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Substructuring is a term used to describe the estimation of the dynamics of a coupled system assembly when only the dynamics of each uncoupled component is available. Existing approaches allow for the coupling of physical-to-physical models, physical-to-modal models, modal-to-modal models referred to as Component Mode Synthesis (CMS), and impedance-to-impedance models referred to as Frequency Based Substructuring (FBS). Often times, the component information may not be just modal data for both components or just FRF data for both components so that modal substructuring or FRF substructuring can be performed. In these cases, the component data needs to be converted from either modal data or FRF data to match the data of the other component. A method for directly coupling impedance- and modal-based components has not yet been addressed. A proposed Impedance to Modal Substructuring (IMS) approach addresses this situation by writing the equations in a form that allows the user to directly utilize modal data for one component and FRF data for the other component, offering more flexibility in coupling different component data sets. While intended to be used with experimental data, this approach may also implement analytical components. In this work, an approach was developed to allow for the direct coupling of impedance and modal models without the need for the user to convert component data type. The IMS approach derived in this work was validated using analytical and experimental data with various models. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power is the property of Electric Power Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

With the increase in the number of power electronic devices in power systems, various techniques for assessing their stability have emerged. Among these techniques, impedance model-based stability analysis techniques have been widely used. However, conducting such analyses across multiple operating points requires abundant impedance measurement data from power electronic devices. In this paper, we propose a method for constructing impedance models of equipment with fewer impedance measurement data in voltage-source converter (VSC) back-to-back high-voltage direct current (HVDC) systems using physics-informed neural networks. Furthermore, given the power system states, we present a neural network approach to estimate grid stability at different operating points. Validation via PSCAD/EMTDC simulations and a PyTorch neural network confirmed the adequacy of these models. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Copyright of Integrated Intelligent Energy is the property of Editorial Department of Integrated Intelligent Energy and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The structure of a DC–DC converter connected in series with a 400 Hz inverter is widely used in aviation airborne and ground power systems to provide a medium-frequency AC power supply within a wide input voltage range. To guarantee the dynamic and steady-state performance of a multi-module series converter, it is necessary to individually optimize the control loop and the parameters of each series-connected module. In addition, it is also necessary to consider the input–output impedance matching issues of each converter. In this study, a phase-shifted full-bridge converter employing an average current control strategy is used as the input-side DC–DC converter, and a medium-frequency three-phase four-leg inverter is used as the output-side inverter. The study also conducts a small-signal modeling analysis to reveal the intrinsic relationship between the closed-loop output impedance of the input-side converter and the circuit parameters. It summarizes the optimization criteria for controlling the parameters of the voltage and current loops. By suppressing the peaks of the output impedance of the input-side converter, the impedance matching between the input- and output-side converters is ensured over the entire frequency range, ensuring the stable operation of the overall system. Finally, the correctness of the theoretical analysis is verified through simulation and experimentation. [ABSTRACT FROM AUTHOR]

The Onshore Wind Power All-DC Generation System (OWDCG) is designed to integrate with renewable energy sources by modifying the grid structure. This adaptation supports the grid infrastructure and addresses the challenges of large-scale wind power AC collection and harmonic resonance during transmission. Crucially, small disturbance stability parameters are essential for ensuring the system's stable operation. Unlike conventional power systems, the OWDCG exhibits strong coupling between subsystems, accentuating the small disturbance stability issue due to the dynamic nature of its converter control system. The impedance method facilitates the decomposition of such systems into subsystems, offering insights into the destabilization mechanism through the lens of negative impedance contribution. This approach is conducive to conducting small disturbance stabilization analyses. To tackle this issue, the initial step involves deriving the input and output equivalent impedance models of the subsystem, considering the topological structure, control features, and operational dynamics of the OWDCG. Subsequently, the impact of circuit and control parameters on the system's impedance characteristics and small-disturbance stability is examined through Bode diagrams and Nyquist curves. This analysis identifies critical parameters for small-disturbance stability, guiding the stable operation and parameter optimization of the OWDCG. The analysis highlights that the main control strategies for stability are the Modular Multilevel Converter (MMC) DC voltage control and the inner-loop current control gain. Validation of the theoretical findings is achieved through simulation results using PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

In photovoltaic grid-connected systems, the interaction between grid-connected inverters and the grid may cause harmonic oscillation, which severely affects the normal operation of the system. To improve the quality of the output electrical energy, photovoltaic grid-connected systems often use LCL filters as output filters to filter out high-frequency harmonics. Taking the three-phase LCL-type photovoltaic grid-connected inverter system as an example, this paper addresses the issue of harmonic resonance. Firstly, based on the harmonic linearization method and considering the impact of the coupling compensation term on the grid-side voltage, a modular positive and negative sequence impedance modeling method is proposed, which simplifies the secondary modeling process of the converter under feedback control. Then, the stability analysis is conducted using the Nyquist criterion, revealing the mechanism of high-frequency resonance in photovoltaic grid-connected systems. Furthermore, this paper delves into the impact of changes in system parameters on impedance characteristics and system stability. The results indicate that the proportional coefficient of the internal loop current controller has a significant influence on system impedance characteristics. Additionally, this paper proposes an active damping design method that combines lead correction and capacitor current feedback to impedance-reconstruct the easily oscillating frequency band. Finally, the effectiveness of this method is verified in the simulation platform. Simulation results confirm the effectiveness of this method in suppressing harmonic resonance while maintaining rapid dynamic response. [ABSTRACT FROM AUTHOR]

