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Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the cost of generating power. Current can either be direct or alternating: while the former yields approximate linear programming formulations, the latter yields formulations of a much more interesting sort: namely, nonconvex nonlinear programs in complex numbers. In this technical survey, we derive formulation variants and relaxations of the alternating current optimal power flow problem.
Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is
In recent years, the power systems research community has seen an explosion of novel methods for formulating the AC power flow equations. Consequently, benchmarking studies using the seminal AC Optimal Power Flow (AC-OPF) problem have emerged as the
The trend in the electric power system is to move towards increased amounts of distributed resources which suggests a transition from the current highly centralized to a more distributed control structure. In this paper, we propose a method which ena
For a graph $G= (V,E)$, a double Roman dominating function (DRDF) is a function $f : V to {0,1,2,3}$ having the property that if $f (v) = 0$, then vertex $v$ must have at least two neighbors assigned $2$ under $f$ or {at least} one neighbor $u$ with
This paper discusses the odds problem, proposed by Bruss in 2000, and its variants. A recurrence relation called a dynamic programming (DP) equation is used to find an optimal stopping policy of the odds problem and its variants. In 2013, Buchbinder,