This paper studies the dynamic behaviors of weak-grid-tied VSCs with simplified transfer functions, which provides an accurate stability analysis and useful indications for tuning system parameters. ...A reduced-order multi-input multi-output (MIMO) transfer function that contains four single-input single-output (SISO) transfer functions for the weak-grid-tied VSC is first presented. It is found that the four SISO transfer functions share the same equivalent open-loop transfer function, i.e., the same stability conclusion. The Bode plots of the equivalent open-loop transfer function show that the inner current loop behaves as a band-pass filter whose maximum gain is approximately at the frequency of the PLL's bandwidth. By stability criterion, the harmonic amplification and instability occur when its maximum gain exceeds 0 dB caused by high PLL's bandwidth, large grid impedance or high active power. It is also found that the target system is less stable when it works as an inverter than as a rectifier, due to the risk of the local positive feedback in the inverter mode. An effective criterion is further proposed to guide the selection of a proper PLL's bandwidth to ensure the stability of the VSC system. Simulation results validate the correctness of the analysis and the efficacy of the criterion.
Wind generation in highly interconnected power networks creates local and centralised stability issues based on their proximity to conventional synchronous generators and load centres. This study ...examines the large disturbance stability issues (i.e. rotor angle and voltage stability) in power networks with geographically distributed wind resources in the context of a number of dispatch scenarios based on profiles of historical wind generation for a real power network. Stability issues have been analysed using novel stability indices developed from dynamic characteristics of wind generation. The results of this study show that localised stability issues worsen when significant penetration of both conventional and wind generation is present because of their non-complementary characteristics. In contrast, network stability improves when either high penetration of wind and synchronous generation is present in the network. Therefore network regions can be clustered into two distinct stability groups (i.e. superior stability and inferior stability regions). Network stability improves when a voltage control strategy is implemented at wind farms, however both stability clusters remain unchanged irrespective of change in the control strategy. Moreover, this study has shown that the enhanced fault ride-through strategy for wind farms can improve both voltage and rotor angle stability locally, but only a marginal improvement is evident in neighbouring regions.
As large-scale offshore wind farms are integrated into the power grid, a hybrid multi-infeed HVDC (HMIDC) system including both LCC-HVDC and VSC-HVDC links is facing a critical steady-state voltage ...stability problem which mainly stems from a weak AC system under high-level DC power injections. To overcome this challenge, this paper proposes a general steady-state voltage stability analysis to accurately measure the critical voltage stability point of HMIDC systems. In this paper, a typical HMIDC system is firstly modeled as a general dual-infeed system composed of an LCC-HVDC, a VSC-HVDC, and a virtual equivalent voltage source behind a virtual equivalent impedance at the AC side. Then a hybrid power sensitive factor (HPSF) is established to indicate the critical voltage stability point with the consideration of dynamic power-voltage characteristics of HVDC links, as well as operational changes in AC system (e.g. dynamics of excitation voltage control in generator and network topology change). Finally, a general voltage stability index, called hybrid generalized short circuit ratio (HGSCR), is further derived to effectively explain the critical voltage stability point of HMIDC systems. Moreover, multiple comparative studies with existing voltage stability indices are conducted in this paper to verify the effectiveness of the proposed general steady-state voltage stability analysis by using both PSCAD/EMTDC™ power flow and time-domain simulations.
This article presents the Lyapunov functions based on the artificial intelligence (AI) method for transient stability assessment and the determination of stability region (SR). First, Lyapunov ...stability theory and the definition of SR are introduced. Then, the characteristics of neural networks as a general function approximator are employed as the Lyapunov function learner, and the Lyapunov function is constructed combined with stochastic gradient descent (SGD). Then, the falsifier's task is to find the state vectors that violate Lyapunov stability conditions, and the counterexamples would be added to the training set for the function learner to accelerate convergence. After obtaining the Lyapunov function of power system, the estimation of SR boundary can be represented by the maximum level set of Lyapunov function. Finally, the IEEE 9-bus 3-machine system is used as test system to demonstrate the validity and effectiveness of the proposed construction method of Lyapunov functions for power system transient stability analysis.
