Discrete Fourier Transform Method Research Articles

Dual grid energy management strategy for electric vehicles in hybrid microgrid utilizing matrix pencil method

Abstract This study introduces a cutting-edge Matrix Pencil-based Dual Grid Energy Management System (MP-DEMS) aimed at seamlessly integrating electric vehicles (EVs) into power grids while enhancing power quality (PQ) and reliability (PR). Operating within an AC-DC hybrid microgrid (HMG) framework, the MP-DEMS reduces the necessity for additional conversion devices, simplifying the integration of EVs and batteries. The core of the proposed DEMS comprises three key modules: the Wind Energy Management Module (WEMS), Smart Storage and EV Power Coordination (SS-EVPC), and Coordinated Power Conversion Control (CPCC). These modules work together to optimize energy usage, leverage renewable sources effectively, and manage EV charging/discharging schedules to minimize grid impact. An innovative aspect of the MP-DEMS is its use of Matrix Pencil-based techniques, offering several advantages over traditional Discrete Fourier Transform (DFT) methods. These advantages include swift dynamic response, resilience to voltage variations, and precise voltage phase estimation. Software simulations and Hardware-in-the-Loop (HIL-402) testing validate the efficacy of the MP-DEMS approach, showcasing enhanced power transfer capabilities, improved harmonic performance, and superior voltage/frequency regulation within EV-HMS applications. Overall, the MP-DEMS presents a promising solution for advancing the integration of EVs into microgrid systems, contributing to a more sustainable and reliable energy future.

Choosing optimal input and sampling frequencies for analog to digital converter testing

The main objective of this paper is to study of the ideal input and sampling frequencies, as well as determining the necessary number of samples for achieving coherent sampling. This aspect holds significant importance when it comes to testing analog-to-digital converters (ADCs) using various techniques such as the Histogram Test Method, Discrete Fourier Transform Method, or Sine-Fitting Method. The study conducted in this paper sheds light on a crucial consideration, which is the trade-off between testing duration and the proximity to the required frequencies. This trade-off is determined by the number of acquired samples. The balance between the amount of time spent on testing and the accuracy achieved in terms of the frequencies being targeted is of great importance. By exploring the ideal input and sampling frequencies, along with the determination of the necessary number of samples for coherent sampling, this research contributes to enhancing the understanding of ADC testing methodologies. It provides valuable information for researchers and practitioners in the field, enabling them to make informed decisions regarding the selection of appropriate testing techniques and algorithms based on their specific requirements and constraints. Ultimately, the findings presented in this paper have the potential to improve the efficiency and effectiveness of ADC testing processes, leading to more accurate and reliable results.

Evaluation of Geothermal Energy Potential in Parts of the Lower Benue Trough, Nigeria, Using Aeromagnetic Data

Abstract Nine sheets of Regional Aeromagnetic data of parts of Lower Benue Trough were evaluated through the use of Centroid and forward modelling of the spectral peak methods with a view to delineating structures and basin geometry of the Southern (Lower) Benue Trough of Nigeria. Geological cross sections were used to determine the number of anomalies from the residual magnetic map after which the Discrete Fourier Transform method was applied in calculating and computing the depth to the top (Zt), depth to the bottom (Zo), Curie point depth (CPD), geothermal gradient and heat flow. From the results, the depth to the top of the magnetic source ranges between 0.5km and 12.5km with the highest points towards the south - western part of the study area. The depth to the bottom of magnetic source (centroid depth) ranges from 2km to 54km and the highest areas are located towards the north-eastern part of the study area. The geothermal gradient ranged between 21oC/Km to 29.5oC/Km., Ogoja, Oturkpo, and Katsina–Ala are situated within the region of high geothermal gradients (>26.5oC/Km). The heat flow values range from 22mW/M2 to 74 mW/M2 and the areas with the high heat flow values are Makurdi, Ogoja, Gboko and Katsina-Ala. The results also show that the Curie temperature isotherm within the study area is not a horizontal level surface, but it is undulating. The study also identified high sedimentary thickness and considerable geothermal potential which could serve as a basis for hydrocarbon accumulation and geothermal exploitation. Keywords: Geothermal Gradient, heat flow, Crustal Temperature, Geothermal Potentials, Total Magnetic Intensity (TMI).

