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Partially Adaptive Stochastic Optimization for Electric Power Generation Expansion Planning

Jikai Zou (jikai.zou***at***gatech.edu)
Shabbir Ahmed (sahmed***at***isye.gatech.edu)
Andy Sun (andy.sun***at***isye.gatech.edu)

Abstract: Electric Power Generation Expansion Planning (GEP) is the problem of determining an optimal construction and generation plan of both new and existing electric power plants to meet future electricity demand. We consider a stochastic optimization approach for this capacity expansion problem under demand and fuel price uncertainty. In a two-stage stochastic optimization model for GEP, the capacity expansion plan for the entire planning horizon is decided prior to the uncertainty realized and hence allows no adaptivity to uncertainty evolution over time. On the other hand a multi-stage stochastic optimization model allows full adaptivity to the uncertainty evolution, but is extremely difficult to solve. To reconcile the trade-off between adaptivity and tractability, we propose a partially adaptive stochastic mixed integer optimization model in which the capacity expansion plan is fully adaptive to the uncertainty evolution up to a certain period and follows the two-stage approach thereafter. Any solution to the partially adaptive model is feasible to the multi-stage model, and we provide analytical bounds on the quality of such a solution. We propose an algorithm that solves a sequence of partially adaptive models, to recursively construct an approximate solution to the multi-stage problem. We identify sufficient conditions under which this algorithm recovers an optimal solution to the multi-stage problem. Finally, we test our algorithm of a realistic scale GEP problem. Experiments show that, given a reasonable computation time limit, the proposed algorithm produces a significantly better solution than solving the multi-stage model directly.

Keywords: generation expansion planning, multi-stage stochastic optimization, approximation algorithm

Category 1: Stochastic Programming

Citation: Submitted for publication, January 2015.

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Entry Submitted: 01/03/2015
Entry Accepted: 01/05/2015
Entry Last Modified: 08/25/2016

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