41 research outputs found

    Model Reduction of Hybrid Systems

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    Utilizing Converter-Interfaced Sources for Frequency Control with Guaranteed Performance in Power Systems

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    To integrate renewable energy, converter-interfaced sources (CISs) keep penetrating into power systems and degrade the grid frequency response. Control synthesis towards guaranteed performance is a challenging task. Meanwhile, the potentials of highly controllable converters are far from fully developed. With properly designed controllers the CISs can not only eliminate the negative impacts on the grid, but also provide performance guarantees.First, the wind turbine generator (WTG) is chosen to represent the CISs. An augmented system frequency response (ASFR) model is derived, including the system frequency response model and a reduced-order model of the WTG representing the supportive active power due to the supplementary inputs.Second, the framework for safety verification is introduced. A new concept, region of safety (ROS), is proposed, and the safe switching principle is provided. Two different approaches are proposed to estimate the largest ROS, which can be solved using the sum of squares programming.Third, the critical switching instants for adequate frequency response are obtained through the study of the ASFR model. A safe switching window is discovered, and a safe speed recovery strategy is proposed to ensure the safety of the second frequency dip due to the WTG speed recovery.Fourth, an adaptive safety supervisory control (SSC) is proposed with a two-loop configuration, where the supervisor is scheduled with respect to the varying renewable penetration level. For small-scale system, a decentralized fashion of the SSC is proposed under rational approximations and verified on the IEEE 39-bus system.Fifth, a two-level control diagram is proposed so that the frequency of a microgrid satisfies the temporal logic specifications (TLSs). The controller is configured into a scheduling level and a triggering level. The satisfaction of TLSs will be guaranteed by the scheduling level, and triggering level will determine the activation instant.Finally, a novel model reference control based synthetic inertia emulation strategy is proposed. This novel control strategy ensures precise emulated inertia by the WTGs as opposed to the trial and error procedure of conventional methods. Safety bounds can be easily derived based on the reference model under the worst-case scenario

    Forecasting Passenger Loads in Transportation Networks

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    This work is part of an ongoing effort to understand the dynamics of passenger loads in modern, multimodal transportation networks (TNs) and to mitigate the impact of perturbations. The challenge is that the percentage of passengers at any given point of the TN that have a certain destination, i.e. their distribution over different trip profiles, is unknown. We introduce a stochastic hybrid automaton model for multimodal TNs that allows to compute how such probabilistic load vectors are propagated through the TN, and develop a computation strategy for forecasting the network's load a certain time into the future

    Towards faster numerical solution of Continuous Time Markov Chains stored by symbolic data structures

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    This work considers different aspects of model-based performance- and dependability analysis. This research area analyses systems (e.g. computer-, telecommunication- or production-systems) in order to quantify their performance and reliability. Such an analysis can be carried out already in the planning phase, without a physically existing system. All aspects treated in this work are based on finite state spaces (i.e. the models only have finitely many states) and a representation of the state graphs by Multi-Terminal Binary Decision Diagrams (MTBDDs). Currently, there are many tools that transform high-level model specifications (e.g. process algebra or Petri-Net) to low-level models (e.g. Markov chains). Markov chains can be represented by sparse matrices. For complex models very large state spaces may occur (this phenomenon is called state space explosion in the literature) and accordingly very large matrices representing the state graphs. The problem of building the model from the specification and storing the state graph can be regarded as solved: There are heuristics for compactly storing the state graph by MTBDD or Kronecker data structure and there are efficient algorithms for the model generation and functional analysis. For the quantitative analysis there are still problems due to the size of the underlying state space. This work provides some methods to alleviate the problems in case of MTBDD-based storage of the state graph. It is threefold: 1. For the generation of smaller state graphs in the model generation phase (which usually are easier to solve) a symbolic elimination algorithm is developed. 2. For the calculation of steady-state probabilities of Markov chains a multilevel algorithm is developed which allows for faster solutions. 3. For calculating the most probable paths in a state graph, the mean time to the first failure of a system and related measures, a path-based solver is developed

    Generating Functions of Switched Linear Systems: Analysis, Computation, and Stability Applications

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    In this paper, a unified framework is proposed to study the exponential stability of discrete-time switched linear systems, and more generally, the exponential growth rates of their trajectories, under three types of switching rules: arbitrary switching, optimal switching, and random switching. It is shown that the maximum exponential growth rates of system trajectories over all initial states under these three switching rules are completely characterized by the radii of convergence of three suitably defined families of functions called the strong, the weak, and the mean generating functions, respectively. In particular, necessary and sufficient conditions for the exponential stability of the switched linear systems are derived based on these radii of convergence. Various properties of the generating functions are established and their relations are discussed. Algorithms for computing the generating functions and their radii of convergence are also developed and illustrated through examples

    Essays on dynamic games.

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    ANALYSIS OF BIOPATHWAY MODELS USING PARALLEL ARCHITECTURES

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    Ph.DDOCTOR OF PHILOSOPH
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