Multi-frequency Method Research Articles

Image Quality Improvement in Sparse-View X-Ray Phase-Contrast Trimodal CBCT With Multifrequency Fringe Modulation and Iterative Methods

X-ray grating interferometer can simultaneously retrieve attenuation, refraction and scattering signals of the imaged sample, which shows its great potential in biomedical imaging. However, fast scan of gratings and high centrifugal forces during rotating in X-ray grating-based cone-beam computed tomography (CBCT) system may lead to phase-stepping errors and grating position fluctuations, which cause reconstruction failure with phase-stepping (PS) method. Whats more, the reconstructed slices usually suffer from severe artifacts under low dose conditions. Herein, we propose a multi-frequency model to simulate the mechanical instability of the system and put forward novel iterative image reconstruction methods named MFM-TLI and MLEM-FISTA-TV to improve image quality in sparse-view trimodal CBCT. Results reveal that the model and MFM-TLI is effective to retrieve high quality absorption, differential phase contrast (DPC) and dark-field (DF) signals under mechanical instability, significantly outperforming the PS method. Image quality reconstructed by MLEM-FISTA-TV is improved compared to other iterative and analytical algorithms with sparse-view data. To the best of our knowledge, this is the first time multi-frequency method is applied in X-ray grating interferometer and iterative MLEM-TV algorithm is evaluated on experimental sparse-view dark-field CBCT data. This work might provide support for future trimodal CBCT reconstruction.

METHOD OF ULTRASONIC PHASE TWO-COORDINATE INFORMATION REGISTRATION FOR AUTOMATED NON-DESTRUCTIVE TESTING SYSTEMS

The article is devoted to the issue of improving the coordinate registration of information in means of automated non-destructive testing. Existing systems of non-contact registration of spatial position sensors of non-destructive testing are mostly focused on the use of signal fields of different physical nature, for example, acoustic or optical, which are created around the position of these sensors and amplitude methods of signal processing. These methods do not provide the necessary accuracy of determining the coordinates in the case of using small-aperture sensors of non-destructive testing.
 The basis of the proposed technical solution is the trilateration method. The distance between the emitter of ultrasonic vibration, which is structurally connected to the sensor, and the two receivers is determined by the phase method. This method provides increased accuracy in determining the coordinates of the sensor. Eliminating the ambiguity of phase measurements is based on the combination of the multi-frequency method and the numerical system of residual classes. This makes it possible to minimize the probability of incorrect resolution of the ambiguity of the results of phase distance measurements and to ensure high accuracy of coordinate determination (with an absolute error of the order of mm). The idea of the method and the main calculation formulas that make it possible to determine the modules of the numerical system of residual classes and the values of the operating frequencies of ultrasonic oscillations are presented. Matching the discretes for determining the phase shifts of signals with the modules of the numerical system of residual classes at different operating frequencies makes it possible to reduce the resolution of the ambiguity of the results of phase measurements to the task of restoring integers in the positional counting system from their representation by residuals in the numerical system of residual classes. The mechanism of occurrence of gross errors in the recovery of whole numbers is considered. An algorithm for eliminating this error is proposed. In general, the correctness of the algorithm for determining the sensor coordinates is confirmed by the simulation results. The considered method of two-coordinate information registration can be used both in the development of new automated means of non-destructive testing, and for the improvement of existing ones, which involve a manual method of scanning the surface of testing objects.

Rough surfaces reconstruction via phase and phaseless data by a multi-frequency homotopy iteration method

Abstract This paper is concerned with the inverse scattering of the rough surfaces with multi-frequency phase and phaseless measurements. We present a high-order recursive iteration method based on the homotopy iteration technique to reconstruct the rough surfaces. The convergence for the multi-frequency homotopy iteration method is obtained under some conditions. Some numerical experiments show the effectiveness of the proposed algorithm.

A schizophrenia study based on multi-frequency dynamic functional connectivity analysis of fMRI.

