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Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather than studying existence in a specific equation, we study properties of spiral waves in general reaction-diffusion systems. We show that many features of spiral waves are robust and to some extent independent of the specific model analyzed. To accomplish this, we present a suitable analytic framework, spatial radial dynamics, that allows us to rigorously characterize features such as the shape of spiral waves and their eigenfunctions, properties of the linearization, and finite-size effects. We believe that our framework can also be used to study spiral waves further and help analyze bifurcations, as well as provide guidance and predictions for experiments and numerical simulations. From a technical point of view, we introduce non-standard function spaces for the well-posedness of the existence problem which allow us to understand properties of spiral waves using dynamical systems techniques, in particular exponential dichotomies. Using these pointwise methods, we are able to bring tools from the analysis of one-dimensional coherent structures such as fronts and pulses to bear on these inherently two-dimensional defects.

Wind shear and tower shadow produce a periodic pulse reduction in mechanical torque captured from wind energy resulting in wind energy conversion system (WECS) active power oscillations. In this study, an adaptive neuro-fuzzy controller for static VAR compensator, used in power networks integrated with WECS, is presented to address the torque oscillation problem. The proposed controller consists of a radial basis function neural network representing a third-order auto-regressive and moving average system model and performing the prediction, and a main controller with adaptive neuro-fuzzy inference system providing the damping signal. A modified two-area four-machine power network with WECS integration is applied to validate the proposed implementation, compared with conventional lead/lag compensation. Time-domain simulations prove that the proposed controller can provide a damping signal to improve the active power oscillation and system dynamic stability, influenced by torque oscillations under WECSs synchronised operating condition.

As the integration of distributed generation units into the power grid continues to grow, the system becomes increasingly vulnerable to power fluctuations and potential failures, which significantly challenge grid stability. Virtual synchronous generators (VSGs) have emerged as a key technology to enhance grid stability by emulating the behavior of traditional synchronous generators. However, with multiple VSGs operating within independent microgrids, coordinating their control parameters becomes critical to ensuring stable and reliable operation. This article proposes an optimization method based on the gradient descent algorithm to fine‐tune the control parameters of multiple VSGs in independent microgrids. A small‐signal model for microgrids with multiple VSGs is developed to analyze the system's dynamic behavior under small disturbances. The proposed method optimizes VSG control parameters to improve the frequency and voltage dynamic response and enhance the overall system stability. The simulation results demonstrate that the proposed multi‐VSG control parameter optimization method significantly enhances the frequency and voltage dynamic response, as well as the stability of the independent microgrid under small disturbances, offering a practical solution for improving microgrid performance in real‐world applications. This article establishes the small signal model of independent microgrid and then the multi‐VSG control parameters are optimized by the gradient descent method based on the proposed small signal model and the optimal damping ratio of the system eigenvalues. The simulation and optimization results show that the proposed multi‐VSG control parameter optimization method based on the gradient descent method can improve the frequency and voltage dynamic response and the stability of independent microgrid system under small disturbances and has practical application value.

Power system stability characteristics are typically evaluated in terms of small‐ and large‐signal (transient) stability. Access to the time‐varying A‐matrix of a state‐space‐based power systems model during transient conditions can be utilized to apply linear time‐varying system concepts for large‐signal stability analysis. In linear time‐varying system analysis, the differential Riccati equation (DRE) plays a vital role when the power system is subjected to a severe disturbance. The Möbius transformation is proposed in this paper to solve the DRE with singularity issues. It is shown that the solution of the DREs follows a specific mathematical pattern when the power system is stable but does not follow this pattern when the system progresses toward instability. The proposed method can be used in large‐signal stability analysis to predict instability and make the stability analysis more efficient. Additionally, the vector‐DRE is proposed to generalize the index in a large‐scale power system. Results show that analyzing the corresponding Riccati equation's behaviour can help researchers predict a power system's performance and improve the control and management of the system. Access to the time‐varying A‐matrix of a state‐space‐based power systems model during transient conditions can be utilized to apply linear time‐varying system. The solution of the DREs follows a specific mathematical pattern when the power system is stable but does not follow this pattern when the system progresses toward instability. Results show that analysing the corresponding Riccati equation's behaviour can help researchers predict a power system's performance and improve the control and management of the system.