Implementation of Phasor Measurement Unit Based on Phase-Locked Loop Techniques: A Comprehensive Review

The dynamic monitoring, control, and protection of modern power systems in real time require time-stamped electrical measurements to accurately estimate the bus voltage phasors using the state estimation function under normal and abnormal conditions. These measurements can be acquired by time-synchronized devices, known as phasor measurement units (PMUs). PMUs can measure bus voltage and branch current phasors of a three-phase network, as well as the frequency and the rate of change of frequency (ROCOF), with high speed, accuracy and time stamping provided by global positioning system (GPS) at the coordinated universal time (UTC). Various phasor estimation algorithms have been proposed in the literature, while most of them are concentrated in the discrete Fourier transform (DFT) algorithm, where an integer number of samples multiple of the nominal frequency is required for the computations. In cases where the frequency of the power grid deviates from its nominal value, the raw application of the DFT approach can lead to large errors during phasor estimation. Another approach of the phasor estimation is based on the phase-locked loop (PLL) techniques, widely used in grid tie inverters. PLL techniques can track dynamically (continuous time) the estimated frequency to the time-variant frequency of the power grid. A brief introduction to the basic concepts of the synchrophasor definition is provided, while the main DFT methods for synchrophasor estimation according to recent literature are mentioned. PLL-based PMU techniques are reviewed for both steady-state and dynamic conditions according to IEEE standards. In conclusion, the performance of PLL-based PMU algorithms presented in this literature review is discussed.

High-performance tooth flank collaborative optimization model for spiral bevel and hypoid gears

The tooth flank collaborative optimization considering both geometric and loaded contact performances is an increasingly significant target in design and manufacturing for spiral bevel and hypoid gears. Recently, numerical loaded tooth contact analysis (NLTCA) is always an important access of mapping of the required performance evaluations and design variables. In addition to the conventional solution to NLTCA, an innovative discrete convolution and fast Fourier transformation (DC-FFT) method focusing on the micro-scale tooth flank topography is developed for high-performance spiral bevel and hypoid gears. Then, combining with accuracy and efficiency, a new top-rem tool modification is proposed to establish a new collaborative optimization model. Where, while the target flank can be prescribed by considering the user needs in the actual manufacturing, a small number of tool parameters are selected as the unknown design variables. It can significantly deal with the strong nonlinearity and coupling effect from the traditional modification and improve the optimization efficiency. Moreover, a top-rem tool modification is used as the optimization strategy to get a high optimization accuracy. The spiral bevel gear set from aerospace industrial applications is exercised to demonstrate the impact of the proposed collaborative optimization model on the tooth flank geometric and loaded contact performances.

An Improved Method of Heart Rate Extraction Algorithm Based on Photoplethysmography for Sports Bracelet

Heart rate measurement employing photoplethysmography (PPG) is a prevalent technique for wearable devices. However, the acquired PPG signal is often contaminated with motion artifacts, which need to be accurately removed. In cases where the PPG and accelerometer (ACC) spectra overlap at the actual heart rate, traditional discrete Fourier transform (DFT) algorithms fail to compute the heart rate accurately. This study proposed an enhanced heart rate extraction algorithm based on PPG to address the issue of PPG and ACC spectral overlap. The spectral overlap is assessed according to the morphological characteristics of both the PPG and ACC spectra. Upon detecting an overlap, the singular spectrum analysis (SSA) algorithm is employed to calculate the heart rate at the given time. The SSA algorithm effectively resolves the issue of spectral overlap by removing motion artifacts through the elimination of ACC-related time series in the PPG signal. Experimental results reveal that the accuracy of the proposed algorithm surpasses that of the traditional DFT method by 19.01%. The proposed method makes up for the deficiency posed by artifact and heart rate signal overlap in conventional algorithms and significantly improves heart rate extraction accuracy.

