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This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability.

Nonlinear waves --- Nonlinear wave equations --- Frequency stability --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematics. --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Statistical physics. --- Partial Differential Equations. --- Nonlinear Dynamics. --- Dynamical Systems and Ergodic Theory. --- Physics --- Mathematical statistics --- Partial differential equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Math --- Science --- Statistical methods --- Differential equations, partial. --- Differentiable dynamical systems. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Nonlinear wave equations. --- Nonlinear waves. --- Frequency stability.

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Dynamic stability basically deals with the interactions between the system's components. Following a disturbance, the system's variables undergo transitions that can induce oscillations in active and reactive power generation, resulting in the occurrence of voltage oscillatory modes and frequency deviation in the system. Depending on the entity of the disturbance, the small- or large-signal stability of the system under consideration can be investigated. The introduction of RES-based generation that does not participate in the network services (i.e., frequency and voltage regulation) due to lack of special controls will undoubtedly affect both the overall frequency and voltage stability. Large-scale transient stability is also a concern not to be overlooked: inverter-based wind and solar generation have different angle/speed swing behaviors with respect to traditional generation due to reduced inertia, different voltage swing behaviors due to different voltage control systems, different power flow patterns, and different displacements of synchronous generation at key locations. Therefore, although power system stability and dynamics have played a very central role in the management and study of electrical power systems thus far, it is also true that the emerging scenario requires new methodologies, technologies, and analyses. In this light, the current Special Issue aims to collect contributions (i.e., research papers and review articles) on power system dynamics and stability from experts in academia and industry.

Technology: general issues --- History of engineering & technology --- power system stability --- inertia estimation --- PMU --- microgrids --- frequency control --- grid-forming --- 100% converter-interfaced generation --- virtual synchronous machine --- forced oscillation --- inverter-based resources (IBRs) --- grid vulnerability analysis --- active power modulation --- virtual inertia --- fast frequency measurement --- fast frequency regulation --- distributed energy resources --- ancillary services --- power hardware-in-the-loop --- legacy resources --- large perturbation angle stability --- small perturbation angle stability --- voltage stability --- synthetic inertia --- demand response --- reactive compensation --- power system restoration --- primary frequency control --- frequency nadir estimation --- low inertia systems --- real-time dynamic simulation --- national power grid --- cyber physical system (CPS) --- co-simulation --- battery energy storage system (BESS) --- energy management system (EMS) --- load modelling --- line modelling --- power system analysis --- transient stability --- small-signal stability --- inverter-based resources --- modular multilevel converters --- primary frequency regulation --- battery energy storage system --- Ornstein–Uhlenbeck stochastic process --- compound poisson stochastic process --- frequency stability --- rotor angle stability --- power system inertia --- converter-interfaced generation --- renewable power generators

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In the first decades of the current millennium, the contribution of photovoltaic and wind energy systems to power generation capacity has grown extraordinarily all around the world; in some countries, these systems have become two of the most relevant sources to meet the needs of energy supply. This Special Issue deals with all aspects of the development, implementation, and exploitation of systems and installations that operate with both sources of energy.

wind energy conversion system --- distributed control --- battery energy storage system --- consensus algorithm --- photovoltaic --- voltage stability --- grid capacity --- penetration level --- frequency stability --- Egypt’s national grid --- renewable energies --- photovoltaic (PV) --- energy challenge --- policy options --- technological development --- market development --- battery storage --- concentrated solar power (CSP), installed capacity --- solar energy resources --- solar thermal plants --- thermal energy storage (TES) --- maximum power point (MPP) --- maximum power point tracking (MPPT) --- perturbe and observe (P&amp --- O) --- incremental conductance (IC) --- off-shore wind farms --- wind farm aggregation --- admittance model order reduction --- HVDC diode rectifiers --- grid-forming wind turbines --- efficiency improvement --- photovoltaic inverters --- parallel inverters --- wind turbine emulator --- wind turbine energy systems --- photovoltaics --- two-stage grid-connected PV inverters --- reduced DC-link --- sensorless MPPT

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Modern power and energy systems are characterized by the wide integration of distributed generation, storage and electric vehicles, adoption of ICT solutions, and interconnection of different energy carriers and consumer engagement, posing new challenges and creating new opportunities. Advanced testing and validation methods are needed to efficiently validate power equipment and controls in the contemporary complex environment and support the transition to a cleaner and sustainable energy system. Real-time hardware-in-the-loop (HIL) simulation has proven to be an effective method for validating and de-risking power system equipment in highly realistic, flexible, and repeatable conditions. Controller hardware-in-the-loop (CHIL) and power hardware-in-the-loop (PHIL) are the two main HIL simulation methods used in industry and academia that contribute to system-level testing enhancement by exploiting the flexibility of digital simulations in testing actual controllers and power equipment. This book addresses recent advances in real-time HIL simulation in several domains (also in new and promising areas), including technique improvements to promote its wider use. It is composed of 14 papers dealing with advances in HIL testing of power electronic converters, power system protection, modeling for real-time digital simulation, co-simulation, geographically distributed HIL, and multiphysics HIL, among other topics.

design methodology --- FPGA --- hardware in the loop --- LabVIEW --- real-time simulation --- power converters --- HIL --- CHIL --- integrated laboratories --- real-time communication platform --- power system testing --- co-simulation --- geographically distributed simulations --- power system protection and control --- holistic testing --- lab testing --- field testing --- PHIL --- PSIL --- pre-certification --- smart grids --- standards --- replica controller --- TCSC --- DPT --- testing --- control and protection --- large-scale power system --- voltage regulation --- distribution system --- power hardware-in-the-loop --- distributed energy resources --- extremum seeking control --- particle swarm optimization --- state estimation --- reactive power support --- volt–VAR --- model-based design --- multi physics simulation --- marine propulsion --- ship dynamic --- DC microgrid --- shipboard power systems --- under-frequency load shedding --- intelligent electronic device --- proof of concept --- hardware-in-the-loop testing --- real-time digital simulator --- frequency stability margin --- rate-of-change-of-frequency --- geographically distributed real-time simulation --- remote power hardware-in-the-Loop --- grid-forming converter --- hardware-in-the-loop --- simulation fidelity --- energy-based metric --- energy residual --- quasi-stationary --- Hardware-in-the-Loop (HIL) --- Control HIL (CHIL) --- Power HIL (PHIL) --- testing of smart grid technologies --- power electronics --- shifted frequency analysis --- dynamic phasors --- real-time hybrid-simulator (RTHS) --- hybrid simulation --- hardware-in-the-loop simulation (HILS) --- dynamic performance test (DPT) --- real-time simulator (RTS) --- testing of replicas --- multi-rate simulation --- EMT --- control --- inverters --- inverter-dominated grids --- power system transients --- predictive control --- hydro-electric plant --- variable speed operation --- ‘Hill Charts’ --- reduced-scale model --- testing and validation