Metal alloy catalysts (e.g., Pt-Co) are widely used in fuel cells for improving the oxygen reduction reaction kinetics. Despite the promise, the leaching of the alloying element contaminates the ionomer/membrane, leading to poor durability. However, the underlying mechanisms by which cation contamination affects fuel cell performance remain poorly understood. Here, we provide a comprehensive understanding of cation contamination effects through the controlled doping of electrodes. We couple electrochemical testing results with membrane conductivity/water uptake measurements and impedance modeling to pinpoint where and how the losses in performance occur. We identify that (1) ∼44% of Co2+ exchange of the ionomer can be tolerated in the electrode, (2) loss in performance is predominantly induced by O2 and proton transport losses, and (3) Co2+ preferentially resides in the electrode under wet operating conditions. Our results provide a first-of-its-kind mechanistic explanation for cation effects and inform strategies for mitigating these undesired effects when using alloy catalysts.

Grid-forming converters can emulate the behavior of a synchronous generator through frequency droop control. The stability of grid-forming modular multilevel converters can be studied via the impedance-based stability criterion. This paper presents an ac-side impedance model of a grid-forming modular multilevel converter which includes a complete grid-forming control structure. The impact of different control schemes and parameters on the closed-loop output impedance of the converter is thoroughly analyzed and the learnings have been used in mitigating undesired control interactions with the grid. The results are verified through simulations in time- and frequency-domains along with experiments on a down-scaled laboratory prototype.

The renewable energy resources integrating HVDC transmission systems, consisting of grid-following and grid-forming converters, have complex physical and control dynamic interactions. Although the impedance analysis method is advisable to study these interactions, impedance modeling is still challenging when taking various converter control schemes into account. This article proposes a modular three-port admittance modeling framework for the hybrid AC/DC power systems. This approach separates the modeling process into three levels: controller, converter, and system levels. The current and voltage feedback loops are subdivided into multiple submodules at the controller level, and the submodule connection method is proposed to obtain the small-signal model of the unified main controller, which thus can eliminate the repetitive work caused by the diversity of control schemes. Due to the modular modeling advantage, the method is also versatile and scalable, as well as using unlimited and expandable interconnecting. In addition, the modeling separates the entire system into three components, and the stability criterion of the hybrid AC/DC power systems is derived by regrouping their transfer function matrix models. Then, the proposed modeling method is applied to assess the stability of hybrid power plants integrating HVDC systems with grid-following and grid-forming sources. The conclusions can be used to plan GFM converter capacity in power System plants, the installation location of HVDC transmission systems, and other scenarios. Simulations are carried out to validate the correctness of the impedance modeling method and stability criterion. Finally, the effect of the different capacity ratios of grid-forming sources to renewable energy power plants on system stability is discussed.

The Advanced Light Source Upgrade (ALS-U) is a 4th generation diffraction-limited soft x-ray radiation source, consisting of a new accumulator ring (AR) and a new storage ring (SR). In both rings coupling-impedance driven instabilities need careful evaluation to ensure meeting the machine's high-performance goals. This paper presents the workflow followed in building the impedance models and the beam-stability analysis based on those models. We follow the commonly accepted approach of separating the resistive-wall and the geometric parts of the impedance; the former is obtained by analytical formulas, the latter by numerical electro-magnetic codes (primarily CST Studio software) with perfectly-conducting boundary conditions. Impedance budgets are established and pseudo-Green functions calculated to be used in beam dynamics studies. We also present various ways to cross-check simulation results for reliable impedance modeling. Finally, the crucial single-bunch instability current thresholds for various operation modes are determined and discussed.

Impedance-based stability analysis (IBSA) is an effective method to analyze the interaction problem between the doubly-fed induction generator-based wind park (DFIG-WP) and series compensated or weakly tied AC grids. The analytical impedance model of DFIG has evolved over the years for better precision. This paper presents a precision comparison of those analytical models where the reference is obtained through EMT-level frequency scanning simulations. Moreover, representative IBSA is also performed with those models on typical test systems in which the DFIG adversely interacts with the series compensated grid and weakly tied AC grid in sub- and super-synchronous frequency ranges, respectively. The common modeling approach, which disregards the coupling between the rotor side converter (RSC) and grid side converter (GSC) at the DC-side, reduces the accuracy of IBSA and may lead to incorrect stability analysis results.

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.

