Direct Current Component Research Articles

Direct Current Ripple Component Detection Algorithm Based on Improved Variational Mode Decomposition

Background: The development of smart grids requires energy meters that enable accurate measurements. Objective: In response to the current issue where Direct Current (DC) energy meters only measure DC components and not ripple components, we propose to design a novel algorithm to achieve accurate separation of DC components and ripple components in DC signals. Methodology: This patent proposes a precise detection algorithm for ripple components. The algorithm is based on the Wavelet Decomposition combined with Flamingo Search Algorithm-Variational Mode Decomposition (WD-FSA-VMD). Firstly, we analyze the ripple characteristics in the DC signal and use the Wavelet Decomposition (WD) algorithm to separate the ripple components in the DC signal accurately. Secondly, we utilize the Flamingo Search Algorithm (FSA) to optimize the number of modal decompositions and the penalty factor in the Variational Mode Decomposition (VMD). This allows us to accurately extract the ripple components. Finally, we conducted simulation experiments comparing the improved algorithm with the original algorithm. Results: The experimental results indicate that the signal correlation coefficient obtained by the WDFSA- VMD algorithm increases by 82.64% compared to traditional VMD, and it increases by 16.72% compared to the combined Wavelet Decomposition with Whale Optimization Algorithm-Variational Mode De-composition (WD-WOA-VMD). Conclusion: The improved algorithm we proposed has good adaptability and separation performance. It is prospective for the new algorithm to provide a valuable reference to ripple detection technology.

An in-phase filter-based flux observation strategy for sensorless control of PMSMs

Due to the complexity of determining the initial rotor flux and detecting errors, conventional rotor flux observation methods are easily affected by direct current (DC) components and harmonics. To address this issue, this paper proposes an in-phase filter (IPF)-based rotor flux observation strategy for sensorless control of permanent magnet synchronous machines (PMSMs). The core components of the IPF consist of a double second-order generalized integrator (DSOGI) and a phase angle compensation transfer function (PACTF). The DSOGI provides a accurate electrical angular frequency, while the PACTF implements a phase correction to the vq′ signals. By employing IPF structure, accurate observations for rotor flux, electronic speed, and rotor position are achieved, which can be effectively used in the sensorless control of PMSMs, eliminating the need for magnitude and phase compensations. Finally, the proposed observation strategy is applied to an experimental bench of a PMSM, and its effectiveness is illustrated by experimental results. From experimental results, it can be concluded that the IPF is significantly better than the LPF, and 5% more accurate than the observer based on cascade second-order generalized integral(CSOGI) overall.

Dynamic resistance of a REBCO tape carrying direct current under a mixture magnetic field of AC field with DC-biased field

Abstract When the REBCO coated conductor tape carries a direct current(DC) transport current whilst exposed to the alternating current(AC) magnetic field, a DC electrical resistance can be observed, which is called “dynamic resistance”. The High Temperature Superconducting(HTS) magnet wound by the REBCO tapes is located in the HTS electrical machine as field winding carrying DC transport current. The operational environment of the HTS electrical machine involves a complex magnetic field, encompassing both AC and DC components. The interaction between the AC magnetic field and the DC transport current induces dynamic resistance and dynamic loss in the REBCO tape which is a distinctive trait of REBCO tape. Additionally, the presence of an extra DC-biased magnetic field can decrease the critical current of the REBCO tape, thereby altering its electromagnetic properties and potentially compromising its safety. As the basis of superconducting magnets, it is particularly important to study the dynamic resistance and loss distribution of the single REBCO tape under a mixture of magnetic field backgrounds, according to the real working environments in various applications. In this paper, the electromagnetic-thermal coupling model of multilayer REBCO tape based on H-formulation is built in COMSOL Multiphysics. The electromagnetic characteristics and dynamic resistance of the tape are presented when the tape is applied AC magnetic field and carries DC transport current. The effects of perpendicular and parallel DC-biased magnetic fields on the dynamic resistance and loss distribution of the REBCO tape are investigated in the paper. And the DC transport current safety margin will be observed in different applied DC-biased magnetic fields. This study comprehensively demonstrates the variation of dynamic resistance and loss distribution under a complex background magnetic field, which is significant for exploring the electromagnetic characteristics and calculating the loss of the HTS magnets in the HTS electrical machine.

