Steady-state Stability Analysis Research Articles

Two-species particle aggregation and stability of co-dimension one solutions

Systems of pairwise-interacting particles model a cornucopia of physical systems, from insect swarms and bacterial colonies to nanoparticle self-assembly. We study a continuum model with densities supported on co-dimension one curves for two-species particle interaction in $\mathbb{R}^2$, and apply linear stability analysis of concentric ring steady states to characterize the steady state patterns and instabilities which form. Conditions for linear well-posedness are determined and these results are compared to simulations of the discrete particle dynamics, showing predictive power of the linear theory. Some intriguing steady state patterns are shown through numerical examples.

Evolution of dispersal in open advective environments

We consider a two-species competition model in a one-dimensional advective environment, where individuals are exposed to unidirectional flow. The two species follow the same population dynamics but have different random dispersal rates and are subject to a net loss of individuals from the habitat at the downstream end. In the case of non-advective environments, it is well known that lower diffusion rates are favored by selection in spatially varying but temporally constant environments, with or without net loss at the boundary. We consider several different biological scenarios that give rise to different boundary conditions, in particular hostile and "free-flow" conditions. We establish the existence of a critical advection speed for the persistence of a single species. We derive a formula for the invasion exponent and perform a linear stability analysis of the semi-trivial steady state under free-flow boundary conditions for constant and linear growth rate. For homogeneous advective environments with free-flow boundary conditions, we show that populations with higher dispersal rate will always displace populations with slower dispersal rate. In contrast, our analysis of a spatially implicit model suggest that for hostile boundary conditions, there is a unique dispersal rate that is evolutionarily stable. Nevertheless, both scenarios show that unidirectional flow can put slow dispersers at a disadvantage and higher dispersal rate can evolve.

Stability analysis and implementation of chopper fed DC series motor with hybrid PID-ANN controller

The attempt is made to enhance the performance of a closed loop control of DC series motor fed by DC chopper (DC-DC buck converter) by hybridization of PID controller with an intelligent control using ANN (Artificial Neural Network) controller. This system consists of inner current controller loop and outer PID-ANN based speed controller loop. The current controller allows the PWM (Pulse Width Modulation) signal when the motor current is less than set value. The PID-ANN speed controller controls the motor voltage by controlling the duty cycle of the chopper thereby the motor speed is regulated. The PID-ANN controller performances are analyzed in both steady state and dynamic operating condition with various set speed and various load torque. The rise time, maximum over shoot, settling time, steady state error and speed drops are taken for comparison with conventional PID controller and existing work. The steady state stability analysis of the system also is made by using the transfer function model with MATLAB. The training data for PID-ANN controller is taken from conventional PID controller. The Hybrid PID-ANN controller with DC chopper has better control over the conventional PID controller and the reported existing work. This system is simulated using MATLAB/Simulink and also it is implemented with a NXP 80C51 family Microcontroller (P89V51RD2 BN) based Embedded System.

Configuration of Jacobian Matrix in Steady-State Voltage Stability Analysis Based on Rotor Flux Dynamics of Rotating Machines

Abstract In the existing literatures, modal analysis for steady-state voltage stability is based on the reduced Jacobian matrix, i.e. active power equations are eliminated, and reactive power equations of the constant power/voltage buses (PV buses) are ignored in the polar coordinate expression, which is actually designed for voltage controllability, but questionable for voltage stability.In this article, power outputs of the rotating machines are newly decomposed to the steady-state and dynamic components, with the latter proportional to derivative of the rotor flux. Therefore, neither the active nor the reactive power equations of the rotating machines may be eliminated or ignored in the Jacobian matrix. Only the static buses with constant load impedance should be eliminated. Numerical results show that elimination of active power equations or ignorance of reactive power equations of the rotating machines will yield optimistic stability margins, while including power equations of static load buses yields pessimistic stability margin. It is also find that more static load component yields larger stability margin.