The Onshore Wind Power All-DC Generation System (OWDCG) is designed to integrate with renewable energy sources by modifying the grid structure. This adaptation supports the grid infrastructure and addresses the challenges of large-scale wind power AC collection and harmonic resonance during transmission. Crucially, small disturbance stability parameters are essential for ensuring the system’s stable operation. Unlike conventional power systems, the OWDCG exhibits strong coupling between subsystems, accentuating the small disturbance stability issue due to the dynamic nature of its converter control system. The impedance method facilitates the decomposition of such systems into subsystems, offering insights into the destabilization mechanism through the lens of negative impedance contribution. This approach is conducive to conducting small disturbance stabilization analyses. To tackle this issue, the initial step involves deriving the input and output equivalent impedance models of the subsystem, considering the topological structure, control features, and operational dynamics of the OWDCG. Subsequently, the impact of circuit and control parameters on the system’s impedance characteristics and small-disturbance stability is examined through Bode diagrams and Nyquist curves. This analysis identifies critical parameters for small-disturbance stability, guiding the stable operation and parameter optimization of the OWDCG. The analysis highlights that the main control strategies for stability are the Modular Multilevel Converter (MMC) DC voltage control and the inner-loop current control gain. Validation of the theoretical findings is achieved through simulation results using PSCAD/EMTDC.

In photovoltaic grid-connected systems, the interaction between grid-connected inverters and the grid may cause harmonic oscillation, which severely affects the normal operation of the system. To improve the quality of the output electrical energy, photovoltaic grid-connected systems often use LCL filters as output filters to filter out high-frequency harmonics. Taking the three-phase LCL-type photovoltaic grid-connected inverter system as an example, this paper addresses the issue of harmonic resonance. Firstly, based on the harmonic linearization method and considering the impact of the coupling compensation term on the grid-side voltage, a modular positive and negative sequence impedance modeling method is proposed, which simplifies the secondary modeling process of the converter under feedback control. Then, the stability analysis is conducted using the Nyquist criterion, revealing the mechanism of high-frequency resonance in photovoltaic grid-connected systems. Furthermore, this paper delves into the impact of changes in system parameters on impedance characteristics and system stability. The results indicate that the proportional coefficient of the internal loop current controller has a significant influence on system impedance characteristics. Additionally, this paper proposes an active damping design method that combines lead correction and capacitor current feedback to impedance-reconstruct the easily oscillating frequency band. Finally, the effectiveness of this method is verified in the simulation platform. Simulation results confirm the effectiveness of this method in suppressing harmonic resonance while maintaining rapid dynamic response.

High-voltage direct current (HVDC) systems linked to AC grids with converters are promising energy transmission systems. These systems present complex AC- and DC-side dynamic interactions. Impedance-based stability studies have recently been proposed to assess DC-side dynamics from DC-side characterization of voltage source converters (VSCs) considering AC-side dynamics. However, the existing approaches used for stability studies in VSC-HVDC systems do not completely model VSCs because they do not consider together the VSC delay, the grid voltage feedforward filter, and all the d- and q-reference current controls. Moreover, these approaches are analytically characterized from dq-real space vectors (less related to circuit theory than dq-complex space vectors), and some work with simple AC grids. The main contribution of this paper is a detailed and complete DC admittance model of VSCs from dq-complex space vectors, which considers the VSC delay, feedforward filter, and d- and q-reference current controls, and also a general AC grid. The proposed model can be used for DC-side stability studies in VSC-HVDC systems considering AC grid dynamics. The capabilities and drawbacks of impedance-based stability methods for DC-side stability assessment were analyzed, and the positive-net-damping criterion was validated as a robust approach. The model was validated by PSCAD/EMTDC simulations and applied to a stability study in a VSC-HVDC system. [ABSTRACT FROM AUTHOR]

With the proposal of the "dual carbon target" in China, the rapid development of renewable energy, mainly photovoltaic and wind power, has been promoted. However, a large amount of renewable energy connected to a grid results in its proportion in the power system going from a low state to a high state. Under a high proportion, the asymmetry of the control structure or parameters in the three-phase grid-connected inverter controller lead to a strong coupling relationship between the sub/super synchronous frequency components, or frequency coupling effect (FCE). This phenomenon can deteriorate the power quality of the inverter system, amplify the harm of frequency oscillation, and even cause system disassembly. To solve the above problems, a unified impedance model considering the FCE induced by the phase-locked loop (PLL), the current loop (CL), and the power outer loop (POL) is established. Based on the established output impedance model, a parameter optimization theoretical analysis method is designed considering the critical stability of the PLL bandwidth and the CL asymmetry degree. Meanwhile, an improved control strategy for the PLL and the POL is proposed. Experimental results show that the proposed parameter optimization and structure improvement strategies can effectively suppress the influence of frequency coupling and enhance system stability. Finally, simulation and experimental results verify the correctness of the theoretical analysis and the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

