Affine decision rule approximation to immunize against demand response uncertainty in smart grids' capacity planning

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Generation expansion planning (GEP) is a classical problem that determines an optimal investment plan for existing and future electricity generation technologies. GEP is a computationally challenging problem, as it typically corresponds to a very large-scale problem that contains several sources of uncertainties. With the advent of demand response (DR) as a reserved capacity in modern smart power systems, recent versions of GEP problems model DR as an alternative for the expansion of generation, transmission and distribution networks. This adds extra uncertainties, since the availability of this resource is not known at the planning phase.In this paper, we model demand response uncertainty in a large-scale multi-commodity energy model, called ETEM, to address the GEP problem. The resulting model takes the form of an intractable multi-period adjustable robust problem which can be conservatively approximated using affine decision rules. To tackle instances of realistic size, we propose a Bender's decomposition scheme that exploits valid inequalities and favors Pareto robustly optimal solutions at each iteration. The performance of our new robust ETEM is evaluated in a realistic case study that surveys the energy system of the Swiss Arc Lémanique region. Our results show that an adjustable robust capacity expansion strategy can potentially reduce the expected total cost of the energy system by as much as 33% compared to a deterministic approach when accounting for electricity shortage penalties. Moreover, an adjustable procurement strategy can be responsible for a 9 billion Swiss francs cost reduction compared to a naive static robust strategy.
Finally, the proposed decomposition scheme improves the run time of the solution algorithm by 31% compared to the traditional Bender's decomposition.

, 28 pages

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