Proposed Impedance Model Research Articles

Harmonic Resonance Mechanisms and Influencing Factors of Distributed Energy Grid-Connected Systems

With the rapid development of global energy transformation and new power system, ensuring the stability of distributed energy grid connections is the key to maintaining the reliable operation of the whole power system. This paper constructs detailed impedance models of grid-following (GFL) and grid-forming (GFM) inverters using a harmonic linearization method and thoroughly investigates the mechanisms of resonance when inverters are connected to the grid, as well as the impact of model parameters on the stability of the grid system. This paper also briefly analyzes the scenario where distributed energy and electric vehicles are integrated into the grid simultaneously, demonstrating that grid system stability can be ensured in complex grid situations through reasonable parameter design. Lastly, the accuracy of the proposed impedance models and analysis is verified through MATLAB/Simulink simulations.

Impedance Modeling and Stability Analysis of Triple-Active-Bridge-Converter-Based Renewable-Electricity-Hydrogen-Integrated Metro DC Traction Power System

DC power supply system has been widely applied in metro traction power system. This article presents a novel framework for future metro traction power system (MTPS) with renewable energy, named renewable electricity-hydrogen-integrated metro traction power system (RMTPS), to reduce overall energy consumption and carbon emission of the MTPS. The framework and operation modes of RMTPS are first developed, where triple active bridge (TAB) converter-based multi-port metro energy router (MMER) is innovatively presented to integrate electricity subsystem, hydrogen subsystem and MTPS. Then, an impedance modelling method of MMER is developed based on the extra element theorem (EET). It can adaptively obtain terminal impedance characteristics of MMER considering the effect of multi-directional power flow and source/load characteristic variation on other terminals. Further, the stability of RMTPS under different operation modes is investigated based on the developed impedance modelling method. Simulation and experimental results are given to validate the effectiveness of the proposed impedance model and stability analysis for RMTPS. The proposed method can further benefit stability design of multi-port metro energy router in practical application.

Impacts of Dynamic Frequency Feedback Loop in SOGI-PLL on Low-Frequency Oscillation in an Electric Railway System

The low-frequency oscillation (LFO) issue has occurred frequently in single-phase electric train and traction network interactive systems (hereinafter train-network systems). On a single-phase electric train, the second-order generalized integrator (SOGI) based phase-locked loops (PLLs) have been widely used and also have significant impacts on the LFO. In the SOGI-PLL, the frequency signal is dynamically feedback from PLL to SOGI for adapting frequency variety, which causes complex nonlinearity and may deteriorate the small-signal stability of train-network systems. In previous works, the small-signal impedance model of train supposes that the feedback frequency is quasi-steady-state, which ignores impacts of dynamic frequency feedback loop (DFFL) on system-level stability and causes inaccurate analysis results. Therefore, this article builds an improved impedance model of train in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> frame with considering the DFFL. Compared with fixed frequency feedback loop (FFFL) based SOGI-PLL, the DFFL-based SOGI-PLL results in an additional negative resistance behavior, which is more likely to induce the LFO. Moreover, based on proposed impedance model of train, three FFFL-based SOGI-PLLs are compared among the filtering capability, phase-locked error and negative resistance range. Finally, experiment results by hardware in the loop (HIL) platform and real low-power experimental platform are employed to verity the correctness of theoretical analysis results.

Multidimensional Design of DC-Link for Two-Stage Solid-State Transformer Cell Considering Second-Order Harmonic Current Distribution

In a two-stage solid-state transformer (SST) cell, the grid power pulsates at the double-line frequency, yielding second-order harmonic current (SHC) across the unit. SHC into the DC/DC stage causes extra losses in the semiconductors and magnetics, resulting in reduced efficiency and lifetime at the gain of lower DC-link requirement. This paper investigates how the DC-link design affects the SHC distribution using a proposed impedance model, which in turn impacts losses, volume and overall reliability. Particularly, the overall lifetime is evaluated considering the reliability interactions between components resulting from varied DC-link design. The newly introduced reliability dimension provides further insight into the DC-link design, in addition to the voltage ripple requirement and efficiency-power density tradeoff. The model and design concept are verified by the simulation and experiment.