The fault characteristics of direct current (DC) grids can be analyzed by addressing the grid damping characteristics. However,the frequency-dependent characteristics of the transmission line parameters are usually ignored in the conventional grid impedance modeling methods,which cannot accurately reflect the grid damping characteristics. To compare and analyze the fault currents characteristics of the DC grids with cables and overhead lines,an impedance model of DC grid considering the frequency-dependent characteristics of the transmission line parameters based on vector fitting is proposed in this paper. Then,the proposed model is applied to compare and analyze the fault current features including time delays,initial rising rates and amplitudes of the DC grids with cables and overhead lines. Meanwhile,the impacts of the DC grids key parameters on the fault current characteristics of the two DC grids are investigated. Compared with the sweeping results of the frequency-dependent line model,the proposed model performs well in reflecting the damping characteristic of the DC grid,where the root square error is less than 0.6,informing that the proposed model is much more accurate than the simplified model. Finally,the simulation is conducted in a symmetrical monopolar two-terminal DC grid with pole-to-pole fault. The simulation results show that the fault current rising rate of the DC grid with cables is 24.96% higher than that of the DC grid with overhead lines when the arm inductance is increased,which validates that the fault currents of the DC grids with cables are more sensitive to the inductive key parameters than the DC grids with overhead lines.

The modular multilevel converter (MMC) is a keystone of modern energy transmission systems. Consequently, there is an ongoing pursue for mathematical models to represent it under different configurations and control approaches. In short, this paper introduces an analytical Thévenin-equivalent model for representing the MMC when it is controlled with inner current- and an outer voltage-loop altogether. The model is based on a linearized representation of the converter and conveys the dynamics of passive components, such as submodule capacitors and arm reactors, as well as both control loops. Besides that, the proposed model is divided into a close-loop transfer matrix and the equivalent impedance matrix, both of which represent the relationships between the ac-side dq voltages and currents. We also propose a framework for implementing electromagnetic–transient simulations using the impedance model of this power electronic converter. The framework reduces a multi-bus power grid to a multi-input multi-output (MIMO) feedback system where impedance/admittance matrices of the MMC and other grid elements compose its loops. For validation purposes, it is considered a three-bus power grid comprising one MMC and another two grid-connected VSC. The proposed model was validated by comparing its results with a switching-level PSCAD model of the system. [ABSTRACT FROM AUTHOR]

Solid-state supercapacitors (SSCs) consist of porous carbon electrodes and gel-polymer electrolytes and are used in novel energy storage applications. The current study aims to simulate the impedance of SSCs using a clearly defined equivalent circuit (EC) model with the ultimate goal of improving their performance. To this end, a conventional mathematical and a physicochemical model were adapted. The impedance was measured by electrochemical impedance spectroscopy (EIS). An EC consisting of electrical elements was introduced for each modeling approach. The mathematical model was purely based on a best-fit method and utilized an EC with intuitive elements. In contrast, the physicochemical model was motivated by advanced theories and allowed meaningful associations with properties at the electrode, the electrolyte, and their interface. The physicochemical model showed a higher approximation ability (relative error of 3.7%) due to the interface impedance integration in a more complex circuit design. However, this model required more modeling and optimization effort. Moreover, the fitted parameters differed from the analytically calculated ones due to uncertainties in the SSC's microscale configuration, which need further investigations. Nevertheless, the results show that the proposed physicochemical model is promising in simulating EIS data of SSCs with the additional advantage of utilizing well-reasoned property-based EC elements. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

With the increasing proportion of wind turbines, the characteristics of low inertia and weak damping of power grid become more obvious, which brings new challenges to the smooth operation of power grid. Traditional current-controlled strategy is difficult to obtain accurate grid synchronization information in weak power grid by using phase-locked loop. Based on voltage-controlled, power balance equation is constructed to obtain synchronization angle, which has good operation performance in weak power grid. For this reason, firstly, the outer loop synchronous mode and the inner loop control structure were classified to study the voltage-controlled structural deformation. Then, for the weak power grid scenario, the impedance/admittance modeling was combined to analyze the stability of the voltage-controlled weak power grid. And the strategy of suppressing medium-high frequency oscillation in the complex power grid scenario was proposed. At the same time, the field operation test of high-power voltage-controlled doubly-fed induction generations (DFIG) was introduced. Finally, the development direction of voltage-controlled was pointed out to provide reference for the follow-up research. [ABSTRACT FROM AUTHOR]

This paper introduces a time–frequency analytic method for the exact identification of wideband DQ impedance models oriented to harmonic stability of converter-driven systems with transmission line models with distributed and frequency-dependent parameters. Wideband models are of great importance in the analysis of harmonic stability over a broad range of frequencies. The transmission line is a crucial component in this regard, but it is not straightforward to incorporate it into the impedance model of AC power-electronics-based power systems. This has led to the use of lumped parameter models or models based on rational approximations. This article proposes a method to include this important element to the impedance model directly from its frequency domain model. Salient features of the proposed modeling approach include the frequency telegrapher's equations with distributed and frequency-dependent parameters, exact delay models of PWM, control implementations of power electronics, and an exact steady-state computation using a balance method based on a hybrid time–frequency approach. The proposal avoids time-domain simulations, rational approximations, or the fast Fourier transform. A converter-driven system with transmission lines is used to validate the proposal and the results of the frequency scanning method conducted in OPAL-RT (ARTEMiS/EMTP-RV) and PSCAD/EMTDC support the effectiveness, speed, and accuracy. • Accurate D Q impedance model of AC systems with frequency-dependent lines. • Impedance model, including lines, avoids rational and approximate models. • Steady state accurately computed using exact equations for lines and converters. • Characterization avoids time-domain simulations, FFTs, and analytical modeling. [ABSTRACT FROM AUTHOR]

