Related papers: Differential Transformation of Nonlinear Power Flo…
Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on…
The massive integration of distributed energy resources changes the operational demands of the electric power distribution system, motivating optimization-based approaches. The added computational complexities of the resulting optimal power…
Fast and accurate load parameters identification has great impact on the power systems operation and stability analysis. This paper proposes a novel transfer reinforcement learning based method to identify composite ZIP and induction motor…
We consider the one-dimensional porous medium equation $u_t=\left (u^nu_x \right )_x+\frac{\mu}{x}u^nu_x$. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some…
Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this article, nonlinear light behaviors in these complex waveguides…
The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network topology, we are interested in finding network parameters…
Nonintegrable systems thermalize, leading to the emergence of fluctuating hydrodynamics. Typically, this hydrodynamics is diffusive. We use the effective field theory (EFT) of diffusion to compute higher-point functions of conserved…
Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…
This paper presents a data-driven method for producing annual continuous dynamic rating of power transformers to serve the long-term planning purpose. Historically, research works on dynamic rating have been focused on real-time/near-future…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
The growing scale of power systems and the increasing uncertainty introduced by renewable energy sources necessitates novel optimization techniques that are significantly faster and more accurate than existing methods. The AC Optimal Power…
As known, physical circuits, e.g. integrated circuits or power system, work in a distributed manner, but these circuits could not be easily simulated in a distributed way. This is mainly because that the dynamical system of physical…
Transient stability analysis (TSA) plays an important role in power system analysis to investigate the stability of power system. Traditionally, transient stability analysis methods have been developed using time domain simulation by means…
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
A logarithm transformation over the matter overdensity field $\delta$ brings information from the bispectrum and higher-order n-point functions to the power spectrum. We calculate the power spectrum for the log-transformed field $A$ at one,…
This letter focuses on the multiplicity of power flow (PF) equations and presents two continuous solutions for widely studied IEEE-14 bus system. The continuous solutions are located by a method combining the semidefinite program (SDP)…
Motivated by the mathematics literature on the algebraic properties of so-called polynomial vector flows, we propose a technique for approximating nonlinear differential equations by linear differential equations. Although the idea of…
We study the nonlinear Schr$\ddot{o}$dinger equation with a PT-symmetric potential. Using a hydrodynamic formulation and connecting the phase gradient to the field amplitude, allows for a reduction of the model to a Duffing or a generalized…
Due to changes in electric distribution grid operation, new operation regimes have been recommended. Distribution grid optimal power flow (DOPF) has received tremendous attention in the research community, yet it has not been fully adopted…