Impedance Shaping Research Articles

Virtual Model Predictive Control for Inverters to Achieve Flexible Output Impedance Shaping in Harmonic Interactions With Weak Grids

Virtual Model Predictive Control for Inverters to Achieve Flexible Output Impedance Shaping in Harmonic Interactions With Weak Grids

Optimized MMC passive impedance shaping method for high frequency oscillation suppression

Recent years, there have been several high-frequency oscillation events in modular multilevel converter (MMC) based DC current projects. Considering the wideband oscillation characteristics of this issue, passive MMC impedance shaping methods are superior solutions for their advantages over the active methods in enhancing the broadband damping level. However, the optimization of parallel passive devices mainly focused on reactive power compensation and the suppression of characteristic harmonics generated by low-level inverters, which is not applicable to MMC systems. To address the optimization design problem of passive damping devices, this paper proposes an optimized design method for passive filters by analyzing the relationship between the passive damping device and the impedance shaping effect of the inverter. The proposed method reduces the capacity of the passive damping device while ensuring system stability margin. Finally, the effectiveness of the proposed passive impedance shaping strategy is verified through time-domain simulations considering changes in AC side operating conditions and power reduction operation of the MMC.

Correlation between Electrocatalytic Activity and Impedance Shape: A Theoretical Analysis

Correlation between Electrocatalytic Activity and Impedance Shape: A Theoretical Analysis

Impedance Shaping Method for System-Level Stabilization of Droop-Controlled DC Microgrids

Impedance Shaping Method for System-Level Stabilization of Droop-Controlled DC Microgrids

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

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

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.

Mitigation of power system oscillations in weak grids with battery energy storage systems: A real-world case study

Sub-synchronous oscillations are becoming commonplace in weak areas of power systems with high levels of renewable generation, affecting their operation. Moreover, there is a lack of methods and techniques that facilitate the understanding of such phenomena and the analysis of mitigation alternatives from a practical-knowledge point of view. In this manuscript, the combination of static and dynamic techniques is utilized and consolidated to derive general conclusions when mitigating sub-synchronous oscillations by means of grid-forming battery energy storage systems (GFM BESSs). The grid impedance shaping effect of GFM BESSs, which allows the mitigation of undesired oscillations, is demonstrated through small-signal (static) and frequency scanning (dynamic) analyses when studying an actual and extremely weak grid, the Australian West Murray Zone. These findings are further validated when performing detailed real-time EMT digital simulations of the grid. Furthermore, additional dynamic simulations demonstrate the ability of GFM BESSs to provide system strength and increment the hosting capacity of renewables in weak areas. The methods and techniques presented in this work can be applied to any power system, further supporting existing industry practices.

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.

Fuzzy logic feed-forward impedance shaping of DAB converter in DC microgrid with CPL load

Fuzzy logic feed-forward impedance shaping of DAB converter in DC microgrid with CPL load

A Deep Reinforcement Learning-Based Intelligent Grid-Forming Inverter for Inertia Synthesis by Impedance Emulation

In this letter, impedance emulation is exploited for synthesizing inertia in autonomous microgrids. An intelligent grid-forming inverter (GFI) is proposed that facilitates sufficient degrees of freedom for adaptive impedance shaping. The latter adaptively changes the effective bandwidth of the inverter's voltage controller, in response to disturbances for inertia synthesis. Deep reinforcement learning is utilized to tackle the lack of explicit quantitative relation between impedance shaping and inertia. Simulation results prove the effectiveness of the method.

A universal model for power converters of battery energy storage systems utilizing the impedance-shaping concepts

Battery energy storage systems (BESSs) render different services in microgrids (MGs) depending on the MG connection mode. In the grid-connected mode, the BESS optimally injects/absorbs power, operated by a power converter controlled as the grid-feeding voltage source converter (GFD-VSC). In the islanded mode, the BESS may work as distributed slack bus controlled by the grid-forming VSC (GFM-VSC). However, for performing with a desirable performance, the GFD-VSC and the GFM-VSC demand different grid characteristics. Specifically, the GFD-VSC has a grid-synchronization issue and may become unstable in weak grids with high inductive impedance. Contrarily, the GFM-VSC reveals better performance when connected to the MG through a feeder with high inductive impedance. Besides, switching between different operating modes may cause undesirable transients. This issue can be addressed by the impedance shaping concept that is realized through the control design of the power converter. However, there is limited flexibility for impedance shaping using conventional PI-based controllers. To this end, in this paper, a universal controller is proposed, which is developed based on the impedance shaping concept. Also, sliding mode control (SMC) is used to overcome the undesirable transients due to switching between operating modes. The effectiveness of the control structure is evaluated in islanded operation, under weak grid connection, and FRT transients in MATLAB/Simulink.

