Harmonic Components Of Signal Research Articles

NEURAL NETWORK PROCESSING OF ELECTROMAGNETIC ACOUSTIC SIGNALS TO IDENTIFY THE STRESS-STRAIN STATE AND DAMAGE OF POWER EQUIPMENT

The purpose of the study is to develop and train an artificial neural network to identify the stress-strain state and damage to the metal of power equipment based on the values of the parameters of the harmonic components of the electromagnetic-acoustic transducer signal.
 
 Materials and methods. Experimental study of the relationship between the parameters of the harmonic components of the signal of an electromagnetic-acoustic transducer with the stress-strain state and damage to the structure of standard metal samples, development of an artificial neural network and methods for its training to identify the stress-strain state and damage to the structure of the metal according to the loading diagram.
 
 Results. Analysis of changes in the microstructure and frequency models of standard steel samples used in power engineering confirmed the possibility of identifying the stress-strain state and damage to the structure of metals based on the values of the parameters of the harmonic components of the electromagnetic-acoustic transducer signal. To solve this problem, an artificial neural network has been developed and trained. After training, the effectiveness of the network in identifying the stress-strain state and damage to the structure of metals reached 92.16%, which is acceptable for the tasks of recognizing the technical condition of metal structural elements of electrical installation equipment.
 
 Conclusions. The use of an artificial neural network to identify the stress-strain state and damage to metal structures based on the harmonic parameters of the electromagnetic-acoustic transducer signal enables to identify areas of concentration of mechanical stress and damage to the metal structure at the early stage of development, thereby increasing reliability and safety operation of electrical equipment.

Quasi newton least mean fourth control for multifunctional grid tied solar photovoltaic system

The quality of power delivered has significantly decreased as distributed energy resources are increasingly incorporated into the current electricity grid. Three-phase voltage source converters with strong and stable control capability are essential for grid-connected solar energy systems. The application of a quasi-newton least mean fourth-based adaptive control strategy for producing the reference grid currents is described in this article. The presented control scheme provides the seamless flow of active and reactive power from the solar system to the grid along with the redressal of significant power quality issues such as harmonic generation at the grid, worsening of power factor, and load unbalancing. The proposed quasi-newton least-mean fourth algorithm aids in effectively filtering the significant lower-order harmonic components. The system is tested under various conditions such as constant irradiance, varying irradiance, and balanced and unbalanced load patterns to demonstrate the robustness and stability of the quasi-newton least-mean fourth algorithm. The simulation results are also presented to illustrate the control strategy's capabilities. dSPACE 1202 controller is utilized for the software-in-loop implementation, and the empirical assessment is verified for both steady-state and dynamic loadconditions.

Comparing Phantom and Animal Metrics Applied in the Determination of Focused Ultrasound Stable and Inertial Cavitation Levels.

The opening of the blood-brain barrier (BBB) to allow therapeutic drug passage can be achieved by inducing microbubble cavitation using focused ultrasound (FUS). This approach can be monitored through analysis of the received signal to distinguish between stable cavitation associated with safe BBB opening and inertial cavitation associated with blood vessel damage. In this study, FUS phantom and animal studies were used to evaluate the experimental conditions that generate several cross-consistent metrics having the potential to be combined for the reliable, automatic control of cavitation levels. Typical metrics for cavitation monitoring involve observing changes in the spectrum generated by applying the discrete Fourier transform (DFT) to the time domain signal detected using a hydrophone during FUS. A confocal hydrophone was used to capture emissions during a 10 ms FUS burst, sampled at 32 ns intervals, to produce 321,500 points and a high-resolution spectrum when transformed. The FUS spectra were analyzed to show the impact that equipment-transients and well-known DFT-related distortions had on the metrics used for cavitation control. A new approach, physical sparsification (PH-SP), was introduced to sharpen FUS spectral peaks and minimize the effect of these distortions. It was demonstrated that the general spectral signal-to-noise ratio (SNR) could be improved by removing the initial noisy phantom hydrophone signal transient. Minor changes in the transient length digitally removed from the sampled values significantly changed the spectral bandwidths of all the harmonically related FUS signals. We evaluated signal processing techniques to minimize the impact these DFT-related distortions on area-under-the-curve (AUC) metric calculations, and we identified the advantages of using PH-SP and proposed new metrics when characterizing FUS spectral properties. The results show many second, third and sub-harmonic metrics provide cross-consistent evidence of changes between stable and inertial cavitation levels. Removing the first harmonic signal component with a hardware low-pass filter allowed the hydrophone gain to be boosted without introducing distortion, leading to an improved analysis of the sub-harmonic signal orders of magnitude smaller in intensity. Metrics that optimized the energy in the real component of the complex-valued PH-SP spectra provided a 32% increase in the sub-harmonic sensitivity compared to standard metrics. A preliminary investigation of existing and proposed metrics showed that system noise could be large enough to mask the transition between stable and inertial cavitation. Strong narrowing of sub-harmonic peak shapes on applying physical sparsification (PH-SP) were seen in both phantom and animal studies. However, validating equivalent trends of the metrics with pressure were limited by the increased system noise level in the animal study combined with the natural variability between subjects studied. The combined use of hardware low-pass filters and physical sparsification to selectively removing distortions in the spectrum allowed the optimization of metrics for cavitation monitoring by improving the sub-harmonic sensitivity.

