This paper presents an ultra-stable current source tailored for the one-mode, two-phase (OMTP) measurement scheme in Tsinghua tabletop Kibble balances. To achieve simultaneous high resolution and nA/A-level stability, a composite 'coarse-fine' control topology is proposed, utilizing a dual-DAC architecture and an active digital feedback loop. Experimental results show that the Allan deviation reaches 1 nA/A at an integration time of approximately 3 minutes, representing a tenfold improvement in measurement speed compared to commercial-source-based setups. Furthermore, the design offers a significant cost advantage, providing a satisfying option for high-precision, cost-effective mass realization.

This paper presents a novel seven-channel optical measurement system for monitoring coil parasitic motion and mass position in the Tsinghua Tabletop Kibble balance. The system employs seven spectrally-confocal displacement sensors arranged in a distributed configuration to simultaneously measure the coil's translational (x_c, y_c), rotational (θ_x,θ_y) degrees of freedom, and the mass position offset (x_m, y_m) due to corner errors. Three vertically oriented sensors target an equilateral triangle target rigidly connected to the coil, enabling real-time calculation of tilt angles through geometric relationships. Two horizontally oriented sensors measure the translational displacement of a frame target on the coil assembly. Two additional horizontal sensors monitor the mass position to quantify corner errors. The initial experimental setup has been completed, featuring sufficient resolution and minimal signal loss, providing a new approach for alignment adjustment and corner error compensation in high-precision Kibble balances.

This study investigates the influence of steel fiber orientation and distribution, induced by rebar arrangement under single-point casting, on the bond behavior of ultra-high performance reinforced concrete (UHPRC). Three rebar configurations (I, III, and V) were designed, and the spatial characteristics of each arrangement were quantified using the spacing-to-fiber-length ratio (SFR), defined as the ratio of the minimum clear spacing between rebars and the fiber length. Bond–slip tests and X-ray computed tomography (CT) analyses were conducted under different fiber volume fractions (0.5%–2%) and sample positions (A, B, and C). The results show that rebar presence significantly alters fiber distribution patterns. Fibers around the rebar displayed pronounced alignment along the rebar direction, and this alignment became more distinct with increasing distance from the casting point. At the tail end position (section C), the combined action of rebar induced disturbance and flow history produced an optimal fiber orientation, which led to enhanced bond performance. The SFR was also found to strongly affect fiber orientation and distribution. A moderate spacing (SFR≥1.35) promoted the formation of a continuous zone of aligned fibers, thereby improving bond behavior. In contrast, a small spacing (e.g., SFR=0.64) tended to randomize fiber orientation and create fiber free regions, both of which reduced interfacial resistance. A three-dimensional nonlinear modification model was developed to integrate casting-induced fiber orientation into the prediction of rebar–matrix bond strength. This research provides quantitative evidence for optimizing rebar layout and construction techniques of ultra-high-performance concrete (UHPC) members.

With the increasing application of quantum electromagnetic references (quantum voltage standards and quantum resistance standards) in precision measurements for power systems, the demand for miniaturized and lightweight cryogenic refrigeration technologies has become more urgent. This paper systematically reviews three mainstream miniaturized refrigeration technologies-G-M cryocoolers, pulse tube cryocoolers, and adiabatic demagnetization refrigerators—covering their basic principles, technical characteristics, development status, advantages, and disadvantages. On this basis, the effects of mechanical vibration and electromagnetic interference (EMI) generated during the operation of these refrigeration systems on quantum chips and sensitive measurement devices are analyzed. Focusing on EMI as a critical issue, finite-element simulations are conducted to investigate the shielding performance of single-layer and double-layer magnetic shielding structures, with emphasis on the effects of shield thickness, number of layers, and inter-layer spacing on the magnetic field attenuation factor. The results show that the attenuation factor of a double-layer shield is approximately one order of magnitude smaller than that of a single-layer shield, and the inter-layer spacing exhibits a saturation effect. This paper provides theoretical support and technical guidance for the integration of small-scale refrigeration systems into quantum electromagnetic references and for the design of magnetic shielding.

In order to further improve the accuracy of the energy metering algorithms for standard electricity meters,this paper,on the basis of a more comprehensive review of the principles and performance of the quasi-synchronous sampling algorithms and fast Fourier transform(FFT)algorithms commonly used in standard electricity meters,combines the advantages of using accurate synchronous sampling algorithms for accurate estimation of the fundamen-tal frequency and fast Fourier transform algorithms with a Flap-top window for accurate amplitude measurements,a new quasi-synchronous sampling-based fast Fourier transform algorithm with Flap-top window is constructed for en-ergy metering.The simulation test results show that the proposed algorithm has higher accuracy and faster calcula-tion speed than the quasi-synchronous sampling algorithm or the FFT energy metering algorithm with Flap-top win-dow alone to measure the fundamental energy,harmonic energy and total energy under different power factors.

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 article introduces a linearization algorithm based on discrete Fourier transform (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 (SVD), 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 ten-power-line-cycle (200 ms) data.