At present, fMRI studies mainly focus on the entire low-frequency band (0. 01-0.08 Hz). However, the neuronal activity is dynamic, and different frequency bands may contain different information. Therefore, a novel multi-frequency-based dynamic functional connectivity (dFC) analysis method was proposed in this study, which was then applied to a schizophrenia study. First, three frequency bands (Conventional: 0.01-0.08 Hz, Slow-5: 0.0111-0.0302 Hz, and Slow-4: 0.0302-0.0820 Hz) were obtained using Fast Fourier Transform. Next, the fractional amplitude of low-frequency fluctuations was used to identify abnormal regions of interest (ROIs) of schizophrenia, and dFC among these abnormal ROIs was implemented by the sliding time window method at four window-widths. Finally, recursive feature elimination was employed to select features, and the support vector machine was applied for the classification of patients with schizophrenia and healthy controls. The experimental results showed that the proposed multi-frequency method (Combined: Slow-5 and Slow-4) had a better classification performance compared with the conventional method at shorter sliding window-widths. In conclusion, our results revealed that the dFCs among the abnormal ROIs varied at different frequency bands and the efficiency of combining multiple features from different frequency bands can improve classification performance. Therefore, it would be a promising approach for identifying brain alterations in schizophrenia.

High-accuracy gastric cancer cell viability evaluation based on multi-impedance spectrum characteristics

The increasing attention to precision medicine is widely paid to greatly rise the cure rate of cancer. Improving the stability and accuracy of cancer cell viability evaluation is one of the keys for precision medicine, as excess dosage of anti-cancer drugs not only kills the cancer cells, but also does harm to normal cells. Electrochemical impedance sensing (EIS) method is well known as a label-free, non-invasive approach for real-time, online monitoring of cell viability. However, the existing EIS methods using single-frequency impedances cannot reflect the comprehensive information of cellular impedance spectroscopy (CIS), ultimately leading to a poor stability and low accuracy of cancer cell viability evaluation. In this paper, we proposed a multi-frequency approach for improving the stability and accuracy of cancer cell viability evaluation based on multi-physical properties of CIS, including cell adhesion state and cell membrane capacitance. The results show that the mean relative error of multi-frequency method is reduced by 50% compared with single-frequency method, while the maximum relative error of the former is 7∼fold smaller than that of the latter. The accuracy of cancer cell viability evaluation is up to 99.6%.

Optimizing foreground mitigation for CMB lensing with combined multifrequency and geometric methods

A key challenge for current and upcoming cosmic microwave background lensing measurements is their sensitivity to biases from extragalactic foregrounds, such as Sunyaev-Zel'dovich signals or cosmic infrared background emission. Several methods have been developed to mitigate these lensing foreground biases, dividing broadly into multifrequency cleaning approaches and modifications to the estimator geometry, but how to optimally combine these methods has not yet been explored in detail. In this paper, we examine which combination of lensing foreground mitigation strategies is best able to reduce the impact of foreground contamination for a Simons Observatory--like experiment while preserving maximal signal-to-noise. Although the optimal combination obtained depends on whether bias reduction or variance reduction is prioritized and on whether polarization data is used, generally, we find that combinations involving both geometric (profile hardening, source hardening, or shear) and multifrequency (symmetric cleaning) methods perform best. For lensing power spectrum measurements from temperature (polarization and temperature), our combined estimator methods are able to reduce the bias below $\ensuremath{\sigma}/4$ or 0.3% (0.1%), a factor of 16 (30) lower than the standard quadratic estimator bias, at a modest signal-to-noise cost of only 18% (12%). In contrast, single-method foreground-mitigation approaches struggle to reduce the bias to a negligible level below $\ensuremath{\sigma}/2$ without incurring a large noise penalty. For upcoming and current experiments, our combined methods therefore represent a promising approach for making lensing measurements with negligible foreground bias.

A Multifrequency Cross-Correlated Contrast Source Inversion Method Using Phaseless Measurements of the Total Fields

Without phase information of the measured field data, the design complexity of the observation equipment can be greatly simplified. In the meantime, the phaseless data inverse scattering problems counter more serious nonlinearity and ill-posedness compared to the full data ones. In this paper, a multi-frequency cross-correlated contrast source inversion method using phaseless measurements of the total fields (referred to as PD-CC-CSI) is proposed. By introducing the cross-correlated error term to the cost functional, PD-CC-CSI shows better robustness against data noise and challenges in more complicated inversion scenarios. Inverted results with transversal magnetic (TM) polarized synthetic and experimental data demonstrate the advantages of PD-CC-CSI in comparison to the phaseless contrast source inversion method (PD-CSI) and its variant PD-MR-CSI. In addition, an empirical approach has been proposed to effectively determine the optimal inverted results. Since a fast algorithm can be straightforwardly applied, phaseless inversion with multi-frequency data can be done within a few minutes.

