Criterion For Stability Analysis Research Articles

Oscillation Mechanism and Suppression of Variable-Speed Pumped Storage Unit with Full-Size Converter Based on the Measured Single-Input and Single-Output Impedances

As the penetration rate of clean energy gradually increases, the demand for flexible regulation resources in the power grid is increasing accordingly. The variable-speed pumped storage unit with a full-size converter (FSC-VSPSU) can provide fast and flexible regulation resources for the power grid, which assists in the stable operation of the clean-energy-dominated power systems. Thus, its application is gradually becoming widespread. FSC-VSPSU relies on the power electronic converter for grid connection. When the impedance mismatch between FSC-VSPSU and the power grid occurs, the grid-connected system will experience oscillations, which seriously threatens its safe and stable operation. Aiming at this, this article firstly relies on the SISO impedance measurement and an equivalent impedance analysis to obtain the stability analysis criterion. Furthermore, applying the impedance matching analysis with the Bode diagram, the influence rules of the parameters of the grid-connected FSC-VSPSU on oscillation are obtained. In addition, with the summarized oscillation analysis results, this study delves into an exploration of pertinent strategies for oscillation suppression. Finally, a grid-connected FSC-VSPSU simulation model is built in MATLAB/SIMULINK, and the simulation results verify the correctness of the oscillation analysis results and the effectiveness of the proposed oscillation suppression strategy.

Stability of the wellbore wall during marine hydrate depressurization production based on a modified Drucker-Prager model

Different from oil and gas production, hydrate reservoirs are shallow and unconsolidated, whose mechanical properties deteriorate with hydrate decomposition, so there is a risk of wellbore wall failure during depressurization production. However, the existing researches of wellbore stability focuses on the drilling process, and the stress model used does not taking the effect of casing into account. Therefore, this paper aims to propose an analytical approach suitable for the analysis of wellbore wall stability during production. We proposed a stability analysis criterion based on a modified Drucker-Prager model, derived an effective stress model considering casing-reservoir interaction, established a multi-field coupling model reflecting the dynamic effect of hydrate decomposition, and developed a solver. An experimental system was designed to verify the models. A case study found that the stability is worst near the casing in the direction of maximum horizontal in-situ stress, relatively better in the direction of minimum horizontal in-situ stress, and progressively increase away from the casing. The stability decreases with the decrease of hydrate saturation, and the lower the saturation, the faster the stability decreases. The inhomogeneous of in-situ stress has great influence on the stability, and if it is too high, the wellbore wall will be damaged.

Enhancing fault diagnosis of undesirable events in oil & gas systems: A machine learning approach with new criteria for stability analysis and classification accuracy

Petroleum serves as a cornerstone of global energy supply, underpinning economic development. Consequently, the effective detection of faults in oil and gas (O&G) wells is of paramount importance. In response to the limitations observed in prior research, this study presents an innovative fault diagnosis system, rooted in machine learning techniques. Our approach encompasses a comprehensive analysis, incorporating stability assessment via standard deviation (STD), and a meticulous evaluation of accuracy and stability for distinct fault scenarios. By integrating data preprocessing, feature selection methods, and deploying a robust random forest classifier, our model achieves a substantial enhancement in fault classification accuracy and stability. Extensive experimentation substantiates the superiority of our approach, surpassing the performance of previous studies that predominantly emphasized overall accuracy while disregarding stability analysis. Notably, our model attains remarkable accuracies, notably achieving a flawless 100% accuracy for scenario 3 faults. Detailed examination of mean accuracies and STDs further reinforces the precision and consistency of our model's predictive capabilities. Additionally, a qualitative assessment underscores the practical utility and reliability of our model in accurately identifying critical fault types. This research significantly advances fault detection methodologies within the O&G industry, providing valuable insights for decision-making systems in oil well operations.

