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To eliminate the common-mode leakage current in the transformerless photovoltaic grid-connected system, an improved single-phase inverter topology is presented. The improved transformerless inverter can sustain the same low input voltage as the full-bridge inverter and guarantee to completely meet the condition of eliminating common-mode leakage current. Both the unipolar sinusoidal pulsewidth modulation (SPWM) as well as the doublefrequency SPWM control strategy can be applied to implement the three-level output in the presented inverter. The high efficiency and convenient thermal design are achieved thanks to the decoupling of two additional switches connected to the dc side. Moreover, the higher frequency and lower current ripples are obtained by adopting the double-frequency SPWM, and thus the total harmonic distortion of the grid-connected current are reduced greatly. Furthermore, the influence of the phase shift between the output voltage and current, and the influence of the junction capacitances of the power switches are analyzed in detail. Finally, a 1-kW prototype has been simulated and tested to verify the theoretical analysis of this paper.

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 Abstract -In this paper, the concept of frequency-coordinating virtual impedance is proposed for the autonomous control of a dc microgrid. This concept introduces another degree of freedom in the conventional droop control scheme, to enable both time-scale and power-scale coordination in a distributed microgrid system. As an example, the proposed technique is applied to the coordinating regulation of a hybrid energy storage system composed of batteries and supercapacitors. With an effective frequency-domain shaping of the virtual output impedances, the battery and supercapacitor converters are designed to absorb low-frequency and high-frequency power fluctuations respectively. In this way, their complementary advantages in energy and power density can be effectively exploited. Furthermore, the proposed concept can be integrated into a mode-adaptive power management framework with autonomous mode transitions. The entire solution features highly versatile functions based on fully decentralized control. Therefore, both flexibility and reliability can be enhanced. The effectiveness of the presented solution is verified by experimental results.Index Terms -dc microgrid, frequency coordinating, virtual impedance, mode-adaptive.I.

The paper establishes a methodology to overcome the difficulty of dynamic frame alignment and system separation in impedance modeling of ac grids, and thereby enables impedance-based whole-system modeling of generator-converter composite power systems. The methodology is based on a framedynamics-embedding transformation via an intermediary steady frame between local and global frames, which yields a locally defined impedance model for each generator or converter that does not rely on a global frame but retains all frame dynamics. The individual impedance model can then be readily combined into a whole-system model even for meshed networks via the proposed closed-loop formulation without network separation. Compared to start-of-the-art impedance-based models, the proposed method retains both frame dynamics and scalability, and is generally applicable to various network topologies (meshed, radial, etc) and combinations of machines (generators, motors, converters, etc). The methodology is used to analyze the dynamic interaction between generators and converters in a composite grid, which yields important findings and potential solutions for unstable oscillation caused by PLL-swing coupling in low-inertia grids.

A reduced-order model that preserves physical meaning is important for generating insight in large-scale power system studies. The conventional model-order reduction for a multiple-timescale system is based on discarding states with fast (short-timescale) dynamics. It has been successfully applied to synchronous machines, but is inaccurate when applied to power converters because the timescales of fast and slow states are not sufficiently separated. In the method proposed here, several fast states are at first discarded but a representation of their interaction with the slow states is added back. Recognizing that the fast states of many converters are linear allows well-developed linear system theories to be used to implement this concept. All the information of the original system relevant to system-wide dynamics, including non-linearity, is preserved, which facilitates judgments on system stability and insight into control design. The method is tested on a converter-supplied mini power system and the comparison of analytical and experiment results confirms high preciseness in a broad range of conditions

The impedance model is widely used for analyzing power converters. However, the output impedance is an external representation of a converter system, i.e., it compresses the entire dynamics into a single transfer function with internal details of the interaction between states hidden. As a result, there are no programmatic routines to link each control parameter to the system dynamic modes and to show the interactions among them, which makes the designers rely on their experience and heuristic to interpret the impedance model and its implications. To overcome these obstacles, this paper proposes a new modeling tool named as impedance circuit model, visualizing the closedloop power converter as an impedance circuit with discrete circuit elements rather than an all-in-one impedance transfer function. It can reveal the virtual impedance essence of all control parameters at different impedance locations and/or within different frequency bandwidths, and show their interactions and coupling effects. A grid-forming voltage-source inverter (VSI) is investigated as an example, with considering its voltage controller, current controller, control delay, voltage/current dq-frame crossdecoupling terms, output-voltage/current feedforward control, droop controllers, and three typical virtual impedances. The proposed modeling tool is validated by frequency-domain spectrum measurement and time-domain step response in simulations and experiments.