In this study, a novel approach is proposed for fast prediction of dynamic voltage instability occurrence (as a short term phenomenon and/or a long term one) and voltage stability stiffness of the system, against load disturbances. The main contribution of this paper is in introducing a procedure for generating novel features to be applied to a pattern classifier, by which dynamic voltage stability status of a power system can be predicted. The proposed feature generation procedure only needs measured pre-disturbance variables and disturbance severity provided by phasor measurement units as inputs whereas a set of output variables are derived from an unconstrained power flow program. Since the proposed method does not need any measured post disturbance data, the prediction task can be performed just after the disturbance. Thus, corrective actions can be executed in a short time after the disturbance to inhibit voltage instability. Moreover as no measured post-disturbance data are needed, the proposed method can also be employed in preventive procedures for voltage stability enhancement and/or decreasing possibility of voltage instability occurrence. Training a decision tree based classifier with the proposed features and testing the method on a modified version of Nordic32 test system, the simulation results have demonstrated that the proposed method effectively predicts the status of dynamic voltage stability in the test system.

The integration of a flexible alternating current transmission system (FACTS) and a power system stabilizer (PSS) can increase dynamic stability. This paper presents the enhancement of power system dynamic stability through the optimal design of a power system stabilizer and UPFC using an ant lion optimization (ALO) technique to enhance transmission line capacity. The gained damping ratio, eigenvalue and time domain results of the suggested ALO technique were compared with a base case system, ALO-based PSS and ALO-based PSS-UPFC to test the effectiveness of the proposed system in different loading cases. Eigenvalues gained from an ant lion approach-based UPFC with a PSS and a base case system are compared to examine the robustness of the ALO method for various loading conditions. Thus, this paper addresses the mechanism regarding the power system dynamic stability of transmission lines by integrating the optimal size of a PSS and UPFC into the power system. Therefore, the main contribution of this manuscript is the optimal coordination of a power system stabilizer, power oscillation damper and unified power flow using ant lion optimization for the mitigation of low-frequency oscillation.

Focusing on the identification of dynamic system stability, a hybrid neural network model is proposed in this research for the rotating stall phenomenon in an axial compressor. Based on the data fusion of the amplitude of the spatial mode, the nonlinear property is well characterized in the feature extraction of the rotating stall. This method of data processing can effectively avoid the inaccurate recognition of single or multiple measuring sensors only depending on pressure. With the analysis on the spatial mode, a chaotic characteristic was shown in the development of the amplitude with the first-order spatial mode. With the prerequisite of revealing the essence of this dynamic system, a hybrid radial basis function (RBF) neural network was adopted to represent the properties of the system by artificial intelligence learning. Combining the advantages of the methods of K-means and Gradient Descent (GD), the Chaos–K-means–GD–RBF fusion model was established based on the phase space reconstruction of the chaotic sequence. Compared with the two methods mentioned above, the calculation accuracy was significantly improved in the hybrid neural network model. By taking the strategy of global sample entropy and difference quotient criterion identification, a warning of inception can be suggested in advance of 12.3 revolutions (296 ms) with a multi-step prediction before the stall arrival.

Consider a general linear Hamiltonian system

In this study, a novel dynamic paradigm aimed at solving the power flow equations in both solvable and unsolvable region is proposed. The challenging idea is to reformulate the power flow equations into a set of ordinary differential equations, whose equilibrium points represent the power flow problem solutions. Starting from the Lyapunov theory, the authors demonstrate that this system of dynamic equations is characterised by an exponential asymptotic convergence to equilibrium points. This feature allows us to overcome the inherent limitations of the traditional iterative minimisation algorithms that can fail to converge because of the highly non-linearities of the first-order condition. Extensive simulation studies aimed at demonstrating the effectiveness of the proposed methodology are presented and discussed.

Quickly getting back the synchronism of a disturbed interconnected multi area power system due to variations in loading condition is recognized as prominent issue related to automatic generation control (AGC). In this regard, AGC system based on fuzzy logic, i.e., so-called FLAGC can introduce an effectual performance to suppress the dynamic oscillations of tie-line power exchanges and frequency in multi-area interconnected power system. Apart from that, simultaneous coordination scheme based on particle swarm optimization (PSO) along with real coded genetic algorithm (RCGA) is suggested to coordinate FLAGCs of the all areas. To clarify the high efficiency of aforementioned strategy, two different interconnected multi area power systems, i.e., three-area hydro-thermal power system and five-area thermal power system have been taken into account for relevant studies. The potency of this strategy has been thoroughly dealt with by considering the step load perturbation (SLP) in both the under study power systems. To sum up, the simulation results have plainly revealed dynamic performance of FLAGC as compared with conventional AGC (CAGC) in each power system in order to damp out the power system oscillations.