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This paper presents the Cross-Border activation of the Regulating Reserve (CBRR) between participating Control Areas (CAs), which is being developed to reduce the costs of balancing energy. The main objective of the CBRR is to activate the regulating reserve in participating CAs, to release the regulating reserve and to reduce the balancing energy as part of the safe operation of the power system. However, the classic CBRR includes a frequency term and, therefore, inherently affects the frequency response of the participating CAs, which is not discussed in the literature. In this paper, the impact of the classic CBRR on frequency quality and the provision of Load-Frequency Control (LFC) is thoroughly evaluated with dynamic simulations of a three-CA test system and an eigenvalue analysis of a two-CA system. It is clearly demonstrated that the classic CBRR reduces the damping of the entire power system. Therefore, a modified implementation of the classic CBRR is presented, and a modified CBRR is proposed, which has no impact on the system's eigendynamics. Furthermore, the results of the dynamic simulations confirm that the frequency quality can be improved by the classic CBRR, although there are also cases where it can deteriorate. However, the modified CBRR improves the frequency quality in all cases. The modified CBRR also improves the indicators for the provision of LFC compared to the classic CBRR. Moreover, the modified CBRR reduces the unintended exchange of energy and the demand power, thus increasing the financial effects of the CBRR's activation.

The significant increase of converter interfaced generation, consumption, storage, and transmission in power systems, results in the need to consider converter-driven stability in detail, as well as to study modelling and analysis methods with which such stability effects can be represented and investigated. Due to the multiple causes of converter-driven stability effects, a classification into further categories of fast and slow converter-driven stability is necessary, which is systematically presented in this paper. We further provide a detailed overview on appropriate modelling methods including static, quasi-dynamic and dynamic modelling and their respective applications. Typical analysis methods such as eigenvalue and impedance based analysis are explained and related to the previous modelling approaches. Based on that, a guide to which modelling and analysis method is appropriate for which type of converter-driven stability, is provided. In addition, open and recent research questions with regard to studies on nonlinear analyses of large systems with acceptable computational costs are pointed out.

This paper presents the small-signal stability performance of a dc microgrid (MG) and investigates the interactions between the converter controllers by studying the critical modes. A comprehensive small-signal analysis using both the impedance-based method and eigenvalue-based analysis method has been presented thoroughly to investigate the high-frequency oscillation in the dc MG. The results show that there are inherent weak modes within the dc MG which could destabilize the MG in the presence of disturbances. Moreover, the controller gains and dc-link capacitance are found to be the most sensitive to substantial disturbance and have a significant influence on the weak modes leading to oscillation and resonance. The source side converter is found to be more influential than the load side converter in regard to various disturbances.

This paper is dedicated to presenting control-tuning methodologies for the rotor-side converter (RSC) and grid-side converter (GSC) of series-compensated DFIG-based wind farms (WF) and to determining the origin of subsynchronous resonance (SSR). Unlike conventional approaches to re-tuning controller gains to achieve desirable performance, these methodologies only consider the mathematical models of the states variables to be controlled. A PI cascade topology is used to control the RSC and GSC. An inner loop is required for current control and an outer loop for voltage control. Special consideration is taken for tuning the RSC because this converter is coupled with the mechanical variables as mechanical rotor speed of the DFIG. Compared with standard tuning, a better system behavior during a resonance condition is achieved with the proposed tuning methodology. Regarding the analysis of the SSR origin, the modal impedance (MI) technique is used as a tool to study SSR issues; its advantages compared to the driving point impedance technique are highlighted. In this context, the small-signal-stability (SSS) analysis is performed to evaluate the overall system. With the combination of MI and SSS, the phenomena of induction generator effect, torque interaction, and torque amplification are analyzed. As a result, the modes involved in the SSR phenomenon are identified and a discrimination procedure is described to determine the origin of the SSR.

This paper is devoted to the convergence problem for second-order signed networks that are associated with two signed graphs in the presence of heterogeneous topologies. An eigenvalue analysis approach is presented to develop convergence results for second-order signed networks, which employs a sign-consistency property for signed graph pairs. When the sign-consistency of two heterogeneous signed graphs and the connectivity of their union are given, bipartite consensus (respectively, state stability) can be derived for second-order signed networks if and only if the union signed graph is structurally balanced (respectively, unbalanced). Two examples are provided to illustrate the effectiveness of the obtained results.

The metal shell vibratory gyro is a branch of Coriolis vibratory gyro, which has the advantage of overload resistance, simplify structure, low cost, wide range and long life. This paper focuses on multi-surface metal resonator. It is important that the eigenvalue analysis of multi-surface of hemisphere, cylinder and hyperbolic. Through analysis multi-surface characteristic, it presents a novel orthogonal curvilinear coordinate used machine error factor based on the traditional coordinate, which realizes boundary linear. We analyze its natural vibration characteristics, research on basic model distribution and built mode shape function of resonator; deeply research on dynamics characteristics of resonator under the condition of angular rate input, establish dynamics equation of multi-surface fusion metal shell vibratory gyroscope based on thin shell mechanics theory of elastic mechanics, solve out the eigenvalue of the resonator, and we also analyze this eigenvalue characteristics to lay the foundation of the follow-up study of the theory of the metal shell vibratory gyroscope. We test the gyro's temperature performance on the last. Finally, we test on the metal shell vibratory gyroscope, the ranges to ±3600°/s, zero-bias stability is 7.862°/h (25 °C), angular random walk is 1.487°/h1/2.

The wind turbine is usually integrated into the power grid via back to back converter, and the inertia is decreased. Virtual synchronous machine (VSM) control was proposed to improve inertia of the wind farm. While for the doubly-fed induction generator (DFIG)-based wind farm with traditional control strategy, sub-synchronous resonance (SSR) has become a significant problem when it is connected to series compensation transmission lines. Therefore, the impacts of VSM control strategy for DFIG on SSR need to be investigated. In this paper, a detailed small-signal stability analysis model of the VSM control strategy is first established and eigenvalue analysis is then carried out. SSR in the wind farm with the VSM control under different series compensation levels, controller parameters and wind speeds is analyzed, and it is also compared to that in the wind farm with the conventional vector control strategy (VC). Simulations are performed in PSCAD/EMTDC to verify the result of SSR analysis.

This paper presents small signal stability analysis of a hybrid microgrid from three different aspects. First, a generalized droop control of interlinking converter (ILC) is proposed which defines voltage and frequency droops at its terminals to achieve a bidirectional, autonomous power flow between grids. The impact of the droop gains on the stability is discussed and an operational range is defined for a stable system operation. Second, contrary to previous literature which have modeled the ac and dc grids by ideal sources and converters, the ac grid in this scheme is represented as a second-order synchronous generator and the dc grid is modeled as a PV system so as to analyze the dc grid dynamics in detail. It is observed that the dc link capacitor and inductor filter can lead to large system oscillations which can compromise stability. Third, the stability of the hybrid grid is analyzed from the aspect of short circuit ratio (SCR). Both rectifier and inverter mode of operation are used to understand how stability is affected with strength of ac grid. The time-domain simulations in PSCAD are used to confirm the validity of results obtained in frequency domain.