LCL Filter Resonance Research Articles

Offset free generalized model predictive control for 3-phase LCL-filter based grid-tied inverters

This paper presents a Generalized Model Predictive Control (GPC) in the natural reference frame for a 3-phase LCL-filter based grid-tied inverter. The proposed controller can track the sinusoidal reference without steady-state phase and amplitude offsets. This is achieved by parameterizing the control law matrices with considering the future reference trajectory.To cope with the LCL filter resonance, traditional controllers need a damping method. The proposed controller has inherent damping against the LCL filter resonance and extra sensors are avoided. The controller parameters are selected by a sensitivity analysis that guarantees the closed-loop stability.The proposed controller provides high accuracy in controlling active and reactive currents, robustness against grid inductance variations, low real-time computation, and a fixed switching frequency. The simulation and experimental results prove the performance of the controller in tracking the grid-side reference currents.

Robust Optimized Current Controller Based on a Two-Step Procedure for Grid-Connected Converters

Proportional-resonant controllers are largely used for grid-connected converters with LCL filters to ensure sinusoidal reference tracking and harmonic disturbance rejection. However, the design of such controllers becomes more difficult when it is necessary to ensure stability and suitable performance for converters operating under uncertain grid conditions, from stiff to weaker, and also when the number of resonants increases. In this more challenging scenario, available design procedures may lead to a poor tradeoff between transient and steady-state performances. To overcome this problem, this paper proposes an off-line automated control design procedure to obtain multiple robust optimized proportional-resonant controllers. The proposed procedure consists of two steps, where a particle swarm algorithm is used to obtain: i) the gains of an inner loop ensuring optimal active damping for the LCL filter resonance; ii) the gains of multiple proportional-resonant controllers by minimizing a tracking error index, taking into account uncertain grid impedance and control signal limits. The robust stability of the closed-loop system with the control gains tuned by the metaheuristics is certificated through a parameter-dependent Lyapunov function, constructed based on linear matrix inequalities. Several results from control Hardware-in-the-loop are presented for a case study, revealing that the proposal provides better performance in terms of reference tracking and disturbance rejection, when compared to similar control strategies from the literature. Experimental results from a prototype connected to the utility grid attest the practical feasibility of the proposed procedure.

A Direct Discrete-Time Output Feedback-based LS-RMRAC for Grid-tied Current Control Loop of a Static 3-Wire Converter under Unbalanced Grid Voltage Conditions

Nowadays, renewable energy generation is a worldwide tendency. These clean sources are generally tied to the grid by voltage-fed static converters. In this work, a direct discrete-time Output Feedback-based LS (Least Squares)-RMRAC (Robust Model Reference Adaptive Control) is proposed for grid-side current loop control of a static 3-wire converter connected to the grid through LCL filter. The proposed control method mitigates the LCL filter resonance,rejects grid disturbances without needing Resonant Controllers implementation, and deals properly with grid uncertainties and parametric variations, being suitable for grids with unbalanced voltage conditions. Simulation results of proposed controller are presented. Keywords: Robust Adaptive Control. Grid-tied converter. LCL filter.

Parameter co-design of active damping loop and grid current controller for a 3-phase LCL-filtered grid-connected inverter

Under non-ideal grid conditions, especially the harmonic grid condition, the proportional resonant controller with multiple harmonic resonant controllers (HR-PR controller) is recommended to provide high quality grid currents for the 3-phase LCL-filtered grid-connected inverter. Besides, in order to solve the resonance problem, the active damping loop with the grid-side currents feedback only is preferred. However, parameters of the HR-PR controller and the active damping loop both affect the performance of LCL filter resonance suppression and stability of the inverter, which is analyzed in this paper. Moreover, the stability constraint and the resonance suppression constraint is derived to maintain the good ability of LCL filter resonance suppression and satisfy the stability requirements of the inverter. Considering the wide control bandwidth for the HR-PR controller, a co-design method of the active damping loop and HR-PR controller is proposed in this paper. By introducing the Lagrange multiplier method, the proposed co-design method obtains the optimized parameters for the active damping loop and grid currents controller in z-domain appropriately. A prototype of 3-phase LCL-filtered three-level neutral point clamped grid-connected inverter is established to validate the proposed method.