Fracture detection, fluid identification and brittleness evaluation in the gas-bearing reservoir with tilted transverse isotropy via azimuthal Fourier coefficients

Seismic characterization of the sweet spot plays a crucial role in the exploration and exploitation of oil and gas reservoirs. Therefore, we focused on fluid discrimination, natural fracture detection and brittleness evaluation in the reservoir permeated by an inclined set of parallel fractures using pre-stacked seismic inversion method. To this end, we proved by numerical experiments that the suggested fluid indicator is available for identifying the gas-bearing reservoir due to its high sensitivity to the gaseous hydrocarbon and extremely weak dependences on the porosity and the fracture density of the gas-bearing formation. To reduce the cumulative errors induced by indirect calculations, we derived the reflection coefficient of the TTI (tilted transverse isotropy) rock in terms of Young's modulus, Poisson's ratio, the fluid indicator and the fracture parameters and then rewrote it in the form of the Fourier series. By comparing with the published results, the derived reflectivity equation was proven rational and of satisfactory accuracy. Furthermore, we proposed a hierarchical inversion method incorporating the discrete Fourier transformation (DFT) and the Bayesian inversion strategy, which consists of three steps. Firstly, the DFT method is utilized to decouple anisotropic seismic components from the isotropic seismic component. In the last two steps, the Bayesian inversion approach is taken to acquire the stable and reliable estimations of the fluid and brittleness indicators and the fracture parameters from the second-order and zeroth-order seismic components, respectively. The synthetic example proved that we can realize rational and reliable predictions of the unknown parameters using the hierarchical method even for the case with moderate noise. The field case demonstrated that the proposed method is feasible and stable, and the suggested sweet spot indicators worked well for gaseous hydrocarbon discrimination, natural fracture detection and brittleness evaluation.

Applying the most frequent values assisted Hilbert transform into seismic attributes

In the present study, we developed a new method to calculate two of the most important seismic attributes that can able to give a huge impact in the interpretation field leading to a better geological and geophysical interpretation of the data. The first attribute was the Reflection Intensity with great improvement in detection of thin layers that show low reflection coefficient and enhance the ability to follow unconformity, the other one is the Instantaneous Phase to discover the discontinuity of events. The new method depends on combining the most frequent values (MFV) with inversion to calculate the Hilbert transform and applying hybrid Seismic Denoising, using also dual inversion and calculated Steiner weight from the iterative reweighted least square method (IRLS). Scaled Hermite function in a series expansion was used to discretize the spectrum of the time trace. The procedure followed with adjusting the process using multi-windows technical on the generated synthetic seismic traces loaded with Gaussian and Cauchy noise at the same time. The result of the method was shown significant effects on outliers or normal Gaussian noise when applied to two seismic attributes better than the old way using the Discrete Fourier Transform (DFT) method.

Optimised extreme gradient boosting model for short term electric load demand forecasting of regional grid system

Load forecast provides effective and reliable guidance for power construction and grid operation. It is essential for the power utility to forecast the exact in-future coming energy demand. Advanced machine learning methods can support competently for load forecasting, and extreme gradient boosting is an algorithm with great research potential. But there is less research about the energy time series itself as only an internal variable, especially for feature engineering of time univariate. And the machine learning tuning is another issue to applicate boosting method in energy demand, which has more significant effects than improving the core of the model. We take the extreme gradient boosting algorithm as the original model and combine the Tree-structured Parzen Estimator method to design the TPE-XGBoost model for completing the high-performance single-lag power load forecasting task. We resample the power load data of the Île-de-France Region Grid provided by Réseau de Transport d’Électricité in the day, train and optimise the TPE-XGBoost model by samples from 2016 to 2018, and test and evaluate in samples of 2019. The optimal window width of the time series data is determined in this study through Discrete Fourier Transform and Pearson Correlation Coefficient Methods, and five additional date features are introduced to complete feature engineering. By 500 iterations, TPE optimisation ensures nine hyperparameters’ values of XGBoost and improves the models obviously. In the dataset of 2019, the TPE-XGBoost model we designed has an excellent performance of MAE = 166.020 and MAPE = 2.61%. Compared with the original model, the two metrics are respectively improved by 14.23 and 14.14%; compared with the other eight machine learning algorithms, the model performs with the best metrics as well.

