Search Results (15)

This paper investigates the system architecture and circuit topology of grid-connected inverters with embedded energy storage (EES), encompassing their modulation strategies and control methodologies. A mathematical model for an EES grid-connected inverter is derived based on capacitor current feedback control, from which the expression for the inverter’s output impedance is obtained. Building on this foundation, this study analyzes the influence of control parameters—such as the proportional coefficient, resonant coefficient, and switching frequency—on the inverter’s output impedance. Subsequently, the stability of single and multiple inverter grid-connected systems under various operating conditions is assessed using impedance analysis and the Nyquist criterion. Finally, the validity of the stability analysis based on the established mathematical model is verified through simulations conducted on the Matlab/Simulink platform, where models for both a single inverter and a two-inverter grid-connected system are constructed. Full article

The development of the elastic balance area within the distribution network places greater demands on the interaction between sources and loads, which impacts the stability of the power system. While achieving symmetry in active power is essential for stable operation, it is challenging to attain perfection due to various disruptions that can exacerbate frequency and voltage instability. Additionally, due to the inherent resonance characteristics of LCL filters and the time-varying nature of weak grid line impedance, grid-connected inverters may interact with the grid, potentially leading to oscillation issues. A grid-forming inverter control method that incorporates resonance suppression is proposed to address these challenges. First, a control model for the grid-forming inverter based on the Virtual Synchronous Generator (VSG) is established, enabling the system to exhibit inertia and damping characteristics. Considering the interaction between the VSG grid-connected system and the weak grid, sequence impedance models of the VSG system, which feature voltage and current double loops within the αβ coordinate system, are developed using harmonic linearization techniques. By combining the impedance analysis method, the stability of the system under weak grid conditions is evaluated using the Nyquist criterion. The validity of the analysis is confirmed through simulations. Finally, in order to ensure the effectiveness and correctness of the simulation, an experimental prototype of an NPC three-level LCL grid-forming inverter is built, and the experimental results have verified that the system has good elastic support capability and resonance suppression capability in the elastic region. Full article

In photovoltaic grid-connected systems, the interaction between grid-connected inverters and the grid may cause harmonic oscillation, which severely affects the normal operation of the system. To improve the quality of the output electrical energy, photovoltaic grid-connected systems often use LCL filters as output filters to filter out high-frequency harmonics. Taking the three-phase LCL-type photovoltaic grid-connected inverter system as an example, this paper addresses the issue of harmonic resonance. Firstly, based on the harmonic linearization method and considering the impact of the coupling compensation term on the grid-side voltage, a modular positive and negative sequence impedance modeling method is proposed, which simplifies the secondary modeling process of the converter under feedback control. Then, the stability analysis is conducted using the Nyquist criterion, revealing the mechanism of high-frequency resonance in photovoltaic grid-connected systems. Furthermore, this paper delves into the impact of changes in system parameters on impedance characteristics and system stability. The results indicate that the proportional coefficient of the internal loop current controller has a significant influence on system impedance characteristics. Additionally, this paper proposes an active damping design method that combines lead correction and capacitor current feedback to impedance-reconstruct the easily oscillating frequency band. Finally, the effectiveness of this method is verified in the simulation platform. Simulation results confirm the effectiveness of this method in suppressing harmonic resonance while maintaining rapid dynamic response. Full article

The central components influencing future grid stability in the future are inverters and their controllers. This paper delves into the pivotal role of inverters and their controllers in shaping the future stability of grids. Focusing on grid-supporting inverters, the study utilizes a microgrid test setup to explore their impact on overall grid stability. Employing impedance-based stability analysis with the Nyquist criterion, the paper introduces variations in internal inverter parameters and external grid parameters using pole-zero map considerations. The inverter’s control structure, resembling standard generators with droop control, facilitates the application of grid operators’ knowledge to inverter control. Mathematical insights into stability principles are provided, highlighting the influence of poles related to the phase-locked loop and the strategic placement of additional poles for enhanced stability. Furthermore, the paper evaluates the effects of rotating inertia, revealing that a 50% increase in system inertia can stabilize unstable microgrid behavior, enabling grid-supporting inverters to actively contribute to grid reliability. Full article

