# Capacity Expansion Planning under Uncertainty subject to Expected Energy Not Served Constraints

arXiv: https://arxiv.org/abs/2501.17484 · HTML: https://mlsanity.com/paper/2501.17484/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2025.

## Built on by (most cited first, 2 of 2)

- [Randomized Feasibility Methods for Constrained Optimization with Adaptive Step Sizes](https://mlsanity.com/paper/2601.20076/) (2026)
- [Tractable Probabilistic Models for Investment Planning](https://mlsanity.com/paper/2511.13888/) (2025)

## Abstract (arXiv)

We present a method for solving a large-scale stochastic capacity expansion problem which explicitly considers reliability constraints, in particular constraints on expected energy not served. Our method tackles this problem by a Lagrange relaxation of the expected energy not served constraints. We solve the relaxed formulation in an iterative manner, using a subgradient-based method. Each iteration requires the solution of a stochastic capacity expansion problem, for which we implement a subgradient decomposition scheme in a high-performance computing infrastructure. We apply the proposed methodology on the Economic Viability Assessment model that is used by ENTSO-E in the annual European Resource Adequacy Assessment, extended to include explicit reliability constraints. The approach is able to solve this model achieving a 1.3% optimality gap. We compare our approach against accounting for reliability through penalizing load shedding at VOLL, and find that the former results in 1.6% savings in total cost. We are also able to quantify the cost savings from allowing some load curtailment in the capacity planning process, which ranges from 1.6 to 6% in the cases analyzed.