With the increasing use of voltage source converters (VSCs) in power electronics dominated power systems, oscillation phenomena in DC-link voltage control (DVC) timescale (around 10 Hz) among multiple VSCs have occurred. Several studies have tried to analyze these oscillation problems, but all associated with the single VSC situation. To consider the dynamic interactions between VSCs in DVC timescale, especially in the weak grid condition, this paper presents a small-signal model to understand VSC external characteristics based on motion equation concept also featured in synchronous generator (SG). Comparisons of time-domain simulation responses and eigenvalues show that the proposed model can hold the main behaviors of concern. The form of the model is very similar to the rotor motion equation in SG, with which power engineers have been very familiar. In addition, by establishing the relationship between the unbalanced powers and state variables of internal voltage (viz., VSC output voltage), the modeling idea introduced in this paper can be applied to other power electronic devices.

Modeling of Grid-Connected VSCs for Power System Small-Signal Stability Analysis in DC-Link Voltage Control Timescale

As the number of inverters increases in the power grid, the stability of grid-tied inverters becomes an important concern for the power industry. In particular, a weak grid can lead to voltage fluctuations at the inverter terminals and consequently cause inverter instability. In this paper, impacts of circuit and control parameters on the stability of voltage source inverters are studied using a small-signal state-space model in the synchronously rotating $dq$ -frame of reference. The full-order state-space model developed in this paper is directly extracted from the pulsewidth modulation switching pattern and enables the stability analysis of concurrent variations in the three-phase circuit and control parameters. This paper demonstrates that the full-order model of a grid-tied active (P) and reactive (Q) power (PQ)-controlled voltage source inverter (VSI) can be significantly reduced to a second-order model, preserving the overall system stability in the case of grid impedance variations. This paper also shows that a decrease in the grid inductance does not necessarily improve the stability of grid-tied VSIs. The system stability is a function of both the grid R/X ratio and grid inductance. Despite the grid-side inductor of the LCL filter is in series with the grid impedance, they have different impacts on the stability of a grid-tied PQ-controlled VSI, i.e., an increase in the filter inductance may improve the system stability in a weak grid. These findings are verified through simulated and experimentally obtained data.

On Stability of Voltage Source Inverters in Weak Grids

LCL -filtered grid-connected converters are widely used for distributed generation systems. However, the current regulation of such converters is susceptible to weak grid conditions, e.g., grid impedance variation and background harmonics. Paralleling multiple harmonic compensators (HCs) is a commonly used method to suppress the current distortion caused by grid background harmonics, but the control bandwidth should be wide enough to ensure system stability. In order to enhance the adaptability of LCL -filtered grid-connected converters under weak grid operation, this paper proposes an improved capacitor-voltage-feedforward control with full delay compensation. When used with converter-side current feedback, the proposed control can keep system low-frequency characteristic independent of grid impedance and provide a high-harmonic rejection capability without using additional HCs. Moreover, it completely avoids the design constraints of an LCL filter, i.e., $\omega _{r} is required for single-loop converter-side current control. Therefore, a higher resonant frequency can be designed to achieve a wider control bandwidth and to lower the current distortion caused by the paralleled filter capacitor branch. Experimental results are finally presented to verify the proposed control, which are also in good agreement with theoretical analysis.

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Capacitor-Voltage Feedforward With Full Delay Compensation to Improve Weak Grids Adaptability of LCL-Filtered Grid-Connected Converters for Distributed Generation Systems

Oscillations have been observed in wind farms with weak grid interconnections. While Texas observes 4 Hz low-frequency oscillations, the west region in China observes subsynchronous oscillations at 30 Hz. Furthermore, this oscillation mode caused torsional interactions with a remote synchronous generator and led to shutdown of the power plant. Inspired by those real-world events, this paper aims to present an analytical model of type-4 wind in weak grids that can demonstrate both low-frequency and subsynchronous frequency oscillations. Critical factors, e.g., the parameters of the phase-locked loop (PLL), are examined using small-signal analysis. The analysis results are validated using a testbed built in MATLAB/SimPowerSystems. Except power electronic switching sequences, the testbed has controls (e.g., wind turbine pitch control, maximum power point control, converter controls), machine dynamics and power system dynamics modeled. This testbed includes a 100 MW Type-4 wind farm, a 600 MW synchronous generator, a long transmission line and a grid. The testbed successfully demonstrates two types of dominant oscillations under different PLLs. In addition, the testbed demonstrates torsional interactions due to the proximity of the subsynchronous mode and one of the torsional modes.

Wind in Weak Grids: Low-Frequency Oscillations, Subsynchronous Oscillations, and Torsional Interactions

Large-scale integration of renewable generation, usually interfaced to the network through power electronics, has led to drastic changes in power system dynamics. This paper presents novel insights into stability properties of such systems. For that purpose, a high-fidelity dynamic model of a generic low-inertia power system has been developed. The full-order, state-of-the-art control schemes of both synchronous and converter-based generators are included, with the latter differentiating between grid-forming and grid-following mode of operation. Furthermore, the dynamics of transmission lines and loads are captured in the model. Using modal analysis techniques such as participation factors and parameter sensitivity, the most vulnerable segments of the system are determined and the adverse effects of timescale coupling and control interference are investigated. More precisely, this work characterizes the maximum permissible penetration levels of inverter-based generation as well as the nature of the associated unstable modes and the underlying dynamics. Finally, potential directions for improving the system stability margin under different generation portfolios are proposed for several benchmark systems.

