Some Results in Stability Analysis of Hybrid Dynamical Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stability analysis of Crank-Nicolson and Euler schemes for time-dependent diffusion equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A new approach on the stability analysis in ELKO cosmology

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A simulation tool for transient stability analysis on vector computers

This paper deals with transient stability analysis based on time domain simulation on vector processing. This approach requires the solution of a set of differential equations in conjunction of another set of algebraic equations. The solution of the algebraic equations has presented a scalar as sequential set of tasks, and the solution of these equations, on vector computers, has required much more investigations to speedup the simulations. Therefore, the main objective of this paper has been to present methods to solve the algebraic equations using vector processing. The results, using a GRAY computer, have shown that on-line transient stability assessment is feasible.

Sensitivity analysis by neural networks applied to power systems transient stability

This work presents a procedure for transient stability analysis and preventive control of electric power systems, which is formulated by a multilayer feedforward neural network. The neural network training is realized by using the back-propagation algorithm with fuzzy controller and adaptation of the inclination and translation parameters of the nonlinear function. These procedures provide a faster convergence and more precise results, if compared to the traditional back-propagation algorithm. The adaptation of the training rate is effectuated by using the information of the global error and global error variation. After finishing the training, the neural network is capable of estimating the security margin and the sensitivity analysis. Considering this information, it is possible to develop a method for the realization of the security correction (preventive control) for levels considered appropriate to the system, based on generation reallocation and load shedding. An application for a multimachine power system is presented to illustrate the proposed methodology. (c) 2006 Elsevier B.V. All rights reserved.

Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Transient stability indices from a hybrid approach

This paper deals with hybrid method for transient stability analysis combining time domain simulation and a direct method. Nowadays, the step-by-step simulation is the best available tool for allowing the uses of detailed models and for providing reliable results. The main limitation of this approach involves the large time of computational simulations and the absence of stability margin. On the other hand, direct methods, that demand less CPU time, did not show ample reliability and applicability yet. The best way seems to be using hybrid solutions, in which a direct method is incorporated in a time domain simulation tool. This work has studied a direct method using the transient potential and kinetic energy of the critical machine only. In this paper the critical machine is identified by a fast and efficient method, and the proposal is new for using to get stability margins from hybrid approaches. Results from systems, like 16-machine, show stability indices to dynamic security assessment. © 2001 IEEE.

Behavioural Analysis of a Nonlinear Mechanical System Using Transient Trajectories

This work aims at a better comprehension of the features of the solution surface of a dynamical system presenting a numerical procedure based on transient trajectories. For a given set of initial conditions an analysis is made, similar to that of a return map, looking for the new configuration of this set in the first Poincaré sections. The mentioned set of I.C. will result in a curve that can be fitted by a polynomial, i.e. an analytical expression that will be called initial function in the undamped case and transient function in the damped situation. Thus, it is possible to identify using analytical methods the main stable regions of the phase portrait without a long computational time, making easier a global comprehension of the nonlinear dynamics and the corresponding stability analysis of its solutions. This strategy allows foreseeing the dynamic behavior of the system close to the region of fundamental resonance, providing a better visualization of the structure of its phase portrait. The application chosen to present this methodology is a mechanical pendulum driven through a crankshaft that moves horizontally its suspension point.

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.

Analysis of electric torque in single machine-infinite bus system using phase shifters

ResumoThe main idea of this work is based on the analysis of the electric torque through the acting of the PS in the power system, provided of a control for the compensation degree (PSC). A linear model of the single machine-infinite bus system is used with a PS installed (SMIB/PS system). The variable that represents the presence of PS in the net is associated to the phase displacement introduced in the terminal voltage of the synchronous machine by PS. For the input signals of the PSC are evaluated variations of the angular speed of the rotor, the current magnitude and the active power through the line where the PS is located. The simulations are accomplished to analyze the influence of the PS in the torque formation (synchronizing and damping), of the SMIB/PS system. The analysis are developed in the time and frequency domain.

