Virtual Impedance Research Articles

Decoupled Distributed Control of Offshore Wind Farms Connected to DR-HVDC Based on Novel Adaptive Virtual Impedance

Decoupled Distributed Control of Offshore Wind Farms Connected to DR-HVDC Based on Novel Adaptive Virtual Impedance

Design, Modeling, and Validation of Grid-Forming Inverters for Frequency Synchronization and Restoration

This paper focuses on the modeling, analysis, and design of grid-forming (GFM) inverter-based microgrids (MGs). It starts with the development of a mathematical model for three-phase voltage source inverters (VSI). The voltage and current controllers consist of two feedback loops: an outer feedback loop of the capacitance-voltage and an inner feedback loop of the output inductance current. The outer voltage loop is employed to enhance the controller’s response time. The inner current loop is used to provide active damping for the resonance created by the LCL filter. A two-layer control scheme is adopted for the GFM inverter control. The primary decentralized control uses droop control and virtual impedance loops to share active and reactive power. Simultaneously, the centralized secondary control addresses frequency and amplitude deviations induced by the droop control. Additionally, a synchronization loop is proposed for seamless reconnection of GFM inverters to the MG and to connect the GFM-controlled MG to the main grid. It has the advantage that the inverter operates in GFM mode even after the synchronization has occurred. The simulation results have shown that the voltage controller ensures a 0.005 s settling time and maintains the steady-state error at its minimum value of 0.1 V. Similarly, the current controller ensures a 0.006 s settling time with a 10−5 steady-state error. The system with the designed controller has a low total harmonic distortion (THD) of 1.46% and improved power quality of the output voltage. Furthermore, a quick restoration time is observed during load steps and tripping events, with a restoration time of 1 s with 10−10 steady-state error. Synchronization is achieved within 0.8 s for the incoming inverters and requires 3 s to synchronize the MG with the main grid, maintaining a steady-state error of 10−9.

A circulating current suppression strategy of VSG based on adaptive virtual complex impedance

By adding inertia and damping elements in droop control, virtual synchronous generators (VSG) can simulate the output characteristics of synchronous generators and effectively reduce the impact of power electronic equipment connected to the power grid. Since the capacity and spatial distribution of each VSG is random, the output impedance of VSG and line impedance are mismatched, which will cause circulating current between VSGs. Considering the influence of line resistance, the traditional dynamic virtual inductance control strategy can be enhanced. A circulating current suppression strategy based on adaptive virtual complex impedance is proposed after analyzing the composition and causes of the circulating current between VSGs. The proposed strategy compensates the line impedance adaptively according to VSG's output reactive power, thus to reduce the reactive power sharing errors and suppress the circulating current between VSGs. The scheme is reliable and robust under fault as there is no need for measurement of line impedance or communication modules. The simulation results are presented to verify the effectiveness of the proposed strategy.

Non-linear virtual impedance shaping strategy for predominantly resistive islanded power networks

Non-linear virtual impedance shaping strategy for predominantly resistive islanded power networks

Analysis of Offline Transient Power Oscillation and Its Suppression Method in the Microgrid with Multiple Virtual Synchronous Generators

When multiple Virtual Synchronous Generators (VSGs) operate in parallel in an islanded grid, power and frequency oscillations will occur when one VSG goes offline. However, the existing literature does not cover the related analysis and transient suppression schemes for this scenario. To analyze these complex high-order system dynamics, this paper first establishes an intuitive equivalent circuit model for multiple VSGs, and the frequency domain expressions of the multi-machine VSG system during the VSG offline transient simulation are then derived. Based on the multi-VSG model and its transient oscillations analysis, this paper further proposes a configuration scheme for the equivalent circuit parameters. Equivalently, the virtual inertia, damping coefficient and virtual impedance of the VSGs can be configured. With the proposed parameter configuration scheme, the power oscillation during the VSG offline transient can be eliminated, as verified by experiments with a microgrid lab platform using three VSGs. Compared with the existing multi-VSG studies, the proposed scheme is not only the first attempt to study the transient suppression when a VSG goes offline, but also is more intuitive in analysis and less complicated in the controller parameter tuning.

Optimized Distributed Cooperative Control for Islanded Microgrid Based on Dragonfly Algorithm

This study introduces novel stochastic distributed cooperative control (SDCC) in the context of island microgrids (MGs). A proportional resonant (PR) controller and virtual impedance droop control in stationary reference frames are employed in cooperation with distributed averaging secondary control optimized by the dragonfly algorithm (DA). The suggested approach demonstrates the capability to achieve mean-square synchronization for the voltage and frequency restoration of distributed generators (DGs) to ensure efficient active power sharing. Therefore, a sparse communication network has been used to avoid data congestion and reduce the need for extensive communication and information exchange. The proposed system offers an instinctive compromise between voltage regulation and reactive power sharing. A conventional centralized secondary control with PR droop control is simulated for performance evaluation and comparison purposes. In this study, empirical evidence is demonstrated to support the MG’s ability to confront communication failure and its ability to work reliably during plug-and-play operations.

