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Abstract As the demand for high-capacity and energy-efficient wireless communications grows, the exploration of cost-effective and power-optimized hybrid digital-analog beamforming techniques for millimeter-wave massive MIMO systems has gained substantial traction. Adopting low-resolution phase shifters offers a more practical solution in terms of reducing power consumption and implementation costs. We investigate hybrid beamforming strategies for mmWave massive MIMO systems that employ low-resolution phase shifters, with a specific focus on designing and optimizing the analog beamforming component. To exploit the full potential of analog phase shifter network (APSN) in mmWave massive MIMO system while maintaining low-power consumption, we propose a two-layer APSN with low-resolution PSs to replace the conventional single-layer APSN with high-resolution PSs. Under the constraints imposed by the two-layer APSN hardware architecture, we propose a two-level codebook structure and an adaptive-weighted cross-entropy optimization algorithm that offers superior performance while substantially reducing the computational burden compared to the conventional cross-entropy optimization algorithm. We further develop two alternative schemes through the maximal gain harvest method to reduce complexity. We also investigate the case that only one steering vector is shared in the inner beamformer and present two low-complexity beamforming algorithms. Through simulations, the proposed two-layer APSN structure and the proposed algorithms have been shown to outperform existing methods, with notable effectiveness in scenarios where low-resolution phase shifters are utilized.

Abstract The rapid development of UAV communication technology makes it have application potential in wireless systems. However, for the optimization problem of UAV base station providing communication for ground personnel in the disaster area under special natural disasters, traditional deep reinforcement learning is used. Algorithms cannot solve such problems well. This article proposes the AD3QN algorithm combined with the attention mechanism, which can communicate with disaster victims on the ground better and more quickly, providing better information collection for rescue missions and completing the task of communication optimization. In the mission simulation environment, in order to make the environment more realistic, we innovatively designed the ground user distribution model, air-to-ground communication model, and electromagnetic interference model. Finally, the effect of the proposed algorithm is evaluated by comparing different deep reinforcement learning algorithms. The results show that the algorithm we proposed can provide communication services faster and has higher practicability in terms of algorithm.

Abstract An emerging paradigm in modern electronics is that of CMOS+ $${\mathsf{X}}$$ X requiring the integration of standard CMOS technology with novel materials and technologies denoted by $${\mathsf{X}}$$ X . In this context, a crucial challenge is to develop accurate circuit models for $${\mathsf{X}}$$ X that are compatible with standard models for CMOS-based circuits and systems. In this perspective, we present physics-based, experimentally benchmarked modular circuit models that can be used to evaluate a class of CMOS+ $${\mathsf{X}}$$ X systems, where $${\mathsf{X}}$$ X denotes magnetic and spintronic materials and phenomena. This class of materials is particularly challenging because they go beyond conventional charge-based phenomena and involve the spin degree of freedom which involves non-trivial quantum effects. Starting from density matrices—the central quantity in quantum transport—using well-defined approximations, it is possible to obtain spin-circuits that generalize ordinary circuit theory to 4-component currents and voltages (1 for charge and 3 for spin). With step-by-step examples that progressively become more complex, we illustrate how the spin-circuit approach can be used to start from the physics of magnetism and spintronics to enable accurate system-level evaluations. We believe the core approach can be extended to include other quantum degrees of freedom like valley and pseudospins starting from corresponding density matrices.

Abstract Spintronic sensors are uniquely positioned to deliver the next generation of high-performance magnetic field measurement tools with re-configurable key features. In this perspective article, we focus on giant and tunnel magnetoresistance sensors that exploit changes in the electrical resistance of thin films in response to an external magnetic field. We discuss strategies to address ongoing open challenges to improve operation limits. The goal is to meet current technological needs and thus expand the scope of existing applications. We also propose innovative approaches to design sensors with adaptable characteristics and embedded multifunctionality, aiming to create opportunities for future magnetic sensing applications. These solutions leverage the versatility of spintronic sensors, from the thin-film multilayers that form their building blocks, to device fabrication methods and potential integration with other technologies. The outlook of novel applications spans multiple areas, including electric vehicles, robotics, remote detection, or biomedicine.

Abstract The Covid-19 pandemic has significantly spurred the development of deep learning (DL) models for the pathology automatic diagnosis based on CT scan images. However, the assumption about the generalization of the proposed models remains to be assessed and shown for concrete clinical use. In this work, we have investigated the real value of widely used public datasets for the elaboration of DL models that are dedicated to automatic diagnosis of Covid-19 using CT scans. We have collected various international public datasets from 13 countries. Different Convolutional Neural Networks (CNNs) have been trained and their performances carefully assessed. Two evaluations have been conducted: (1) an internal evaluation following a cross-validation procedure, and (2) an external evaluation on real patients coming from new and different sources. The objective is to assess the generalization capabilities considering real-world conditions: different acquisition conditions, devices and configurations. Three families from the most effective CNN models have been selected (ResNet, DenseNet and EfficientNet). These have been fine-tuned, evaluated and used within a training methodology based on transfer learning. The most effective models have been further customized in order to create new models that are dedicated to the task at hand. These models have significantly improved the diagnosis performance.

Abstract A wearable microgrid that centralizes and distributes harvested energy across different body regions can optimize power utilization and reduce overall battery weight. This setup underscores the importance of developing cable-free wireless power transfer (WPT) systems for mobile and portable devices to eliminate the risks posed by wired connections, especially in dynamic and hazardous environments. We introduce a thin, stretchable, and safe hand band capable of watt-level wireless charging through the widely adopted Qi protocol operating at 130 kHz. The implementation of non-adhesive fabric encapsulation serves to protect the 50-μm-thin spiral copper antenna from mechanical strain, ensuring an overall hand band stretchability of 50%. We also create a stretchable “Ferrofabric”, characterized by a magnetic permeability of 11.3 and a tensile modulus of 75.3 kPa, that provides magnetic shielding for the antenna without compromising wearability. The “Ferrofabric” improves the coil inductance but induces core loss in AC application. By fully understanding and managing loss mechanisms such as the skin effect, proximity effect, core loss, and joule heating, we achieve a wireless charging efficiency of 71% and power delivery of 3.81 W in the kHz frequency range. Our WPT hand band is unobstructive to hand motion and can charge a handheld smartphone as fast as a desktop charger or power a battery-free chest-laminated e-tattoo sensor, with well-managed thermal and electromagnetic safety. Through a holistic electromagnetic, structural, and thermal design, our device culminates in a safe, rugged, and versatile solution for wearable WPT systems.

