Control Techniques for LCL-Type Grid-Connected Inverters

After 200 years of continuous extraction and recent massive consumption, fossil fuels have rapidly become depleted. At the same time, the process of consuming fossil energy has produced a large amount of waste, which has seriously polluted the environment, jeopardizing the long-term sustainability of development of our society. The renewable energy-based distributed power generation system (RE-DPGS) has been attracting a great deal of attention due to its sustainable and environmental-friendly features, and its use represents an effective approach to dealing with future energy shortage and environmental pollution. As the energy conversion interface between the renewable energy power generation units and the grid, the grid-connected inverter plays an important role for the safe, stable, and high-quality operation of RE-DPGS. The worldwide energy situation is first reviewed in this chapter, and then, the typical configurations and the advantages of the RE-DPGS are introduced. The key control technologies of the LCL-type grid-connected inverter are also systematically elaborated including: (1) design and magnetic integration of LCL filter, (2) resonance damping methods, (3) design of controller parameters, (4) control delay effects and the compensation methods, (5) suppressing grid current distortion caused by grid-voltage harmonics, and (6) grid-impedance effects on system stability and the improvement methods.

As the interface between renewable energy power generation system and the power grid, the grid-connected inverter is used to convert the dc power to the high-quality ac power and feed it into the power grid. In the grid-connected inverter, a filter is needed as the interface between the inverter and the power grid. Compared with the L filter, the LCL filter is considered to be a preferred choice for its cost-effective attenuation of switching frequency harmonics in the injected grid currents. To achieve high-quality grid current, the LCL filter should be properly designed. In this chapter, the widely used pulse-width modulation (PWM) schemes are introduced, including the bipolar sinusoidal pulse-width modulation (SPWM), unipolar SPWM and harmonic injection SPWM. The spectrums of the output PWM voltage with different SPWM are studied and compared. A design procedure for LCL filter based on the restriction standards of injected grid current is presented and verified by simulations.

An LCL filter has two individual inductors. In order to reduce the volume of magnetic components, magnetic integration of these two inductors is introduced in this chapter. First, the integration method of the two inductors of an LCL filter is proposed, and the magnetic circuit model of integrated inductors is built. Then, based on this model, the coupling caused by the nonzero reluctance of the common core is analyzed, and the coupling effect on the ability of attenuating high-frequency harmonics of LCL filter is evaluated. According to the harmonic limits of the grid current, the maximum allowable coupling coefficient is derived, which provides the guidelines for selecting cross-sectional area and magnetic material of the common core. Finally, with the help of Ansoft Maxwell software, design examples of integrated magnetics for both single-phase and three-phase LCL filters are presented, and experiments are performed to verify the proposed method.

The control challenges of LCL-type grid-connected inverter arise from the resonance problem. At the resonance frequency, the LCL filter resonance causes a sharp phase step down of −180° with a high resonance peak. This resonance peak would easily lead to system instability and should be damped. In this chapter, the resonance hazard resulted by the LCL filter is reviewed first, and then, the existing passive- and active-damping solutions are described systematically to reveal the relationship among them. Among the six basic passive-damping solutions, adding a resistor in parallel with capacitor shows the best damping performance, but it results in a high power loss. In order to avoid the power loss in the damping resistor, the active-damping solutions equivalent to a resistor in parallel with capacitor are derived, and the capacitor-current-feedback active damping is superior for its simple implementation and effectiveness. This chapter provides the basis for the study of the control techniques of LCL-type grid-connected inverter in the following chapters.

For the LCL-type grid-connected inverter, the capacitor-current-feedback active-damping is equivalent to a resistor in parallel with the filter capacitor to damp the LCL filter resonance. This active-damping method has no power loss and has been widely used. Based on the capacitor-current-feedback active-damping and the proportional-integral (PI) regulator as the grid current regulator, this chapter proposes a step-by-step controller design method for the LCL-type grid-connected inverter. By carefully examining the steady-state error, phase margin, and gain margin, a satisfactory region of the capacitor-current-feedback coefficient and PI regulator parameters for meeting the system specifications is obtained. With this satisfactory region, it is very convenient to choose the controller parameters and optimize the system performance. Besides, the proposed design method is extended to the situations where PI regulator with grid voltage feedforward scheme or proportional-resonant (PR) regulator is adopted. Finally, design examples of capacitor-current-feedback coefficient and current regulator parameters are presented for a single-phase LCL-type grid-connected inverter, and experiments are performed to verify the proposed design method.

The grid-connected inverter plays an important role in injecting high-quality power into the power grid. The injected grid current is affected by the grid voltage at the point of common coupling (PCC). This chapter studies the feedforward scheme of the grid voltage for single-phase LCL-type grid-connected inverter. First, the mathematical model for the LCL-type grid-connected inverter with capacitor-current-feedback active-damping is presented, and then it is simplified through a series of equivalent transformations. After that, a full-feedforward of the grid voltage is proposed to eliminate the effect of the grid voltage on the steady-state error and harmonics in the injected grid current. The feedforward function consists of three parts, namely proportional, derivative, and second-derivative components. A comprehensive investigation shows that if the grid voltage contains only the third harmonic, the proportional feedforward component is adequate to suppress the harmonic distortion in the grid current caused by the grid voltage; when the grid voltage contains harmonic distortion up to the thirteenth harmonic, the proportional and derivative components are required; and when the grid voltage contains harmonic distortion higher than the thirteenth harmonic, the second-derivative component must be incorporated, i.e., the full-feedforward scheme is necessary.