Decentralized Control for Multiple Network-Forming Inverters in a Solar PV-BESS Based Standalone Microgrid System

—This research paper focuses on decentralized control of an AC microgrid in standalone mode. The microgrid includes three solar PV arrays accompanied by three battery energy storage systems (BESS), utilizing renewable distributed energy resources (DERs). The connection between each DER system and the microgrid is established through a network-forming three-phase voltage source inverter (VSI). The microgrid’s operation is regulated using modified droop control, incorporating virtual impedance and feed-forward derivative in primary control, along with a phase-locked loop (PLL) system for inverter synchronization. A master-slave control configuration is employed between the VSIs to mitigate voltage amplitude and frequency deviations induced by primary control. These enhancements ensure smooth power distribution and maintain voltage amplitude and frequency within specified limits across different operational scenarios. Control operations are performed in a stationary frame ( frame) using Clarke’s transformation, and PR controllers regulate VSI’s output voltage and current. The research paper shows the effectiveness of controlled microgrid operations using MATLAB/Simulink software in various conditions including intermittent PV system behavior, load dynamics, and DER connection/disconnection challenges. Simulation results show that the proposed approach enhances stability and performance of the microgrid system, especially in managing power fluctuations and maintaining a constant frequency response.

Virtual impedance based low-voltage distribution grid topology detection using double hidden layer recurrent neural network

Low-voltage distribution grid (LVDG) topology detection refers to detecting whether the topology connection between distribution grid nodes is correct. Accurate topology connection is critical for the normal operation and planning of LVDG. However, due to the incomplete measurement device, unknown line parameters, and rapid growth of renewable energy, the topology detection of LVDG becomes one of the most prominent challenges. This paper proposes an LVDG topology detection method based on virtual impedance, utilizing measurement data from nodes in the LVDG to achieve the detection of abnormal topological connections. Specifically, the electrical distances between nodes are analyzed to establish a topology detection model using virtual impedance. Then, the double hidden layer recurrent neural network is proposed to fit the mapping relationships between variables in the power flow constraints. The virtual impedance between nodes is solved. The value of virtual impedance is used to determine whether the topological connection between nodes is correct. Finally, the test results in the actual LVDG prove the effectiveness of the proposed method.

Harmonic power sharing control using adaptive virtual harmonic impedance in islanded microgrids

Abstract Existence of nonlinear loads makes load power sharing more challenging in the islanded microgrids. Conventional droop control may cause the poor harmonic power sharing among the distributed generations (DGs) due to the mismatched line impedance. This paper proposes an adaptive regulation method of the virtual harmonic impedance for the accurate harmonic power sharing. Consensus algorithm is used to regulate adaptively the virtual harmonic impedance according to the harmonic power sharing error among the DGs with considering of the mismatched line impedance. This method does not require the prior knowledge of the line impedance. The feasibility of the proposed method is demonstrated by simulation result for achieving the accurate harmonic power sharing to reduce the voltage distortion at the point of common coupling (PCC).

Power Equalization Strategy Based on Adaptive Virtual Impedance

Due to the differences in the line resistance of each distributed generation unit, conventional sag control does not allow for precise distribution of power, which also reduces the problem of system reactive power accuracy. To address this problem, this paper analyzes the power equalization and distribution conditions. A method for adaptive adjustment of virtual resistance by system output power feedback is submitted. Reducing the variance among the original line resistances aims to solve the problem of power not being evenly divided and improve the equalization of reactive power. By building a Simulink parallel simulation model of the inverter, it is verified that the power feedback-based fetching and the improved droop control is effective.

Enhancement of low-voltage ride-through capability for virtual synchronous generators based on virtual impedance voltage control

Virtual Synchronous Generator (VSG)-based grid-forming converters (GFC) increasingly serve as interfaces between renewable energy resources and the power grids with high penetration. Although the emulation of the characteristics of Synchronous Generator (SG) enables GFC to provide virtual inertia and oscillation damping under the VSG control, it remains challenging to replicate the short-circuit behaviors of SGs under the grid voltage sag/recovery conditions. The existing technologies are limited and lack full functionalities in terms of power synchronization, overcurrent suppression and capability of dealing with asymmetric grid-faults. This paper presents a Virtual Impedance Voltage Control (VIVC) strategy to enhance the fault-ride-through capability of the converter under a variety of fault conditions. In the case of asymmetric faults, a negative-sequence current control is performed to mitigate the negative-sequence voltages and achieve the grid current balance. The fault current is restrained and the power synchronization is improved by the virtual reactance without oversizing the GFC. The simulation and experimental results validate the effectiveness of the proposed control strategies.