Abstract Electrocardiography (ECG) and photoplethysmography (PPG) are non-invasive methods used to quantify signals originating from the cardiovascular system. Although there is a strong correlation between the cycles of the two measures, the correlation between the waveforms has received little attention in research. Measuring the PPG is significantly simpler and more convenient compared to the ECG measure. Recent research has demonstrated that PPG signals can be utilized to rebuild the ECG signals, suggesting that healthcare professionals might acquire a comprehensive comprehension of patients' cardiovascular well-being by only measuring PPG. With the advancement of artificial intelligence, the deep learning model has made significant progress in reconstructing ECG signals from PPG signals. However, the quality of the reconstructed ECG signal is still in need of more enhancement. In order to enhance the quality of the reconstructed ECG signal, we propose an innovative hybrid attention-based bidirectional recurrent neural network (Bi-RNN) that incorporates a dilated convolutional neural network technique for the purpose of reconstructing ECG signals from PPG signals. This addresses issues that occur when standard dilated CNN (DCNN) models neglect the link between circumstances and dispersion of gradients. The suggested approach maximizes the utilization of the DCNN and Bi-RNN unit design to provide fusion features. In order to ensure the model's resilience to deformation, it is imperative to initially extract spatial properties utilizing convolutional neural networks (CNNs). Once we have obtained geographic data, we employ BiLSTM to extract temporal features. The proposed model is so-called hybrid attention-based CNN and BiLSTM (HA-CNN-BiLSTM). BiLSTM mitigates the issues of gradient vanishing and exploding while maintaining accuracy. To showcase the advantages of the suggested model, we conduct a comparison between HA-CNN-BiLSTM and each separate state-of-the-art method. The simulation results indicated that the proposed method yielded superior root mean square error (RMSE) when reconstructing the ECG signal across different optimizers. The results also demonstrated that the proposed method results in the lowest RMSE with SGDM optimizer which is 0.031.

Abstract With the development of brain–computer interfaces in recent years, deep learning models have been widely used in EEG-based personal identification. The training of complex models requires a large amount of data, but the acquisition of EEG signals is very time-consuming and energy-consuming. EEG data augmentation can reduce the overhead of EEG data acquisition and provide the data volume required by various complex models, which is conducive to applying EEG identification in practice. The generative adversarial network (GAN) has been applied to augment EEG data features. But the augmentation of temporal EEG signals is less studied. Therefore, this paper proposes a method of temporal EEG data augmentation based on an attention mechanism time series generative adversarial network (ATGAN), which can expand the original EEG dataset to facilitate the training of downstream deep learning classifiers. The experiment is conducted on the BCI Competition IV 2a dataset. The ATGAN model is trained with the temporal EEG signals after preprocessing, and the generated augmentation data by ATGAN is used to expand the original dataset. The accuracy of the EEG-based identification task on the augmented dataset is 7.78% higher than that on the original dataset, which proves the effectiveness of the proposed method.

Abstract Target identification of ship-radiated noise is a crucial area in underwater target recognition. However, there is currently a lack of multi-target ship datasets that accurately represent real-world underwater acoustic conditions. To tackle this issue, we conducted experimental data acquisition, resulting in the release of QiandaoEar22—a comprehensive underwater acoustic multi-target dataset. This dataset encompasses 9 h and 28 min of real-world ship-radiated noise data and 21 h and 58 min of background noise data. To demonstrate the availability of QiandaoEar22, we executed two experimental tasks. The first task focuses on assessing the presence of ship-radiated noise, while the second task involves identifying specific ships within the recognized targets in the multi-ship mixed data. In the latter task, we extracted eight features from the data and employed six deep learning networks for classification, aiming to evaluate and compare the performance of various features and networks. The experimental results reveal that ship-radiated noise can be identified from background noise in over 99% of cases. For the specific identification of individual ships, the optimal recognition accuracy achieves 99.56%. Finally, we found using spectrum and MFCC as feature inputs and DenseNet as classifier can achieve excellent recognition performance. Considering the computational efficiency, CRNN and ECAPA-TDNN are also good choices. Our work not only establishes a benchmark for algorithm evaluation but also inspires the development of innovative methods to enhance underwater acoustic target detection (UATD) and underwater acoustic target recognition (UATR).

Abstract In recent years, wide voltage range DC/DC converters have been widely used in telecom power, solar generation and electric vehicle charger applications. Based on this, a new multi‐resonant converter with wide input voltage is proposed here. Compared with the traditional LLC converter, the proposed converter can maintain the output voltage within a narrow frequency regulation range in both under‐resonance and over‐resonance areas. Thus, a wide voltage range can be realized without additional switch components or complex control strategies. The topology and the corresponding working principle of the proposed converter are introduced. In addition, the equivalent model by considering the fundamental wave is established and the influence of the resonance parameters on the voltage gain characteristic is analysed in detail. With these considerations, the resonance parameters are designed. Finally, a 500 W experiment platform is established to verify the effectiveness and feasibility of the proposed converter.

Abstract Modern power system networks are under statutory obligations to integrate renewable energy sources (RES). The primary reason is to meet ever‐increasing energy demand and also to curtail environmental pollution by greenhouse gases. However, the higher penetration of RES has the tendency of reducing inertia of overall power system network. Consequently, frequency stability is affected and deviates beyond allowable permissible limits leading to power blackouts, load shedding, and even total system failure. To address the issues associated with reduced inertia, an optimal control of hybrid energy storage system (HESS) has been proposed. HESS is basically a combination of battery and ultracapacitor, where ultracapacitor addresses rapidly varying power component by mimicking inertia while the battery compensates long‐term power variations. Thus, the HESS is effectively controlled to compensate the loss of inertia by regulating its energy flow. For the purpose of improved efficiency and better power management of the HESS, an improvised particle swarm optimization (MPSO)‐based virtual inertia control design has been proposed. The proposed MPSO is utilized to tune the gains of bidirectional dc–dc converter in such a way that improves frequency nadir with faster response to transient disturbances. This proposed method is simulated in MATLAB and its merits are validated in real time using hardware in loop. On analysing of the results, it can be observed that frequency nadir is improved by 48.96% with significant reduction in rate of change of frequency in comparison to conventional particle swarm optimization.