Frequency-domain stability criteria are developed for converter-based power systems with any number of converters. The converters may be grid following or grid forming, and the grid can be an ac or hybrid ac-dc network. The converters and the network are all modeled in a common (stationary) reference frame based on small-signal sequence immittances. Coupling over frequency and ac-dc coupling are considered in the most general form. For each type of systems, a frequency-domain model is developed first by nodal analysis and then reformulated to fit the form of a feedback loop with open-loop stability guaranteed by practical conditions. System stability is then determined by a Nyquist-like criterion without the need to check open-loop right-half-plane poles. Further simplification of the system models is made possible by a) generalized $n$-port equivalent circuits that include both types of coupling, b) equivalence of stability at internal and external nodes, and c) relationship between dynamics at the perturbation and the coupling frequency. Reduction of a system model into separate single-input-single-output models is presented for several special systems along with their practical applications. Quantitative and experimental results are presented to verify the developed theories.

To achieve the efficient application of impedance analysis in the stability assessment and enhancement of multi-terminal DC distribution systems, this paper proposes the DC-side reduced-order impedance models with power control and AC voltage control, respectively, by taking the load converter station as the object. By using the DC-side current as the feed-forward state, the active compensator applied to the load converter station with two control modes is also derived as well as the corresponding reduced-order impedance models. Combined with the reduced-order impedance models, a method based on damping factor sensitivity is further proposed to design the parameters of the derived active compensators. The verification results in the frequency domain and time domain demonstrate the accuracy of the reduced-order impedance and the effectiveness of the proposed compensator parameter design method.

The point-of-load (POL) converters integrated with the input LC filter are essential to supply the ac load in the dc microgrid. The interaction between the LC filter and the POL converter will bring instability problems to the dc-link voltage. This paper proposes a series-connected virtual impedance regulator based on the detailed small-signal model of the POL converter that feeds a linear three-phase load. The proposed method can improve the stability by modifying only the phase of the input impedance of the POL converter within the interaction frequency range. Therefore, the impact of the regulator on the converter’s dynamic performance is minimized. The experiments show that the proposed stabilization methods exhibit good performance under different linear load scenarios.

Similar to the conventional three-phase parallel-connected MMC (PC-MMC), the three-phase series-connected MMC (SC-MMC) is a strong potential solution for high-voltage direct current (HVDC) applications. The study of SC-MMC focuses on the control strategy, neglecting its small-signal dynamics, not to mention its stability when interacting with the AC grid. Work on small-signal modeling of MMC is limited to parallel-connected configurations. SC-MMC differs from PC-MMC in structure and harmonic content; hence, it is necessary to establish an accurate model of SC-MMC according to its own characteristics. This paper introduces the circuit and control of SC-MMC and compares it with PC-MMC. Multi-harmonic linearization is used to establish the AC impedance model of SC-MMC over the whole control system, including the third harmonic suppression controller. We take a PC-MMC station of the Wudongde HVDC project as a benchmark to explore the potential application of SC-MMC when constructing new HVDC stations to extract power from an existing DC transmission corridor. The strengths and weaknesses of SC-MMC in HVDC applications are discussed, and it is compared to PC-MMC with regard to the impedance characteristic. [ABSTRACT FROM AUTHOR]

In recent years, a series of studies concerning the oscillation of interconnected systems has shown that frequency coupling has important effects on the stability of the system. In this paper, a more accurate theoretical model considering the frequency coupling effects is adopted to derive the transmission process in vector control, phase lock loop, and proportional–resonant controller of the harmonic perturbation in the frequency domain. This model is used to further deepen the application of harmonic linearization modeling to impedance modeling. An integrated three-phase modular multilevel converter simulation model based on the PSCAD platform is built to verify the accuracy of the theoretical modeling through the frequency sweep method. The influence of related system parameters on sequence and coupling impedance is analyzed in detail. The generalized Nyquist criterion is used to study the importance of coupling impedance to the stability analysis of the system. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

High-voltage direct current (HVDC) systems linked to AC grids with converters are promising energy transmission systems. These systems present complex AC- and DC-side dynamic interactions. Impedance-based stability studies have recently been proposed to assess DC-side dynamics from DC-side characterization of voltage source converters (VSCs) considering AC-side dynamics. However, the existing approaches used for stability studies in VSC-HVDC systems do not completely model VSCs because they do not consider together the VSC delay, the grid voltage feedforward filter, and all the d- and q-reference current controls. Moreover, these approaches are analytically characterized from dq-real space vectors (less related to circuit theory than dq-complex space vectors), and some work with simple AC grids. The main contribution of this paper is a detailed and complete DC admittance model of VSCs from dq-complex space vectors, which considers the VSC delay, feedforward filter, and d- and q-reference current controls, and also a general AC grid. The proposed model can be used for DC-side stability studies in VSC-HVDC systems considering AC grid dynamics. The capabilities and drawbacks of impedance-based stability methods for DC-side stability assessment were analyzed, and the positive-net-damping criterion was validated as a robust approach. The model was validated by PSCAD/EMTDC simulations and applied to a stability study in a VSC-HVDC system.

