Related papers: Power Flow as an Algebraic System
Part II of this paper elaborates on the unique capability of the proposed power flow analysis framework to obtain the true solution corresponding to the stable operating point of a network. It explains the significance of obtaining the true…
The way in which electric power depends on the topology of circuits with mixed voltage and current sources is examined. The power flowing in any steady-state DC circuit is shown to depend on a minimal set of key variables called fundamental…
We conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
We consider the problem of characterizing and assessing the voltage stability in power distribution networks. Different from previous formulations, we consider the branch-flow parametrization of the power system state, which is particularly…
We report the existence of algebraically localized eigenstates embedded within the continuum spectrum of 2D non-Hermitian systems with a single impurity. These modes, which we term algebraic states in continuum (AICs), decay algebraically…
Systems kept out of equilibrium in stationary states by an external source of energy store an energy $\Delta U=U-U_0$. $U_0$ is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine $\Delta U$…
Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…
The optimal power flow problem plays an important role in the market clearing and operation of electric power systems. However, with increasing uncertainty from renewable energy operation, the optimal operating point of the system changes…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
Charney and DeVore [J. Atmos. Sci. 36 (1979), 1205-1216] found multiple equilibrium states as a consequence of bottom topography in their pioneering work on the quasi-geostrophic barotropic flow over topography in a $\beta$-plane channel.…
It is pointed out that the concepts and methods introduced by Bachelier and by Mandelbrot to Finance and Economics can be used to examine the fluctuations observed in high-energy hadron production processes. Theoretical arguments and…
The Alternating Current Optimal Power Flow (ACOPF) problem is a core task in power system operations, aimed at determining cost-effective generation dispatch while satisfying physical and operational constraints. However, conventional ACOPF…
A series of laboratory experiments has been carried out in a thermally driven rotating annulus to study the onset of baroclinic instability, using horizontal and uniformly sloping bottom topographies. Different wave flow regimes have been…
On the basis of the transfer matrix technique an analytical method to investigate the stationary states, for an electron in one-dimensional periodic structures in an external electrical field, displaying the symmetry of the problem is…
We show that a steady-state solution ${\bf U}$ to the system of equations of a Navier-Stokes flow past a rotating body is nonlinearly unstable if the associated linear operator $\cal L$ has a part of the spectrum in the half-plane…
This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one…
Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion…
With the increasing penetration of Inverter-Based Resources (IBRs), power system stability constraints must be incorporated into the operational framework, transforming it into stability-constrained optimization. Currently, there exist…
We introduce a new model to study the oscillations of opposite flows sharing a common bottleneck and moving on two Totally Asymmetric Simple Exclusion Process (TASEP) lanes. We provide a theoretical analysis of the phase diagram, valid when…