Noise-induced phase error comparison in multi-frequency phase-shifting profilometry based on few fringes

For fringe projection profilometry (FPP), the combination of phase-shifting profilometry (PSP) and multi-frequency temporal phase unwrapping (MFTPU) is a phase extraction scheme with high accuracy and robustness, which is widely used in three dimensional (3D) measurement equipment. To make it suitable for real-time or dynamic objects 3D measurement, reducing the number of fringes is an effective method. To this end, this paper introduces four phase extraction algorithms based on few fringes. We introduce the unit phase accuracy, and analyze the phase extraction accuracy and reliability of the above four algorithms. Experiments are carried out to confirm the theoretical analysis conclusions. Our theoretical and experimental results include that the wrapped phase error variance is inversely proportional to the number of phase-shifting steps, and that the phase unwrapping reliability is proportional to the wrapped phase accuracy and inversely proportional to the frequency ratio between fringe sequences. Compared with the existing four standard multi-frequency phase-shifting methods, the measurement efficiency of the four non-standard multi-frequency phase-shifting methods supplemented in this paper are improved by 16.7%, 37.5%, 22.2% and 41.7%, respectively. However, the phase unwrapping reliability decreases. The balance between phase extraction accuracy and efficiency needs to be determined according to the actual application. This paper can provide a reference for the selection of phase extraction algorithm.

A Switched Planar Multicoil Transmitter Antenna Designed With Nonuniform H-Field Forming for Small Device Localization

To monitor 3-D position and orientation of a small device having planar receiver (Rx) coil, a switched multicoil transmitter (Tx) antenna is proposed by adopting time-divisional approach. The existing multifrequency methods require eight or more input ports to feed the coils with multifrequency signals for localization. In contrast, the proposed Tx antenna is driven by a single frequency source and uses only three input ports for reduced complexity. Moreover, the multiple coils of the proposed antenna are optimally grouped to form nonuniform magnetic-field distribution using three switches (SWs) in such a manner that better localization accuracy is achieved as compared to the multifrequency design. Rigorous analysis and simulations are performed to investigate the performance of the proposed design and localization approach. To validate the claim, experimental study results proved the potential of the proposed antenna employed for tracking a planar Rx in applications like medical robots, navigation of people with limited vision, virtual reality, etc.

Optimization of multi-frequency electromagnetic surveying for investigating waste characteristics in an open dumpsite

ABSTRACT Multi-frequency electromagnetic (EM) surveying is a type of frequency-domain electromagnetic (FDEM) survey, a new geophysical exploration approach used as a scanning tool to investigate waste characteristics within a final disposal site before electrical resistivity tomography (ERT) surveying. EM surveys provide information about shallow subsurface conditions; however, to date, no studies on waste bodies or waste characteristics in open dumpsites have assessed the optimal frequency for use in multi-frequency EM surveys. This research aims to determine the optimal frequency set for multi-frequency EM surveying for initial waste quality assessment in open dumpsites. These initial waste quality data are critical to assess the feasibility of open dump mining projects. First, a multi-frequency EM survey was performed in this study, which was measured at the exact electrode positions of the three ERT profiles. This FDEM survey used 15 frequencies ranging from 1,000–⁠15,000 Hz, which were grouped into frequency sets for inversion modeling of the electrical conductivity. Second, an ERT survey was carried out along all three profiles, each of which was around 144 m long. Subsequently, synthetic electrical resistivity data were generated by processing the electrical conductivity model. Data from each frequency set were then generated at the same depth, with interpolation techniques used to analyze the linear correlation between synthetic electrical resistivity and real electrical resistivity data and compare the Pearson’s correlation coefficient (R) values to determine the optimum frequency set for FDEM surveys in the open dumpsite. The results showed that the E4 frequency set, consisting of 5,000, 11,000, and 15,000 Hz values, typically had the highest positive correlations (R = 0.74–0.91) across all profiles and provided waste characteristics information close to the true conditions. Thus, these frequencies represent the optimal set for multi-frequency EM surveys for the primary assessment of waste characteristics in open dumpsites. Implications: Open dump mining (ODM) is now applied as a sustainable approach to combat improper waste disposal and reduce municipal solid waste (MSW) in the open dumpsite. To implement ODM for producing RDF, business developers must know the amount and composition of waste that can be converted into RDF before mining. This study used multi-frequency EM surveys with frequencies of 5,000, 11,000, and 15,000 Hz. This multi-frequency method effectively determined the waste composition and identified potential excavation points in the open dumpsite prior to ODM. This method can mitigate the limitations of traditional surveying, due to its improved mobility, lower time consumption, and reduced labor needs.

