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An online measurement method is proposed in this paper, and a system is established for detecting the excitation impedance of current transformers (CTs) based on Norton's theorem. The theorem is carried out by connecting a resistance and an inductance at the secondary side port of the CT to get the equations for calculating the impedance. The iterative method is used to solve the equations, and the solution is revised to consider the nonlinearity of the core. The main variable in the equations is the variation of the secondary current with the resistance or inductance. To obtain the secondary current variation accurately, which is less than 1‱ of the current, a differential method is proposed, which is based on charging two capacitors and measuring the difference of their voltages instead of measuring each current separately first and then obtaining the current variation by subtraction. This is equivalent to saving two currents first and then measuring the current difference. The differential method avoids the problem of error amplification in the process of measuring two currents separately first and then subtracting them to obtain the current variation and solves the problem that two currents do not appear simultaneously. The results verify the correctness and accuracy of the proposed method and system. The acquisition of the excitation impedance is the basis for obtaining the working characteristics of CT cores, including magnetic and loss characteristics, as well as the error of CTs.

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This paper reports on the testing and evaluation of a passive autoranging (AR) method designed to dynamically extend the measurement range of a photonic current transducer (PCT) to pave the way toward a realization of a combined metering- and protection-class current sensor. The PCT utilizes a current transformer (CT), a piezoelectric transducer (PZT), and a fiber Bragg grating (FBG) to enable current measurement at multiple points in an electrical power network whereby multiple sensors are deployed and interrogated serially using a single optical fiber. The autoranging technique relies on incorporating static MOSFET switches to instantaneously short individual serially connected CT burdens in response to a measured current magnitude exceeding pre-set thresholds. The AR circuit switching events produce distinctive signal features that are used by the proposed switching algorithm to apply appropriate scaling factors to reconstruct the measured current from the optical signal. It is shown through laboratory experiments that the AR circuit correctly reacts to pre-set burden current thresholds of 130% of the nominal value and 22 times the nominal value, signifying its "metering" and "protection" range boundaries. The circuit reaction time is below 4 ms, rendering it suitable for standard power system protection purposes. Moreover, the operation of the AR circuit is demonstrated for burden currents of up to 100 A for over 1 s, satisfying a test procedure for the secondary CT circuit, as required by some power system operators. It is demonstrated that the proposed switching algorithm allows for a correct reconstruction of the burden currents from the optical signal acquired by the FBG interrogator, offering the potential to realize a dual-class optical current sensor.

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Objective.Beam current transformers (BCT) are promising detectors for real-time beam monitoring in ultra-high dose rate (UHDR) electron radiotherapy. However, previous studies have reported a significant sensitivity of the BCT signal to changes in source-to-surface distance (SSD), field size, and phantom material which have until now been attributed to the fluctuating levels of electrons backscattered within the BCT. The purpose of this study is to evaluate this hypothesis, with the goal of understanding and mitigating the variations in BCT signal due to changes in irradiation conditions.Approach.Monte Carlo simulations and experimental measurements were conducted with a UHDR-capable intra-operative electron linear accelerator to analyze the impact of backscattered electrons on BCT signal. The potential influence of charge accumulation in media as a mechanism affecting BCT signal perturbation was further investigated by examining the effects of phantom conductivity and electrical grounding. Finally, the effectiveness of Faraday shielding to mitigate BCT signal variations is evaluated.Main Results.Monte Carlo simulations indicated that the fraction of electrons backscattered in water and on the collimator plastic at 6 and 9 MeV is lower than 1%, suggesting that backscattered electrons alone cannot account for the observed BCT signal variations. However, our experimental measurements confirmed previous findings of BCT response variation up to 15% for different field diameters. A significant impact of phantom type on BCT response was also observed, with variations in BCT signal as high as 14.1% when comparing measurements in water and solid water. The introduction of a Faraday shield to our applicators effectively mitigated the dependencies of BCT signal on SSD, field size, and phantom material.Significance.Our results indicate that variations in BCT signal as a function of SSD, field size, and phantom material are likely driven by an electric field originating in dielectric materials exposed to the UHDR electron beam. Strategies such as Faraday shielding were shown to effectively prevent these electric fields from affecting BCT signal, enabling reliable BCT-based electron UHDR beam monitoring.