Abstract To solve the problems of difficulty in speed measurement and low accuracy of speed measurement of induction motor (IM) during fast starting, the electromagnetic field coupling circuit (EFCC) and open‐loop control of IM considering rapid speed change are proposed. First, the EFCC of IM is established through the stator circuit, air gap magnetic field circuit and rotor circuit, and the stator voltage and electromagnetic torque of the fast starting process are deduced from the air gap magnetic density on the basis of constant slip angular velocity, and then the open‐loop control method based on the EFCC is given. Finally, compared with the open‐loop control based on the TEC, the results of simulation and experiment show that the open‐loop control based on the EFCC can follow the acceleration starting more quickly and the starting current is smaller, which is conducive to reducing the cost of the drive.

Abstract This paper proposes a new control method for loss reduction of two series buck converters. The proposed method can be applied to each series of buck converters with two power switches. To enhance the efficiency of the converter compared to other structures, a method based on determining operating cycles for loss reduction is employed, leading to increased output efficiency of the converter. Additionally, to demonstrate the efficiency improvement using the proposed method compared to the conventional approach, the efficiency of converter is calculated through theoretical computations under real conditions, and the output results are compared for both losses and efficiency. In addition, the proposed high‐buck converter in this paper benefits from a common ground advantage and exhibits a suitable conversion ratio. The high‐buck converters are used in numerous applications for situations with low voltage and low power. The most important applications for these converters are the power supply for mobile phones, tablets, and other portable electronic devices, battery chargers, and LED drivers. Here, in order to demonstrate the validity of the proposed method, the MATLAB‐Simulink results are provided. Moreover, in order to show the feasibility of the high‐buck converter, a 100‐W prototype has been implemented and the experimental results are provided.

Abstract The linear power amplifier (LPA) suffers from low power supply utilization in the DC power supply mode, leading to reduced output efficiency. This paper constructs an efficient power supply mode based on closed‐loop dynamic power supply system (CLDPSs). The CLDPSs can generate a pair of bipolar dynamic power supplies based on a predetermined signal to provide power to LPA, which can maintain a small voltage drop between the power supply and the output of LPA, thereby improving the power supply utilization of LPA. In addition, the study also focuses on the conflicting relationship between the output ripple and the dynamic performance of the CLDPSs, for which a new parametric design of the LC filter circuit is proposed, aiming to achieve a balance between these two aspects. Finally, a voice coil motor driving platform is constructed for experimental testing. The results demonstrate that the output ripple and dynamic performance of the CLDPSs can be balanced. In comparison to the DC power supply mode, the CLDPSs power supply mode can enhance the efficiency of LPA by 2 times while the driving accuracy of voice coil motor is basically unchanged.

Abstract Finite control set model predictive control (FCS‐MPC) has been widely used in the control of three‐phase voltage source converter (VSC), but its control performance declines sharply at low sampling frequencies. This paper proposes an optimal control set expansion method with slip window selection and online parameter modification to improve the performance and robustness of FCS‐MPC. First, the performance of different control set expansion methods is compared. Then, an optimal control set expansion method that carries 12 virtual vectors is proposed. Last, a slip window selection strategy and an online parameter modification algorithm are proposed to reduce the computational burden and improve the controller's robustness respectively. Experimental result show that the proposed method significantly improves the control accuracy and carries good robustness and anti‐disturbance ability. Compared with existing typical MPC strategies, the proposed method obtains better current quality with lower switching frequency and requires less calculation. Moreover, the design of the proposed method is simple and there is no weighting factor to be tuned, which increases the method's practicality.

Abstract This paper investigates and technically demonstrates a capacitive power transfer (CPT) system applicable to the charging of emerging very‐low‐power portable devices. The constant‐current operation of the primary LCL compensation in CPT is implemented and analysed to simplify the system design process and minimize the configuration on the receiving side. Additionally, the system design considerations for the capacitive coupler and the diode rectifier are presented based on the battery charging specifications. All the design concepts and considerations are validated through experimentation with a 13.56 MHz CPT system, which achieves load‐independent constant‐current output from full‐load to light‐load (one‐tenth of the full load) charging operations.

Abstract In the traditional predictive torque control strategy, the cost function considers two different control objectives: stator flux and torque. Therefore, it is necessary to reasonably set the weighting factor to ensure that the optimal voltage vector is accurately selected during the control process, thereby achieving better torque and flux control performance. In view of the complex tuning process caused by traditional predictive torque control setting method of weighting factor, a new weighting factor selection method for permanent magnet synchronous motor control system is proposed in this paper. The derivation process is based on the equivalent transformation between the torque–flux prediction and the voltage vector prediction. If both the cost functions of the torque–flux and voltage vector reach their minimum values, the same output voltage vector will be selected. Compared with previous studies, the algorithm proposed in this paper can find the precise location of the optimal weighting factor without changing the form of the cost function, which simplifies the parameter tuning process. Experimental results are also provided to validate the effectiveness of the proposed algorithm.

Abstract This article details the design process for a new three‐phase coil array. All of the coils are made to be mutually decoupled from one another which is achieved by introducing a high reluctance path in the ferrite structure for mutual flux using an airgap in addition to controlling the coil overlap. Simulation and experimental results of a matched three‐phase primary and secondary coupler, designed using the proposed novel decoupling mechanism, are presented to show that the high reluctance path introduced to decouple the coils still allows the main couplings to be maintained within an acceptable range. In contrast, negligible interphase couplings between coils in the primary or secondary were observed. Effective coupling, voltage and uncompensated power measurements are shown to verify the design is able to meet SAE J2954 WPT3 requirements. Finally, the leakage magnetic flux density, simulated under WPT3 conditions, shows that its RMS value remains significantly less than 27 µT at a 800 mm distance from the centre of the secondary coupler.

Abstract Series connection of Silicon Carbide (SiC) Metal‐Oxide‐Semiconductor Field‐Effect Transistors (MOSFETs) is an interesting solution to design switches for voltages that are not yet commercially available or limited for single‐die devices. However, inherent static and dynamic voltage balancing must be achieved. Voltage imbalance is caused by the device parameters spread, whose impact is pronounced in low‐inductive circuit layouts. This study investigates the optimal design and tuning limits of resistor‐capacitor (RC)‐snubber circuits and non‐adaptive, standard, voltage‐source gate drivers for achieving the best balancing in transient and steady‐state voltage distributions among series‐connected discrete SiC MOSFETs operating at speeds up to 90kV/μs. It has been shown that a larger parameter mismatch will lead to uneven switching energy losses and larger voltage imbalances. It was also experimentally shown that increasing the gate resistor to slow down the devices will not always improve balancing when their parameter spread is large. Thus, tuning recommendations for the RC‐snubber circuit and gate driver were developed based on these findings.

