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In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is…
In environments with increasing uncertainty, such as smart grid applications based on renewable energy, planning can benefit from incorporating forecasts about the uncertainty and from systematically evaluating the utility of the forecast…
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…
Optimal power flow (OPF) is one of the most important optimization problems in the energy industry. In its simplest form, OPF attempts to find the optimal power that the generators within the grid have to produce to satisfy a given demand.…
We consider the worst-case load-shedding problem in electric power networks where a number of transmission lines are to be taken out of service. The objective is to identify a pre-specified number of line outage that leads to the maximum…
Uncertainty from renewable energy and loads is one of the major challenges for stable grid operation. Various approaches have been explored to remedy these uncertainties. In this paper, we design centralized or decentralized state-feedback…
This letter proposes an energy efficient distributed worst case robust power allocation in massive multiple input multiple output (MIMO) system. We assume a bounded channel state information (CSI) error and all channels lie in some bounded…
With the increase of distributed energy resources in the distribution grid, planning to ensure sufficient infrastructure and resources becomes critical. Planning at the distribution level is limited by the complexities of optimizing…
The optimal power flow is an optimization problem used in power systems operational planning to maximize economic efficiency while satisfying demand and maintaining safety margins. Due to uncertainty and variability in renewable energy…
We formulate the optimal flow problem in a multi-area integrated electrical and gas system as a mixed-integer optimization problem by approximating the non-linear gas flows with piece-wise affine functions, thus resulting in a set of…
This paper proposes a linear approximation of the alternating current optimal power flow problem for multiphase distribution networks with voltage-dependent loads connected in both wye and delta configurations. We establish a set of linear…
In recent years, several applications have been proposed in the context of distribution networks. Many of these can be formulated as an optimal power flow problem, a mathematical optimization program which includes a model of the…
Optimal power flow (OPF) is a critical optimization problem that allocates power to the generators in order to satisfy the demand at a minimum cost. Solving this problem exactly is computationally infeasible in the general case. In this…
The aim of this paper is a short survey of models and methods that developed by the authors. These models and methods are used to optimize general networks with nonlinear non-convex restrictions and objectives possessing mixed…
Uncertainty in renewable energy generation has the potential to adversely impact the operation of electric networks. Numerous approaches to manage this impact have been proposed, ranging from stochastic and chance-constrained programming to…
Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments,…
This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is…
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…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
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…