Virtual Impedance Control Research Articles

Harmonic voltage compensation and harmonic current sharing strategy of grid-forming inverter

In a multi-inverter parallel system, the harmonic governance control strategy may worsen the system's current circulation problem due to the line impedance difference, which could further affect the stable operation of the system. To solve the problem, the strategy considering both power sharing and harmonic control is proposed in this paper. First, the microgrid system with background harmonics is modeled and analyzed. Based on the modeled system, a comprehensive control strategy for the grid inverter with harmonic voltage compensation and harmonic current sharing is established. In this paper, the output signal is controlled by frequency division. This paper adopts grid-forming control in the fundamental wave domain and employs harmonic voltage compensation control in the harmonic domain. The harmonic voltage is synthesized by collecting the specific harmonic current through the band-pass filter, compensating for the harmonic voltage drop on the line to improve the harmonic voltage quality of the point of common coupling(PCC). Aiming at the sharing problem caused by line impedance difference, virtual impedance control is introduced, harmonic impedance is redesigned according to the adjusted output impedance, and the harmonic output impedance before and after adjustment is measured and compared. The simulation results show that the proposed control strategy can not only reduce the harmonic content of the PCC voltage but also achieve the effect of equal harmonic current division.

Enhancing Robot End‐Effector Trajectory Tracking Using Virtual Force‐Tracking Impedance Control

This article presents an extended Cartesian space robot control framework that features a virtual force tracking impedance control to enhance the end‐effector trajectory tracking performance. Initially, the concept of a virtual surface is introduced, which is assumed to be at some constant distance from the desired end‐effector trajectory. This virtual surface generates a virtual contact force when interacting with the torque‐controlled robot end‐effector. The interaction is then manipulated using an impedance control model to track a constant desired force. If the robot end‐effector deviates from the desired trajectory, the constant force‐tracking impedance control generates a compliance trajectory that regulates the end‐effector movements, constraining it to the desired trajectory. For robust force tracking, impedance parameters are optimally tuned using a closed‐loop dynamic model incorporating both robot and impedance dynamics. Additionally, super twisting sliding mode control (STSMC) is integrated to overcome uncertainties and the impact of robot dynamics on force‐tracking performance. Experimental validation confirms the theoretical claims of the proposed approach. It demonstrates that force‐tracking impedance control improves the end‐effector trajectory tracking by quickly reacting to the dynamic trajectories compared to position control only and effectively maintains it on the desired trajectories.

Virtual impedance control of double-fed induction generator for damping enhancement in hvdc collection system

Virtual impedance control of double-fed induction generator for damping enhancement in hvdc collection system

A Virtual Synchronous Generator-Based Control Strategy and Pre-Synchronization Method for a Four-Leg Inverter under Unbalanced Loads

Virtual synchronous generator (VSG) control has positive effects on the stability of microgrids. In practical power systems, both single-phase loads and three-phase unbalanced loads are present. The four-leg inverter is an alternative solution for the power supply of unbalanced loads and grid connections. The traditional VSG control strategy still faces challenges when using a four-leg inverter to provide a symmetrical voltage and stable frequency in the load power supply and pre-synchronization. This paper proposes a VSG-based control strategy along with a pre-synchronization method for four-leg inverters. An improved VSG control strategy is put forward for four-leg inverters. The improved virtual impedance control and power calculation methods are integrated into the control loop to suppress the voltage asymmetry and frequency ripples. Building on the improved VSG control strategy, a pre-synchronization control approach is proposed to minimize the amplitude and phase angle discrepancies between the inverter output voltage and the power grid voltage. In addition, an optimized design method for control parameters is presented to improve VSG dynamic performance. A hardware prototype of the four-leg inverter is built; the results show that the voltage unbalance ratio can be reduced by 89%, and the response time can be shortened by 50%.

A modified droop-based decentralized control strategy for accurate power sharing in a PV-based islanded AC microgrid

This paper introduces a novel droop-based decentralized control scheme to address the power-sharing challenges within a PV-fed islanded AC microgrid. This novel approach integrates both conventional (P-f/Q-V) and virtual impedance concepts to optimize and manage the precise distribution of active and reactive power among parallel operating inverters posing a significant research challenge. The conventional droop control methods encounter limitations such as voltage and frequency deviations and inaccuracies in power-sharing due to line impedance disparities. To overcome these limitations, the proposed solution integrates an enhanced virtual impedance control loop alongside the conventional control loop (P-f/Q-V). The efficacy of this approach is showcased through simulations conducted using the OPAL-RT OP4510 simulator within the MATLAB/Simulink platform. The Real-time simulation outcomes confirm the efficiency of the suggested control strategy, guaranteeing precise distribution of both active and reactive power while upholding stable voltage and frequency profiles within the system.

