Stability Performance of Power Electronic Deviceswith Time Delays

This paper deals with the impact of time delays on small-signal stability of power systems with an all converter-interfaced generation. For this purpose, a delay differential algebraic equation model of the voltage source converter and its control scheme is developed. The regulation is based on replicating the dynamical properties of a synchronous machine through appropriate controller configuration. Therefore, a virtual inertia emulation is included in the active power control loop. A transcedental nature of the characteristic equation is resolved by implementing the Chebyshev's discretization method and observing a finite number of critical, low-frequency eigenvalues. Based on the proposed approach, a critical measurement delay is evaluated. Furthermore, a bifurcation analysis of the droop gains and inertia constant is conducted. Stability regions and optimal parametrization of the voltage source converter controls are evaluated and discussed

Computer Aided Analysis of Periodically Switched Linear Networks

Interest in analysing periodically switched linear networks has developed in response to the rapid development of sampled data communications systems. In particular, integrated circuit switched capacitor networks play an important part in modern analogue signal processing systems. This thesis addresses the problem of developing techniques for analysing periodically switched linear networks in the time and frequency domains that are suited to computer implementation and therefore facilitate the development of efficient computer aided analysis tools for these networks. Systems of large sparse complex linear equations arise in many network analysis problems and efficient techniques for solving these systems are crucial to the analysis methods developed in this thesis. By extending the concept of sparsity to include the type of the nonzero elements, very efficient solution and optimal ordering algorithms are developed. A new method for computing the time domain response of linear networks is presented. The method is based on numerical inversion of the Laplace transform and polynomial approximation of the excitations. This high accuracy method is well suited to solving large stiff systems and is extremely efficient. The method is extended to periodically switched linear networks and provides the basis for frequency domain analysis. A new frequency domain analysis method is presented that is orders of magnitude faster than existing techniques. This efficiency is achieved by developing a formulation such that AC analysis is not required, which allows the system to be solved as a discrete system. A special system compression reduces the solution of this discrete system to the solution of the network in one phase only. This solution step, which ordinarily requires O(N3) operations, is made more efficient by reducing the system to upper Hessenberg form in a preprocessing step, which then reduces the solution cost to O(N2) operations

Aproximación de ecuaciones diferenciales mediante una nueva técnica variacional y aplicaciones

[SPA] En esta Tesis presentamos el estudio teórico y numérico de sistemas de ecuaciones diferenciales basado en el análisis de un funcional asociado de forma natural al problema original. Probamos que cuando se utiliza métodos del descenso para minimizar dicho funcional, el algoritmo decrece el error hasta obtener la convergencia dada la no existencia de mínimos locales diferentes a la solución original. En cierto sentido el algoritmo puede considerarse un método tipo Newton globalmente convergente al estar basado en una linearización del problema. Se han estudiado la aproximación de ecuaciones diferenciales rígidas, de ecuaciones rígidas con retardo, de ecuaciones algebraico‐diferenciales y de problemas hamiltonianos. Esperamos que esta nueva técnica variacional pueda usarse en otro tipo de problemas diferenciales. [ENG] This thesis is devoted to the study and approximation of systems of differential equations based on an analysis of a certain error functional associated, in a natural way, with the original problem. We prove that in seeking to minimize the error by using standard descent schemes, the procedure can never get stuck in local minima, but will always and steadily decrease the error until getting to the original solution. One main step in the procedure relies on a very particular linearization of the problem, in some sense it is like a globally convergent Newton type method. We concentrate on the approximation of stiff systems of ODEs, DDEs, DAEs and Hamiltonian systems. In all these problems we need to use implicit schemes. We believe that this approach can be used in a systematic way to examine other situations and other types of equations.Universidad Politécnica de Cartagen

Differential-Algebraic Equations

Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed

Hybrid analysis of nonlinear circuits: DAE models with indices zero and one

We extend in this paper some previous results concerning the differential-algebraic index of hybrid models of electrical and electronic circuits. Specifically, we present a comprehensive index characterization which holds without passivity requirements, in contrast to previous approaches, and which applies to nonlinear circuits composed of uncoupled, one-port devices. The index conditions, which are stated in terms of the forest structure of certain digraph minors, do not depend on the specific tree chosen in the formulation of the hybrid equations. Additionally, we show how to include memristors in hybrid circuit models; in this direction, we extend the index analysis to circuits including active memristors, which have been recently used in the design of nonlinear oscillators and chaotic circuits. We also discuss the extension of these results to circuits with controlled sources, making our framework of interest in the analysis of circuits with transistors, amplifiers, and other multiterminal devices

Numerical Solutions of Systems of Neutral Delay Differential- Algebraic Equations

This paper studies the numerical stability of spline collocation technique for finding the numerical solutions of neutral delay algebraic differential equations (DDEs). The conditions necessary to ensure the widest areas of p-stability of the proposed numerical technique are determined when they are applied to a test problem. The numerical study of convergence shows that the numerical technique proposed when applied to the test of these equations was consistent and convergent from the order ninth. The effectiveness of the proposed spline technique was verified by solving four standard problems in both linear and nonlinear cases. The results of numerical comparisons with some other methods indicate the superiority of our results and the most accurate ones.