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Constrained partially observable Markov decision processes (CPOMDPs) have been used to model various real-world phenomena. However, they are notoriously difficult to solve to optimality, and there exist only a few approximation methods for…
We study an online linear programming (OLP) problem under a random input model in which the columns of the constraint matrix along with the corresponding coefficients in the objective function are generated i.i.d. from an unknown…
There is an emerging need for efficient solutions to stochastic AC Optimal Power Flow ({AC-}OPF) to ensure optimal and reliable grid operations in the presence of increasing demand and generation uncertainty. This paper presents a highly…
This paper presents a method that generates affine inequalities to strengthen the second-order conic programming (SOCP) relaxation of an alternating current optimal power flow (AC OPF) problem. The affine inequalities serve as cuts to get…
In advancing parallel programming, particularly with OpenMP, the shift towards NLP-based methods marks a significant innovation beyond traditional S2S tools like Autopar and Cetus. These NLP approaches train on extensive datasets of…
This paper presents a solver-friendly logic-based mixed-integer nonlinear programming model (LB-MINLP) to solve economic dispatch (ED) problems considering disjoint operating zones and valve-point effects. A simultaneous consideration of…
We propose a linear cutting-plane pricing algorithm tailored for large-scale electricity markets, addressing nonconvexities arising from the Alternating Current Optimal Power Flow equations. We benchmark our algorithm against a Direct…
A linear programming (LP) model is proposed to improve the performance of a controlled freeway during an emergency evacuation. Based on reasonable assumptions, the main relationships among key factors are kept without the uncertain impact…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core…
Optimal power flow (OPF) is a very fundamental but vital optimization problem in the power system, which aims at solving a specific objective function (ex.: generator costs) while maintaining the system in the stable and safe operations. In…
The recent literature has discussed the use of the relaxed Second Order Cone Programming (SOCP) to formulate Optimal Power Flow problems (OPF) for radial power grids. However, if the shunt parameters of the lines, composing the power grid,…
The problems of determining the optimal power allocation, within maximum power bounds, to (i) maximize the minimum Shannon capacity, and (ii) minimize the weighted latency are considered. In the first case, the global optima can be achieved…
In this paper, a novel quadratic convex optimal power flow model, namely, MDOPF, is proposed to determine the optimal dispatches of distributed generators. Based on the results of MDOPF, two price mechanisms, distribution locational…
The alternating-current optimal power flow (ACOPF) is one of the best known non-convex non-linear optimisation problems. We present a novel re-formulation of ACOPF, which is based on lifting the rectangular power-voltage rank-constrained…
Many power systems operation and planning computations (e.g., transmission and generation switching and placement) solve a mixed-integer nonlinear problem (MINLP) with binary variables representing the decision to connect devices to the…
We propose a robust model predictive control (MPC) method for discrete-time linear time-invariant systems with norm-bounded additive disturbances and model uncertainty. In our method, at each time step we solve a finite time robust optimal…
Enforcing state and input constraints during reinforcement learning (RL) in continuous state spaces is an open but crucial problem which remains a roadblock to using RL in safety-critical applications. This paper leverages invariant sets to…
This paper introduces a framework for solving alternating current optimal power flow (ACOPF) problems using graphics processing units (GPUs). While GPUs have demonstrated remarkable performance in various computing domains, their…
The alternating current optimal power flow (ACOPF) problem is central to modern power system operations, determining how electricity is generated and transmitted to maximize social welfare while respecting physical and operational…