As a common interface circuit for renewable energy integrated into the power grid, the inverter is prone to work under a three-phase unbalanced weak grid. In this paper, the instability of grid-connected inverters under the unbalanced grid condition is investigated. First, a dual second-order generalized integrator phase-locked loop (DSOGI-PLL)-based inverter under balanced and unbalanced conditions is modeled. A fourth-order impedance model is established to describe its impedance characteristics under the unbalanced grid condition. To analyze this multi-input multi-output system, a simplified stability analysis method based on the generalized Nyquist stability criterion and matrix theory is proposed. Then, the influences of circuit and control parameters on the stability of the grid-connected inverter system under the unbalanced grid condition are investigated. Finally, the accuracy of the derived frequency-coupled impedance model is verified via simulations, and the effectiveness of the proposed simplified stability analysis method on the system stability analysis is verified via both simulations and hardware experiments. Full article

Power-converter-based energy-harvesting and storage systems are becoming more prevalent in the electrical grid, replacing conventional synchronous generators. Consequently, grid inertia is diminishing, and to address this, inverter-based energy conversion systems are required by grid codes to provide frequency control support to the main grid. This is undertaken to increase the equivalent inertia of the system and reduce frequency variations. This type of control is necessary and designed for handling large system transients. However, it also impacts the small-signal stability of the grid-connected converters. To investigate this issue, this paper addresses the influence of synthetic inertia control on the output admittance of a grid-following inverter and its interaction with the grid equivalent impedance. A synchronous reference frame dynamic model of the grid-following inverter closed-loop system is obtained and linearized at an operating point to analyze the small-signal stability of the low-switching frequency inverter. The models are validated through numerical simulations. The analysis verifies the interactions of the internal control loops, such as the AC current control with voltage feedforward, DC-link voltage control with power-feedforward, phase-locked loop, and AC voltage control with inertial control. Additionally, the interactions between the output admittance of the inverter and the grid impedance are verified using the generalized Nyquist criterion. The stability regions are validated through simulations, and the results show that the system gain margin is reduced for increasing values of synthetic inertia gain and lower grid short-circuit ratios. Furthermore, there is a limit in the voltage and power-feedforward bandwidth to avoid degrading the system stability when utilizing the synthetic inertia control. Full article

With the increasing maturity of new energy technologies, distributed power systems have been widely used in the field of new energy power generation. The grid-connected rectifier is an important device in the distributed power system. When the grid-connected rectifier operates in a weak power grid environment, its operating performance deviates from the design value, endangering the operation safety of the power system. In this paper, the small-signal impedance model of the three-phase LCL grid-connected rectifier in the DQ coordinate system is established. This model considers the influence of the phase-locked loop on the rectifier impedance characteristics and improves the accuracy of the model, and on this basis, the theoretical stability of the system is analyzed. The stability judgment of the system has important engineering guidance significance. The traditional generalized Nyquist stability criterion requires a lot of calculations and is difficult to use. Therefore, a system stability criterion based on the Gerschgorin circle theorem is proposed, which reduces the amount of calculation and provides a higher size for the system design. The simulation results are consistent with the theoretical analysis, which verifies the correctness of the method proposed in this paper. Full article

Due to the internal dynamics of the modular multilevel converter (MMC), the coupling between the positive and negative sequences in impedance, which is defined as frequency coupling, inherently exists in MMC. Ignoring the frequency coupling of the MMC impedance model may lead to inaccurate stability assessment, and thus the multi-input multi-output (MIMO) impedance model has been developed to consider the frequency coupling effect. However, the generalized Nyquist criterion (GNC), which is used for the stability analysis of an MIMO model, is more complicated than the stability analysis method applied on single-input-single-output (SISO) models. Meanwhile, it is not always the case that the SISO model fails in the stability assessment. Therefore, the conditions when the MIMO impedance model needs to be considered in the stability analysis of an MMC system should be analyzed. This paper quantitatively analyzes the effect of frequency coupling on the stability analysis of grid-connected MMC, and clarifies the frequency range and grid conditions that the coupling effect required to be considered in the stability analysis. Based on the quantitative relations between the frequency coupling and the stability analysis of the grid-connected MMC system, a simple and accurate stability analysis method for the grid-connected MMC system is proposed, where the MIMO impedance model is applied when the frequency coupling has a significant effect and the SISO impedance model is used if the frequency coupling is insignificant. Full article

Offshore Direct Current (DC) collector grids are a promising technology for decreasing the installation and operation costs of offshore wind parks. Nevertheless, the stability properties and hence the design of such DC collector grids is not common or standardised. Hence, this paper describes an attempt to fill these gaps by analysing the stability of two different types of DC collector grids—star and string—by considering identical operating conditions. The approach follows a non-parametric formulation of the impedance based Nyquist Stability Criterion. The hyperbolic $\mathrm{\Pi }$ equivalent formulation of the telegraph equation is adopted for modelling the submarine cable due to high capacitance that is distributed and thus the conventional 50 Hz $\mathrm{\Pi }$-model is not sufficient anymore. Furthermore, the paper shows how to integrate the complex dynamics of wind turbines into the overall stability assessment through an impedance building algorithm. Finally, it is shown how to stabilise the collector grids by means of active control parameter changes and it has been observed that the star configuration of wind turbines is more favourable on account of stability and controllability. Full article

