Virtual Impedance In Parallel Research Articles

Passivity-Oriented Impedance Shaping for LCL-Filtered Grid-Connected Inverters

The passivity theory provides an effective way to tackle the instability due to the inverter-grid interaction, which tells that the system stability can be guaranteed if the grid impedance and the inverter output impedance are both passive. Since the grid impedance is generally passive, the system stability can be immune to the grid impedance variation if the inverter output impedance is also passive. This paper develops a series and parallel impedance shaping method to ensure that the output impedance of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -filtered grid-connected inverter is dissipative up to the Nyquist frequency. Since the inverter output impedance can be decomposed into two passive elements and one active element, its non-dissipative property results from the latter, and thus the virtual series impedance shaping is introduced to cancel out the active element. Unfortunately, it poses impact on the low-frequency loop gain and system phase margin in the meantime. To alleviate this impact, a high-pass filter is inserted in the series impedance shaping function. Subsequently, a virtual parallel impedance is introduced to enhance the passivity robustness, such as against filter parameter variations. Moreover, the proposed method does not require any additional sensors. Experiments from a 6-kW prototype confirm the effectiveness of the proposed method.

Output Voltage Drop and Input Current Ripple Suppression for the Pulse Load Power Supply Using Virtual Multiple Quasi-Notch-Filters Impedance

To balance the instantaneous power difference between the pulsed output power and the constant input power of the pulse load power supply (PLPS), an active capacitor converter (ACC), which can compensate the pulsed current, is connected in parallel with the output of the dc-dc converter in the PLPS. In this paper, based on the Fourier decomposition results of the load current, it is evident that square waves have significant harmonic content. Hence, to provide the lower impedance at the frequencies of the high content harmonics in the load current, a virtual impedance that consisted of the multiple quasi-notch-filters (MQNF) is proposed to be in parallel at the port of the ACC for the suppression of output voltage drop and input current ripple. The virtual parallel impedance is implemented by the output voltage feedforward control (FFC) of the ACC. The design considerations of the virtual parallel impedance are presented to ensure the stability of the PLPS. Finally, a synchronous rectifier buck (SR-buck) converter with a bidirectional buck/boost converter is tested at the pulse repetition frequency (PRF) of 100-300 Hz and the pulse duty cycle of 0.15 to verify the validity of the proposed control scheme.

Current Control Scheme for LC-Equipped PMSM Drive Considering Decoupling and Resonance Suppression in Synchronous Complex-Vector Frame

Permanent-magnet synchronous machine drive with sine wave filter has features of low insulation stress and current harmonics. However, the filter can affect the current control of machine. Specifically, the increased axes cross-coupling degrades the response performance in the transient state, and the introduced resonant frequency oscillations can make the system unstable. To solve the issues, a complex-vector frequency-domain model of LC -equipped permanent-magnet synchronous machine drive is established in this article. Moreover, a quantitative index related to the symmetrical extent of double-sided frequency responses is introduced to evaluate the performance. A decoupling strategy based on the modified complex-vector controller is proposed and compared against conventional methods in terms of decoupling performance and parameter robustness based on the aforementioned evaluation index. Furthermore, an active damping method based on virtual impedance in parallel with the stator inductance is proposed to suppress the resonance. The quantified double-sided frequency-domain analysis is performed to illustrate the relationship between cross-coupling and system stability. Then, the systematic codesign procedure of decoupling controller and active damping link in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> -domain is proposed. Finally, the experimental results show that the proposed scheme can improve the overall control performance in both transient and steady states.

