Virtual Impedance Control Research Articles

Dynamic Interactions between Parallel Grid-Forming Inverters in a Microgrid

The potential instability issues caused by the dynamic interactions between parallel grid-forming inverters are examined. The approach adopted for analysis is s-domain admittance-based eigenvalue and mode shape analysis. This admittance is based on a five-node circuit diagram after the conversion of each electric circuit element and inverter control unit into impedance models. Eigenvalue analysis results show that unstable resonance modes may exist due to the interactions of two parallel inverters. Impacts of transmission line length, the converter control’s virtual impedance unit, and the voltage feed-forward unit are examined via the eigenvalue and mode shape analysis. The results show that the virtual impedance control has a negligible influence on the resonance while the voltage feed-forward unit stabilizes the resonance. Finally, the stability analysis is validated using electromagnetic transient (EMT) simulations.

Analysis and Optimization Strategy of Active Power Dynamic Response for VSG under a Weak Grid

A virtual synchronous generator (VSG) has a good adaptability to the weak grid but its grid-connected active power (GCAP) has the problem of a slow dynamic response under the active power command step. An optimization strategy of the GCAP dynamic response for the VSG based on the virtual negative impedance combined with the active power transient damping control algorithm is proposed in this paper. The optimization strategy first uses the virtual negative impedance control method to reduce the VSG equivalent output impedance and the GCAP dynamic response time of the VSG. Then, the transient damping as well as the inhibition ability of the GCAP dynamic oscillation for the VSG are enhanced by the active power transient damping control algorithm. The Matlab/Simulink simulation software is used to study the GCAP dynamic response performances of the VSG in the condition of the active power command step, and the experimental test platform of a VSG grid-connected system is established. The simulation and experimental results jointly verify the feasibility and superiority of the proposed strategy in improving the GCAP dynamic response characteristics of the VSG under a weak grid.

Vision-Based Virtual Impedance Control for Robotic System Without Prespecified Task Trajectory

This article proposes a vision-based virtual impedance control (VBVIC) scheme for the robotic system without pre-specified task trajectory, where a neural network (NN) is used to compensate for the unmodeled dynamics and parameter uncertainties. In the proposed scheme, a novel control framework combined virtual potential field (VPF) with the impedance control is proposed to achieve non-contact impedance control, where the task trajectory does not need to be pre-specified but is generated by integrating the bio-inspired Tau-J into the virtual impedance model. Moreover, the virtual force generated by VPF is utilized to achieve the shaping and tracking of the task trajectory in the virtual impedance control scheme, and the information of target and obstacle is obtained by the visual sensing. The proposed VPF-based VBVIC scheme is analyzed by the Lyapunov stability theory and validated by a carrying task in simulations and experiments, respectively.

Distributed Power Sharing Control Based on Adaptive Virtual Impedance in Seaport Microgrids With Cold Ironing

In a seaport microgrid (SMG), power sharing among distributed generation (DG) units is hindered by power coupling, line changes as well as frequent power fluctuations caused by ship charging and discharging through cold ironing, which in turn threatens system stability and inverter security. This paper proposes a delay-tolerant distributed adaptive virtual impedance control strategy for assigned active and reactive power sharing, so as to suppress the circulating current among DGs. Firstly, the nonlinear impedance-power droop equations (IPDEs) are derived to actively update the resistive and inductive components of virtual impedance, which can accommodate changes in line structure and output power. Secondly, by means of low-bandwidth communication with quantized data and time delay, the desired power terms derived from practical consensus protocols are fed into the IPDEs, for which the proposed scheme gives a quantitative maximum tolerable communication delay with respect to power sharing accuracy. Thirdly, considering the voltage drop caused by virtual impedance, inspired by traditional synchronous generators, we design a virtual impedance loop based on virtual damping and inertia to preserve voltage dynamics. Finally, an SMG containing four DG units is simulated to verify the effectiveness of the proposed strategy on both active and reactive power sharing.

Research on coordinated control strategy of photovoltaic energy storage system

In this paper, the modular design is adopted to study the control strategy of photovoltaic system, energy storage system and flexible DC system, so as to achieve the design and control strategy research of the whole system of “photovoltaic + energy storage + DC + flexible DC”. This realizes the flexibility and diversity of networking. Due to space reasons, this article focuses on the detailed explanation of the photovoltaic energy storage system control strategy, including the maximum power tracking control strategy of photovoltaic power generation, photovoltaic power generation boost chopper circuit control strategy, photovoltaic power generation DC/AC converter control strategy, PCS device control strategy, PCS virtual impedance control algorithm, etc. Simulation experiments are carried out according to the specific case setting parameters. The simulation results prove that the proposed flexible DC system coordinated control strategy can ensure grid frequency stability and grid voltage stability, and improve the consumption capacity of distributed new energy.

