Virtual impedance-based active damping for LCL resonance in grid-connected voltage source inverters with grid current feedback

Several active damping strategies have been proposed in the literature for grid-connected converters with LCL filter but there are not specific strategies for DFIG wind turbines. In this system, there is an interaction between the two converters of the back-to-back conversion structure, which must be properly modeled in order to design effective damping strategies for the LCL filter resonant poles. This paper proposes a robust active damping strategy for DFIG wind turbines with LCL filter that considers the special features of this system. In this technique the filter capacitor current is fed back through a lag compensator that adjusts the delay of the feedback loop to emulate a virtual impedance that has dominant resistive behavior in the range of possible resonance frequencies. It is shown that a similar damping of the LCL filter resonance is achieved when the strategy is implemented in either of the two converters.

Grid-connected inverters connect distributed generation and renewable energy sources to the grid. Various filters, including inductor-capacitor-inductor (LCL) filter, are utilized to increase the quality of grid-injected power. In addition to the inherent resonance of the LCL filter, the weak network with variable network impedance leads to instability of the power transmission system. This paper aims to improve the injection power quality of the LCL filter-based grid-connected fuel cell with control based on the grid current feedback and capacitor current active damping. Although active damping can theoretically guarantee the grid-connected passive inverter behavior, the system performance is sensitive to both the current controller phase lag and the variations of the filter parameters. To control these two factors, a suitable phase compensator has been proposed to enhance the passive behavior. In this paper, the control of LCL based grid-tied fuel cell power conditioning system with control based on LCL filter-based utilizing the grid current feedback and capacitor current active damping scheme has been studied, and the passive and stable performance of this system has been evaluated considering the effect of the current regulator phase compensation. The process of systematic design of the control system parameters has been described with necessary details and the passive performance of the grid-connected system has been evaluated. The obtained results for the simulation of the grid-connected fuel cell power optimization system indicate the current injection with very high quality and the passive behavior of the system under variations in the impedance of the weak network.

Currently, the Passivity-Based Control (PBC) has been used successfully in Grid-Connected Voltage Source Inverter (GCVSI) with L or LC filter. In practice, an LCL filter is widely used for the GCVSI. However, only a few papers have discussed how to apply the PBC for the GCVSI with LCL filter, where there is a complex structure in a three phase system due to using six state variables, and the variation of grid impendence is not addressed at the same time. In this paper, a PBC controller with only two state variables is presented. Furthermore, an active damping (AD) method is inserted into the control loop to resist the reverse effect of grid impendence variation, and to achieve a wide control bandwidth. The modeling and controller design are detailed described. The simulation platform is carried out in Matlab/simulink to verify the theoretical analysis.

The control of a grid connected voltage source inverter (VSI) with an LCL filter is a very challenging task, since the LCL network causes a resonance phenomenon near to the control stability boundary. While many active damping methods have been proposed to overcome this issue, the role that PWM transport delay plays in the effectiveness of these strategies is still not fully resolved. This paper presents a theoretical discrete time analysis frame work that identifies three distinct regions of LCL filter resonance - a high resonant frequency region where active damping isn't required; a critical resonant frequency where a controller cannot stabilise the system; and a low resonant frequency region where active damping is essential. Suitable controllers are then proposed for the two stable regions, with gain calculations that allow for the greatest system bandwidth and damping. Simulation and experimental results verify the presented analysis.

Systematic controller design for digitally controlled LCL-type grid-connected inverter with grid-current-feedback active damping

Conventional linear controllers with active damping (AD) cannot stabilise LCL-filters for certain ranges of filter parameters due to resonances. This limits the design space of the filter design and can lead to sub-optimal designs in terms of filter volume and efficiency. When model predictive control (MPC) with a long-prediction horizon is applied, the inherent damping capability of MPC can stabilise the system despite the resonance phenomenon and expands the design space. In this paper, the limited design space due to insufficient damping of linear controllers with AD is analyzed based on capacitor current feedback AD. Exemplary LCL-filter optimization solutions and the resulting Pareto fronts are presented to illustrate the achiev-able volume and/or loss reductions with the extended design space. A novel MPC formulation is proposed to adopt explicit MPC and to enable a real-time implementation even at a high switching frequency. Simulation results validate the presented analysis.

