × 10⁻⁶ (k=1) at DC 1000V and 120 A. When used with a time pulse counter, the system can also serves as a direct calibration reference for DC energy meters. Finally, this paper discusses potential future advancements in quantum-based standards for DC power calibration technology.

A precision resistance measurement method based on synchronous sampling is proposed to enable accurate resistance measurement under low-current testing conditions. This method utilizes a single current source input, connecting the standard resistor and the test resistor in series. The setup is simple, easy to operate, and allows for the convenient and rapid comparison of the voltage across the resistors. The resistance value of the test resistor is determined through calculation, achieving high measurement accuracy. An experimental comparison of two standard resistors under a low current of 1 μA demonstrated that the data dispersion reached the 10⁻⁶ level, and the measurement error was within the 10⁻⁶ range. This study also employed a resistance ratio measurement method based on room-temperature Direct Current Comparator (DCC) technology to validate the superiority of the proposed synchronous sampling approach under low-current measurement conditions. The comparative analysis demonstrated that our method exhibits significant advantages over conventional DCC techniques under a low current of 1 μA. This paper presents the first demonstration of high-accuracy resistance ratio measurement using synchronous sampling under weak current conditions. Experimental results verify that at 1 μA current level, the proposed method achieves superior measurement accuracy and lower uncertainty compared to conventional precision DC current comparator techniques under identical test conditions.

Superconducting quantum interference devices (SQUIDs) with large input inductance and octagonal double transformer were designed and fabricated using Nb/Al-AlO_x/Nb Josephson junctions for cryogenic current comparator. A 30-turn input coil of 1.5 μH is coupled to a large octagonal transformer of 3.6 nH, the counterpart of transformer is a 1.5-turn coil of 3.0 nH coupled to a second-order gradiometric SQUID of 97 pH. The octagonal double transformer makes low-inductance SQUID easily match to the large-inductance input coil. A current sensitivity of 1.1 μA/Φ₀, a flux noise of 3.8 μΦ₀/√Hz at 4 kHz and 9.7 μΦ₀/√Hz at 1 Hz were achieved at 4.2 K. Another SQUID sensor with 10-turn input coil of 0.5 μH coupled to a large octagonal transformer of 6.0 nH, which is coupled to a first-order gradiometric SQUID of 580 pH, achieves a lower current sensitivity of 0.5 μA/Φ₀ and a flux noise of 17 μΦ₀/√Hz at 4 kHz.

A self-calibration method is proposed for determining the current ratio for DC current ratio devices. To demonstrate the feasibility of the proposal, an experimental test with nominal current ratios of 10:1 100:1 and 1000:1 is performed, and a three-step calibration procedure is used: Firstly, eleven magnetic modulator-based DC current transducers (DCCTs) with a nominal current ratio of 10:1 are used to realize the self-calibration of a 10:1 current ratio through the reference current method; secondly, the eleven DCCTs are series-parallel to achieve the current ratio build-up from 10:1 to 100:1; finally, another DCCT with a 100:1 auxiliary current ratio is used to realize the 1000:1 current ratio calibration, combining the two steps before. The merit of the proposed self-calibration method is that the measurement does not need a high-precision current source or ammeter. Current ratio calibration based on this technology offers a lower-cost, more robust alternative to those using other devices. The experimental results show that the uncertainty of the calibration, mainly dominated by the noise and the stability of the magnetic modulator used, is within a few parts in 10⁻⁷ or better in the 1000 A range.

The effect of phase jitter on differential sampling using the programmable Josephson voltage standard (PJVS) system is studied in this paper. A phase jitter model is established for the measured signal, and compensation coefficients for phase jitter removal are derived for three different post-processing methods based on the discrete Fourier transform algorithm (DFT). Based on our analysis, the phase jitter compensation coefficients are determined by the phase jitter angle distribution and harmonic order. Furthermore, after analyzing and simulating various common distributions, the phase jitter compensation coefficients have been verified. The simulation shows that when the standard deviation of the phase jitter angle is 20 ns, and the frequency of the measuring waveform is 3.46 kHz, the influence of the phase jitter is 1 × 10⁻⁷. The results of the simulation indicate that, in the differential sampling of AC waveforms using a PJVS system, phase jitter is one of the error terms for an uncertainty budget that cannot be neglected, particularly as the frequency of the measured waveforms increases.

This paper introduces an innovative differential sampling technique for calibrating AC waveforms, leveraging a commercially available 16-bit digital-to-analog converter (DAC) as the reference standard. The novelty of this approach lies in its enhanced stability over traditional direct sampling methods, especially as the frequency of the AC waveform increases. Notably, this technique provides a cost-effective sampler alternative to the differential sampling methods that rely on a programmable Josephson voltage standard (PJVS). A critical aspect of this methodology is the precise measurement of the DAC’s output voltage, for which a static measurement strategy is adopted to utilize the exceptional linearity and transfer accuracy of the Keysight 3458A (Santa Rosa, CA, USA) in its standard DCV mode. The differential sampling method has demonstrated good accuracy, achieving a near 1 µV/V agreement with a pulse-driven AC Josephson voltage standard (ACJVS) across a 40 Hz to 200 Hz frequency range. The method attained an expanded uncertainty (k = 2) of 1 part in 10⁶ while measuring a 0.707107 V_RMS sine wave at 50 Hz, showcasing its efficacy in precise AC waveform calibration.