Frequency Response Analysis Method Research Articles

Reduced-order modeling and solution method for nonlinear frequency response analysis of large space truss structures

Reduced-order modeling and solution method for nonlinear frequency response analysis of large space truss structures

Quality Index for Assessment of the Mechanical Condition of Transformers’ Active Part with Frequency Response and Vibroacoustic Measurements

The paper describes the application of the numerical tool quality index for an objective evaluation of complementary frequency response analysis (FRA) and vibroacoustic method (VM) test methods. These diagnostic methods are used in the industrial practice of transformer diagnostics for the assessment of the mechanical condition of windings and a core. The quality index is based on a numerical comparison of the curve obtained from measurements and the reference curve in a frequency domain. The quality index is based on estimators for the covariance, variance, and expected values. First, both methods of analysis were applied to a group of transformers of similar construction, leading conclusions on quality index values being quickly drawn. Next, it was applied to another transformer’s FRA and VM measurement results. The results showed problems with its mechanical condition, thus confirming that the proposed methods can be used in the practical assessment of transformers with these two diagnostic methods. The assessment of transformer’s active-part mechanical condition with complementary FRA and VM methods can be performed much more easily with the proposed quality indices.

Artificial bee colony with predator effect algorithm for proportional integral derivative controller tuning

This paper proposes a novel artificial bee colony with predation effect (ABCPE) algorithm for tuning a proportional integral derivative (PID) controller. The mathematical model of ABCPE algorithm to introduce predator effect in the foraging behavior of artificial bees colony algorithm has been formulated. The proposed algorithm has been tested on tuning problems of different process models. The simulation results reveal that the closed-loop responses are relatively fast and non-oscillatory as compared to the frequency response analysis method for reference tracking. Further, the results obtained using ABCPE are also compared with other evolutionary algorithms. The exhaustive analysis shows that the ABCPE-based solution approach leads to a set of tuning parameters having smaller overshoot, less setting time, and rise time compared to other solution approaches. The stability analysis using Nichols plot reveals that the phase margin of proposed algorithm is higher as compared to other tuning methods. Finally, the convergence behavior and robustness analysis reveals the effectiveness of the proposed approach to solve engineering design problems.

Power Transformer Winding Deformation Diagnosis Based on the Sum of Two‐Way Shortest Distance

Frequency response analysis (FRA) method has been widely used in the world, but the interpretation of its signatures is still a hard problem to solve. This paper introduces a method of the sum of two‐way shortest distance for transformer winding deformation fault diagnosis, which is based on trajectory similarity between FRA signatures. Compared with most existing methods, it does not need order preservation; however, it focuses more on the trajectory itself. The geometric principle of the sum of two‐way shortest distance is introduced and analyzed in detail. By using the circuit analysis software, the equivalent circuit model of the transformer is established, a group of the FRA signatures of three types of transformer winding fault, including axial displacement, radial deformation, and disk space variation fault, are obtained. The distribution of different type of faults is studied by using the sum of two‐way shortest distance to process the FRA signatures in three different frequency bands. Using the sum of two‐way shortest distance as input, the support vector machine (SVM) is employed to train a predictive engine for transformer winding deformation fault diagnosis. Result shows that the proposed method can well classify and diagnose transformer winding deformation fault. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Transformer Winding Fault Classification and Condition Assessment Based on Random Forest Using FRA

At present, the condition assessment of transformer winding based on frequency response analysis (FRA) measurements demands skilled personnel. Despite many research efforts in the last decade, there is still no definitive methodology for the interpretation and condition assessment of transformer winding based on FRA results, and this is a major challenge for the industrial application of the FRA method. To overcome this challenge, this paper proposes a transformer condition assessment (TCA) algorithm, which is based on numerical indices, and a supervised machine learning technique to develop a method for the automatic interpretation of FRA results. For this purpose, random forest (RF) classifiers were developed for the first time to identify the condition of transformer winding and classify different faults in the transformer windings. Mainly, six common states of the transformer were classified in this research, i.e., healthy transformer, healthy transformer with saturated core, mechanically damaged winding, short-circuited winding, open-circuited winding, and repeatability issues. In this research, the data from 139 FRA measurements performed in more than 80 power transformers were used. The database belongs to the transformers having different ratings, sizes, designs, and manufacturers. The results reveal that the proposed TCA algorithm can effectively assess the transformer winding condition with up to 93% accuracy without much human intervention.