Evaluation of the Nonlinear Response of KCl Solution to High-Amplitude Stimulation Using a Four-Point Cylindrical Gold Electrode.

A four-electrode system and high-voltage amplitude stimulation (with a voltage of more than 1 V) are always used for nonlinear spectroscopy of biological solutions like yeast suspension. Multiple studies indicate that yeast membrane activities are the primary source of the harmonics detected from yeast suspensions. However, other investigations have demonstrated that at least part of the harmonics are mainly due to the nonlinear impedance of the electrode-electrolyte interface. Here, we want to find a mathematical model to analyze the odd harmonics generated by the interface. The KCl solution is the basis of the essential medium used in yeast culture. No study models the nonlinear behavior of the KCl solution using four-electrode. We used a sinusoidal voltage with a low frequency and a high amplitude to test an ionic solution with 1, 30, and 130 mM of potassium chloride. The voltage had no direct current component. Here, we show that the relationship between the amplitude of the excitation voltage and the third harmonic of the current can be accurately represented using the Butler-Volmer equation. Additionally, we analyze the impact of potassium chloride (KCl) concentration on the behavior of the third harmonic. This paper presents a method and model that can be used for nonlinear spectroscopy studies of biological solutions using a four-electrode system with the aim of deriving information from cells without considering the interface effect.

Evaluation Method of Magnetic Field Stability for Robotic Arc Welding Based on Sample Entropy and Probability Distribution

In this study, we analyzed the arc magnetic field to assess the stability of the arc welding process, particularly in robotic welding where direct measurement of welding current is challenging, such as under water. The characteristics of the magnetic field were evaluated based on low-frequency fluctuations and the symmetry of the signals. We used double-wire pulsed MIG welding for our experiments, employing Q235 steel with an 8.0 mm thickness as the material. Key parameters included an average voltage of 19.8 V, current of 120 A, and a wire feeding speed of 3.3 m/min. Our spectral analysis revealed significant correlations between welding stability and factors such as the direct current (DC) component and the peak power spectral density (PSD) frequency. To quantify this relationship, we introduced a novel approach using sample entropy and mix sample entropy (MSE) as new evaluation metrics. This method achieved a notable accuracy of 88%, demonstrating its effectiveness in assessing the stability of the robotic welding process.

Passive imaging through inhomogeneous scattering media

According to the atmospheric scattering model (ASM), the object signal’s attenuation diminishes exponentially as the imaging distance increases. This imposes limitations on ASM-based methods in situations where the scattering medium one wish to look through is inhomogeneous. Here, we extend ASM by taking into account the spatial variation of the medium density, and propose a two-step method for imaging through inhomogeneous scattering media. In the first step, the proposed method eliminates the direct current component of the scattered pattern by subscribing to the estimated global distribution (background). In the second step, it eliminates the randomized components of the scattered light by using threshold truncation, followed by the histogram equalization to further enhance the contrast. Outdoor experiments were carried out to demonstrate the proposed method.

Analysis of Parameter Sensitivity to Overvoltage under DC Commutation Failure

Abstract In recent years, the growing integration of renewable energy sources into power systems has highlighted the significance of enhancing the grid’s capacity to accommodate these resources efficiently. Direct Current (DC) transmission stands out as a pivotal solution to bolster the integration of renewable energy. This study delves into the critical issue of overvoltage occurrences at the sending end, particularly triggered by failures in DC commutation. Through the development of a comprehensive PSCAD electromagnetic simulation model encompassing synchronous machines, centralized renewable energy sources, along with DC components, the research rigorously investigates the intricacies of DC commutation failures. Specifically, it explores their underlying mechanisms responsible for inducing overvoltage at the sending end. Furthermore, the paper undertakes an extensive analysis of the voltage dynamic processes and their associated sensitivity factors, shedding light on crucial aspects of grid stability and resilience in the face of evolving energy landscapes.