Adaptive low voltage crossing strategy for symmetrical faults of networked inverters

Abstract Due to the inability of grid-following control methods to compensate for the comprehensive reduction in system inertia, strength, and short-circuit capacity caused by the decreased proportion of synchronous machines, the grid exhibits insufficient resilience to disturbances, leading to severe stability risks in terms of rotor angle, frequency, and voltage. Grid-forming inverters have emerged to address this issue. During symmetrical faults, the low-voltage ride-through of grid-forming inverters often involves freezing the reactive power loop, resulting in a direct output of higher voltage and reactive current. However, an increase in reactive power command leads to a sharp rise in the internal potential magnitude of grid-forming inverters. Upon clearance of the grid fault, the excessively high internal potential may cause a rapid, short-term increase in terminal voltage, potentially resulting in overvoltage, which is detrimental to the operation of grid-connected equipment. In response to this issue, this paper proposes an adaptive low-voltage ride-through control strategy for grid-forming inverters under symmetrical faults controlled by a virtual synchronous machine control method. Initially, a virtual synchronous machine control model is established. Limiting current is achieved through the construction of a fixed virtual impedance loop. The issues associated with fixed virtual impedance current limiting are analyzed, leading to the proposal of an adaptive virtual impedance control strategy. Finally, the feasibility of the proposed method is verified through simulation experiments.

Decentralized Virtual Impedance Control for Power Sharing and Voltage Regulation in Islanded Mode with Minimized Circulating Current

Decentralized Virtual Impedance Control for Power Sharing and Voltage Regulation in Islanded Mode with Minimized Circulating Current

Propagation Mechanism and Suppression Strategy of DC Faults in AC/DC Hybrid Microgrid

Due to their efficient renewable energy consumption performance, AC/DC hybrid microgrids have become an important development form for future power grids. However, the fault response will be more complex due to the interconnected structure of AC/DC hybrid microgrids, which may have a serious influence on the safe operation of the system. Based on an AC/DC hybrid microgrid with an integrated bidirectional power converter, research on the interaction impact of faults was carried out with the purpose of enhancing the safe operation capability of the microgrid. The typical fault types of the DC sub-grid were selected to analyze the transient processes of fault circuits. Then, AC current expressions under the consideration of system interconnection structure were derived and, on this basis, we obtained the response results of non-fault subnets under the fault process, in order to reveal the mechanism of DC fault propagation. Subsequently, a current limitation control strategy based on virtual impedance control is proposed to address the rapid increase in the DC fault current. On the basis of constant DC voltage control in AC/DC hybrid microgrids, a virtual impedance control link was added. The proposed control strategy only needs to activate the control based on the change rate of the DC current, without additional fault detection systems. During normal operations, virtual impedance has a relatively small impact on the steady-state characteristics of the system. In the case of a fault, the virtual impedance resistance value is automatically adjusted to limit the change rate and amplitude of the fault current. Finally, a DC fault model of the AC/DC hybrid microgrid was built on the RTDS platform. The simulation and experimental results show that the control strategy proposed in this paper can reduce the instantaneous change rate of the fault state current from 19.1 kA/s to 2.73 kA/s, and the error between the calculated results of equivalent modeling and simulation results was within 5%. The obtained results verify the accuracy of the mathematical equivalent model and the effectiveness of the proposed current limitation control strategy.

Optimized virtual impedance solar restoration droop emulated SEPIC controller under low irradiation

This paper is focused on PV-based reduced order pade’s approximation SEPIC (single-ended primary inductor converter) virtual Impedance, restoration controller with parallel impedance emulation condition. However, the complexity of the higher-order SEPIC controller has been reduced and compared using Pade’s approximation with different reduction techniques. It covers the time response, oscillation, overshoot, dynamic performance, and controller stability. The computational time and need of the sensor are less, and better responses occur compared to the other reduction technique under the solar irradiance variation. However, in PV, the dynamic resistance is generalized by a nonlinear solar I–V (current–voltage) curve dependent on the operating point, such as irradiance, temperature, and its I–V curve. The nonlinearity effect affects the stability of the system. The SEPIC outer voltage and inner current controller with virtual impedance controller enhance the stability, and comparative response is demonstrated through the bode plot. A virtual impedance controller (VIC) cascaded with voltage restoration minimizes the voltage notching and oscillations under variation of inertia coefficients. The transient and dynamic performance of reduced order using a genetic algorithm controller has been used to demonstrate and discuss the PV-SEPIC system’s stability.