Network Security Assessments for Integrating Large-Scale Tidal Current and Ocean Wave Resources Into Future Electrical Grids

Marine energy, especially tidal current and ocean wave resources, bear immense potential for generating renewable power toward meeting global electricity needs. A number of conversion technologies have been successfully demonstrated worldwide and precommercial/commercial deployments are expected to appear in the near future. While electric power utilities foresee renewable technologies as a viable alternative to fossil fuels, marine energy technologies are generally excluded in their energy planning processes. Lack of technological preparedness and unavailability of device information are two major obstacles in that regard. This article provides an insight on how such novel schemes of power generation can be analyzed under conventional network planning exercises using generic information. The first study focuses on wave power integration along the coasts of Oregon, USA for the year 2019 and analyzes the Northwest electrical network. The second study considers both tidal current and ocean wave resources in South Korea for the years 2017 and 2022. The primary objective of these high-level grid scenario analysis is to identify the practical potential for longer term large-scale wave and/or tidal power generation, particularly focusing on the transmission networks. Steady-state (overloading and voltage deviations/collapses), time-domain (angular stability and dynamic voltage recovery characteristics), and small-signal (eigenvalue) stability analysis are carried out for these systems. Subsequent to establishing a number of study scenarios, N-1 contingencies and various suitable violation criteria are prepared, which are used in identifying the underlying network bottlenecks, especially within the coastal areas. Simplified generic dynamic models of tidal current and ocean wave devices are developed for the time-domain analysis. It is expected that similar studies, once conducted by the interested utilities, will equip them better toward considering marine energy in their future portfolios. In addition, device manufacturers and project developers will have greater confidence in the emerging marine energy market.

Transient Analysis of Large Scale PV Systems with Floating DC Section

The increasing penetration of renewable sources with power-electronic interfaces in power systems is raising technical problems and the overall efficiency of photovoltaic systems can decrease dramatically. In this context, the optimal layout for the photovoltaic system is required. The most adequate strategy to connect the renewable system to the electrical power grid or to supply the end users must be adopted. The present paper proposes a design layout of a PV plant using a DC bus system to improve the overall energy conversion efficiency. An analysis of steady-state system stability, voltage drop and DC cable conduction losses is conducted. The leakage currents to the ground are investigated through simulations. Experimental results are shown focused on the analysis of optimal layout of photovoltaic systems under particular operating conditions.

Dynamic analysis of a simply supported beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes techniques under three-to-one internal resonance condition

In this paper, the Nonlinear Normal Modes (NNMs) analysis for the case of three-to-one (3:1) internal resonance of a slender simply supported beam in presence of compressive axial load resting on a nonlinear elastic foundation is studied. Using the Euler–Bernoulli beam model, the governing nonlinear PDE of the beam’s transverse vibration and also its associated boundary conditions are extracted. These nonlinear motion equation and boundary condition relations are solved simultaneously using four different approximate-analytical solution techniques, namely the method of Multiple Time Scales, the method of Normal Forms, the method of Shaw and Pierre, and the method of King and Vakakis. The obtained results at this stage using four different methods which are all in time–space domain are compared and it is concluded that all the methods result in a similar answer for the amplitude part of the transverse vibration. At the next step, the nonlinear normal modes are obtained. Furthermore, the effect of axial compressive force in the dynamic analysis of such a beam is studied. Finally, under three-to-one-internal resonance condition the NNMs of the beam and the steady-state stability analysis are performed. Then the effect of changing the values of different parameters on the beam’s dynamic response is also considered. Moreover, 3-D plots of stability analysis in the steady-state condition and the beam’s amplitude frequency response curves are presented.

On estimating the basic reproduction number in distinct stages of a contagious disease spreading

In epidemiology, the basic reproduction number R0 is usually defined as the average number of new infections caused by a single infective individual introduced into a completely susceptible population. According to this definition, R0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R0>1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable; when R0<1, the corresponding pathogen tends to naturally disappear because the disease-free stationary solution is asymptotically stable. Here we intend to answer the following question: Do these two different approaches for calculating R0 give the same numerical values? In other words, is the number of secondary infections caused by a unique sick individual equal to the threshold obtained from stability analysis of steady states of ODE? For finding the answer, we use a susceptible-infective-recovered (SIR) model described in terms of ODE and also in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. The values of R0 obtained from both approaches are compared, showing good agreement.

Stability and Oscillations of Electrical Machines of Alternating Current

AbstractAn induction machine with the squirrel cage rotor and a synchronous machine with the four-pole rotor are considered and the new mathematical models of these machines are developed. The analysis of steady-state and dynamic stability of the systems, describing the electrical machines, is performed. The limit load problem is discussed and analytical and numerical estimations of the limit load for considered electrical machines are obtained by the equal-area method and the non-local reduction method. In the case of second method improved estimates of the limit load in comparison to the estimates, obtained by the equal-area criterion, are found.