A subjective evaluation of different music preprocessing approaches in cochlear implant listeners.

Cochlear implants (CIs) can partially restore speech perception to relatively high levels in listeners with moderate to profound hearing loss. However, for most CI listeners, the perception and enjoyment of music remains notably poor. Since a number of technical and physiological restrictions of current implant designs cannot be easily overcome, a number of preprocessing methods for music signals have been proposed recently. They aim to emphasize the leading voice and rhythmic elements and to reduce their spectral complexity. In this study, CI listeners evaluated five remixing approaches in comparison to unprocessed signals. To identify potential explaining factors of CI preference ratings, different signal quality criteria of the processed signals were additionally assessed by normal-hearing listeners. Additional factors were investigated based on instrumental signal-level features. For three preprocessing methods, a significant improvement over the unprocessed reference was found. Especially, two deep neural network-based remix strategies proved to enhance music perception in CI listeners. These strategies provide remixes of the respective harmonic and percussive signal components of the four source stems "vocals," "bass," "drums," and "other accompaniment." Moreover, the results demonstrate that CI listeners prefer an attenuation of sustained components of drum source signals.

Mathematical models of truck failures in the North

The article studies the failures of 50 KAMAZ trucks operated in the Republic of Sakha (Yakutia). The statistical analysis results of failures of KAMAZ truck parts and assembly units groups which limit its reliability in adverse climatic and road conditions of the North are given. Autocorrelation of the failure time series of the observed groups revealed the presence of a linear trend for every series, and the statistical significance of the linear regression equation parameters was confirmed for all groups, except for the steering. The wear rate in harsh natural and climatic conditions can be estimated in terms of the value of the regression slope. The groups of parts and assembly units were ranked by the values of the regression slope. After the failure time series have been centred, the harmonic analysis was carried out. The significant harmonic components were allocated from the Fourier series to describe the regular change in the failure series. Mathematical models, consisting of equations of linear trend and significant harmonics, approximate the failure time series with an acceptable confidence level, which makes it possible to determine the rhythmological features of vehicle operability changes in extreme conditions of permafrost zone.

Anomalous wavefront control via nonlinear acoustic metasurface through second-harmonic tailoring and demultiplexing

We propose a nonlinear acoustic metasurface concept by exploiting the nonlinearity of locally resonant unit cells formed by curved beams. The analytical model is established to explore the nonlinear phenomenon, specifically the second-harmonic generation (SHG) of the nonlinear unit cell, and validated through numerical and experimental studies. By tailoring the phase gradient of the unit cells, nonlinear acoustic metasurfaces are developed to demultiplex different frequency components and achieve anomalous wavefront control of SHG in the transmitted region. To this end, we numerically demonstrate wave steering, wave focusing, and self-bending propagation. Our results show that the proposed nonlinear metasurface provides an effective and efficient platform to achieve significant SHG and separate different harmonic components for wavefront control of individual harmonics. Overall, this study offers an outlook to harness nonlinear effects for acoustic wavefront tailoring and develops potential toward advanced technologies to manipulate acoustic waves.

