17,033 research outputs found
Commitment and Dispatch of Heat and Power Units via Affinely Adjustable Robust Optimization
The joint management of heat and power systems is believed to be key to the
integration of renewables into energy systems with a large penetration of
district heating. Determining the day-ahead unit commitment and production
schedules for these systems is an optimization problem subject to uncertainty
stemming from the unpredictability of demand and prices for heat and
electricity. Furthermore, owing to the dynamic features of production and heat
storage units as well as to the length and granularity of the optimization
horizon (e.g., one whole day with hourly resolution), this problem is in
essence a multi-stage one. We propose a formulation based on robust
optimization where recourse decisions are approximated as linear or
piecewise-linear functions of the uncertain parameters. This approach allows
for a rigorous modeling of the uncertainty in multi-stage decision-making
without compromising computational tractability. We perform an extensive
numerical study based on data from the Copenhagen area in Denmark, which
highlights important features of the proposed model. Firstly, we illustrate
commitment and dispatch choices that increase conservativeness in the robust
optimization approach. Secondly, we appraise the gain obtained by switching
from linear to piecewise-linear decision rules within robust optimization.
Furthermore, we give directions for selecting the parameters defining the
uncertainty set (size, budget) and assess the resulting trade-off between
average profit and conservativeness of the solution. Finally, we perform a
thorough comparison with competing models based on deterministic optimization
and stochastic programming.Comment: 31 page
Ensemble updating of binary state vectors by maximising the expected number of unchanged components
In recent years, several ensemble-based filtering methods have been proposed
and studied. The main challenge in such procedures is the updating of a prior
ensemble to a posterior ensemble at every step of the filtering recursions. In
the famous ensemble Kalman filter, the assumption of a linear-Gaussian state
space model is introduced in order to overcome this issue, and the prior
ensemble is updated with a linear shift closely related to the traditional
Kalman filter equations. In the current article, we consider how the ideas
underlying the ensemble Kalman filter can be applied when the components of the
state vectors are binary variables. While the ensemble Kalman filter relies on
Gaussian approximations of the forecast and filtering distributions, we instead
use first order Markov chains. To update the prior ensemble, we simulate
samples from a distribution constructed such that the expected number of equal
components in a prior and posterior state vector is maximised. We demonstrate
the performance of our approach in a simulation example inspired by the
movement of oil and water in a petroleum reservoir, where also a more na\"{i}ve
updating approach is applied for comparison. Here, we observe that the
Frobenius norm of the difference between the estimated and the true marginal
filtering probabilities is reduced to the half with our method compared to the
na\"{i}ve approach, indicating that our method is superior. Finally, we discuss
how our methodology can be generalised from the binary setting to more
complicated situations
Convex Optimal Uncertainty Quantification
Optimal uncertainty quantification (OUQ) is a framework for numerical
extreme-case analysis of stochastic systems with imperfect knowledge of the
underlying probability distribution. This paper presents sufficient conditions
under which an OUQ problem can be reformulated as a finite-dimensional convex
optimization problem, for which efficient numerical solutions can be obtained.
The sufficient conditions include that the objective function is piecewise
concave and the constraints are piecewise convex. In particular, we show that
piecewise concave objective functions may appear in applications where the
objective is defined by the optimal value of a parameterized linear program.Comment: Accepted for publication in SIAM Journal on Optimizatio
Nonparametric estimation of concave production technologies by entropic methods
An econometric methodology is developed for nonparametric estimation of concave production technologies. The methodology, bases on the priciple of maximum likelihood, uses entropic distance and concvex programming techniques to estimate production functions.convex programming, production functions, entropy
Graphical Models for Optimal Power Flow
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 this paper, we formulate the optimal power flow problem over tree
networks as an inference problem over a tree-structured graphical model where
the nodal variables are low-dimensional vectors. We adapt the standard dynamic
programming algorithm for inference over a tree-structured graphical model to
the OPF problem. Combining this with an interval discretization of the nodal
variables, we develop an approximation algorithm for the OPF problem. Further,
we use techniques from constraint programming (CP) to perform interval
computations and adaptive bound propagation to obtain practically efficient
algorithms. Compared to previous algorithms that solve OPF with optimality
guarantees using convex relaxations, our approach is able to work for arbitrary
distribution networks and handle mixed-integer optimization problems. Further,
it can be implemented in a distributed message-passing fashion that is scalable
and is suitable for "smart grid" applications like control of distributed
energy resources. We evaluate our technique numerically on several benchmark
networks and show that practical OPF problems can be solved effectively using
this approach.Comment: To appear in Proceedings of the 22nd International Conference on
Principles and Practice of Constraint Programming (CP 2016
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