Effect of Test Cable Termination on Frequency Response of Transformer Winding

Sweep Frequency Response Analysis (SFRA) method is the most powerful tool to predict the condition of transformer winding. The reliable measurement of frequency response is equally important as its interpretation. A few standards (IEEE std. C57.149-2012, IEC 60076, the Chinese Electrical Power Industry Standard ICS27.100.F24-2005) & much research work have been published, stating dos & don’ts while measuring the frequency response of transformer winding. In this paper, an attempt is made to introduce an additional factor affecting frequency response, while doing measurements. Here, the effect of test cable termination at transformer winding terminals, to prevent signal reflection, on frequency response is presented. A possible way to select suitable value/s of terminating resistance that can correct frequency response is also proposed.

Online Prediction Method for Power System Frequency Response Analysis Based on Swarm Intelligence Fusion Model

Instability at transient frequency caused by faults in complex power systems is one of the greatest threats to operational safety. By analyzing the frequency response of power system in real-time and adopting control strategies promptly, power system accidents can be efficiently prevented. While existing online analysis methods integrate physical-driven and data-driven methodologies, they do not effectively utilize frequency timing characteristics. Consequently, a swarm intelligence fusion model, which integrates physical-driven and data-driven methods, is proposed as an improved frequency response analysis method. The transient frequency affecting components are separated into primary state variables and system time series data based on the properties of the time sequence. To preserve the actual relationship of the electrical mechanism model, the system frequency response (SFR) model is used as the physical-driven method for the primary state variables of the system. The Long Short Term Memory (LSTM) network was used as the data-driven method to extract timing features and correct the SFR model’s prediction using the system time series data as input. The two methods are combined using the bootstrap mode to form the fusion model, and the structure of the model is optimized using an improved sparrow search algorithm (ISSA), a swarm intelligence optimization algorithm. The model structure is adapted autonomously, implementing a method for online frequency response analysis. The simulation on the New England 39-bus system has verified that the method can quickly and accurately calculate the dynamic process of frequency response after a large-scale disturbance.

Curved flexoelectric and piezoelectric micro-beams for nonlinear vibration analysis of energy harvesting

Micro/nano-scale energy harvester is an enabling technology to provide sustained energy solutions for various micro/nano-electromechanical devices, this has attracted intensive research interests in both academia and industry in the past decades. Exploring various design possibilities for energy harvesters in terms of geometry, topology, materials as well as harnessing the interesting nonlinear responses have the potential to break the current limit of energy harvesters in terms of energy efficiency and power density. While most designs were limited to straight beams, in this work, we demonstrate that the nonlinear vibration of energy harvester is significantly affected by curved shapes and we show the possibility of improving its performance by tuning the structural curvature. By developing a couple stress-based piezo-flexoelectric curved beam model and using the multiple time scale method for the nonlinear frequency response analysis, the effect of structural curvature in the nanoscale arc-shaped beam is quantitatively evaluated.

Experimental and numerical vibration analysis of surface mechanical attrition treatment

The surface mechanical attrition treatment creates a nanocrystal layer with improved mechanical properties without changing the surface chemistry. Vibration produces residual stresses in a layer close to the surface by successive impacts on the material surface. Vibration treatments represent a “green” alternative to surface treatments without the use of chemicals and high temperatures. Depending on the operating frequency and amplitude of a particular vibration platform, the most decisive parameter to be controlled for the efficiency of the application is the velocity. Vibration platforms in the SMAT process are ultrasonic and mechanically based platforms. This work presents a vibration platform where velocity is below 1 m/s, which is the lowest operating speed defined in the SMAT process. This work includes both analytical and numerical solutions to the natural frequency values of the vibrating table. The operating conditions were determined by finding the natural frequency values. The amplitude, velocity, and acceleration relations of the vibrating table that will occur during the process were found using the frequency response analysis method. ANSYS and MATLAB were used for numerical and analytical solutions, respectively. Numerical and analytical results were in agreement with the experimental modal analysis.