Multi-terminal modular multilevel converter (MMC) power transmission is the current development trend in DC transmission. However, owing to its fast control and dynamic characteristics, it may interact with the other inductive devices or the grid and cause stability issues. This paper describes the use of the impedance analysis method in the frequency domain to analyze system stability. First, the multi-harmonic linearization method is used to model the impedance of a three-terminal MMC system. To make the model more accurate, the modeling considers the effect of frequency coupling caused by an asymmetric controller and the AC sampling site position. This paper then proposes an equivalent method of the grid impedance for the three-terminal system that can accurately judge the stability of the grid-connected system when the AC side is coupled. This work provides a theoretical basis for the prediction and suppression of the oscillation of MMC grid-connected system with coupling on the AC side. Finally, a three-terminal MMC model is built in Matlab/Simulink and the Nyquist stability criterion is used to verify the correctness of the analysis. [ABSTRACT FROM AUTHOR]

Transparent microelectrodes that facilitate simultaneous optical and electrophysiological interfacing are desirable tools for neuroscience. Electrodes made from transparent conductors such as graphene and indium tin oxide (ITO) show promise but are often limited by poor charge‐transfer properties. Herein, microelectrodes are demonstrated that take advantage of the transparency and volumetric capacitance of poly(3,4‐ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS). Ring‐shaped microelectrodes are fabricated by inkjet‐printing PEDOT:PSS, encapsulating with Parylene C, and then exposing a contact site that is much smaller than the microelectrode outer diameter. This unique structure allows the encapsulated portion of the microelectrode volume surrounding the contact site to participate in signal transduction, which reduces impedance and enhances charge storage capacity. While using the same 100 μm diameter contact site, increasing the outer diameter of the encapsulated electrode from 300 to 550 μm reduces the impedance from 294 ± 21 to 98 ± 2 kΩ, respectively, at 1 Hz. Similarly, the charge storage capacity is enhanced from 6 to 21 mC cm−2. The PEDOT:PSS microelectrodes provide a low‐haze, high‐transmittance optical interface, demonstrating their suitability for optical neuroscience applications. They remain functional after a million 1 V stimulation cycles, up to 600 μA of stimulation current, and more than 1000 mechanical bending cycles. [ABSTRACT FROM AUTHOR]

The isolated dual active bridge (DAB)-based two-stage AC-DC-DC converters have been widely applied in grid-connected power electronics systems. However, the impedance interactions between the DAB converter and the AC-DC rectifier can cause instability problems to the two-stage converter systems. The accurate terminal impedance characteristics of the DAB converters are still not clear due to the high frequency ac conversion stage. This makes it difficult to assess the impacts of the DAB circuit parameters on the stability of the two-stage converters. To address these issues, the impedance models of the DAB converters are originally derived in this paper. Based on the developed impedance models, the stability of the DAB-based two-stage AC-DC-DC converters is analyzed. The impacts of the DAB converter circuit parameters on the stability of the two-stage AC-DC-DC converters are comprehensively revealed by the Bode and Nyquist plots. The analysis results offer instructive implications to finetune the design rules of the DAB converters. The conclusions are validated by comprehensive simulation and experimental results.

The modular multilevel converter (MMC) is a keystone of modern energy transmission systems. Consequently, there is an ongoing pursue for mathematical models to represent it under different configurations and control approaches. In short, this paper introduces an analytical Thévenin-equivalent model for representing the MMC when it is controlled with inner current- and an outer voltage-loop altogether. The model is based on a linearized representation of the converter and conveys the dynamics of passive components, such as submodule capacitors and arm reactors, as well as both control loops. Besides that, the proposed model is divided into a close-loop transfer matrix and the equivalent impedance matrix, both of which represent the relationships between the ac-side dq voltages and currents. We also propose a framework for implementing electromagnetic–transient simulations using the impedance model of this power electronic converter. The framework reduces a multi-bus power grid to a multi-input multi-output (MIMO) feedback system where impedance/admittance matrices of the MMC and other grid elements compose its loops. For validation purposes, it is considered a three-bus power grid comprising one MMC and another two grid-connected VSC. The proposed model was validated by comparing its results with a switching-level PSCAD model of the system.