Abstract For the purpose of enhancing the performance of interior permanent magnet synchronous motors (IPMSMs) sensorless control, a flux observer based on a third‐order generalized integrator with enhanced frequency‐locked loop (TOGI‐EFLL) is introduced in this paper. Compared with the traditional second‐order generalized integrator with frequency‐locked loop (SOGI‐FLL), the proposed TOGI‐EFLL can effectively mitigate the direct current (DC) bias stemming from non‐ideal factors, such as the inverter non‐linearities and detection errors, without introducing additional parameters. Initially, the active flux observer model and the limitations of the conventional SOGI‐FLL are presented. Subsequently, the proposed flux observer based on TOGI‐EFLL has been intensively investigated. Furthermore, the design of the damping factor and the digital implementation of the algorithm are developed to ensure seamless integration into digital systems. Finally, the effectiveness of the proposed sensorless control strategy is validated through the comprehensive experimental results.

Abstract This paper presents an innovative adaptive strategy implemented in wireless power transmission (WPT) systems to overcome efficiency challenges due to coupling structure misalignment and load variability. A novel versatile transmitter, capable of alternating between single and dual voltage source states via two MOSFETs has been designed. Initially, the system operates in a single voltage source mode, mutual inductance and load characteristics are pinpointed using a particle swarm optimization algorithm. Subsequently, the system transitions to dual voltage source mode, where it fine‐tunes the auxiliary voltage source's amplitude and phase based on the determined mutual inductance and load values to realize zero phase angle for optimal impedance matching. The experimental results show that this method can obviously improve the output power of WPT system. This method stands out for its simplicity, adaptability and rapid response, suggesting its potential for practical use in dynamic charging applications.

Abstract Under the condition of weak grid, the phase‐locked loop (PLL) is one of the main reasons for the sub‐synchronous oscillation of the grid‐connected inverter. Therefore, it is necessary to identify the PLL parameters of the grid‐connected inverter for the analysis of the inverter operating performance. This paper uses the sequence impedance model and measured impedance data of grid‐connected inverter to construct the identification function for parameter identification of PLL, and the function is calculated by particle swarm optimization algorithm to overcome the nonlinear problem of sequence impedance model. In addition, the identification frequency band is selected based on PLL parameter sensitivity to improve the parameter identification accuracy under the same impedance measurement error. At different frequencies, the positive correlation between the sensitivity of the PLL parameters and the identification accuracy is proven to determine the definite frequency band for PLL parameter identification of grid‐connected inverter. Finally, the feasibility and effectiveness of the above research are verified by simulation and semi‐physical experiments.

Abstract The active power control of photovoltaic (PV) inverters without energy storage can flatten the fluctuating power and support the voltage amplitude and frequency of the grid. When operated in grid‐forming voltage‐control mode, because the PV power can change rapidly and widely, the PV inverter needs to track the power commands quickly and precisely. Traditionally, this goal is achieved with the estimation of PV power curve or PI‐based multiple‐loop feedback control, where flexibility, availability and accuracy are not satisfactory. Therefore, a CC/VC‐based power tracking (CVPT) method is proposed, which only uses single‐loop in control. The proposed method does not need to tune multiple loops and can respond faster, which is important for grid‐forming voltage control. Furthermore, the different operating modes due to the limitation of PV maximum power are analysed, and a mode switch method is proposed. Simulation and experimental results demonstrate that the PV inverter can cope with power disturbances from both the power and grid sides and maintain the quality of grid voltage.

Abstract This study proposes a cutting‐edge AC/DC converter designed for medium‐power PFC applications. The converter is a single‐phase, single‐stage boost‐push–pull model. It consists of three key components: an interleaved boost, a push–pull, and a resonant tank circuit. The interleaved boost operates in DCM mode and serves as power factor correction. The push–pull converter includes a resonant tank on the secondary side of the transformer to achieve ZVS. The two switches control the boost and the push–pull circuits to create a single‐stage converter. The converter in question provides an array of advantages, such as zero voltage switching (ZVS), an intermediate bus voltage that is independent of the load, and a low‐ripple input current, all of which can be achieved without the need for additional filtering. The present article provides a comprehensive overview of the design procedure, simulation and experimental results, and separate operating modes analysis. To verify the design and simulation results, a 200‐W interleaved boost push–pull converter (IBPPC) prototype is implemented. Finally, because it is crucial to maintain the voltage of the bus capacitor within an acceptable range, this study investigated the impact of load variation on the bus voltage.

Abstract This paper proposes a novel non‐isolated ultrahigh step‐down interleaved DC‐DC converter with an extremely extended duty cycle based on the series capacitor and coupled‐inductor techniques. The proposed converter utilizes a three‐winding coupled inductor (TWCI) to enhance the step‐down conversion ratio. In contrast to conventional coupled inductor‐based step‐down converters, its voltage gain improves as the turn ratio approaches unity. Consequently, coupled inductors have significantly lower winding losses. Furthermore, there is no extra constraint on the turn ratio of the TWCI. It results in a highly flexible voltage gain and more design freedom. Other advantages of the employed series capacitor and coupled inductor techniques can be listed as, zero voltage switching (ZVS) condition for all switches, significant reduction of the total switching device power (SDP) and recovery of the energy of leakage inductors. They all reduce power losses and costs. Steady‐state analysis, derivation of voltage gain and design considerations are discussed in detail. Finally, a 200 W, 400‐to‐12 V experimental prototype is implemented to verify the effectiveness and feasibility of the proposed converter.

Abstract In a modular multilevel converter (MMC) system, the sub‐module capacitors account for a large proportion of the cost, volume, and weight. This paper proposed a method to reduce the total capacitance of MMC based on the combination of boosting the modulation index (m) and second‐harmonic circulating current injection (SCCI). A small amount of full‐bridge sub‐modules was added to conventional half‐bridge sub‐modules (HBSM) based MMC to form the hybrid MMC. The third‐harmonic voltage injection technology was used to increase the m of hybrid MMC without the common‐mode voltage injected on the ac‐side. An optimized SCCI method determined by m was introduced, which limited the root mean square (RMS) of arm current. An improved modulation approach is used to eliminate the coupling effect of third‐harmonic voltage injection and SCCI in boosting m, ensuring that the m increases to 1.15 with the optimized SCCI. Compared with conventional HBSM‐MMC, the proposed method reduced the total capacitance by approximately half when m = 1.15. A comprehensive comparison of different capacitance reduction methods was presented to demonstrate the cost and effect. Simulation and experiment verified the proposed method.

