Unified knowledge model for stability analysis in cyber physical systems

The amalgamation and coordination between computational processes and physical components represent the very basis of cyber-physical systems. A diverse range of CPS challenges had been addressed through numerous workshops and conferences over the past decade. Finding a common semantic among these diverse components which promotes system synthesis, verification and monitoring is a significant challenge in the cyber-physical research domain. Computational correctness, network timing and frequency response are system aspects that conspire to impede design, verification and monitoring. The objective of cyber-physical research is to unify these diverse aspects by developing common semantics that span each aspect of a CPS. The work of this thesis revolves around the design of a typical smart grid-type system with three PV sources built with PSCADʼ. A major amount of effort in this thesis had been focused on studying the system behavior in terms of stability when subjected to load fluctuations from the PV side. The stability had been primarily reflected in the frequency of the generator of the system. The concept of droop control had been analyzed and the parameterization of the droop constant in the shape of an invariant forms an essential part of the thesis as it predicts system behavior and also guides the system within its stable restraints. As an extension of a relationship between stability and frequency, the present study goes one step ahead in describing the sojourn of the system from stability to instability by doing an analysis with the help of tools called Lyapunov-like functions. Lyapunov-like functions are, for switched systems, a class of functions that are used to measure the stability for non linear systems. The use of Lyapunov-like functions to judge the stability of this system had been tested and discussed in detail in this thesis and simulation results provided --Abstract, page iii

Application of unified invariants for cyber physical systems in smart grids

Cyber-Physical Systems (CPS) are complex engineered systems which consist of physical components with an underlying cyber network. The three main components of a cyber-physical System are: physical system, networking and communications element and a distributed cyber system. The primary challenge for cyber-physical systems is to understand what happens when various sub-systems, which have been developed in an isolated environment, are integrated. CPS studies need to ensure sub-systems that had been designed in isolation to meet certain specifications, when combined, do not cause the overall system to fail. The crux of cyber-physical research is thus to find a common platform to bind all these different components, so as to monitor the overall system performance. This dissertation discusses how to unify these different aspects and tackles the issue of synthesizing, verifying and monitoring highly diverse environments by introducing the concept of Unified Invariants. In this dissertation, a smart grid has been used to implement and validate this concept of Unified Invariants towards building a robust cyber-physical system. There are several ways to compromise the reliable operation of a smart grid. Examples of such contingent events are voltage collapse, line overloading and dynamic instability. Physical system invariants have been developed to identify and thwart such events which threaten the integrity of the physical system. These physical invariants have be integrated with cyber controllers to ensure a safe, stable and reliable operation of the smart grid. This is an unique concept and differs from previous methods in the fact that while earlier methods have tried to compose functionality of each domain of the cyber-physical world, the Unified Invariant method serves as a transformative approach to express and impose system properties that are common to all the domains (cyber, physical, networking). The net outcome of such an approach is that the resulting CPSs will be safe and stable at the system level, rather than just the sub-system level. --Abstract, page iii

Metal-Alloy Cu Surface Passivation Leads to High Quality Fine-Pitch Bump-Less Cu-Cu Bonding for 3D IC and Heterogeneous Integration Applications

In this paper, we report a low temperature, fine-pitch, bump-less, damascene compatible Cu-Cu thermocompression bonding, using an optimized ultra-thin passivation layer, Constantan, which is an alloy (Copper-Nickel) of 55% Cu and 45% Ni. Surface oxidation and its roughness are the major bottlenecks in achieving high quality, low temperature, and fine-pitch Cu-Cu bonding. In this endeavor, we have used Cu rich alloy (Constantan) for passivation of Cu surface prior to bonding. We have systematically optimized the constantan passivation layer thickness for high quality low temperature, low pressure, bump-less Cu-Cu bonding. Also, we have studied systematically the efficacy of Cu surface passivation with optimized ultra-thin constantan alloy passivation layer. After rigorous trial and optimization, we successfully identified 2 nm passivation layer thickness, at which very high quality Cu-Cu bonding could be accomplished at sub 200 °C with a nominal contact pressure of 0.4 MPa. Post-bonding, electrical and mechanical characterization were validated using four-probe IV measurement and bond strength measurement respectively. Furthermore, Cu-Cu bonding interface was analyzed using IR wafer bonder inspection tool. Very high bond strength of 163 MPa and defect free interface observed by WBI-IR clearly suggests, Cu-Cu finepitch bonding with optimized ultra-thin alloy of 2 nm thick constantan, is of very high quality and reliable. Moreover, this novel bonding approach with alloy based interconnect passivation technique is the prime contestant for future heterogeneous integration

Topological Deep Learning: Going Beyond Graph Data

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains. Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that maintain certain desirable properties. Similar to hypergraphs, combinatorial complexes impose no constraints on the set of relations. In addition, combinatorial complexes permit the construction of hierarchical higher-order relations, analogous to those found in simplicial and cell complexes. Thus, combinatorial complexes generalize and combine useful traits of both hypergraphs and cell complexes, which have emerged as two promising abstractions that facilitate the generalization of graph neural networks to topological spaces. Second, building upon combinatorial complexes and their rich combinatorial and algebraic structure, we develop a general class of message-passing combinatorial complex neural networks (CCNNs), focusing primarily on attention-based CCNNs. We characterize permutation and orientation equivariances of CCNNs, and discuss pooling and unpooling operations within CCNNs in detail. Third, we evaluate the performance of CCNNs on tasks related to mesh shape analysis and graph learning. Our experiments demonstrate that CCNNs have competitive performance as compared to state-of-the-art deep learning models specifically tailored to the same tasks. Our findings demonstrate the advantages of incorporating higher-order relations into deep learning models in different applications