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Energy efficiency is an important issue in industry, especially with the ever-increasing consumption of electrical energy. The power quality and the traceability of metering devices are essential when integrating energy metering systems for energy efficiency. This management requires an understanding of electrical current events such as pulse and transient currents. Current transducers are widely used to measure these electrical current events up to a few megahertz. Their use makes it possible to measure not only the main current flowing through the transducer, but also the bypass current that affects electrical equipment. Calibration of these sensors up to a few megahertz then becomes an essential step. Currently, most calibration methods are limited to 100 kHz frequency for a current of 10 A. This paper presents an improvement of a traceable calibration methodology for current transducers up to 10 A and 1 MHz, thus increasing, by 10 times, the current level for such high frequency applications. This calibration methodology is based on a metrological traceability chain (uninterrupted link to the International System of Units) with respect to a calculable current shunt and is currently the only traceable method for calibrating current transducers at 10 A and up to 1 MHz. The uncertainty obtained for the transimpedance ratio is less than 0.2%, which is considerably reduced with respect to the existing capabilities.

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With the growing adoption of wide bandgap devices in power electronic applications, current sensor design for switching current measurement has become more important. The demands for high accuracy, high bandwidth, low cost, compact size, and galvanic isolation pose significant design challenges. The conventional modeling approach for bandwidth analysis of current transformer sensors assumes that the magnetizing inductance remains constant, which does not always hold true in high-frequency operations. This can result in inaccurate bandwidth estimation and affect the overall performance of the current sensor. To address this limitation, this paper provides a comprehensive analysis of nonlinear modeling and bandwidth, considering the varying magnetizing inductance in a wide frequency range. A precise and straightforward arctangent-based fitting algorithm was proposed to accurately emulate the nonlinear feature, and the fitting results were compared with the magnetic core's datasheet to confirm its accuracy. This approach contributes to more accurate bandwidth prediction in field applications. In addition, the droop phenomenon of the current transformer and saturation effects are analyzed in detail. For high-voltage applications, different insulation methods are compared and an optimized insulation process is proposed. Finally, the design process is experimentally validated. The bandwidth of the proposed current transformer is around 100 MHz and the cost is around $20, making it a low-cost and high-bandwidth solution for switching current measurements in power electronic applications.

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The article elaborates on the accuracy of current transformers (CT) in interaction with temperature and frequency using Pearson's correlation. The first part of the analysis compares the accuracy of the mathematical model of the current transformer and the result of the measurement on the real CT using the Pearson correlation calculation. The mathematical model of CT is determined by deriving the formula of the functional error with the display of the accuracy of the measured value. The accuracy of the mathematical model is affected by the accuracy of current transformer model parameters and the calibration characteristic of the ammeter used to measure the CT current. Variables that cause deviation in the accuracy of CT are temperature and frequency. The calculation shows the effects on accuracy in both cases. The second part of the analysis refers to the calculation of the partial correlation of three quantities: (1) CT accuracy, (2) temperature, and (3) frequency on a set of 160 measurements. First, the influence of temperature on the correlation of CT accuracy and frequency is proven, following the proof of the influence of frequency on the correlation of CT accuracy and temperature. In the end, the analysis is combined by comparing the measured results of the first and second part of the analysis.

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In this paper, we present a novel technique for passively autoranging a photonic current transducer (PCT) that incorporates a current transformer (CT), piezoelectric transducer (PZT) and fiber Bragg grating (FBG). Due to the usage of single-mode fiber and FBG, multiple PCTs can be interconnected and distributed over a long distance, for example along a power network, greatly reducing the cost of sensor deployment and offering other unique advantages. The autoranging technique relies on the usage of multiple, serially connected CT burden resistors and associated static MOSFET switches to realize instantaneous shortening of the resistors in response to increasing measured current. This functionality is realized passively, utilizing a modular, µW-power comparator circuit that powers itself from the electrical energy supplied by the CT within a small fraction of the 50/60 Hz cycle. The resultant instantaneous changes in sensor gain will be ultimately detected by the central FBG interrogator through real-time analysis of the optical signals and will be used to apply appropriate gain scaling for each sensor. The technique will facilitate the usage of a single PCT to cover an extended dynamic range of the measurement that is required to realize a combined metering- and protection-class current sensor. This paper is limited to the description of the design process, construction, and testing of a prototype passive autoranging circuitry for integration with the PCT. The two-stage circuitry that is based on two burden resistors, 1 Ω and 10 Ω, is used to prove the concept and demonstrate the practically achievable circuit characteristics. It is shown that the circuit correctly reacts to input current threshold breaches of approximately 2 A and 20 A within a 3 ms reaction time. The circuit produces distinct voltage dips across burden resistors that will be used for signal scaling by the FBG interrogator.