Active Damping Method for LC-DAB System Based on a Power-Based Impedance Model

A cascaded system, consisting of an LC filter and a dual active bridge (DAB), can exhibit certain instability due to terminal impedance mismatch. In this regard, the existing impedance models of DAB are not convenient for designing the active damping methods, owing to strong coupling between the phase-shift ratios. To solve this problem, this work proposes an active damping method based on the power-based impedance model (PBIM) for LC-DAB. First, the input impedance of DAB is derived using PBIM, which shows high simplicity and generality because it is decoupled from the modulation methods. Then, based on PBIM, the stability of LC-DAB is discussed. Next, to achieve stabilization of LC-DAB, an active damping method without any additional sensors, named the virtual-current series virtual impedance control (VC-SVIC) is proposed, which assists in maintaining the original fast-dynamic performance of DAB. Finally, the performance of VC-SVIC is validated by the relevant experiments. Essentially, this work puts forward an easy and effective way to guarantee the stability of cascaded LC-DAB system, while achieving a good dynamic performance.

Power quality enhancement in islanded microgrids via closed-loop adaptive virtual impedance control

The high proportion of nonlinear and unbalanced loads results in power quality issues in islanded microgrids. This paper presents a novel control strategy for harmonic and unbalanced power allocation among distributed generators (DGs) in microgrids. Different from the existing sharing strategies that allocate the harmonic and unbalanced power according to the rated capacities of DGs, the proposed control strategy intends to shape the lowest output impedances of DGs to optimize the power quality of the microgrid. To achieve this goal, the feasible range of virtual impedance is analyzed in detail by eigenvalue analysis, and the findings suggest a simultaneous adjustment of real and imaginary parts of virtual impedance. Because virtual impedance is an open-loop control that imposes DG to the risk of overload, a new closed-loop structure is designed that uses residual capacity and absorbed power as feedback. Accordingly, virtual impedance can be safely adjusted in the feasible range until the power limit is reached. In addition, a fuzzy integral controller is adopted to improve the dynamics and convergence of the power distribution, and its performance is found to be superior to linear integral controllers. Finally, simulations and control hardware-in-the-loop experiments are conducted to verify the effectiveness and usefulness of the proposed control strategy.

An improved distributed secondary control for multi‐voltage‐level DC distribution networks with virtual impedance arrangement

AbstractThe distributed secondary control of the DC distribution network is becoming increasingly important in modern power systems to achieve accurate power sharing of each distributed unit. Here, an improved secondary control strategy for energy storage systems (ESSs) in the multi‐voltage‐level DC distribution network (MVL‐DCDN) is proposed. At the primary control level, the interlinked DC transformers (DCT) are controlled by difference‐of‐v2 to support bidirectional voltage making the MVL‐DCDN regarded as a single‐voltage‐level one using only the local information of DCT. At the secondary control level, it can be observed that the voltage correction term and virtual impedance correction term have a coupling relationship. In order to tackle this coupling effect, a distributed secondary control is imposed in an MVL‐DCDN based on improved droop control. Concretely, this proposed secondary control strategy contains a power sharing controller, a virtual impedance controller, an average voltage restoration controller, and a reference voltage consensus controller. With the proposed method, this coupling effect can be eliminated to ensure the steady operation of the virtual impedance. Furthermore, a steady‐state analysis is performed to discuss the unique solution of the DC distribution network and conduct hardware‐in‐loop experiments to demonstrate that this method achieves effective results.

Inertia and Grid Impedance Emulation of Power Grid for Stability Test of Grid-Forming Converter

The virtual synchronous generator (VSG) control is a promising solution for the grid-forming converters to enhance the inertia of the converter-based power grid. The virtual inertia and output impedance of the VSG are the important behaviors to be focused. However, the virtual inertia of grid-forming converters may cause active power oscillation due to the interaction with the power inertia of grid through the low-frequency band grid impedance. Besides, the resonance can be also triggered by the interaction between middle-frequency impedance of power grid and output impedance of converter. In order to test the stability of grid-forming converter, accurate emulation of grid behaviors from more aspects, including inertia and impedance under wider frequency ranges, is becoming critical. This article proposes a grid emulation method to mimic the inertia and impedance characteristics of power grid, targeting for the stability test of grid-forming converter under multifrequency bands. A high-switching-frequency converter and a low-switching-frequency converter are adopted in the proposed emulator structure to achieve both high capability in respect to control bandwidth and power level. Moreover, the virtual impedance control is integrated with the VSG control to emulate the line impedance and inertia within relatively wider frequency ranges. The realization of virtual impedance is achieved without derivation terms nor low pass filter. Finally, the performance of the proposed emulator is verified by various simulations and experimental measurements.