In order to alleviate the effect of the grid voltage on the grid current, Chap. 6 presented the full-feedforward scheme of grid voltages for the single-phase LCL-type grid-connected inverters, and the harmonics of the injected grid current are effectively suppressed. In this chapter, the full-feedforward scheme is extended to the three-phase LCL-type grid-connected inverter. In this chapter, the mathematical models of the three-phase LCL-type grid-connected inverter in both the stationary α–β frame and synchronous d–q frame are derived first. Then, based on the mathematical models, the full-feedforward schemes of the grid voltages for the stationary α–β frame, synchronous d–q frame, and decoupled synchronous d–q frame-controlled three-phase LCL-type grid-connected inverter are proposed. After that, the full-feedforward functions are discussed, and it will be illustrated that the simplification of the full-feedforward function should be taken with caution and simplifying the full-feedforward functions to a proportional feedforward function will give rise to the amplification of the high-frequency injected grid current harmonics. The effect of LCL filter parameter mismatches between the actual and theoretical values is also evaluated. Finally, the effectiveness of the proposed full-feedforward schemes is verified by the experimental results. Meanwhile, the performance of the proposed full-feedforward schemes under unbalanced grid voltage condition is intentionally investigated.

The capacitor-current-feedback active-damping is an effective approach for damping the resonance peak of the LCL filter. When the LCL-type grid-connected inverter is digitally controlled, the control delay will be generated. This will result in different behavior of the capacitor-current-feedback active-damping from that with analog control. In this chapter, the mechanism of the control delay in the digital control system is introduced first. Then, a series of equivalent transformations of the control block diagram considering the control delay are performed, and it reveals that the capacitor-current-feedback active-damping is no longer equivalent to a virtual resistor in parallel with the filter capacitor, but a virtual frequency-dependent impedance. A forbidden region for choosing the LCL filter resonance frequency is presented in order to guarantee the system stability. Then, the controller design for digitally controlled LCL-type grid-connected inverter with capacitor-current-feedback active-damping is studied. Since the control delay leads to a phase lag and consequently changes the location of −180°-crossing in the phase curve of the loop gain, the system stability might be guaranteed even without damping the resonance of LCL filter. For this case, the necessary condition for system stability is studied, and the controller design method is presented. Finally, the controller parameters design examples for the grid current regulator with and without the capacitor-current-feedback active-damping are given, and the effectiveness of the theoretical analysis is verified by the experimental results.

As illustrated in Chap. 8, in the digitally controlled LCL-type grid-connected inverters, proportional feedback of the capacitor current is equivalent to a frequency-dependent virtual impedance connected in parallel with the filter capacitor due to the control delay including the computation and pulse-width modulation (PWM) delays. This virtual impedance leads to the change of the LCL filter resonance frequency. At the frequencies higher than one-sixth of the sampling frequency (f _s /6), the virtual impedance contains a negative resistor component. So, if the actual resonance frequency is higher than f _s /6, a pair of open-loop right-half-plane (RHP) poles are generated. As a result, the LCL-type grid-connected inverter is easier to be unstable if the resonance frequency is moved closer to f _s /6 due to the variation of grid impedance. Meanwhile, the computation and PWM delays also reduce the control bandwidth greatly and thus impose a severe limitation on the low-frequency gains. Therefore, it is desirable to reduce the control delay so as to improve the stability and the control performance of the grid-connected inverter. In this chapter, the influence of the control delay on the LCL-type grid-connected inverter is firstly analyzed. Then, the real-time sampling method [1] and real-time computation method with dual sampling modes [2] are proposed to reduce or even remove the computation delay. Finally, the experimental results from a 6-kW prototype verify the effectiveness of the proposed methods.

The full-feedforward scheme of grid voltages for three-phase LCL-type grid-connected inverter has been introduced in Chap. 7, and the injected grid current harmonics and imbalance caused by grid voltages can be effectively suppressed. However, during the derivation of the full-feedforward scheme, the grid impedance is assumed to be zero. For weak grid condition, as the grid impedance becomes large, the full-feedforward scheme might cause the instability of the grid-connected inverter. In this chapter, the stationary α-β frame-controlled three-phase LCL-type grid-connected inverter with the full-feedforward scheme is taken as the example to analyze the system stability under weak grid condition, and the weighted-feedforward scheme is proposed to achieve a trade-off between the stability and the harmonic suppression. With the weighted-feedforward scheme, the extracted and weighted grid voltages are fed forward, and the injected grid current harmonics can be effectively suppressed while the stability of grid-connected inverter under weak grid condition is also guaranteed. Finally, the experimental results verify the analysis in this chapter.

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 chapter 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 sequences decoupling/cancellation, and dynamic performance of these systems. Besides, 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 chapter. 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 chapter is presented. The effectiveness of the CVFM and the proposed two complex-vector filters are verified by the simulation and experimental results.