Second Harmonic Current Reduction for Flying Capacitor Clamped Boost Three-Level Converter in Photovoltaic Grid-Connected Inverter

In a two-stage single-phase photovoltaic (PV) grid-connected inverter, the second harmonic current (SHC) in the PV panel will affect the maximum power point tracking operation and degrade the energy harvesting efficiency. In order to solve this problem, a flying capacitor clamped (FCC) boost three-level (TL) converter is adopted in this article, and the flying capacitor is employed to compensate the SHC for removing a large electrolytic capacitor. The propagation mechanism of the SHC is analyzed from the perspective of impedance, and a virtual impedance in parallel with the intermediate dc bus is introduced, achieving a perfect SHC compensation performance. The implementation of the virtual parallel impedance is illustrated, and the key parameters design of the FCC boost TL converter is given. A 3-kW two-stage single-phase PV grid-connected inverter is fabricated and tested, and the experimental results verify the validity of the theoretical analysis and the proposed control scheme.

Robust AD for LCL‐type grid‐connected inverter with capacitor current quasi‐integral feedback

Considering the time delay introduced by the digital control, it turns out that capacitor current proportional feedback active damping (AD) is equivalent to a frequency-dependent virtual impedance in parallel with the filter capacitor. Unstable open-loop poles will arise due to the presence of virtual negative resistor, which causes that the system stability is highly sensitive to grid-impedance variation. Therefore, this study proposes a novel capacitor current quasi-integral feedback AD method. Theoretical analysis shows the proposed AD method can extend the region of the virtual positive resistor, i.e. damping region to the half of sampling frequency (f s/2). Hence, strong robustness against the grid-impedance variation is achieved. Finally, experimental results including the proposed AD method as well as capacitor current proportional feedback AD method are given and compared, which validates the superior damping performance of the proposed scheme.

A Virtual Impedance Based Control Scheme for Modular Electrolytic Capacitor-Less Second Harmonic Current Compensator

The second harmonic current compensator (SHCC) can be added into the single-phase converters for compensating the second harmonic current (SHC) and thus removing the undesired electrolytic capacitor. In this paper, a virtual impedance, which is in the form of a capacitor and a resistor connected in parallel, is introduced to be in parallel at the bus-side port of the SHCC for effectively compensating the SHC while guaranteeing the system stability. This virtual parallel impedance is realized by feeding forward the bus-side port voltage of the SHCC, and thus the SHCC can be modular designed. The closed-loop parameter design of the SHCC is also presented. A 3.3-kW prototype of a two-stage single-phase power factor correction converter is built and tested in the laboratory, and the experimental results verify the effectiveness and feasibility of the proposed control method.

Parameter-Independent Control for Battery Chargers Based on Virtual Impedance Emulation

Effective battery voltage regulation is fundamental to extend battery lifetime and to avoid overvoltage. However, the design of this regulation is complicated due to the wide battery impedance range, which, when dealing with universal chargers, is dependent not only on the operating point but also on the battery type and size. This paper first shows how the voltage response becomes highly variable when designing the controller as described in the literature. Then, it proposes to emulate virtual impedance in parallel with the battery, making it possible to achieve a voltage control which is independent of battery characteristics. Experimental results are carried out for a new lithium-ion battery with 25 mΩ impedance and an overused lead-acid battery with 400 mΩ impedance. For this large impedance variation, the results evidence the problems of the conventional control and validate the superior performance of the proposed control.

Robust multisampled capacitor voltage active damping for grid-connected power converters

The derivative feedback of the capacitor voltage is one of the most extended active damping strategies, used to eliminate stability problems in grid-connected power converters with an LCL filter. This strategy is equivalent to the implementation of a virtual impedance in parallel with the filter capacitor. This virtual impedance is strongly affected by the control loop delays and frequency, creating changes in the sign of the emulated virtual resistor, and raising instability regions where the active damping is ineffective. As a consequence, the LCL resonance frequency is restricted to vary, as the effective grid inductance changes, within the active damping stability region. This is an additional restriction imposed on the LCL filter design that can compromise the achievement of an optimised design. For this reason, in this work, a different strategy is presented; by adjusting the delay in the active damping feedback path, it becomes stable within the range where the LCL resonance frequency can be located for a given filter design, achieving a robust damping. Analytical expressions are provided to adjust this delay. To widen the stability region of the capacitor voltage derivative active damping, a multisampled derivative is implemented, overcoming its limitations close to the control Nyquist frequency. Experimental and simulation results validate the active damping strategy presented.