Improving the stability conditions of TS fuzzy systems with fuzzy Lyapunov functions

In this paper, the fuzzy Lyapunov function approach is considered for stabilizing continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing a slack LMI variable into the problem formulation. The stability results are thus used in the state feedback design which is also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilizing conditions presented. © 2011 IFAC.

Robust control applied to power flow control in single-phase inverter with LCL filter, using droop control and D-stability

This paper proposes a new methodology to control the power flow between a distributed generator (DG) and the electrical power distribution grid. It is used the droop voltage control to manage the active and reactive power. Through this control a sinusoidal voltage reference is generated to be tracked by voltage loop and this loop generates the current reference for the current loop. The proposed control introduces feed-forward states improving the control performance in order to obtain high quality for the current injected to the grid. The controllers were obtained through the linear matrix inequalities (LMI) using the D-stability analysis to allocate the closed-loop controller poles. Therefore, the results show quick transient response with low oscillations. Thus, this paper presents the proposed control technique, the main simulation results and a prototype with 1000VA was developed in the laboratory in order to demonstrate the feasibility of the proposed control. © 2012 IEEE.

Stability of nonlinear system using takagi-sugeno fuzzy models and hyper-rectangle of LMIs

This paper presents a theorem based on the hyper-rectangle defined by the closed set of the time derivatives of the membership functions of Takagi-Sugeno fuzzy systems. This result is also based on Linear Matrix Inequalities and allows the reduction of the conservatism of the stability analysis in the sense of Lyapunov. The theorem generalizes previous results available in the literature. © 2013 Brazilian Society for Automatics - SBA.

Semi-analytical study of the rotational motion stability of artificial satellites using quaternions

This study at aims performing the stability analysis of the rotational motion to artificial satellites using quaternions to describe the satellite attitude (orientation on the space). In the system of rotational motion equations, which is composed by four kinematic equations of the quaternions and by the three Euler equations in terms of the rotational spin components. The influence of the gravity gradient and the direct solar radiation pressure torques have been considered. Equilibrium points were obtained through numerical simulations using the softwares Matlab and Octave, which are then analyzed by the Routh-Hurwitz Stability Criterion.

Estabilidade de agregados do solo após manejo com rotações de culturas e escarificação

O objetivo desse trabalho foi avaliar, em solo compactado, a estabilidade dos agregados influenciada pelo cultivo de espécies de cobertura em esquema de rotações de culturas, em sistema de semeadura direta, mediante o efeito da escarificação mecânica. As rotações de culturas repetidas por três anos consecutivos envolveram o cultivo de triticale e girassol, no outono-inverno, associados ao cultivo de milheto, de sorgo forrageiro e de Crotalária júncea como plantas de cobertura, antecedendo o da soja (cultura de verão). No tratamento envolvendo a escarificação mecânica, a área permaneceu em pousio entre os cultivos de outono-inverno e de verão. O experimento foi realizado na Fazenda Experimental Lageado (Botucatu-SP), nos anos agrícolas de 2003/2004, 2004/2005 e 2005/2006. O delineamento experimental foi o de blocos ao acaso, com quatro repetições, em esquema de parcelas subdivididas. As amostras para a análise da estabilidade de agregados foram coletadas nas profundidades de 0 a 0,05 m e de 0,05 a 0,10 m após o manejo das plantas de cobertura em dezembro de 2003 e de 2005. Logo no primeiro ano de instalação do experimento, o cultivo de triticale resultou em maior porcentagem de agregados com mais de 2 mm, maior DMG e maior DMP na camada de 0 a 5 cm, além de maior DMP na camada de 0,05 a 0,10 m. Já a escarificação do solo e a ausência do cultivo de plantas de cobertura proporcionaram menor porcentagem de agregados maiores que 2 mm e menor DMP na camada de 0,05 a 0,10 m. A estabilidade dos agregados foi influenciada pela rotação de culturas, sendo maior na camada de 0 a 0,05 m e de 0,05 a 0,10 m quando o triticale foi introduzido como espécie de outono-inverno.