Vehicle lateral stability control is one of the most critical aspects of vehicle safety control. In this paper, aiming at keeping the vehicle states (lateral velocity and yaw rate) always in the ...vehicle stability regions, a novel lateral stability control method, which consists of shiftable region-based stability analyses and a corresponding stability controller, is proposed. In the stability analyses, two features of the stability regions are introduced. First, a shifting vector is formulated to explicitly describe the shifting feature of lateral stability regions, so that the shiftable regions are not necessarily re-estimated with respect to a varying steering angle input. Second, dynamic margins of the stability regions are formulated and applied to avoid the penetration of vehicle state trajectory with respect to the stability region boundaries. With these two features, the shiftable stability regions are feasible for an accurate stability analysis, where a projection method is adopted to determine the relative location/distance between the vehicle state point and the closest boundary of the stability region. Based on the analyses, a dynamic sliding mode controller, where the sliding surfaces are selected as the stability region boundaries with the proposed dynamic margins, is designed to keep the vehicle states always in the shiftable stability region. To validate the effectiveness of the proposed control design and analyses, two maneuvers through the co-simulation between Matlab/Simulink and CarSim, namely a high-speed constant cornering and a double lane change maneuvers, are presented and discussed.
In this article, using Lyapunov's stability theorem, the transient stability conditions for a grid-following voltage-source converter (VSC) are found. These conditions take into account both the grid ...specifications and the VSC's dynamics. The derived conditions are based on a well-known nonlinear model of the VSC's phase-locked loop. To evaluate the stability of the nonlinear system, Lyapunov's direct method is employed. To this end, a new Lyapunov's function is proposed, and its characteristics are analyzed. Using this Lyapunov's function, the domain of attraction of the system's equilibrium point is calculated. In addition, a novel system strength index based on the domain of attraction of the system is proposed. The privileges of this index over the conventional indices are absoluteness, VSC's dynamics consideration, and comparability of different VSCs with each other from a stability point of view. In the end, the correctness of the proposed stability analysis is validated via simulation in MATLAB/PLECS and experiment.
We prove characterizations of input-to-state stability (ISS) for a large class of infinite-dimensional control systems, including some classes of evolution equations over Banach spaces, time-delay ...systems, ordinary differential equations (ODE), and switched systems. These characterizations generalize well-known criteria of ISS, proved by Sontag and Wang for ODE systems. For the special case of differential equations in Banach spaces, we prove even broader criteria for ISS and apply these results to show that (under some mild restrictions) the existence of a noncoercive ISS Lyapunov functions implies ISS. We introduce the new notion of strong ISS (sISS) that is equivalent to ISS in the ODE case, but is strictly weaker than ISS in the infinite-dimensional setting and prove several criteria for the sISS property. At the same time, we show by means of counterexamples that many characterizations, which are valid in the ODE case, are not true for general infinite-dimensional systems.
This document is a summary of a report prepared by the IEEE PES Task Force (TF) on Microgrid Stability Definitions, Analysis, and Modeling, IEEE Power and Energy Society, Piscataway, NJ, USA, Tech. ...Rep. PES-TR66, Apr. 2018, which defines concepts and identifies relevant issues related to stability in microgrids. In this paper, definitions and classification of microgrid stability are presented and discussed, considering pertinent microgrid features such as voltage-frequency dependence, unbalancing, low inertia, and generation intermittency. A few examples are also presented, highlighting some of the stability classes defined in this paper. Further examples, along with discussions on microgrid components modeling and stability analysis tools can be found in the TF report.
Grid-synchronization stability (GSS) is an emerging stability issue of grid-tied voltage source converters (VSCs), which can be provoked by severe grid voltage sags. Although a qualitative ...understanding of the mechanism behind the loss of synchronization has been acquired in recent studies, an analytical method for quantitative assessment of GSS of grid-tied VSCs is still missing. To bridge this gap, a dedicated Lyapunov function is analytically proposed, and its corresponding stability criterion for GSS analysis of grid-tied VSCs is rigorously constructed. Both theoretical analysis and simulation result demonstrate that the proposed method can provide a credible GSS evaluation compared to the previous EAC/EF-based method. Therefore, it can be applied for fast GSS evaluation of the grid-tied VSCs as is exemplified in this letter, as well as an analytical tool for some GSS-related issues, e.g., GSS-oriented parameter design and stabilization control.
The large-scale integration of power electronic-based systems poses new challenges to the stability and power quality of modern power grids. The wide timescale and frequency-coupling dynamics of ...electronic power converters tend to bring in harmonic instability in the form of resonances or abnormal harmonics in a wide frequency range. This paper provides a systematic analysis of harmonic stability in the future power-electronic-based power systems. The basic concept and phenomena of harmonic stability are elaborated first. It is pointed out that the harmonic stability is a breed of small-signal stability problems, featuring the waveform distortions at the frequencies above and below the fundamental frequency of the system. The linearized models of converters and system analysis methods are then discussed. It reveals that the linearized models of ac-dc converters can be generalized to the harmonic transfer function, which is mathematically derived from linear time-periodic system theory. Lastly, future challenges on the system modeling and analysis of harmonic stability in large-scale power electronic based power grids are summarized.
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