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Current transformer saturation affects measurement accuracy and, consequently, protection reliability. One important concern in the case of overcurrent protections is the discrimination between faults and inrush current in power transformers. This paper presents an FPGA-based smart sensor to detect current transformer saturation, especially during inrush current conditions. Several methods have been proposed in the literature, but some are unsuitable for inrush currents due to their particular waveform. The proposed algorithm implemented on the smart sensor uses two time-domain features of the measured secondary current: the second-order difference function and the third-order statistic central moment. The proposed smart sensor presents high effectiveness and immunity against noise with accurate results in different conditions: different residual flux, resistive burdens, sampling frequency, and noise levels. The points at which saturation starts are detected with an accuracy of approximately 100%. Regarding the end of saturation, the proposed method detects the right ending points with a maximum error of a sample. The smart sensor has been tested on experimental online and real-time conditions (including an anti-aliasing filter) with accurate results. Unlike most existing methods, the proposed smart sensor operates efficiently during inrush conditions. The smart sensor presents high-speed processing despite its simplicity and low computational cost.

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Electronically enhanced current transformers (EECT) have gained much interest in power quality assessment. Their magnitude and phase angle error, which mainly relates to the properties of the ferromagnetic materials used, the impedance of the secondary load, and the inter-turns capacitance, are thoroughly analyzed. In contrast, the capacitance between the windings, i.e., inter-winding capacitances and their limiting effects on EECT operation, are rarely analyzed in detail-in particular, no details on the control design of the assisting electronic unit, its tuning recommendations, or both are provided. In this paper, the capacitive coupling between indication and compensating winding of EECT with simplified feedthrough construction is analyzed thoroughly in terms of current ratio error and stability of the implemented configuration of the trans-conductance amplifier. The preliminary assumption about the adverse effect of the inter-winding capacitance shunting both ends of the original amplifier, composed of two series-connected inverting amplifier stages, was confirmed and resolved within a modified amplifier with the help of a simplified simulation model and was experimentally proven with measurements on a custom-built EECT prototype. Furthermore, the analyzed phenomena were linked to trans-conductance amplifier parameters, explicitly with its compensating networks, and summarized in their design guidelines. Throughout the paper, the EECT features obtained with original and modified amplifier designs are compared with the plain composite current transformer to demonstrate the benefits of the modified amplifier, especially its robustness against inter-winding capacitance variations.

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Objective. The aim of the presented study is to evaluate the dose response of the PTB's secondary standard system, which is based on alanine and electron spin resonance (ESR) spectroscopy measurement, in ultra-high-pulse-dose-rate (UHPDR) electron beams.Approach. The alanine dosimeter system was evaluated in the PTB's UHPDR electron beams (20 MeV) in a range of 0.15-6.2 Gy per pulse. The relationship between the obtained absorbed dose to water per pulse and the in-beamline charge measurement of the electron pulses acquired using an integrating current transformer (ICT) was evaluated. Monte Carlo simulations were used to determine the beam quality conversion and correction factors required to perform alanine dosimetry.Main results. The beam quality conversion factor from the reference quality60Co to 20 MeV obtained by Monte Carlo simulation, 1.010(1), was found to be within the standard uncertainty of the consensus value, 1.014(5). The dose-to-water relative standard uncertainty was determined to be 0.68% in PTB's UHPDR electron beams.Significance. In this investigation, the dose-response of the PTB's alanine dosimeter system was evaluated in a range of dose per pulse between 0.15 Gy and 6.2 Gy and no evidence of dose-response dependency of the PTB's secondary standard system based on alanine was observed. The alanine/ESR system was shown to be a precise dosimetry system for evaluating absorbed dose to water in UHPDR electron beams.

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High-frequency current transformers (HFCT) are widely used to measure fast transient current. Their advantages are simple structure and relatively moderate price. Their lower and upper bandwidth are limited, but the HFCT can be easily applied to many measuring applications in power electronics. The disadvantages of HFCT are substantial dimensions and a large weight. The paper proposes a system of a cascade connection of two transformers, which allows us to reduce these disadvantages. The properties of such an HFCT combination were investigated and described. In the article, the expression for double current transformer transmittances is derived. The frequency response of the sensor was determined, and the results were verified in a practical arrangement. An experimental setup of a cascade CT connection was made and tested, allowing for fast-changing signals in transients to be measured. This paper presents the theoretical basis and results of laboratory work on a wide range of static and dynamic tests of the proposed sensor.

