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Source-side virtual synchronous machines (VSG) and load-side virtual synchronous machines (LVSM) are gradually utilized together in the microgrid to provide virtual inertia and damping. However, instability occurs in the islanded microgrid system due to the interaction dynamics between the VSG and the LVSM, which has been investigated in this paper. At first, the dq-frame impedance models of the VSG and the LVSM are established and compared. It is revealed that the d-d channel impedance of LVSM behaves the negative resistor with a V-type magnitude in the low-frequency range, which easily interacts with the d-d channel impedance of the VSG and leads to instability of the system. Thus, the inductor current feedforward control and the additional voltage feedback control are proposed for the VSG to reshape its impedance. It diminishes the impedance magnitude and generates the active impedance of the VSG. In this way, the low-frequency interaction between the VSG and the LVSM can be mitigated. Besides, the proposed control preserves the dynamic performance of the system. Finally, simulations and experiments verify the effectiveness of stability analyses and the proposed suppression method.

Direct power control (DPC) is widely used in grid-connected inverters. First, considering the effects of phase-locked loop (PLL), voltage outer loop, power inner loop, control delay, and frequency coupling, a broadband admittance model of the grid-connected inverter with DPC is established. The admittance characteristics of grid-connected inverters with DPC and closed-loop current control (CCC) are compared and analyzed. Due to the different inner loop control objects, the components produced by the power calculation in DPC and the Park's transformation in CCC cause the admittance differences between the grid-connected inverters with DPC and CCC. Then, the effects of grid impedance, output power, and control parameters on system stability are analyzed. It is revealed that the stability of the grid-connected inverter with DPC is very sensitive to grid impedance and easily affected by output power and inner loop bandwidth, while the grid-connected inverter with CCC has a better adaptability to weak grid, high output power, and inner loop bandwidth. Moreover, the PLL bandwidth has little effect on the stability of the grid-connected inverter with DPC, but has a great impact on the stability of the grid-connected inverter with CCC when the inverter is connected to weak grid. Finally, the correctness of the analysis is verified by experiments.

When the control parameters and operating conditions remain unchanged, it is usually believed that the admittance characteristic of grid-connected inverter is time-invariant. However, considering the effect of frequency-coupling, an abnormal phenomenon is observed in the admittance measurement of the grid-connected inverter: the phase of the off-diagonal elements Y12 and Y21 in the admittance matrix is always changed with time, which presents a time-varying admittance characteristic. To explore this phenomenon, the theoretical analyses based on the traditional frequency-coupling admittance measurement method are made. Because the initial phase of the signal cannot be obtained from Fast Fourier Transform (FFT) in experiments and the disturbance frequency and coupling frequency are different, the phase difference between the two frequency components changes with time. However, the influence is not considered in the traditional frequency-coupling admittance measurement method, which makes the measurement results exhibit the confusing time-varying characteristic. The phenomenon is defined as pseudotime-varying admittance characteristic in this letter. To accurately measure the admittance characteristic of the grid-connected inverter, a frequency-coupling admittance measurement method based on phase correction is proposed, which corrects the phase of disturbance frequency components and coupling frequency components. Finally, the effectiveness of the proposed measurement method is verified by experiments.

The load-side virtual synchronous machine (LVSM) enables the load to actively participate in the grid regulation, but it might still induce oscillations in a weak grid. Considering the dc-link voltage controller, power loops, ac voltage and current loops, the control delay, and sampling filters, the wideband dq -frame impedance model of the LVSM is first established, and it is found that $Z_{dd}$ exhibits negative resistor impedance within 10 Hz. In addition, the dq -frame impedance of the LVSM is approximately inductive above 10 Hz. Then, using the dq -frame impedance-based approach, the comparative study shows that the smaller the proportional gain and integral gain of the dc-link voltage controller are, the more stable the conventional voltage source rectifier (VSR) is in a weak grid. However, the larger the proportional gain is, the smaller the integral gain is, the more stable the LVSM is in a weak grid. Furthermore, the voltage feedforward decreases the stability margin of the VSR in a weak grid, while the virtual moment of inertia $J$ and the damping gain $D_{p}$ affect the stability of the LVSM, and the smaller $J$ and $D_{p}$ are, the more stable the LVSM is in weak grid. Finally, simulations and experimental results verify the impedance model and the stability analysis.

