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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…
Mixed-integer convex programming (MICP) has seen significant algorithmic and hardware improvements with several orders of magnitude solve time speedups compared to 25 years ago. Despite these advances, MICP has been rarely applied to…
Transmission system operators face a variety of discrete operational decisions, such as switching of branches and/or devices. Incorporating these decisions into optimal power flow (OPF) results in mixed-integer non-linear programming…
Formulating the alternating current optimal power flow (ACOPF) as a polynomial optimization problem makes it possible to solve large instances in practice and to guarantee asymptotic convergence in theory.
The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use…
We formulate the Alternating Current Optimal Power Flow Problem (ACOPF) as a Linear Constrained Quadratic Program (LCQP) with many negative eigenvalues ($r$) and linear constraints, making it NP-hard. We propose two algorithms, Feasible…
In this paper, we present an optimization algorithm based on an alternating projection method to solve the large-scale security constraint optimal power flow (SCOPF) problem in power systems. The SCOPF is first partitioned into…
Many steady-state problems in power systems, including rectangular power-voltage formulations of optimal power flows in the alternating-current model (ACOPF), can be cast as polynomial optimisation problems (POP). For a POP, one can derive…
Computational speed and global optimality are key needs for practical algorithms for the optimal power flow problem. Two convex relaxations offer a favorable trade-off between the standard second-order cone and the standard semidefinite…
Solving the Alternating Current Optimal Power Flow (AC OPF) problem to global optimality remains challenging due to its nonconvex quadratic constraints. In this paper, we present a unified framework that combines static piecewise…
This paper develops a novel second order cone relaxation of the semidefinite programming formulation of optimal power flow, that does not imply the `angle relaxation'. We build on a technique developed by Kim et al., extend it for complex…
The integration of large-scale renewable energy sources, such as wind power, poses significant challenges for the optimal operation of power systems owing to their inherent uncertainties. This paper proposes a solution framework for…
The optimal power flow (OPF) problem seeks to control power generation/demand to optimize certain objectives such as minimizing the generation cost or power loss in the network. It is becoming increasingly important for distribution…
We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone…
A fast and scalable iterative methodology for solving the security-constrained optimal power flow (SCOPF) problem is proposed using problem decomposition and the inverse matrix modification lemma. The SCOPF formulation tackles system…
Optimal power flow (OPF) problem is a class of large-scale and non-convex optimization problem. Various algorithms are proposed to solve the challenging OPF problem. Recent studies show that semidefinite programming (SDP) can either provide…
The Alternating Current Optimal Power Flow (ACOPF) problem remains one of the most fundamental yet computationally challenging tasks in power systems operation and planning due to its nonconvex, nonlinear, and multimodal nature. This paper…
With the increasing energy demand and the growing integration of renewable sources of energy, power systems face operational challenges such as overloads, losses, and stability concerns, particularly as networks operate near their capacity…
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…
We present a pure linear cutting-plane relaxation approach for rapidly proving tight and accurate lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF) and its multi-period extension with ramping constraints. Our…