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After a sudden disturbance, the energy balance of generators is disturbed, and the power outputs of synchronous generators vary as their rotor angles shift from their equilibrium points. This trend essentially presents the versatile…

High percentage of voltage harmonics has been observed in transmission networks due to harmonic currents penetrated from the load side amplified by resonant conditions. This requires the use of suitable harmonic filters in transmission…

The power system state estimation (SE) algorithm estimates the complex bus voltages based on the available set of measurements. Because phasor measurement units (PMUs) are becoming more widely employed in transmission power systems, a fast…

This paper presents a model for detecting high-impedance faults (HIFs) using parameter error modeling and a two-step per-phase weighted least squares state estimation (SE) process. The proposed scheme leverages the use of phasor measurement…

This paper presents the intrinsic geometric model for the solution of power system planning and its operation. This problem is large-scale and nonlinear, in general. Thus, we have developed the intrinsic geometric model for the network…

This paper address the problem of voltage regulation in power distribution networks with deep penetration of distributed energy resources (DERs) without any explicit communication between the buses in the network. We cast the problem as an…

An important monitoring task for power systems is accurate estimation of the system operation state. Under the nonlinear AC power flow model, the state estimation (SE) problem is inherently nonconvex giving rise to many local optima. In…

The choice of stabilization term is a critical component of the virtual element method (VEM). However, the theory of VEM provides only asymptotic guidance for selecting the stabilization term, which ensures convergence as the mesh size…

This work presents a Virtual Element Method (VEM) formulation tailored for two-dimensional axisymmetric problems in linear elasticity. By exploiting the rotational symmetry of the geometry and loading conditions, the problem is reduced to a…

Characterizing long-range electric fields and built-in potentials in functional materials at nano- to micrometer scales is of supreme importance for optimizing devices. E.g., the functionality of semiconductor heterostructures or battery…

In this article, we propose and analyze a fully coupled, nonlinear, and energy-stable virtual element method (VEM) for solving the coupled Poisson-Nernst-Planck (PNP) and Navier--Stokes (NS) equations modeling microfluidic and…

We present the non-conforming Virtual Element Method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component…

This paper aims to proactively diagnose and manage frequency instability risks from a steady-state perspective, without the need for derivative-dependent transient modeling. Specifically, we jointly address two questions (Q1) Survivability:…

The topology of a power grid affects its dynamic operation and settlement in the electricity market. Real-time topology identification can enable faster control action following an emergency scenario like failure of a line. This article…

This paper presents a mass-lumped Virtual Element Method (VEM) with explicit Strong Stability-Preserving Runge--Kutta (SSP-RK) time integration for two-dimensional parabolic problems on general polygonal meshes. A diagonal mass matrix is…

In this paper, a wide-area measurement system (WAMS)-based method is proposed to estimate the system state matrix for AC system with integrated voltage source converters (VSCs) and identify the electromechanical modes. The proposed method…

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible…

Predicting power system component outages in response to an imminent hurricane plays a major role in preevent planning and post-event recovery of the power system. An exact prediction of components states, however, is a challenging task and…

We study the $h$- and $p$-versions of non-conforming harmonic virtual element methods (VEM) for the approximation of the Dirichlet-Laplace problem on a 2D polygonal domain, providing quasi-optimal error bounds. Harmonic VEM do not make use…

We present a new empirical pseudopotential (EPM) calculation approach to simulate the million atom nanostructured semiconductor devices under potential bias using the periodic boundary conditions. To treat the non-equilibrium condition,…