Evaluation of Harmonic Signals Derived From Multiple Spatially Separated Samples for Magnetic Particle Imaging

We studied the harmonic components of signals derived from magnetization of magnetic nanoparticles depending on the direct current magnetic field at magnetic particle imaging (MPI). When single sample was located, the field free point confirmed that the third harmonic has the maximum value and the second harmonic has the minimum value. We proposed a new analytical method that takes the ratio of the third harmonic to the second harmonic to improve the resolution. Moreover, the complex signal obtained from separately located two samples was measured under a gradient magnetic field. We discussed the important issues with respect to the even harmonics in application of MPI for diagnostics in human body.

Heat release rate response of azimuthal thermoacoustic instabilities in a pressurized annular combustor with methane/hydrogen flames

In this study, the heat release rate (HRR) response during self-excited azimuthal thermoacoustic instabilities in a pressurized annular combustor is investigated for hydrogen/methane blended flames. The equivalence ratio and hydrogen power fraction were varied for a constant air mass flow rate, resulting in self-excited azimuthal instabilities of varying amplitudes. Although significant harmonic components were observed in the pressure response, the spatially integrated HRR response was dominated by the fundamental component of the mode. Despite the wide range of operating conditions, an approximately linear relationship was observed between limit cycle velocity and HRR oscillation amplitudes for both the fundamental and first harmonic components, and the phase varied slowly as a function of amplitude. As the phase lag between the HRR and pressure oscillations reduced, the instability amplitude increased due to the increased driving through the Rayleigh criterion. Fuel blends with higher hydrogen fractions produced larger phase differences and lower amplitude responses. High-speed flame imaging was used to analyze the spatial distribution of the HRR oscillations which exhibited significant harmonic content and only provided small contributions to the integrated HRR. The high frequencies associated with these harmonics resulted in the presence of multiple structures with opposing phases simultaneously on the flame brush. This explains why the integrated contributions to the HRR were small. Fourier mode decomposition was employed to better understand the observed reduction in instability amplitude with increasing hydrogen power fraction. When the hydrogen content is higher, multiple fluctuations of the HRR are present simultaneously on the flame, resulting in global cancellation. In contrast, for lower hydrogen content, higher amplitude instabilities are generated, resulting in different flame dynamics. At high amplitudes, the response is more asymmetric as a result of the azimuthal nature of the instability.

Modelling and Control Development of a Cascaded NPC-Based MVDC Converter for Harmonic Analysis Studies in Power Distribution Networks

Today’s power distribution networks are predicted to incorporate more Power Electronics (PE)-based power conversion systems, widely acknowledged as harmonic sources. Concerns about power harmonic severity in the distribution networks can arise, especially with the growing numbers of Medium Voltage Direct Current (MVDC) systems, which are also facilitated by such power converters. Yet, an accurate harmonic model of the MVDC converter is required to investigate its harmonic emissions, propagations, effects, and solutions in today’s distribution networks. This article is devoted to the development of a detailed model of a cascaded Neutral Point-Clamped (NPC)-based MVDC converter for accurate harmonic analysis studies. An appropriate control system with a simple Proportional Integral (PI) controller tuned using the loop-shaping technique is developed. An interleaved Sinusoidal Pulse-Width Modulation (SPWM) scheme aiming to improve the harmonic performance of such an application is introduced. The detailed model of the MVDC system was developed using the Simulink/MATLAB simulation environment, for which the concept of operation was validated, control system performance was investigated, and the effectiveness of the harmonic reduction method was analysed. The key finding is that the interleaved SPWM technique has significantly reduced the Total Harmonic Distortion (THD) to 2% with no significant even-order harmonic components in comparison to the reported models.

NEURAL NETWORK SIGNAL PROCESSING WITH NONLINEAR DISTORTIONS IN A “SLIDING TIME WINDOW”

Continuous monitoring of the signals harmonic components level in electrical networks is an important task in ensuring high-quality power supply to consumers. This applies to both normal and emergency power system operation modes. One of the nonlinear signal distortions sources in measuring devices are nonlinear operating transformers modes. Saturation effects and hysteresis phenomena in measuring current transformers make it difficult to identify the actual operating parameters of electric power equipment. The paper shows that the apparatus of artificial neural networks can be used to control the nonlinear distortions of industrial frequency signals. The proposed algorithm based on a direct propagation neural network is tested on the example of distortion of current signals in the secondary winding of a measuring transformer. It is shown that it is possible to determine the amplitude, frequency and phase of the signal harmonic components in a “sliding time window” with an accuracy of a few percent. Estimates of the required frequency and interval of signal digitization are made; a comparison is made using the discrete Fourier transform algorithm.

