Multivariate bias reduction in capacity expansion planning

Marie-Liesse Cauwet (1, 2) , Olivier Teytaud (2, 1)

1 TAO - Machine Learning and Optimisation
2 LRI - Laboratoire de Recherche en Informatique

The optimization of capacities in large scale power systems is a stochastic problem, because the need for storage and connections (i.e. exchange capacities) varies a lot from one week to another (e.g. power generation is subject to the vagaries of wind) and from one winter to another (e.g. water inflows due to snow melting). It is usually tackled through sample average approximation, i.e. assuming that the system which is optimal on average over the last 40 years (corrected for climate change) is also approximately optimal in general. However, in many cases, data are high-dimensional; the sample complexity, i.e. the amount of data necessary for a relevant optimization of capacities, increases linearly with the number of parameters and can be scarcely available at the relevant scale. This leads to an underestimation of capacities. We suggest the use of bias correction in capacity estimation. The present paper investigates the importance of the bias phenomenon, and the efficiency of bias correction tools (jackknife, bootstrap; combined with possibly penalized cross-validation) including new ones (dimension reduction tools, margin method)

Mots clés: power systems; bias reduction; optimization

Domaines: Optimisation et contrôle [math.OC]; Applications [stat.AP]

Marie-Liesse Cauwet, Olivier Teytaud. Multivariate bias reduction in capacity expansion planning. 19th Power Systems Computation Conference, Jun 2016, Gênes, Italy. ⟨hal-01306643⟩