A smooth model for periodically switched descriptor systems

Switched descriptor systems characterized by a repetitive finite sequence of modes can exhibit state discontinuities at the switching time instants. The amplitudes of these discontinuities depend on the consistency projectors of the modes. A switched ordinary differential equations model whose continuous state evolution approximates the state of the original system is proposed. Sufficient conditions based on linear matrix inequalities on the modes projectors ensure that the approximation error is of linear order of the switching period. The theoretical findings are applied to a switched capacitor circuit and numerical results illustrate the practical usefulness of the proposed model

Stability results for constrained dynamical systems

Differential-Algebraic Equations (DAE) provide an appropriate framework to model and analyse dynamic systems with constraints. This framework facilitates modelling of the system behaviour through natural physical variables of the system, while preserving the topological constraints of the system. The main purpose of this dissertation is to investigate stability properties of two important classes of DAEs. We consider some special cases of Linear Time Invariant (LTI) DAEs with control inputs and outputs, and also a special class of Linear switched DAEs. In the first part of the thesis, we consider LTI systems, where we focus on two properties: passivity and a generalization of passivity and small gain theorems called mixed property. These properties play an important role in the control design of large-scale interconnected systems. An important bottleneck for a design based on the aforementioned properties is their verification. Hence we intend to develop easily verifiable conditions to check passivity and mixedness of Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) DAEs. For linear switched DAEs, we focus on the Lyapunov stability and this problem forms the basis for the second part of the thesis. In this part, we try to find conditions under which there exists a common Lyapunov function for all modes of the switched system, thus guaranteeing exponential stability of the switched system. These results are primarily developed for continuous-time systems. However, simulation and control design of a dynamic system requires a discrete-time representation of the system that we are interested in. Thus, it is critical to establish whether discrete-time systems, inherit fundamental properties of the continuous-time systems from which they are derived. Hence, the third part of our thesis is dedicated to the problems of preserving passivity, mixedness and Lyapunov stability under discretization. In this part, we examine several existing discretization methods and find conditions under which they preserve the stability properties discussed in the thesis

Stability results for constrained dynamical systems

Differential-Algebraic Equations (DAE) provide an appropriate framework to model and analyse dynamic systems with constraints. This framework facilitates modelling of the system behaviour through natural physical variables of the system, while preserving the topological constraints of the system. The main purpose of this dissertation is to investigate stability properties of two important classes of DAEs. We consider some special cases of Linear Time Invariant (LTI) DAEs with control inputs and outputs, and also a special class of Linear switched DAEs. In the first part of the thesis, we consider LTI systems, where we focus on two properties: passivity and a generalization of passivity and small gain theorems called mixed property. These properties play an important role in the control design of large-scale interconnected systems. An important bottleneck for a design based on the aforementioned properties is their verification. Hence we intend to develop easily verifiable conditions to check passivity and mixedness of Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) DAEs. For linear switched DAEs, we focus on the Lyapunov stability and this problem forms the basis for the second part of the thesis. In this part, we try to find conditions under which there exists a common Lyapunov function for all modes of the switched system, thus guaranteeing exponential stability of the switched system. These results are primarily developed for continuous-time systems. However, simulation and control design of a dynamic system requires a discrete-time representation of the system that we are interested in. Thus, it is critical to establish whether discrete-time systems, inherit fundamental properties of the continuous-time systems from which they are derived. Hence, the third part of our thesis is dedicated to the problems of preserving passivity, mixedness and Lyapunov stability under discretization. In this part, we examine several existing discretization methods and find conditions under which they preserve the stability properties discussed in the thesis

Modeling, Simulation, and Analysis of Lithium-Ion Batteries for Grid-Scale Applications

Lithium-ion batteries have become universally present in daily life, being used across a wide range of portable consumer electronics. These batteries are advantageous compared to other forms of energy storage due to their high energy density and long cycle life. These characteristics make lithium-ion batteries advantageous for many new and developing applications that require large scale energy storage such as electric vehicles and the utility grid. Typical uses for lithium-ion batteries require consistent cycling patterns that are predictable and easy to approximate across all uses, but new large scale applications will have much more dynamic demands. The cycling patterns for electric vehicles will vary based on each individuals driving patterns and batteries used for energy storage in the grid must be flexible enough to account for continuous fluctuations in demand and generation with little advanced notice. Along with these requirements, large scale applications do not want to sacrifice on cycle life and need to know that adding batteries will make operational and economic sense in specific cases. It is not possible to experimentally validate every possible driving pattern or grid storage need because of the great expense of these large systems and the long timescale required for testing. Therefore modeling of these systems is advantageous to help study specific application constraints and understand how lithium-ion batteries operate under those constraints. A systems level model is developed to study lithium-ion battery systems for use with solar energy (in a solar-battery hybrid system) and electric vehicles. Electrochemical based battery models are used as a component within larger systems. To facilitate fast simulation a single step perturbation and switch method is outlined for increasing the speed and robustness of solving the systems of DAEs that result from the systems level model. Operational characteristics are studied for lithium-ion batteries used to store solar energy within the electric grid. Different grid demands are tested against the system model to better understand the best uses for the solar-battery hybrid system. Both generic site studies and site specific studies were conducted. Solar irradiance data from 2010-2014 was obtained from 10 US based sites and used as an input to the system model to understand how the same system will operate differently at various locations. Technological benefits such as system autonomy were simulated for each site as well as economic benefits based on a time-of-use pricing scenario. These models included the growth of the solid-electrolyte interface layer on the battery electrodes to measure capacity fade during operation. This capacity fade mechanism allowed tracking of the site specific effects on battery life. A systems level model for an electric vehicle was also developed to simulate the growth of the SEI layer caused from different types of driving cycles and charging patterns. Results from both system models are presented along with an optimization method for the solar-battery hybrid model. In addition to modeling, experimental tests of LiFePO4 lithium-ion battery cells were conducted to measure capacity fade associated with different types of cycling throughout a batterys life. Cycling protocols were tested to study traditional capacity fade and also to focus on increasing a cells lifetime benefit through application switching

