Chenlei Bao

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

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.

Step-by-Step Controller Design for LCL-Type Grid-Connected Inverter with Capacitor–Current-Feedback Active-Damping

The injected grid current regulator and active damping of the LCL filter are essential to the control of LCL-type grid-connected inverters. Generally speaking, the current regulator guarantees the quality of the injected grid current, and the active damping suppresses the resonance peak caused by the LCL filter and makes it easier to stabilize the whole system. Based on the proportional-integral (PI) and proportional-resonant (PR) compensator together with capacitor-current-feedback active-damping which are widely used for their effectiveness and simple implementations, this paper proposes a simple step-by-step controller design method for the LCL-type grid-connected inverter. By carefully dealing with the interaction between the current regulator and active damping, the complete satisfactory regions of the controller parameters for meeting the system specifications are obtained, and from which the controller parameters can be easily picked out. Based on these satisfactory regions, it is more convenient and explicit to optimize the system performance. Besides, the insight of tuning the controller parameters from these satisfactory regions is also discussed. Simulation and experimental results verify the proposed step-by-step design method.

Optimized Controller Design for

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 (fs/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 (fs/6). Second, in order to improve system stability for a resonance frequency of (fs/6), a phase-lag compensation for the loop gain is proposed. Finally, a 6-kW prototype is tested to verify the proposed design procedure.

LCL

Due to the significance of extracting the grid voltage information, the grid synchronization system plays an important role in the control of grid-connected power converters, and various grid voltage synchronization schemes have been proposed. This paper adopts the complex-vector-filter method (CVFM) to analyze the grid synchronization systems. With this method, the pairs of scalar signals, for example, the α- and β-axis components in the stationary α-β frame, are combined into one complex vector. As a consequence, the grid synchronization systems can be described with the complex transfer functions, which is very convenient to evaluate the steady-state performance, for example, the fundamental and harmonic sequence decoupling/cancellation, and dynamic performance of these systems. Moreover, the CVFM also provides a more generalized perspective to understand and develop the grid synchronization systems. Therefore, some of the representative systems are reanalyzed with the CVFM in this paper. A generalized second-order complex-vector filter and a third-order complex-vector filter are proposed with the CVFM to achieve better dynamic performance or higher harmonic attenuation. Moreover, a brief comparison of the complex-vector filters analyzed in this paper is presented. The effectiveness of the CVFM and the proposed two complex-vector filters are verified by the simulation and experimental results.

-Type Grid-Connected Inverter to Achieve High Robustness Against Grid-Impedance Variation

The injected grid current regulator and active damping of the LCL filter are essential to the control of LCL-type grid-connected inverters. Generally speaking, the current regulator guarantees the quality of the injected grid current, and the active damping reduces the resonance peak caused by the LCL filter and makes it easier to stabilize the whole system. However, the frequency responses of the current regulator and active damping interact with each other, making it difficult to design the proper controller parameters and investigate the effect of the controller parameters. Taking proportional-integral (PI) compensator together with capacitor-current-feedback active-damping as an instance, this paper proposes a step-by-step design method of the current regulator and capacitor current feedback coefficient in both analog control and digital control. By carefully dealing with the interaction between the current regulator and active damping, the satisfactory regions of the controller parameters are obtained based on stability margin and steady-state error checking, making it more convenient and explicit to optimize the performance of the system. The convenient trial-and-error procedures are successfully reduced. Experimental results verify the effectiveness of the proposed design method.

Grid Synchronization Systems of Three-Phase Grid-Connected Power Converters: A Complex-Vector-Filter Perspective

This letter investigates the magnetic integration of the LCL filter in grid-connected inverters. By sharing an ungapped core and arranging the windings properly, the fundamental fluxes generated by the two inductors of an LCL filter cancel out mostly in the common core. Thus, the common core with low flux level can be dramatically reduced. Although the reluctance of the common core can hardly be zero, which implies an inevitable coupling between the integrated inductors, the proposed magnetic integration scheme is still attractive if the cross-section area and magnetic material of the common core are made reasonable. Experimental results from both single-phase and three-phase grid-connected inverters verify the effectiveness of the proposed method.

Design of injected grid current regulator and capacitor-current-feedback active-damping for LCL-type grid-connected inverter

Due to the effect of the computation and modulation delays on the capacitor-current-feedback active damping, the digitally controlled LCL-filtered inverter tends to be unstable as the LCL-filter resonance frequency approaching to one-sixth of the sampling frequency. Therefore, to guarantee sufficient stability margins, the guideline for choosing the LCL-filter resonance frequency is proposed in this paper. After the resonance frequency is selected, a systematic design method is proposed to facilitate the selection of the proper controller parameters. With this design method, a satisfactory region of the controller parameters for meeting the system specifications is obtained, from which the proper controller parameters can be easily determined. Moreover, it is convenient and explicit to optimize the system performance according to the satisfactory region. A 6-kW prototype is built and tested. The simulation and experimental results validate the theoretical analysis.

Magnetic Integration of the LCL Filter in Grid-Connected Inverters

The LCL filter is widely used in grid-connected inverter due to its powerful ability of attenuating the switching-frequency harmonics. However, the frequency response of the LCL filter has a resonance peak, which would amplify the harmonics around the resonant frequency or even cause the inverter to be unstable. Active damping based on the feedback of capacitor current is an effective solution to damp the resonance oscillation. Since the one-timestep delay of the digital signal processor (DSP) can hardly be avoided, the stable margin of the inverter will be weakened. Besides, the optional range of the capacitor-current feedback coefficient will be shrunk. This paper discusses the effect of the one-timestep delay firstly, and proposes a step-by-step design method to choose the parameters of the PI-based current regulator and the capacitor-current feedback coefficient. Based on Jury stability criterion, the selectable 3D region surrounded by the parameters of PI-based regulator and capacitor-current feedback coefficient can be plotted. Further, some specific constraints such as steady-state error and phase margin etc. will decide the suitable values of PI regulator and capacitor-current feedback coefficient. A 6-kW single-phase grid-connected inverter is built to verify the proposed design method.

Design Considerations of Digitally Controlled LCL -Filtered Inverter With Capacitor- Current-Feedback Active Damping

The LCL filter is widely used in grid-connected inverters due to its outstanding performance of attenuating the switching frequency current harmonics. An LCL filter has two individual inductors. Numbers of magnetic cores are required, and large volume has to be reserved for these two inductors. In order to reduce the core volume, magnetic integration of these two inductors is introduced in this paper. Since the attenuating ability of the LCL filter would be weakened by the coupling between the two inductors, decoupled magnetic integration is chosen consequently. Though the reluctance of the common core can hardly be zero, the decoupled magnetic integration scheme is still attractive. A 6-kW prototype is built in the lab, and the experimental results validate the effectiveness of the proposed magnetic integration scheme.

Design of the PI regulator and feedback coefficient of capacitor current for grid-connected inverter with an LCL filter in discrete-time domain

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.