To address the issue that current ripple in traditional switching power amplifiers (SPA) for active magnetic bearing (AMB) systems is constrained by the switching frequency, this paper proposes a novel LCL filter-based switching power amplifier (LCL-SPA) along with its parameter design and high-performance control strategy. Without altering the original full-bridge topology or the switching frequency, the proposed scheme achieves superior ripple suppression. To tackle the inherent resonance problem of the LCL filter, a sensorless capacitor current feedback active damping (CCFAD) strategy is proposed. This approach effectively suppresses resonance without additional hardware sensors and ensures system stability under digital control delays. Furthermore, to overcome the limitations of traditional PI controllers in terms of the dynamic performance and parameter tuning of the LCL-SPA, a high-performance LESO-based control algorithm within the Linear Active Disturbance Rejection Control (LADRC) framework is designed. By utilizing a Linear Extended State Observer (LESO) to estimate and compensate for total lumped disturbances in real-time, the algorithm simplifies the parameter tuning process and achieves rapid current tracking with nearly zero overshoot. Experimental results demonstrate that the proposed LCL-SPA achieves extremely low current ripple across various reference currents, with the ripple minimized to 20 mA at a 3 A load. Frequency response tests confirm that the system possesses a closed-loop bandwidth of up to 2 kHz, satisfying the high dynamic requirements of magnetic bearings.

This paper presents a control scheme for a grid-connected three-phase voltage source inverter with an LCL filter, which is suited for renewable energy applications. The proposed method has the following properties: fast tracking, optimized dynamics, grid disturbance rejection, and active resonance damping. The controller is based on an augmented linear quadratic regulation (LQR) scheme, which is optimized based on a weighted cost function. The LQR controller is augmented to include two complex conjugate poles at the grid frequency for sinusoidal voltage disturbance rejection upon connection to the grid. Furthermore, this control scheme actively damps the resonance introduced into the closed-loop system through the third-order LCL filter. Finally, the current reference is found by calculating the instantaneous power, which allows for faster power tracking compared to using the technique of measuring average power. Results verify the validity of the proposed control scheme.

This paper investigates the capacitor-current-feedback active damping for the digitally controlled LCL-type grid-connected inverter. It turns out that proportional feedback of the capacitor current is equivalent to virtual impedance connected in parallel with the filter capacitor due to the computation and pulse width modulation (PWM) delays. The LCL-filter resonance frequency is changed by this virtual impedance. If the actual resonance frequency is higher than one-sixth of the sampling frequency (fs/6), where the virtual impedance contains a negative resistor component, a pair of open-loop unstable poles will be generated. As a result, the LCL-type grid-connected inverter becomes much easier to be unstable if the resonance frequency is moved closer to fs/6 due to the variation of grid impedance. To address this issue, this paper proposes a capacitor-current-feedback active damping with reduced computation delay, which is achieved by shifting the capacitor current sampling instant towards the PWM reference update instant. With this method, the virtual impedance exhibits more like a resistor in a wider frequency range, and the open-loop unstable poles are removed; thus, high robustness against the grid-impedance variation is acquired. Experimental results from a 6-kW prototype confirm the theoretical expectations.

For the grid-connected LCL -filtered inverter, the grid current feedback active damping (AD) can assure a desirable bandwidth and a good robustness against certain parameter variations by using a minimal number of sensors. However, the inverter performance was seriously endangered by nonideal conditions at the point of common coupling (PCC), including background voltage distortions and grid impedance variation. The grid current AD could not work well for wide grid impedance variation. Hence, in this study, the robustness with such control is discussed and its relations with system parameters are derived through mathematic derivations. It is proved that, for the typical grid current AD control, a contradiction between high bandwidth and high robustness exists. On the basis of analyzing the reasons for the limitations of the typical control, a systematic approach for enhancing the robustness under complex grid conditions has been proposed. The proposed fundamental PCC voltage feedforward enhances the robustness, while the proposed phase shaping compensator assures a higher robustness with a desired bandwidth. Comparative waveforms with the typical grid current AD control have been provided to verify the correctness of the analysis and the improvement of the proposed approach.