Stability Analysis of Active Front End and Permanent Magnet Synchronous Generator With Back EMF-Based Sensorless Control for DC Marine Vessels

This article studies the influence of sensorless control on the permanent magnet synchronous generator (PMSG) and pulsewidth modulation (PWM) converter (active front end rectifier, AFE) system for dc marine vessels. Back EMF-based sensorless control is adopted in this article because the minimum speed of PMSG in a dc marine vessel is enough for obtaining a sufficient back EMF signal. First, the output impedance of “PMSG+AFE” system with a typical topology and controller is deduced by small-signal analysis. The stability analysis with constant power load (CPL) is analyzed, including the influence of sensorless control bandwidth on PMSG with a significant per-unit impedance value. Since the inductance parameter affects both the current control and sensorless control, the influence of error in the estimated inductance parameter on the stability of “PMSG+AFE” system is analyzed. To verify the proposed impedance model, output impedance is measured in the simulation and experiment. The stability analysis with the proposed impedance model and load impedance of CPL is provided in MATLAB, and simulation results and experimental measurements are given to verify the analysis.

Input Impedance Modeling and Experimental Validation of a Single-Phase PFC in the D-Q Frame

This article models and characterizes the input impedance of a single-phase totem-pole power factor correction (PFC) converter in a virtual synchronous reference (d-q) frame. Due to the dc voltage controller, its d-d channel impedance behaves like a negative resistor, and the cascaded dc–dc converter load reduces its gain and phase at low frequency. Both are detrimental to system stability. The proposed impedance model can be employed to analyze instability issues. As examples, the low-frequency stability of a single-phase and a three-phase four-wire system is analyzed using the model. It is found that the single-phase system will confront the issue of settling to an operating point before any small-signal instability occurs. Whereas in a four-wire system, high neutral line inductance or high dc voltage control bandwidth could lead to small-signal instability. The impedance modeling results are validated by experiments.

The acoustic transfer impedance of baffled injectors in three-dimensional combustion chambers

Baffled injectors are typical passive control devices to restrain combustion instabilities in liquid rocket engines. However, there still has been no appropriate model to describe the acoustic characteristics of baffled injectors. In this work, the baffled injector gap is modeled as a narrow passageway with a cross-sectional surface area gradient. An acoustic transfer impedance model is derived from the momentum conservation equation to relate the acoustic disturbances between the inlet and outlet of injector gaps. Validation is conducted by comparing the first tangential mode frequency of a three-dimensional combustion chamber without flame from the detailed structures model and that using the proposed acoustic transfer impedance model. The proposed impedance model is embedded in a numerical simulation model of a three-dimensional combustion chamber considering the unsteady heat release; the effects of baffled injectors geometry parameters on the first tangential acoustic mode are then investigated. Results show that the presence of baffled injectors not only damps the acoustic energy due to the viscothermal effect, but also can longitudinalise the original transverse mode.

The Detection of Self-Similar/Branching Processes in Complex Biological Systems: Analysis of the Temporal Evolution of Impedance Measurements in Tulsi (Holy Basil) Leaves "Ocimumtenuiflorum".

In this paper, a theoretical model has been proposed for the first time to illustrate the living Tulsi (Holy Basil) leaf evolution in describing the branching systems in the intermediate range of frequencies. The proposed fitting function following the applied model portrays the whole stages of the temporal evolution of Tulsi (Holy Basil, "Ocimumtenuiflorum") leaf during the six days of impedance measurements with a high degree of accuracy (with fitting error less than 0.1 percent). The developed fitting parameter enables to identify the three stages of temporal evaluation of the Tulsi leaf as "vital leaf activity" (first stage), "quasi-chaotic behaviour" (second stage), and the "dying" (third stage). The theoretical model proposed in this work incorporated a fractal element having complex conjugated power law of exponents and a fractal element with a time lagged branching process. This novel approach introduces an additional degree of freedom over the previously proposed impedance models in terms of its imaginary part of complex conjugated power-law exponent. Further, it increases flexibility and versatility in accurately modeling the behavioral variations of complex branching systems, whose seemingly nondeterministic temporal nature had been considered earlier as counterintuitive and random. The incorporation of branching processes in comprehensively explaining the complex biological systems allows us to gain a deeper insight into the transfer of charge processes in the intermediate range of available frequency scales. Furthermore, the proposed model validates the presence of new fractal elements with a complex conjugated power law of exponents in naturally occurring biological processes. The experimental confirmation can play a key role in explaining a wide class of branching processes in complex systems and enrich the modern theory of fractional calculus.

