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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…
Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…
This note outlines the exact solution to the power flow problem in AC electrical networks under the assumption of 'flat' or uniform voltage profiles. This solution generalises the common 'DC power flow' approach to electrical network…
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…
Unbalanced optimal power flow refers to a class of optimization problems subject to the steady state physics of three-phase power grids with nonnegligible phase unbalance. Significant progress on this problem has been made on the…
The optimal power flow (OPF) is an optimization model dedicated to the development of computational tools used for the planning and operation of electric power systems (EPS). In this work, based on the polar formulation, an extended convex…
The common linear optimal power flow (LOPF) formulation that underlies most transmission expansion planning (TEP) formulations uses bus voltage angles as auxiliary optimization variables to describe Kirchhoff's voltage law. As well as…
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…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
The AC Optimal Power Flow (AC-OPF) is a key building block in many power system applications. It determines generator setpoints at minimal cost that meet the power demands while satisfying the underlying physical and operational…
Linear optimal power flow (LOPF) algorithms use a linearization of the alternating current (AC) load flow equations to optimize generator dispatch in a network subject to the loading constraints of the network branches. Common algorithms…
Forecast-then-optimize is a widely-used framework for decision-making problems in power systems. Traditionally, statistical losses have been employed to train forecasting models, but recent research demonstrated that improved decision…
This paper proposes a novel and simple linear model to capture line losses for use in linearized DC models, such as optimal power flow (DC-OPF) and security-constrained economic dispatch (SCED). The \textit{Line Loss Outer Approximation}…
In recent years, the power system research community has seen an explosion of novel methods for formulating and solving power network optimization problems. These emerging methods range from new power flow approximations, which go beyond…
Secondary distribution networks (SDNets) play an increasingly important role in smart grids due to a high proliferation of distributed energy resources (DERs) in SDNets. However, most existing optimal power flow (OPF) problems do not take…
Optimal transport (OT) and unbalanced optimal transport (UOT) are central in many machine learning, statistics and engineering applications. 1D OT is easily solved, with complexity O(n log n), but no efficient algorithm was known for 1D…
With the proliferation of distributed generation into distribution networks, the need to consider fault currents in the dispatch problem becomes increasingly relevant. This paper introduces a method for adding fault current constraints into…
This paper introduces a framework to capture previously intractable optimization constraints and transform them to a mixed-integer linear program, through the use of neural networks. We encode the feasible space of optimization problems…
We consider a cell-free massive multiple-input multiple-output (CFmMIMO) network operating in dynamic time division duplex (DTDD). The switching point between the uplink (UL) and downlink (DL) data transmission phases can be adapted…
Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of…