Equivalent Current Source Research Articles

3D modeling of deep borehole electromagnetic measurements with energized casing source for fracture mapping at the Utah Frontier Observatory for Research in Geothermal Energy

AbstractWe present a 3D numerical modelling analysis evaluating the deployment of a borehole electromagnetic measurement tool to detect and image a stimulated zone at the Utah Frontier Observatory for Research in Geothermal Energy geothermal site. As the depth to the geothermal reservoir is several kilometres and the size of the stimulated zone is limited to several 100 m, surface‐based controlled‐source electromagnetic measurements lack the sensitivity for detecting changes in electrical resistivity caused by the stimulation. To overcome the limitation, the study evaluates the feasibility of using a three‐component borehole magnetic receiver system at the Frontier Observatory for Research in Geothermal Energy site. To provide sufficient currents inside and around the enhanced geothermal reservoir, we use an injection well as an energized casing source. To efficiently simulate energizing the injection well in a realistic 3D resistivity model, we introduce a novel modelling workflow that leverages the strengths of both 3D cylindrical‐mesh‐based electromagnetic modelling code and 3D tetrahedral‐mesh‐based electromagnetic modelling code. The former is particularly well‐suited for modelling hollow cylindrical objects like casings, whereas the latter excels at representing more complex 3D geological structures. In this workflow, our initial step involves computing current densities along a vertical steel‐cased well using a 3D cylindrical electromagnetic modelling code. Subsequently, we distribute a series of equivalent current sources along the well's trajectory within a complex 3D resistivity model. We then discretize this model using a tetrahedral mesh and simulate the borehole electromagnetic responses excited by the casing source using a 3D finite‐element electromagnetic code. This multi‐step approach enables us to simulate 3D casing source electromagnetic responses within a complex 3D resistivity model, without the need for explicit discretization of the well using an excessive number of fine cells. We discuss the applicability and limitations of this proposed workflow within an electromagnetic modelling scenario where an energized well is deviated, such as at the Frontier Observatory for Research in Geothermal Energy site. Using the workflow, we demonstrate that the combined use of the energized casing source and the borehole electromagnetic receiver system offer measurable magnetic field amplitudes and sensitivity to the deep localized stimulated zone. The measurements can also distinguish between parallel‐fracture anisotropic reservoirs and isotropic cases, providing valuable insights into the fracture system of the stimulated zone. Besides the magnetic field measurements, vertical electric field measurements in the open well sections are also highly sensitive to the stimulated zone and can be used as additional data for detecting and imaging the target. We can also acquire additional multiple‐source data by grounding the surface electrode at various locations and repeating borehole electromagnetic measurements. This approach can increase the number of monitoring data by several factors, providing a more comprehensive dataset for analysing the deep‐localized stimulated zone. The numerical analysis indicates that it is feasible to use the combination of the energized casing and downhole electromagnetic measurements in monitoring localized stimulated zone at large depths.

Stability Analysis of Autonomous Microgrid Operated at Constant-Frequency with the Consideration of Reactive Power Balance

Large-scale autonomous microgrids have potential application values as they can increase renewable energy penetration level without compromising the stability of the existing large power systems. Before their widespread implementation, critical issues like stability analysis etc need to be solved. This paper analyses the stability in an autonomous microgrid operated at constant frequency with the consideration of reactive power balance. Difference equations of reactive power for the grid-forming generator are constructed separately from those for the grid-supporting and grid-feeding generators while the difference equations of the real power for all the generators are the same. For the voltage source inverter with its current controlled by proportional resonant controller, at the fundamental frequency, its output current is disentangled from its terminal voltage and is controlled to trace its reference accurately, namely . Therefore, each inverter can be modelled as an equivalent current source and the equivalent circuits for d-component and q-component can be separated from each other. Then, the nodal equations in matrix form for the microgrid system can be established readily. With these, the system level state-space equations are built to study the distribution of eigenvalues. By choosing proper coefficients for real power and reactive power reference generations and controller’s parameters, one can make all the eigenvalues falling in the left-hand-side of the complex plane. Therefore, the system is stable. Such a research paves the way for systematically searching good sets of coefficients and controller’s parameters which make system operate safely away from unstable region with necessary margin.