Protection of HDG Steel Using ORMOSIL Coatings Enhanced with CeO2(5-ATDT)- Ceramic Nanocontainers

First, we studied the anticorrosion efficiency of the corrosiveness inhibitors CeO2, 5-amino-1,3,4-thiadiazole- 2-thiol (5-ATDT), Ce(NH4)2(NO3)6 in hot-dip galvanized zinc (HDG) steel. The best protection is shown by the compound Ce(NH4)2(NO3)6 among the three. Second, CeO2 ceramic nanocontainers were prepared, which were loaded with 5-ATDT. Third, organically modified silica (ORMOSIL) coatings were produced on hot-dip galvanized zinc (HDG) steel, which was reinforced with CeO2(5-ATDT) nanocontainers. Finally, the anticorrosion protection of these composites was studied using the Frequency Response Analysis (FRA) method, and it was established to reinforce ORMOSIL with CeO2(5-ATDT); inducing the phenomenon of “self-healing”.

Application of Frequency Response Analysis Method to Detect Short-Circuit Faults in Three-Phase Induction Motors

The industry has widely accepted Frequency Response Analysis (FRA) as a reliable method to detect power transformers mechanical deformations. While the FRA technique has been recommended in recent literature as a potential diagnostic method to detect internal faults within rotating machines, detailed feasibility studies have not been fully addressed yet. This paper investigates the feasibility of using the FRA technique to detect several short circuit faults in the stator winding of three-phase induction motors (TPIMs). In this regard, FRA testing is conducted on two sets of induction motors with various short circuit faults. Investigated faults include short circuits between two phases, short circuit turns within the same phase, phase-to-ground, and phase-to-neutral short circuit. The measured FRA signatures are divided into three frequency ranges: low, medium, and high. Several statistical indicators are employed to quantify the variation between faulty and healthy signatures in each frequency range. Experimental results attest the feasibility of the FRA technique as a diagnostic tool to detect internal faults in rotating machines, such as induction motors.

Interpretation of Inter-Turn Fault in Transformer Winding Using Turns Ratio Test and Frequency Response Analysis

The transformer is critical equipment in electrical power systems as it is continuously exposed to various failures. Inter-turns fault in the transformer reduces the turns of the winding, thus it can be detected using a transformer-turns-ratio (TTR) test. On the other hand, the Frequency Response Analysis (FRA) method is used for assessing the mechanical condition of the transformer winding and core. In this paper, the TTR, and FRA methods are proposed to detect the inter-turns fault in the transformer winding. The winding inter-turn fault was investigated using FRA inductive inter-winding measurement and compared with the TTR test. Findings from the statistical analysis showed that FRA inductive inter-winding can detect the inter-turn fault. Finally, acceptance limits for the absolute sum of logarithmic error and standard deviation were proposed. The limits were established based on TTR’s acceptance limit from the IEEE standard. This finding proves that the FRA test can be used to complement the result in the conventional TTR test.

Equivalent Broadband Electrical Circuit of Synchronous Machine Winding for Frequency Response Analysis Based on Gray Box Model

Frequency response analysis (FRA) is a popular tool to detect transformer winding deformation faults. It has been recently used to diagnose the winding inter-turn short circuit fault of the electric machine. The application of FRA is based on the fact that the winding can be equivalent to an electrical circuit consisting of resistance, inductance, and capacitance. Therefore, to obtain an accurate broadband equivalent circuit model of synchronous machine and perform the fault analysis and diagnosis, this paper introduces the gray box model technique based on the state space and genetic algorithm. The electrical circuit of a form-wound coil of a 4 kW machine with known electrical parameters is used to verify the proposed method primarily. Besides, the equivalent circuit modeling is carried out and experimentally verified on an actual 5 kW synchronous machine. Finally, the fault simulation analyses of winding inter-turn short circuits are performed based on the proposed equivalent electrical circuit. The verification result shows that the circuit parameters identified by the proposed method are accurate. Moreover, the fault simulation results indicate that the inter-turn short circuit faults can cause apparent variations in the frequency response curves. It is feasible to detect the winding fault of the synchronous machine by the FRA method.