Analysis of Harmonic Resonance Characteristics in Grid-Connected LCL Virtual Synchronous Generator

The virtual synchronous generator (VSG), which emulates the essential behavior of the conventional synchronous generator, has attracted great attention. This paper proposes to analyze the harmonic resonance characteristics in VSG using the state-space model. The analysis is based on a full-order state-space small-signal model that fully considers the dynamic of the inner loops and the VSG-based outer power control loop. Participation analysis is used to point out the contributions of different states to the eigenvalues. Moreover, eigenvalue locus and singular value decomposition (SVD) are applied together to evaluate the impact of the inner loop parameters on the harmonic resonance characteristics around the LCL filter resonance frequency. The analysis indicates that the harmonic resonance instability is mainly caused by decreasing the proportional gains of the current loop and the voltage loop. Finally, extensive numerical simulation and experimental results are given to verify the validity of the theoretical analysis. Both the simulation and experimental results indicate that the voltage of the common coupling point is unstable after decreasing the proportional gains of the current and voltage controllers. As Kpc decreases from 5 to 0.4 or Kpv decreases from 0.6 to 0.2, the harmonic distortion factor (HDF) around the LCL filter resonance frequency increases. Furthermore, the consistency of simulation results, experimental results, and the theoretical analysis results is validated.

An Improved Active Damping Method Based on Single-Loop Inverter Current Control for LCL Resonance in Grid-Connected Inverters

This paper investigates active damping of LCL filter resonance in grid-connected inverters with only inverter current feedback control, since it only needs to sample one current to realize both current control and inverter protection. The traditional single-loop inverter current control (SLICC) can damp the LCL filter resonance actively. However, if the control delay is considered in digital control, the system stability will depend on the ratio of the LCL resonance frequency f res to the sampling frequency f s , and the valid damping region is only up to f s / 6 . Considering that the design region of the LCL resonance frequency f res is up to f s / 2 , the system can easily become unstable due to the LCL resonance frequency shifting. Thus, this paper proposes an improved active damping method based on SLICC, including the asymmetric regular sampling method and delay compensation method. The improved sampling method minimizes the control delay without introducing a switching ripple, and the delay compensation method further compensates for the delay effect. With a proper parameter design, the upper limit of the valid damping region is extended up to f s / 2 , which can cover all the possible resonance frequencies, and it has inherent robustness against grid-impedance variation. Finally, a few simulations in MATLAB/SIMULINK and experiments based on a 6 kW prototype are performed to verify the theoretical analysis.

Active damping method for voltage source inverter-based distributed generator using multivariable finite-control-set model predictive control

Despite its advantages, the LCL filter can significantly distort the grid current and constitute a substantially more complex control issue for the grid-connected distributed generators (DGs). This paper presents an active damping approach to deal with the LCL filter's oscillation for the finite-control-set model predictive control (FCS-MPC)-three-phase voltage source inverters (VSIs)-based DG. The new approaches use the multivariable control of the inverter side's filter current and capacitor voltage to suppress the LCL filter resonance. The proposed method has been tested in steady-state and under grid voltage disturbances. The comparative study was also conducted with the existing virtual resistance active damping approaches for an FCS-MPC algorithm. The study validates the developed control schemes' superior performance and shows its ability to eliminate lower-order grid current harmonics and decrease sensitivity to grid voltage distortion.

