Related papers: Sample-Based Piecewise Linear Power Flow Approxima…
Motivated by the mathematics literature on the algebraic properties of so-called polynomial vector flows, we propose a technique for approximating nonlinear differential equations by linear differential equations. Although the idea of…
Training learning parameterizations to solve optimal power flow (OPF) with pointwise constraints is proposed. In this novel training approach, a learning parameterization is substituted directly into an OPF problem with constraints required…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
In integrated power and gas energy system optimization models (ESOMs), pipeline gas transmission with linepack is a particularly complex problem due to its non-linear and non-convex character. For ESOMs based on mixed-integer linear…
This paper considers state-of-the-art convex relaxations for the AC power flow equations and introduces new valid cuts based on convex envelopes and lifted nonlinear constraints. These valid linear inequalities strengthen existing…
Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of open-loop control on the linear stability properties of unstable flows. Sensitivity maps identify regions where small-amplitude control is the…
Physics-informed neural networks (PINNs) and their variants have recently emerged as alternatives to traditional partial differential equation (PDE) solvers, but little literature has focused on devising accurate numerical integration…
Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov's algorithm and the Fast…
A novel trust region method for solving linearly constrained nonlinear programs is presented. The proposed technique is amenable to a distributed implementation, as its salient ingredient is an alternating projected gradient sweep in place…
We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
Understanding the feasible power flow region is of central importance to power system analysis. In this paper, we propose a geometric view of the power system loadability problem. By using rectangular coordinates for complex voltages, we…
Nonlinear expressions are often approximated by piecewise affine (PWA) functions to simplify analysis or reduce computational costs. To reduce computational complexity, multivariate functions can be represented as compositions of functions…
In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic…
We demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We…
In the present contribution, we investigate first-order nonlinear systems of partial differential equations which are constituted of two parts: a system of conservation laws and non-conservative first order terms. Whereas the theory of…
We consider the problem of deriving an explicit approximate solution of the nonlinear power equations that describe a balanced power distribution network. We give sufficient conditions for the existence of a practical solution to the power…
Flow records, that summarize the characteristics of traffic flows, represent a practical and powerful way to monitor a network. While they already offer significant compression compared to full packet captures, their sheer volume remains…
The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It…
Nonlinear approximation methods such as the Zeldovich approximation, and more recently the frozen flow and linear potential approximations, are sometimes used to simulate nonlinear gravitational instability in the expanding Universe. We…