Investigations on using white noise as a test signal for performing frequency response measurements on transformers

White noise is a random signal mathematically analogous to an impulse function in time and flat spectrum in frequency. Naturally, the white noise may be used as an alternative test signal for determining the frequency response analysis (FRA) of transformers. Such an attempt not only enhances the power of FRA testing but also enable development of an online diagnostic test method. At present, the concept of using white noise is well-defined, but the crucial knowledge of applying the same on a real-time power transformer is currently not available or at least in the public domain. The study attempts to bridge this gap between theoretical contribution and practical requirement. The mathematical concept, experimental illustrations, and onsite / field validation altogether provides a complete insight into the identified problem. In this regard, an experimental study that investigates on using white noise as a test signal in determining the frequency response of a two-winding transformer is initiated. First, the possibilities of application of theoretical and mathematical concepts of using white noise as a test signal for measuring the frequency response of winding-core assembly is verified. Following this, the white noise signal applied to the circuit model and the corresponding response is recorded and the arbitrary choice of data samples measured from the circuit model is ensured using brute-force approach. In this procedure, the number of samples are manually increased until the magnitude and natural frequencies of resonant peaks matches atleast within 2 % accuracy with conventional FRA measurements. This is performed to ensure the repeatability of the method. Later, the time and frequency dependent statistical properties of the measured signals are computed and the respective transfer function is obtained. Subsequently, the transfer function obtained from the white noise method and the respective natural frequency (tabulated) are compared with the values measured using conventional FRA method. Once this is accomplished, these findings are experimentally validated on an actual high voltage transformer.

Hybrid CNN-LSTM approaches for identification of type and locations of transmission line faults

Timely and accurate detection of transmission line faults is one of the most important issues in the reliability of the power systems. In this paper, in order to assess the effects of impedance and location of the fault in identifying and classifying it, the frequency response analysis (FRA) method is utilized. This method clearly shows the smallest effects of the faults on voltage and current signals in the frequency domain. Interpretation of the results associated with the FRA procedure is considered a weakness of this method. To overcome this issue and accurately categorize types and locations of various transmission lines faults such as asymmetric faults and symmetric faults, machine learning, and deep learning applications called support vector machine (SVM), decision tree (DT), k-Nearest Neighbors (k-NN), convolutional neural network (CNN), long short term memory (LSTM), and a hybrid model of convolutional LSTM (C-LSTM) are utilized. Introduced faults are applied with various impedances in 6 segments of an IEEE standard transmission line system. Then, the frequency response curves (FRCs) for them are computed and selected as input datasets for the suggested networks. After categorizing the types and locations of faults, the results for each network are analyzed via different statistical performance evaluation metrics. Finally, in order to early detection of faults, the new high impedance faults (7000 and 9000 O) are applied based on the previous routine in the transmission line. At this stage, evaluations demonstrate the capability of the C-LSTM followed by SVM, DT, k-NN, CNN, and LSTM in categorizing the type and location of transmission line faults.

Decoupling oxygen and water transport dynamics in polymer electrolyte membrane fuel cells through frequency response methods based on partial pressure perturbations

Concentration frequency response analysis (CFRA) applies partial pressure of a certain reactant and detects current or voltage response depending on the electric control applied. In this paper experimental and theoretical spectra of this novel frequency response analysis method of polymer electrolyte fuel cells are analyzed. It is shown that the dynamic contribution of oxygen transport in the channel and water sorption in Nafion could be separated from other ones if oxygen and water partial pressure are respectively used as inputs. This allows to study these phenomena separately and to avoid ambiguities encountered in EIS spectra where several dynamics are often overlapped and indistinguishable. The time required to the oxygen to diffuse in the channel and in the porous electrode was directly estimated through analysis of patterns in the CFRA spectra.

