To measure the current on each conductor in a three-phase three-core cable or a three-phase four-core cable without an armor or the armor that is made of nonmagnetic material, one has to remove its sheath/armor and applies a traditional device, such as a current transformer (CT) to each conductor, which is invasive and inconvenient. In this article, a Coreless current probe, composed of a tunnel-magnetoresistance (TMR)-based magnetic sensor array, is presented to nondestructively achieve current measurement for multicore cables. The conductor positions, incline angles, and current phasors of a multicore cable are simultaneously identified by solving a nonlinear least square (NLLS) problem. The current waveforms are reconstructed in real time through a real-valued matrix multiplication using the measured time-domain TMR sensor voltage signals. Both simulation and experiment are performed to validate the feasibility of the proposed method. The simulation study is first conducted and demonstrates that a maximum relative current amplitude error of less than 5% and a maximum phase error of lower than 4° can be achieved, and three-phase current waveforms with many harmonics are also successfully reconstructed by simulation. A prototype Coreless current probe is designed and fabricated. The experimental study involving fundamental current phasor measurement and current waveform reconstruction is subsequently performed on a three-phase three-core cable. The experimental results indicate that the maximum relative current amplitude error and phase error, respectively, have average values of 5.44% and 2.58°. Meanwhile, three-phase current waveforms with many harmonics generated by three types of appliances are also successfully reconstructed.

Magnetic sensor arrays have been employed to measure currents for multicore cables due to their advantages of compact size, lightweight, low power consumption, and large dynamic range. However, the existing methods are applicable only to cases where the cable must be perpendicular to the sensor array plane due to the lack of capability of the 2-D magnetic field model to consider conductor inclination. To solve this problem, this article presents a method using a circular array of single-axis magnetic sensors to measure magnetic fields along and perpendicular to the sensor array plane. A 3-D magnetic field model that involves conductor incline angles is first derived. On the basis of the derived model, two main steps are performed to realize current sensing. First, an off-site calibration method is used to calibrate magnetic sensor parameters, including sensor position, orientation, gain factor, and phase shift. Second, not only the conductor currents and positions but also the incline angles are simultaneously calculated based on the detected magnetic fields and calibrated sensor parameters. Both steps are formulated as nonlinear least-square problems and solved efficiently. Both simulation and experiment are performed to demonstrate the superiority of the proposed method compared to the existing ones based on the 2-D magnetic field model when inclinations are introduced. The proposed method may have the potential for designing a clamp-on current sensor dedicated to multicore cables similar to hand-held current probes with a relatively large inner diameter for single-conductor systems.

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.

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.

This article presents a semi-contactless power measurement method aimed at offering power measurements of residential homes, which are power supplied by the single-phase two-wire entrance lines, for studying the nonintrusive load monitoring (NILM) technique. The active power is calculated using the waveforms of the line current and voltage. To measure the line current, a magnetic sensor array consisting of seven tunnel magnetoresistance (TMR) sensors is utilized to detect the magnetic fields around the entrance lines. The single-phase time-domain current is then reversely calculated on real time by matrix multiplication using the time-domain output signals of the TMR sensor array once the entrance line positions are identified through solving the formulated nonlinear least square (NLLS) problem. In terms of the line voltage, a capacitively coupling voltage sensor is proposed to achieve almost in-phase tracking with the line voltage waveform. The voltage ratio of the voltage senor is calibrated using the measured rms value of line voltage from the outlet sockets or power strips in situ by a multimeter (thus called semi-contactless) due to the main disadvantage for capacitively coupling voltage sensing. That is, accuracy in voltage amplitude measurement is low because of the great difficulty in accurately determining the coupling capacitances. Numerical integration method for calculating the active power based on quasi-synchronous algorithm is proposed to eliminate the errors caused by the noninteger period sampling. Prototype instrument is designed and fabricated. Frequency response characterization shows that the TMR sensor (voltage sensor) has an almost constant gain factor (voltage ratio) and an approximate zero-phase shift (<1°) over a frequency range of $50-3.05$ kHz. Laboratory tests for both fundamental current phasor and active power measurement along with their measurement uncertainty evaluations are first conducted to verify the feasibility of the proposed method. Field tests in a residential home are subsequently performed to further demonstrate the effectiveness of the proposed method. A power measurement error of less than 5% can be obtained, which is sufficient for home energy tracking.

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.