A new type of subsynchronous oscillation (SSO) has been observed recently in double-fed induction generator (DFIG)-based wind farm integrated via voltage source converter-based HVdc (VSC-HVdc) system. However, the mechanism of this emerging oscillation is not entirely understood. In this paper, the impedance models of DFIG with and without considering the phase-locked loop (PLL) dynamics are both derived. Then, the impedance-based simplified equivalent circuit of the multiple DFIGs interfaced with VSC-HVdc system is established. This model can be further represented as the RLC series resonance circuit to quantify the start-oscillating condition intuitively. The theoretical analysis results show that DFIGs behave as an inductance in series with a negative resistance at the resonance point, whose interaction with wind farm side VSC (WFVSC) (regard as a resistance–capacitance) constitutes an equivalent RLC resonance circuit with negative resistance. Therefore, the oscillation tends to occur due to the negative damping. In addition, the impact of various factors including number of grid-connected DFIG-wind turbines (WTs), wind speed, and parameters of PI controllers and PLL on the SSO characteristics is analyzed based on the proposed simplified model. Finally, the correctness of the theoretical analysis is validated by both the time-domain simulation and hardware-in-loop experiments.

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Impedance Modeling and Stability Analysis of Grid-Connected DFIG-Based Wind Farm With a VSC-HVDC

When LCL -type converter is attached to weak grid, its current control and phase-locked loop (PLL) will interact with each other, via the point of common coupling voltage. Unfortunately, the conventional PLL controller design methods are mainly for PLL independent systems, regardless of the aforesaid interaction. As a consequence, PLL dynamic might deteriorate the grid current control and even leads to instability problem. For this issue, this article proposes an improved design of PLL controller parameters to mitigate the negative effect of PLL on the current control. First, the small-signal model of the current control system considering PLL effect is established, and the system stability with the conventional PLL controller design method is analyzed. Then, an improved design of PLL controller parameters is proposed, and the design guideline is given in detail. With the method, not only the dynamic and static response performance of PLL independent system can be maintained, but also the negative influence of PLL dynamic on the current control can be effectively reduced in weak grid. Moreover, the grid current control has a strong robustness to the grid impedance variation. Finally, the proposed method is validated by the simulation and experiment.

Improved Design of PLL Controller for LCL -Type Grid-Connected Converter in Weak Grid

Due to the advantages of superior harmonics attenuation ability and reduced size, the LCL filter has been widely adopted to interface between the inverter and the grid for improving the quality of injected grid currents. However, the high-order characteristics and various constraints of the LCL filter complicate the filter design. Moreover, the stability of the internal current control loop of the individual inverter is susceptible to the inherent LCL -filter resonance peak. Meanwhile, the overall system stability would be aggravated by the external interactions between the inverter and the weak grid as well as among the paralleled inverters. Both the LCL -filter resonance peak and two types of interaction would cause severely distorted grid currents. Motivated by the existing problems, a comprehensive review on the modeling and stability analysis of the LCL -type grid-connected inverters is conducted in this paper. Concretely, the generalized parameter constraints of the LCL filter are outlined to facilitate the passive components selection, and the magnetic integration techniques of filter inductors are also introduced to reduce the weight and size of filter for increasing the power density of the system. Then, the various damping methods for enhancing the individual internal stability and the relevant application issues are also discussed. Furthermore, the impedance-based method for evaluating the system-level interactive stability is subsequently reviewed, with the emphasis on different modeling methods of inverter output impedance and online impedance measurement techniques. Finally, the future research trends on the modeling and stability analysis of LCL -type grid-connected inverters are also presented.

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Modeling and Stability Analysis of $LCL$ -Type Grid-Connected Inverters: A Comprehensive Overview

Synchronization is the key part to ensure the high performance of grid-connected systems. Phase-locked loop (PLL) is one of the most popular synchronizations due to its simple implementation and robustness under certain grid variations. Particularly, in single-phase applications, PLL based on second-order generalized integrator (SOGI-PLL) is widely used because of its simple structure, certain filtering ability and frequency adaptability. The sensitivity of SOGI-PLL to the dc offset and low-order harmonics has been studied a lot in the literature and many solutions have been proposed. However, as more and more power electronic devices are integrated into the power grid recently, the grid condition becomes more complex. As a result, the nonlinear loop coupling phenomenon of SOGI-PLL is more severe and obvious and thus the performance of SOGI-PLL is degraded a lot, especially under the conditions of grid frequency variations and weak grid. A popular method is to use the frequency-fixed SOGI-PLL (FFSOGI-PLL) while how to eliminate the estimation error under frequency variations remain an important task. Though some scattered methods have been proposed, a simple yet effective strategy is still missing. Besides, it has been shown that the system stability margin will be reduced due to the negative-resistance behavior of PLL. However, the models derived in the current documents cannot accurately reveal the instabilities caused by the standard SOGI-PLL for missing the dynamics of the frequency feedback loop. Moreover, the PLL parameters are usually designed according to the PLL bandwidth to guarantee system stability under a weak grid. How to optimize the parameters is still unclear. In view of this, this article further summarizes and reviews the existing achievements of single-phase SOGI-PLL, and points out the problems to be solved and the development direction to improve the SOGI-PLL under more complex and non-ideal grid conditions.

