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Although the so-called magnetic geometrical factor, $Bl$, of a Kibble balance does not appear in the Kibble equations, it offers the precision link between electrical and mechanical quantities and furthers a quasi-quantum traceability path for mass metrology. This feature makes the magnet system, supplying the $Bl$ in Kibble equations, play a core role in Kibble balances. Following the open-hardware idea, we report here on the design, manufacture, assembly, optimization, and finally performance of a compact magnet system for the Tsinghua tabletop Kibble balance. Notably, the magnet system showcased in this study facilitates a straightforward upper levitation of splitting through a streamlined mechanism guide, substantially enhancing the ease of open and close operations. Experimental tests show the realized magnet systems can yield a high $Bl$ value (e.g., 400 Tm for a bifilar coil and 800 Tm for a single coil with a wire gauge of 0.2 mm) meanwhile a low volume/weight (40 kg) thanks to the uniformity improvement of magnetic profiles. Furthermore, important parameters related to systematic effects, such as the current effect, are checked, aiming for a final mass-realization accuracy at the $10^{-8}$ level., Comment: 12 figures, submitted to IEEE Trans. I & M

A high-precision current source, capable of supporting weighing measurements with a relative uncertainty at the $10^{-9}$ level, is essential for Kibble balance experiments. However, most current sources utilized in Kibble balances to date are homemade and not commercially available. In this paper, we introduce a digital-feedback, two-stage current source designed for the Tsinghua tabletop Kibble balance, relying solely on commercially available sources and voltmeters. A high-resolution, small-range current source is employed to digitally compensate for current output fluctuations from a large-range current source. Experimental tests show the proposal can offer an easy realization of a current source with nA/A stability to support Kibble balance measurements., Comment: 10 figures, submitted to IEEE Trans. Instrum. Meas

For the past three years, Kaggle has been hosting the Image Matching Challenge, which focuses on solving a 3D image reconstruction problem using a collection of 2D images. Each year, this competition fosters the development of innovative and effective methodologies by its participants. In this paper, we introduce an advanced ensemble technique that we developed, achieving a score of 0.153449 on the private leaderboard and securing the 160th position out of over 1,000 participants. Additionally, we conduct a comprehensive review of existing methods and techniques employed by top-performing teams in the competition. Our solution, alongside the insights gathered from other leading approaches, contributes to the ongoing advancement in the field of 3D image reconstruction. This research provides valuable knowledge for future participants and researchers aiming to excel in similar image matching and reconstruction challenges., Comment: 8 Pages, 9 figures

The Kibble balance requires a measurement of the local gravitational acceleration, $g$, with a typical relative measurement uncertainty of $10^{-9}$. In this paper, the determination of $g$ for the Tsinghua tabletop Kibble balance is presented. A polynomial fitting method is proposed for blind transfers of the absolute gravitational acceleration using relative gravimeters, showing agreement with the value obtained by the tide correction within a few parts in $10^{9}$. Horizontal and vertical gravity gradients are extracted by mapping the gravity distribution at different heights. The self-attraction effect of major components in the experiment, as well as some time-varying systematic effects, are modeled. The final determination of the gravitational acceleration at the mass position, with an uncertainty of 5.4 $\mu$Gal ($k=2$), is achieved for the Tsinghua tabletop Kibble balance experiment., Comment: 11 figures, submitted to IEEE Trans. Instrum. Meas

Magnetic-array-type current sensors have garnered increasing popularity owing to their notable advantages, including broadband functionality, a large dynamic range, cost-effectiveness, and compact dimensions. However, the susceptibility of the measurement error of one or more magnetic measurement units (MMUs) within the current sensor to drift significantly from the nominal value due to environmental factors poses a potential threat to the measurement accuracy of the current sensor. In light of the need to ensure sustained measurement accuracy over the long term, this paper proposes an innovative self-healing approach rooted in cyber-physics correlation. This approach aims to identify MMUs exhibiting abnormal measurement errors, allowing for the exclusive utilization of the remaining unaffected MMUs in the current measurement process. To achieve this, principal component analysis (PCA) is employed to discern the primary component, arising from fluctuations of the measured current, from the residual component, attributed to the drift in measurement error. This analysis is conducted by scrutinizing the measured data obtained from the MMUs. Subsequently, the squared prediction error (SPE) statistic (also called $Q$ statistic) is deployed to individually identify any MMU displaying abnormal behavior. The experimental results demonstrate the successful online identification of abnormal MMUs without the need for a standard magnetic field sensor. By eliminating the contributions from the identified abnormal MMUs, the accuracy of the current measurement is effectively preserved., Comment: 11 pages, 10 figures