Double-End Excitation of a Single Isolated Transformer Winding: An Improved Frequency Response Analysis for Fault Detection

Frequency Response Analysis (FRA) is a comparison based method and is useful to identify the mechanical fault in transformer winding only when the ‘healthy’ or ‘reference’ magnitude response is available. But, in practice, ‘healthy’ response may not be always available and the subsequent FRA measurement alone also cannot detect the fault. This is one serious limitation for conventional FRA method and the desired solution is still far away. To this effect, this paper presents an innovative way of measuring the frequency responses of transformer winding with two equal and opposite polarity sinusoidal excitations from two ends. For viability test, the present work is limited to fault-detection only in a single isolated uniformly-wound transformer winding followed by verification on an actual single-phase autotransformer. The two equal and opposite polarity excitations for such winding are likely to impose a virtual ground at the centre and hence the two admittances measured from the two source-ends are likely to be identical. Two admittances also get dissimilar for a fault in transformer winding and therefore the fault could be identified simply by measuring and comparing these two responses in absence of ‘healthy’ response. Pertinent simulation and experimental results are also included in the paper.

Intelligent Classifiers in Distinguishing Transformer Faults Using Frequency Response Analysis

With the expansion of the use of frequency response analysis (FRA) as a reliable tool for fault detection in transformers, more capabilities of this method are discovered every day. So that today the number of transformer faults that can be identified by FRA method has also increased. One of the most critical steps in fault detection with FRA is to distinguish faults and classify them in different classes. In this paper, well-known intelligent classifiers (probabilistic neural network, decision tree, support vector machine, and k-nearest neighbors) are used to classify transformer faults. For this purpose, the necessary measurements are performed on the model transformers under the healthy condition and under different fault conditions (axial displacement, radial deformation, disc space variation, short-circuits, and core deformation). Then, by dividing the frequency ranges of the measured transfer functions of the transformer, a new feature based on numerical and statistical indices for training and validation of classifiers is proposed. After completing the training process, the performance of the classifiers is evaluated and compared by applying the data obtained from real transformers.

Polymer Electrolyte Fuel Cell Degradation Mechanisms and Their Diagnosis by Frequency Response Analysis Methods: A Review

Several experimental techniques involving dynamic electrical variables are used to study the complex behaviour of polymer electrolyte membrane fuel cells in order to improve performance and durability. Among them, electrochemical impedance spectroscopy (EIS) is one of the most employed methods. Like any frequency response analysis (FRA) methodology, EIS enables one to separate the contribution of many processes to performance losses. However, it fails to identify processes with a similar time constant and the interpretation of EIS spectra is often ambiguous. In the last decade, alternative FRA methodologies based on non-electrical inputs and/or outputs have been developed. These studies were mainly driven by requirements for a better diagnosis of polymer electrolyte membrane fuel cells (PEMFCs) faulty operation conditions as well as better component and material design. In this contribution, a state-of-the-art EIS and novel FRA techniques for PEMFC diagnosis are summarised. First, common degradation mechanisms and their causes are discussed. A mathematical framework based on linear system theory of time invariant systems is described in order to explain the theoretical implications of the use of different input/output configurations. In relation to this, the concepts and potential are depicted as well as the problematic aspects and future prospective of these diagnostic approaches.

Research Situation Analysis of On-line Detection Technology for Power Transformer Winding Deformation

Background: Winding deformation is one of the most common faults in power transformers, which seriously threatens the safe operation of transformers. In order to discover the hidden trouble of transformer in time, it is of great significance to actively carry out the research of transformer winding deformation detection technology. Methods: In this paper, several methods of winding deformation detection with on-line detection prospects are summarized. The principles and characteristics of each method are analyzed, and the advantages and disadvantages of each method as well as the future research directions are expounded. Finally, aiming at the existing problems, the development direction of detection method for winding deformation in the future is prospected. Results: The on-line frequency response analysis method is still immature, and the vibration detection method is still in the theoretical research stage. Conclusion: The ΔV − I1 locus method provides a new direction for on-line detection of transformer winding deformation faults, which has certain application prospects and practical engineering value.