相关论文: Analytic solution to swing equations in power grid…

This paper considers the extreme type-II Ginzburg-Landau equations, a nonlinear PDE model that describes the states of a wide range of superconductors. For two-dimensional grids, a robust method is developed that performs a numerical…

We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures…

We present an adjoint sensitivity method for hybrid discrete -- continuous systems, extending previously published forward sensitivity methods. We treat ordinary differential equations and differential-algebraic equations of index up to two…

We study the existence of nonnegative solutions for a system of impulsive differential equations subject to nonlinear, nonlocal boundary conditions. The system presents a coupling in the differential equation and in the boundary conditions.…

In the present paper, the nonlinear differential equation of pendulum is investigated to find an exact closed form solution, satisfying governing equation as well as initial conditions. The new concepts used in the suggested method are…

Recent advances in nonlinear dynamical systems theory provide a new insight into numerical properties of discrete algorithms developed to solve nonlinear initial value problems. Basic features like accuracy and stability are well pointed…

In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…

We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and…

This paper concerns the numerical valuation of swing options with discrete action times under a linear two-factor mean-reverting model with jumps. The resulting sequence of two-dimensional partial integro-differential equations (PIDEs) are…

This paper studies the oscillatory behavior of solutions to linear nonautonomous impulsive differential equations with piecewise constant arguments, including both advanced and delayed cases \[ x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in…

In this work, it is demonstrated that the usual power system dynamic model exhibits a feedforward-feedback control structure. The distinct properties of the feedforward and feedback subsystems are identified and studied using respective…

The paper is now published in PRX Enegry. Please refer to the PRX version from now on. Anna B\"uttner and Frank Hellmann. "Complex Couplings-A Universal, Adaptive, and Bilinear Formulation of Power Grid Dynamics." The energy transition…

In this paper a unifying energy-based approach is provided to the modeling and stability analysis of power systems coupled with market dynamics. We consider a standard model of the power network with a third-order model for the synchronous…

We will show that there is a universal connection between the achievable closed-loop dynamics and the corresponding feedback controller that produces it. This connection shows promise to lead to new methods for robust nonlinear control in…

Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within…

We present a new numerical scheme to treat the non-linear evolution of cosmological power spectra. Governing equations for matter power spectra have been previously derived by a non-perturbative technique with closure approximation.…

We determine the late-time dynamics of a generic spin ensemble with inhomogeneous broadening - equivalently, qubits with arbitrary Zeeman splittings - coupled to a dissipative environment with strength decreasing as $1/t$. The approach to…

This paper explores solutions to linearized powerflow equations with bus-voltage phasors represented in rectangular coordinates. The key idea is to solve for complex-valued perturbations around a nominal voltage profile from a set of linear…

The complexity arising in AC microgrids from multiple interacting distributed generation units (DGUs) with intermittent supply behavior requires local voltage-source inverters (VSIs) to be controlled in a distributed or decentralized manner…

In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…