Small Signal Stability of an Unregulated Power System

Rotor angle stability is the ability of the interconnected synchronous machines of a power system to remain in synchronism. This stability problem is concerned with the behavior of one or more synchronous machine after they have been perturbed. These perturbations can be small or large depending upon the type of disturbances considered. The work presented in this thesis is focused on the power system behavior when subjected to small disturbances. The ?small signal? disturbances are considered sufficiently small for the linearization of system equations to be permissible for the purpose of the analysis. The first step in the small signal stability studies is to obtain initial steady state conditions using load flow solutions. After establishing initial conditions, an unregulated mathematical model of the power system is formed. The mathematical model obtained is a set of nonlinear coupled first order differential equations. The method of small changes, called the perturbation method, is used to linearize these nonlinear differential equations. The equations are then written in a linear state space model form. The eigenvalues and the participation factors are obtained from the state matrix and the contribution of a particular machine in a particular mode or oscillations (or eigenvalue) can be examined for the small signal stability studies

Transient Stability Analysis of Multi-machine Power System with Automatic Voltage Regulators via Lyapunov's Direct Method

In this paper, Lyapunov's direct method is applied to a multi-machine power system where generators are installed with atuomatic voltage regulators. The automatic voltage regulator and the thyrister exciter are represented by a third order transfer function. The stability of the power system is checked according to a generalized Popov criterion. This criterion guarantees that the system is stable if the gains of the voltage regulators are lower than the limit values. A Lur'e type Lyapunov function is constructed by the systematic method established by J. L. Willems. The obtained Lyapunov function is used in a transient stability analysis of a 10-machine power system. The direct method yields results which are very close to those obtained by simulations. It is concluded that Lyapunov's direct method is applicable with sufficient accuracy to transient stability analyses of power systems, where automatic voltage regulators are installed in generators on the condition that the gains of the automatic voltage regulators must be enlarged to practically used values in the future

Invariant Sets in Quasiperiodically Forced Dynamical Systems

This paper addresses structures of state space in quasiperiodically forced dynamical systems. We develop a theory of ergodic partition of state space in a class of measure-preserving and dissipative flows, which is a natural extension of the existing theory for measure-preserving maps. The ergodic partition result is based on eigenspace at eigenvalue 0 of the associated Koopman operator, which is realized via time-averages of observables, and provides a constructive way to visualize a low-dimensional slice through a high-dimensional invariant set. We apply the result to the systems with a finite number of attractors and show that the time-average of a continuous observable is well-defined and reveals the invariant sets, namely, a finite number of basins of attraction. We provide a characterization of invariant sets in the quasiperiodically forced systems. A theoretical result on uniform boundedness of the invariant sets is presented. The series of theoretical results enables numerical analysis of invariant sets in the quasiperiodically forced systems based on the ergodic partition and time-averages. Using this, we analyze a nonlinear model of complex power grids that represents the short-term swing instability, named the coherent swing instability. We show that our theoretical results can be used to understand stability regions in such complex systems.Comment: 23 pages, 4 figure

Self-Organized Synchronization and Voltage Stability in Networks of Synchronous Machines

The integration of renewable energy sources in the course of the energy transition is accompanied by grid decentralization and fluctuating power feed-in characteristics. This raises new challenges for power system stability and design. We intend to investigate power system stability from the viewpoint of self-organized synchronization aspects. In this approach, the power grid is represented by a network of synchronous machines. We supplement the classical Kuramoto-like network model, which assumes constant voltages, with dynamical voltage equations, and thus obtain an extended version, that incorporates the coupled categories voltage stability and rotor angle synchronization. We compare disturbance scenarios in small systems simulated on the basis of both classical and extended model and we discuss resultant implications and possible applications to complex modern power grids.Comment: 9 pages, 9 figure