It tends to cause system oscillation when the inverter with a phase-locked loop based on proportional integral controller (PI-PLL) is connected to the weak grid. To improve the oscillation suppression ability of the grid-connected inverter, a linear active disturbance rejection controller is applied to PLL (LADRC-PLL). Considering the influence of linear extended state observer, voltage outer-loop, current inner-loop and frequency coupling, the admittance model of the grid-connected inverter with LADRC-PLL is established. Based on the established admittance model and the generalized Nyquist criterion, the system stabilities of the grid-connected inverters with LADRC-PLL and PI-PLL are compared. The comparison results indicate that the grid-connected inverter with LADRC-PLL has better adaptability to the weak grid and shows a certain ability to suppress the sub- and super-synchronous oscillation. Then, the influence of the control parameters of LADRC-PLL on the system stability is studied. It is found that the system keeps stable when the control parameter of LADRC-PLL is changed in a relatively wide range, which indicates LADRC-PLL has good robustness. Furthermore, the dynamic performances of the grid-connected inverters with LADRC-PLL and PI-PLL are analyzed. It is revealed that the grid-connected inverter with LADRC-PLL has better dynamic performance. Finally, the correctness of the analysis is verified by experiments.

Phase-locked loop (PLL) and grid impedance easily negatively affect the stability of the grid-connected inverter system and even cause the system oscillation. To suppress this oscillation, a stability enhancing voltage feed-forward inverter control method is proposed to reduce the effects of PLL and grid impedance. Then, considering the effects of the frequency coupling characteristic, the admittance model of the grid-connected inverter with the proposed stability enhancing control method is established, and the admittance characteristic and the system stability of the inverters with the traditional control method and the proposed stability enhancing control method are compared and analyzed. Analysis results indicate that the proposed stability enhancing control method improves the system stability in different short-circuit ratio (SCR) conditions. What is more, the system with the proposed stability enhancing control method keeps stable under a relative larger PLL bandwidth, while the system with the traditional control method oscillates. Finally, the effectiveness of the proposed stability enhancing control method is verified by experiments.

The premise that the virtual synchronous generator (VSG) can actively support the weak grid is that the VSG can operate stably. In this paper, the small-signal sequence impedance models of the voltage-controlled VSG and the current-controlled VSG are built and the sequence impedance characteristics of these two types of VSGs are compared and analyzed. The sequence impedance of the voltage-controlled VSG, being consistent with the grid impedance characteristics, is generally inductive. By contrast, the sequence impedance of the current-controlled VSG is mainly negative impedance in the middle- and high-frequency area and the impedance amplitude is quite low. Based on the built sequence impedance models and the impedance stability criterion, the influence of the weakness of the grid on the stability of these two types of VSG grid-connected system is analyzed. The results of stability analysis show that the current-controlled VSG is prone to instability while the voltage-controlled VSG remains stable. Therefore, the voltage-controlled VSG is more suitable than the current-controlled VSG for grid-connected renewable energy generation in an ultraweak grid from the point of view of system stability. Finally, experiment results validate the stability analysis.