Abstract Although single‐stage inverters are popular for simpler design they face difficulties in shoot‐through mode operation. Insufficient DC voltage regulation and complicated LC network are principal drawbacks of these topologies. A new split source inverter (SSI) can solve problems with single‐stage inverters. In this paper, SSI replaced the voltage source inverter (VSI) of a shunt active power filter (SAPF) which alleviates power quality (PQ) issues in power system. Furthermore, a VSI‐based SAPF faces challenges to maintain consistent voltage across DC‐link capacitor, exactly compensating current generation, and switching loss reduction in inverter. This study examined efficacy of two inverter‐based SAPFs considering a modified synchronous reference frame approach for generating reference current; fuzzy logic controller for regulating DC‐link voltage; and adaptive fuzzy hysteresis current controller for generating switching pulses. Ideal and non‐ideal sources were considered when running the simulations for various load circumstances. The proposed SSI‐based SAPF with an advanced control approach can eradicate source current harmonics to 0.52% and 0.45% under ideal source conditions, and 0.65% and 0.54% under non‐ideal source conditions for non‐linear loads. Similarly, the ripples in the DC‐link voltage are also reduced to 2–3 V for the ideal case and 4–5 V for non‐ideal case.

Abstract This article presents an innovative approach for real‐time allocation of weighting factor values in model predictive control of electrical drive systems. In the proposed dynamic weighting factor assignment method, the cost associated with a specific variable is determined based on its corresponding set of predictions. This approach can be employed to optimize weighting factor values for a given system or even enhance performance metrics in comparison to conventional approaches that employ fixed weighting factors. Furthermore, the method determines the optimal value of weighting factors in real‐time with low added calculation complexity. The proposed method is able to provide reliable constant weighting factors for a given working point as well. The practical application of this method is demonstrated through a case study of an LC filter equipped PMSM drive; the system encompasses six independent variables that require regulation. Experimental results utilizing both two and three level voltage source inverters and using various transient and steady‐state situations prove the feasibility of the proposed dynamic weighting factor assignment method.

Abstract While conventional control techniques for stabilizing power electronic converters with constant‐power load (CPL) often rely on complete system state information, the associated challenges, including the cost and increased size due to the installation of multiple sensors, necessitate exploration of alternative methodologies. To address these concerns, a novel observer‐based sliding‐mode control approach is proposed. This approach aims to enhance cost‐effectiveness and reliability in the context of a DC‐DC buck converter supplying power to an unknown CPL. The core concept involves designing a state observer to estimate the system's current based on voltage measurements. A non‐certainty equivalent adaptive update law is then introduced to estimate the unknown CPL, incorporating feedback from voltage measurements and current estimation. To guarantee stability in the face of uncertainties in system parameters, a thorough analysis utilizing the Lyapunov theorem is conducted on the closed‐loop system. The efficacy and feasibility of the proposed control algorithm are substantiated through experimental results on the OPAL‐RT platform, showcasing its promising performance.

Abstract Marine current power is attracting more attention as a renewable energy option. Similar to wind power, marine current power often requires a maximum power point tracking (MPPT) method to optimize power extraction from the free‐flowing water. Research into MPPT methods for marine current power remains limited. Therefore, this paper presents a comprehensive investigation of MPPT methods for marine current power, building upon similar research in wind power. Three methods, namely the optimal tip speed ratio (OTSR), optimal torque (OT), and two variants of the perturb and observe (P&O) method, are explored. Using a simulation model developed for a specific marine current energy converter, where hydrodynamic calculations are coupled with electrical simulations, the study demonstrates that the OTSR method achieves MPPT with a comparably fast convergence time. After a change in water speed, the OTSR method achieves optimal operation within two turbine rotations. Additionally, the P&O methods are shown to achieve MPPT, albeit with a significantly longer convergence time. However, the P&O methods can be more convenient since no model of the system is required, and no water speed measurements are necessary. The proposed implementation of the OT method underperforms but positions the system close to the optimal operational point.

Abstract Dual active bridge (DAB) is an isolated DC‐DC converter gaining wider attention in power electronics applications. The high frequency (HF) transformer is an integral part of the DAB which is prone to saturation. Silicon carbide (SiC) based DAB are generally preferred for highly efficient power conversions, calling for an extremely low DC resistance of the transformer. This aggravates the DC bias issue significantly. The DC bias current generally flows due to the mismatch in static and transient switching of active devices, leading to eventual saturation of the transformer. This paper proposes an active method to precisely control the dead time of the devices (8–100 ns) without sacrificing the voltage utilization of the converter. This method does not require a sophisticated DC offset current measurement technique. The field programmable gate array (FPGA) based control platform on the gate driver side executes the proposed algorithm. The proposed control is experimentally verified in a 5 kW SiC based converter. The control implementation methodology is discussed with the support of necessary experimental results.

Abstract A dc voltage restorer (dc‐VR) with optimal droop control is developed to reduce the power loss and solve the dynamic current imbalance simultaneously of the zonal dc distribution system integrating multi‐parallel energy storage. Firstly, the power loss model composed of line loss and converter loss is built and it is proved to be a strictly convex function with respect to droop coefficients, which indicates the power loss can be mitigated by optimizing the current distribution. Thus, an image‐based droop optimization method is proposed to search for the optimal droop coefficients. Then, the economy of voltage compensation on power loss reduction is investigated and an ESS‐combined dc‐VR is designed, including an interleaved parallel architecture and a capacitor‐integrated electric spring (C‐ES). Unified virtual inertia is proposed for interleaved parallel bridge arms to make their dynamic performance consistent. And the newly introduced C‐ES can keep the bus voltage at the rated level to reduce the system cost. Therefore, the problem of dynamic currents imbalance is addressed from the points of converter structure (dc‐VR) and control system (unified inertia), and the power loss can be reduced by voltage recovery (C‐ES) and optimizing the current reallocation which is achieved by updating sharing coefficients from the image‐based droop optimization method. Finally, the simulation cases validate the effectiveness of the proposed optimal‐droop dc‐VR on dynamic current balance and power loss reduction, and hardware in the loop experiment results prove the consistent dynamic characteristics of the dc‐VR's arms.