On the acoustic wedge absorber design in underwater and its interior pressure computation in a chamber

This study presents a design of wedged shape absorber used in underwater in range of high frequency. The analysis of a set of periodical wedges, where each wedge is oriented 90 deg with other wedges. The set of periodical wedges is analyzed using finite element methods as a 3-D virtual impedance tube. The incident wave is on the normal direction of the tube. This 3-D model is able to simplify to a simple 2-D model and a two-point transfer function method is employed to compute reflection coefficient. The ation of frequencies higher than the cut-off plane wave frequency is addressed of that higher duct acoustic modes are excited by the wedge. These higher modes are recognized as stationary non-propagating waves, not contributing reflected waves away from the wedge. An impedance value associated with the reflection coefficient is identified based on plane wave condition. The impedance value is applied to surfaces of a closed space to computed interior pressures.

Power decoupling control of paralleled virtual synchronous generators based on virtual complex impedance

With the high ratio of distributed generation (DG) linked to power system via converters, power system stability is degraded in terms of inertia and damping. In recent years, the virtual synchronous generator (VSG) has become a potential solving method to deal with these issues. However, the power coupling problem exists in the traditional VSG control method, which severely impacts the VSG power control performance. The impedance characteristics of the transmission line are closely related to the effect of the power decoupling control of VSGs. To solve the voltage sag and poor robustness issues resulting from traditional virtual impedance control, a virtual complex impedance power decoupling and sharing control strategy for VSGs based on coordinate transformation is proposed. Combining the characteristics of traditional virtual impedance control and virtual power control, the power coupling mechanism in parallel VSGs caused by line impedance is analyzed. The virtual complex impedance control loop is introduced in VSG control to realize the matching of the equivalent line impedance and the precise decoupling of VSG power output. Then the load can be accurately allocated in the light of the proportion of VSG capacity.

Retracted: Optimization of Voltage Dynamic Performance at Inverter Output with Machine Learning and Intelligent Virtual Impedance

Retracted: Optimization of Voltage Dynamic Performance at Inverter Output with Machine Learning and Intelligent Virtual Impedance

MMC-HVDC High-Frequency Resonance Suppression Strategy Based on Multi-Band Band-Stop Filters

Renewable energy generation is a manifestation of global economic and societal advancement and serves as a fundamental assurance for humanity’s pursuit of sustainable development. However, recent years have witnessed several instances of high-frequency resonance events in high-voltage direct current (HVDC) transmission systems based on modular multilevel converters (MMC), which have resulted in converter station tripping and significant repercussions on the alternating current (AC) grid. This paper addresses the mid-to-high frequency resonance issues prevalent in flexible DC transmission systems employing modular multilevel converters (MMC-HVDC). To tackle these concerns, an impedance model for MMC’s AC side is established. Utilizing impedance analysis, the essential factors contributing to the negative damping characteristics of MMC are identified as delay and voltage feedforward loops, predominantly causing negative damping in the frequency range exceeding 400 Hz. In response, a suppression strategy is proposed, involving the incorporation of a multi-band stop filter and virtual impedance. This strategy ensures that within the 0–2000 Hz frequency range, only the impedance phase within 230–430 Hz slightly surpasses 90°. Consequently, the phase difference between MMC’s positive-sequence impedance and the AC system impedance is reduced from 222° to 174.7°, thus guaranteeing secure grid operation. Lastly, the accuracy and effectiveness of the theoretical analysis and suppression methodology are verified through the development of an electromagnetic transient model in MATLAB/Simulink, considering delay fluctuations of ±10%.

