Related papers: Power System Differential-Algebraic Equations
We present a generalized equations-of-motion method that efficiently calculates energy spectra and matrix elements for algebraic models. The method is applied to a 5-dimensional quartic oscillator that exhibits a quantum phase transition…
Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of parameters that affect the final design leads to a need for new approaches to quantify…
Due the complexity of modern power systems, modeling based on first-order principles becomes increasingly difficult. As an alternative, dynamical models for simulation and control design can be obtained by black-box identification…
Here we give a complete group classification of the general case of linear systems of three second-order ordinary differential equations excluding the case of systems which are studied in the literature. This is given as the initial step in…
A mathematical model is formulated for the evolution of plane perturbations in a cosmological two-component statistical system of completely degenerate scalarly charged fermions with an asymmetric scalar Higgs interaction. A complete closed…
Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
Use of explicit integration methods for power electronic circuits with ideal switch models significantly improves simulation speed. The PLECS package [1] has effectively used this idea; however, the implementation details involved in PLECS…
Power systems, including synchronous generator systems, are typical systems that strive for stable operation. In this article, we numerically study the fault transient process of a synchronous generator system based on the first benchmark…
In this work we introduce PowerModelsDistribution, a free, open-source toolkit for distribution power network optimization, whose primary focus is establishing a baseline implementation of steady-state multi-conductor unbalanced…
Power system dynamics are naturally nonlinear. The nonlinearity stems from power flows, generator dynamics, and electromagnetic transients. Characterizing the nonlinearity of the dynamical power system model is useful for designing superior…
High levels of penetration of distributed generation and aggressive reactive power compensation with modern power electronics may result in the reversal of active and reactive power flows in future distribution grids. The voltage stability…
In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of St\"ackel equivalent systems for both degenerate and…
This paper proposes a novel method for solving and tracing power flow solutions with changes of a loading parameter. Different from the conventional continuation power flow method, which repeatedly solves static AC power flow equations, the…
This paper describes a simplified model of an electric circuit with a DC-DC converter and a PID-regulator as a system of integral differential equations with an identically singular matrix multiplying the higher derivative of the desired…
Analyzing the stability of the power system by using a few machines is promising for transient stability assessment. A hybrid direct-time-domain method that is fully based on the thinking of partial energy function is proposed in this…
In this article, I introduce the differential equation model and review their frequentist and Bayesian computation methods. A numerical example of the FitzHugh-Nagumo model is given.
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
We provide algorithms computing power series solutions of a large class of differential or $q$-differential equations or systems. Their number of arithmetic operations grows linearly with the precision, up to logarithmic terms.
The partitioned approach for the numerical integration of power system differential algebraic equations faces inherent numerical stability challenges due to delays between the computation of state and algebraic variables. Such delays can…