## 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}

min_{x}{c^{T} 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

function values and gradients 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.