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. Full article

The island microgrid is composed of a large number of inverters and various types of power equipment, and the interaction between inverters with different control methods may cause system instability, which will cause the power equipment to malfunction. Therefore, effective methods for analyzing the stability of the microgrid system have become particularly important. Generally, impedance modeling methods are used to analyze the stability of power electronic converter systems. In this paper, the impedance models of a PQ-controlled inverter and droop-controlled inverter are established in d-q frame. In view of the difference of output characteristics between the two control methods, the island microgrid is equivalent to a double closed-loop system. The impedance model of the parallel system is derived and the open loop transfer function of the system is extracted. Based on the generalized Nyquist criterion (GNC), the stability of parallel system working in island microgrid mode is analyzed using this proposed impedance model. The simulation and experiment results are presented to verify the analysis. Full article

The dq impedance stability analysis for a grid-connected current-control inverter is based on the impedance ratio matrix. However, the coupled matrix brings difficulties in deriving its eigenvalues for the analysis based on the general Nyquist criterion. If the couplings are ignored for simplification, unacceptable errors will be present in the analysis. In this paper, the influence of the couplings on the dq impedance stability analysis is studied. To take the couplings into account simply, the determinant-based impedance stability analysis is used. The mechanism between the determinant of the impedance-ratio matrix and the inverter stability is unveiled. Compared to the eigenvalues-based analysis, only one determinant rather than two eigenvalue s-function is required for the stability analysis. One Nyquist plot or pole map can be applied to the determinant to check the right-half-plane poles. The accuracy of the determinant-based stability analysis is also checked by comparing with the state-space stability analysis method. For the stability analysis, the coupling influence on the current control, the phase-locked loop, and the grid impedance are studied. The errors can be 10% in the stability analysis if the couplings are ignored. Full article

It is a common practice that one converter controls DC voltage and the other controls power in two-terminal voltage source converter (VSC)–based high voltage DC (HVDC) systems for AC gird interconnection. The maximum transmission power from a DC-voltage-controlled converter to a power-controlled converter is less than that of the opposite transmission direction. In order to increase the transmission power from a DC-voltage-controlled converter to a power-controlled converter, an improved virtual impedance control strategy is proposed in this paper. Based on the proposed control strategy, the DC impedance model of the VSC–HVDC system is built, including the output impedance of two converters and DC cable impedance. The stability of the system with an improved virtual impedance control is analyzed in Nyquist stability criterion. The proposed control strategy can improve the transmission capacity of the system by changing the DC output impedance of the DC voltage-controlled converter. The effectiveness of the proposed control strategy is verified by simulation. The simulation results show that the proposed control strategy has better dynamic performance than traditional control strategies. Full article

AC distribution grid is prone to instability due to negative impedance and constant power nature of the load if it is dominant with power electronics-based components. There are various time-domain and frequency-domain modelling methods which use various methodologies and analytical tools. Also, there are many small-signal stability analysis (SSSA) methods and their different variants for different specific conditions and situation. This paper presents a review of SSSA methods in AC distribution grid using impedance-based models in a synchronous reference frame (SRF). By simplifying and converting the system into load and source subsystem, the impedances of both subsystems are determined by perturbation method. For a single-phase system, Hilbert transform can be used to derive the equivalent SRF model. Afterwards, the Nyquist stability criterion can be used for stability analysis. Full article

The growth of power-electronic-based components is inescapable in future distribution grids (DGs). The introduction of these non-linear components poses many challenges, not only in terms of power quality, but also in terms of stability. These challenges become more acute when active loads are behaving as generators and power is flowing in reverse direction. The frequency-domain-based impedance modeling methods are preferred for small signal stability analysis (SSSA) of DGs involving such non-linear components. The harmonic linearization method can be used for impedance estimation, and afterwards, the Nyquist stability criterion can be used for stability analysis. In this paper, a parametric-based stability analysis of grid-connected active loads at the point of common coupling (PCC) is done by changing the parallel clustering distance and size of active loads. The results verify a positive impact on the stability of increasing parallel clustering and distance from the PCC and a negative impact of increasing the size of individual active loads. Full article