A Hybrid Master–Slave Control Strategy for Multiple Distributed Generators in Microgrid

The problem of insufficient regulation ability in isolated microgrid operations in traditional master–slave control is targeted in this research. A hybrid master–slave control strategy is proposed to operate multiple distributed generators (DGs) in a microgrid with alleviated regulation characteristics. Firstly, a virtual synchronous generator control is adopted in the master DG to provide voltage and frequency support for the system; however, the lack of participation of the slave DG control in traditional PQ droop control in the system regulation makes a master DG susceptible to any load variation. The problem is resolved by proposing an improved droop control strategy, which ensures that the slave DG has similar output droop characteristics as the master DG and thus can respond to system load disturbances alongside the master DG. Secondly, virtual coordinate transformation and virtual impedance control are introduced to realize the decoupling and precise distribution of output power of multiple DGs. Finally, a simulation and experimental platform for a multi-DGs parallel system are established to verify the effectiveness of the proposed strategy.

Control Methodologies to Mitigate and Regulate Second-Order Ripples in DC–AC Conversions and Microgrids: A Brief Review

Second-order ripples occur in the voltage and current during any DC–AC power conversion. These conversions occur in the voltage source inverters (VSIs), current source inverters (CSIs), and various single-stage inverters (SSIs) topologies. The second-order ripples lead to oscillating source node currents and DC bus voltages when there is an interconnection between the AC and DC microgrids or when an AC load is connected to the DC bus of the microgrid. Second-order ripples have various detrimental effects on the sources and the battery storage. In the storage battery, they lead to the depletion of electrodes. They also lead to stress in the converter or inverter components. This may lead to the failure of a component and hence affect the reliability of the system. Furthermore, the second-order ripple currents (SRCs) lead to ripple torque in wind turbines and lead to mechanical stress. SRCs cause a rise in the temperature of photovoltaic panels. An increase in the temperature of PV panels leads to a reduction in the power generated. Furthermore, the second-order voltage and current oscillations lead to a varying maximum power point in PV panels. Hence, the maximum power may not be extracted from it. To mitigate SRCs, oversizing of the components is needed. To improve the lifespan of the sources, storage, and converter components, the SRCs must be mitigated or kept within the desired limits. In the literature, different methodologies have been proposed to mitigate and regulate these second-order ripple components. This manuscript presents a comprehensive review of different effects of second-order ripples on different sources and the methodologies adopted to mitigate the ripples. Different active power decoupling methodologies, virtual impedance-based methodologies, pulse width modulation-based signal injection methodologies, and control methods adopted in distributed power generation methods for DC microgrids have been presented. The application of ripple control methods spans from single converters such as SSIs and VSIs to a network of interconnected converters. Furthermore, different challenges in the field of virtual impedance control and ripple mitigation in distributed power generation environments are discussed. This paper brings a review regarding control methodologies to mitigate and regulate second-order ripples in DC–AC conversions and microgrids.

Reduction in Voltage Harmonics of Parallel Inverters Based on Robust Droop Controller in Islanded Microgrid

In this article, a distributed control scheme to compensate for voltage harmonics in islanded microgrids is presented, where each distributed generation (DG) source has a primary control level and a secondary control level. In addition to the voltage and current control loops, the primary control level of DGs includes virtual impedance control loops in the main and harmonic components, which are responsible for dividing the power of the main component and the non-main component (harmonic) between the DGs of the microgrid, respectively. For coordinated operation between the inverters when facing the islanding phenomenon, it is very beneficial to use a droop controller structure. Here, the traditional droop controller is modified in such a way that the power is proportionally divided between the DGs, which causes accurate voltage regulation at the output of the DGs. By presenting a model for the inverter connected to the nonlinear load, a harmonic droop controller is designed. Through the droop controller related to each harmonic, the harmonic voltages are calculated and added to the reference voltage, which improves the quality of the output voltage. Then, the inverter voltage control loop is modified with resistive impedance in the presence of nonlinear loads in such a way that, when combined with the harmonic droop controller, the total harmonic distortion (THD) of the output voltage is significantly reduced. Lastly, the proposed method is implemented on the microgrid through MATLAB software, and the results show the ability of the proposed method to reduce voltage harmonics in the parallel operation of inverters.

