Recently, the converters controlled by droop controller with phase-locked loop (PLL) were observed in islanded ac microgrids. However, only state-space-based approach was applied to investigate the stability of this converter in the previous works. Compared with state-space-based approach, characteristic equation approach has plenty of advantages, such as convenient stability margin analysis (Phase Margin, Gain Margin, and so on) and simply stability criterion (Routh Criterion). Thus, a novel small-signal modeling approach based on characteristic equation for converter-dominated ac microgrids is proposed to assess the system low-frequency stability in this paper. Firstly, considering zero-order holder (ZOH) and time delay, the smallsignal characteristic equation of this converter is presented by Padé approximation and dynamic phasor model. Furthermore, the implementation and parameter design of the converters are studied under the practical considerations. Compared with the existing characteristic equation methods, the proposed approach can be verified that the performance is significantly improved. Eventually, simulations and experimental results are presented, indicating that the proposed approach can assess the system lowfrequency stability conveniently and accurately.

Although the low-frequency/harmonic oscillation of grid-tied inverters under weak grids has been widely researched, the classical impedance-based approach focuses more on the identification of stable operating points and the stability margin of return-ratio matrix. Furthermore, it cannot provide stability regions of system parameters. Therefore, this paper proposes a line impedance cooperative stability region identification method. Firstly, the output impedance matrix and the input admittance matrix are respectively built in d-q axis. Secondly, a novel stability forbidden region is proposed. It is less conservative than the forbidden region criteria in existing literatures. Based on the stability forbidden region, the stability operation region is established via mirror, translation and rotation mappings. It is less conservative compared with the norm-based stability criteria. The solving of stability operation region is first transformed into the eigenvalue identification problem in this paper. Furthermore, the detailed line impedance cooperative stability region is solved by guardian map theory. It can provide guidance for system planning and stabilization method researches with simplified computational process. Finally, the simulation and experimental results show that the proposed line impedance cooperative stability region identification method is more effective and less conservative.

The droop control is an advantageous approach for stand-alone supply systems consisting of multiple batteries, allowing among various inverters without intercommunication. The droop coefficients of batteries always vary with their state-of-charge (SoC) and charge/discharge mode, resulting in small-signal instability. Nevertheless, the existing impedance-based approaches can only assess the droop coefficients stability point, but not the stability region. Therefore, this article proposes a droop coefficients stability region analysis approach. First, the charge/discharge SoC-based droop controlled battery, the P&Q controlled distributed generator and the constant power load are separately discussed. Meanwhile, the state matrix and return-ratio matrix are established, respectively. Furthermore, the novel forbidden region criterion based on the return-ratio matrix is constructed, which reduces conservatism compared with norm-based impedance criteria and partial forbidden region criteria. Such a forbidden region criterion is first switched to the Hurwitz identification problem regarding the equivalent return-ratio matrix. Combined the state matrix and the equivalent return-ratio matrix, the generalized incidence matrix is constructed to simultaneously identify subsystem stability and interactive stability. Based on the generalized incidence matrix, an adaptive step search strategy is proposed to obtain the droop coefficients coordinated stability region. Finally, the simulation and experimental results illustrate the validity of the proposed method.

This paper proposes a reduced-order small-signal closed-loop transfer function model based on Jordan continued fraction expansion to assess the dynamic characteristics of the droop-controlled inverter and provide the preprocessing method for the real-time simulation of power systems. Firstly, dynamic phasors, time delay and zero-order hold are embedded into the small-signal model at the same time, then the closed-loop transfer function of the droop-controlled inverter is built. Compared with the existing closed-loop transfer function approaches, the accuracy of the built transfer function model is dramatically enhanced. Meanwhile, the inner cascaded voltage/current controller parameters are also designed. In order to directly obtain and preserve the maximum overshoot and settling time, which are main features to evaluate the system input-output dynamic response characteristics, the reduced second order closed-loop transfer function is proposed through the continued-fraction expansion regarding arbitrary points on the real frequency axis. Therein, this second order closed-loop transfer function with dynamic response of the original inverter is reduced to the lowest order. Furthermore, combined with the impedance-based approach, the proposed stability assessment approach is utilized to analyze the stability of the microgrid with multiple converters. Finally, simulations and experimental results demonstrate the convenience and accuracy of the proposed approach.

In practical microgrids, the inhomogeneous initial values are widely appeared due to soft-starting operation. If traditional model order reduction approaches are applied, the input-output maps error between the original system and reduced-order system is large. To address this problem, this paper proposes a reduced-order aggregate model based on balanced truncation approach to provide the preprocessing approach for the real-time simulation of large-scale converters with inhomogeneous initial conditions in DC microgrid. Firstly, the standard linear time-invariant model with inhomogeneous initial conditions is established through non-leader multiagents concept. To end this, it is convenient for scholars to build complex system modeling with switched topology. Furthermore, the full system is divided into two components, i.e., the unforced component with nontrivial initial conditions and forced component with null initial conditions. Moreover, this paper presents an aggregated approach that involves independent reducing component responses and combining reducing component responses. Based on this, the input-output maps error is reduced. Then, the approximated error estimate of the reduced-order aggregate model regarding large-scale converters in DC microgrid is first provided, which provides prior knowledge and theoretical basis for DC microgrid designers. Finally, the simulation results illustrate the accuracy of the proposed approach.

Although smart home has received wide attention in recent years, numerous scholars focus more on energy optimization strategy than energy dispatch hardware device (named energy router). Meanwhile, this energy router should have several features, i.e., high renewable energy utilization, energy multi-port and low volume. Thus, this paper designs a nine-port energy router regarding smart home and proposes a multimode hierarchical management strategy for this energy router. First, for the multi-port demand of wind, solar, storage and utilization, this paper presents a nine-port energy router to improve the renewable energy consumption and power supply flexibility. In addition, to reduce the volume of the energy router, a non-isolated AC/DC hybrid topology is constructed through embedding the integrated power electronic converters, which achieves the miniaturization of the energy router. In order to improve the renewable energy utilization rate, the decentralized module control is proposed for the components of energy router to provide the voltage and frequency support for system, and realizes the power sharing of distributed generations (DGs). Furthermore, the power exchange control with three-mode switching is proposed to guarantee the global energy flow balance under complex conditions. Eventually, the feasibility of the energy router is verified by the simulation and experiments.