Анализ частотных характеристик токовых датчиков цифрового трансформатора тока и напряжения

Digital measuring current and voltage transformers (DCVT), which incorporate various current and voltage sensors are the key sources of information about processes at modern digital substations. Classic small-sized current transformers, Rogowski coils, magnetotransistor sensors, Hall effect sensors, fiber-optic Faraday effect sensors, as well as shunts can be used as current sensors in DCVTs. For redundancy purposes, current channels are performed in several copies and on different sensors. Sensors that are different in nature have their own set of advantages, which together makes it possible to obtain the effect of eliminating the shortcomings of specific sensors. For example, they may not have a saturation effect or transmit the direct current component quite accurately, which is a significant advantage over classic current transformers. At the mains frequency, the behavior of these sensors is predictable, but their behavior is not well studied at higher and lower frequencies. Thus, it is decided to study the frequency response and phase response of these sensors in a wide frequency range. To solve the problems within the framework of this study, physical experiment, analytical and empirical solution methods have been used. As a result of the study, the frequency response and phase response of current sensors of DCVT in a wide frequency range have been obtained. Analog filter has been designed to correct the signal of the magnetotransistor sensor. The results obtained coincide with theoretical data and can be considered when developing digital relay protection and automation algorithms.

An experimental study on the combustion characteristics of the cavity-stabilized supersonic premixed flame

With the overwhelming trend of fast and economic aviation, it is becoming increasingly difficult for fuel to burn stably and efficiently in a constrained space and time period in the combustor of a hypersonic air-breathing vehicle. Conventional supersonic diffusion flame runs the risk of blowing out in the incoming flow at such high velocity. Upstream fuel injection of the flame holder is gaining popularity due to its prominent advantage in improving mixing efficiency, and this fuel injection method contributes to the organization of supersonic premixed combustion. In order to study the combustion characteristics of the supersonic premixed flame, corresponding experiments are carried out on a direct-connected scramjet platform with the inflow total temperature of 1700 K and the inflow Mach Number of 2.0. Gaseous ethylene with an equivalence ratio of 0.15 was injected transversely 670 mm upstream of a cavity. Optical measurements including laser-induced fluorescence on the hydroxyl radical (OH-LIF), CH*chemiluminescence photography, and high-speed photography were performed to investigate the steady-state and transient combustion characteristics of the cavity-stabilized supersonic premixed flame. From steady-state OH-LIF and CH* results, the flame could be divided into reactant zone, preheating zone, intense reacting zone, and product zone. It could be inferred that the preheating zone induced by the hot product in the cavity acts as a radical source and heat source for combustion stabilization in the cavity. In addition, the transient flame morphology analysis was carried out from the high-speed photography results. The flame base position and flame spreading angle were abstracted from the binarized image. The results showed that there existed a subtle flame flashback phenomenon for the flame base, whereas the flame spreading angle maintained a relatively constant value with a small deviation. The frequency-domain analysis revealed that both the flame base position and flame spreading angle reached the peak amplitude in the direct current component (0 Hz), exhibiting no explicit high-amplitude resonance component within 1500 Hz compared to those in the diffusion combustion mode. In all, the supersonic premixed flame presented a stabilized flame morphology.

Microstructure evolution, stress state and electromagnetic performance of Fe-based nanocrystalline alloy induced by stress-annealing

Stress-induced anisotropy has been applied for FeSiBCuNb nanocrystalline alloy ribbons in transformers with large direct current (DC) component. However, the physical mechanism of anisotropy induced by stress annealing during crystallization remains controversial. Here, a systematic study was conducted on the microstructure, residual stress state, dynamic domain structure and properties of the stress-annealed FeSiBCuNb nanocrystalline ribbons. Present results demonstrate that, the increase of the applied stress greatly increases the residual tensile stress and induces lattice distortion, which acts as pinning site during magnetization, resulting in enhanced domain-wall energy and narrower wall width. Meanwhile, stress annealing promotes the flattening of hysteresis loops and decreases the effective permeability, which improves the DC-bias characteristics of the ribbons, thereby promoting the transition from “hard saturation” to “soft saturation” behavior. Also, stress-induced grain refinement is beneficial to obtaining high hardness. Owing to the stress-induced anisotropy, the stress-annealed sample with applied stress of 113 MPa exhibits excellent combined properties, including low constant effective permeability of 438 at wide frequency range (1 kHz–8 MHz), high DC-bias capability of 74% (30 Oe), low power loss of 49 kW/m3 (100 mT, 100 kHz), and high hardness of 644 HV. This discovery provides an insightful understanding of stress-induced anisotropy mechanism on the high-performance Fe-based nanocrystalline alloys.