Deep learning based source reconstruction method using asymmetric encoder–decoder​ structure and physics-induced loss

This paper proposes a novel deep learning (DL) based source reconstruction method (SRM). The proposed DL-based SRM employs the deep convolutional asymmetric encoder–decoder structure (DCAEDS), which only demands one-time single-frequency far-field measurement on EM scattered field as its input and further predicts the equivalent source on target scatterers. During the offline training, an EM scattering simulator is designed to compute EM scattered field originated from the predicted equivalent source on target scatterers. The DCAEDS is combined with the EM scattering simulator to optimize the loss function, including two parts: (1) Data-induced loss, which directly evaluates the difference between the prediction of the proposed DCAEDS and the true-labelled equivalent source of target scatterers; (2) Physics-induced loss, which evaluates the difference between received EM scattered field and the computed EM scattered field originated from the prediction of DCAEDS. Moreover, the proposed DL-based SRM can overcome the limitation of conventional methods, involving high computation cost and strong ill-conditions. Consequently, the proposed DL-based SRM can realize the reconstruction of the equivalent current source with higher accuracy and lower computation complexity. Numerical examples illustrate the feasibility of the proposed DL-based SRM, which opens the new path for DL-based EM computation approaches.

Direct Estimation of Equivalent Bioelectric Sources Based on Huygens' Principle.

An estimation of the electric sources in the heart was conducted using a novel method, based on Huygens' Principle, aiming at a direct estimation of equivalent bioelectric sources over the heart's surface in real time. The main scope of this work was to establish a new, fast approach to the solution of the inverse electrocardiography problem. The study was based on recorded electrocardiograms (ECGs). Based on Huygens' Principle, measurements obtained from the surfaceof a patient's thorax were interpolated over the surface of the employed volume conductor model and considered as secondary Huygens' sources. These sources, being non-zero only over the surface under study, were employed to determine the weighting factors of the eigenfunctions' expansion, describing the generated voltage distribution over the whole conductor volume. With the availability of the potential distribution stemming from measurements, the electromagnetics reciprocity theorem is applied once again to yield the equivalent sources over the pericardium. The methodology is self-validated, since the surface potentials calculated from these equivalent sources are in very good agreement with ECG measurements. The ultimate aim of this effort is to create a tool providing the equivalent epicardial voltage or current sources in real time, i.e., during the ECG measurements with multiple electrodes.

Virtual Admittance Feedforward Compensation and Phase Correction for Average-Current-Mode-Controlled Totem-Pole PFC Converters

This paper explores a current distortion problem in totem-pole bridgeless power factor correction (PFC) converters with average current mode (ACM) control. With in-depth modeling for the current and voltage loops, it was found that the current distortion is caused by the limited current loop bandwidth and input filter capacitor. These factors lead to the presence of a susceptance component in the input admittance, which degrades the power factor (PF) and total harmonic distortion (THD) of the PFC converter. To solve this problem, this paper proposes virtual admittance feedforward compensation (VAFC) and phase correction methods to adjust the input admittance to pure conductance. The VAFC can generate virtual admittance that compensates for susceptance components in the input admittance, while phase correction can generate an equivalent current source that offsets the current in input capacitors. Furthermore, a phase lock loop (PLL) is introduced to realize the VAFC, which reduces the feedforward interference caused by input voltage sampling noise. Finally, an experimental prototype was built to verify the effectiveness of the proposed strategies. According to the test results, the proposed compensation strategy improves the PF by 1.23%, while reducing the THD by 2.52% and achieving a peak efficiency of 98.69%.

An Analytical Model to Evaluate Well-Potential Modulation and Bipolar Amplification Effects

An analytical model to evaluate well potential modulation and the resulting bipolar amplification effects was proposed and integrated into circuit-level simulation approach in this paper. The key point was to produce equivalent resistance network and current source between N-well and P-well, so that well potential modulation at arbitrary points could be estimated. It was shown that the simulation results reflected the contribution of bipolar amplification effects and the influence of well contact placement. The simulated cross sections were consistent with those of heavy ion experimental data, highlighting the reasonableness of the proposed model.

고조파원의 등가 전류원 모델 추정에 기반한 고조파 전류 기여도 평가

This paper presents a method for evaluating harmonic contributions to current distortion injected into a utility system from multiple harmonic sources at the point of common coupling (PCC). For effective harmonic management, it is necessary to identify harmonic sources and to evaluate their contribution to harmonic current distortion. Basically, to evaluate the harmonic contribution, the equivalent current source model of each harmonic source is required. The proposed method estimates the harmonic current source and impedance parameters of the equivalent model using the data measured at PCC and the recursive least squares (RLS) algorithm with variable forgetting factor. The harmonic current contribution can be also evaluated using the principle of current superposition with the estimated harmonic equivalent current model. The performance of equivalent model parameter estimation and harmonic contribution evaluation of the proposed method was analyzed through a case study using the PSCAD/EMTDC test system.