Harmonic Components Analysis of Emitted Ultraviolet Signals of Aged Transmission Line Insulators under Different Surface Discharge Intensities.

Flashover on transmission line insulators is one of the major causes of line outages due to contamination from the environment or ageing. Power utility companies practicing predictive maintenance are currently exploring novel non-contact methods to monitor insulator surface discharge activities to prevent flashover. This paper presents an investigation on the UV pulse signals detected using UV pulse sensor due to the discharges on the insulator surfaces under varying contamination levels and insulator ages. Unaged and naturally aged insulators (0 to >20 years) were artificially contaminated (none, light to heavy contamination). The electrical stresses on the insulator surfaces were varied to generate varying discharge intensity levels on the surfaces of the insulator. The DC and harmonic components of UV pulse signals detected during surface discharges were recorded and analysed. Results show a positive correlation between the discharge intensity level of contaminated and aged transmission insulators with the DC and harmonic components of the UV pulse signals. Furthermore, the study revealed that under dry insulator surface conditions, insulator ageing has a more profound effect during discharges than contamination level. The findings from this study suggest that the use of UV pulse sensors to monitor UV pulse signals emitted during insulator surface discharges can be another novel non-contact method of monitoring transmission line insulator surface conditions.

Characteristic Parameter Optimization of Wireless Flaw Sensing System Based on Active Interference Suppression Algorithm

Based on the active interference suppression algorithm, this study combines the radar working mode and the interference type and realizes the effective detection of the flaw detection signal by successively processing the radar receiving signal and the filtering processing. Firstly, this article builds a simulation platform similar to the actual situation to verify the existing conventional active interference suppression algorithms. Secondly, for the detection of chirp active deception jamming signals entering from the main lobe, a radar active deception jamming detection method based on the characteristic parameter matching of the harmonic components of active deception jamming signals is proposed. After that, the spectral characteristics of the harmonic components of the deception interference signal are analyzed, and the center frequency and the tuning frequency of the real target echo are obtained. Finally, by establishing a frequency modulation parameter library for possible interference harmonic signal components, the acquisition phase of the radar gate by the jammer matched analysis with the preestablished frequency modulation parameter library is implemented to achieve active deception interference detection. This method can effectively detect active deception jamming signals in a complex tunnel environment. The interference suppression algorithms verified by simulation include noise FM interference suppression algorithm based on cancellation and distance false target interference suppression algorithm based on LFM radar summary processing. Through actual measurement data processing and analysis, the effectiveness of the method is verified and the idea of interference suppression is expanded. The construction of the simulation platform is obtained by appropriately modifying the actual parameters, a certain type of suppression jammer, and a certain type of deception jammer used in a certain countermeasure field test at a radar station.

Transient Thermo-Acoustic Responses of Methane/Hydrogen Flames in a Pressurized Annular Combustor

Abstract The present article experimentally investigates the triggering and transient growth of azimuthal instabilities in a pressurized laboratory-scale annular combustor featuring 12 methane/hydrogen flames, as the equivalence ratio is ramped up and down. The ramping rate of equivalence ratio is varied to examine its effect on the transient thermo-acoustic response and the driving mechanisms, highlighting a number of previously unseen features. As the equivalence ratio is dynamically increased, all cases were observed to feature a distinct modal trajectory, during the onset of high-amplitude instabilities. Strongly spinning counterclockwise modes are first excited before a dynamic transition to strongly spinning clockwise modes occurs. Furthermore, the strength of the spinning mode (quantified through the spin ratio or nature angle) was shown to feature a local minima before the spinning mode stabilized in the system, which corresponds to an almost pure spinning state. Hysteresis behavior was observed in both the amplitude and nature of the mode, resulting in different thresholds for the onset and decay of the instability, depending on the time history of the combustor. Increasing the ramping rate was found to reduce the amount of hysteresis in the system. Furthermore, the high amplitude of the instability resulted in significant harmonic components. The behavior of the harmonics generally resembles the fundamental component, albeit with some notable exceptions.