Abstract To address the issue of poor robustness in the model predictive control of grid‐connected inverters due to disturbances in load model parameters, this article developed an ultra‐local model robust predictive controller based on Linear Matrix Inequality (LMI). First, to avoid dependence on model parameters, an ultra‐local model of the system was constructed. Second, in the process of setting the state variable compensation gain, to simplify the complex computational steps of the traditional Lyapunov algorithm, the task of finding the gain that satisfies the Lyapunov stability condition was ingeniously transformed into an optimization problem of solving constrained LMI. Third, the optimized state variables are utilized to design a new cost function predictive model, thereby enhancing the precision of system control. Finally, the effectiveness of the proposed approach has been validated through simulations and experiments.

Abstract The voltage reinjection strategy is an effective solution to improve the voltage quality of the voltage source inverters for high‐power applications. In this article, the fundamentals of voltage reinjection strategy are analyzed to reduce voltage harmonics of the output voltage. Then, a novel voltage reinjection circuit is proposed which can generate a 5‐level voltage to be injected on the voltages of the DC sources. The reinjected voltage can create a 60‐pulse voltage waveform for a three‐phase load. Turn ratio optimization of the reinjection transformer has a significant effect on the improvement of the harmonic situation of the output voltage. Furthermore, the proposed reinjection circuit provides ZVS conditions for the main switches to reduce switching losses considerably. The simulation results indicate that the proposed reinjection circuit can reduce the output voltage THD to 3.16% without any type of filter or modulation, and the load variation does not have a considerable effect on the voltage quality. The experimental results approve the analytical trend and simulation process and also confirm the reinjection circuit performance. According to the results, the proposed method has generated a semi‐sinusoidal voltage waveform with THDV=3.78% in the laboratory.

Abstract The bidirectional DC‐DC conversion, as an important application scenario, places certain requirements on the topology structure. The four‐switch buck‐boost (FSBB) converter has received widespread attention due to its simple structure, flexible control and state switchability. However, the traditional control strategy makes it difficult to meet the requirements of high performance, high stability and high security at the same time. Furthermore, the control methods commonly adopted in domestic and international practical applications rely heavily on analogue control, which cannot maintain efficiency over a wide stability range. The use of digital control methods allows for optimized control algorithms, maintaining stable system operation and improving efficiency. Therefore, it is very important to use the digital control method to further improve the smoothness and steady‐state efficiency of the system multi‐mode switching while maintaining a wide input and output range, based on this, this study proposes two new three‐mode control modes: interleaved bias control mode and dual‐edge bias control mode.

Abstract The modular multilevel DC–DC transformer (MMDCT) provides a reliable solution to overcome the challenges of conventional dual‐active‐bridge converters in terms of power semiconductors ratings and dv/dt stress on transformer coupling windings. An alternative modulation method, quasi‐square‐wave, was proposed to reduce the cell capacitance of modular multilevel bridges. However the application of quasi‐square‐wave modulation is found to result in underdamped switching transients and losses when resetting energy stored in arm inductance. This paper presents a detailed transient analysis of MMDCT arm insertion based on an equivalent circuit, which contributes to a more accurate component sizing and gives voltage estimation for individual half‐bridge submodules. Additionally, a revised switching sequence is proposed to recover this inductor energy and lower the oscillation‐related losses. Simulated and experimental results from a scaled test rig of MMDCT are implemented and validate the proposed component sizing and switching sequence, indicating that the converter efficiency can be improved under revised switching sequence. Finally, a silicon carbide based, high‐frequency MMDCT is proposed and simulated.

Abstract This study investigates the low‐frequency oscillations (LFOs) in MMC‐MVDC systems with high photovoltaic (PV) penetration, considering the whole operating conditions of the grid‐connected MMC, including both the inverter and rectifier modes. First, the multi‐port impedance models of converters and networks are developed, upon which a stability criterion is defined. The mechanism of LFOs is then identified using bus participation analysis and parameter sensitivity analysis. In addition, the stable zones of the dominant parameters are identified, taking into account the whole operating conditions of the grid‐connected MMC. Interestingly, a phase‐locked loop may induce LFOs in two low‐frequency ranges. Finally, the experimental results confirm the correctness of the theoretical analysis.

Abstract A multi‐input single‐output converter that is based on the impedance network and the standard isolated converters is presented. The topology is named quasi Z‐source full‐bridge isolated converter (qZSFBIC). The proposed topology helps to integrate various renewable power generation systems with a common three‐phase grid‐connected inverter. It was also capable of providing isolation between the input and output circuits in addition to the boost function. The integration of multiple energy sources is achieved using fewer components than conventional converters. As a result, it achieves greater conversion efficiency and has improved circuit characteristics. It offers a larger voltage control range as compared to the conventional ZSC and enhances the input‐output voltage transformation ratio. To determine whether or not the suggested converter is technically feasible, the circuit architecture, operating principle, control mechanism, and simulation results are presented. An improved proportional resonant‐second order general integrator (IPR‐SOGI) has been utilized to provide a gating signal for the voltage source inverter. The 1.5 kW, 400 V, 50 Hz model is designed to authenticate the proposed scheme with qZSFBIC. The results showed that the proposed converter offered double the time of boosting than the conventional ZSC converter and the conversion efficiency is around 89%.

Abstract Unbalanced voltages are becoming increasingly common in distribution networks due to the growing integrations of distributed renewable energy resources as well as large loads such as electric vehicle chargers. Such unbalanced voltages introduce significant control challenges as they produce ripples in the controlling signals, impacting the operation of inverters during the unbalanced conditions. Therefore, this paper proposes a controlling algorithm for three‐level inverters aimed at suppressing these ripples on controlling signals; improving the overall performance of inverters, and consequently enhancing the fault ride‐through capability under unbalanced conditions and faults. The proposed controlling algorithm enables inverters to operate in either a balanced current output mode or a suppressed‐ripple active power output mode, depending on the specific event scenario and demands from the grid operators. Current harmonics are suppressed even under severe faults. For improving the voltage balance on the DC capacitors in three‐level inverters, an enhanced method of neutral point current prediction is presented. The proposed method ensures higher balancing accuracy through the use of weighted switching costs, avoiding the requirement of a balancing controller or current extrapolation. Simulation and experimental results demonstrate the effectiveness of the proposed controller for reliable grid operation.