Gramians Method of Steady-State Stability Analysis for Large Electrical Power Systems

This paper provides a new approach to computing infinite and finite time Gramians and cross-Gramians relying on the usage of the Laplacian transformation of matrix exponential time functions and expansion of the product of these functions. The expansions are bilinear and quadratic forms of sequences of the Faddeev matrices generated by resolvents of original matrices. Matrix identities are obtained for bilinear and quadratic forms of these Faddeev sequences. Asymptotic expansions of controllability and observability Gramians of dynamic systems at the proximity of stability limit are found. Illustrative examples are given to demonstrate the perspective of using Gramians for the small-signal stability analysis of the electric power systems.

Analysis of Steady State Stability of a Csi Fed Synchronous Motor Drive System with Damper Windings Included

Analysis of Steady State Stability of a Csi Fed Synchronous Motor Drive System with Damper Windings Included

Steady-State Stability of Current-Mode Active-Clamp ZVS DC–DC Converters

Active-clamp dc-dc converters are pulsewidth-modulated converters having two switches featuring zero-voltage switching at frequencies beyond 100 kHz. Generalized equivalent circuits valid for steady-state and dynamic performance have been proposed for the family of active-clamp converters. The active-clamp converter is analyzed for its dynamic behavior under current control in this paper. The steady-state stability analysis is presented. On account of the lossless damping inherent in the active-clamp converters, it appears that the stability region in the current-controlled active-clamp converters get extended for duty ratios, a little greater than 0.5 unlike in conventional hard-switched converters. The conventional graphical approach fails to assess the stability of current-controlled active-clamp converters, due to the coupling between the filter inductor current and resonant inductor current. An analysis that takes into account the presence of the resonant elements is presented to establish the condition for stability. This method correctly predicts the stability of the current-controlled active-clamp converters. A simple expression for the maximum duty cycle for subharmonic-free operation is obtained. The results are verified experimentally.

Stability Analysis of Series Parallel Resonant Converter with Fuzzy Logic Controller Using State Space Techniques

A closed-loop inductance capacitance inductance-T (LCL-T) series parallel resonant converter has been simulated and presented in this article. The fuzzy logic controller has been used for closed-loop operation, and the performance of the proposed converter has been estimated with a closed-loop condition. The steady-state stability analysis of the LCL-T series parallel resonant converter has been analyzed using the state-space model and simulated using MATLAB (The MathWorks, Natick, Massachusetts, USA). The proposed approach is expected to provide better voltage regulation for dynamic load conditions. A prototype 300-W, 100-kHz converter is designed and built for experimental demonstrations, and transient and steady-state performances for the LCL-T series parallel resonant converter are compared from the simulation studies.

The Glansdorff–Prigogine stability criterion for biochemical reaction networks

Local stability analysis of steady states in mathematical models of biochemical reaction networks is an important tool for systems biology. The second variation of the Gibbs energy around a steady state is a positive definite function and a candidate for a Lyapunov function. A sufficient condition for the local stability is the local negative definiteness of the time derivative of this function. This is expressed by the Glansdorff–Prigogine stability criterion. Previously, the criterion was criticized to be overly conservative and difficult to check. Here, we derive an easily testable form of the criterion for models of biochemical networks. The criterion can be evaluated with incomplete knowledge of the parameters. For ideal mass-action kinetics, it depends only on the steady state fluxes. For reaction systems in ideal solutions, the Glansdorff–Prigogine criterion is overly conservative and we give a tighter criterion that depends on the same subset of the parameters as the Glansdorff–Prigogine criterion. Whenever these criteria are indefinite, there exist parameter values such that the steady state is unstable. By means of simple example systems we explore these aspects and discuss the possible uses of the criteria for systems biology.

A stability analysis of the power-law steady state of marine size spectra

This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.

Lewis number effect on the propagation of premixed flames in narrow adiabatic channels: Symmetric and non-symmetric flames and their linear stability analysis

The propagation of premixed flames with different Lewis numbers in a planar channel subject to a Poiseuille flow is considered within the diffusive-thermal model for steady and time-dependent cases. It was found that, depending on the Lewis number and the flow rate, symmetric and non-symmetric flames are possible. The existence of multiple steady solutions in cases of the low Lewis number is demonstrated. The time-dependent simulations carried out for high Lewis number flames also showed the symmetric and non-symmetric oscillatory solutions. Linear stability analysis of two-dimensional steady-states was performed using a practical method developed in the paper and applied to calculate the main eigenvalue. It was shown that for symmetric flames with a low Lewis number the increase in the flow rate leads to a loss of stability with subsequent formation of non-symmetric solutions. For flames with a high Lewis number the Poiseuille flow produces a stabilization effect. The results of the stability analysis were successfully compared with the results of direct numerical simulations.

