Smart Grid On-line Impedance Identification

I dag er det en kontinuerlig overgang fra distribuert kraftnettverk til fremtidens Smartnett. Det er en tydelig trend med økende innslag av fornybare energiressurser og kraftelektroniske komponenter i nettverket. Faktorer som ulineære laster og lavt treghetsmomentet fører til økte forstyrrelser i systemet. Det øker risikoen til overoppheting og redusert levetid av nettverkkomponentene. Det er derfor av interesse å måle og identifisere disse forstyrrelsene. Disse forstyrrelsene består av harmoniske svingninger, som er multipler av grunnfrekvensen. Frekvensskanningsmetoder er ofte brukt for å måle harmoniske svingninger, men lider på grunn av tidsforsinkelsen som skapes ved konverteringen fra tids- til frekvensdomenet. Det er derfor behov for en sanntidsidentifikasjonsmetode som kan måle disse svingningene og muliggjøre en videre stabilitetsevaluering av systemet. Denne masteroppgaven analyserer flere Kalman-filtre basert på sanntidsidentifikasjonsmetoder i et likerettersystem, blant annet Utvidet Kalman-filtre og Adaptivt Kalman-filtre. Resultatene er sammenlignet med en impedansemodeleringsmetode basert på harmonisk linearisering. Det Adaptive Kalman-filtret gir svært gode resultater. Videre analyserer basert på ikke-karakteriske harmoniske svingninger. Ved å injisere systemet med en stegfunksjon klarer vi å hente ut informasjon av ikke-karakteriske signalkomponenter fra transientresponsen. Det viser lovende resultater og åpner for videre utvikling og fremtidig forskning av transientanalyse basert impedanseestimering.As the current electrical grids are progressing towards SmartGrid, an increasing amount of renewable energy sources and power electronics are connected to the grid. Distortions caused by the nonlinear loads and small inertia of the power source are becoming more severe, and lead to unwanted effects in the system including overheating and reduced component life expectancy. This calls for a way of identifying and accessing these distortions. The nonlinear distortion consists of harmonics, which are the integer multiples of the grid fundamental frequency. Frequency scanning methods are predominantly used for identifying the harmonics parameters, but have to deal with the time delay caused by the conversion of time domain to frequency domain. There are needs for a real-time identification method that can identify the harmonics impedance which enables further stability assessment of the system. \noindent This thesis analyzes the use of several Kalman filter based on-line identification methods to estimate the harmonics impedance in a rectifier system, including the Extended Kalman Filter(EKF), Adaptive Extended Kalman Filter(AEKF) and Adaptive Kalman Filter(AKF). The results of these method is compared to a impedance mapping method based on harmonics linearization. The AKF yields the most accurate estimation. To further analyze the impedance of non-characteristic harmonics, we injected the system with a step signal and looked into its transient response. The AKF estimation shows promising results and points to potential use cases in future studies

Pointwise equidistribution for almost smooth functions with an error rate and Weighted L\'evy-Khintchin theorem

The purpose of this article is twofold: to prove a pointwise equidistribution theorem with an error rate for almost smooth functions, which strengthens the main result of Kleinbock, Shi and Weiss (2017); and to obtain a L\'evy-Khintchin theorem for weighted best approximations, which extends the main theorem of Cheung and Chevallier (2019). To do so, we employ techniques from homogeneous dynamics and the methods developed in the work of Cheung-Chevallier (2019) and Shapira-Weiss (2022).Comment: 32 page

Causal Inference for Human-Language Model Collaboration

In this paper, we examine the collaborative dynamics between humans and language models (LMs), where the interactions typically involve LMs proposing text segments and humans editing or responding to these proposals. Productive engagement with LMs in such scenarios necessitates that humans discern effective text-based interaction strategies, such as editing and response styles, from historical human-LM interactions. This objective is inherently causal, driven by the counterfactual `what-if' question: how would the outcome of collaboration change if humans employed a different text editing/refinement strategy? A key challenge in answering this causal inference question is formulating an appropriate causal estimand: the conventional average treatment effect (ATE) estimand is inapplicable to text-based treatments due to their high dimensionality. To address this concern, we introduce a new causal estimand -- Incremental Stylistic Effect (ISE) -- which characterizes the average impact of infinitesimally shifting a text towards a specific style, such as increasing formality. We establish the conditions for the non-parametric identification of ISE. Building on this, we develop CausalCollab, an algorithm designed to estimate the ISE of various interaction strategies in dynamic human-LM collaborations. Our empirical investigations across three distinct human-LM collaboration scenarios reveal that CausalCollab effectively reduces confounding and significantly improves counterfactual estimation over a set of competitive baselines.Comment: 9 pages (Accepted for publication at NAACL 2024 (Main Conference)