The Kibble balance is a precision instrument for realizing the mass unit, the kilogram, in the new international system of units (SI). In recent years, an important trend for Kibble balance experiments is to go tabletop, in which the instrument's size is notably reduced while retaining a measurement accuracy of $10^{-8}$. In this paper, we report a new design of a tabletop Kibble balance to be built at Tsinghua University. The Tsinghua Kibble balance aims to deliver a compact instrument for robust mass calibrations from 10 g to 1 kg with a targeted measurement accuracy of 50 $\mu$g or less. Some major features of the Tsinghua Kibble balance system, including the design of a new magnet, one-mode measurement scheme, the spring-compensated magnet moving mechanism, and magnetic shielding considerations, are discussed., Comment: 8 pages, 9 figures

The diffusion of nonlinear loads and power electronic devices in power systems deteriorates the signal environment and increases the difficulty of measuring harmonic phasors. Considering accurate harmonic phasor information is necessary to deal with harmonic-related issues, this paper focuses on realizing accurate dynamic harmonic phasor estimation when the signal is contaminated by certain interharmonic tones, i.e. the out-of-band interference (OBI). Specifically, this work introduces the singular value decomposition into the Taylor-Fourier transform algorithm, deriving a general decomposition form for harmonic phasor filters, and yielding a set of adjustable parameters. Then these parameters are configured to minimize the negative influence of OBI on the dynamic harmonic phasor filters. Based on the recommended parameter values, the optimized harmonic estimator is obtained, and then tested under signals distorted by OBI, harmonic, noise, and in worse cases, frequency deviation, and some dynamic conditions. Test results show the proposal achieves good harmonic phasor estimation even under multiple interferences and dynamic scenarios, and has a much weaker dependence on OBI tones compared to conventional approaches., Comment: 10 pages, 14 figures, manuscript accepted for publication on IEEE Transactions on Power Delivery

The increasing use of renewable generation, power electronic devices, and nonlinear loads in power systems brings more severe interharmonic tones to the measurand, which can increase estimation errors of P-class PMUs, cause misoperation of protection relays, and even threaten the stability of the power systems. Therefore, the performance of the P-class synchrophasor estimator under interharmonic interference should be evaluated and new estimation schemes that can improve the operational robustness are needed for various protection and control applications. In this paper, a synchrophasor estimator design for P-class PMUs that introduces singular value decomposition to the least square algorithm based on the Taylor series is proposed. By constructing an optimization with proposed adjustable parameters, finite impulse response filters with high transition band attenuation are designed. Numerical and experimental tests verify the proposed dynamic synchrophasor estimator performance and show an effective improvement in rejecting interharmonic tones, especially when a short time window and light computational burden are required., Comment: 10 pages, 10 figures, submitted to IEEE Access

As the complexity increases in modern power systems, power quality analysis considering interharmonics has become a challenging and important task. This paper proposes a novel decomposition and estimation method for instantaneous power quality indices (PQIs) monitoring in single-phase and three-phase systems with interharmonics and transient disturbances. To separate the interharmonic components, a set of new scaling filter and wavelet filter with narrow transition bands are designed for the undecimated wavelet packet transform (UWPT). Further, a two-stage decomposition method for multi-tone voltage and current signals is proposed. The Hilbert transform (HT) is applied to calculate the instantaneous amplitude and phase of each frequency component, which accordingly allows the monitoring of different PQI parameters. Numerical tests are conducted to check the performance of the proposed method. The test results show that compared to other conventional approaches, instantaneous PQIs estimated by the proposed method present significant advances for tracking transitory changes in power systems, and could be considered as a helpful tool for high-accuracy PQ detections., Comment: 13 pages, 8 figures, accepted for publication in IEEE Trans. Instrum. Meas