Impedance Shaping Effects and Stability Assessment of Circulating Current Control Schemes in Modular Multilevel Converters

Control of circulating current can help modular multilevel converters (MMCs) improve the internal performance, but only the conventional circulating current suppression control has been considered in impedance models to investigate MMC-grid interactions. In this paper, the sequence impedance responses of circulating current injection methods based on instantaneous information are modeled for stability analysis. Compared with circulating current control schemes based on predefined references, the circulating current injection methods based on instantaneous information introduce couplings among circulating current, output current and capacitor voltage control loops, which influence the MMC impedance in the low frequency range. This paper reveals that injection of second harmonics in the circulating current reduces the capacitor voltage ripples, but the system stability is compromised due to the couplings. The MMC stability boundaries for different circulating current controllers are defined with the help of sequence impedance model and Bode-plot-based analysis. The impedance model and stability assessment are validated by frequency scan results and case studies.

Joint Limiting Control Strategy Based on Virtual Impedance Shaping for Suppressing DC Fault Current and Arm Current in MMC-HVDC Systems

Joint Limiting Control Strategy Based on Virtual Impedance Shaping for Suppressing DC Fault Current and Arm Current in MMC-HVDC Systems

A Hybrid-Frame Control Based Impedance Shaping Method to Extend the Effective Damping Frequency Range of the Three-Phase Adaptive Active Damper

The grid-connected inverter may get unstable due to variation of grid impedance. To improve the system stability, an adaptive active damper, which emulates an adaptive tuning virtual resistor, can be introduced at the point of common coupling. However, subject to the control bandwidth, the virtual resistor is actually a frequency- dependent impedance, and its damping performance is impaired. In this article, we propose an impedance shaping method to make the virtual impedance be resistive in a wider frequency range, and it is implemented under hybrid frame for directly controlling the active power of the active damper and eliminating the influence of the cross-coupling terms on the emulation of a virtual resistor. Finally, the prototypes of a 3-kVA three-phase active damper and a 6-kVA three-phase <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL-</i> type grid-connected inverter are fabricated and tested in the lab. The experimental results are provided to verify the effectiveness of the proposed control methods for the three-phase adaptive active damper.

Impedance modelling and stability analysis of modular multilevel converter with different types of grid‐forming control schemes

With the increasing penetration of power electronics, grid-forming modular multilevel converters (MMCs) have attracted great attention in the upcoming MMC-based high-voltage direct current transmission (HVDC) projects. Power synchronization control (PSC) and direct power control (DPC) are two typical grid-forming control schemes for MMCs. This paper sets out to investigate the impedance-based stability characteristics of PSC-MMC and DPC-MMC. Utilizing the harmonic state space (HSS), equivalent impedance models of PSC-MMC and DPC-MMC are developed with the consideration of complete controllers and MMC internal dynamic characteristics. Impedance shaping effects of the major controllers are further analyzed to identify the frequency bands where the MMCs have negative resistive impedance characteristics. Finally, potential instability phenomena of the interconnected system are shown through the case studies, and the virtual impedance method is introduced as the stabilization control scheme. The electromagnetic transient simulation results based on PSCAD/EMTDC verify the accuracy of the impedance models and the effectivity of the stabilization control scheme.

Revisiting Grid-Forming and Grid-Following Inverters: A Duality Theory

Power electronic converters for integrating renewable energy resources into power systems can be divided into grid-forming and grid-following inverters. They possess certain similarities, but several important differences, which means that the relationship between them is quite subtle and sometimes obscure. In this article, a new perspective based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">duality</i> is proposed to create new insights. It successfully unifies the grid interfacing and synchronization characteristics of the two inverter types in a symmetric, elegant, and technology-neutral form. Analysis shows that the grid-forming and grid-following inverters are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">duals</i> of each other in several ways including a) synchronization controllers: frequency droop control and phase-locked loop (PLL); b) grid-interfacing characteristics: current-following voltage-forming and voltage-following current-forming; c) swing characteristics: current-angle swing and voltage-angle swing; d) inner-loop controllers: output impedance shaping and output admittance shaping; and e) grid strength compatibility: strong-grid instability and weak-grid instability. The swing equations are also derived in dual form, which reveal the dynamic interaction between the grid strength, the synchronization controllers, and the inner-loop controllers. Insights are generated into cases of poor stability in both small-signal and transient/large-signal. The theoretical analysis and simulation results are used to illustrate cases for single-inverter systems, two-inverter systems, and multi-inverter networks.