Stability Enhancement of Inverters in Grid-Connected Microgrids Using FIR Filter

Under weak grid conditions and in microgrids, the gird impedance is often large and has a highly varying nature. In such a scenario, stabilizing grid-connected inverters with an LCL output filter could be a challenging task. The control delay that comes from sampling and PWM may contribute to worsen this condition. In particular, the mentioned delay causes a critical frequency at one-sixth of the sampling frequency (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> /6), which may jeopardize the converter's stability in the case of grid impedance variations. Also, the coupling effect among parallel converters, which is a likely scenario in microgrid applications, is another factor that may threaten the system stability. To deal with these challenges, this article proposes an LCL filter resonance damping method that employs a finite-impulse response filter to amend the delay effect. In this way, the system robustness is enhanced and the system keeps its stability irrespective of grid impedance variations and interaction between inverters. Experimental results show the correctness of the theoretical conclusions and confirm the efficiency of the suggested technique.

A novel active damping control based on grid-side current feedback for LCL-filter active power filter

LCL filter is widely used in grid-connected converters for good harmonic mitigation performance. However, resonance poles of LCL filter challenge system stability, especially in a digital control system. This paper studies the suppression method of the active power filter output LCL filter resonance. Because of the defect that the traditional active damping based on the filter capacitor current or capacitor voltage feedback needs to add additional sensors, a novel active damping with grid-side current component feedback is proposed. And analysis and design of the feedback function, the resonance suppression characteristics, and the impact on harmonic compensation performance are analyzed in detail respectively and proposes a novel active damping control method based on a quasi-resonant controller grid-side current feedback. On this basis, a mathematical model of the SAPF system with the proposed novel active damping was established, and the resonance characteristics were analyzed. Finally, the proposed method was verified through relevant experiments.

Capacitor Voltage Full Feedback Scheme for LCL-Type Grid-Connected Inverter to Suppress Current Distortion Due to Grid Voltage Harmonics

For the LCL -type grid-connected inverter, grid voltage full feedforward scheme is an effective method to improve the quality of the injected grid current. However, in the applications where a step-up transformer is adopted and its leakage inductance serves as the grid-side inductor, it is difficult to directly measure the grid voltage. For this case, the capacitor voltage full feedback scheme is proposed in this article to suppress the injected grid current distortion due to the grid voltage harmonics, and the full feedback function includes proportional, derivative, and second-derivative components. It is found that the derivative component counteracts the capacitor current feedback active damping, and both of them can be removed. Thus, the current sensor for sensing the capacitor current is saved. Instead, the LCL filter resonance is damped by the proportional and second-derivative feedback components, and a low-pass filter is added to the second-derivative component for ensuring a positive equivalent resistance within the full controllable frequency range. Experimental results from a 6-kW single-phase grid-connected inverter are provided to verify the effectiveness of the proposed method.

Critical Damping Ratio to Ensure Design Efficiency and Stability of LCL Filters

The resonance of LCL filter gives challenge to the control stability of LCL -filter-based converter systems. To suppress the filter resonance, damping methods are widely adopted. Nevertheless, the determination of damping parameters for LCL filters can be vague, insufficient or excessive, because the filter resonance is affected by multiple factors. Furthermore, due to the effect of damping resistor, the attenuation of switching-frequency current ripple may vary from the expected value, and thus, can lead to unwanted iterations to ensure proper filtering performances. The purpose of this article is to provide an efficient and accurate design method for the damping in LCL filters. A metric of “critical damping ratio” is introduced and solved for the first time. With the critical damping ratio setting at 0.28, the resonance peak on the magnitude-frequency curve of LCL filter can be precisely flattened without introducing unnecessary damping losses, and the grid-side inductor and damping resistor can be designed in an accurate and less iterative way. Moreover, a “peace-of-mind” stability performance of LCL filter can be also achieved. The simulation and experiment results are provided to verify the analysis.

Research on Adaptive Suppression of LCL Converter Resonance Grid-Connected System

LCL-type converters are widely used in grid-connected systems due to their small size and good filtering performance. However, the resonance suppression problem brought by the LCL filter cannot be ignored. The capacitive current feedback is a commonly used resonance suppression method. In applications, the grid impedance can cause LCL filter resonance. Thus, this paper presents an adaptive resonance suppression method based on the RBF network optimized by particle swarm optimization. This method optimizes the initial parameters of the RBF network through particle swarm optimization, identifies the parameters of the PI controller by RBF neural network’s own identification capability, and updates the active damping coefficient based on constraints such as stability margin, thereby realizing the LCL-type inverter to maintain the system stability when the grid impedance changes. The effectiveness of the method is verified by experiments.

