The interconnection stability of a grid-connected voltage-source converter (VSC) can be assessed by the passivity properties of the VSC input admittance. If critical grid resonances fall within regions where the input admittance acts passively, i.e., has nonnegative real part, then their destabilization is generally prevented. This paper presents an overview of passivity-based stability assessment, including techniques for space-vector modeling of VSCs whereby expressions for the input admittance can be derived. Design recommendations for minimizing the negative-real-part region are given as well.

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Passivity-Based Stability Assessment of Grid-Connected VSCs—An Overview

Grid-tied voltage source inverters using LCL filter have been widely adopted in distributed power generation systems (DPGSs). As high-order LCL filters contain multiple resonant frequencies, switching harmonics generated by the inverter and current harmonics generated by the active/passive loads would cause the system resonance, and thus the output current distortion and oscillation. Such phenomenon is particularly critical when the power grid is weak with the unknown grid impedance. In order to stabilize the operation of the DPGS and improve the waveform of the injected currents, many innovative damping methods have been proposed. A comprehensive overview on those contributions and their classification on the inverter- and grid-side damping measures are presented. Based on the concept of the impedance-based stability analysis, all damping methods can ensure the system stability by modifying the effective output impedance of the inverter or the effective grid impedance. Classical damping methods for industrial applications will be analyzed and compared. Finally, the future trends of the impedance-based stability analysis, as well as some promising damping methods, will be discussed.

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Damping Methods for Resonances Caused by LCL-Filter-Based Current-Controlled Grid-Tied Power Inverters: An Overview

Resonant poles of LCL filters may challenge the entire system stability especially in digital-controlled pulse width modulation (PWM) inverters. In order to tackle the resonance issues, many active damping solutions have been reported. For instance, a notch filter can be employed to damp the resonance, where the notch frequency should be aligned exactly to the resonant frequency of the LCL filter. However, parameter variations of the LCL filter as well as the time delay appearing in digital control systems will induce resonance drifting, and thus break this alignment, possibly deteriorating the original damping. In this paper, the effectiveness of the notch filter-based active damping is first explored, considering the drifts of the resonant frequency. It is revealed that when the resonant frequency drifts away from its nominal value, the phase lead or lag introduced by the notch filter may make itself fail to damp the resonance. Specifically, the phase lag can make the current control stable despite of the resonant frequency drifting, when the grid current is fed back. In contrast, in the case of an inverter current feedback control, the influence of the phase lead or lag on the active damping is dependent on the actual resonant frequency. Accordingly, in this paper, the notch frequency is designed away from the nominal resonant frequency to tolerate the resonance drifting, being the proposed robust active damping. Simulations and experiments performed on a 2.2-kW three-phase grid-connected PWM inverter verify the effectiveness of the proposed design for robust active damping using digital notch filters.

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Design and Analysis of Robust Active Damping for LCL Filters Using Digital Notch Filters

This paper presents a harmonic instability analysis method using state-space modeling and participation analysis in the inverter-fed ac power systems. A full-order state-space model for the droop-controlled distributed generation (DG) inverter is built first, including the time delay of the digital control system, inner current and voltage control loops, and outer droop-based power control loop. Based on the DG inverter model, an overall state-space model of a two-inverter-fed system is established. The eigenvalue-based stability analysis is then presented to assess the influence of controller parameters on the harmonic instability of the power system. Moreover, the harmonic-frequency oscillation modes are identified, where participation analysis is presented to evaluate the contributions of different states to these modes and to further reveal how the system gives rise to harmonic instability. Based on the participation analysis, a reduced-order model for harmonic instability analysis is also proposed. The experimental results are presented for validating the theoretical analyses.

Harmonic Instability Assessment Using State-Space Modeling and Participation Analysis in Inverter-Fed Power Systems

The middle capacitor voltage of an LCL -filter, if fed back for synchronization, can be used for active damping. An extra sensor for measuring the capacitor current is then avoided. Relating the capacitor voltage to existing popular damping techniques designed with capacitor current feedback would however demand a noise-sensitive derivative term. Digital implementation of this derivative term is generally a challenge with many methods presently developed for resolving it. These methods are however still facing drawbacks, which have comprehensively been explained in this paper. Two derivatives are then proposed, based on either second-order or nonideal generalized integrator. Performances of these derivatives have been found to match the ideal “ s ” function closely. Active damping based on capacitor voltage feedback can therefore be realized accurately. Experimental results presented have verified the effectiveness of the proposed derivative, which can similarly be used with other applications, where differentiation is needed.