Characterization of electrochemical kinetics of SiOx using single-particle electrode technique: An impedance study

In this study, single-particle electrode technique is adopted to measure the impedance response of SiOx materials for the first time. The electrochemical impedance spectroscopies of two SiOx particles are measured at different insertion ratios and different temperatures. Two kinetic parameters, namely Li+ diffusivity and exchange current density, are obtained using our previously proposed impedance model which takes into account the stress effect on Li+ diffusion and surface reaction. The dependence of the two parameters on the Li+ insertion ratio and temperature is obtained. The fitted results are found to be strongly consistent with previous research. Lastly, through comparison with the results of earlier studies with the help of the single-particle electrode technique, we find that the kinetic performance of SiOx is much poorer than graphite, and smaller particles are recommended to use compared with graphite when applying SiOx as the anode material. The single-particle electrode can serve as an effective tool to evaluate the electrochemical kinetics of various materials and provides a new index for material evaluation.

Modeling and Analysis of the Harmonic Interaction between Grid-Connected Inverter Clusters and the Utility Grid

The virtual synchronous generator (VSG) is a promising technology for future utility grids, since it can mimic the output characteristics of a synchronous generator, which provides the necessary inertia to a utility grid. However, the large-scale application of VSGs is limited due to the harmonic interaction between VSGs and the utility grid. Therefore, in order to investigate the stability issue as well as improve the practical application for large-scale power stations, the harmonic interaction mechanism between the VSG cluster and the utility grid is addressed. Firstly, the output impedance model of a single VSG is established, and it is found that the resonance frequency is related to parameters including the output filter, controller, and grid impedance. On this basis, the capacitor current control for a grid-connected inverter based on a VSG is proposed to enhance the resonance suppression. Furthermore, the output impedance of the VSG cluster is established, which reveals the harmonic interaction characteristics between the VSG cluster and the utility grid. In addition, in order to suppress the resonance and improve the stability, an inner-loop control strategy of VSG is introduced. Finally, the simulation and experimental results verified the correctness of the established modeling and analysis of the harmonic interaction between the clustered VSGs and the utility grid. The results show that the proposed impedance model is correct and can predict the resonant point accuracy (which is around 2.3 kHz in the simulation and experimental cases). The total harmonic distortion (THD) can be reduced to 3.2% which meets the requirements of IEEE standard 519.

Impedance modelling and stability assessment for grid‐connected dual‐PWM adjustable speed drives with motor torque oscillations

The grid-connected dual-PWM adjustable speed drives (ASDs) modulate the energy of the motor torque oscillation and inject it into the power system, potentially causing low-frequency oscillation (LFO) in the grid. In this study, considering the motor torque oscillation and harmonic common-modulation of the both-side converters, the precise sequence impedance models are derived for dual-PWM ASDs using the harmonic linearisation method. Based on the derived impedance of dual-PWM ASD, the torque oscillation, which is equivalent to the time-varying impedance, causes a series of discontinuities at the torque-oscillation-related frequencies on its amplitude-frequency curve. Moreover, these discontinuous drops make it more likely to intersect with the amplitude-frequency curve of the grid impedance, which may lead to LFO of the grid. Then, by applying the proposed impedance model and Bode plot, the stability of the grid-ASD cascade system with motor torque oscillation is assessed. The conclusions of stability analysis demonstrate the exact mechanism that the mechanical system oscillations lead to the grid-converter cascade system instability through the common-modulation and coupling of the dual-PWM ASD. Finally, experimental results on a 3 kW ASD system in the laboratory and measured results on the distribution grid in the Shanghai Yangshan Deepwater Port area verify the correctness and effectiveness of the proposed model and stability assessment.

