Journal ArticleDOI
On the Road Between Robust Optimization and the Scenario Approach for Chance Constrained Optimization Problems
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This work proposes a new method for solving chance constrained optimization problems that lies between robust optimization and scenario-based methods, and imposes certain assumptions on the dependency of the constraint functions with respect to the uncertainty.Abstract:
We propose a new method for solving chance constrained optimization problems that lies between robust optimization and scenario-based methods. Our method does not require prior knowledge of the underlying probability distribution as in robust optimization methods, nor is it based entirely on randomization as in the scenario approach. It instead involves solving a robust optimization problem with bounded uncertainty, where the uncertainty bounds are randomized and are computed using the scenario approach. To guarantee that the resulting robust problem is solvable we impose certain assumptions on the dependency of the constraint functions with respect to the uncertainty and show that tractability is ensured for a wide class of systems. Our results lead immediately to guidelines under which the proposed methodology or the scenario approach is preferable in terms of providing less conservative guarantees or reducing the computational cost.read more
Citations
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Optimal Bidding Strategy of a Plug-In Electric Vehicle Aggregator in Day-Ahead Electricity Markets Under Uncertainty
TL;DR: In this paper, the problem of an aggregator bidding into the day-ahead electricity market with the objective of minimizing charging costs while satisfying the PEVs' flexible demand is addressed.
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A Probabilistic Framework for Reserve Scheduling and ${\rm N}-1$ Security Assessment of Systems With High Wind Power Penetration
TL;DR: A probabilistic framework to design an N-1 secure day-ahead dispatch and determine the minimum cost reserves for power systems with wind power generation is proposed and a reserve strategy according to which the reserves are deployed in real-time operation is identified.
Journal ArticleDOI
Distributionally Robust Chance-Constrained Optimal Power Flow With Uncertain Renewables and Uncertain Reserves Provided by Loads
TL;DR: In this article, the authors formulate a chance constrained optimal power flow problem to procure minimum cost energy, generator reserves, and load reserves given uncertainty in renewable energy production, load consumption and load reserve capacities, which ensures that chance constraints are satisfied for any distribution in an ambiguity set built upon the first two moments.
Journal ArticleDOI
Critical review of recent advances and further developments needed in AC optimal power flow
TL;DR: This paper provides an up-to-date critical review of the recent major advancements in the OPF state-of-the-art since 2010, identifies further challenging developments needed in order to adapt to the transition toward smarter grids, and indicates ways to address these challenges.
Journal ArticleDOI
Chance-Constrained AC Optimal Power Flow: Reformulations and Efficient Algorithms
Line Roald,Göran Andersson +1 more
TL;DR: A chance-constrained AC optimal power flow formulation, which guarantees that generation, power flows, and voltages remain within their bounds with a predefined probability, and an analytical reformulations that accurately and efficiently enforces chance constraints.
References
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Proceedings ArticleDOI
YALMIP : a toolbox for modeling and optimization in MATLAB
TL;DR: Free MATLAB toolbox YALMIP is introduced, developed initially to model SDPs and solve these by interfacing eternal solvers by making development of optimization problems in general, and control oriented SDP problems in particular, extremely simple.
Journal ArticleDOI
The Price of Robustness
Dimitris Bertsimas,Melvyn Sim +1 more
TL;DR: In this paper, the authors propose an approach that attempts to make this trade-off more attractive by flexibly adjusting the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations.
The price of the robustness
D Bertsimas,M Sim +1 more
TL;DR: An approach is proposed that flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations, and an attractive aspect of this method is that the new robust formulation is also a linear optimization problem, so it naturally extend to discrete optimization problems in a tractable way.
Journal ArticleDOI
Robust Convex Optimization
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: If U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods.
Journal ArticleDOI
Robust solutions of uncertain linear programs
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: It is shown that the RC of an LP with ellipsoidal uncertainty set is computationally tractable, since it leads to a conic quadratic program, which can be solved in polynomial time.
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