In this work, with the aim of delivering the raw materials cost savings, P-containing Finemet-type Fe73(Si0.64B0.27P0.09)23+xCu1Nb3-x (x = 0, 1 and 2) amorphous alloys were fabricated by the single roller melt spinning technique to decrease Nb content. The dependence of (Si + B + P)23+x/Nb3-x ratio on crystallization behaviors and magnetic properties were investigated. The decrease of (Si + B + P)23+x/Nb3-x ratio reduced the onset temperature of ɑ-(Fe,Si) and boride phase, the interval of two onset crystallization temperatures decreases slightly, however, the crystallized alloys show a small coercivity (Hc) and moderate saturation magnetization (Ms) after annealed at the temperature higher or lower about 30 or 40 °C than the first crystallization peak temperature (Tp1-30 °C

In the maritime VSC-HVDC system supplying power to passive network on the island, the dc side of the system is prone to oscillation and even instability, which is resulted from the negative incremental input resistance characteristic of the inverter station. First, a virtual phase-lead impedance stability control strategy aiming at rectifier station is proposed. This control strategy can effectively mitigate the dc-side oscillation of the VSC–HVDC system without affecting the load performance of the inverter station. Then, the dc impedance model of the VSC–HVDC system is built, including the output impedance of the rectifier station, dc cable impedance, and the input impedance of the inverter station. In addition, the oscillation mechanism of the VSC–HVDC system is analyzed by impedance-based Nyquist stability criterion. The reason why rectifier station fails to mitigate the dc-side oscillation using traditional virtual resistance stability control is that the output impedance of the rectifier station exhibits negative damping characteristic outside the control bandwidth of voltage outer loop. For this issue, the proposed control strategy can correct the output impedance of the rectifier station to exhibit positive damping characteristic outside the control bandwidth of voltage outer loop, thus mitigating the dc-side oscillation of the VSC–HVDC system. Finally, simulation and experiment results validate the proposed control strategy and analysis.

In LCL-type grid-connected inverter, an optimized design method for grid-current-feedback active damping (AD) is proposed to improve the system dynamic characteristic. By analyzing the equivalent virtual impedance model, the essential relationship between the system dynamic characteristic indicators and damping control parameters is obtained, and the damping control parameters are contradictory that difficult to optimize. Then, a parameters optimization design method combining zero-pole model and Routh stability criterion is proposed to reduce the complexity of the parameters design and improve the system dynamic. Moreover, the influence of the control delay on system stability and parameters design is analyzed in the discrete domain. Simulation and experimental results verified the validity of the proposed method.

In the series-compensated grid-connected system (SCGCS), there is an impedance interaction between the inverter impedance and the grid impedance that is prone to cause resonance in the SCGCS. In this paper, firstly, considering the effects of the phase-locked loop (PLL), current-loop, and frequency coupling, the broadband impedance model of the SCGCS is established. The stability of the SCGCS is analyzed by the impedance-based Nyquist stability criterion. It is found from the stability analysis that the impedance interaction between the inverter impedance and the grid impedance is the leading cause of the resonance. An impedance reshaping based resonance suppression method is proposed to suppress the resonance. The phase characteristics of the inverter equivalent output impedance are reshaped from the perspective of impedance. The phase margin at the intersection frequency of the inverter impedance and the grid impedance is improved. The proposed resonance suppression approach mainly consists of reshaping the current loop impedance and the novel phase-locked loop impedance. Finally, simulations and experiments are used to verify the feasibility of the resonance analysis and the effectiveness of the proposed control strategy.

In the grid-connected inverter based on the deadbeat current control, the filter inductance variation and single update PWM affect the distortion of the grid current, stability, and dynamic of the system. For this, a double update PWM method for the deadbeat current controller in three-phase grid-connected system is proposed, which not only effectively decreases the grid current distortion and control delay, but also improves the system stability and dynamic response speed due to reducing the characteristic root equation order of the closed-loop transfer function. The influence of the filter inductance deviation coefficient on the system performance is analyzed. As a conclusion, the corresponding filter inductance deviation coefficient in the system critical stability increases with increase in the parasitic resistance of the filter inductance and line equivalent resistance and decreases with increase in the sampling frequency. Considering the system stability and dynamic response, the optimal range of the control parameters is acquired. Simulation and experimental results verify the effectiveness of the proposed method.