Generalized Nonlinear Sector Approaches for Takagi-Sugeno Models

The Nonlinear Sector Approach (NLSA) is a way to construct Takagi-Sugeno (T-S) models which exactly represent nonlinear systems with bounded nonlinearities. Generally, the nonlinearities are bounded by a box-shaped set, however, this paper generalizes the NLSA for polytopic and smooth convex bounding sets, providing new ways of reducing the intrinsic conservatism of T-S representations with interdependent scheduling parameters. Some Linear Matrix Inequalities (LMI) criteria for stability analysis of these models are provided throughout the paper.

Adaptive Fixed-Time Stabilization for a Class of Uncertain Nonlinear Systems

This paper studies the problem of fixed-time stabilization for a class of nonlinear systems with parametric uncertainties, where the nonlinear functions are constrained by an unknown linear growth condition. By establishing a new adaptive fixed-time stability analysis criterion, it is proved that the closed-loop system is fixed-time stable and all the states can be regulated to zero. In addition, the singularity problem caused by the backstepping method under fixed-time control can be avoided. Finally, the effectiveness of the control strategy is verified by a simulation example.

Distributed Fixed Time Control for DC Microgrid with Input Delay

This paper develops a distributed fixed-time quadratic coordinated control strategy for isolated DC microgrids with time delays. The proposed control scheme based on the droop control strategy is intended to realize bus voltage recovery and current balance distribution under time delays. We first model the isolated DC microgrids as a single integrator system with input delays by the Artstein’s transform. The current balance and voltage recovery are achieved by using fixed time control, which does not depend on the initial state of the system. Based on the Lyapunov functional method, the stability analysis criterion of the system is derived. In order to verify the effectiveness of the proposed control method, the DC microgrid system is simulated in Matlab/Simulink.

Robust Delay-Dependent Load Frequency Control of Wind Power System Based on a Novel Reconstructed Model.

This article presents a novel reconstructed model for the delayed load frequency control (LFC) schemes considering wind power, which aims to improve the computational efficiency for PID controllers while retaining their dynamic performance. Via fully exploiting system states influenced by time delays directly, this novel reconstructed method is proposed with a controller isolated. Hence, when the PID controllers are unknown, the stability criterion based on this model can resolve controller gains with less time consumed. For given PID gains, this model can be employed to establish criteria for stability analysis, which can realize the tradeoff between the calculation accuracy and efficiency. The case study is first based on a two-area traditional LFC system to validate the merits of a novel reconstructed model, including accurately estimating the influence of time delay on system frequency stability with increased computational capability. Then, under traditional and deregulated environments, case studies are carried out on the two-area and three-area schemes, respectively. Through the novel reconstructed model, the efficiency of obtaining controller parameters is highly improved while their robustness against the random wind power, tie-line power changes, inertial reductions, and time delays remains almost unchanged.

Optimal Control Measures of COVID-19 in Infected Prey with Harvesting Effort

This paper presents a mathematical model for a prey-predator system in which there are two prey species and one predator species where prey population is taken as competitive of the infected-susceptible species. We analyze and propose the positive, boundedness, and positive equilibrium point of trivial, disease-free, and interior equilibrium point with stability analysis criteria for local stability and applied harvesting effort to control the spread of disease. We analyze numerical simulations showing different scenarios from the maple 15 and 20 programming.

Construction a distributed order smoking model and its nonstandard finite difference discretization

<abstract><p>Smoking is currently one of the most important health problems in the world and increases the risk of developing diseases. For these reasons, it is important to determine the effects of smoking on humans. In this paper, we discuss a new system of distributed order fractional differential equations of the smoking model. With the use of distributed order fractional differential equations, it is possible to solve both ordinary and fractional-order equations. We can make these solutions with the density function included in the definition of the distributed order fractional differential equation. We construct the Nonstandard Finite Difference (NSFD) schemes to obtain numerical solutions of this model. Positivity solutions are preserved under positive initial conditions with this discretization method. Also, since NSFD schemes can preserve all the properties of the continuous models for any discretization parameter, the method is successful in dynamical consistency. We use the Schur-Cohn criteria for stability analysis of the discretized model. With the solutions obtained, we can understand the effects of smoking on people in a short time, even in different situations. Thus, by knowing these effects in advance, potential health problems can be predicted, and life risks can be minimized according to these predictions.</p></abstract>

