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.

Capacitor-Current-Feedback Active Damping With Reduced Computation Delay for Improving Robustness of LCL-Type Grid-Connected Inverter

Capacitor-current-feedback active damping is an effective method to suppress the $LCL$ -filter resonance in grid-connected inverters. However, due to the variation of grid impedance, the $LCL$ -filter resonance frequency will vary in a wide range, which challenges the design of the capacitor-current-feedback coefficient. Moreover, if the resonance frequency is equal to one-sixth of the sampling frequency $(f_{s}/6)$ , the digitally controlled $LCL$ -type grid-connected inverter can be hardly stable no matter how much the capacitor-current-feedback coefficient is. In this paper, the optimal design of the capacitor-current-feedback coefficient is presented to deal with the wide-range variation of grid impedance. First, the gain margin requirements for system stability are derived under various resonance frequencies. By evaluating the effect of grid impedance on gain margins, an optimal capacitor-current-feedback coefficient is obtained. With this feedback coefficient, stable operations will be retained for all resonance frequencies except $f_{s} /6$ . Second, in order to improve system stability for a resonance frequency of $f_{s} /6$ , a phase-lag compensation for the loop gain is proposed. Finally, a 6-kW prototype is tested to verify the proposed design procedure.

Optimized Controller Design for $LCL$ -Type Grid-Connected Inverter to Achieve High Robustness Against Grid-Impedance Variation

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

Due to the higher attenuation of switching frequency current harmonics, the $LCL$ filter has been widely used in grid-connected inverters. To deal with the resonance of the $LCL$ filter, the capacitor current is usually fed back to damp the resonance actively. However, the computation and pulsewidth modulation (PWM) delays in the digital control system have a significant influence on the active damping method, resulting in poor system robustness. Meanwhile, these delays also reduce the control bandwidth greatly and thus impose a severe limitation on the low-frequency gains. In this paper, a real-time computation method with dual sampling mode is proposed to remove the computation delay from the inner active damping loop and the outer grid-current control loop simultaneously; thus, the system robustness and the control performance can be greatly improved. Moreover, the time duration between the sampling instant and the switching transition of the inverter bridge is extended by the proposed method, which effectively prevents the switching noise distorting the sampled signals. Therefore, the noise immunity of the inverter is also improved greatly. Experimental results from a 6-kW $LCL$ -type single-phase grid-connected inverter confirm the theoretical expectations and the effectiveness of the proposed method.

A Real-Time Computation Method With Dual Sampling Mode to Improve the Current Control Performance of the $LCL$ -Type Grid-Connected Inverter

Small-signal stability in balanced three-phase systems is typically investigated by means of the generalized Nyquist stability criterion (GNC) that involves operations on the source and load subsystems’ impedance matrices. Eigenvalues of the ratio of these impedance matrices should be calculated for stability judgment. This paper shows that for a power-electronics-based distributed power system, impedance matrices of subsystems can be designed as diagonal dominant. Therefore, stability, in this case, is fully determined by the scalar ratios formed by the impedance elements seen across the ${d}$ -axis and ${q}$ -axis interfaces. A three-phase ac system can then be treated as two decoupled dc systems. As a result, the ac stability analysis can also be conducted based on insightful impedance quantities; impedance specification criteria developed for dc systems can be readily applied to ensure stability in ac systems. The major contribution of this paper is related to the simplification of the GNC analysis with good experimental validations. Limitation of the proposed method is that the systems have to work under high power factor condition. However, such limitation is not a problem for many power-electronics-based distributed power systems.

AC Stability Analysis and dq Frame Impedance Specifications in Power-Electronics-Based Distributed Power Systems

For longer life of alternating-current (ac) machines, it is desirable to feed them by sinusoidal voltages. This can be achieved by connecting an LC filter between the voltage source inverter and the motor. However, the LC filter creates unwanted oscillation at system resonant frequency. A resistance connected in series with the capacitor is a solution to damp out the resonant-frequency oscillation, but this damping technique increases loss in the system. In this paper, a simple active damping technique is proposed for lossless damping of vector-controlled ac motor drives with an LC filter. In the proposed technique, the resistance drop is emulated in the control using the terminal motor voltages. The proposed technique is carried out in the three-phase domain for better accuracy of the control. The proposed technique neither affects the dynamic response of the drive nor changes the design of the standard vector control loops. Results from experimental ac motor drives are presented.

D. Banerjee

Papers

Active Damping of Output $LC$ Filter Resonance for Vector-Controlled VSI-Fed AC Motor Drives