Non-linear model predictive energy management strategies for stand-alone DC microgrids

Due to substantial generation and demand fluctuations in stand-alone green micro-grids, energy management strategies (EMSs) are becoming essential for the power sharing purpose and regulating the microgrids voltage. The classical EMSs track the maximum power points (MPPs) of wind and PV branches independently and rely on batteries, as slack terminals, to absorb any possible excess energy. However, in order to protect batteries from being overcharged by realizing the constant current-constant voltage (IU) charging regime as well as to consider the wind turbine operational constraints, more flexible multivariable and non-linear strategies, equipped with a power curtailment feature, are necessary to control microgrids. This dissertation work comprises developing an EMS that dynamically optimises the operation of stand-alone dc microgrids, consisting of wind, photovoltaic (PV), and battery branches, and coordinately manage all energy flows in order to achieve four control objectives: i) regulating dc bus voltage level of microgrids; ii) proportional power sharing between generators as a local droop control realization; iii) charging batteries as close to IU regime as possible; and iv) tracking MPPs of wind and PV branches during their normal operations. Non-linear model predictive control (NMPC) strategies are inherently multivariable and handle constraints and delays. In this thesis, the above mentioned EMS is developed as a NMPC strategy to extract the optimal control signals, which are duty cycles of three DC-DC converters and pitch angle of a wind turbine. Due to bimodal operation and discontinuous differential states of batteries, microgrids belong to the class of hybrid dynamical systems of non-Filippov type. This dissertation work involves a mathematical approximation of stand-alone dc microgrids as complementarity systems (CSs) of Filippov type. The proposed model is used to develop NMPC strategies and to simulate microgrids using Modelica. As part of the modelling efforts, this dissertation work also proposes a novel algorithm to identify an accurate equivalent electrical circuit of PV modules using both standard test condition (STC) and nominal operating cell temperature (NOCT) information provided by manufacturers. Moreover, two separate stochastic models are presented for hourly wind speed and solar irradiance levels

Development of a Dynamic Performance Management Framework for Naval Ship Power System using Model-Based Predictive Control

Medium-Voltage Direct-Current (MVDC) power system has been considered as the trending technology for future All-Electric Ships (AES) to produce, convert and distribute electrical power. With the wide employment of highrequency power electronics converters and motor drives in DC system, accurate and fast assessment of system dynamic behaviors , as well as the optimization of system transient performance have become serious concerns for system-level studies, high-level control designs and power management algorithm development. The proposed technique presents a coordinated and automated approach to determine the system adjustment strategy for naval power systems to improve the transient performance and prevent potential instability following a system contingency. In contrast with the conventional design schemes that heavily rely on the human operators and pre-specified rules/set points, we focus on the development of the capability to automatically and efficiently detect and react to system state changes following disturbances and or damages by incooperating different system components to formulate an overall system-level solution. To achieve this objective, we propose a generic model-based predictive management framework that can be applied to a variety of Shipboard Power System (SPS) applications to meet the stringent performance requirements under different operating conditions. The proposed technique is proven to effectively prevent the system from instability caused by known and unknown disturbances with little or none human intervention under a variety of operation conditions. The management framework proposed in this dissertation is designed based on the concept of Model Predictive Control (MPC) techniques. A numerical approximation of the actual system is used to predict future system behaviors based on the current states and the candidate control input sequences. Based on the predictions the optimal control solution is chosen and applied as the current control input. The effectiveness and efficiency of the proposed framework can be evaluated conveniently based on a series of performance criteria such as fitness, robustness and computational overhead. An automatic system modeling, analysis and synthesis software environment is also introduced in this dissertation to facilitate the rapid implementation of the proposed performance management framework according to various testing scenarios