An Improved Impedance Modeling Method of Grid-Tied Inverters With White-Box Property

Small-signal modeling of grid-tied inverters (GTIs) is an essential work in stability analysis of GTIs-weak grid coupling system. Different from the previous small-signal modeling methods of GTIs with black-box property, a reduced-order modeling method has been proposed in this article to provide an impedance model with white-box property. First, impedance and admittance are seamlessly incorporated into the modeling method, where concepts of partial admittances, partial impedance, active power admittance, and reactive power admittance are especially introduced. As a result, simplified expressions of impedance model of GTIs have been obtained with physical interpretations of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> impedances strengthened. After that, dominated relationships between terms of GTI's impedance matrix and its internal physical parts are explicitly revealed to represent white-box property of the proposed impedance model. Specifically, the influence and effect mechanism of feedforward voltage compensation, current controller, phase lock loop, and power points ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_d</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_q</i> ) are emphasized based on the proposed impedance model. Finally, perturbations generated independent with PLL are injected into a hardware in-loop experiment platform, and impedance measurement results are provided to verify the conclusions drawn from the improved modeling method.

An Accurate Impedance Model of Line Commutated Converter With Variable Commutation Overlap

This paper proposes an accurate impedance model for line commutated converter (LCC) in the stationary frame. The commutation overlap process caused by the transformer leakage inductance complicates the modeling for LCC. Traditional impedance models are derived in positive sequence and negative sequence frame based on the simplified commutation overlap process, which degrades the modeling accuracy and limits the description of frequency coupling. This paper systematically analyzes the effects of the commutation overlap process on the impedance model, and the impedance model with the accurate commutation overlap process is established in the <i>dq</i>-frame. For clearly revealing the frequency coupling phenomenon of the LCC, the complex space vector is employed to extend the impedance model in the <i>dq</i>-frame to the complex <i>&#x03B1;&#x03B2;-</i>frame. A closed-loop model on PSCAD&#x002F;EMTDC is used to verify the proposed impedance model in the time-domain and the frequency-domain. The consistency between the simulation results and theoretical analysis effectively verifies the accuracy of the proposed model.

Impedance Reshaping and Stability Analysis of the Unbalanced Three-phase System Considering the Grid-tied Inverter based Imbalance Compensation

Grid-tied inverters have been adopted both as the interface of renewable energy resources and as a solution to address power quality issues. To compensate the imbalance distortion caused by asymmetric local load, DQ transformation based compensation method is introduced into the control scheme of the grid-tied inverter. Taking both the inverter control scheme and circuit topology into account, the space vector based impedance modelling and stability analysis approaches are proposed in this paper to analyse the dynamic of the asymmetric system with active imbalance compensation. The proposed impedance models indicate that the compensation control method can reshape the output impedance features, and affect the stability of the system. The stability analysis results are verified in this paper by experimental results.

Research on pressure fluctuation of coolant with new type of boundary impedance at opening ports of water chamber

Liner cavitation erosion results from pressure fluctuation of water coolant around cylinders. The characteristics of acoustic field of water chamber are especially important to estimate the potential of liner cavitation. The specialty of water chamber geometry requires a new impedance model of the opening ports, which was simulated by combining a one dimensional sound pipe with piston sound source at infinite plate. The validity of the proposed impedance model has been confirmed by the comparison of attenuation ratio with experiment of actual cylinder block. By changing the clearance between piston and cylinder liner, the influence of cylinder vibration acceleration on water pressure variation was studied, which revealed that the larger clearance results in stronger pressure fluctuation dominated by certain frequencies components. The pressure fluctuation induced by the vibration of whole walls was compared with that induced by the vibration of one cylinder, it revealed that integration of liner and cylinder block may reduce the amplitude of pressure fluctuation.

A maximum available power algorithm for multi-infeed HVDC system based on equivalent impedance

High-voltage direct current transmission is widely used due to its asynchronous interconnection, fast and controllable transmission power adjustment and economy. The maximum available power calculation of an HVDC system is important in voltage stability analysis and control strategy design. The maximum available power is generally acquired based on repetitive power flow calculations for the system model and results in a low computational efficiency. In this paper, the equivalent impedance model of an HVDC system is deduced based on the external characteristic equivalence, and the model of an AC/DC system is converted to an AC system. For a single-infeed HVDC system, the boundary condition of the maximum available power is deduced based on the proposed impedance model. For a multi-infeed HVDC system, an equivalent model is acquired based on the impedance model, and the maximum available power algorithm is proposed. Finally, the effects of the network parameters and the operation status of neighboring HVDC links on the equivalent impedance are analyzed. The proposed method simplifies the mathematical model; hence, the computational efficiency is enhanced. The case study results demonstrate the effectiveness of the proposed method.