Rolling bearing fault diagnosis method based on multi-sensor two-stage fusion

Despite the great achievements of deep learning methods based on a single sensor in fault diagnosis, learning useful information from multi-sensor data is still a challenge. In order to make full use of multi-sensor information and improve the performance of rolling bearing fault diagnosis, a novel multi-sensor information fusion framework is proposed in this paper. First, a multi-sensor-based multi-frequency information fusion method is proposed. The multi-frequency information of each sensor is segmented first to enhance the datasets, and then a weighted fusion rule based on fuzzy entropy is constructed to fuse the information of different frequency components for multi-sensors. Second, a multi-kernel attention convolutional neural network is designed to realize multi-frequency feature capture, fusion, and fault classification of multi-sensors. Finally, two different rolling bearing datasets are used to implement fault diagnosis experiments. Experimental results show that the proposed method outperforms the comparative methods in terms of diagnostic performance and robustness.

Improving image quality in diffuse optical tomography

Diffuse optical tomography (DOT) modality uses diffusion equation solution of low power laser distribution in the imaging tissue. DOT method has three main running mode and three geometric subbranches. Run modes are: Continuous Wave (CW), Time Resolved (TR) and Frequency Domain (FD) modes. These run modes might have transmission-through, back-reflected or ring geometry depend on the source and detector placements on tissue surface. In this work, we tested our novel imaging method on the frequency-domain back-reflected DOT simulation model. Our novelty is: selecting a great number of multi-frequency data in the wide frequency spectrum which was not tested before in the literature. Most of the literature works consist of narrow frequency band with the limited number of frequencies such as maximum 12 multi-frequency-data which cover from 100 up to 700 MHz. In our work, we tested and compared reconstructed inclusion images generated by our 500 wide spectrum multi-frequency data versus reconstructed inclusion images generated by 20 narrow band multi-frequency data which was generally used in FD DOT studies. We observed that our novel imaging method which used wide spectrum multi-frequency data is superior to the traditionally used narrow-band multi-frequency method based on the reconstructed inclusion image localization errors. Since most of the homogenous geometry consists of fat tissue, we selected background absorption coefficient µa = 0.2 cm−1 and tissue scattering coefficient $${\upmu }$$ s = 80 cm−1 for 800 nm laser source wavelength. Three-dimensional cubic imaging simulation media has 75-mm grid sizes in each direction. Two different imaging scenarios were tested. In the first scenario, one inclusion with absorption coefficient µa = 0.7 cm−1 was put inside the three-dimensional imaging geometry at 27 mm depth. In the second scenario one inclusion with absorption coefficient µa = 0.7 cm−1 was embedded in 48 mm depth location. Inclusions are cubic and they have 6 mm xyz length at each direction.

A Novel Voltammetric Electronic Tongue Based on Nanocomposites Modified Electrodes for the Discrimination of Red Wines from Different Geographical Origins

A novel voltammetric electronic tongue (VE-tongue) system based on three nanocomposites modified working electrodes was used for the discrimination of red wine from different geographical origins. The three types of modified working electrodes were fabricated to detect glucose (Glu), tartaric acid (TA), and non-specific flavor information in a red wine sample, respectively. The electrochemical properties of three electrodes were tested by cyclic voltammetric method, and pH, accumulation time, and scan rates were optimized for Glu and TA sensors. Scanning electron microscopy (SEM), X-ray proton spectrum (XPS), and X-ray diffraction (XRD) were used for the characterization of modified materials. This sensor array was then applied to identify four kinds of red wines from different geographical origins, and the multi-frequency and potential steps (STEP) method was used to obtain flavor information regarding rice wines. The classification ability of this VE-tongue system was evaluated by using partial least squares (PLS) regression and principal component analysis (PCA), while back propagation neural network (BPNN), random forest (RF), support vector machines (SVM), deep neural network (DNN), and K-nearest neighbor (KNN) were used for the prediction. The results showed that PCA could explain about the 95.7% of the total variance, and BPNN performed best in the prediction work (the prediction accuracy was 95.8%). Therefore, the VE-tongue system with BPNN was chosen to effectively discriminate red wines from different geographical origins, and the novel VE-tongue aiming at red wine discrimination with high accuracy and lower cost was established.