Analysis and verification of harmonic interaction between DDWTs based on αβ stationary coordinate system

This study presents an analysis method of harmonic interaction characteristics between direct-drive wind turbines (DDWTs) based on αβ coordinates and the relative gain array (RGA). First, considering the digital delay of inverters, the capacitive current feedback active damping is applied to suppress the resonance of LCL filter, and the output current of DDWT is regulated by quasi-proportional resonant controller in the αβ coordinates and then combined with the topology of the direct-drive wind farm (DDWF), the transfer function matrix of the DDWF is established. Second, based on the RGA principle, the relationship between parameters and harmonic interaction characteristics is quantitatively analysed. The results show that with the proportional coefficient increasing, the degree of negative interaction between DDWTs is strengthened, which increases the harmonic content in the negative interaction frequency band. However, the increase of resonance coefficient and number of DDWTs will weaken the degree of negative interaction. In addition, with the increase of capacitive current feedback coefficient and grid inductance, the interaction frequency gradually decreases. Finally, the DDWF model is built both on Matlab/Simulink and StarSim + PXI hardware-in-the-loop platform to verify the analytical results. The harmonic interaction characteristics can be used to guide the parameter design of DDWTs, so as to optimise power quality of the wind farm.

Simple Finite-Control-Set Model Predictive Control of Grid-Forming Inverters With LCL Filters

Grid-forming inverters (GFI) play an important role as power interfaces for distributed generation units in islanded microgrids, where inductive-capacitive-inductive (LCL) output filters are commonly employed to mitigate the harmonics injected by voltage-source inverters. Due to advantages such as fast dynamic response and straightforward handling of constraints, Finite-control-set model predictive control (FCS-MPC) has become an attractive option for voltage control in GFI systems. However, conventional FCS-MPC algorithms with short prediction horizon have performance limitations in the tracking of ac references in systems with high-order dynamics, such as LCL-filtered GFIs. On the other hand, predictive algorithms with extended prediction horizons suffer from an increased computational burden. This paper proposes a new FCS-MPC algorithm to accurately control the capacitor voltage in an LCL-filtered GFI, using a discrete-time prediction model to dynamically compute the reference for a FCS-MPC inverter-side current controller. The main advantages of the proposed method are its simple implementation without requiring the tuning of weighting factors in its cost function; and its short prediction horizon, which maintains a reduced computational cost. Moreover, active resonance damping elements such as digital filters or ad hoc feedback loops to deal with the LCL filter resonance are not required. Simulation tests and experimental results in a laboratory-scale setup confirm the effectiveness of the proposed control algorithm, yielding lower distortion of output voltage waveforms and increased robustness to modeling errors compared with the conventional FCS-MPC approach.

A New Dynamic Voltage Restorer with Multi-level Open-end Winding Topology

In this paper, a variety of main circuit structures of DVR based on open-end winding are presented. Two inverters are connected in series to realize the multi-level structure and simplify the hardware cost. According to the mathematical model of open-end DVR, a three loop control strategy based on load voltage feedback is implemented to suppress the resonance of LCL filter. Aiming at the common mode voltage problem of open-end winding DVR, a common mode voltage suppression strategy based SVPWM is proposed to completely suppress the common mode voltage of high frequency and low frequency of the system. Finally, an open-end DVR experimental platform is built to verify the effectiveness of the control strategy and modulation strategy.