Impedance Modeling and Stability Analysis of AC/AC Modular Multilevel Converter for Railway System

The ac/ac modular multilevel converter (MMC) application in the electric railway poses new challenges to the stability of the railway system. The impedance analysis method is an effective way to assess the stability of ac/ac MMC-based railway systems. Due to the internal dynamics of ac/ac MMC, there are steady-state harmonic components in the arm currents and capacitor voltages, and these harmonic components have a significant impact on the dynamic characteristics and stability of ac/ac MMCs. To accurately predict the stability of ac/ac MMC-based railway systems, this article proposes an impedance model of ac/ac MMC with consideration of dominant steady-state harmonics. Simulation and experimental results obtained from a prototype are presented to demonstrate the accuracy of the proposed impedance model. Besides, the proposed model is compared with the impedance model ignoring the steady-state harmonics, and the results show the advantage of the proposed model in the description of impedance characteristics of ac/ac MMCs. The stability of an example ac/ac MMC-based railway system is analyzed using the proposed model, and the stability analysis results are validated by simulations. The effect of control parameters on the impedance characteristics is further analyzed, and this provides the guidance for controller design to damp the instability of the system.

Output impedance modeling and grid-connected stability study of virtual synchronous control-based doubly-fed induction generator wind turbines in weak grids

Virtual synchronous control (VSynC) technology that mimics the behavior of a conventional synchronous generator can be applied in wind turbines (WTs), where it can effectively improve equivalent inertia, damping coefficient, and wind power permeability. Given the unique partial-scale converter structure of a doubly-fed induction generator (DFIG) and its complicated DFIG-grid coupling effect, the grid-connected VSynC-based DFIG WTs have gained little attention. Moreover, under a weak grid condition, some unstable modes of VSynC can interact with the wind power system, which impacts the DFIG’s dynamic characteristics and system stability. To bridge the gap, this study proposes an output impedance model for a VSynC-based DFIG to analyze the grid-connected stability in weak grids. First, the output impedance mathematical model for a VSynC-based DFIG is derived and explained. On the basis of this novel model, the low-frequency characteristics and vital unstable factors of a VSynC-based DFIG are comprehensively investigated. The impact of different VSynC parameters and grid strengths are extensively studied. Finally, the proposed output impedance model is validated by direct current disturbing theory, frequency scanning method, generalized Nyquist criterion, and time-domain simulation (MATLAB/Simulink). All the obtained results are consistent with each other and prove the effectiveness and accuracy of the proposed impedance model.

DC Side Harmonic Resonance Analysis of MMC-HVDC Considering Wind Farm Integration

In a modular multilevel converter (MMC) based wind farm integration system, the wind farm may influence the harmonic resonance characteristics of DC system through the connected MMC. An effective way to assess the harmonic resonances in DC system is the impedance analysis method, in which the key is to develop the DC side impedance model. This paper develops the dc impedance of the wind farm connected MMC by harmonic transfer function (HTF) method that considers both the dynamics of the MMC and wind farm. As a result, the proposed DC impedance model can effectively reveal the impact of the wind farm on the small-signal characteristics of the DC system. Compared to the existing model, the proposed model can improve the accuracy of DC system resonance analysis with consideration of connected wind farm. Therefore, the proposed model can be further used to assist the stability design of wind farm connected MMC-HVDC systems. The time-domain simulations in PSCAD/EMTDC validate the proposed impedance models and stability analyses.

Modeling and Stability Analysis of Parallel Inverters in Island Microgrid

The island microgrid is composed of a large number of inverters and various types of power equipment, and the interaction between inverters with different control methods may cause system instability, which will cause the power equipment to malfunction. Therefore, effective methods for analyzing the stability of the microgrid system have become particularly important. Generally, impedance modeling methods are used to analyze the stability of power electronic converter systems. In this paper, the impedance models of a PQ-controlled inverter and droop-controlled inverter are established in d-q frame. In view of the difference of output characteristics between the two control methods, the island microgrid is equivalent to a double closed-loop system. The impedance model of the parallel system is derived and the open loop transfer function of the system is extracted. Based on the generalized Nyquist criterion (GNC), the stability of parallel system working in island microgrid mode is analyzed using this proposed impedance model. The simulation and experiment results are presented to verify the analysis.