Understanding Small-Signal Stability of Low-Inertia Systems

Voltage problems are challenging in modern power systems with a high penetration of renewables integrated via power electronics. This paper extends the transient time-scale classification to identify voltage dynamics in modern power systems. Voltage dynamics in the current control time-scale is firstly proposed and then the mechanism of terminal voltage change is elaborated. After that the significant influences of the voltage source converter (VSC), current control (CC) loop and voltage feed forward (VFF) on the voltage dynamics in the current control time-scale are discussed. The VSC current control loop provides positive damping on the terminal voltage, while the VFF scheme results in an additional loop that deteriorates terminal voltage dynamic performance and stability. In addition, a sensitivity analysis was carried out to investigate the influence of critical parameters on stability. Finally, simulation results of a current-controlled VSC attached to different strength of AC grids (including a weak grid) are presented to validate the phenomenon and the influencing factors of voltage dynamics in the current control time-scale.

Voltage Dynamics of Current Control Time-Scale in a VSC-Connected Weak Grid

High-frequency oscillations caused by voltage source converters (VSCs) are constantly emerging in power systems with the increasing penetration of renewable energies VSC models in current control timescale play a pivotal role in the analysis of these oscillation issues Conventional VSC models show few physical mechanisms of VSC dynamics during system oscillations Hence, this paper proposes a VSC model from the viewpoint of its internal voltage (namely, VSC output voltage), which is driven by current balancing between the current reference and the feedback in a stationary frame The proposed model can be used to study VSC dynamic characteristics in an intuitionistic physical way Based on the proposed model, it is found that VSC current reference in a stationary frame varies with internal voltage dynamic due to the essence of active and reactive current control in a current control timescale Additionally, in a stationary frame, the dynamic relation between internal voltage and error current embodies a generalized integrating characteristic with adaptable center frequency determined by a phase-locked loop, which guarantees the zero steady state error of VSC current control Comparisons of simulations between the proposed model and a switch-based model validates the effectiveness of the proposed model

Stationary-Frame Modeling of VSC Based on Current-Balancing Driven Internal Voltage Motion for Current Control Timescale Dynamic Analysis

This paper investigates the dynamic interaction of multi grid-connected voltage source converters (VSCs) in the current control time-scale. To illustrate the physical mechanism of interaction, a model is proposed based on the physical motion law of VSC's controlled current in frequency domain. The proposed model distinguishes the current control of VSCs into two branches, namely the self-stabilizing loop and interacting loop, according to their different physical influences on the inductor current. The analysis of a two-converter system reveals that the interaction caused by fast dynamic current control can decrease the positive damping on controlled current through the interacting loop and deteriorate system stability. Time-domain simulation results of a two-converter system implemented in MATLAB/Simulink validate the correctness of analysis and the effectiveness of the proposed model.

Interaction analysis of multi VSCs integrated into weak grid in current control time-scale

The invention discloses a self-adaptive current control system for inhibiting system high-frequency oscillation. The self-adaptive current control system comprises three main parts of dual-PI control under conventional rotational coordinates, a harmonic wave online detection link, special frequency band gain adjustment of a current loop, and the like. The value of amplitude of a harmonic component is obtained by detecting current waveform, during operation, of a filter capacitor of the grid-connected inverter in real time and analyzing harmonic wave components in the waveform; and when the detected value of amplitude of the harmonic component is greater than a set threshold value, the gain, at the harmonic wave frequency, of a current controller is inhibited by regulating a wave trap corresponding to the output end of the current controller, thereby preventing the grid-connected inverter from interacting with the system at the frequency point, and amplifying the harmonic waves. According to the control method disclosed by the invention, under different power grid harmonic oscillation environments, the automatic adjustment for the gain, at the harmonic oscillation frequency point, of the current controller can be realized, thereby improving the stable operation capacity of the grid-connected inverter.

Self-adaptive current control system of grid-connected converter for inhibiting system high-frequency oscillation

Wind turbine generators (WTGs) are required to ride through grid faults due to the increasing wind power penetrations. The existing grid codes around the world concerning low voltage ride-through (LVRT) were designed under the assumption that wind turbine operates in strong AC grid. However, under weak AC grid condition, the secure operating area (SOA) of WTG has changed obviously. Thus the behaviors of WTG restrained by the existing grid codes during LVRT may put itself at the risk of instability in weak grid, which may lead to the WTGs' disconnection from the grid and deteriorate the system transient stability after faults. The Limitations of WTGs' SOA caused by weak grid during LVRT are studied in this paper. And the results are verified by time domain simulations in Simulink/MATLAB.

Yabing Yan

Papers

Voltage Dynamics of Current Control Time-Scale in a VSC-Connected Weak Grid

Stationary-Frame Modeling of VSC Based on Current-Balancing Driven Internal Voltage Motion for Current Control Timescale Dynamic Analysis

Interaction analysis of multi VSCs integrated into weak grid in current control time-scale

Self-adaptive current control system of grid-connected converter for inhibiting system high-frequency oscillation

Concerns to the emerging grid codes for wind turbines' LVRT in weak AC grid