Donghua Pan

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

This paper investigates the feedforward schemes of grid voltages for a three-phase LCL-type grid-connected inverter. The full-feedforward functions of grid voltages are derived for the stationary α- β frame, synchronous d - q frame, and decoupled synchronous d - q frame-controlled three-phase LCL-type grid-connected inverters. The derived full-feedforward functions mainly consist of three parts which are proportional, derivative, and second derivative parts. The use of the traditional proportional feedforward function in the three-phase LCL -type grid-connected inverter will result in the amplification of the high-frequency injected grid current harmonics. With the proposed full-feedforward schemes, the injected grid current harmonics and unbalance caused by grid voltages can be greatly reduced. The effectiveness of the proposed feedforward schemes is verified by the experimental results.

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

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.

Full-Feedforward Schemes of Grid Voltages for a Three-Phase

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.

LCL

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.

-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.

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

For a current controlled grid-connected inverter, the grid voltage distortion will give rise to the injected grid current harmonics. Besides, for the three-phase grid-connected inverter, under the unbalanced grid voltage condition, the injected grid currents will become unbalanced. This paper aims at weakening the effect of the grid voltages on the injected grid currents for a three-phase grid-connected inverter with an LCL filter. The full-feedforward scheme of the grid voltages is investigated in this paper. The full-feedforward function of the grid voltages in the stationary α-β frame for a three-phase grid-connected inverter with an LCL filter is proposed. This full-feedforward function consists of three parts, which is proportional part, derivative part and second derivative part. With the proposed full-feedforward scheme of the grid voltages, approximately zero steady-state error of the injected grid currents at line frequency can be achieved even with proportional-integral (PI) compensators as the injected grid current regulators in the stationary α-β frame. The injected grid current distortion and unbalance caused by the grid voltages are also greatly reduced. At last, the effectiveness of the proposed full-feedforward scheme is verified by the experimental results.

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

For the LCL-type grid-connected inverter, there are basically three current control schemes, namely the grid current control, the inverter-side inductor current control, and the weighted average current control. This paper builds a general mathematical model to describe the three current control schemes. In this model, the grid current is an equivalent target control variable, the capacitor current feedback serves as a damping solution, and the computation and pulse-width modulation delays are taken into account. Based on the general mathematical model, a comparative analysis of different control schemes is carried out in terms of the grid current stability. It reveals that when the inverter-side inductor current is controlled, the grid current shows the same stability as the inverter-side inductor current; but when the weighted average current is controlled, both the grid current and the inverter-side inductor current are critically stable even though the weighted average current can be easily stabilized. Moreover, the general mathematical model also provides a unified perspective to design different control schemes, which makes the controller parameter tuning more straightforward and effective. In this way, a set of controller parameters which yields high robustness against the grid-impedance variation can be selected for all the three current control schemes. Finally, a 6-kW prototype is built, and experiments are performed to verify the theoretical analysis.