Virtual composite impedance circulating current suppression strategy with adaptive adjustment capability

AbstractIn the process of accessing distributed power sources in microgrid, there will be serious coupling between active power and reactive power, which will lead to significant changes in the inverter outlet voltage and impedance and increase the circulating current phenomenon. The generation of circulating current will accelerate the aging of devices, reduce the inverter efficiency, and threaten the stable operation of the system. In this paper, the mechanism of circulating current generation is analysed, the basic characteristics of circulating current are studied, and an inverter parallel circulating current suppression strategy with adaptive virtual composite impedance and droop control dynamic adjustment algorithm is proposed. The virtual impedance setting can weaken the influence of line difference on system stability, make the system equivalent output impedance resistive, weaken the inductive device characteristics and reduce the circulating current amplitude; the adaptive droop algorithm implantation dynamically correlates the control power with the droop coefficient, enhance the power decoupling accuracy and weaken the circulating current influenced by power changes. The simulation platform and experimental setup established by the large‐scale simulation software PSCAD/EMTDC are used to study the basic scenarios of the inverter under two conditions of equal and unequal capacity, and the rationality of the proposed control strategy is tested.

Modified Virtual Impedance Control to Improve Real and Reactive Power Output in Islanded Microgrid

In this paper, modified virtual impedance control technique is proposed to bring back the sum of real power and reactive power output of all the distributed generators (DGs) to the nominal value. The value of real and reactive power output falls down in the conventional virtual impedance control technique for reactive power sharing improvement in islanded microgrid. The proposed technique modifies the d-axis component of virtual impedance voltage which in turns brings back the sum of real and reactive power output of distributed generators to nominal value keeping achieved reactive power sharing and output voltage intact. The impact of modified virtual impedance technique on the stability of the system is also investigated using eigenvalue analysis. No communication link or optimization technique is required in this work which reduces the complexity of the system making it more reliable and easier to design. The proposed technique works satisfactory for local load as well as the loads which are connected distantly from the distributed generators. The feasibility of the proposed technique is validated in time domain simulation in MATLAB/Simulink. The MATLAB R2020b version 9.9 is used in this research work.

An Improved Virtual Impedance Control Based Oscillation Suppression Method for MMC DC System

The oscillation phenomenon has detrimental effects on the stable operation of the module multilevel converter (MMC)-based high voltage DC (MMC-HVDC) transmission system. The virtual inductance or resistance control can be used as the oscillation suppression method to limit the system instability. To improve the oscillation suppression effectiveness based on the existing virtual impedance control methods. This paper first analyzes the DC output impedance of the MMC-HVDC system and verify the correctness of the DC output impedance. Then an improved virtual impedance control (IVIC) method is presented based on the traditional virtual resistance control (TVRC) and the phase lag compensation control (PLCC) method. Under the same conditions, the Nyquist stability analysis is presented to verify the MMC system stability can be more improved by using the IVIC method compared with the TVRC and PLCC. In PSCAD/EMTDC, the simulation results verify that the IVIC can suppress the MMC DC system oscillation and can improve the oscillation suppression effectiveness compared with the TVRC and PLCC. The stability analysis and simulation results verify that the proposed IVIC method can help to mitigate the detri-mental effects caused by system instabilities and oscillations.

Control Strategy of Doubly-Fed Induction Generator under Zero Voltage Fault of Power Grid

For improving the zero-voltage ride through the capability of a doubly fed induction generator in high proportion new energy grid in extreme faults, a coordinated control scheme of hardware and optimal control strategy is proposed. A high-temperature superconductive-fault current limiter suppresses stator fault current, adaptive virtual impedance control and active dynamic reactive power support control act on the back-to-back converter of wind turbines as optimal control strategies. Optimizing the control strategy without changing the controller structure is beneficial to engineering implementation. After mathematical derivation and simulation verification, the coordinated control strategy adopted in this paper can effectively avoid the rotor current and voltage exceeding the limit when the wind turbine is facing extreme faults, actively provide reactive power support for the busbar, realize zero voltage ride through and reduce the risk of high voltage failure at the point of failure. The control effect is obviously better than the traditional virtual impedance control.