Suppression Strategy of Subsynchronous Oscillation Based on Dynamic Voltage Compensation Control for Grid-Forming D-PMSG in Weak Grid

The virtual impedance can suppress the low-frequency oscillation effectively caused by the power coupling effect for the grid-forming direct-drive permanent magnet synchronous generator (D-PMSG). However, there are few studies on the influence of virtual impedance on the subsynchronous oscillation caused by the interaction between the grid-forming D-PMSG and the weak grid. In this paper, the mechanism of virtual impedance improving the stability of virtual synchronous generator (VSG) control for the converter is revealed from the perspective of power coupling, and the influence of virtual impedance on the system stability in subsynchronous frequency range was analysed based on the sequence impedance model. The analysis results show that the virtual inductance cannot effectively improve the oscillation suppression effect, but the virtual resistance can greatly improve the damping characteristics of the system which has a good oscillation suppression effect. However, excessive increase in virtual resistance will cause power coupling oscillation, even subsynchronous oscillation, which shows limitations in subsynchronous oscillation suppression. To solve the problem, a dynamic voltage compensation control method based on active disturbance rejection control (ADRC) was proposed, and the parameters are designed by bandwidth method. The method can suppress the subsynchronous oscillation effectively in a certain frequency range under different grid strength and disturbance conditions. And it shows strong adaptability and good system robustness in weak grid. Finally, the effectiveness of the proposed oscillation suppression strategy was verified by time domain simulation.

Transient Stability Enhancement Strategy for Islanded Microgrids Based on Energy Storage–Virtual Synchronous Machine Control

In a high percentage of new energy-islanded microgrids, the overall inertia of the system gradually decreases, and the transient stability requirements of the microgrid frequency and voltage become more and more demanding under low-inertia conditions. To improve the transient stability of low-inertia islanded microgrid frequencies and voltages, this paper proposes a transient stability enhancement strategy for islanded microgrids based on energy storage system (ESS)–virtual synchronous generator (VSG) control. Model predictive control (MPC) is added within the active control loop of the VSG to achieve dynamic correction of the active power reference value of the VSG; PI control link is added within the reactive control loop to achieve a fast dynamic response of the reactive power command value. The ESS achieves fast and accurate regulation of frequency and voltage according to the power reference value of the VSG active control loop and the power command value of the reactive control loop simultaneously. Considering the need to ensure the ability of VSG to operate stably during transients, a comprehensive current-limiting technique combining virtual impedance and phase limiting is used to limit the fault current of VSG and maintain its synchronization and stability. Finally, the simulation results verify the strategy’s effectiveness and the superiority of the transient stability enhancement effect.

Passivity-Oriented Impedance Shaping for LCL-Filtered Grid-Connected Inverters

The passivity theory provides an effective way to tackle the instability due to the inverter-grid interaction, which tells that the system stability can be guaranteed if the grid impedance and the inverter output impedance are both passive. Since the grid impedance is generally passive, the system stability can be immune to the grid impedance variation if the inverter output impedance is also passive. This paper develops a series and parallel impedance shaping method to ensure that the output impedance of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -filtered grid-connected inverter is dissipative up to the Nyquist frequency. Since the inverter output impedance can be decomposed into two passive elements and one active element, its non-dissipative property results from the latter, and thus the virtual series impedance shaping is introduced to cancel out the active element. Unfortunately, it poses impact on the low-frequency loop gain and system phase margin in the meantime. To alleviate this impact, a high-pass filter is inserted in the series impedance shaping function. Subsequently, a virtual parallel impedance is introduced to enhance the passivity robustness, such as against filter parameter variations. Moreover, the proposed method does not require any additional sensors. Experiments from a 6-kW prototype confirm the effectiveness of the proposed method.

Current-Fed Phase-Shifted Full-Bridge Converter With Secondary Harmonic Current Reduction for Two-Stage Inverter in Energy Storage System

For the low voltage, high current, isolated DC-DC converter applications, current-fed type converter has the chance to achieve higher efficiency due to the lower transformer root mean square current compared with other well-known converters such as dual active bridge or LLC. A current-fed phase-shifted full-bridge, CFPSFB converter has the advantages of nearly full range zero-voltage-switching and soft-commutating without large size of passive or active snubber circuit because the phase-shift of secondary full-bridge is controlled to be proportional to the input current. However, as a front-end stage of a single phase inverter, the input secondary harmonic current (SHC) propagating from the output AC load may cause large voltage spike to damage the primary MOSFETs due to losing the soft-commutating property. SHC may also reduce the conversion efficiency and the lifespan of battery intensely. This paper proposes a simple control scheme based on virtual series impedance method with a notch filter in control loop to reduce the SHC and maintain good dynamic performance. A small-signal model of CFPSFB for a reliable controller design is derived and verified by simulation. A 48 V/3 kW maximum output power inverter prototype is built to verify the theoretical analysis. The maximum efficiency of the DC-DC stage is 97.4% and the peak to peak SHC is less than 10% of the average input current.

Power-Sharing in Microgrids by Adaptive Virtual Impedance and Fuzzy Logic

Power-Sharing in Microgrids by Adaptive Virtual Impedance and Fuzzy Logic