Markov jump linear system analysis of microgrid stability

In a typical microgrid, the power generation capacity is similar to the maximum total load. The low inertia of the system provides little margin for error in the power balance, both active and reactive, and requires rapid control response to load changes. In the present work, a microgrid is modeled as a Markov jump linear system (MJLS). An MJLS is a dynamic system with continuous states governed by one of a set of linear systems, and a continuous-time Markov process that determines which linear system is active. When the discrete state of the Markov process changes, there is a \u27jump\u27 in the dynamics of the continuous states. In addition, the jump may be impulsive. The present work first explores impulsive MJLS stability. Conservative bounds on the expected value of the state are determined from a combination of the Markov process parameters, the dynamics of each linear system, and the magnitude of the impulses. Then the microgrid model is cast into the MJLS framework and stability analysis is performed. The conclusions are verified with detailed simulations

On magnon mediated Cooper pair formation in ferromagnetic superconductors

Identification of pairing mechanism leading to ferromagnetic superconductivity is one of the most challenging issues in condensed matter physics. Although different models have been proposed to explain this phenomenon, a quantitative understanding about this pairing is yet to be achieved. Using the localized-itinerant model, we find that in ferromagnetic superconducting materials both triplet pairing and singlet pairing of electrons are possible through magnon exchange depending upon whether the Debye cut off frequency of magnons is greater or lesser than the Hund's coupling (J) multiplied by average spin (S) per site. Taking into account the repulsive interaction due to the existence of paramagnons, we also find an expression for effective interaction potential between a pair of electrons with opposite spins. We apply the developed formalism in case of UGe2 and URhGe. The condition of singlet pairing is found to be fulfilled in these cases, as was previously envisaged by Suhl [Suhl, Phys. Rev. Lett. 87, 167007 (2001)]. We compute the critical temperatures of URhGe at ambient pressure and of UGe2 under different pressures for the first time through BCS equation. Thus, this work outlines a very simple way to evaluate critical temperature in case of a superconducting system. A close match with the available experimental results strongly supports our theoretical treatment

Voltage Stability Preserving Invariants for Smart Grids

Voltage stability analysis is essential in any power system. This paper addresses the voltage stability in a typical smart grid type system with multiple independent entities. A typical smart grid operation involves various loading excursions (changes in power, both generated and consumed) undertaken by all these independent entities. For a smooth functioning of any generic smart grid type system, correct behavior of all these independent entities must be preserved when one or more of these entities are subjected to various loading levels. Correct behavior of all the entities (sub-systems) will ensure correct behavior of the overall system (smart grid). Invariants, if forced to be true, ensure correct behavior on a subsystem level and thus preserve the overall system correctness. An invariant is a logical predicate on a system state that should not change its truth value if satisfied by system execution [1]. This paper derives an invariant that preserves voltage stability. This invariant is based on an online indicator which is derived from fundamental Kirchhoff s laws and will predict the proximity of voltage collapse at one or more entities in a smart grid. The efficiency of the invariant in predicting voltage collapse has been verified with simulations performed on a typical seven node smart grid system. Thus an online monitoring of the system parameters gives an indication of the system voltage stability. The voltage stability invariant works for both static and dynamic states. This method is also a fast and powerful tool to predict the voltage stability margin of a generic smart grid system by a simple monitoring of the system parameters

Invariants As a Unified Knowledge Model for Cyber-Physical Systems

Cyber-Physical Systems (CPS) consist of distributed computation interconnected by computer networks that monitor and control switched physical entities interconnected by physical infrastructures. Finding a common semantic among these diverse components that facilitates system synthesis, verification, and monitoring is a significant challenge of a CPS research program. In the emerging smart grid, for example, system state provides input into distributed computer algorithms that manage power and energy via local computation with messaging passing over a computer network collectively resulting in control signals to advanced power electronics. Computational correctness, network timing, and frequency response are all system aspects that conspire to impede design, verification, and monitoring. This paper seeks to unify the knowledge present in these diverse aspects through developing common semantics that span each aspect of a CPS. Specifically, a smart grid type system is considered. Power commands to various loads and alternative energy sources are stepped in response to cyber controllers that are networked. This paper shows the development of a physical invariant, based on the theory of Lyapunov-like functions, and a cyber invariant, the governs the correctness of a power dispatch algorithm, and couples the two to develop an overall system stability invariant. The invariant approach is tested with two scenarios. In the first case, the system is subjected to two commanded pulses beyond the stable limit, with the second perturbing pulse being of a magnitude greater than the first, which makes the system unstable. In the second case, the system is subjected to two commanded pulses beyond its stable limit but with a comparatively smaller magnitude of the perturbing second pulse, which allowed the system to remain stable. The measure of stability is an energy function which, under certain conditions, serves as a Lyapunov-like invariant that is used to prove stability