An improved exponential stability criterion and distributed H ∞ filter design for spatially interconnected discrete-time systems with time-varying delay

This paper proposes an improved exponential stability analysis criterion and designs a distributed filter for a spatially interconnected discrete-time time-varying delay (SIDTD) system. Firstly, combining the Wirtinger-based inequality with reciprocally convex combination inequality, a new and less conservative exponential stability criterion, which guarantees the well-posedness, exponential stability, and performance of the SIDTD system, is reduced to standard linear matrix inequalities. Moreover, we design a distributed structure-preserving filter based on the new stability result. The structure-preserving filter and the delay-free filter can be obtained by employing the Finsler lemma. Finally, the validity and advantages of the derived results are shown by a numerical example and a practical example.

Influence of roll-pitch seeker DRR and parasitic loop on Lyapunov stability of guidance system

This paper focuses on the influence of the disturbance rejection rate (DRR) and parasitic loop parameters on the stability domain of the roll-pitch seeker's guidance system. The DRR models of the roll-pitch seeker caused by different types of disturbance torques and the scale deviation of different sensors are established. The optimal DRR model of the roll-pitch seeker, which contains the scale deviation model, is proposed by formula derivation. The model of the roll-pitch seeker's guidance system is established and equivalently simplified by the dimensionless method. The Lyapunov stability criterion for stability analysis of the guidance system is given by means of the passivity theorem and related definitions and lemmas. A simplified model of the roll-pitch seeker's guidance system, which is suitable for the Lyapunov stability criterion, is established by formula derivation and equivalent transformation. Three conditions that satisfy the Lyapunov stability criterion are obtained. Mathematical simulation with Nyquist plots is used to analyze the influence of different DRR parameters on the stability domain of the roll-pitch seeker's guidance system. Simulation results of this paper can provide reference for the stability analysis of systems related to the roll-pitch seeker.

Delay-Dependent Stability Analysis of Load Frequency Control for Power System With EV Aggregator

In this paper, the stability of load frequency control (LFC) for delayed power systems with an electric vehicle (EV) aggregator is studied based on Lyapunov theory and linear matrix inequalities (LMIs). Through mechanism analysis, the LFC of power systems with an EV aggregator based on a proportional–integral–differential (PID) controller is modeled. By constructing a delay interval information correlation functional and estimating its derivative using Wirtinger inequality and extended reciprocally convex matrix inequality, a new stability analysis criterion is proposed. Finally, in order to verify its advantage, the proposed method is used to discuss the influence of EV aggregator gains and PID controller gains on the delay margins for LFC of power systems with EV aggregator participation in frequency regulation.

Output-feedback photovoltaic WADC by H∞ criterion using auxiliary function

The wide-area damping controller (WADC) is vital in suppressing wide-area oscillations. However, the power system is now developing very fast, traditional output-feedback linear matrix inequality (LMI) criteria adopted in this field may not be very applicable. This paper proposes an output-feedback H∞ robust criterion to design a WADC installed in the photovoltaic plant considering the wide-area signal delay. We use the auxiliary function technique, and adopt Lyapunov functions containing triple summation, augmented variables and cross terms to deduce a stability analysis criterion followed by the corresponding controller design criterion. The low conservatism and control performance of the proposed criteria are verified in a 68-bus 16-machine test system. In addition, as system parameters often change, the control performance of integrating the proposed controller design criterion into a gain scheduling algorithm to handle the system parameter variance is validated.

An effective approach to solving the system of Fredholm integral equations based on Bernstein polynomial on any finite interval

Integral equations are extensively used in many physical models appearing in the field of plasma physics, atmosphere–ocean dynamics, fluid mechanics, mathematical physics and many other disciplines of physics and engineering. In this research work, a new numerical technique for the solution of the system of Fredholm integral equations (FIEs) of both first and second kinds is established, which is based on Bernstein basis functions. Here, the system of FIEs of both kinds has been taken, then reduces the equations to an algebraic linear system and can be solved using any standard rule. Convergence analysis of the proposed technique and some useful numerical results are presented so that the reader could understand this idea easily. Further, Hyers-Ulam stability analysis criteria is used for analyzing the stability of the proposed technique. The comparison of exact and approximate solutions of some problems is demonstrated in tables and their graphs are plotted to show the efficiency of the given technique.

