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The magnitude of inertia is often used to assess the ability to withstand frequency perturbations. However, the inertia of wind turbines (WTs) is time-varying, equipped with magnitude-phase characteristics. Existing studies have only focused on the magnitude characteristic of WT's inertia but rarely on phase characteristic, which is a limited understanding of WT's inertial response and hard to reveal its effect on system frequency dynamics. Therefore, this article is the first to study the inertial response mechanism of WTs from the perspective of magnitude-phase characteristics. First, the equivalent inertia model of WT is extracted, considering multiple-loop dynamics. Then, the relationship among magnitude-phase characteristics of WT's inertia, active power, and frequency dynamics is revealed according to the definition of equivalent inertia. Furthermore, the extended system frequency response model including the inertia of WT is established and the effect of WT's inertia on system frequency metrics is analyzed. Subsequently, the effects of phase-locked-loop, speed, and reactive power controller parameters on the magnitude-phase characteristics of WT's inertia and frequency metrics are analyzed. Finally, the analysis is verified by hardware-in-loop experiments.

The power boost and response speed are two critical indexes to evaluate the inertia control performances. However, it is hard to obtain the two indexes directly in the time domain for different inertia control methods. How to justify the inertia control performances becomes a critical issue to address. Besides, the issue of whether the inertia control methods of wind turbines can present similar inertia characteristics as synchronous generators also attracts great attention. Targeting the above two questions, this article focuses on the representation, evaluation, and optimization of the inertia characteristics for the doubly fed induction generator (DFIG) based wind turbine. First, the phase motion model and inertia transfer function for the DFIG are established. On this basis, the relations between the inertia control performance in the time domain and the inertia transfer function in the frequency domain are clarified, which is explained through the conventional emulated inertia control. Furthermore, optimization methods for DFIGs to achieve constant inertia, combined with the parameter design guidelines, are demonstrated. Finally, the analysis and the optimized methods are validated by experiments.

We studied the temperature effects on the resonant frequency of nano piezoelectric mechanical resonators based on Hf0.5Zr0.5O2 thin films. Two square-shaped resonators of 30 $\mu$ m and 50 $\mu$ m in length were fabricated and tested, having a resonant frequency of 225.8 kHz and 98.5 kHz, respectively. The temperature coefficient of frequency (TCF) of the devices was characterized in the range from −20 °C to 147 °C. Both devices exhibited a positive TCF around 83.6 ppm/°C to 105 ppm/°C in the range from 30 °C to 147 °C, which may result from the combined effect of thermal expansion mismatch between the materials and the temperature coefficient of Young’s modulus of the HZO material. Moreover, the 50 $\mu$ m device shows a negative TCF around −110 ppm/°C to −99.9 ppm/°C within the range from −20 °C to 30 °C, which may be due to stress relaxation during the heating process. These results underscore the significance of HZO material in nanoscale piezoelectric resonator applications and lay the foundation for our future work aimed at developing nanoscale piezoelectric devices based on HZO. [2024-0040]

To achieve the fault ride through (FRT) operation of DFIG-based wind turbines, various improved control methods have been proposed. However, it is difficult to reveal their essential relations and quantitatively evaluate their performance differences, due to the wide assortment of solving ideas and control structures. To cope with this issue, this paper revisits the FRT control from a new perspective of rotor-port impedance characteristics (RPIC). First, a unified RPIC model of nine typical FRT controls is established and it is found that their RPIC are manifested as the pure inductance, but the inductance values are different in the phase sequence. Subsequently, the influence of RPIC on FRT performance is analyzed and some practical design guidelines for FRT control are given. On this basis, nine typical FRT control methods are quantitatively evaluated and compared in terms of six key performance dimensions. Moreover, the study contributes to the understanding, analysis and redesign of FRT control, and the RPIC perspective features the definite physical meaning and simple. Finally, the analysis is validated by the experiments.

For grid-connected voltage source converters (VSCs), the transient instability in dc-link voltage control (DVC) timescale threatens the dc capacitor safety and grid stable operation. However, the transient stability analysis presents great challenges, due to the high-order and nonlinear coupling characteristics of VSC. Existing studies mainly consider single control loop to reduce order and simplify analysis, failing to fully reveal the transient instability mechanism. To cope with it, this article develops a reduced-order model based on singular perturbation, and the fourth-order full model of VSC is decomposed into a second-order nonlinear slow subsystem and a third-order linearized fast subsystem. Subsequently, the transient stability of slow and fast subsystem is analyzed by Lyapunov’s direct method and eigenvalue method, respectively. Meanwhile, a set of sufficient conditions for transient stability are derived, and the influence of several factors (e.g., grid impedance and multiple control loop parameters) on stability are revealed. Furthermore, some guidelines for transient stability enhancement are proposed. Finally, the analysis is validated by the experiments.