0.79\u2009ppm scale-factor nonlinearity whole-angle microshell gyroscope realized by real-time calibration of capacitive displacement detection

Whole-angle gyroscopes have broad prospects for development with inherent advantages of excellent scale factor, wide bandwidth and measurement range, which are restrictions on rate gyroscopes. Previous studies on the whole-angle mode are based mostly on the linear model of Lynch, and the essential nonlinearity of capacitive displacement detection is always neglected, which has significant negative effects on the performance. In this paper, a novel real-time calibration method of capacitive displacement detection is proposed to eliminate these nonlinear effects. This novel method innovatively takes advantage of the relationship between the first and third harmonic components of detective signals for calibration. Based on this method, the real-time calibration of capacitive displacement detection is achieved and solves the problems of traditional methods, which are usually related to the vibration amplitude, environmental variations and other factors. Furthermore, this novel calibration method is embedded into a whole-angle control system to restore the linear capacitive response in real time and then combined with a microshell resonator for the first time to exploit the enormous potential of an ultrahigh Q factor and symmetric structure. The effectiveness is proven because the angle drift is reduced significantly to improve the scale-factor nonlinearity by 14 times to 0.79 ppm with 0.0673°/h bias instability and a 0.001°/s rate threshold, which is the best reported performance of the MEMS whole-angle gyroscope thus far. More importantly, this novel calibration method can be applied for all kinds of resonators with the requirement of a linear capacitive response even under a large resonant amplitude.

Nonlinear Error Compensation of PGC Demodulation With the Calculation of Carrier Phase Delay and Phase Modulation Depth

We propose a novel phase generated carrier (PGC) demodulation method by simultaneously calculating the carrier phase delay ( θ ) and the phase modulation depth ( m ) to compensate the nonlinear error introduced by θ and m . Firstly, θ is calculated by adopting the fundamental in-phase and quadrature harmonic components and their differential components. Secondly, this calculated θ is used to set the phases of the harmonic components of reference carrier signal to obtain three new harmonic components independent of θ . Later, m is calculated and compensated by adopting the three new harmonic components and their differential components to obtain the demodulated result. Theoretical analysis and realization of the method are described in detail. Simulation and displacement measurement experiments with different θ and m are carried out to validate the proposed method. The experimental results demonstrate that the proposed method can accurately calculate and compensate θ and m , and effectively eliminate the nonlinear error of the demodulated signal.

Compound fault diagnosis of rolling element bearings using multipoint sparsity–multipoint optimal minimum entropy deconvolution adjustment and adaptive resonance-based signal sparse decomposition

The rolling element bearings used in rotating machinery generally include multiple coexisting defects. However, individual defect–induced signals of bearings simultaneously arising from multiple defects are difficult to extract from measured vibration signals because the impulse-like fault signals are very weak, and the vibration signal is commonly affected by the transmission path and various sources of interference. This issue is addressed in this study by proposing a new compound fault feature extraction scheme. Vibration signals are first preprocessed using resonance-based signal sparse decomposition to obtain the low-resonance component of the signal, which contains the information related to the transient fault–induced impulse signals, and reduce the interference of discrete harmonic signal components and noise. The objective used for adaptively selecting the optimal resonance-based signal sparse decomposition parameters adopts the ratio of permutation entropy to the frequency domain kurtosis, as a new comprehensive index, and the optimization is conducted using the cuckoo search algorithm. Subsequently, we apply multipoint sparsity to the low-resonance component to automatically determine the possible number of impulse signals and their periods according to the peak multipoint sparsity values. This enables the targeted extraction and isolation of fault-induced impulse signal features by multipoint optimal minimum entropy deconvolution adjustment. Finally, the envelope spectrum of the filtered signal is used to identify the individual faults. The effectiveness of the proposed scheme is verified by its application to both simulated and experimental compound bearing fault vibration signals with strong interference, and its advantages are confirmed by comparisons of the results with those of an existing state-of-the-art method.

A Numerical Investigation of Gap and Shape Effects on a 2D Plunger-Type Wave Maker

The installation of plunger-type wave makers in experimental tanks will generally include a gap between the back of the wedge and the wall of the tank. In this study, we analyze the influence of this gap on the wave making performance of the plunger using two-dimensional (2D) CFD calculations for a range of nearly linear wave conditions and compare the results with both experimental measurements and linear potential flow theory. Three wedge-shaped profiles, all with the same submerged volume, are considered. Moreover, the generated waves are compared with the predictions of linear potential flow theory. The calculations are made using the commercial ANSYS FLUENT finite-volume code with dynamic meshes to solve the Navier–Stokes equations and the volume of fluid scheme to capture the air–water interface. Furthermore, the linear potential flow solution of Wu (J Hydraul Res 26:481–493, 1988) is extended to consider an arbitrary profile and serve as a reference solution. The amplitude ratios of the generated waves predicted by the CFD calculations compare well with the predictions of linear potential flow theory for a simple wedge, indicating that viscous effects do not influence this ratio for small-amplitude motions in 2D. By contrast, significant higher harmonic components are produced by larger amplitude motions. Also, the simple wedge is found to produce the smallest spurious higher harmonic content in the far-field wave.