Highly Accurate Derivatives for LCL -Filtered Grid Converter With Capacitor Voltage Active Damping

LCL filters have been widely used for grid-connected inverters. However, the problem that how time delay affects the stability of digitally controlled grid-connected inverters with LCL filters has not been fully studied. In this paper, a systematic study is carried out on the relationship between the time delay and stability of single-loop controlled grid-connected inverters that employ inverter current feedback (ICF) or grid current feedback (GCF). The ranges of time delay for system stability are analyzed and deduced in the continuous s -domain and discrete z -domain. It is shown that in the optimal range, the existence of time delay weakens the stability of the ICF loop, whereas a proper time delay is required for the GCF loop. The present work explains, for the first time, why different conclusions on the stability of ICF loop and GCF loop have been drawn in previous studies. To improve system stability, a linear predictor-based time delay reduction method is proposed for ICF, while a time delay addition method is used for GCF. A controller design method is then presented that guarantees adequate stability margins. The delay-dependent stability study is verified by simulation and experiment.

Delay-Dependent Stability of Single-Loop Controlled Grid-Connected Inverters with LCL Filters

Pseudo-derivative-feedback (PDF) control is, for the first time, applied to the current control of three-phase grid-connected inverters with LCL filters, which significantly improves the transient response of the system to a step change in the reference input through the elimination of overshoot and oscillation. Two PDF controllers with different terms in the inner feedback path are developed for an inverter current feedback system and a grid current feedback system, respectively. For the inverter current feedback system, a simple PDF controller with a proportional term is used. The influence of the controller parameters on the transient performance is discussed in detail. Compared with a PI controller, the PDF controller is able to eliminate the transient overshoot and oscillation easily, while maintaining a fast response. For the gird current feedback system, a PDF controller with a proportional term and a second-order derivative is developed. The implementation and design of the PDF controller are presented. Active damping is achieved with only the feedback from the grid current, and at the same time, the system transient response is improved. Both theoretical analysis and experimental results verify the advantages of the PDF control over PI control methods.

Pseudo-Derivative-Feedback Current Control for Three-Phase Grid-Connected Inverters With LCL Filters

A direct grid-current control method is proposed to attenuate low-order current harmonics in three-phase LCL-filtered grid-connected inverters. This method allows the use of a distorted reference current, thus the reference can be generated directly from grid voltage or by a simple phase-locked loop (PLL). It is found that the direct control is necessary for effectively attenuating the current harmonics caused by the distortion in the grid voltage. Active damping is achieved with an inner inverter-current feedback loop, which is found to be superior to the widely used capacitor-current feedback damping in improving system stability. A systematic controller design procedure is proposed to optimize system performance. Experimental results confirm the improved harmonic attenuation ability of the proposed method in comparison to that of conventional control methods.

Attenuation of low-order current harmonics in three-phase LCL-filtered grid-connected inverters

This paper studies the inherent damping of digitally controlled LCL-filtered voltage source inverters (VSIs) that adopt single-loop inverter-current feedback (ICF) or grid-current feedback (GCF), through investigating the virtual impedance introduced by each feedback control method. The virtual impedance consists of resistance and reactance which are found to be delay-dependent. The virtual resistor provides an inherent damping to the resonance of LCL filters when its resistance is positive, and thus making it is possible for the system to be stable. Subsequently, the damping ranges of time delay of the single-loop control systems are easily derived, within which a positive virtual resistance at the LCL resonance frequency is obtained. The time delay should fall into the damping ranges to ensure a possible stable operation. The study of the inherent damping of single-loop digitally controlled VSIs with LCL filters is validated and verified by simulated and experimental results.

Jiu Dun Yan

Papers

Delay-Dependent Stability of Single-Loop Controlled Grid-Connected Inverters with LCL Filters

Pseudo-Derivative-Feedback Current Control for Three-Phase Grid-Connected Inverters With LCL Filters

Attenuation of low-order current harmonics in three-phase LCL-filtered grid-connected inverters

Inherent damping of single-loop digitally controlled voltage source inverters with LCL filters