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Overview of SOGI-Based Single-Phase Phase-Locked Loops for Grid Synchronization Under Complex Grid Conditions

In this paper, a feedforward virtual inductance control strategy is developed for the stability of voltage source inverters (VSIs) in weak grids. A weak grid is characterized by a low short-circuit ratio and a low inertia constant, in which VSIs become susceptible to voltage distortions and instability. The proposed feedforward virtual inductance term is integrated into the current control loops of grid-tied VSIs. In this paper, the effectiveness of the virtual inductance control strategy in weak grids is first proved through closed-loop transfer function analysis and then the system's root locus analysis to determine the stability region of the system versus the grid impedance. The developed virtual inductance controller is also verified through laboratory experiments for different weak grid scenarios.

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Virtual Inductance for Stable Operation of Grid-Interactive Voltage Source Inverters

For three-phase LCL -type grid-connected converter, when it is attached to weak grid, current control interacts with phase-locked loop (PLL) via point of common coupling voltage. Consequently, PLL dynamic might deteriorate grid current control and even result in system instability. However, the conventional design method of current controller neglects the impact of PLL, and therefore, it is hard for the current controller to mitigate the negative effect of PLL. In this paper, an improved design of current controller, i.e., proportional–integral controller and capacitor-current-feedback active damping, is proposed to reduce the negative effect of PLL on current control. First, a small-signal impedance model is developed to analyze the impact of PLL on current control. Then, the effect of current controller parameters on the converter output impedance is analyzed, and a design guideline to improve the current controller parameters is presented. With the improved parameters, in precondition of satisfying system stability margin under both stiff and weak grid, the negative effect of PLL on current control can be effectively mitigated without employing additional control strategies. Furthermore, the current control has a strong robustness against wide-range variation of grid impedance. Finally, the experiment demonstrates the effectiveness of the proposed design method.

An Improved Design of Current Controller for LCL -Type Grid-Connected Converter to Reduce Negative Effect of PLL in Weak Grid

Systematic controller design for digitally controlled LCL-type grid-connected inverter with grid-current-feedback active damping

For the testing of 400-Hz inverters, a power hardware-in-the-loop (PHIL) platform is presented. However, the selections of power interface circuit parameters, such as filter of hardware interface (HI) and operating DC bus voltage of power amplifier (PA), remarkably affect the performance of the PHIL system. To solve this problem, an analytical and quantitative design method for power interface of PHIL is proposed. With the proposed design method, the relationships of the power interface circuit parameters and the PHIL system performances can be sufficiently taken into account and intuitively illustrated on a graph. Hence, the choices and optimizations of these parameters can be convenient and explicit. Moreover, a PHIL setup is built for testing a 400-Hz inverter to verify the effectiveness of the design method. Simulation and experimental results indicate that the setup achieves good performance.

Analysis and design of power hardware-in-the-loop testing for 400-Hz inverters

Machine learning approaches are available for the fault diagnosis issues of the dual active bridge (DAB) converter. However, influenced by noise and multimodal diagnostic signals, the data-driven methods are still in the initial phase for certain fault diagnoses of the DAB converter. To fill this gap, a multimodal fusion neural controlled differential equation (MFNCDE) is presented to detect and locate the DAB converter’s fault diagnosis in early phases. An improved low-rank matrix fusion (LMF) method is employed to fuse the multimodal signals (voltage and current signals) of the DAB converter. The neural controlled differential equations (NCDEs) with sparse transformer (ST) extract significant information from the diagnostic signal, based on which the fault classifier obtains the fault state of the DAB converter. The datasets are collected from a real DAB converter under single-phase shift control. Contrastive experiment results demonstrate that the presented method is superior to other fault diagnosis methods.

Yingying Zhao

Papers

An Improved Design of Current Controller for LCL -Type Grid-Connected Converter to Reduce Negative Effect of PLL in Weak Grid

Systematic controller design for digitally controlled LCL-type grid-connected inverter with grid-current-feedback active damping

Analysis and design of power hardware-in-the-loop testing for 400-Hz inverters

An Online Open-Switch Fault Diagnosis Method for the DAB Converter Based on Multimodal Fusion Neural Controlled Differential Equations

The Prediction and Optimization of Hydraulic Fracturing by Integrating the Numerical Simulation and the Machine Learning Methods