Optimal scenario tree reduction for stochastic streamflows in power generation planning problems

Abstract

The mid-term operation planning of hydro-thermal power systems needs a large number of synthetic sequences to represent accurately stochastic streamflows. These sequences are generated by a periodic autoregressive model. If the number of synthetic sequences is too big, the optimization planning problem may be too difficult to solve. To select a small set of sequences representing the stochastic process well enough, this work employs two variants of the Scenario Optimal Reduction technique. The first variant applies such a technique at the last stage of a tree defined a priori for the whole planning horizon while the second variant combines a stage-wise reduction, preserving the periodic autoregressive structure, with resampling. Both approaches are assessed numerically on hydrological sequences generated for real configurations of the Brazilian power system.

Keywords:

• scenario reduction
• stochastic programming
• operation planning of hydro-thermal systems

AMS Subject Classification :

• 65K05
• 49J52
• 60G07

Acknowledgements

The authors wish to thank the reviewers for the careful reading and for offering interesting suggestions and comments. We are particularly grateful to the reviewers for pointing out the continuity property of conditional distributions in Section 6.2, crucial for showing stability for the LOR technique. Research of the second author is supported in part by CNPq Grant 30345-2008/9, by PRONEX-Optimization, and by FAPERJ.

Notes

A ‘subsystem’ is an electrical geographical system, in our case corresponding to North, Northeast, South, and Southeast Brazilian regions.

Different branches come from different pasts.