With the continuous penetration and development of renewable energy power generation, distributed grids and microgrids are becoming increasingly important in power systems. In the distribution networks and microgrids, the grid impedance is comparatively large and cannot be ignored. Usually, the parallel compensation is used to improve the grid quality. In these three-phase four-wire power systems, analyzing the impedance characteristics of the grid-connected inverter is vital to carry out the small-signal stability analysis. Thus, it is vital to consider the influence of the zero-sequence component in addition to the positive-sequence component and the negative-sequence component when it comes to analyzing system stability. In this paper, the impedances of three-phase four-wire split capacitor inverter and three-phase four-leg inverter are established. Based on the achieved impedance, the similarities and differences between the impedances of three-phase four-wire split capacitor inverter and impedance of three-phase four-leg inverter are studied. The main difference is reflected in zero-sequence impedance. Additionally, the zero-sequence impedance characteristics and the dominating factors deciding the zero-sequence impedance are analyzed. Then, the stability of the system considering the grid impedance and impedance of three-phase four-wire inverter is investigated by separately considering the stability of the positive–negative-sequence component and the stability of the zero-sequence component. Several cases of small-signal instability caused by the positive–negative-sequence component or zero-sequence component are revealed. The experimental results validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

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This article presents a small-signal model for power-electronics converters that use a typical control structure in wind energy applications: the double synchronous reference frame current control. The article considers the presence of unbalanced currents and voltages, and analyzes their impact on the frequency couplings of the converter. In addition, it is revealed that, in the presence of negative-sequence voltage synchronization, the converter presents an additional coupling at $-2f_1-f_{\text{p}}$. [ABSTRACT FROM AUTHOR]

With the increasing applications of grid-connected voltage source converters, it is important to analyze the impedance characteristic of the grid-connected system to implement the stability analysis of the grid connection operation. Compared with the three-phase three-wire system, an additional zero-sequence path exists in the three-phase four-wire system. Therefore, it is necessary to consider the influence of the zero sequence when analyzing the stability of the system. In this paper, an impedance model including positive-sequence, negative-sequence and zero-sequence impedance of the three-phase four-leg grid-connected inverter is established. Through impedance characteristic analysis, the relationships between zero-sequence impedance and positive-sequence, negative-sequence impedance can be found which are decupled. Based on the developed zero-sequence impedance model, the main factors affecting the zero-sequence impedance model are revealed. Then, the system stability consisting of the grid and three-phase four-wire inverter is investigated, and the experimental results validate the theoretical analysis.

Medium-voltage direct current (MVDC) systems are widely used to ship power-distributed systems, wind farms, and photovoltaic power plants. With the increase of load converters interfacing into the MVDC system, the power quality deteriorates. Few research studies focused on the factors affecting the MVDC power quality, and effects caused by multiple load converters are often neglected. In this study, the mechanism of power quality deterioration caused by interfacing multiple load converters on the MVDC system has been discussed. The impedance model of the MVDC system is developed with the state-space averaging method and the small-signal analysis method. A three-level H-bridge DC/DC converter is employed as the load converter. The results by the analysis of the impedance model show that the more the load converters connect to the MVDC system, the more fragile the MVDC system is to background harmonics. Simulation cases are implemented to verify this conclusion.

Impedance modeling of a permanent magnet synchronous generator (PMSG)-based wind energy conversion system (WECS) usually ignores the machine-side dynamics, instead, the machine-side system is simplified as a constant power source, while merely keeping the detailed grid-side converter model. This simplification is mainly based upon the intuition that the dc-bus capacitor is large enough so that the machine- and grid-side dynamics can be decoupled. However, the simplification probably does not hold in practice since there is always a tendency to minimize the capacitor size to achieve a smaller package for installation. Therefore, the machine-side system should not be ignored, otherwise maybe leading to error for stability analysis. To address this issue, this paper developed a complete ac-side impedance model of the PMSG-based WECS. Then, impact factors about the coupling characteristics between machine- and grid-side systems of the PMSG-based WECS are discussed. Finally, a case study of sub/super synchronous oscillation is carried out on a practical offshore wind farm integrated with a modular multilevel converter based high-voltage dc (MMC-HVDC) transmission system in China. The results show that ignoring the machine-side system would lead to an optimistic stability judgement, which confirms the necessity of the complete model of PMSG-based WECS. Furthermore, the system can be stabilized by either changing the couplings between machine- and grid-side systems of PMSG-based WECS or implementing active damping in the wind farm side MMC. [ABSTRACT FROM AUTHOR]

This article presents the grid-forming control (GFC) for doubly-fed induction generator (DFIG)-based wind farm to enhance the stability of line-commutated converter (LCC) based high voltage direct current (HVDC) transmission system. GFC is a grid friendly control strategy to build or follow the grid voltage and provide inertia support for power grid. The GFC for DFIG can not only improve the stability of HVDC sending-terminal system, but also reduce the dependence of synchronous generator (SG) in HVDC sending-terminal system. Impedance analysis is used to analyze the stability of HVDC sending-terminal system. The impedance modeling process of the GFC for DFIG is introduced in detail. Based on the impedance analysis, the GFC for DFIG shows the better stability than the conventional vector control (VC) for DFIG in HVDC sending-terminal system. When the capacity of SG decreases and transmission line impedance increases, the GFC for DFIG can keep stable, while the VC for DFIG will lose the stability in HVDC sending-terminal system. Vector graph of impedance characteristic is applied to illustrate the mechanism of instability. The time domain simulations are presented to verify the impedance analysis. Moreover, the simulation in islanded condition is also given to illustrate the stability and effectiveness of the GFC for DFIG.