High precision three-dimensional ellipse fitting correction for galloping monitoring

In this paper, we propose and demonstrate a high precision three-dimensional (3D) ellipse fitting correction method for optical fiber composite overhead ground wire (OPGW) galloping monitoring, based on weak fiber Bragg grating array. 3D ellipse formed by three outputs of the system is fitted by the coordinate rotation and least square methods, and direct current (DC) components and alternate current (AC) component coefficients of the three outputs are obtained. By differentiating and cross-multiplying the three outputs, those DC components are zeroized, AC component coefficients are normalized, and finally, the interference phase signal is calculated. The experimental results show that the proposed method can demodulate the vibration signals better, and the fitted R2 is above 0.99. The system is implemented on a 220 kV transmission line in the plateau region of Western China, forecasting a galloping period with a wavelength of about 60 m within the span accurately. This method demonstrates suitability for monitoring OPGW transmission line galloping events.

Electrohydrodynamic deformation of a compound droplet in an alternating current and direct current superposed electric field

In this study of a compound droplet subjected to alternating current (AC) and direct current (DC) superposed (AC/DC) electric fields, both core and shell deformations oscillate, albeit with reduced amplitude compared to solely alternating current electric fields. As surface tension relaxes, periodic cyclic deformation ensues, with mean deformation amplifying alongside electric field amplitude. Concurrently, normal and tangential Maxwell stresses escalate with amplitude, thus augmenting interfacial surface velocities. Manipulating the offset ratio of alternating and direct current superposed electric field modulates mean deformations. Across low frequencies, stable deformation remains constant, yet a delayed onset characterizes higher frequencies. The presence of a core affects the electrohydrodynamics of the compound droplet and shell deformation, thereby mitigating phase differences between cyclic deformations. Contrasting alternating current (AC)—only fields, alternating current and direct current superposed (AC/DC) electric field scenarios exhibit heightened surface charge densities and prompter stable deformation onset. Furthermore, the direct current component magnifies mean deformations while harmonizing phase disparities between core and shell deformations. This study illuminates the intricate interplay between alternating current and direct current fields on compound droplet behavior, offering profound insight with broad implications for applications necessitating precise deformations under electric fields.

Increasing the Energy Efficiency of Traction Electric Drives of Direct Current

Purpose. The work is aimed at improving the energy efficiency of direct current traction electric drives of electric transport by introducing transistor pulse width converters (PWC) with an optimal switching frequency to minimize total electrical losses in the electric drive. The electrical losses of traction electric drives consist of electrical losses in the armature winding and in the PWC transistors. Methodology. To study the dependence on the switching frequency of transistors, the electrical losses in the armature winding and PWC transistors are divided into two parts: static losses from the direct current component of the current and dynamic losses, i.e., losses in the armature winding from harmonic current components and losses in the transistors from transient switching currents. Since the dynamic electrical losses in transistors increase with increasing frequency and decrease in the armature winding, it is necessary to find the optimal PWC co-mutation frequency at which the total dynamic losses in the traction electric drive will be minimal. The goal of increasing energy efficiency in a traction electric drive is achieved by determining the dependence of dynamic electrical losses in the armature winding on the switching frequency of the PWC and computer modeling of the transistor electric drive. Findings. It is found that the relative dynamic electrical losses in the armature winding in the case of polyharmonic power supply are equal to the square of the armature current ripple coefficient. An algorithm for determining the optimal switching frequency of the PWC is developed: 1) the dependence of dynamic electrical losses on the switching frequency of transistors is determined experimentally on computer models of the motor and PWC; 2) the graph of the dependence of total dynamic electrical losses of the transistor electric drive on the time-tothe point of minimum losses, which corresponds to the optimal frequency value, is determined. Originality. For the first time, the authors obtained an analytical expression for the relative dynamic electrical losses in the armature windings, which are equal to the square of the armature current ripple factor. Practical value. Establishing the optimal switching frequency of the PWC according to the developed methodology reduces electrical losses in traction electric drives, i.e., increases their energy efficiency.

