## Invited Session Wed.2.MA 549

#### Wednesday, 13:15 - 14:45 h, Room: MA 549

Cluster 18: Optimization in energy systems [...]

### Robust aspects of optimization in energy management

Chair: Wim van Ackooij

Wednesday, 13:15 - 13:40 h, Room: MA 549, Talk 1

Wim van Ackooij
Decomposition methods for unit-commitment with coupling joint chance constraints

Coauthors: René Henrion, Claudia Sagastizabal

Abstract:
An important optimization problem in energy management, known as the "Unit-Commitment Problem'', aims at computing the production schedule that satisfies the offer-demand equilibrium at minimal cost. Often such problems are considered in a deterministic framework. However uncertainty is present and non-negligible. Robustness of the production schedule is therefore a key question. In this paper, we will investigate this robustness when hydro valleys are made robust against uncertainty on inflows, by using bilateral joint chance constraints. Moreover, we will make the global schedule robust, by using a bilateral joint chance constraint for the offer-demand equilibrium constraint. Since this is a fairly big model, we will investigate several decomposition procedures and compare these on a typical numerical instance. We will show that an efficient decomposition schedule can be obtained.

Wednesday, 13:45 - 14:10 h, Room: MA 549, Talk 2

Andris Möller
Probabilistic programming in power production planning

Coauthors: René Henrion, Wim Van Ackooij, Riadh Zorgati

Abstract:
Power production planning applications depend on stochastic quantities like
uncertain demand, uncertain failure rates and stochastic inflow into water
reservoirs, respectively.
To deal with the stochastic behaviour of these quantities we consider
optimization problems with joint probabilisitc constraints of the type
%
\begin{displaymath}
minx{cT x | {\mathrm{P}}(A(x) \xi ≤ b(x)) ≥ p, x ∈ X}
\end{displaymath}
%
where p ∈ (0,1) is the required probability level.
\par
The treatment of this optimization problem requires the computation of
\varphi(x) := {\mathrm{P}}(A(x) \xi ≤ b(x)).
We will present derivative formulae for special cases which extend a
classical result (see Prekopa 1995).
As in the classical result the derivative formulae reduces the computation
of gradients to the computation of function values again.
Thus the same existing codes may be used to compute \varphi(x) and
∇\varphi(x).
\par
Numerical results for selected power production applications
will be reported.

Wednesday, 14:15 - 14:40 h, Room: MA 549, Talk 3

Raimund M. Kovacevic
A process distance approach for scenario tree generation with applications to energy models

Coauthor: Alois Pichler

Abstract:
We develop algorithms to construct tree processes which are close to bigger trees or empirical or simulated scenarios and can e.g., be used for multistage stochastic programming. Our approach is based on a distance concept for stochastic processes, developed in Pflug and Pichler (2011): The process-distance used is based on the process' law, accounts for increasing information over time and generalizes the Wasserstein distance, which itself is a distance for probability measures.
In this framework we implement an algorithm for improving the distance between trees (processes) by changing the probability measure and the values related to the smaller tree. In addition we use the distance for stepwise tree reduction. Algorithms are applied to energy prices, leading to tree based stochastic programs in the area of electricity industry, involving e.g., electricity, oil and gas spot prices.

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