A modular multilevel converter (MMC) is an emerging converter technology widely used in wind power applications using high-voltage direct current (HVDC) transmission, and it has been largely investigated in medium-voltage solar harvesting as well as electric motor drives. Different from studies dealing with active circulating current control loops, this paper focuses on impedance modeling and harmonic stability studies for MMCs with passive circulating current filters (PCCFs). A power stage circuit including a PCCF is transformed and remodeled to obtain small-signal formulations. This transformation leads to additional high-order matrix computing complexity due to the added impedance subnetwork matrix from the PCCF as well as relevant crossed-frequency impacts. To simplify the computational burden, the proposed model aims to solve one arm equation instead of all six MMC arm equations. To achieve this result, additional challenges occur when the MMC is connected to a renewable energy source instead of the grid voltage, where low-level zero-sequence components might exist in the neutral point of three phases, especially in the case of no integrated advanced modular voltage balancing control, which prevents computational simplification. To overcome this challenge, further impedance matrix adjustments are conducted in this paper to theoretically suppress the impact of zero-sequence harmonics when obtaining small-signal impedance, taking into account the frequency coupling effect. Finally, simulations are carried out to validate the developed impedance model under different operating scenarios. Harmonic stability case studies of MMCs with PCCFs connected to renewable energy current sources are also presented, where frequency-domain stability analyses based on Bode diagrams are compared to time-domain simulation waveforms and FFTs, which validate the effectiveness of the proposed impedance model.

In this paper, impedance modeling of a DC microgrid system consisting of a source and load converter, including an input filter, is performed. Impedance-based modeling has been used to derive mathematical models of the output impedance of the source converter and the input impedance of the load converter. The correlation between the converter interaction and system stability is analyzed based on the mathematical model. An impedance-based stability analysis is used to determine the system stability by analyzing the interactions among the converters in the DC microgrid system. Middlebrook's stability criterion, which uses the impedance transfer function, is applied to determine system stability. Moreover, in this paper, a stability enhancement control algorithm is proposed to resolve the system instabilities resulting from interaction among the converters and the distortion caused by the harmonics emanating from the AC input. The proposed stability enhancement control algorithm consists of a feed-forward type virtual impedance (VI) and a proportional-resonant (PR) controller. The validity of the proposed method is demonstrated by the results of the response characteristics in the frequency domain, and the effectiveness of the proposed control algorithm is verified via simulations and prototype experimental models.

Solid-state supercapacitors (SSCs) consist of porous carbon electrodes and gel-polymer electrolytes and are used in novel energy storage applications. The current study aims to simulate the impedance of SSCs using a clearly defined equivalent circuit (EC) model with the ultimate goal of improving their performance. To this end, a conventional mathematical and a physicochemical model were adapted. The impedance was measured by electrochemical impedance spectroscopy (EIS). An EC consisting of electrical elements was introduced for each modeling approach. The mathematical model was purely based on a best-fit method and utilized an EC with intuitive elements. In contrast, the physicochemical model was motivated by advanced theories and allowed meaningful associations with properties at the electrode, the electrolyte, and their interface. The physicochemical model showed a higher approximation ability (relative error of 3.7%) due to the interface impedance integration in a more complex circuit design. However, this model required more modeling and optimization effort. Moreover, the fitted parameters differed from the analytically calculated ones due to uncertainties in the SSC’s microscale configuration, which need further investigations. Nevertheless, the results show that the proposed physicochemical model is promising in simulating EIS data of SSCs with the additional advantage of utilizing well-reasoned property-based EC elements.

Intraoral functions are results of complex and well-orchestrated sensorimotor loop operations, and therefore vulnerable to small functional or neural defects. To secure the vital intraoral functions, it is important to find a way to favorably intervene the intraoral sensorimotor loop operations. The tongue and the soft palate are heavily associated with intraoral sensorimotor loops, with their dense neural innervations and occupancy of intraoral space. Therefore, electrical stimulation onto the tongue and the soft palate has a great potential to solve the problems in the intraoral functions. However, the electrical interface for both of them have not been characterized yet as a lumped-element model, for designing electrical stimulation and analyzing its effect. In this study, we measured stimulation thresholds to evoke electrotactile feedback and characterized electrical impedance across electrodes using lumped-element models. We found that average perception/discomfort thresholds for the tongue tip, lateral-inferior side of the tongue, and anterolateral side of the soft palate as 0.18/1.31, 0.37/3.99, and 1.19/7.55 mA, respectively. An R-C-R-R-C model represented the electrical interface across the tongue and the soft palate with the highest accuracy. The average component values of the R-C-R-R-C model were found as 2.72kΩ, 45.25nF, 1.27kΩ, 22.09GΩ, and 53.00nF, on average. [ABSTRACT FROM AUTHOR]