Shaping Impedances to Comply With Constrained Task Dynamics

Humans are capable of managing multiple tasks simultaneously. It is widely assumed that human motor control can be emulated by impedance control. To achieve human-like behavior, however, the impedance parameters of multiple tasks may vary during task execution. We propose an algorithm that shapes task impedance as a function of the robot’s time-varying inertial properties. These properties involve virtually constrained masses and virtually constrained inertias that counteract a task in order to comply with a given constraint. In this work, we not only detect task conflicts, but also show how to handle them. Our method is able to control kinematically redundant robots. We developed a damping-design method that does not interfere with our desired Cartesian task-space behavior. The control approach was verified in experiments on a real robot. We compared our impedance shaping method with two alternative control approaches: simple impedance superposition and nullspace projection. Our method preserved the passivity while improving the Cartesian task performance of an impedance controller. The method has computational advantages, beneficial to control robots with many degrees of freedom.

LMI-based impedance control synthesis: a case study on fixed-stiffness actuators (FSAs)

Impedance control is frequency-dependent in the twofold sense: (1) the impedance matching error can only be attenuated arbitrarily small over a low-frequency range due to the water bed effect (Freudenberg et al., 2003), and (2) the impedance matching error always diverges to infinity as the frequency tends to infinity since no causal controller can track arbitrarily fast signals. To sum up, we can only shape the robot impedance over some low-frequency range which may be very small due to the limitation resulting from the robot's inherent high-frequency characteristics. Unfortunately, this fact was underestimated in the existing impedance control schemes. In this paper, a frequency-aware linear impedance control synthesis technique is developed for FSAs based on control theory, which is also suitable for the general robot system in the condition that the robot dynamics is linearised around an equilibrium configuration or compensated with its inverse dynamics model to form an exact-linearised system a priori. With the powerful tool, we study the impedance shaping technique and address the two long-standing issues: (1) Under what conditions, an impedance-controlled FSA can exceed its physical stiffness? (2) Can a stiff FSA render a wider stiffness range than its softer counterparts?

Improving the Stability of Standalone MMCs by Shaping the AC Side Impedance Using Insertion Index Compensation

Due to the significant coupling of the internal dynamics on the ac-side in a modular multilevel converter (MMC), its terminal characteristics are quite different from a conventional two-level voltage source converter (TL-VSC). Thus, the stability analysis and controller parameters design of the MMC without ignoring internal dynamics must adopt complicated modeling approaches, like the harmonic state-space (HSS) method, which doesn’t have an intuitive insight. Therefore, to simplify the modeling process and give a clear physical meaning, this paper proposes a decoupling method with ac-side impedance shaping by feedforwarding the capacitor voltages to compensate the arm insertion indices, which can also improve the stability of the MMC. Consequently, the ac-side impedance characteristics of the MMC are similar to that of the TL-VSCs, and the stability and controller parameters can be design-oriented by using a simple averaged state-space model. Finally, the effectiveness of the theoretical analysis and correctness of the proposed approach are verified by time-domain simulations in PSCAD/EMTDC.

Adaptive Grid Impedance Shaping Approach Applied for Grid-Forming Power Converters

This paper proposes an adaptive grid impedance shaping approach, implemented through a variable structure virtual impedance control strategy (VS-VIS), to improve the power flow control of grid-forming power converters (GF-PC). In this strategy, an equivalent grid impedance estimator (EGIE) evaluates the feeder X/R ratio to determine the required virtual impedance to reach the grid shaping objective. Besides, the virtual impedance definition also considers the converter power rating to ensure the system&#x2019;s feasibility. A virtual negative resistance series interconnected with a positive virtual reactance implements the virtual impedance. Moreover, the required virtual impedance is only updated when the X/R ratio extrapolates deviation limits determined by allowed grid voltages boundaries specified by the standards. Besides, the virtual reactance is split into two parts that use the conventional and sliding mode (SMC) approaches. The first implements the main part of required virtual reactance, while the second provides a fine-tuning action matching the X/R control objectives and compensating grid impedance uncertainties. This grid-shaping method provides a smooth compensation increasing the GF-PC resilience under grid impedance variation. These features constitute a novelty compared to the shaping methods presented in the literature. Experimental tests obtained from a GF-PC laboratory setup demonstrate the effectiveness and robustness of the proposed grid impedance shaping method.