Stability and Reactive Power Sharing Enhancement in Islanded Microgrid via Small-Signal Modeling and Optimal Virtual Impedance Control

In the context of integrating Renewable Energy Sources, Microgrid (MG) development is pivotal, particularly as a foundational technology for Smart-Grid evolution. Despite advancements in control techniques, challenges persist in ensuring system stability and accurate power sharing across diverse operational conditions and load types. The objective of this research is to control numerous paralleled inverters-based distributed generators (DGs) that contribute to power sharing in an island MG. The proposed methodology involves developing an innovative small-signal model for islanding MGs that incorporate virtual impedances. Subsequently, optimization algorithms based on Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are proposed and compared for designing the virtual impedances. These algorithms analyze all potential operating points, aiming to minimize reactive power mismatches while maximizing MG stability. The suggested objective function facilitates the simultaneous achievement of these objectives. The proposed approaches were tested using MATLAB-Simulink software, and the comparison of the results between conventional approach and the proposed optimal approaches shows significant improvement in terms of the dynamic response during load changes, such as a decrease in response time by up to 20%, a reduction in overshoot percentage by approximately 15%, and a settling time improvement of nearly 25%. These quantified improvements highlight the effectiveness of the GA and PSO methods in minimizing the reactive power-sharing error while optimizing MG performance and stability.

Virtual Impedance Control for Load Sharing and Bus Voltage Quality Improvement in Low-Voltage AC Microgrid

Virtual Impedance Control for Load Sharing and Bus Voltage Quality Improvement in Low-Voltage AC Microgrid

Unified Voltage Control for Grid-Forming Inverters

This article proposes a unified voltage control for grid-forming (GFM) inverters, which enables to flexibly synthesize six commonly used voltage control methods through a universal and simple structure. The unified control scheme is composed by three loops, i.e., the voltage magnitude control, the virtual impedance control, and the voltage reference feedforward control. By flexibly combining the three loops and applying different forms of virtual impedance, the six voltage control methods can be readily realized. Experimental tests confirm the effectiveness of the unified voltage control structure.

High frequency resonance characteristics analysis of voltage‐source virtual synchronous generator and suppression strategy

AbstractThe voltage‐source virtual synchronous generator is a grid‐forming type power electronic control technology and is able to support converters that have the ability of inertial, primary frequency and voltage regulation. Firstly, the authors build the small‐signal model of the voltage‐source virtual synchronous generator and conventional converters, compare and analyse the characteristics of the high‐frequency resonance modes, the results show that the voltage‐source virtual synchronous generator has almost the same high‐frequency resonance characteristics as the conventional converter. Secondly, the different control parameters and power grid strength that affect the high‐frequency resonance characteristic are analysed with eigenvalue, and the mechanism of voltage‐source VSG that caused high‐frequency resonance is derived. The leading factor that causes high‐frequency resonance is power grid strengths, and the authors proposed introducing virtual impedance into the front‐end channel of the current inner loop control strategy to suppress resonance for the voltage‐source virtual synchronous generator based on the theoretical analysis with the small‐signal model and eigenvalue analysis. In addition, the electromagnetic transient simulation model and RT‐LAB controller‐in‐loop platform are built, and the simulation and experiment results indicate the effectiveness of the virtual impedance control strategy.

Adaptive Virtual Impedance Control with MPC’s Cost Function for DG Inverters in a Microgrid with Mismatched Feeder Impedances for Future Energy Communities