On-Chip Power Integrity Simulation Using LSI-Core Macromodels Considering Voltage Fluctuations Caused by Inter-Function-Block Interference

When designing on-chip power distribution networks (PDNs) of a large-scale integrated circuit (LSI), power integrity (PI) must be ensured not to cause malfunctions. LSI-core macromodels are expected to be used for fast PI simulation. When building LSI-core macromodels from design information, the impedance and equivalent current sources are often extracted for each function block or smaller operating block. In the stage of modeling function blocks, the layout and operation of the surrounding function blocks are not fixed, so equivalent current sources of the macromodel of each function block are extracted under ideal power supply conditions. However, in an actual LSI, the on-chip PDNs have a certain impedance and the power supply voltage of each function block is not ideal dc voltage because of its own operation and the interference from the operation of surrounding function blocks in the same power domain. Since operating currents of transistors are affected by on-chip supply voltage fluctuations, this effect must be taken into account when simulating the PI of the entire LSI or the simulation accuracy will degrade. This article proposes a PI simulation method using LSI-core macromodels that takes into account on-chip supply voltage fluctuations due to the interference between function blocks in the same power domain. To verify the proposed method, a test chip with several function blocks was built, and it was confirmed that the proposed method can simulate PI with high accuracy.

A Fine Modified Calculation Model with Experimental Verification for the Holding Force of the Permanent Magnet

For the common technical applications of permanent magnets such as cylindrical and rectangular permanent magnets, the formula of the holding force, which is based on the idea of equivalent current source and associated with Lorentz force, is fine modified with introducing two parameters, the chamfer size of the magnet and the thickness of the outer protective film. Furthermore, the model is verified by external experimental data. The accuracy of our proposed model has been significantly improved compared to the base model, with an average improvement of 6.3 %. With external data, the average error of the refined model is within 6 %. Compared to other currently available online calculators, our calculation model offers superior calculation accuracy.

Wide-Area backup protection against asymmetrical faults in the presence of renewable energy sources

Conventional protection schemes have essentially been developed for power systems dominated by synchronous generators. High penetration of power-electronic interfaced renewable energy sources (PEIRESs) can adversely impact the reliability of protection systems, thereby increasing the risk of widespread disturbances. This paper proposes a robust wide-area backup protection (WABP) scheme against asymmetrical faults for transmission systems with high penetration of renewables. The scheme exploits the full potential of available synchrophasors without placing any rigid constraints on PMU locations. To this end, the faulted line and a few appropriately selected PEIRESs are replaced by equivalent current sources using the Substitution Theorem. The remaining PEIRESs are substituted by their equivalent impedances accounting for their response to a fault, considering the control strategies and overcurrent limits of these PEIRESs. This results in a linear system of equations whose solution readily indicates the faulted line on account of the weighted sum of squared residuals (WSSR) concept. To add to the security of the proposed scheme, the fault distance on the pinpointed line is also calculated and checked to ensure it lies within the acceptable range. A total of more than 80,000 simulations conducted on the IEEE 39-bus test system verify that the proposed scheme performs properly irrespective of the numbers/locations of PEIRESs and their control strategies.

Compensating Method of Equivalent Current Sources of LSI-Core Macromodel Considering Voltage Fluctuations in On-Chip Power Distribution Network

Electro-magnetic compatibility (EMC) macromodels of a large-scale integrated (LSI) circuit core have been proposed to predict conducted RF emission and power integrity issues not only on a printed circuit board but also inside an LSI. They are equivalent circuit models that consist of lumped element impedance blocks of an LSI-core and equivalent current sources expressing internal switching activities. In conventional macromodeling, equivalent current sources have been extracted under ideal power supply conditions, i.e., with constant supply voltage. However, there exists transient supply voltage fluctuations in an actual on-chip power distribution network (PDN), and the operating current and its equivalent current sources are expected to vary with such fluctuations. Such issues with transient supply voltage fluctuations have not been extensively investigated. We propose a method of compensating the equivalent current sources of a macromodel by introducing amplitude and time correction factors, taking into account the voltage fluctuations in an on-chip PDN.

A Transfer Function Method to Calculate Radiation of Sources With Stochastic Signals

Standardized radiation measurements can be simulated by various numerical or analytical approaches. In this article, a transfer function method is proposed for a fast and accurate antenna voltage prediction. Assuming that the interference source can be characterized as a linear Norton equivalent current source, its internal admittances and source currents are determined from measurements made with a vector network analyzer and an oscilloscope. The setup of the radiation measurement is described as a transfer function using its scattering parameters. A system of equations is set up with the multiport theory and solved for the antenna voltage, which is fed into a spectrum analyzer model. The result is compared to a measurement in a fully anechoic chamber. The method is extended to interference sources with stochastic signals, and, in the course of this, an approach for the estimation of the radiation measurement is developed. A dc motor is used as an application example.

