5,602 research outputs found
Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems
This paper deals with the impact of linear approximations for the unknown
nonconvex confidence region of chance-constrained AC optimal power flow
problems. Such approximations are required for the formulation of tractable
chance constraints. In this context, we introduce the first formulation of a
chance-constrained second-order cone (SOC) OPF. The proposed formulation
provides convergence guarantees due to its convexity, while it demonstrates
high computational efficiency. Combined with an AC feasibility recovery, it is
able to identify better solutions than chance-constrained nonconvex AC-OPF
formulations. To the best of our knowledge, this paper is the first to perform
a rigorous analysis of the AC feasibility recovery procedures for robust
SOC-OPF problems. We identify the issues that arise from the linear
approximations, and by using a reformulation of the quadratic chance
constraints, we introduce new parameters able to reshape the approximation of
the confidence region. We demonstrate our method on the IEEE 118-bus system
Temperature Overloads in Power Grids Under Uncertainty: a Large Deviations Approach
The advent of renewable energy has huge implications for the design and
control of power grids. Due to increasing supply-side uncertainty, traditional
reliability constraints such as strict bounds on current, voltage and
temperature in a transmission line have to be replaced by computationally
demanding chance constraints. In this paper we use large deviations techniques
to study the probability of current and temperature overloads in power grids
with stochastic power injections, and develop corresponding safe capacity
regions. In particular, we characterize the set of admissible power injections
such that the probability of overloading of any line over a given time interval
stays below a fixed target. We show how enforcing (stochastic) constraints on
temperature, rather than on current, results in a less conservative approach
and can thus lead to capacity gains.Comment: 12 pages (10 pages + 2 pages appendix), 2 figures. Revised version
with extended numerical sectio
Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets
We present a data-driven approach for distributionally robust chance
constrained optimization problems (DRCCPs). We consider the case where the
decision maker has access to a finite number of samples or realizations of the
uncertainty. The chance constraint is then required to hold for all
distributions that are close to the empirical distribution constructed from the
samples (where the distance between two distributions is defined via the
Wasserstein metric). We first reformulate DRCCPs under data-driven Wasserstein
ambiguity sets and a general class of constraint functions. When the
feasibility set of the chance constraint program is replaced by its convex
inner approximation, we present a convex reformulation of the program and show
its tractability when the constraint function is affine in both the decision
variable and the uncertainty. For constraint functions concave in the
uncertainty, we show that a cutting-surface algorithm converges to an
approximate solution of the convex inner approximation of DRCCPs. Finally, for
constraint functions convex in the uncertainty, we compare the feasibility set
with other sample-based approaches for chance constrained programs.Comment: A shorter version is submitted to the American Control Conference,
201
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
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