Dual-Frequency Bands Grid Impedance Emulator for Stability Test of Grid-Connected Converters

The grid-connected converters are becoming a fundamental building block in the modern power grid, and the stability of grid-connected converters, especially when they are connected to weak grid, has drawn increasing attention. In order to test the interaction with various grid impedances and validate the stability behaviors, more accurate and advanced emulation of grid impedance is becoming an emerging need. However, the existing approaches are still difficult to flexibly shape the grid impedance under medium-to-high frequency range. In this article, a novel configuration for programable impedance emulation of power grid is proposed. The proposed grid emulator is composed of two power electronics converters with special control functions, i.e., the impedance forming converter (IFC) and power supporting converter (PSC). The IFC is designed with a higher switching frequency to virtually emulate different grid impedances under medium-to-high frequency band. On the other hand, the PSC is designed with a lower switching frequency to generate/absorb the power of the converter under test. Besides, a Norton-circuit-based virtual impedance control strategy is introduced to eliminate the derivation term in the control structure of virtual impedance. Finally, the performance of the proposed emulator is verified by various simulations and experimental prototype.

A Novel Droop Control Strategy of Reactive Power Sharing Based on Adaptive Virtual Impedance in Microgrids

Droop control strategy is widely used to control parallel inverters in a microgrid. However, due to the mismatched line impedance, the traditional droop control strategy is difficult to evenly share the reactive power and restrain the circulating current among multiple parallel inverters. In this article, an adaptive virtual impedance-based droop control strategy without communications is proposed to solve the reactive power sharing problem caused by the difference of line impedance. The reactive power output and voltage of each distribution generator are introduced into the adaptive virtual impedance controller to achieve a tradeoff between reactive power sharing accuracy and voltage drop. Small-signal stability analysis of the inverters equipped with the proposed controller is conducted to determine the optimal control parameters. Simulation and experimental results demonstrate the effectiveness of the proposed droop control strategy.

A novel current-limiting method for MMC-HVDC by coordinating virtual impedance control and fault current limiter

The modular multilevel converter (MMC) topology is very suitable for high voltage direct current (HVDC) system to achieve feasible power control, favorable black start capability as well as long-distance power transmission. This paper proposes a novel current-limiting method based on the coordination of virtual impedance control (VIC) and resistive fault current limiter (R-FCL) for MMC-HVDC, and it aims to effectively decrease the DC fault current level and assist the DC circuit breaker (DCCB) to remove the fault reliably and smoothly. Firstly, the MMC-HVDC’s topology and control strategy are expounded, and the modeling method of the VIC and the R-FCL is presented. According to the DC fault evolution, the time sequence coordination scheme of the VIC and the R-FCL for the MMC-HVDC is put forward. Then, considering the introduction of the proposed current-limiting method, the fault characteristics of the MMC-HVDC are theoretically deduced, and the capacity design of the VIC and the R-FCL is conducted. Using MATLAB, a typical ±320 kV MMC-HVDC system with VIC, R-FCL, and DCCB is built, and comparative simulations are performed. The results indicate the proposed approach can strongly limit the DC fault current within the acceptable range, and reduce the electrical stress and thermal stress in the MMC and DCCB. The proposed approach possesses better techno-economics than the R-FCL alone to solve the DC fault problem, and a more efficient protection of the MMC-HVDC is realized.

New Framework of RoCoF-FD for Wideband Stability Evaluation in Renewable Energy Generators With Virtual Impedance Control

This research proposes a new perspective for identification of wideband stability in virtual synchronous generator (VSG) with virtual impedance control strategy. At first, the drawback of magnitude-phase-motion-equation (MPME) of grid-forming VSG system is briefly discussed. Then, based on the derived MPME model, a RoCoF-FD framework, which includes two most important indices of frequency performance, e.g., rate of change of frequency (RoCoF) and frequency nadir/deviation (FN/FD), is established to illustrate the interaction between RoCoF and FD based on feedback effect. Moreover, the vector analysis can quantitatively sketch the dynamics of RoCoF impacted by the FD via the loop of feedback effect. In addition, the secure operation regions are defined for the VSG system. It is found that system has a higher risk of oscillation instability when ratio of grid resistance divided by grid inductance gets smaller. However, greater ratio will lessen grid strength/stiffness, which will trigger aperiodic loss of synchronization. To cope with such issues, an adjustable-parameter virtual impedance control strategy (APVICS), based on principle of energy conservation, is proposed to dampen oscillation as well as avoid loss of synchronization of the system, thereby enhance damping behaviors and grid stiffness. Finally, theoretical analysis is validated experimentally.