Enhancing Prony’s method for fault location

The paper presents a phasor estimator combining Prony’s method and discrete analytic signal generation for use in impedance-based fault location. The precision of impedance-based fault location hinges on accurately extracting the fundamental component in the presence of transient components, including inter-harmonics, which compromises the accuracy of the industry-adopted full-cycle Discrete Fourier Transform (DFT) method. The analytic signal gives rise to half the model order, excluding the purely damped exponential, thus producing more accurate results from Prony’s process while also contributing to its speedup. The discrete analytic signal is generated so that its length is half of the original signal, meaning its sampling frequency is effectively halved, yielding better numerical conditioning and faster processing in Prony’s method. The proposal does not trade accuracy for speed, yet the speed up makes fault location closer to the vision of installing its software module on protection devices. The proposed Prony’s method with discrete-time analytic signals is compared with the classical Prony’s method applied to discrete-time real-valued signals, the full-cycle DFT with special provisions for eliminating the decaying DC component, and Kung’s method. The results obtained by the different approaches show the superiority of Prony’s method when combined with analytic signal generation.

Low-Complexity One-Bit DOA Estimation for Massive ULA with a Single Snapshot

Existing one-bit direction of arrival (DOA) estimate methods based on sparse recovery or subspace have issues when used for massive uniform linear arrays (MULAs), such as high computing cost, estimation accuracy depending on grid size, or high snapshot-number requirements. This paper considers the low-complexity one-bit DOA estimation problems for MULA with a single snapshot. Theoretical study and simulation results demonstrate that discrete Fourier transform (DFT) can be applied to MULA for reliable initial DOA estimation even when the received data are quantized by one-bit methods. A precise estimate is then obtained by searching within a tiny area. The resulting method is called one-bit DFT. This method is straightforward and simple to implement. High-precision DOA estimates of MULA can be obtained with a single snapshot, and the computational complexity is significantly less than that of existing one-bit DOA estimation methods. Moreover, the suggested method is easily extensible to multiple snapshot scenarios, and increasing the number of snapshots can further improve estimation precision. Simulation results show the effectiveness of the one-bit DFT method.

A DFT-based phasor estimation method robust to primary and secondary decaying DC components

Fault current signals typically suffer from primary and secondary decaying DC (DDC) components due to the transient response of the power system and current transformer. On the other hand, the conventional phasor estimation method, discrete Fourier transform (DFT), is severely sensitive to these components and exhibits a significant oscillatory error. This paper proposes a new modification for the conventional DFT-based phasor estimation method to improve its performance in the face of fault current signals containing DDC components. The proposed method accurately estimates both DDC components using the fault current signal and an auxiliary signal generated using high-frequency modulation. The averaging filter is applied to the fault current and auxiliary signal over one cycle, and then parameters of the DDC components are estimated using its three successive results. In the last step, the undesired effect of DDC components is eliminated from DFT output. The efficiency of the proposed method is validated through fault current signals generated by mathematical formulation and simulated using the PSCAD/EMTDC environment. The overall analysis of the obtained results demonstrates that the new modification makes the DFT method robust against both DDC components.