Gray-code fringe order jump error self-correction based on shifted phase encoding for phase measuring profilometry

Temporal phase unwrapping based on Gray-code method (TPU-GC) has prospective application in three-dimensional (3D) shape measurement due to its high-speed measurement and high-efficiency code. Currently, it is still an essential task to remove jump error that may be caused by edge ambiguity of Gray-code pattern or uneven reflectivity of the measured object. So, a Gray-code fringe order jump error self-correction method based on shifted phase encoding (FOSC-SP) is proposed. By changing the calculating sequences of N-step phase-shifting patterns, a series of wrapped phases with a shifted phase of 2π/N can be obtained to identify the 2π discontinuities uniquely. The fringe order error caused by the misalignment between the edges of fringe order and the 2π discontinuities can be located and then corrected accurately. Subsequently, the fringe order caused by uneven reflectivity can be identified by the difference map of wrapped phase and the primary unwrapped phase without edge fringe order error, and then eliminated by a statistical method. Experimental results demonstrate the feasibility and validity of the proposed method. It performs good anti-noise capability and robustness to correct the above two kinds of jump errors in TPU-GC and it is also a generalized correct method that can be used to others TPU, such as multi-frequency and phase-coded methods.

Temperature Fluctuations Compensation with Multi-Frequency Synchronous Manipulation for a NV Magnetometer in Fiber-Optic Scheme.

Nitrogen-vacancy (NV) centers in diamonds play a large role in advanced quantum sensing with solid-state spins for potential miniaturized and portable application scenarios. With the temperature sensitivity of NV centers, the temperature fluctuations caused by the unknown environment and the system itself will mix with the magnetic field measurement. In this research, the temperature-sensitive characteristics of different diamonds, alongside the temperature noise generated by a measurement system, were tested and analyzed with a homemade NV magnetometer in a fiber-optic scheme. In this work, a multi-frequency synchronous manipulation method for resonating with the NV centers in all axial directions was proposed to compensate for the temperature fluctuations in a fibered NV magnetic field sensing scheme. The symmetrical features of the resonance lines of the NV centers, the common-mode fluctuations including temperature fluctuations, underwent effective compensation and elimination. The fluorescence change was reduced to 1.0% by multi-frequency synchronous manipulation from 5.5% of the single-frequency manipulation within a ±2 °C temperature range. Additionally, the multi-frequency synchronous manipulation improved the fluorescence contrast and the magnetic field measurement SNR through an omnidirectional manipulation scheme. It was very important to compensate for the temperature fluctuations, caused by both internal and external factors, to make use of the NV magnetometer in fiber-optic schemes’ practicality. This work will promote the rapid development and widespread applications of quantum sensing based on various systems and principles.

Computational Fluid Dynamics Analysis of the Influence of Gas Content on the Rotordynamic Force Coefficients for a Circumferentially Grooved Annular Seal for Multiple Phase Pumps

Abstract Pumping efficiency and rotordynamic stability are paramount to subsea multiphase pump operation since, during the life of a well, the process fluid transitions from a pure liquid to a mixture of gas in the liquid to just gas. Circumferentially grooved seals commonly serve as balance pistons in pumps while also restricting secondary flow. Prior experimental results obtained with a grooved seal operating with a mixture of air and mineral oil show the seal rotordynamic force coefficients vary significantly with the gas volume fraction (GVF). This paper, complementing an exhaustive experimental program, presents a computational fluid dynamics (CFD) analysis to predict the leakage and dynamic force coefficients of a circumferentially grooved seal supplied with air in an oil mixture with a GVF varying from 0 to 0.7. The test seal has 14 grooves, an overall axial length of 43.6 mm, and radial clearance of 0.211 mm. The 127 mm diameter rotor spins at constant angular speed (Ω = 3500 rpm). The mixture enters the seal at a supply pressure (Pin) of 2.9 bar(a), and the seal exit pressure (Pout) is 1 bar(a). The CFD two-phase flow simulations utilize the Euler–Euler multiphase model to predict the mass flowrate and the pressure field as a function of the operating conditions. Using a multi-frequency shaft orbit motion method, the CFD simulations deliver the variations of reaction force on the rotor with respect to the excitation frequency. For a pure liquid condition (GVF = 0), both the CFD and experimental results produce constant stiffness, damping, and added mass coefficients. The experimental and CFD results demonstrate the seal rotordynamic force coefficients are quite sensitive to the GVF. When introducing a small amount of air into the oil (GVF = 0.1), the direct damping coefficient increases by approximately 10%. For operation with a mixture with inlet GVF > 0.1, the cross-coupled stiffness coefficients develop strong frequency-dependent characteristics. In contrast, the direct damping coefficient has a negligible variation with excitation frequency. The CFD predictions, as well as the experimental results, evidence that air injection in a liquid stream can significantly change the seal rotordynamic characteristics, and thus can affect the rotordynamic stability of a pump. An accurate CFD analysis provides engineers to design reliable grooved seals operating under two-phase flow conditions.