A milestone revision of the International System of Units (SI) was made at the 26th General Conference on Weights and Measures that four of the seven SI base units, i.e. kilogram, ampere, kelvin, and mole, are redefined by fundamental physical constants of nature. The SI base unit founding the electrical measurement activities, i.e. ampere, is defined by fixing the numerical value of the elementary charge to $e=1.602\,176\,634\times10^{-19}$C. For electrical measurement, several major adjustments, mostly positive, are involved in this SI revision. In this paper, the main impacts of the new SI for electrical measurement activities are surveyed under the new framework., Comment: 10 pages, 3 figures, submitted to IEEE Trans. Instrum. Meas

Topology identification (TI) in distribution networks is a challenging task due to the limited measurement resources and therefore the inevitable need to use pseudo-measurements that are often inaccurate. To address this issue, a new method is proposed in this paper to integrate harmonic synchrophasors into the TI problem in order to enhance TI accuracy in distribution networks. In this method, topology identification is done jointly based on both fundamental synchrophasor measurements and harmonic synchrophasor measurements. This is done by formulating and then solving a mixed-integer linear programming (MILP) problem. Furthermore, an analysis is provided to capture the number of and the location of harmonic sources and sensors that are needed to ensure full observability. The benefits of the proposed TI scheme are compared against those of the traditional scheme that utilizes only the fundamental measurements. Finally, through numerical simulations on the IEEE 33-Bus power system, it is shown that the proposed scheme is considerably accurate compared to the traditional scheme in topology identification.

The watt balance is an experiment being pursued in national metrology institutes for precision determination of the Planck constant $h$. In watt balances, the $1/r$ magnetic field, expected to generate a geometrical factor $Bl$ independent to any coil horizontal displacement, can be created by a strict two dimensional, symmetric (horizontal $r$ and vertical $z$) construction of the magnet system. In this paper, we present an analytical understanding of magnetic field distribution when the $r$ symmetry of the magnet is broken and the establishment of the $Bl$ conservation is shown. By using either Gauss's law on magnetism with monopoles or conformal transformations, we extend the $Bl$ conservation to arbitrary two dimensional magnetic planes where the vertical magnetic field component equals zero. The generalized $Bl$ conservation allows a relaxed physical alignment criteria for watt balance magnet systems., Comment: 5pages, 6 figures, submitted to MST

Permanent magnets with high-permeability yokes have been widely used in watt balances for supplying a robust and strong magnetic field at the coil position. Subjected to the mechanical realization, only several $B_r(z)$ (radial magnetic field along the vertical direction) profiles can be measured by coils for field characterization. In this article, we present an algorithm that can construct the global magnetic field of the air gap based on $N(N\geq1)$ additional measurements of $B_r(z)$ profiles. The proposed algorithm is realized by polynomially estimating the $B_z(r)$ function with analysis of basic relations between two magnetic components in air gap, i.e., $B_r(r,z)$ and $B_z(r,z)$, following the Maxwell's equations. The algorithm, verified by FEM simulations, can characterize the three-dimensional contribution of the magnetic field for a watt balance magnet with acceptable accuracy, which would supply basic field parameters for alignment and misalignment corrections., Comment: 15 pages, 7 figures, submitted to Metrologia

The Planck constant $h$ is one of the most significant constants in quantum physics. Recently, the precision measurement of the numeral value of $h$ has been a hot issue due to its important role in establishment for both a new SI and a revised fundamental physical constant system. Up to date, two approaches, the watt balance and counting atoms, have been employed to determine the Planck constant at a level of several parts in $10^8$. In this paper, the principle and progress on precision measurement of the Planck constant using watt balance and counting atoms at national metrology institutes are reviewed. Further improvements for the Planck constant determination and possible developments of a revised physical constant system in future are discussed., Comment: 24 pages, 15 figures, accepted for publication in Chinese Physics B