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Facing a lack of high accuracy current standards in the calibration of AC (Alternating Current) + DC (Direct Current) measurement devices that function to measure DC and AC simultaneously, a measurement method with high accuracy is proposed based on zero-flux self-oscillating fluxgate. An iron core and two windings are added onto the single-iron-core double-winding structure of the traditional self-oscillating fluxgate. The added iron core and its upper winding are used to weaken the influence of ripple on the sensor's accuracy. The other one of the added windings is used for the feedback from the AC+DC magnetic potential, allowing the sensor to work in a zero-flux state and to measure AC+DC simultaneously. An AC+DC transducer prototype with an AC ranging from 0-500 A and DC 0-300 A is developed by selecting the core parameters and an optimized design of the circuit. The test results of the prototype show that the prototype can measure the AC and DC simultaneously, and the measurement accuracy reaches class 0.05 level in the nominal current range. This transducer can be used as a calibration standard of measurement devices for AC only, DC only, or AC and DC simultaneously. Compared with the AC+DC current transducer with the same accuracy level, the proposed transducer has fewer cores and simpler measuring circuit.

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PURPOSE: The Oriatron eRT6 is a linear accelerator (linac) used in FLASH preclinical studies able to reach dose rates ranging from conventional (CONV) up to ultrahigh (UHDR). This work describes the implementation of commercially available beam current transformers (BCTs) as online monitoring tools compatible with CONV and UHDR irradiations for preclinical FLASH studies. METHODS: Two BCTs were used to measure the output of the Oriatron eRT6 linac. First, the correspondence between the set nominal beam parameters and those measured by the BCTs was checked. Then, we established the relationship between the total exit charge (measured by BCTs) and the absorbed dose to water. The influence of the pulse width (PW) and the pulse repetition frequency (PRF) at UHDR was characterized, as well as the short- and long-term stabilities of the relationship between the exit charge and the dose at CONV and UHDR. RESULTS: The BCTs were able to determine consistently the number of pulses, PW, and PRF. For fixed PW and pulse height, the exit charge measured from BCTs was correlated with the dose, and linear relationships were found with uncertainties of 0.5 % and 3 % in CONV and UHDR mode, respectively. Short- and long-term stabilities of the dose-to-charge ratio were below 1.6 %. CONCLUSIONS: We implemented commercially available BCTs and demonstrated their ability to act as online beam monitoring systems to support FLASH preclinical studies with CONV and UHDR irradiations. The implemented BCTs support dosimetric measurements, highlight variations among multiple measurements in a row, enable monitoring of the physics parameters used for irradiation, and are an important step for the safety of the clinical translation of FLASH radiation therapy.

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Current measurements from electromagnetic current transformers are essential for the construction of secondary circuit systems, including for protection systems. Magnetic core of these transformers are at risk of saturation, as a result of which maloperation of protection algorithms can possibly occur. The paper considers methods for recovering a current signal in the saturation mode of current transformers. The advantages and disadvantages of methods for detecting the occurrence of current transformers core saturation are described. A comparative analysis of mathematical methods for recovering a current signal is given, their approbation was carried out, and the most promising of them was revealed. The stability and sensitivity of recovery methods were tested by adding white noise to the measured signal and taking into account the initial flux density (remanent magnetization) in the current transformers core. Their comparison is given on the basis of angular, magnitude, and total errors at a given simulation interval.

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In this paper, open loop and closed loop Tunneling Magnetoresistance (TMR) DC Current Transformers (DCCTs) for ion beam diagnostics are presented. The DCCTs employ MR sensors to measure the DC component of the accelerator's ion beam. A comparative study between Giant Magnetoresistance (GMR) and TMR sensors is presented to illustrate the sensor selection criterion for the DCCT application. The two proposed DCCTs are studied in open and closed loop configurations. A closed loop feedback electronic system is designed to generate a feedback current equivalent to the ion beam current such that the sensor operates at zero flux. Furthermore, theoretical and experimental results for the TMR-based DCCT including noise analysis are presented for both open loop and closed loop configurations. Both configurations' minimum detectable currents are in the range of microampere. The proposed closed loop hardware prototype has a settling time of less than 15 µs. The measured minimum detectable currents for the open and closed loop TMR-based DCCTs are 128.2 µA/Hz and 10.14 µA/Hz at 1 Hz, respectively.

