Optimal Decentralized Load Frequency Control for Power System: A Mean-Field Team Approach

RÉSUMÉ Le problème de réglage fréquence-puissance (RFP) dans les réseaux électriques connaît un regain récent d’intérêt vu la pénétration de plus en plus importante dans ces réseaux de sources d’énergie renouvelable solaire ou éolienne, c’est à dire avec caractéristiques d’intermittence. En effet, la fréquence est un signal dont le comportement est sensible à tout déséquilibre entre génération et demande d’électricité, et son maintien dans un voisinage serré de sa valeur nominale (60 Hz en Amérique du Nord), est essentiel pour la stabilité du réseau. Le RFP vise à contrôler la puissance de sortie des générateurs en réponse aux changements de fréquence (dans le cas d’une zone unique) ainsi qu’à ceux des échanges d’énergie par rapport à leur valeur programmée dans les lignes de raccordement (dans le cas de zones multiples). Les techniques actuelles de RFP présentent un mélange de caractéristiques de centralisation et de décentralisation. Dans ce mémoire, nous souhaitons revisiter les algorithmes de RFP à la lumière des derniers développements de la théorie des équipes et jeux à champ moyens (mean field teams and mean field games), en exploitant le fait que le signal de fréquence global utilisé pour coordonner les générateurs est en réalité une moyenne pondérée des fréquences locales à un grand nombre de générateurs. Nous explorerons ainsi dans ce mémoire des approches de commande intégrale-proportionnelle avec structure de coût quadratique pour le RFP. Le problème de commande est formulé comme un problème d’équipe linéaire quadratique selon la structure d’information champ-moyen partagé, c’est-à-dire que chaque générateur observe son propre état (incluant 3 variables internes supposées mesurables) ainsi que le champ moyen consistant en une moyenne des états de tous les générateurs. La commande décentralisée correspond à la solution du problème d’équipe à champ moyen. Cette dernière est obtenue en résolvant 2 équations de Riccati dans le cas d’une zone isolée, l’une associée au générateur local et l’autre associée au champ moyen (ces équations deviennent des équations de Riccati couplées dans le cas d’un problème à 2 zones). Le mémoire est composé de deux parties dédiées respectivement à l’analyse de la commande pour une zone isolée, et celle associée à deux zones interconnectées. Dans la première partie, nous introduisons la théorie de l’équipe dans le contrôle RFP à zone unique. Il s’agit de problèmes de décision multi-agents dans lesquels tous les agents (générateurs individuels) partagent un coût commun [Mahajan et al., 2012]. L’approche de commande actuelle utilise une contrainte de taux de génération unique [Tan, 2010] pour contrôler le comportement de tous les agents/machines et la répartition de la charge se fait en se référant à la taille de la machine, ce qui est simple mais apriori un peu trop grossier.----------ABSTRACT Load frequency control or LFC is a fundamental mechanism for maintaining the stability of electric power systems. It aims at controlling the power output of generators in response to either changes in frequency (in a single area case) or in response to both changes in frequency and tie-line power interchange (in multi- area cases). Indeed frequency is a ubiquitous signal in power systems and its excursions away from its nominal value are indicative of imbalances between generation and load. Interest in LFC has come back to the fore in view of the challenges raised by increasing levels of penetration of renewable intermittent sources (Wind and solar energy). This situation creates frequent and important mismatches between system generation and system load, and thus create the need for more effective LFC schemes. The current set up is based on estimating a single integral control based power mismatch variable and redistributing a share of the correspondingly needed generation increase or decrease among units according to their power rating [Tan, 2010]. While this has proved to be a robust and algorithmically simple scheme, it is a rather rough approach, as it tends to ignore the particular current state of each generator when provided with a new set point. In order to allow more flexible and less aggressive control to each individual generator, normally only represented as a single aggregate unit, novel decentralized linear quadratic-proportional integral control methods for load frequency control respectively based on so-called mean field team theory (for single and two area systems) and mean field games ( for two area systems) are discussed in this thesis. The control problem is formulated as a linear quadratic (LQ) team problem under meanfield sharing (MFS) information structure, i.e., each generator observes its own state (3 state variables) and the mean field, that is in this context the average state of all generators if they are all identical, or the vector of class specific mean states in a non homogeneous multi-class situation. Also, following a team solution scheme developed in [Arabneydi and Mahajan, 2016], a separate mean field control term is a feedback on the vector of mean class specific individual states. The overall result is a decentralized control policy with coordination by the mean field term. The optimal solution is obtained by solving 2 Riccati equations, one for the local generator and another one associated with the mean field (this becomes instead a system of coupled Riccati equations in the subsequent mean field game game solution of the 2 area problem), for the full observation model