Abstract In this study, a 13‐level switched‐capacitor inverter with triple voltage gain is proposed. The proposed structure generates 13‐level output voltage using only one DC source, eleven switches, and three capacitors. The capacitors have the capability of self‐balancing without the use of additional circuits or complex control methods. Additionally, the inrush current of the capacitors has been reduced using a soft charging method. The proposed structure has been compared with different 13‐level structures presented in recent studies in terms of various parameters such as the number of semiconductor devices, the number of DC sources, voltage gain, Maximum Blocking Voltage (MBV), and Total standing Voltage (TSV). Another advantage of the proposed structure is the non‐use of any diode and its cost‐effectiveness. In addition, the power losses of the proposed structure have been evaluated, and its efficiency has been calculated for various output powers. Finally, the performance of the proposed structure has been verified through simulation and laboratory implementation under both stable and various dynamic conditions.

Abstract This paper proposes an adaptive complex coefficient filtered (CCF) full order extended state observer (ESO) type three phase enhanced phase locked loop (EPLL), which is employed in matrix reactance frequency converter (MRFC) for rotating vectors measurement estimation. EPLL phase detector was analysed first to track not only the rad frequency and transient phase, but also the amplitude of the rotating vectors. Full order ESO can filter out more high frequency disturbance, so it can track frequency and phase more accurately than proportion and integration algorithm. CCF modules were analysed in theory to attenuate the disturbance within two times of the EPLL's cut‐off frequency. The whole adaptive CCF‐ESO‐EPLL design, including stability and parameter tuning were then interpreted. The proposed CCF‐ESO‐EPLL adapts the estimated frequency with CCF to attenuate the MRFC switching non‐linear disturbance as well as unknown disturbance by the full order ESO. The MRFC topology necessary measured vectors, as well as the input side reactive power adjustment capacity, were discussed. The theoretical conclusion has been verified on a MRFC prototype. The proposed CCF‐ESO‐EPLL has less parameter tuning, less computation resource requirement, better steady and dynamic performance, and outstanding disturbance robustness.

Abstract Due to its limited load capacity, the piggybacking of wireless charging systems for micro unmanned aerial vehicles has become a challenging task in the design of micro unmanned aerial vehicles. Therefore, this paper proposes an improved lightweight design method for micro unmanned aerial vehicles to carry a wireless charging system. The improved system uses an inductor–capacitor–capacitor‐parallel (LCC‐P) topology compensation network instead of a bilateral inductor–capacitor–capacitor (LCC) topology compensation network to achieve constant current charging (CC) and constant voltage charging (CV). Then the adaptive frequency conversion control is used to realize the automatic conversion from CC charging to CV charging during the charging process. Compared with the traditional wireless charging system based on a direct current‐direct current converter (DC‐DC converter) to achieve CC charging and CV charging, this improved system reduces the total weight of the receiving end of the wireless charging system based on ensuring the charging efficiency, which meets the demand of wireless charging systems carried by micro drone aircraft. The test results of the constructed physical system coincide with the simulation design results, and the total weight of the receiving end is only 8 g, which verifies the correctness and effectiveness of the improved design scheme.

Abstract This paper proposes a maximum torque per ampere (MTPA) control method for a permanent magnet reluctance hybrid rotor dual stator synchronous motor (PMRHRDSSM) based on a sliding mode speed controller, in response to the complex and special electromagnetic relationship of the motor. The paper focuses on the special electromagnetic relationship of PMRHRDSSM with stator winding series structure. Firstly, the trajectory equation of PMRHRDSSM MTPA stator current vector is derived, and based on the relationship between PMRHRDSSM torque and reluctance dq‐axis current, a PMRHRDSSM current controller that meets MTPA constraints is designed. Afterwards, a PMRHRDSSM sliding mode speed controller was designed with input speed error and output reference torque. Finally, an experimental platform for the proposed control method was established, and the control method was experimentally validated.

Abstract Torque ripple is an important factor affecting the smoothness of permanent magnet synchronous motor. However, for high saturation permanent magnet synchronous motor (HSPMSM), the flux linkage of permanent magnet is nonlinear, which leads to poor effect of traditional torque ripple suppression methods. Therefore, by systematically considering the amplitude and phase changes of the permanent magnet flux link‐age for the first time, this paper analyzes the torque ripple mechanism of high saturation motors and establishes a corresponding mathematical model. To minimize the loss caused by harmonic currents, two torque ripple suppression methods are proposed: one based on the NSGA‐II algorithm and the other based on an analytical method. Finally, the effectiveness of the two algorithms is verified by the experimental comparison. The experimental results show that compared with the traditional methods, the two algorithms can effectively suppress the torque ripple under the premise of considering the influence of the motor magnetic saturation on the flux linkage and inductance, and improve the output torque smoothness of HSPMSM.

Abstract We developed high-performance flexible oxide thin-film transistors (TFTs) using SnO2 semiconductor and high-k ZrO2 dielectric, both formed through combustion-assisted sol-gel processes. This method involves the exothermic reaction of fuels and oxidizers to produce high-quality oxide films without extensive external heating. The combustion ZrO2 films were revealed to have an amorphous structure with a higher proportion of oxygen corresponding to the oxide network, which contributes to the low leakage current and frequency-independent dielectric properties. The ZrO2/SnO2 TFTs fabricated on flexible substrates using combustion synthesis exhibited excellent electrical characteristics, including a field-effect mobility of 26.16 cm2/Vs, a subthreshold swing of 0.125 V/dec, and an on/off current ratio of 1.13 × 106 at a low operating voltage of 3 V. Furthermore, we demonstrated flexible ZrO2/SnO2 TFTs with robust mechanical stability, capable of withstanding 5000 cycles of bending tests at a bending radius of 2.5 mm, achieved by scaling down the device dimensions.

The design of two-dimensional superatomic materials, which form their atomic structures through covalently bonded clusters with variable chemical compositions, will enable the development of new materials with promised electronic properties that are beneficial for modern nanoelectronics. This paper presents ab initio calculations of the atomic and electronic structures of both bulk and 2D Re6Se8Cl2. The calculations were carried out using density functional theory, incorporating noncollinear spin density and the pseudopotential method. The results include data on the atomic structure, band gap value, formation energy of the Re6Se8Cl2 2D layer, and the redistribution of atomic charges within the structures. The differences in effective masses for electrons and holes in the two-dimensional and bulk Re6Se8Cl2 materials are demonstrated, along with an explanation of how these differences impact their transport properties. The findings are expected to be of great significance for the design, synthesis, and implementation of new two-dimensional superatomic materials with controlled properties in modern nanoelectronics.