Phase extraction accuracy comparison based on multi-frequency phase-shifting method in fringe projection profilometry

For fringe projection profilometry (FPP), phase extraction accuracy determines three-dimensional (3D) measurement precision. The combination of phase-shifting (PS) and multi-frequency temporal phase unwrapping (MTPU) can reconstruct discontinuous or isolated surfaces with high accuracy and robustness. However, due to the introduction of inevitable random noise, the phase extraction is biased. To this end, this paper firstly compares the wrapped phase errors based on various PS methods in detail. Then, the phase errors and unwrapping reliability based on various dual-frequency temporal phase unwrapping methods are compared. Finally, the effects of three-frequency temporal phase unwrapping and reasonable selection of fringe frequency on phase extraction accuracy are further discussed. The accuracy of the wrapped and unwrapped phase extraction and the phase unwrapping reliability are compared experimentally. This paper can provide a reference for algorithm selection in 3D measurement applications.

Prediction method of multi-frequency non-intermodulation electromagnetic radiation blocking effect of BeiDou navigation receiver

In the test of the electromagnetic radiation blocking effect of the navigation receiver, it is found that the sensitivity of the navigation receiver to single frequency continuous waves and sinusoidal amplitude modulation waves will change with the change in the satellite useful signal strength. This phenomenon reflects that the sensitivity of frequency equipment to multi-frequency electromagnetic radiation is not fixed to a certain extent. In order to make up for the deficiency that the existing multi-frequency electromagnetic radiation evaluation methods can only deal with a single situation, this paper uses the time delay characteristics of the circuit response, introduces the concepts of normalized interference levels and signal duty cycles, establishes the evaluation model of the multi-frequency non-intermodulation electromagnetic radiation blocking effect of frequency equipment, and puts forward the prediction method of the multi-frequency electromagnetic radiation blocking effect of frequency equipment. Taking a certain type of BeiDou navigation receiver as the test object, the single-frequency continuous wave and double-frequency continuous wave electromagnetic radiation blocking effect tests are carried out by using the full-level irradiation method. The test data are substituted into the model established in this paper for verification. The results show that the maximum evaluation error of the model is 2.23 dB. The model and the effect prediction method established in this paper are of great significance for the survival ability evaluation of frequency equipment in complex electromagnetic environments.

Multi-step-ahead solar irradiance modeling employing multi-frequency deep learning models and climatic data

In this paper two enhanced long-short-term memory (LSTM) models of sequenced-LSTM (SLSTM) and wavelet-LSTM (WLSTM), provided for multi-step-ahead simulation of solar irradiance of six stations, located in Iran and USA. In this respect, twenty-year recorded solar irradiance and climate data were employed. The proposed multi-frequency models serve all the capabilities of classic LSTM network and also handle its weakness in detecting and modeling multi-frequency information that often included in natural datasets. The suggested methodology improved the long-short auto-regressive term of climate-solar irradiance data by including very long frequencies of time series. The results revealed that the suggested multi-frequency LSTM methods could exceed the feed forward neural network and classic LSTM network in test phase up to 23% and 13%, respectively.

Generic Multi-Frequency Modelling of Converter-Connected Renewable Energy Generators Considering Frequency and Sequence Couplings

Frequency and sequence couplings can compromise the trustworthiness of multi-frequency models for converter-based systems. There have been effective attempts to address the couplings mainly by linearized averaged models. Only a few studies have been conducted on practical optimization of such models with enormous matrices and experimental results. This paper provides a generic theory for coupling patterns and proposes a multi-frequency modelling method to detect and address only the main couplings in the sequence domain for converter-connected renewable energy generators. The proposed generic model is based on empirical tests using small-signal perturbations and adopting Fourier transform on the switching converter response. The proposed theory and modelling methodology are verified using a 7MVA grid emulator for voltage perturbation tests on a 2MVA photo-voltaic converter. Accordingly, the couplings can exist in more generic forms, including multiples of perturbation and fundamental frequencies. To the best of our knowledge, the patterns with the multiples of the perturbation frequency have been overlooked in the literature. Furthermore, the mirror frequency concept is valid for all coupling patterns and is included in the proposed model. Besides, the proposed patterns and the environment noise levels have been practical criteria for selecting the main couplings.