Tabletop version Kibble balances are a significant developing trend for mass realizations following the revised International System of Units. A key innovation through the miniaturization of the Kibble balance from a large-scale instrument into a tabletop device is making the quantum-based realization of mass accessible to a wider range of calibration laboratories and industries. This paper presents a tabletop Kibble balance design at Tsinghua University targeting E2-accuracy class mass calibrations from 1 g to 1 kg. For calibrating a mass of 1 kg, for instance, the required relative standard measurement uncertainty must be below 0.27 ppm to meet E2-accuracy class. Major components and features of the proposed system are discussed. A novel method of multi-harmonic excitation is proposed to improve the coil-motion linearity during velocity measurement. We show that injecting odd-order harmonics into the motion-driving current can significantly improve the uniformity of the coil's moving velocity, while the second-order component can address the asymmetry between upward and downward movements. This achieves a flat velocity Delta v/v<5% over 60% of the motion cycle.

In this paper, we introduce the moving-anchored extra-gradient (MAEG) method for solving monotone inclusion problems involving the sum of a continuous monotone operator and a maximal monotone operator. Notably, the distance from the anchor point to the solution set is designed to be monotonically non-increasing. Under Lipschitz continuity of the forward operator, MAEG attains an 𝒪(1/k) non-asymptotic iteration complexity, and when a positive anchor-update parameter is used, it further achieves an o(1/k) asymptotic rate. Furthermore, leveraging the specific behavior of the anchor point, we propose a tailored restart strategy. We demonstrate that this strategy ensures convergence even in the absence of local Lipschitz continuity, while preserving the original iteration complexity guarantees whenever the Lipschitz condition holds.

Accurate electric energy metering (EEM) of fast-charging stations (FCSs) is the cornerstone for ensuring fair electric energy transactions in the electric vehicle (EV) industry. Hence, monitoring EEM errors of FCSs is of significant practical importance. However, traditional field verification methods are constrained by high costs and low efficiency,s while existing data-driven approaches struggle to achieve highly reliable and accurate estimation of EEM errors. In response, a novel estimation method, i.e., metering performance comparison (MPC) method, is proposed. In the MPC method, by utilizing the measurement data from EVs' battery management system (BMS) as a medium, comparison chains of EEM errors of multiple FCSs are established. Combining with big data analytics, high-accuracy estimation of EEM errors is achieved. According to on-site charging data, the simulation results indicate that for FCSs with an accuracy grade of 2%, the discriminative accuracy of the MPC method exceeds 95%. In the future, with the continuous increase of FCSs, the MPC method is expected to enhance the foundation for a fair electricity trading market at a low cost. However, the MPC method is anticipated to accelerate the digital transformation of EEM errors verification for FCSs.

This paper presents recent advances in the KBmini Kibble balance, a tabletop system for E2-accuracy mass calibration up to 1 kg. The Bl(z) profile is characterized by manually setting the magnet at different vertical positions, and the extremum point is selected as the weighing position. The spring constant of the weighing cell around this point is measured. With a new coil of a larger number of turns and a multi-harmonic excitation technique, a near-constant velocity profile over a moving range of 180 μm, producing an induced-voltage flat-top region exceeding 1 V, is achieved. These results establish a foundation for subsequent mass calibration experiments.

This paper presents a customized weighing unit developed for the Tsinghua tabletop Kibble balance. The system is based on a flexure hinge mechanism sourced from a commercial weighing cell, with a major modification to the feedback control loop. The redesigned loop incorporates a capacitive displacement sensor for high-resolution position detection and a novel PID control strategy that ensures both fast dynamic response and high static stability. Initial characterization results demonstrate a repeatability better than 0.1 mg in air for 1 kg mass exchanges, validating the system's potential for high-accuracy mass metrology in Kibble balances.

Data-driven methods enable online assessment of error states in magnetic-array-type current sensors, and long-term measurement stability can be enhanced through further self-error correction. However, when the magnetic-array-type current sensors are applied to multiconductor systems such as multicore cables, the time-varying correlations among conductor currents may degrade the performance of multilatent-variable data-driven models for error evaluation. To address this issue, this article proposes a robust self-error correcting method for magnetic-array-type current sensors even under significant variations in phase current correlations (e.g., large fluctuations in three-phase current imbalance). By incorporating phase current decoupling and principal component analysis (PCA), the correlation analysis of multilatent variables (i.e., multiconductor currents) is transformed into a single-latent-variable (corresponding to single-phase current) modeling problem. Experimental results demonstrate that the proposed method effectively detects error drifts of magnetic field sensors as low as 2 x 10(-3) in relative error and 2 x 10(-3) rad in phase error. Accurate evaluation and correction of each magnetic field sensor's error drifts substantially eliminates the overall error drift in the magnetic-array-type current sensor, validating the feasibility and effectiveness of the proposed self-error correcting method.