Calculation of static transmission errors associated with thermo-elastic coupling contacts of spur gears

The static transmission error is one of the key incentives of gear dynamics and addressed by many scholars. However, the traditional calculation method of static transmission errors of spur gears does not take into account the influence of thermo-elastic coupling caused by the gear temperature field, and it limits the accuracy of the dynamic characteristic analysis. Thus, in this study, the calculation method of static transmission errors associated with thermo-elastic coupling is proposed. Furthermore, the differences between static transmission errors associated with thermo-elastic coupling contacts and traditional method of gear is discussed. The study is helpful to improve the accuracy of dynamic analysis of gear transmission system

Collective behavior of squirmers in thin films

Bacteria in biofilms form complex structures and can collectively migrate within mobile aggregates, which is referred to as swarming. This behavior is influenced by a combination of various factors, including morphological characteristics and propulsive forces of swimmers, their volume fraction within a confined environment, and hydrodynamic and steric interactions between them. In our study, we employ the squirmer model for microswimmers and the dissipative particle dynamics method for fluid modeling to investigate the collective motion of swimmers in thin films. The film thickness permits a free orientation of non-spherical squirmers, but constraints them to form a two-layered structure at maximum. Structural and dynamic properties of squirmer suspensions confined within the slit are analyzed for different volume fractions of swimmers, motility types (e.g., pusher, neutral squirmer, puller), and the presence of a rotlet dipolar flow field, which mimics the counter-rotating flow generated by flagellated bacteria. Different states are characterized, including a gas-like phase, swarming, and motility-induced phase separation, as a function of increasing volume fraction. Our study highlights the importance of an anisotropic swimmer shape, hydrodynamic interactions between squirmers, and their interaction with the walls for the emergence of different collective behaviors. Interestingly, the formation of collective structures may not be symmetric with respect to the two walls. Furthermore, the presence of a rotlet dipole significantly mitigates differences in the collective behavior between various swimmer types. These results contribute to a better understanding of the formation of bacterial biofilms and the emergence of collective states in confined active matter.Comment: 17 pages, 12 figure

Fast Conditional Mixing of MCMC Algorithms for Non-log-concave Distributions

MCMC algorithms offer empirically efficient tools for sampling from a target distribution $\pi(x) \propto \exp(-V(x))$. However, on the theory side, MCMC algorithms suffer from slow mixing rate when $\pi(x)$ is non-log-concave. Our work examines this gap and shows that when Poincar\'e-style inequality holds on a subset $\mathcal{X}$ of the state space, the conditional distribution of MCMC iterates over $\mathcal{X}$ mixes fast to the true conditional distribution. This fast mixing guarantee can hold in cases when global mixing is provably slow. We formalize the statement and quantify the conditional mixing rate. We further show that conditional mixing can have interesting implications for sampling from mixtures of Gaussians, parameter estimation for Gaussian mixture models and Gibbs-sampling with well-connected local minima.Comment: Camera ready versio

Discrete forecast reconciliation

While forecast reconciliation has seen great success for real valued data, the method has not yet been comprehensively extended to the discrete case. This paper defines and develops a formal discrete forecast reconciliation framework based on optimising scoring rules using quadratic programming. The proposed framework produces coherent joint probabilistic forecasts for count hierarchical timeTwo discrete reconciliation algorithms are proposed and compared to generalisations of the top-down and bottom-up approaches to count data. Two simulation experiments and two empirical examples are conducted to validate that the proposed reconciliation algorithms improve forecast accuracy. The empirical applications are to forecast criminal offences in Washington D.C. and the exceedance of thresholds in age-specific mortality rates in Australia. Compared to the top-down and bottom-up approaches, the proposed framework shows superior performance in both simulations and empirical studies