The biophysics of bacterial collective motion: Measuring responses to mechanical and genetic cues

Mechanobiology is an emerging field investigating mechanical signals as a necessary component of cellular and developmental regulation. These mechanical signals play a well-established role in the differentiation of animal cells, whereby cells with identical genes specialize their function and create distinct tissues depending on the physical properties of their environment, such as shear stiffness. These differences arise from the cell’s ability to use those incoming signals to inform which genes it expresses and what molecular machinery it builds and activates. Understanding the various missing factors that cause cells with specific genes to express an emergent phenotype is termed the genotype-to-phenotype problem, and mechanical signaling pathways present themselves as a significant piece of this puzzle. Despite the strong evidence for mechanosensing in eukaryotes, the pathways by which prokaryotes respond to mechanical stimuli are still largely unknown. Bacteria are among the simplest and yet most abundant forms of life. Many of their survival strategies depend on multicellular development and the coordinated formation of a colony into functional structures that may also feature cellular differentiation. This dissertation employs bacteria as a model system to investigate multiple biophysical questions of collective motion through novel experimental and analytical techniques. This work addresses the understudied mechanical relationship between a bacterial colony and the substrate it colonizes by asking “what is the effect of substrate stiffness on colony growth?” This is done by measuring bacterial growth on hydrogel substrates that decouple the effects of substrate stiffness from other material properties of the substrate that vary with stiffness. We report a previously unobserved effect in which bacteria colonize stiffer substrates faster than softer substrates, in opposition to previous studies done on agar, where permeability, viscoelasticity, and other material properties vary with stiffness.A second theme of this work probes the genetic inputs to the genotype-to-phenotype problem in multicellular development. The bacterial species Myxococcus xanthus producing macroscopic aggregates called fruiting bodies is used as a model organism for these studies. It has long been conjectured that genes may stand in for each other functionally, allowing for development to be more consistent and stable, but the extent of this redundancy has resisted measurement. We approach the question “how does redundancy among related genes lead to robust collective behavior?” by quantifying developmental phenotype in a large dataset of time lapse microscopy videos that show development in many mutant strains. We observe that when knocking out multiple genes that have a common origin (i.e. homologous genes), the resulting phenotypes differ from wild-type in a similar way. These phenotype clusters also differ from knockouts from other homologous gene families. These distinct phenotypic clusters provide evidence for the existence of networks of redundant genes that are larger than could previously be tested directly. Because of this robustness, the effects of individual gene mutations can be hidden or damped. We thus develop our analytical techniques further to address the question “how can subtle changes in phenotype be measured?” This involves quantifying the breadth of variation observed in wild-type development and creating a statistical technique to distinguish probabilistic distributions of phenotypic outcomes. We present a coherent method of visualizing large phenotypic datasets that include multiple metrics that we use to distinguish small developmental differences from wild-type, giving each mutant strain a phenotypic fingerprint that can be used in future studies on gene annotation and environmental impacts on phenotype