New Instability Criterion for Stability Analysis of Homogeneous Slopes with Double Strength Reduction

Abstract A new instability criterion based on the critical slope concept and the double strength reduction is proposed to evaluate the stability of slopes. In this method, the critical slope contou...

Dual-terminal event triggered control for cyber-physical systems under false data injection attacks

This paper deals with the problem of security-based dynamic output feedback control of cyber-physical systems (CPSs) with the dual-terminal event triggered mechanisms (DT-ETM) under false data injection (FDI) attacks. Considering the limited attack energy, FDI attacks taking place in transmission channels are modeled as extra bounded disturbances for the resulting closed-loop system, thus enabling $H_{\infty}$ performance analysis with a suitable $\varrho$ attenuation level. Then two buffers at the controller and actuator sides are skillfully introduced to cope with the different transmission delays in such a way to facilitate the subsequent security analysis. Next, a dynamic output feedback security control (DOFSC) model based on the DT-ETM schemes under FDI attacks is well constructed. Furthermore, novel criteria for stability analysis and robust stabilization are carefully derived by exploiting Lyapunov-Krasovskii theory and LMIs technique. Finally, an illustrative example is provided to show the effectiveness of the proposed method.

New Instability Criterion for Stability Analysis of Homogeneous Slopes

Abstract A new instability criterion based on the strength reduction method (SRM) is proposed, where the slope is in the limit equilibrium state when the critical slope contour determined by the sl...

Stability Analysis of a Nonlinear MIMO System using Fractional Order Active Disturbance Rejection Controller

The study illustrates a study of fractional order proportional-integral-derivative (FOPID) controller using active disturbance rejection controller. The strategy is applied to a helicopter model of multiple input multiple output system after designing with tuned controller parameters. The motive of the system is to accomplish the control criteria and to investigate the stability of the structure using the principle of non-integer PID controller with a nonlinear feedback and active disturbance rejection. The immense criteria for stability analysis of the coupled system along with the disturbance rejection characteristics are given here in this study. Two new fractional variables as λ and μ are introduced to get better performance. In addition, disturbance control is also implemented from the designed controller.

Net damping criterion for stability analysis of grid-tied VSCs in DC voltage control timescale

Stability of grid-connected VSCs in DC voltage control (DVC) timescales (i.e., the frequency range of dynamics covering converter outer controls) has recently caught increased attention, while the existing approaches, such as eigenvalue analysis and dq-domain impedance analysis, have respective limitations on addressing these types of stability issues. This paper proposes an alternative net damping criterion dedicated for analyzing the DVC timescale stability in a multi-VSC system. This criterion is strictly mapped from the Nyquist stability criterion utilizing the gain margin concept, which preserves the advantages of the classical positive net damping criterion suggested by Canay [20]-allowing for decomposition analysis of a subsystem's contribution to the closed-loop stability in a single-input single-output (SISO) framework, but overcomes its deficiency of possibly erroneous prediction of system dynamic behaviors. Case studies show that the proposed criterion can correctly predict some unstable conditions (e.g., monotonic divergence) which cannot be identified by the classical net damping criterion. Additionally, the condition for when the classical criterion is available is also pointed out, the proposed criterion can also act as a complement of the classical criterion for stability examination.

Stability Analysis for a Class of Discrete-Time Switched Systems With Partial Unstable Subsystems

This brief is concerned with the stability problem for a class of discrete-time switched systems with unstable subsystems. By constructing a quasi-time-dependent Lyapunov function, stability analysis criterion for nonlinear switched systems is developed under a designed switching rule in which the fast and slow switching techniques are adopted for unstable and stable subsystems, respectively. Then, stability criteria for linear switched systems are presented. It is shown that the obtained results are more general and less conservative than existing ones. Some comparative simulations are provided to demonstrate the effectiveness of the proposed method.