Linear and Nonlinear Stability Analysis of a Supercritical Natural Circulation Loop

Supercritical water (SCW) has excellent heat transfer characteristics as a coolant for nuclear reactors. Besides it results in high thermal efficiency of the plant. However, the flow can experience instabilities in supercritical water cooled reactors, as the density change is very large for the supercritical fluids. A computer code SUCLIN has been developed employing supercritical water properties to carry out the steady-state and linear stability analysis of a SCW natural circulation loop (SCWNCL). The conservation equations of mass, momentum, and energy have been linearized by imposing small perturbation in flow rate, enthalpy, pressure, and specific volume. The equations have been solved analytically to generate the characteristic equation. The roots of the equation determine the stability of the system. The code has been benchmarked against published results. Then the code has been extensively used for studying the effect of diameter, heater inlet temperature, and pressure on steady-state and stability behavior of a SCWNCL. A separate computer code, NOLSTA, has been developed, which investigates stability characteristics of supercritical natural circulation loop using nonlinear analysis. The conservation equations of mass, momentum, and energy in transient form were solved numerically using finite volume method. The stable, unstable, and neutrally stable points were identified by examining the amplitude of flow and temperature oscillations with time for a given set of operating conditions. The stability behavior of loop, predicted using nonlinear analysis has been compared with that obtained from linear analysis. The results show that the stability maps obtained by the two methods agree qualitatively. The present paper describes the linear and nonlinear stability analysis models and the results obtained in detail.

Steady-State Stability of Current Mode Active-Clamp ZVS DC–DC Converters

Active-clamp dc-dc converters are pulsewidth-modulated converters having two switches featuring zero-voltage switching at frequencies beyond 100 kHz. Generalized equivalent circuits valid for steady-state and dynamic performance have been proposed for the family of active-clamp converters. The active-clamp converter is analyzed for its dynamic behavior under current control in this paper. The steady-state stability analysis is presented. On account of the lossless damping inherent in the active-clamp converters, it appears that the stability region in the current-controlled active-clamp converters get extended for duty ratios, a little greater than 0.5 unlike in conventional hard-switched converters. The conventional graphical approach fails to assess the stability of current-controlled active-clamp converters, due to the coupling between the filter inductor current and resonant inductor current. An analysis that takes into account the presence of the resonant elements is presented to establish the condition for stability. This method correctly predicts the stability of the current-controlled active-clamp converters. A simple expression for the maximum duty cycle for subharmonic-free operation is obtained. The results are verified experimentally.

A Steady-State Voltage Stability Analysis of Power Systems With High Penetrations of Wind

As wind generation begins to contribute significantly to power systems, the need arises to assess the impact of this new source of variable generation on the stability of the system. This work provides a detailed methodology to assess the impact of wind generation on the voltage stability of a power system. It will also demonstrate the value of using time-series ac power flow analysis techniques in assessing the behavior of a power system. Traditional methods are insufficient in describing the nature of wind for steady-state analyses, and as such, a new methodology is presented to address this issue. Using this methodology, this paper will show how the voltage stability margin of the power system can be increased through the proper implementation of voltage control strategies in wind turbines.

Turing bifurcation in a reaction–diffusion system with density-dependent dispersal

Motivated by the recent finding [N. Kumar, G.M. Viswanathan, V.M. Kenkre, Physica A 388 (2009) 3687] that the dynamics of particles undergoing density-dependent nonlinear diffusion shows sub-diffusive behaviour, we study the Turing bifurcation in a two-variable system with this kind of dispersal. We perform a linear stability analysis of the uniform steady state to find the conditions for the Turing bifurcation and compare it with the standard Turing condition in a reaction–diffusion system, where dispersal is described by simple Fickian diffusion. While activator–inhibitor kinetics are a necessary condition for the Turing instability as in standard two-variable systems, the instability can occur even if the diffusion constant of the inhibitor is equal to or smaller than that of the activator. We apply these results to two model systems, the Brusselator and the Gierer–Meinhardt model.