More and more distributed generations (DGs), such as wind, PV or battery bank sources, are connected to electric systems or customer loads. However, the locations of these DGs are based on the highest energy that can be potentially harvested for electric power generation. Therefore, these locations create different line impedances based on the distance from the DGs to the loads or the point of common coupling (PCC). This paper presents an adaptive virtual impedance (AVI) in the predictive control scheme in order to ensure power sharing accuracy and voltage stability at the PCC in a microgrid network. The reference voltage from mismatched feeder impedances was modified by utilizing the suggested AVI-based predictive control for creating equal power sharing between the DGs in order to avoid overburdening any individual DG with low-rated power. The AVI strategy used droop control as the input control for generating equal power sharing, while the AVI output was used as the reference voltage for the finite control set–model predictive control (FCS-MPC) for creating a minimum voltage error deviation for the cost function (CF) for the inverter’s vector switching pattern in order to improve voltage stability at the PCC. The proposed AVI-based controller was tested using two DG inverter circuits in a decentralized control mode with different values of line impedance and rated power. The performance of the suggested controller was compared via MATLAB/Simulink with that of a controller based on static virtual impedance (SVI) in terms of efficiency of power sharing and voltage stability at the PCC. From the results, it was found that (1) the voltage transient magnitude for the AVI-based controller was reduced within less than 0.02 s, and the voltage at the PCC was maintained with about 0.9% error which is the least as compared with those for the SVI-based controller and (2) equal power sharing between the DGs increased during the change in the load demand when using the AVI-based controller as compared with using the SVI-based controller. The proposed controller was capable of giving more accurate power sharing between the DGs, as well as maintaining the voltage at the PCC, which makes it suitable for the power generation of consumer loads based on DG locations for future energy communities.

Multiple High-Frequency Resonances Analysis and Adaptive Virtual Impedance Control of MMC-Based System

Multiple High-Frequency Resonances Analysis and Adaptive Virtual Impedance Control of MMC-Based System

Stability Enhancement Method Based on Adaptive Virtual Impedance Control for a PV-integrated Electrified Railway System

Stability Enhancement Method Based on Adaptive Virtual Impedance Control for a PV-integrated Electrified Railway System

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.

Decoupled Mitigation Control of Series Resonance and Harmonic Load Current for HAPFs With a Modified Two-Step Virtual Impedance Shaping

Hybrid active power filter (HAPF) with large series capacitor can reduce the rating of power converter, but it is associated with the risk of low frequency <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> resonance. The overlapping of series <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> resonance frequencies and the dominated load harmonic current frequencies makes the conventional active damping approaches less effective. To overcome this challenge, a two-step harmonic virtual impedance control approach is developed to compensate the load harmonic current and reshape the closed-loop equivalent circuit of the HAPF for resonance damping. First, the shunt capacitor harmonic voltage is regulated according to a term that is associated with both the harmonic load current and the HAPF harmonic line current. Further investigation on the equivalent circuit transformations indicates that HAPF is equivalent to a controlled current source to compensate for load harmonic current and a virtual harmonic damping resistor between the series capacitor and grid impedance. Accordingly, the resonance damping and the nonlinear load low order harmonic current compensation can be well decoupled with minimal interference.

Parallel Power Sharing Control of Multi-Controllable Rectifiers in a High-Power DC Fast Charging Station

The increase in demand for the fast charging of electric vehicles (EVs) has promoted research and the application of high-power direct current (DC) fast charging stations, and research on the stability control of charging stations with a parallel structure of multi-controllable rectifier modules is of great significance. Taking into account the dynamic and steady-state performance, the parameters of the dual-loop controller based on virtual impedance control are designed to realize the power sharing of multi-controllable rectifier modules. The constant power load model of EV charging at a constant current is established, and the load capacity of the cascaded system of converters is studied by using the impedance analysis method. The experimental and simulation results verify the effectiveness and correctness of the power sharing control strategy and the cascaded system stability analysis.

Circulating Current Suppression Strategy Based on Virtual Impedance and Repetitive Controller for Modular Multilevel Converter Upper and Lower Bridge Arm Capacitance Parameter Asymmetry Conditions

In recent years, modular multilevel converters (MMCs) have been increasingly used in the field of electric vehicle charging and discharging due to their unique performance advantages. However, the unique cascade structure of MMCs raises the problem of the circulating current. Due to chemical processes, aging effects, etc., the capacitance parameters of the upper and lower bridge arms will be asymmetric, which will introduce odd harmonics into the circulating current, increasing system losses and threatening the system reliability. To address this phenomenon, this paper proposes a circulating current suppression strategy with additional virtual impedance (VI) based on a repetitive controller (RC). The corresponding simulation models were built for the comparative study of different circulating current suppression strategies. The results show that the VI-RC circulating current suppression strategy can significantly reduce the odd and even harmonics in the circulating current under asymmetric conditions, and the total harmonic distortion (THD) of the bridge arm current is only 0.98%, which verifies the effectiveness of the proposed strategy.