Spectrum analysis for deterministic storage sizing in an isolated microgrid

This paper demonstrates a method of sizing Energy Storage Devices (ESD) and back up Diesel Generator (DG) using Discrete Fourier Transform (DFT) in an Isolated Microgrid. ESD and DG have different operational response characteristics. In an isolated microgrid, they can contribute to the supply demand imbalance in a complimentary way. The DFT method can allocate the balance power to be supplied between the ESD and DG through the frequency domain approach. High level generation can be delivered by DG, while the ES compensates for frequent and small fluctuations. The sizing of the ESD and DG are also determined based on the strategy presented.

Robust attitude estimation of rotating space debris based on virtual observations of neural network

SummaryHigh precise estimation and prediction of the target's attitude motion are key technologies for capturing and removing rotating space debris. In this article, a neural‐network‐enhanced Kalman filter (NNEKF) is proposed to improve the precision and robustness of attitude estimation algorithm. The main innovation of the NNEKF is to utilize virtual observations of the inertia characteristics to improve the filter's performances. The virtual observations are obtained using a neural network, which is offline trained using simulation data. In order to decrease the number of nodes of the network, the input data are preprocessed using the discrete Fourier transformation method. Moreover, by involving the characteristic frequencies in the input vector, the neural network can extract information from all the past observations, so as to grasp long‐term characteristics of the dynamical system. Therefore, the NNEKF can provide more precise estimation of the target's moment of inertia, and furthermore improve the accuracy and robustness of attitude estimation and prediction. Simulation results indicate that the NNEKF can reduce the estimation errors by 39% compared with the conventional EKF method when using the same measurement data. And the accumulation errors of prediction using estimates of the NNEKF is just as 24% as the conventional EKF.

Improved DFT Method for DOA Estimation with Extended Coprime Array:Based on Large Difference CoArray

In this paper, Direction of arrival estimation (DOA) in coprime array is investigated, and an advanced method for DOA estimation is presented with extended coprime array (ECA). Specifically, we use Discrete Fourier Transform (DFT) to obtain initial DOA estimation with large difference co-arrays generated by ECA, then perform Taylor series approximation and total least squares (TLS) method around the initial estimation to compensate the estimation offset. Compared to conventional DFT method, the proposed method enjoys better estimation accuracy with fewer computational burden since it avoids extra searches and benefits more from large difference co-array. Besides, in contrast to spatial smoothing based methods which halve array aperture, the proposed method avoids the process of spatial smoothing and fully utilizes uniform degrees of freedom (DOFs). In this case, the proposed method has advantages on estimation accuracy and computational efficiency with multiple impinging signals, especially under the condition of large difference co-array. Furthermore, the proposed method is applicable to other types of advanced coprime array. The superiority of the proposed method has been proved by numerical simulations.

Frequency estimator of sinusoid by interpolated DFT method based on maximum sidelobe decay windows

A frequency estimator of sinusoid by interpolated Discrete Fourier Transform (DFT) method based on maximum sidelobe decay (MSD) windows is proposed. Unlike other frequency estimators which use spectral lines located in fixed positions, the proposed estimator utilizes the maximum spectral line and two auxiliary spectral lines arbitrarily located within the weighted sinusoid spectrum main lobe. An accurate formula for the estimator MSE due to additive white noise is derived. To further improve the estimation performance, iterative procedure is used. It is analytically and numerically shown that the MSE increases with the increment of the interval length between the maximum spectral line and the auxiliary spectral line in additive white noise. The proposed estimator is more general and performs better than the competing estimators.

Robust high precision multi-frame motion detection for PMLSMs’ mover based on local upsampling moving least square method

This paper studies a multi-frame visual sub-pixel measurement technique to achieve the precise positioning of the permanent magnet linear synchronous motor (PMLSM) rapidly. A new matrix multiplication discrete Fourier transform (DFT) upsampling moving least square (MLS) algorithm is proposed to improve the accuracy and robustness of PMLSM positioning. Firstly, a line-scan vision-based measurement system is designed, and an aperiodic sinusoidal fringe image is placed on the pedestal as target image. Secondly, the local upsampling cross-correlation curve of adjacent one-dimensional signals is calculated to obtain sub-pixel displacement using the matrix-multiplied DFT method. Finally, to further improve the displacement accuracy, the MLS method is applied. Simulation tests verify that the proposed method is superior to other algorithms in measurement accuracy, calculation efficiency and measurement range. The experiment results confirm the feasibility and validity of the proposed method for detecting the mover motion under different working environments.

