This book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds. The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system. This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.

This comprehensive guide offers a new approach for developing and implementing robust computational methodologies that uncover the key geometric and topological information from signals and images. With the help of detailed real-world examples and applications, readers will learn how to solve complex signal and image processing problems in fields ranging from remote sensing to medical imaging, bioinformatics, robotics, security, and defence. With an emphasis on intuitive and application-driven arguments, this text covers not only a range of methods in use today, but also introduces promising new developments for the future, bringing the reader up-to-date with the state of the art in signal and image analysis. Covering basic principles as well as advanced concepts and applications, and with examples and homework exercises, this is an invaluable resource for graduate students, researchers, and industry practitioners in a range of fields including signal and image processing, biomedical engineering, and computer graphics.

This book provides an accessible yet rigorous first reference for readers interested in learning how to model and analyze cellular network performance using stochastic geometry. In addition to the canonical downlink and uplink settings, analyses of heterogeneous cellular networks and dense cellular networks are also included. For each of these settings, the focus is on the calculation of coverage probability, which gives the complementary cumulative distribution function (ccdf) of signal-to-interference-and-noise ratio (SINR) and is the complement of the outage probability. Using this, other key performance metrics, such as the area spectral efficiency, are also derived. These metrics are especially useful in understanding the effect of densification on network performance. In order to make this a truly self-contained reference, all the required background material from stochastic geometry is introduced in a coherent and digestible manner. This Book: Provides an approachable introduction to the analysis of cellular networks and illuminates key system dependencies Features an approach based on stochastic geometry as applied to cellular networks including both downlink and uplink Focuses on the statistical distribution of signal-to-interference-and-noise ratio (SINR) and related metrics

This book presents a unified framework for the tractable analysis of large-scale, multi-antenna wireless networks using stochastic geometry. This mathematical analysis is essential for assessing and understanding the performance of complicated multi-antenna networks, which are one of the foundations of 5G and beyond networks to meet the ever-increasing demands for network capacity. Describing the salient properties of the framework, which makes the analysis of multi-antenna networks comparable to that of their single-antenna counterparts, the book discusses effective design approaches that do not require complex system-level simulations. It also includes various application examples with different multi-antenna network models to illustrate the framework’s effectiveness.

Geometric Methods in System Theory In automatic control there are a large number of applications of a fairly simple type for which the motion of the state variables is not free to evolve in a vector space but rather must satisfy some constraints. Examples are numerous; in a switched, lossless electrical network energy is conserved and the state evolves on an ellipsoid surface defined by x'Qx equals a constant; in the control of finite state, continuous time, Markov processes the state evolves on the set x'x = 1, xi ~ O. The control of rigid body motions and trajectory control leads to problems of this type. There has been under way now for some time an effort to build up enough control theory to enable one to treat these problems in a more or less routine way. It is important to emphasise that the ordinary vector space-linear theory often gives the wrong insight and thus should not be relied upon.

This book introduces electric circuits with variable loads and voltage regulators. It allows to define invariant relationships for various parameters of regime and circuit sections and to prove the concepts characterizing these circuits. Generalized equivalent circuits are introduced. Projective geometry is used for the interpretation of changes of operating regime parameters. Expressions of normalized regime parameters and their changes are presented. Convenient formulas for the calculation of currents are given. Parallel voltage sources and the cascade connection of multi-port networks are described. The two-value voltage regulation characteristics of loads with limited power of voltage source is considered. The book presents the fundamentals of electric circuits and develops circuit theorems. It is useful to engineers, researchers and graduate students who are interested in the basic electric circuit theory and the regulation and monitoring of power supply systems.

Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrated with practical Long-Term Evolution (LTE) applications and compared with real-world deployment results.

Control and Optimization Methods for Electric Smart Grids brings together leading experts in power, control and communication systems, and consolidates some of the most promising recent research in smart grid modeling, control and optimization in hopes of laying the foundation for future advances in this critical field of study. The contents comprise eighteen essays addressing wide varieties of control-theoretic problems for tomorrow’s power grid. Topics covered include control architectures for power system networks with large-scale penetration of renewable energy and plug-in vehicles, optimal demand response, new modeling methods for electricity markets, cyber-security,data analysis and wide-area control using synchronized phasor measurements.