A method of measuring the thermovoltaic effect in heterogeneous media with gradient doping impurity distributions producing gradient carrier distributions has been proposed. Iron doped zinc oxide specimens have been produced using ion beam sputtering on thin foil tantalum substrates for thermovoltaic effect measurements, glass-ceramic substrates for Hall measurements and silicon substrates for structural study. The doping impurity concentration хFe in the specimens has been varied from 0.34 to 4.18 at.%. X-ray phase analysis has shown that all the specimens have a hexagonal zinc oxide crystal structure. The films have preferential [002] orientation. The carrier concentration in the experimental specimen layers according Hall data obtained on an ECOPIA 5500 measurement system in a 0.5 T DC magnetic field has varied in the 1016–1020 cm-3 range. The specimens have an n-type conductivity. Thermovoltaic measurements have been carried out for two-layered iron doped zinc oxide specimens with different carrier and iron doping impurity concentrations using the method proposed. The maximum thermovoltaic response (U ~ 80 μV) has been observed in the two-layered thin-film specimen with the carrier concentration difference between the layers (Δn ≈ 2∙103 cm-3). The observed saturation of the thermovoltaic response has been attributed to the establishment of dynamic equilibrium between carrier diffusion from the high carrier concentration layer to the low carrier concentration layer and carrier drift due to internal electric field.

Boron-adsorbing carbon nanotubes receive considerable attention in materials science due to their unique properties and potential applications. In particular, boron-adsorbing double-walled carbon nanotubes (DWNTs) exhibit a wide range of tunable electronic and optoelectronic properties. This study explores the influence of boron atoms on metallic (5,5@10,10) and semiconducting (8,0@17,0) DWNTs. We examine alterations in partial charge depending on the quantity of boron atoms adsorbed and affixed to the DWNT surface across temperatures from 300 K to 900 K. The results show that in both DWNTs, with the increase of energy corresponding to the temperature, the adsorption index of boron atoms (adsorbed to the first layer of DWNT) and the positive partial charge increase. Specifically, the maximum partial charge of DWNT(8,0)@(17,0) and DWNT(5,5)@(10,10) is 1.94e and 1.30e (at 300 K), 4.87e and 3.66e (at 600 K), 6.97e and 6.16e (at 900 K). Increasing boron concentration leads to heightened positive partial charge of DWNTs. This, in turn, affects the conductivity of the nanotube.

Background. Presence of possibility of analytical definition of a part of parametres of various radio devices, optimum by criterion of maintenance of preset values of modules and phases of transfer functions on necessary quantity of frequencies, considerably reduces time of numerical optimisation of other part of parametres by criterion of formation demanded frequency response and phase response in a strip of frequencies. Till now such problems dared concerning radio devices only with one cascade of type «a nonlinear part - the coordination the device» or «the coordination the device – a nonlinear part». In quality «the coordination devices were used the jet, resistive, complex or mixed two-port networks. The problem of multicascade radio devices with jet two-port networks is solved also. Change of basis for the coordination two-port networks and a place of inclusion of a nonlinear part leads to change of area of a physical realizability. Aim. Working out of algorithms of parametrical synthesis of radio devices with any quantity of identical and unequal cascades of type «a nonlinear part ‑the coordination the mixed two-port network» by criterion of maintenance of the set frequency characteristics. Nonlinear parts are presented in the form of a nonlinear element and parallel either consecutive on a current or pressure of a feedback. Methods. The theory of two-port networks, matrix algebra, a decomposition method, a method of synthesis of actuation microwave devices, numerical methods of optimisation. Results. In interests of achievement of the specified purpose systems of the algebraic equations are generated and solved. Models of optimum two-port networks in the form of mathematical expressions for definition of interrelations between elements of their classical matrix of transfer and for search of dependences of mixed of two-poles from frequency are received. It is shown, that at certain parities between quantity of cascades and values of resistance of a source of a signal and loading of the one-cascade radio device frequency characteristics of one-cascade and multicascade radio devices appear identical or similar. Such schemes are named by equivalent. Conclusion. The comparative analysis of theoretical results (frequency response and phase response radio devices, value of parametres), received by mathematical modelling in system MathCad, and the experimental results received by схемотехнического of modelling in systems OrCad and MicroCap, shows their satisfactory coincidence.

Background. The work is aimed at developing and researching rigorous methods for solving internal problem of electrodynamics for multi-element structures (metastructures) consisting from the final number of elements, as well as to study the physical processes occurring in them. A special case of such structures are two-dimensional lattices with a fixed interelement distance, consisting of identical elements having the same spatial orientation (regular lattices). Aim. In this work, based on an iterative approach, the internal solution is solved. problems of electrodynamics for a finite regular two-dimensional lattice of spiral elements. In order to obtain a priori information about the electrodynamic characteristics of elements lattice and justification for the choice of projection function systems are analyzed spectral characteristics of the integral operator of the internal problem for a single spiral element. Then the currents on the structure elements are calculated, their spectral characteristics are determined. The results of spectral analysis allow increase the efficiency of solving an internal problem. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). The solution of the internal problem within the framework of the method of moments is reduced to solving a SLAE with a block matrix. Results. A mathematical model of a finite two-dimensional lattice of spiral elements is proposed radiating structure. For the specified structure, in the case of its excitation by a flat electromagnetic wave, based on the iterative approach, the internal problem of electrodynamics was solved. The following were carried out in a wide frequency range: analysis of the convergence of the iterative process, spectral analysis of the integral operator of the internal problem for a single spiral element, as well as spectral analysis of external field and current functions functions on lattice elements. Conclusion. The feasibility of determining the spectral characteristics of integral operators is shown internal task for the elements forming the metastructure. A relationship has been identified between the frequency dependence eigenvalues of the integral operator of the internal problem of single elements, forming a metastructure, with resonance phenomena arising in the metastructure, the influence of resonances on the convergence of the iterative process was confirmed. The feasibility of considering averaged amplitude current spectra is shown. It was revealed that the averaged spectrum of current functions is close to degenerate, especially near resonant frequencies. This allows for use as projection functions a compact set of eigenfunctions that have significant amplitudes in the vicinity of the frequency under study, which significantly simplifies the solution of the internal problem.