Invited Session Tue.1.MA 549

Tuesday, 10:30 - 12:00 h, Room: MA 549

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

Multi-stage stochastic programming models for electricity systems


Chair: Andy Philpott



Tuesday, 10:30 - 10:55 h, Room: MA 549, Talk 1

Vitor Luiz de Matos
On solving multistage stochastic programs with general coherent risk measures

Coauthors: Erlon C. Finardi, Andrew B. Philpott


In this work we discuss the solution of multi-stage stochastic linear programs with general coherent risk measures, using sampling-based algorithms such as stochastic dual dynamic programming (SDDP). We describe a computational approach that changes the probability measure of the outcomes of next stage problems to compute the outer approximation of the future cost function (cuts in SDDP). This provides a lower bound on the certainty-equivalent value of the optimal policy, and requires little modification of conventional algorithms. We provide a new convergence test for this class of risk-averse problems by computing an upper bound on the certainty-equivalent value of the optimal policy, using an inner approximation algorithm. Finally, we show the results of computations on a large scale problem (the Brazilian long term hydrothermal scheduling problem), in which we compare the proposed implementation strategy with the one used previously by these authors.



Tuesday, 11:00 - 11:25 h, Room: MA 549, Talk 2

Pierre Girardeau
Modelling electricity prices and capacity expansions over a long-term horizon

Coauthor: Andrew B. Philpott


We consider a power producer who wants to minimize in the long-term the sum of its production costs and investment costs. We make a distinction between two sorts of randomness: "Day-to-day randomness'' that affects the system, like power demand, water inflows, etc. and more "sporadic randomness'' like political decisions (recently Germany decided to stop nuclear power production), long-term fuel prices trends, etc. These two kinds of randomness are treated differently.
Unlike most existing approaches which consider two-step problems, our model is a multi-stage stochastic MIP and thus allows us to obtain investment strategies rather than simple decisions. However, this program is too big to be solved directly by a commercial solver. Hence we develop a specific Dantzig-Wolfe decomposition scheme that consists in the iterative resolution of yearly subproblems coordinated by a master problem that ensures satisfaction of the non-anticipativity constraints and, in the end, optimality of the solution.
We show an experiment on the real-life problem of choosing generation and transmission investments for the New Zealand electricity system.



Tuesday, 11:30 - 11:55 h, Room: MA 549, Talk 3

Kengy Barty
A quantities decomposition scheme for energy management

Coauthors: Anes Dallagi, Arnaud Lenoir


Each country in the European electricity market has its own way to cope with its electricity demand. The utilities perform strategies that minimize their production cost under technical constraints together with information constraints. They can use to supply consumer's demand, various electricity generation units together with market offers.
The problem for each actor is to schedule its generation and determine whether or not he has to import/export electricity.
The countries are linked through the electricity grid, we propose a decomposition scheme that iterates over the interconnection flows. This scheme allows flexibility to build subproblems. We are going to present the algorithm and we are going to show how it behaves.


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