Analysis of differences in vegetation phenology cycle of abandoned farmland, using harmonic analysis of time-series vegetation indices data: the case of Gwangyang City, South Korea

ABSTRACT Globally, countries have experienced substantial increases in farmland abandonment. Although vegetation phenology is a key factor for the classification of land use, understanding of the phenological change of abandoned farmland is lacking. Using harmonic analysis of NDVI and NDWI extracted from Landsat imagery, this study investigates the distinctive phenological characteristics of abandoned farmland, which contrasts with that of three other agricultural types (paddy, agricultural field, orchard) in the study site of Gwangyang City in Jeollanam Province, South Korea. The results suggest that abandoned farmland has higher overall greenness coverage and overall water content in vegetation than the other uses. In terms of both indices, abandoned farmlands changed with relatively less fluctuation than those of other uses, suggesting the existence of constant and unmanaged vegetation from ecological succession, which differs from crop fields that undergo cultivation procedures. The significant harmonic components differed among agricultural types and vegetation indices. In paddy, NDVI was explained with multiple, higher-order harmonic components, while in other types only first-order components met the 5% statistical significance level. With NDWI, land types were more clearly discernible, because of the different cultivation procedures involving water: wet-field method (paddy), dryland farming (orchard, agricultural field), and no cultivation (abandoned farmland). The analysis confirms that harmonic analysis could be useful in discerning abandoned farmland among areas of active agricultural use and shows that the statistical significance of harmonic terms can be employed as indicators of different agricultural types. The observed pattern of the geographic distribution of abandoned farmland has policy implications for the promotion of sustainable reuse of marginal farmland.

Temporal Modulation of Steady-State Visual Evoked Potentials.

Electroencephalographic responses to periodic stimulation are termed steady-state visual evoked potentials (SSVEP). Their characteristics in terms of amplitude, frequency and phase are commonly assumed to be stationary. In this work, we tested this assumption in 30 healthy participants submitted to 50 trials of 60 s flicker stimulation at 15 Hz frequency. We showed that the amplitude of the first and second harmonic frequency components of SSVEP signals were in general not stable over time. The power (squared amplitude) of the fundamental component was stationary only in 30% the subjects, while the power at the second harmonic frequency was stationary in 66.7% of the group. The phases of both SSVEP frequency components were more stable over time, but could exhibit small drifts. The observed temporal changes were heterogeneous across the subjects, implying that averaging results over participants should be performed carefully. These results may contribute to improved design and analysis of experiments employing prolonged visual stimulation. Our findings offer a novel characterization of the temporal changes of SSVEP that may help to identify their physiological basis.

Harmonic State-Space Based Small-Signal Impedance Modeling of a Modular Multilevel Converter With Consideration of Internal Harmonic Dynamics

The small-signal impedance modeling of a modular multilevel converter (MMC) is the key for analyzing resonance and stability of MMC-based power electronic systems. The MMC is a power converter with a multifrequency response due to its significant steady-state harmonic components in the arm currents and capacitor voltages. These internal harmonic dynamics may have great influence on the terminal characteristics of the MMC, which, therefore, are essential to be considered in the MMC impedance modeling. In this paper, the harmonic state-space (HSS) modeling approach is first introduced to characterize the multiharmonic coupling behavior of the MMC. On this basis, the small-signal impedance models of the MMC are then developed based on the proposed HSS model of the MMC, which are able to include all the internal harmonics within the MMC, leading to accurate impedance models. Besides, different control schemes for the MMC, such as open-loop control, ac voltage closed-loop control, and circulating current closed-loop control, have also been considered during the modeling process, which further reveals the impact of the MMC internal dynamics and control dynamics on the MMC impedance. Furthermore, an impedance-based stability analysis of the MMC-high-voltage direct current connected wind farm has been carried out to show how the HSS-based MMC impedance model can be used in practical system analysis. Finally, the proposed impedance models are validated by both simulation and experimental measurements.