The Kibble balance realizes the kilogram by linking mechanical and electrical quantities via a magnet system. In an improved BIPM-type magnet design by Tsinghua University, an open/close surface was incorporated, facilitating operation. However, an unavoidable mechanical air gap at the splitting plane introduces asymmetry in the magnetic flux density profile, degrading field uniformity. This study proposes a two-step yoke compensation method to restore symmetry by adjusting the upper outer yoke's inner radius and the splitting gap height. Finite element simulations show linear relationships between asymmetry and these parameters, enabling predictive compensation. Experimental results confirm that sequential tuning successfully eliminates asymmetry and recovers the designed uniform field range. The method provides an effective solution for enhancing magnetic field quality in openable Kibble balance magnets.

Power measurement algorithms based on Fourier transform are susceptible to errors caused by interharmonics, while wavelet transform algorithms are particularly sensitive to even harmonics due to band decomposition effects. The empirical wavelet transform (EWT) has been demonstrated to improve measurement accuracy by effectively partitioning transition bands. However, for detecting interharmonic components, the limitation of the observation time window restricts spectral resolution, thereby limiting measurement accuracy. To address this challenge, this paper proposes a Compressive Sensing Empirical Wavelet Transform (CSEWT). The approach aims to enhance frequency resolution by integrating compressive sensing with the EWT, allowing precise identification of components across different frequency bands. This enables accurate determination of the power associated with the fundamental frequency, harmonics, and interharmonics. Test results indicate that the proposed CSEWT method can significantly improve the precision of individual frequency component measurements, even under dynamic and noisy conditions.

With the adoption of the revised International System of Units (SI), the Kibble balance has become a pivotal instrument for mass calibrations against the Planck constant, $h$. One of the major focuses in the Kibble balance community is prioritizing experiments that achieve both high accuracy and compactness. The Tsinghua tabletop Kibble balance experiment seeks to develop a compact, high-precision, user-friendly, cost-effective, and open-hardware apparatus for mass realization, specifically within the kilogram range. This paper reports on the progress of the Tsinghua tabletop Kibble balance project over the past two years. Various aspects of the Tsinghua tabletop system, including electrical, magnetic, mechanical, and optical components, are summarized. Key achievements, such as the construction and characterization of the magnet system, determination of absolute gravitational acceleration, investigation of a capacitor-sensor-based weighing unit, and development of a high-precision current source, are presented to provide a comprehensive understanding of the experiment's status.

The novel power system characterized by"double high"is easy to cause 0～kilohertz wide-band oscilla-tion,which poses a great threat to the safe and stable operation of power grid.Under this background,it is urgent to develop wide-band measurement technology.The time-varying multimodal characteristics of wide-band oscillating signals make it necessary to study dynamic measurement algorithms,and one of the important tasks is to simulate the wide-band oscillating dynamic signals,so as to provide test signal samples for algorithm design and performance test.In this paper,a novel dynamic simulation method using chaos modulation is proposed based on the mechanism of wide-band oscillation caused by wind turbine,and the practical method generating wide-band oscillation signal samples by numerical integration is also given.The simulation results show that chaos modulation can well charac-terize the time-varying multimodal characteristics of wide-range frequency oscillations and provide effective test sam-ples for the dynamic performance test of wide-band measurement algorithms,which provides theoretical model and test data support for the in-depth study of the dynamic measurement algorithm.

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 quasiquantum 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.

Fiber-optic current sensor (FOCS) technology offers intrinsic galvanic isolation, a wide linearity range, immunity to electromagnetic interference, and non-invasive measurement, making it a strong candidate for applications in on-site calibration. However, its use as a traceable reference in metrological applications remains limited so far. Laboratory calibration and cross-institutional comparisons are essential steps toward establishing the reliability and traceability of FOCS in real-world conditions. This paper provides an overview of the FOCS operating principle and evaluates the key performance of a new FOCS sensor tested in two National Metrology Institutes (NMIs), including accuracy, stability, linearity, and temperature dependence. It furthermore describes the on-site measurement campaign using the FOCS for efficiency measurement in a medium-voltage substation. The test results reveal that FOCS can meet the performance requirements under practical conditions and demonstrate excellent repeatability and traceability for on-site calibration in operational environments: the linearity is better than $0.1 \%$ over the 2.4 kA current range, with temperature effects less than $0.2 \%$ from -10 to 60 degrees Celsius. This work contributes to understanding the metrological characteristics of FOCS and supports their broader adoption in on-site calibration.

magnet-moving measurement scheme in Kibble balances avoids displacing force-sensitive components, such as the weighing cell, and enables a broader magnetic profile measurement range during the velocity phase. However, this mechanism introduces the risk of asymmetry in the Bl measurement due to external magnetic flux, leading to a potential systematic error in the final measurement results. Using the Tsinghua tabletop Kibble balance magnet as a case study, this article investigates the error mechanism through finite element analysis (FEA) and experimental investigations. An evaluation method combining external weak-field measurements with attenuation factor analysis is proposed to assess external magnetic flux errors in magnet-moving measurement schemes. The findings demonstrate that selecting an optimal weighing position can reduce the far-end flux effect to the order of 10(-9). In contrast, the near-end flux effect can be quantified by monitoring the magnetic field surrounding the magnet system. In the Tsinghua Kibble balance system, we show that with proper control of external flux sources, the relative error can be reduced below 1 x 10(-8) without requiring additional magnetic shielding.