Analytical Approximations of Critical Clearing Time for Parametric Analysis of Power System Transient Stability

An analytic approximation for the critical clearing time (CCT) metric is derived from direct methods for power system stability. The formula has been designed to incorporate as many features of transient stability analysis as possible such as different fault locations and different post-fault network states. The purpose of this metric is to analyse trends in stability (in terms of CCT) of power systems under the variation of a system parameter. The performance of this metric to measure stability trends is demonstrated on an aggregated power network, the so-called two machine infinite bus network, by varying load parameters in the full bus admittance matrix using numerical continuation. The metric is compared to two other expressions for the CCT which incorporate additional non-linearities present in the model

Ultra-small low power temperature-to-digital converter and verification methods of analog circuit with Trojan states

Accurate, small and low-power CMOS temperature sensors designed for multi-position temperature monitoring of power management in multi-core processors are proposed. The temperature sensors utilize the temperature characteristics of the threshold voltage of a MOS transistors to sense temperature and are highly linear from 60°C to 90°C. This is the temperature range needed for the power management applications where temperature sensors are strategically placed at multiple locations in each core to protect the processor from temperature-induced reliability degradation. A temperature-to-digital converter (TDC) that does not require either a reference generator or an ADC is also introduced, and it exhibits low supply sensitivity, small die area, and low power consumption. Both analog threshold voltage based temperature sensor and a prototype TDC designed to support multi-position thermal-sensing for power management applications from 60°C to 90°C are implemented in an IBM 0.13μm CMOS process with a 1.2V power supply. A new verification approach with several variants for identifying the number of stable equilibrium points in supply-insensitive bias generators, references, and temperature sensors based upon self-stabilized feedback loops is introduced. This provides a simple and practical method for determining if these circuits require a “start-up” circuit and, if needed, for verifying that the startup circuit is effective at eliminating undesired stable equilibrium points in the presence of process and temperature variations. These undesired stable equilibrium points are often referred to as Trojan states. It will be shown that some widely used approaches for verification do not guarantee Trojan states have been removed. Some of the methods introduced appear to be more practical to work with than others. A group of benchmark circuit with Trojan states will be introduced and used to demonstrate the effectiveness of the new method

Assessment and control of transition to turbulence in plane Couette flow

Transition to turbulence in shear flows is a puzzling problem regarding the motion of fluids flowing, for example, through the pipe (pipe flow), as in oil pipelines or blood vessels, or confined between two counter-moving walls (plane Couette flow). In this kind of flows, the initially laminar (ordered and layered) state of fluid motion is linearly stable, but turbulent (disordered and swirling) flows can also be observed if a suitable perturbation is imposed. This thesis concerns the assessment of transitional properties of such flows in the uncontrolled and controlled environments allowing for the quantitative comparisons of control strategies aimed at suppressing or trigerring transition to turbulence. Efficient finite-amplitude perturbations typically take the form of small patches of turbulence embedded in the laminar flow and called turbulent spots. Using direct numerical simulations, the nonlinear dynamics of turbulent spots, modelled as exact solutions, is investigated in the transitional regime of plane Couette flow and a detailed map of dynamics encompassing the main features found in transitional shear flows (self-sustained cycles, front propagation and spot splitting) is built. The map represents a quantitative assessment of transient dynamics of turbulent spots as a dependence of the relaminarisation time, i.e. the time it takes for a finite-amplitude perturbation, added to the laminar flow, to decay, on the Reynolds number and the width of a localised perturbation. By applying a simple passive control strategy, sinusoidal wall oscillations, the change in the spot dynamics with respect to the amplitude and frequency of the wall oscillations is assessed by the re-evaluation of the relaminarisation time for few selected localised initial conditions. Finally, a probabilistic protocol for the assessment of transition to turbulence and its control is suggested. The protocol is based on the calculation of the laminarisation probability, i.e. the probability that a random perturbation decays as a function of its energy. It is used to assess the robustness of the laminar flow to finite-amplitude perturbations in transitional plane Couette flow in a small computational domain in the absence of control and under the action of sinusoidal wall oscillations. The protocol is expected to be useful for a wide range of nonlinear systems exhibiting finite-amplitude instability

Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion

In this tutorial, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attractors were obtained analytically.Comment: submitted to EP