Transient behaviors and mathematical model of proton exchange membrane electrolyzer

The transient characteristics of proton exchange membrane water electrolysis for hydrogen production are crucial for the study of the load control and durability of the electrolyzer under the fluctuating conditions of renewable energy sources. In this study, a dynamic model of the electrolyzer is established based on various equivalence theories used to describe the transient characteristics of the electrolyzer during operation. Differential-equation-based transient models of the RC (resistance and capacitance) equivalent circuit and the equivalent controlled current source, their advantages and disadvantages, and their typical transient response spectra are presented. Among these, the graphical method based on the polarization curve is recommended because it has the advantages of intuitive and simple expression and can help researchers precisely and efficiently predict the response form and time of current or voltage using various control methods. The transient characteristics of the shutdown process reflect electrochemical processes similar to those of fuel cells in the electrolyzer during the OCV (open circuit voltage) period. The performance of the transient process is related to the structure of the electrolyzer and the operating conditions of the measurement. Low-voltage sustenance with manual intervention following shutdown may have a positive effect on the durability of the electrolyzer.

Distributed Nonlinear Model and Fast Analysis for In-Band IMD3 Prediction of Surface Acoustic Wave Resonators.

The motivation of this work is to analyze the in-band intermodulation distortion (IMD) occurring in surface acoustic wave (SAW) devices, using a recently developed fast method based on the input-output equivalent sources (IOES). The method calculates the equivalent current sources of a given harmonic (H) or IMD, which when applied at the boundaries of any uniform nonlinear region produce the same nonlinearities as the full distributed circuit. The accuracy of the method is validated with a very simplified SAW resonator with ten digits, which is modeled by a discretized Mason-based circuit. The IOES method provides equal results to the ones obtained through harmonic balance (HB) simulations, performed by means of commercial software, being the first 1000 times faster. Once the accuracy of the method is guaranteed, it is used to analyze the measured in-band IMD3 of several lithium tantalite 42° cut leaky SAW (LSAW) resonators with different pitches and duty factors at the B66 long term evolution (LTE) frequency band. Those resonators are comprised of 100 and 20 electrode pairs for the active region and each of the reflectors, respectively, which implies the analysis of a very large distributed nonlinear problem with thousands of nonlinear local sources. The IOES method takes 35.4 s in simulating 51 frequency points, whereas this simulation is not possible using a commercial HB simulator on a general-purpose computer.

Analysis of the influence factors of VSC–HVDC on AC three-phase short-circuit current level

PurposeThis paper aims to clarify voltage sourced converter’s (VSC’s) influence rules on the alternating current (AC) short-circuit current and identify the key factors, so as to propose the short-circuit current suppression strategy.Design/methodology/approachThis paper investigates the key factors which impact the short-circuit current supplied by the VSC based on the equivalent current source model. This study shows that the phase of the VSC equivalent current source is mainly affected by the type of fault, whereas the amplitude is mainly decided by the control mode, the amplitude limiter and the electrical distance. Based on the above influence mechanism, the dynamic limiter with short-circuit current limiting function is designed. The theoretical analysis is verified by simulations on PSCAD.FindingsThe short-circuit current feeding from VSC is closely related to the control mode and control parameters of the VSC, fault type at AC side and the electrical distance of the fault point. The proposed dynamic limiter can make VSC absorb more reactive power to suppress the short-circuit current.Research limitations/implicationsThe dynamic limiter proposed in this paper is limited to suppress three-phase short-circuit fault current. The future work will focus more on improving and extending the dynamic limiter to the fault current suppression application in other fault scenarios.Practical implicationsThe research results provide a reference for the design of protection system.Originality/valueThe key influence factors are conducive to put forward the measures to suppress the fault current, eliminate the risk of short-circuit current exceeding the standard and reduce the difficulty of protection design.

