Related papers: Differential Transformation of Nonlinear Power Flo…

In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

The non-linearity and non-convexity of power flow models and the phase coupling challenge the analysis and optimization of unbalanced distribution networks. To tackle the challenges, this paper proposes an online feedback-based linearized…

This research focuses on the evolving dynamics of the power grid, where traditional synchronous generators are being replaced by non-synchronous power electronic converter (PEC)-interfaced renewable energy sources. The non-linear dynamics…

Electromagnetic transient (EMT) simulation is a crucial tool for power system dynamic analysis because of its detailed component modeling and high simulation accuracy. However, it suffers from computational burdens for large power grids…

Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…

Unitary transformations can allow one to study open quantum systems in situations for which standard, weak-coupling type approximations are not valid. We develop here an extension of the variational (polaron) transformation approach to open…

Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid…

The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compared with multiple precision arithmetic, and also be applied…

We consider the problem of deriving an explicit approximate solution of the nonlinear power equations that describe a balanced power distribution network. We give sufficient conditions for the existence of a practical solution to the power…

In this paper, we present two multidimensional power flow formulations based on a fixed-point iteration (FPI) algorithm to efficiently solve hundreds of thousands of power flows in distribution systems. The presented algorithms are the base…

By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Cameron-Martin formula for solutions of a…

Energy transfer among various spectral components of fluctuating physical parameters in plasma occurs due to the nonlinear interactions, but these effects are typically not captured by the traditional linear spectral methods. Plasma density…

The AC power flow equations are fundamental in all aspects of power systems planning and operations. They are routinely solved using Newton-Raphson like methods. However, there is little theoretical understanding of when these algorithms…

Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…

This paper presents a variational approach to doubly-nonlinear (gradient) flows (P) of nonconvex energies along with nonpotential perturbations (i.e., perturbation terms without any potential structures). An elliptic-in-time regularization…

This paper proposes a time-domain fault location identification method for mixed overhead-underground power distribution systems that can handle challenging fault scenarios such as sub-cycle faults, arcing faults and evolving faults. The…

For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…

Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities.…

A methodology is developed to learn a feedback linearization (i.e., nonlinear change of coordinates and input transformation) using a data-driven approach for a single input control-affine nonlinear system with unknown dynamics. We employ…