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In the last decade, we observed a noticeable increase in direct-current systems (DC), particularly in solar power generation, grid storage systems, and electric mobility. Some of these systems may require high-voltage isolation and peak currents in excess of kA. The existing standard compact and lower cost current sensing solutions hardly ever achieve an overall measurement uncertainty below 1% mainly due to offsets and hysteresis; their typical bandwidth is about 250 kHz, and they may also be noisy. This article presents a new method of isolated DC and AC current measurement based on a single gapless core and the innovative Platise Flux Sensor. After verification in a mixed-signal simulator, the method was implemented in a functional prototype of a DC current transducer (CT) and thoroughly tested in a reference setup. The performance tests showed a low offset and hysteresis, a bandwidth in the MHz range, low power consumption, and low noise operation. Furthermore, the low current transducer achieved a typical uncertainty of less than 0.2% and a linearity of less than 200 ppm, which indicates an overall superior performance compared to representative comparable CTs based on alternative technologies. In addition to the areas of application mentioned above, the new type of DC-CT can be used for general purpose metering, measurement instrumentation, and high power DC and AC systems.

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The research in this paper consists of practical experimentation on a gas insulated section of high voltage equipment filled with carbon dioxide and technical air as a direct replacement to sulphur hexafluoride (SF6) and analyses the results of PD measurement by way of internal UHF sensors and external HFCTs. The results contribute to ongoing efforts to replace the global warming gas SF6 with an alternative such as pure carbon dioxide or technical air and are applicable to mixtures of electronegative gases that have a high content of buffer gas including carbon dioxide. The experiments undertaken involved filling a full-scale gas insulated line demonstrator with different pressures of CO2 or technical air and applying voltages up to 242 kV in both clean conditions and particle contaminated conditions. The results show that carbon dioxide and technical air can insulate a gas section normally insulated with SF6 at phase-to-earth voltage of 242 kV and that both HFCT and UHF sensors can be used to detect partial discharge with natural gases. The internal UHF sensors show the most accurate PD location results but external HFCTs offer a good compromise and very similar location accuracy.

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With the spread of new Low-Power Instrument Transformers (LPITs), it is fundamental to provide models and characterization procedures to estimate and even predict the LPITs' behavior. In fact, distribution system operators and designers of network models are looking for all forms of information which may help the management and the control of power networks. For this purpose, the paper wants to contribute to the scientific community presenting a smart characterization procedure which easily provides sufficient information to predict the output signal of a Low-Power Current Transformer (LPCT), the Rogowski coil. The presented procedure is based on a synthetized signal applied to the Rogowski coil. Afterwards, the validity of the procedure is assessed within the Matlab environment and then by applying it on three off-the-shelf Rogowski coils. Simulations and experimental tests and results involving a variety of distorted signals in the power quality frequency range and by adopting a quite simple measurement setup demonstrated the effectiveness and the capability of the procedure to correctly estimate the output of the tested device.

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This paper describes a simplified model and a generic model of high-frequency current transformer (HFCT) sensors. By analyzing the models, a universal charge estimation method based on the double time integral of the measured voltage is inferred. The method is demonstrated to be valid irrespective of HFCT sensor, assuming that its transfer function can be modelled as a combination of real zeros and poles. This paper describes the mathematical foundation of the method and its particularities when applied to measure nanosecond current pulses. In practice, the applicability of the method is subjected to the characteristics and frequency response of the sensor and the current pulse duration. Therefore, a proposal to use the double time integral or the simple time integral of the measured voltage is described depending upon the sensor response. The procedures used to obtain the respective calibration constants based on the frequency response of the HFCT sensors are explained. Two examples, one using a HFCT sensor with a broadband flat frequency response and another using a HFCT sensor with a non-flat frequency response, are presented.

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Nowadays, non-toroidal shape primary pass-through current transformers are commonly used for large current machines with several cables per phase. As these transformers exhibit no radial symmetry, it is not clear if they can be tested using the indirect test described in the IEC 61869 standard. In order to answer this question, two non-toroidal shaped current transformers of different secondary winding designs have been tested and simulated. One transformer has a uniformly distributed secondary winding and the other has a partially distributed secondary winding. Both transformers have the same nameplate characteristics. Both perform correctly in the indirect test. However, only the transformer with the uniformly distributed secondary winding performs correctly in a direct test. A finite element simulation shows that the iron core of the partially distributed secondary winding transformer was saturated, while the iron core of the uniformly distributed one was not. This result explains their different performance. The main conclusion is that the indirect test is not sensitive enough to cover all cases and therefore under doubtful situations, the transformers should be tested using the direct test.