Mechanical impact of electromagnetic transients on the European DEMO divertor. Part 1: Vertical displacement event

This paper presents the study of the forces and moments expected on the European DEMO divertor, due to the fast electromagnetic transients associated to plasma instabilities events. A 3D Magneto-Quasi-Static (MQS) model is here adopted to solve such a problem, implemented in Ansys EMAG. A hybrid modelling approach is proposed, that can be placed between a pure global model (where the divertor is modelled along with all the external passive and active components) and a local one, where only the divertor is present in the model and the external world is represented through equivalent boundary conditions (submodelling). Indeed, the model proposed here includes a detailed description of all the divertor components (cassettes, targets, liner, cooling pipes, etc..) and a coarser description of the main passive external components (vessel, blanket, rails, etc..). The active components (coils and plasma currents) are instead replaced by suitable equivalent current sources and by a known equilibrium magnetic field. The analysis is here carried out with reference to one of the most challenging events for the divertor, namely a downward directed Vertical Displacement Event. The forces and moments associated to the whole divertor and to its cooling subsystem are evaluated, and a sensitivity analysis is performed to check the impact of the choice of the materials to be used to realize the supports inside the divertor and between the divertor and the vacuum vessel.

Spatio-temporal analysis the results of solving the inverse problem of electrocardiography

The results of the development and testing an algorithm for the physiological interpretation the results of solving the inverse problem of electrocardiography are presented. The solution to the inverse problem of electrocardiography is the distributions of equivalent current sources on the quasi-epicardium, restored from the electric potentials created by the heart on the surface of the chest. The developed algorithms are based on the space-time analysis of the distributions of equivalent current sources on the quasi-epicardium. The development and testing of the algorithm was carried out using a simulation model of the electrical activity of the heart based on cellular automata. The efficiency of the algorithm has been demonstrated when simulating the electrical activity of the heart in normal conditions, as well as in the presence of pathological changes in the myocardium in the form of areas with delayed conduction of excitation.

Design of wideband end‐fire composite microstrip‐monopole antenna

This article introduces a wideband composite antenna with end-fire radiation. The structure is achieved by uniting a center-fed microstrip shorted patch and a parasitical monopole. The monopole is vertical to the substrate and work as an electric current source. Because the loaded monopole breaks the symmetry of the center-fed microstrip antenna, the original patch antenna can work as in-phase equivalent magnetic current sources radiation. Then complementary sources are generated by orthometric magnetic current source and electric current source. The typical unidirectional radiation capacity has a good endfire beam. The loaded monopole adds a resonant mode to the original microstrip antenna, which makes the composite microstrip-monopole antenna to exhibit an enhanced bandwidth of 26.9% and an average gain of 7.5 dBi. The complementary sources radiation mechanism can generate special unidirectional radiation patterns in a compact space, so this antenna type is an excellent candidate for array applications. The prototype's planar size is only 0.36λ0 × 0.39λ0 (λ0 is the free space wavelength in center frequency). The eight elements phased array with the proposed antenna show perfect simulated scanning performance.

The Input-Output Equivalent Sources Method for Fast Simulations of Distributed Nonlinearities in Bulk Acoustic Wave Resonators and Filters.

This work presents a new method to analyze weak distributed nonlinear (NL) effects, with a focus on the generation of harmonics (H) and intermodulation products (IMD) in bulk acoustic wave (BAW) resonators and filters composed of them. The method consists of finding equivalent current sources [input-output equivalent sources (IOES)] at the H or IMD frequencies of interest that are applied to the boundary nodes of any layer that can contribute to the nonlinearities according to its local NL constitutive equations. The new methodology is compared with the harmonic balance (HB) analysis, by means of a commercial tool, of a discretized NL Mason model, which is the most used model for NL BAW resonators. While the computation time is drastically reduced, the results are fully identical. For the simulation of a seventh-order filter, the IOES method is around 700 times faster than the HB simulations.

Research on Performance of Real-Time Simulation Based on Inverter-Dominated Power Grid

This paper proposes two methods to improve the performance in real-time simulation. The increased inverter-based generations are gradually shifting the operation of the power grid. Consequently, the investigation for the safe operation and further application is essential in the inverter-dominated power grid. As the simulated number of non-linear switch elements like inverter increases, the numerical complexity of the simulation model rises exponentially. Accordingly, the scale of the simulated power grid with inverters is normally constricted by taking account of the burdensome numerical calculation. The emerging of real-time simulator provides the opportunity to enable the simulation of the large-scale power grids. Nevertheless, the simulation boundary condition is still exceeded in the inverter-dominated model. Hence, the improvement of the performance to extend the limitation in real-time simulation is constituted in this paper. The first method proposed is co-simulation. This approach is to simulate the power grid and inverters by models in different deep levels. The phasor model and electrical-mechanical-transient model are utilized to develop the co-simulation model. The second method is network reduction. Based on the dynamic feature of the inverter, it is reduced to an equivalent current source, which decreases the complexity of the model and retains its characteristics. The evaluation of the methods is demonstrated by two indexes: real-time capability and the similarity degree.