A Novel Inverter-Side Current Control Method of $LCL$ -Filtered Inverters Based on High-Pass- Filtered Capacitor Voltage Feedforward

LCL filters have been widely used as the interface between inverters and power grids, but damping methods must be taken to solve the resonance of LCL filters. Considering overcurrent protection and inherent active damping, this paper focuses on the inverter-side current feedback (ICF) control. Some literatures have proposed that the capacitor voltage feedforward (CVF) is beneficial to the stability of the ICF control. However, in practical applications, it is found that the ICF control with CVF mainly faces two problems. Firstly, the CVF can be seen as a positive feedback loop, and it tends to cause low-frequency oscillation, especially in weak grid. Secondly, low-frequency harmonics in the grid voltage can easily distort the grid-side current of the inverter, even though the inverter-side current has been regulated well. In order to solve these two problems simultaneously, this paper proposes a novel inverter-side current control method, which adds a high-pass filter into the CVF path. In this paper, the design process of the high-pass filter parameters is analyzed, and the specific voltage feedforward structure of the proposed method to avoid the inverter startup inrush current is also discussed in detail. Simulations in MATLAB/SIMULINK and experiments based on a 6.6 kW prototype have been utilized to verify the effectiveness of the proposed method.

A Decoupled Hybrid Current Control for Improving the Performance of 60° DPWM-Based Three-Phase Grid-Connected Inverter

Nonlinear boundary control technique can offer superior dynamic behavior and eliminate the LCL-filter resonance in the grid-connected inverter. However, the chattering might be aroused by the distorted intracycle voltage information in the control law. It becomes worse when the nonlinear boundary controller is directly applied in three-phase three-wire inverter configuration. A hybrid current control scheme utilizing the decoupled predictive hysteresis capacitor current controller integrated with the linear grid current controller is proposed in the paper. By applying the 60° discontinuous pulse-width modulation scheme and using the virtual dual-buck decoupled structure, two separate sets of switching criteria for dictating the switching states of two specific half-bridge legs are formulated to avoid the interactions amongst phases. A small-signal ac model is also built to study the transfer characteristics of such hybrid current controlled inverter system. Simulation and experimental results have been offered to evaluate the effectiveness of the proposed method. Both results meet the theoretical predictions.

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

An LCL filter is commonly used in grid-connected inverter to attenuate the switching harmonics; nevertheless, the stability problems will arise in the grid current control if the resonance of LCL filter is not properly damped. High pass filter-based grid current feedback active damping is an effective solution to solve the aforesaid problem. However, for systems with digital control, the system may exhibit non-minimum phase system characteristics due to the control delay effect, which will affect the system stability. Moreover, the frequency responses of current controller parameters and active damping parameters are coupled. Therefore, to ensure the system stability and good dynamic performance, the current controller parameters and active damping parameters should be designed together, considering the control delay effect. For this issue, a systematic controller design method is proposed for the digitally controlled LCL-type grid-connected inverter with grid-current-feedback active damping. With the proposed method, the satisfactory regions of the control parameters for satisfying the system specifications can be obtained, from which the proper control parameters can be easily and quickly picked out, without the trial and error. Finally, the proposed design method is verified by the experiment.

Stability Regions of Nonlinear LCL-Filtered Converter with Converter-Current-Feedback Control Without Damping

The stability regions of a LCL-filtered converter adopting converter-current-feedback control without damping are analyzed. The nonlinear LCL-filtered model is presented to investigate its influence on the system stability. The stability analysis is performed by means of the Nyquist diagram in s domain. It reveals that three factors have the dominant effects on the system stability, including internal loss of LCL-filtered model, PWM transport delay and controller parameters. The undamped stability boundaries of the system gain calculated by the symmetrical optimum method are obtained. It can be found that stable regions for the nonlinear LCL-filtered system are extended into a continuous region of ratios of LCL filter resonance frequency to control frequency from three distinct regions. Finally, the stable regions are validated by the nonlinear model simulation, and experimental results verify the theoretical analysis.

New design approach for grid-current-based active damping of LCL filter resonance in grid-connected converters

New design approach for grid-current-based active damping of LCL filter resonance in grid-connected converters