Second-Harmonic Current Reduction for Two-Stage Inverter With Boost-Derived Front-End Converter: Control Schemes and Design Considerations

The instantaneous output power of the two-stage single-phase inverter pulsates at twice the output frequency $(2f_{{\rm{o}}})$ , generating notorious second-harmonic current (SHC) in the front-end dc–dc converter and the input dc voltage source. This paper focuses on the SHC reduction for a two-stage single-phase inverter with boost-derived front-end converter. To reduce the SHC, a virtual series impedance, which has high impedance at $2f_{{\rm{o}}}$ while low impedance at other frequencies, is introduced in series with the boost diode or the boost inductor to increase the impedance of the boost-diode branch or boost-inductor branch at $2f_{{\rm{o}}}$ . Meanwhile, for achieving good dynamic performance, a virtual parallel impedance, which exhibits infinite impedance at $2f_{{\rm{o}}}$ while low impedance at other frequencies, is introduced in parallel with the dc-bus capacitor to reduce the output impedance of the boost-derived converter at the frequencies except for $2f_{{\rm{o}}}$ . The virtual series impedance is realized by the feedback of the boost-diode current or the boost-inductor current, while the virtual parallel impedance is implemented by the feedback of the dc-bus voltage. Based on the virtual-impedance approach, a variety of SHC reduction control schemes are derived. A step-by-step closed-loop parameters design approach with considerations of reducing the SHC and improving the dynamic performance is also proposed for the derived SHC reduction control schemes. Finally, a 1-kW prototype is built and tested, and experimental results are presented to verify the effectiveness of the proposed SHC reduction control schemes.

Stabilization of a Cascaded DC Converter System via Adding a Virtual Adaptive Parallel Impedance to the Input of the Load Converter

Connecting converters in cascade is a basic configuration of dc distributed power systems (DPS). The impedance interaction between individually designed converters may make the cascaded system become unstable. The previous presented stabilization approaches not only need to know the information of the regulated converter, but also have to know the characteristics of the other converters in the system, which are contradictory to the modularization characteristic of dc DPS. This letter proposes an adaptive-input-impedance-regulation (AIIR) method, which connects an adaptive virtual impedance in parallel with the input impedance of the load converter, to stabilize the cascaded system. This virtual impedance can adaptively regulate its characteristic for different source converters. Therefore, with the AIIR method, all the load converters can be designed to a fixed standard module to stably adapt various source converters. In addition, at any cases, the AIIR approach only changes the load converter's input impedance in a very small frequency range to keep the load converter's original dynamic performance. The requirements on the AIIR method are derived and the control strategies to achieve the AIIR method are proposed. Finally, considering the worst stability problem that often occurs at the system whose source converter is an LC filter, a load converter cascaded with two different LC input filters is fabricated and tested to validate the effectiveness of the proposed AIIR control method.

Improving the Stability of Cascaded DC/DC Converter Systems via Shaping the Input Impedance of the Load Converter With a Parallel or Series Virtual Impedance

Interactions between individually designed power subsystems in a cascaded system may cause instability. This paper proposes an approach, which connects a virtual impedance in parallel or series with the input impedance of the load converter so that the magnitude or phase of the load converter's input impedance is modified in a small range of frequency, to solve the instability problem of a cascaded system. The requirements on the parallel virtual impedance (PVI) and series virtual impedance (SVI) are derived, and the control strategies to implement the PVI and SVI are proposed. The comparison and general design procedure of the PVI and SVI control strategies are also discussed. Finally, considering the worst stability problem that often occurs at the system whose source converter is an $LC$ filter, two cascaded systems consisting of a source converter with an $LC$ input filter and a load converter, which is either a buck converter or a boost converter, are fabricated and tested to validate the effectiveness of the proposed control methods.