Reconstruction methods for super-resolution imaging with PSF modulation

Recently, a super-resolution imaging method called the PSF (point spread function) modulation method was developed (Lu, IEEE TUFFC 2024). In this method, the amplitude, phase, or both of the PSF of a linear shift-invariant (LSI) imaging system is modulated so that the modulated PSF has a higher spatial frequency than that of the original PSF to reconstruct super-resolution images. The modulator can be produced and manipulated remotely by methods such as radiation force or it can be a physical particle such as micro- or nano-particle manipulated by an external force such as electrical and electromagnetic force. In principle, the super-resolution imaging method can be applied to any LSI imaging system, such as ultrasound, optical, photoacoustic, electromagnetic, underwater, nondestructive evaluation (NDE), and magnetic resonance imaging (MRI) system. These include pulse-echo ultrasound imaging, transmission imaging, wave source/field imaging, acoustical camera, and optical bright-field microscope. To optimize the quality of the images, methods for the reconstruction of pulse-echo and wave source/field super-resolution images are studied and the results will be presented. These methods include the uses of an analytic envelope of radio-frequency (RF) signals with and without windowing, “I” (in-phase) and “Q” (quadrature) signals, and the DC (direct current) component removal.

Analysis of DC bias characteristics of transformer by using fixed-point time-step FEM and dynamic J–A hysteresis model

The injection of the Direct Current (DC) bias component will lead to oversaturation of the transformer core and affect its safe operation. In this paper, the vector magnetic potential A and winding current I are used as the variables solved in the time-step finite element method to simulate the nonlinear transient magnetization characteristics of the transformer under DC bias, and the fixed-point reluctivity is introduced to deal with the nonlinear iterative problem. The field-circuit coupling relationship is established through the electromagnetic induction law, and the two-dimensional time-step finite element model of the transformer core is found. The dynamic J–A hysteresis model is used to deal with the hysteresis effect of iron cores. The fixed-point reluctivity of difference form is introduced to solve the problem of uneven transition and multi-value of magnetization curve with hysteresis in the iterative process. The determination scheme for the equivalent thickness of the core model and the initial iterative value are discussed. A laminated core transformer is made for experiments, and the accuracy and applicability of the model proposed in this paper are verified by comparing the calculation and experimental results. The influence of different voltages and different DC bias components on the electromagnetic characteristics of the transformer is analyzed.

Non-sweep DC component estimation method for a virtual-carrier assisted Kramers-Kronig receiver

The Kramers-Kronig (KK) receiver has attracted much attention in short-range optical interconnection because of its ability to recover the phase of the signal from the intensity information through KK algorithm. In high-speed KK systems, such as virtual-carrier (VC) assisted ones, an alternating current (AC) coupled photo-detector (PD) is preferred due to relaxing the requirements of analog-to-digital converter (ADC) and electronic amplifier by filtering direct current (DC) component. However, the loss of the DC component will cause the KK algorithm to break down, so it is necessary to accurately recover DC value in the digital domain with multiple-sweep. In this paper, we propose what we believe is a novel non-sweep DC component estimation scheme based on optimized digital carrier-to-signal power ratio (OD-CSPR) method, which can accurately estimate the DC component with only 3-4 iterations in the scenario of VC-assisted KK receiver optical transmission. The scheme utilizes the one-dimensional search optimization algorithm based on golden section search and parabolic interpolation without sweeping. The simulation and experimental results of the proposed non-sweep OD-CSPR method show that the DC component can be estimated accurately in a large CSPR range, and the system performance is close to that of the conventional DC-sweep method. Compared with the typical defined digital CSPR (DD-CSPR) based optimization method, the proposed one can realize optical signal-to-noise ratio (OSNR) gains of 0.9 dB in the back-to-back (B2B) and 0.7 dB under 80 km fiber transmission scenarios respectively with a total bit rate of 160Gb/s.

Energy efficiency optimization in a parallel relay-assisted UWOC system with simultaneous lightwave information and power transfer.

In this paper, we investigate the energy efficiency optimization for a parallel relay-assisted underwater wireless optical communication (UWOC) system with simultaneous lightwave information and power transfer (SLIPT) over an aggregate channel. In this system, relay nodes are equipped with energy harvesting devices, getting energy from the direct current component of the received signal transmitted by the source node. These nodes utilize the harvested energy to transmit the signal to the destination node with the decoding and forwarding strategy. The harvested energy for each relay node is derived by the Gauss-Laguerre quadrature formula and the outage probability is deduced by the Meijer-G function. Then, the system's energy efficiency can be calculated and an energy efficiency maximization problem is built up with respect to the bias current. We propose a three-level-iteration algorithm to solve this problem. In the first level, the Dinkelbach method is used to represent energy efficiency in a parametric subtractive form. In the second level, we use the penalty function method to convert the object function and constraint. In the third level, the objective function is transformed into a quadratic function by using a successive convex approximate method, thereby solving for the bias current. The effects of system parameters on energy efficiency are also analyzed. Theoretical results and Monte Carlo simulations suggest that employing the solved bias current can significantly improve the system's energy efficiency.