In order to improve the grid-connected stability of wind power grid-connected inverter, solve the harmonic and resonance problems encountered at the grid-connected interface of inverter when the load jumps. An improved linear active disturbance rejection control strategy combined with active damping (ILADRC-AD) is designed. Firstly, the mathematical model of inductance-capacitance-inductance (LCL) inverter is established, and the principle of traditional third order active disturbance rejection controller is analyzed. Based on the idea of lead correction, an improved LADRC is designed by series lead correction links on the total disturbance channel of the linear extended state observer (LESO). Capacitive current feedback active damping is introduced in combination with improved LADRC to generate an ILADRC-AD control strategy. The stability and robustness of the system are effectively improved. Finally, the frequency characteristics of the ILADRC-AD inverter system are analyzed by frequency domain analysis method, and the MATLAB simulation comparison of improved control and traditional PI and LADRC the grid current waveform. The results show that the improved control not only has more stable grid-connected current, but also has fast dynamic response and strong harmonic suppression when the load fluctuates.

Capacitive current feedback active damping is widely used in the LCL-type grid-connected inverter, which can effectively suppress the resonance peak of the system. However, the control delay in digital control system can change the characteristic of capacitive current feedback active damping and make the positive and negative boundary frequency of equivalent resistance is f s /6, which affects the stability of the grid-connected inverter and the robustness to grid impedance. At the same time, the control delay would introduce phase lag and limit the bandwidth of the control loop. Therefore, a delay compensation method considering both active damping characteristics and loop bandwidth is proposed, which can expand the boundary frequency to 0.43f s and greatly improve the robustness and dynamic performance of the system. Moreover, the sampling method is synchronous sampling, which strong switching-noise immunity. Simulation results verify the validity of the proposed method.

This paper explores the effect of the computation and pulsewidth modulation (PWM) delays on the capacitor-current-feedback active damping for the LCL-type grid-connected inverter. It turns out that proportional feedback of the capacitor current is equivalent to a virtual impedance connected in parallel with the filter capacitor in digital control. The LCL-filter resonance frequency is changed by this virtual impedance. And if the actual resonance frequency is higher than one-sixth of the sampling frequency (fs/6), where the virtual impedance contains a negative resistor component, a pair of open-loop unstable poles will be generated. As a result, the LCL-type grid-connected inverter becomes much easier to be unstable if the resonance frequency is moved closer to fs/6 due to the variation of the grid impedance. To address this issue, this paper proposes a capacitor-current-feedback active damping with reduced computation delay, which is achieved by shifting the capacitor current sampling instant towards the PWM reference update instant. With this method, the virtual impedance exhibits more like a resistor in a wider frequency range, and the open-loop unstable poles are removed, thus high robustness against the grid-impedance variation is acquired. Experimental results confirm the theoretical expectations.

The active damping method based on proportional voltage feedforward is usually used to solve the inherent resonance and low-order harmonics of LCL filter. However, in the case of low short-circuit capacity and high impedance of weak grid, the grid impedance has a great influence on the control performance, especially for high-frequency inverters based on SiC MOSFET. In order to improve the stability of the inverter, this paper proposes a robust composite control method, which combines grid-connected current feedback active damping, full voltage feedforward and improved current controller. This method can not only adapt to the wide range of changes in grid impedance, but also suppress background harmonics. The simulation and experimental results verify the effectiveness of the proposed method.

The present work focuses on the harmonic control of plate vibration and radiation using distributed collocated piezoceramic units. The objective is to add virtual impedance units on the plate and to optimize its complex value for each frequency. In active damping (velocity feedback controllers), the added virtual impedance is equivalent to a resistive effect. In the present study, the added virtual impedance is chosen arbitrarily in the complex plane. Each added impedance unit is composed of a collocated PZT actuator and a PVDF sensor. This approach allows obtaining dual variables for harmonic control. In order to tune the PZT voltage at each frequency, the virtual impedance approach is implemented with a harmonic adaptive control. The stability is always ensured with a centralized processing, and for certain frequencies, a decentralized processing can be used. Preliminary theoretical study is carried out to assess the behavior of the smart panel for different added virtual impedances for a mechanical excitation by a shaker. Those numerical results are compared to experimental measurements performed in an anechoic chamber. Our proposed strategy compare favorably to common strategy of active damping to reduce harmonic sound radiation. Hence, a reduction of 20 dB can be achieved at certain frequencies.