Fractional derivative models for the spread of diseases

This thesis considers the mathematical modelling of disease, using fractional differential equations in order to provide a tool for the description of memory effects. In Chapter 3 we illustrate a commensurate fractional order tumor model, and we find a critical value of the fractional derivative dependent on the parameter values of the model. For fractional derivatives of orders less than the critical value an unstable equilibrium point of the system becomes stable. In order to show changes in the observed areas of attraction of two stable points in the system, we then consider a fractional order SIR epidemic model and investigate the change from a monostable to a bistable system.;Chapter 4 considers a model for virus dynamics where the fractional orders for populations are different, called an incommensurate system. An approximate analytical solution for the characteristic equation of the incommensurate model is found when the different fractional orders are similar and close to the critical value of the fractional order of the commensurate system. In addition, the instability boundary is found as a function of both parameters. A comparison between analytical and numerical results shows the high accuracy of this approximation.;Chapter 5 consists of two parts, in the first part we generalise the integer Fisher's equation to be a space-time fractional differential equation and consider travelling wave solutions. In the second part we generalise an integer SIR model with spatial heterogeneity, which was studied by Murray [117], to a space-time fractional derivative model. We apply the (G0/G)-expansion method and find travelling wave solutions, although in this case we must consider the Jumarie's modified Riemann-Liouville fractional derivative. Finally, we consider the effect of changing the orders of time and space fractional derivatives on the location and speed of the travelling wave solution.This thesis considers the mathematical modelling of disease, using fractional differential equations in order to provide a tool for the description of memory effects. In Chapter 3 we illustrate a commensurate fractional order tumor model, and we find a critical value of the fractional derivative dependent on the parameter values of the model. For fractional derivatives of orders less than the critical value an unstable equilibrium point of the system becomes stable. In order to show changes in the observed areas of attraction of two stable points in the system, we then consider a fractional order SIR epidemic model and investigate the change from a monostable to a bistable system.;Chapter 4 considers a model for virus dynamics where the fractional orders for populations are different, called an incommensurate system. An approximate analytical solution for the characteristic equation of the incommensurate model is found when the different fractional orders are similar and close to the critical value of the fractional order of the commensurate system. In addition, the instability boundary is found as a function of both parameters. A comparison between analytical and numerical results shows the high accuracy of this approximation.;Chapter 5 consists of two parts, in the first part we generalise the integer Fisher's equation to be a space-time fractional differential equation and consider travelling wave solutions. In the second part we generalise an integer SIR model with spatial heterogeneity, which was studied by Murray [117], to a space-time fractional derivative model. We apply the (G0/G)-expansion method and find travelling wave solutions, although in this case we must consider the Jumarie's modified Riemann-Liouville fractional derivative. Finally, we consider the effect of changing the orders of time and space fractional derivatives on the location and speed of the travelling wave solution

Analog hardware security and hardware authentication

Hardware security and hardware authentication have become more and more important concerns in the manufacture of trusted integrated circuits. In this dissertation, a detailed study of hardware Trojans in analog circuits characterized by the presence of extra operating points or modes is presented. In a related study, a counterfeit countermeasure method based upon PUF authentication circuits is proposed for addressing the growing proliferation of counterfeit integrated circuits in the supply chain. Most concerns about hardware Trojans in semiconductor devices are based upon an implicit assumption that attackers will focus on embedding Trojans in digital hardware by making malicious modifications to the Boolean operation of a circuit. In stark contrast, hardware Trojans can be easily embedded in some of the most basic analog circuits. In this work, a particularly insidious class of analog hardware Trojans that require no architectural modifications, no area or power overhead, and prior to triggering, that leave no signatures in any power domains or delay paths is introduced. The Power/Architecture/Area/Signature Transparent (PAAST) characteristics help the Trojan “hide” and make them very difficult to detect with existing hardware Trojan detection methods. Cleverly hidden PAAST Trojans are nearly impossible to detect with the best simulation and verification tools, even if a full and accurate disclosure of the circuit schematic and layout is available. Aside from the work of the author of this dissertation and her classmates, the literature is void of discussions of PAAST analog hardware Trojans. In this work, examples of circuits showing the existence of PAAST analog hardware Trojans are given, the PAAST characteristics of these types of hardware Trojans are discussed, and heuristic detection methods that can help to detect these analog hardware Trojans are proposed. Another major and growing problem in the modern IC supply chain is the proliferation of counterfeit chips that are often characterized by different or inferior performance characteristics and reduced reliability when compared with authentic parts. A counterfeit countermeasure method is proposed that should lower the entry barrier for major suppliers of commercial off the shelf (COTS) parts to offer authenticated components to the military and other customers that have high component reliability requirements. The countermeasure is based upon a PUF authentication circuit that requires no area, pin, or power overhead, and causes no degradation of performance of existing and future COTS components