Thordur Runolfsson

Uncertainty propagation in dynamical systems

Dynamical propagation of parametric and initial condition uncertainty is studied. The notion of input measure of an observable is defined and its propagation to output measure of the observable is studied by means of transfer operators. Uncertainty of these measures is defined in terms of their cumulative probability distributions. Comparison with alternative uncertainty metrics such as variance and entropy is pursued. The developed formalism is illustrated through an analysis of the effect of pitchfork bifurcation on uncertainty. Finally, the implications of these concepts in the design of nonlinear systems are discussed.

Model reduction of nonreversible Markov chains

In many uncertain complex systems it is observed that the system trajectories cluster in several subsets of the state space. In this paper we model the system behavior as a Markov process and consider the problem of finding a low dimensional approximation of the process that captures the clustering phenomena. Furthermore, we concentrate on Markov chain approximations on a finite state space of large dimension. The problem of finding an approximate low dimensional operator is much simpler when the Markov chain is reversible and several solution approaches have been developed for this case. Most of these approaches rely on spectral properties of the Markov chain. In this paper we consider the general nonreversible case. Our approach is based on a reversibilization procedure, spectral methods for the identification of the dominant components and constrained projection of the original system onto the low dimensional space.

Cluster analysis of wind turbines of large wind farm

Understanding the dynamics of the power output of a wind farm is important to the integration of large scale wind energy into the power system. In a large complex dynamic engineering system, such as a wind farm, clustering is an effective way to reduce the model complexity and improve the understanding of its local dynamics.

State Estimation and Mode Detection for Stochastic Hybrid System

A central issue in real time applications of particle filtering is high computational cost. This problem is particularly compounded when particle filters are used in hybrid system estimation and especially in algorithms based on the interacting multiple model (IMM) algorithm. In this paper a new method for nonlinear/non-Gaussian Markovian switching system state estimation is proposed. The new method combines IMMPF (IMM particle filtering) with ideas from OTPF (observation and transition-based most likely modes tracking particle filtering) in order to get high accuracy estimation with reduced computational load. Simulations are carried out to evaluate the performance of the proposed algorithm. It is shown that the proposed algorithm outperforms OTPF in both accuracy and computation complexity aspect. Compared with IMMPF, the new method performs almost as well as IMMPF but with much lower computational cost.

Efficient estimation of hybrid systems with applications to tracking

Particle filtering has been recognised as a superior alternative to the traditional estimation methods as it is applicable to nonlinear/non-Gaussian system. A central issue in real-time applications of particle filtering is its high computational cost. This problem is compounded when it is used in hybrid system estimation. A new particle filtering method for nonlinear/non-Gaussian hybrid system estimation is proposed in this article. The new method integrates the high-accuracy interacting multiple model particle filtering algorithm with the computationally efficient observation and transition-based most likely modes tracking particle filtering algorithm to get high-accuracy estimation with reduced computational load. The algorithm is applied to a manoeuvring target tracking application to demonstrate its efficiency.

Analysis of wind farm dynamics using multiple doubly fed induction generators

In transient stability analysis, detailed model consisting of hundreds of wind turbines requires an excessive amount of computation. This computation and complexity demands a reduced equivalent model to facilitate the investigation of the impact of a wind farm on the dynamics of the power system to which it is connected. Although few approaches have been developed in aggregating wind turbines, the accuracy of the developed models may not be adequate because aggregation of nonlinear subsystems in a group is inevitably approximate and has to be quantified. This research presents a new mathematical approach of a simplified, reduced order approximate model derived from the aggregation of wind turbines. The effectiveness of the approximate model is demonstrated in an open-loop numerical analysis by comparing the dynamic response of the approximate model with a detailed multi-machine model. Stochastic variation is taken into account for the case studies performed.

A study of short-term impact of wind generation on LOLP

This paper presents a study on the short-term impact of wind generation on Loss of Load Probability, an important generation adequacy measure. Although the capacity provided by wind generation improves the generation adequacy in general, the intermittent and variable wind generation causes short-term variation of LOLP which may impose immediate risks on the system reliability.

Gaussianization of random inputs by filtering plants: The case of poisson white and telegraph processes

It is well known that low-pass filtering plants “harmonize” periodic inputs in the sense that the steady state response in close to harmonic. It has been observed, both experimentally and analytically, that low-pass filters “Gaussianize” some random inputs in the sense that the steady state response is close to being Gaussian. This Technical Note is intended to formalize the notion of Gaussianization and prove that it takes place for two types of input signals: Poisson white noise and telegraph processes. The general case is a subject of future work.

Computation of uncertainty distributions in complex dynamical systems

The computation of the stationary distribution of an uncertain nonlinear dynamical system is an important tool in analysis of the long term behavior of the system. One common approach is to use a Monte Carlo type method. However, that type of method requires many simulations runs to achieve a reasonable accuracy and can be computationally excessive. In this paper we formulate an alternative approach based on the theory of Random Dynamical Systems to solve this problem. Using the properties of the invariant measure of the Perron-Frobenius operator for the dynamical systems we obtain a simple characterization of the stationary distribution. The state space is discretized to obtain a finite dimensional approximation for the infinite dimensional Perron-Frobenius operator. Furthermore, an efficient subdivision algorithm for state space partition is discussed. The approach is demonstrated through a catalytic reactor system.

Risk-sensitive and robust control of discrete time hybrid systems

In this paper we study systems that are subject to sudden structural changes due to either changes in the operational mode of the system or due to failure. We consider linear dynamical systems that depend on a modal variable which is either modeled as a finite state Markov chain or generated by an automaton that is subject to an external disturbance. In the Markov chain case the objective of the control is to minimize a risk sensitive cost functional. The risk sensitive cost functional measures the risk sensitivity of the system to transitions caused by the random modal variable. In the case when a disturbed automaton describes the modal variable, the objective of the control is to make the system as robust to changes in the external disturbance as possible. Optimality conditions for both problems are derived and it is shown that the disturbance rejection problem is closely related to a certain risk sensitive control problem for the hybrid system.