Applying Directly Modified RDFT Method in Active Power Filter for the Power Quality Improvement of the Weak Power Grid

The recursive discrete Fourier transformation (RDFT) method can be used for grid voltage phase-locking and harmonic current detection in a shunt active power filter (SAPF). However, in weak power grids such as microgrids, significant errors might occur in the amplitude and phase detection due to grid frequency deviation. In this study, to resolve this problem, a directly modified RDFT (DMRDFT) method is proposed for SAPF weak grid application. Through theoretical analysis, the errors of phase and amplitude detection were found to consist of fixed error and fluctuating error. The fixed error is only determined by frequency deviation, whereas the fluctuating error is also related to the recursive pointer and the initial phase. The DMRDFT algorithm can obtain the real grid frequency through the calculation of the phase angle difference for two consecutive periods. Then it can employ the grid frequency deviation and the recursive pointer value to directly correct the detection results gathered by the conventional RDFT algorithm. As a result, DMRDFT can yield accurate amplitude and phase information of the grid voltage or current with a simple calculation. Simulation results verify the high precision of the proposed DMRDFT method in both steady and dynamic situations. Experimental results show that the DMRDFT method can significantly increase the SAPF compensation performance when grid frequency shifts.

IMPLEMENTASI TRANSFORMASI FOURIER UNTUK TRANSFORMASI DOMAIN WAKTU KE DOMAIN FREKUENSI PADA LUARAN PURWARUPA ALAT PENDETEKSIAN GULA DARAH SECARA NON-INVASIF

Diabetes mellitus is the result of changes in the body caused by a decrease of insulin performance which is characterized by an increase of blood sugar level. Detection of blood sugar can be done with Invasive methods or non-invasive methods. However, non-invasive methods are considered better because they can check early, faster and accurate. The prototype output is values of intensity in the time domain, thus fourier transformation is very much needed to transform into the frequency domain. In this study, Fourier transformation methods used are Discrete Fourier Transform (DFT), Fast Fourier Transform Radix-2, and Fast Fourier Transform Radix-4. Evaluation for the best method is done by comparing the processing speed of each method. The FFT Radix-4 method is more effective to perform the transformation into the frequency domain. The average processing speed with the FFT Radix-4 method reaches 2.67×105 nanoseconds, and this is much faster 5.06×106 nanoseconds than the FFT Radix-2 method and 2.40×107 nanoseconds faster than the DFT method.

Fast heart rate extraction using CW Doppler radar with interpolated discrete Fourier transform algorithm

Doppler radar-based fast heart rate (HR) extraction has great application potential in stress and emotion recognition, anxiety treatments, etc. However, fast extraction of HR is still a great challenge for the vital sign detection applying the traditional discrete Fourier transform (DFT) method based on a continuous-wave (CW) Doppler radar sensor. When applying traditional DFT to the baseband signal analysis, the spectrum resolution will become insufficient if the time window is less than 10 s. In this paper, an interpolated DFT algorithm based on a poly-item cosine window is introduced to achieve fast extraction of HR with only 3 s data length. In addition, the leakage and grid effect phenomenon is presented to show the defects caused by the traditional DFT method. To verify the effectiveness of the proposed method, simulations are performed and experiments are executed using a 10-GHz CW Doppler radar sensor platform. Compared with the traditional DFT method, the interpolated DFT method reduces the average HR error from 8.48% to 1.87% based on the Hanning window and from 8.48% to 1.45% based on the rectangular window.