Related papers: Differential Transformation of Nonlinear Power Flo…
A fundamental challenge in computer analysis of power flow is the rigorous understanding of the impact of different loading levels on the solutions of the power flow equation. This letter presents a comprehensive study of possible numerical…
In power system dynamic simulation, up to 90% of the computational time is devoted to solve the network equations, i.e., a set of linear equations. Traditional approaches are based on sparse LU factorization, which is inherently sequential.…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
The differential transform method (DTM) is a relatively new technique that may be used to find a series solution to differential equations (both linear and nonlinear) through an iterative process. This brief manuscript is an initial effort…
Power distribution systems are increasingly exposed to large voltage fluctuations driven by intermittent renewable generation and time varying loads (e.g., electric vehicles and storage). To address this challenge, a number of advanced…
This paper introduces a new model for highly accurate distribution voltage solutions, coined as a parameterized linear power flow model. The proffered model is grounded on a physical model of linear power flow equations, and uses…
The iterative problem of solving nonlinear equations is studied. A new Newton like iterative method with adjustable parameters is designed based on the dynamic system theory. In order to avoid the derivative function in the iterative…
This paper presents a cold-start linear branch flow model named modified DistFlow. In modified DistFlow, the active and reactive power are replaced by their ratios to voltage magnitude as state variables, so that errors introduced by…
Building on the theoretical insights of Part I, this paper, as the second part of the tutorial, dives deeper into data-driven power flow linearization (DPFL), focusing on comprehensive numerical testing. The necessity of these simulations…
Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all…
Achieving robust and scalable convergence for simulation of realistic power flow cases can be challenging. One specific issue relates to the disconnected solution space that is created by the use of piecewise-discontinuous models of power…
This paper proposes a linear approximation of the alternating current optimal power flow problem for multiphase distribution networks with voltage-dependent loads connected in both wye and delta configurations. We establish a set of linear…
This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear…
Separated flow transition is a very popular phenomenon in gas turbines, especially low-pressure turbines (LPT). Low-fidelity simulations are often used for gas turbine design. However, they are unable to predict separated flow transition…
This paper investigates the performance limits of differential power processing (DPP) and presents quantitative and systematic design guidelines for the selection and comparison of DPP topologies. A stochastic model is developed to evaluate…
Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern identification that interprets patterns as probability density functions,…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
This two-part tutorial dives into the field of data-driven power flow linearization (DPFL), a domain gaining increased attention. DPFL stands out for its higher approximation accuracy, wide adaptability, and better ability to implicitly…
Within the theoretical framework of divergence-type theories (DTTs), we set up a consistent nonlinear hydrodynamical description of a conformal fluid in flat space-time. DTTs go beyond second-order (in velocity gradients) theories, and are…
Most methodologies for modeling Transmission Line (TL) based channels define the input-output relationship in the frequency domain (FD) and handle the TL resorting to a two-port network (2PN) formalism. These techniques have not yet been…