Related papers: A Dynamized Power Flow Method based on Differentia…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
To cope with fast-fluctuating distributed energy resources (DERs) and uncontrolled loads, this paper formulates a time-varying optimization problem for distribution grids with DERs and develops a novel non-iterative algorithm to track the…
The increasing scale and nonlinearity of modern energy and power system problems pose significant challenges to classical numerical solvers. In parallel, advances in quantum and quantum-inspired hardware are expected to improve scalability…
Dynamic network flows, sometimes called flows over time, extend the notion of network flows to include a transit time for each edge. While Ford and Fulkerson showed that certain dynamic flow problems can be solved via a reduction to static…
To address computational challenges associated with power flow nonconvexities, significant research efforts over the last decade have developed convex relaxations and approximations of optimal power flow (OPF) problems. However, benefits…
Classical Computational Fluid Dynamics (CFD) of long-time processes with strongly separated time scales is computationally extremely demanding if not impossible. Consequently, the state-of-the-art description of such systems is not capable…
We propose a systematic training-free method to transform the probability flow of a "linear" stochastic process characterized by the equation X_{t}=a_{t}X_{0}+\sigma_{t}X_{1} into a straight constant-speed (SC) flow, reminiscent of…
Optimal power flow (OPF) is a critical optimization problem for power systems to operate at points where cost or other operational objectives are optimized. Due to the non-convexity of the set of feasible OPF operating points, it is…
Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input--output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due…
We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from…
Power flow analysis plays a critical role in the control and operation of power systems. The high computational burden of traditional solution methods led to a shift towards data-driven approaches, exploiting the availability of digital…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The…
Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the…
The impact of different linearisation and iterative solution strategies for fully-coupled pressure-based algorithms for compressible flows at all speeds is studied, with the aim of elucidating their impact on the performance of the…
In this study, electric power is processed using the logic operation method and the error correction algorithms to meet load demand. Electric power was treated as physically flow through the distribution network, which was governed by…
We present a nonparametric way to retrieve a system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long term predictions. We demonstrate the…
Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient…
With an increasing share of renewable energy sources, accurate and efficient modeling of grid-forming inverters is becoming crucial for system stability. Linear methods are a powerful tool for understanding dynamics close to an operating…
Conservation principles like conservation of charge or energy provide a natural way to couple and constrain different physical variables. In this letter, we propose a dynamical system model that exploits these constraints for solving…