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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…
The recent rise of electricity generation based on renewable energy sources increases the demand for transmission capacity. Capacity expansion via the upgrade of transmission line capacity, e.g., by conversion to a high-voltage direct…
This is the second part of a two-part paper on data-based distributionally robust stochastic optimal power flow (OPF). The general problem formulation and methodology have been presented in Part I [1]. Here, we present extensive numerical…
Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In…
We study the optimal transport problem for pairs of stationary finite-state Markov chains, with an emphasis on the computation of optimal transition couplings. Transition couplings are a constrained family of transport plans that capture…
Optimal transmission switching (OTS) determines which transmission lines to remove from service to minimize dispatch costs. Unlike topology design, it alters the operational status of operating lines. Sensitivity-based methods, as advanced…
Optimal power flow problems (OPFs) are mathematical programs used to determine how to distribute power over networks subject to network operation constraints and the physics of power flows. In this work, we take the view of treating an OPF…
Large horsepower induction motors play a critical role as industrial drives in production facilities. The operational safety of distribution networks during the starting transients of these motor loads is a critical concern for the…
Optimal power flow (OPF) is an important tool for Independent System Operators (ISOs) to deal with the power generation management. With the increasing penetration of renewable energy into power grids, challenges arise in tackling the OPF…
The transmission-constrained unit commitment (TC-UC) problem is one of the most relevant problems solved by independent system operators for the daily operation of power systems. Given its computational complexity, this problem is usually…
The mitigation of unbalanced grid voltages or currents by voltage source converters results in power ripple on the dc link, and is a key converter design parameter due to hardware or stability considerations. Despite the importance of this…
Cascading failures in power systems normally occur as a result of initial disturbance or faults on electrical elements, closely followed by errors of human operators. It remains a great challenge to systematically trace the source of…
This paper deals with the secure Optimal Transmission Switching (OTS) problem in situations where the TSO is forced to accept the risk that some contingencies may result in the de-energization of parts of the grid to avoid the violation of…
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…
This paper focuses on the AC Optimal Power Flow (OPF) problem for multi-phase systems. Particular emphasis is given to systems with high integration of renewables, where adjustments of the real and reactive output powers from renewable…
The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The…
This paper considers the decentralized (discrete) optimal transport (D-OT) problem. In this setting, a network of agents seeks to design a transportation plan jointly, where the cost function is the sum of privately held costs for each…
Despite significant economic and ecological effects, a higher level of renewable energy generation leads to increased uncertainty and variability in power injections, thus compromising grid reliability. In order to improve power grid…
We introduce a quadratically-constrained approximation (QCAC) of the AC optimal power flow (AC-OPF) problem. Unlike existing approximations like the DC-OPF, our model does not rely on typical assumptions such as high reactance-to-resistance…
Deep Neural Networks (DNNs) approaches for the Optimal Power Flow (OPF) problem received considerable attention recently. A key challenge of these approaches lies in ensuring the feasibility of the predicted solutions to physical system…