Affine decision rule approximation to address demand response uncertainty in smart Grids’ capacity planning

Generation expansion planning is a classical problem that determines an optimal investment plan for the expansion of electricity network. With the advent of demand response as a reserved capacity in smart power systems, recent versions of this class of problems model demand response as an alternative for the expansion of the network. This adds uncertainties, since the availability of this resource is not known at the planning phase. In this paper, we model demand response uncertainty in a multi-commodity energy model, called ETEM, to address the generation expansion planning 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 Benders decomposition 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. Results show that an adjustable robust strategy can potentially reduce the expected cost of the 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. The proposed decomposition scheme improves the run time of the solution algorithm by 40% compared to the traditional Benders decomposition. To conclude, we provide a discussion on other possible problem formulations and implementations.