Infobiotics : computer-aided synthetic systems biology

Until very recently Systems Biology has, despite its stated goals, been too reductive in terms of the models being constructed and the methods used have been, on the one hand, unsuited for large scale adoption or integration of knowledge across scales, and on the other hand, too fragmented. The thesis of this dissertation is that better computational languages and seamlessly integrated tools are required by systems and synthetic biologists to enable them to meet the significant challenges involved in understanding life as it is, and by designing, modelling and manufacturing novel organisms, to understand life as it could be. We call this goal, where everything necessary to conduct model-driven investigations of cellular circuitry and emergent effects in populations of cells is available without significant context-switching, “one-pot” in silico synthetic systems biology in analogy to “one-pot” chemistry and “one-pot” biology. Our strategy is to increase the understandability and reusability of models and experiments, thereby avoiding unnecessary duplication of effort, with practical gains in the efficiency of delivering usable prototype models and systems. Key to this endeavour are graphical interfaces that assists novice users by hiding complexity of the underlying tools and limiting choices to only what is appropriate and useful, thus ensuring that the results of in silico experiments are consistent, comparable and reproducible. This dissertation describes the conception, software engineering and use of two novel software platforms for systems and synthetic biology: the Infobiotics Workbench for modelling, in silico experimentation and analysis of multi-cellular biological systems; and DNA Library Designer with the DNALD language for the compact programmatic specification of combinatorial DNA libraries, as the first stage of a DNA synthesis pipeline, enabling methodical exploration biological problem spaces. Infobiotics models are formalised as Lattice Population P systems, a novel framework for the specification of spatially-discrete and multi-compartmental rule-based models, imbued with a stochastic execution semantics. This framework was developed to meet the needs of real systems biology problems: hormone transport and signalling in the root of Arabidopsis thaliana, and quorum sensing in the pathogenic bacterium Pseudomonas aeruginosa. Our tools have also been used to prototype a novel synthetic biological system for pattern formation, that has been successfully implemented in vitro. Taken together these novel software platforms provide a complete toolchain, from design to wet-lab implementation, of synthetic biological circuits, enabling a step change in the scale of biological investigations that is orders of magnitude greater than could previously be performed in one in silico “pot”

Infobiotics : computer-aided synthetic systems biology

Until very recently Systems Biology has, despite its stated goals, been too reductive in terms of the models being constructed and the methods used have been, on the one hand, unsuited for large scale adoption or integration of knowledge across scales, and on the other hand, too fragmented. The thesis of this dissertation is that better computational languages and seamlessly integrated tools are required by systems and synthetic biologists to enable them to meet the significant challenges involved in understanding life as it is, and by designing, modelling and manufacturing novel organisms, to understand life as it could be. We call this goal, where everything necessary to conduct model-driven investigations of cellular circuitry and emergent effects in populations of cells is available without significant context-switching, “one-pot” in silico synthetic systems biology in analogy to “one-pot” chemistry and “one-pot” biology. Our strategy is to increase the understandability and reusability of models and experiments, thereby avoiding unnecessary duplication of effort, with practical gains in the efficiency of delivering usable prototype models and systems. Key to this endeavour are graphical interfaces that assists novice users by hiding complexity of the underlying tools and limiting choices to only what is appropriate and useful, thus ensuring that the results of in silico experiments are consistent, comparable and reproducible. This dissertation describes the conception, software engineering and use of two novel software platforms for systems and synthetic biology: the Infobiotics Workbench for modelling, in silico experimentation and analysis of multi-cellular biological systems; and DNA Library Designer with the DNALD language for the compact programmatic specification of combinatorial DNA libraries, as the first stage of a DNA synthesis pipeline, enabling methodical exploration biological problem spaces. Infobiotics models are formalised as Lattice Population P systems, a novel framework for the specification of spatially-discrete and multi-compartmental rule-based models, imbued with a stochastic execution semantics. This framework was developed to meet the needs of real systems biology problems: hormone transport and signalling in the root of Arabidopsis thaliana, and quorum sensing in the pathogenic bacterium Pseudomonas aeruginosa. Our tools have also been used to prototype a novel synthetic biological system for pattern formation, that has been successfully implemented in vitro. Taken together these novel software platforms provide a complete toolchain, from design to wet-lab implementation, of synthetic biological circuits, enabling a step change in the scale of biological investigations that is orders of magnitude greater than could previously be performed in one in silico “pot”

Applications of Deep Neural Networks

Deep learning is a group of exciting new technologies for neural networks. Through a combination of advanced training techniques and neural network architectural components, it is now possible to create neural networks that can handle tabular data, images, text, and audio as both input and output. Deep learning allows a neural network to learn hierarchies of information in a way that is like the function of the human brain. This course will introduce the student to classic neural network structures, Convolution Neural Networks (CNN), Long Short-Term Memory (LSTM), Gated Recurrent Neural Networks (GRU), General Adversarial Networks (GAN), and reinforcement learning. Application of these architectures to computer vision, time series, security, natural language processing (NLP), and data generation will be covered. High-Performance Computing (HPC) aspects will demonstrate how deep learning can be leveraged both on graphical processing units (GPUs), as well as grids. Focus is primarily upon the application of deep learning to problems, with some introduction to mathematical foundations. Readers will use the Python programming language to implement deep learning using Google TensorFlow and Keras. It is not necessary to know Python prior to this book; however, familiarity with at least one programming language is assumed