Recording physiological and pathological cortical activity and exogenous electric fields using graphene microtransistor arrays in vitro.

Graphene-based solution-gated field-effect transistors (gSGFETs) allow the quantification of the brain's full-band signal. Extracellular alternating current (AC) signals include local field potentials (LFP, population activity within a reach of hundreds of micrometers), multiunit activity (MUA), and ultimately single units. Direct current (DC) potentials are slow brain signals with a frequency under 0.1 Hz, and commonly filtered out by conventional AC amplifiers. This component conveys information about what has been referred to as "infraslow" activity. We used gSGFET arrays to record full-band patterns from both physiological and pathological activity generated by the cerebral cortex. To this end, we used an in vitro preparation of cerebral cortex that generates spontaneous rhythmic activity, such as that occurring in slow wave sleep. This examination extended to experimentally induced pathological activities, including epileptiform discharges and cortical spreading depression. Validation of recordings obtained via gSGFETs, including both AC and DC components, was accomplished by cross-referencing with well-established technologies, thereby quantifying these components across different activity patterns. We then explored an additional gSGFET potential application, which is the measure of externally induced electric fields such as those used in therapeutic neuromodulation in humans. Finally, we tested the gSGFETs in human cortical slices obtained intrasurgically. In conclusion, this study offers a comprehensive characterization of gSGFETs for brain recordings, with a focus on potential clinical applications of this emerging technology.

DarLoc: Deep learning and data-feature augmentation based robust magnetic indoor localization

Magnetic-based indoor localization has attracted considerable attention due to the pervasiveness of geomagnetic fields and is free of extra infrastructures. However, existing approaches still face heterogeneity problems caused by the type of devices, the holding attitudes, and the moving speeds of pedestrians. To cope with it, we propose a novel deep learning and data-feature augmentation based magnetic localization framework (DarLoc). First, we invoke orientation-insensitive magnetic signal extraction to remove the Direct Current (DC) component of the sequence and to eliminate the impact caused by different holding attitudes and various mobile devices. Second, we propose novel data augmentation and feature augmentation methods to extract features of speed information, thus tackling the multi-scale sequence problem caused by different moving speeds. Finally, we propose a deep multi-scale spatial–temporal learning model to extract both spatial and temporal features of the augmented sequences and to provide a robust localization for people with various moving speeds and attitudes. Extensive experiments, including a total of 189 volunteers with 4 different mobile devices and multiple moving speeds, are employed to evaluate the performance of DarLoc over 14 months. Experiment results reveal that: (1) DarLoc obtains an average localization accuracy of 0.47 m and 0.56 m under constant and variable moving speeds scenarios, respectively; (2) DarLoc obtains about 41% and 60% localization accuracy improvement compared with the state-of-the-art localization methods.

A High-Precision Error Calibration Technique for Current Transformers under the Influence of DC Bias

A bias current in the power system will cause saturation of the measuring current transformer (CT), leading to an increase in measurement error. Therefore, in this paper, we first conducted measurements of the direct current component in a 10 kV distribution system. Subsequently, a reverse extraction method for the CT distorted current under direct current bias conditions based on Random Forest Classification (RFC) and Long Short-Term Memory (LSTM) was proposed. This method involves two stages for the reverse extraction of CT distorted currents under direct current bias conditions. In the offline stage, data samples were generated by changing the operating environment of the CT. The RFC classification algorithm was used to divide the saturation levels of the CT, and for each sub-class, Particle Swarm Optimization–Long Short-Term Memory Network (PSO-LSTM) models were trained to establish the mapping relationship between the secondary distorted current and the primary current fundamental component. In the online stage, the saturated data segments were extracted from the secondary current waveform using wavelet transform, and these segments were input into the offline model for current reverse extraction. The simulation results show that the proposed method exhibited strong robustness under various CT conditions, and achieved high reconstruction accuracy for the primary current.