Voltage Multistability and Pulse Emergency Control for Distribution System with Power Flow Reversal

High levels of penetration of distributed generation and aggressive reactive power compensation may result in the reversal of power flows in future distribution grids. The voltage stability of these operating conditions may be very different from the more traditional power consumption regime. This paper focused on demonstration of multistability phenomenon in radial distribution systems with reversed power flow, where multiple stable equilibria co-exist at the given set of parameters. The system may experience transitions between different equilibria after being subjected to disturbances such as short-term losses of distributed generation or transient faults. Convergence to an undesirable equilibrium places the system in an emergency or \textit{in extremis} state. Traditional emergency control schemes are not capable of restoring the system if it gets entrapped in one of the low voltage equilibria. Moreover, undervoltage load shedding may have a reverse action on the system and can induce voltage collapse. We propose a novel pulse emergency control strategy that restores the system to the normal state without any interruption of power delivery. The results are validated with dynamic simulations of IEEE $13$-bus feeder performed with SystemModeler software. The dynamic models can be also used for characterization of the solution branches via a novel approach so-called the admittance homotopy power flow method.Comment: 13 pages, 22 figures. IEEE Transactions on Smart Grid 2015, in pres

Practical dwell times for switched system stability with smart grid application

Switched systems are encountered throughout many engineering disciplines, but confirming their stability is a challenging task. Even if each subsystem is asymptotically stable, certain switching sequences may exist that drive the overall system states into unacceptable regions. This thesis contains a process that grants stability under switching to switched systems with multiple operating points. The method linearizes a switched system about its distinct operating points, and employs multiple Lyapunov functions to produce modal dwell times that yield stability. This approach prioritizes practicality and is designed to be useful for large systems with many states and subsystems due to its ease of algorithmic implementation. Power applications are particularly targeted, and several examples are provided in the included papers that apply the technique to boost converters, electric machines, and smart grid architectures --Abstract, page iv

State dependent switching control of affine linear systems with dwell time: application to power converters

This paper addresses a state dependent switching law for the stabilization of continuous-time, switched affine linear systems satisfying dwell time constraints. Such a law is based on the solution of Lyapunov-Metzler inequalities from which stability conditions are derived. The key point of this law is that the switching rule calculation depends on the evolution forward by the dwell time of quadratic Lyapunov functions assigned to each subsystem. As such, the proposed law is readily applicable to power converters showing that it is an interesting alternative to other switching control techniques

Mathematical model of brain tumour with glia-neuron interactions and chemotherapy treatment

Acknowledgements This study was possible by partial financial support from the following Brazilian government agencies: Fundação Araucária, EPSRC-EP/I032606/1 and CNPq, CAPES and Science Without Borders Program Process nos. 17656125, 99999.010583/2013-00 and 245377/2012-3.Peer reviewedPreprin

Structural Systems Inspired by the Architecture of Skeletal Muscle

Modern engineering applications call for structural and material systems that exhibit advanced performance. To achieve this performance, researchers often look to nature for inspiration. Skeletal muscle is a multifunctional system with remarkable versatility and robustness, offering a great example on how to effectively store, convert, and release energy for force generation and shape change. To date, most efforts seeking to emulate muscle have focused on its bulk characteristics. However, it has recently been shown that many of muscle’s advantageous properties arise from the assembly and geometry of its microscale constituents. This dissertation will aim to develop new concepts for structural and material systems inspired by a fundamental understanding of the assembly of muscle’s constituent elements into contractile units. This is achieved by exploiting two key ingredients expressed by these constituents: metastability, which is the existence of multiple stable conformations for a prescribed global geometry, and ¬¬local conformation changes to switch between these stable topologies. Rather than faithfully emulating or seeking to explain the complex chemo-mechanical processes that govern muscle contraction, the major contributions of this thesis arise from the exploitation of the aforementioned key features within the context of engineered structures and materials systems. First, a fundamental metastable unit is studied under harmonic excitation. Experimental, numerical, and analytical investigations uncover the coexistence of multiple response regimes with significantly different amplitudes. These distinct regimes are exploited to achieve highly adaptable energy dissipation characteristics that vary by up to two orders of magnitude among them, even as excitation parameters are held constant. On the other hand, introducing asymmetry by varying a static bias parameter allows for smooth, finer variation of energy dissipation performance. Then, inspired by the ability of the myofibril lattice in skeletal muscle to trap strain energy that can be released on-demand, this thesis explores structural systems that leverage asymmetric multistability for energy capture and storage. The initial kinetic energy from impulsive excitation is shown to trigger state transitions that result in the capture of recoverable strain energy in higher-potential states. Reverse transitions to lower-energy states exploit this stored energy to facilitate efficient deployment and length change in the structure. Lastly, the effect of myofibril lattice spacing in skeletal muscle, and shear-like motions of adjacent filaments during contraction, serves as inspiration for the development of an architected modular material system that uses transverse confinements in conjunction with oblique, shear-like motions to give rise to sudden state transitions. Numerical results provide insight into the experimentally-observed behaviors, revealing that these energy-releasing transitions correspond to discrete changes in reaction force magnitude and direction Mechanical response properties can be tailored by strategic variation of transverse confinement and system geometry. Analytical tools using relatively simple models are developed to offer meaningful prediction of the above features. The overall outcomes of this thesis reveal great potential to develop high-performance, versatile, and adaptable structural and material systems by exploiting fundamental features of skeletal muscle architecture.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145893/1/kidambi_1.pd

Infectious Disease Modeling with Interpersonal Contact Patterns as a Heterogeneous Network

In this thesis, we study deterministic compartmental epidemic models. The conventional mass-mixing assumption is replaced with infectious disease contraction occurring within a heterogeneous network. Modeling infectious diseases with a heterogeneous contact network divides disease status compartments into further sub-compartments by degree class and thus allows for the finite set of contacts of an individual to play a role in disease transmission. These epidemiological network models are introduced as switched systems, which are systems that combine continuous dynamics with discrete logic. Many models are investi- gated, including SIS, SIR, SIRS, SEIR type models, and multi-city models. We analyze the stability of these switched network models. Particularly, we consider the transmission rate as a piecewise constant that changes value according to a switching signal. We establish threshold criteria for the eradication of a disease or stability of an endemic equilibrium using Lyapunov function techniques. Simulations are also conducted to support our claims and conclude conjectures. We test constant control and pulse control schemes, including vaccination, treatment, and screening processes for the application of these infectious disease models. Necessary critical control values are determined for the eradication of the disease