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The wide deployment of renewable generation and the gradual decrease in the overall system inertia make modern power grids more vulnerable to transient instabilities and unacceptable frequency fluctuations. Time-domain simulation-based…
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…
Time series forecasting remains a central challenge problem in almost all scientific disciplines. We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system using Dynamic Mode Decomposition…
We simulate the transition from amplified spontaneous emission (ASE) to lasing in random systems with varying degrees of mode overlap. This is accomplished by solving the stochastic Maxwell-Bloch equations with the finite-difference…
Power System State Estimation (PSSE) has been a research area of interest for power engineers for a long period of time. Due to the intermittent nature of renewable energy sources, which are applied in the power network more than before,…
This work considers state dynamics driven by Periodic Autoregressive Moving Average noise, and control of the system over time. Such processes appear frequently in applications involving the environment, such as energy and agriculture.…
Identifying the location of a disturbance and its magnitude is an important component for stable operation of power systems. We study the problem of localizing and estimating a disturbance in the interconnected power system. We take a…
Conventionally, the dynamic state estimation of variables in power networks is performed based on the forecasting-aided model of bus voltages. This approach is effective in the stiff grids at the transmission level, where the bus voltages…
State space is widely used for modeling power systems and analyzing their dynamics but it is limited to representing causal and proper systems in which the number of zeros does not exceed the number of poles. In other words, the system…
A variety of algorithms have been proposed to address the power system state estimation problem in the presence of uncertainties in the data. However, less emphasis has been given to handling perturbations in the model. In the context of…
We present a perturbation method for determining the moment stability of linear ordinary differential equations with parametric forcing by colored noise. In particular, the forcing arises from passing white noise through an $n$th order…
The free energy landscapes of several fundamental processes are characterized by high barriers separating long-lived metastable states. In order to explore these type of landscapes enhanced sampling methods are used. While many such methods…
We present the winning strategy of an electricity demand forecasting competition. This competition was organized to design new forecasting methods for unstable periods such as the one starting in Spring 2020. We rely on state-space models…
A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…
Landau damping is the mechanism of plasma and beam stabilization; it arises through energy transfer from collective modes to the incoherent motion of resonant particles. Normally this resonance requires the resonant particle's frequency to…
This paper presents a novel centralized, variational data assimilation approach for calibrating transient dynamic models in electrical power systems, focusing on load model parameters. With the increasing importance of inverter-based…
We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on…
The initialization process of a novel power system transient simulation scheme for stability studies is put forward, by further developing a "time-domain harmonic power-flow algorithm". The initialization process is formulated as an…
Conditions for net fast ion drive are derived for beam-driven, co-propagating, sub-cyclotron compressional (CAE) and global (GAE) Alfv\'en eigenmodes driven by the Landau resonance with super-Alfv\'enic fast ions. Approximations applicable…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…