# Optimal Operation of Power Systems with Energy Storage under Uncertainty: A Scenario-based Method with Strategic Sampling

arXiv: https://arxiv.org/abs/2107.10013 · HTML: https://mlsanity.com/paper/2107.10013/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 21 Jul 2021.

## Builds on (most cited first, 9 of 9)

- [Sparsity-Exploiting Moment-Based Relaxations of the Optimal Power Flow Problem](https://mlsanity.com/paper/1404.5071/) (2014)
- [DC Optimal Power Flow with Joint Chance Constraints](https://mlsanity.com/paper/1911.12439/) (2019)
- [Ensemble Learning Based Convex Approximation of Three-Phase Power Flow](https://mlsanity.com/paper/1909.05748/) (2019)
- [Ensemble learning based linear power flow](https://mlsanity.com/paper/1910.08655/) (2019)
- [Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow](https://mlsanity.com/paper/1410.1004/) (2014)
- [Convex Hull of the Quadratic Branch AC Power Flow Equations and Its Application in Radial Distribution Networks](https://mlsanity.com/paper/1701.07146/) (2017)
- [Accurate Semidefinite Programming Models for Optimal Power Flow in Distribution Systems](https://mlsanity.com/paper/1711.07853/) (2017)
- [Uncertainty-aware Three-phase Optimal Power Flow based on Data-driven Convexification](https://mlsanity.com/paper/2005.13075/) (2020)
- [Efficient Solution Strategy for Chance-Constrained Optimal Power Flow based on FAST and Data-driven Convexification](https://mlsanity.com/paper/2105.05336/) (2021)

## Abstract (arXiv)

The multi-period dynamics of energy storage (ES), intermittent renewable generation and uncontrollable power loads, make the optimization of power system operation (PSO) challenging. A multi-period optimal PSO under uncertainty is formulated using the chance-constrained optimization (CCO) modeling paradigm, where the constraints include the nonlinear energy storage and AC power flow models. Based on the emerging scenario optimization method which does not rely on pre-known probability distribution functions, this paper develops a novel solution method for this challenging CCO problem. The proposed meth-od is computationally effective for mainly two reasons. First, the original AC power flow constraints are approximated by a set of learning-assisted quadratic convex inequalities based on a generalized least absolute shrinkage and selection operator. Second, considering the physical patterns of data and motived by learning-based sampling, the strategic sampling method is developed to significantly reduce the required number of scenarios through different sampling strategies. The simulation results on IEEE standard systems indicate that 1) the proposed strategic sampling significantly improves the computational efficiency of the scenario-based approach for solving the chance-constrained optimal PSO problem, 2) the data-driven convex approximation of power flow can be promising alternatives of nonlinear and nonconvex AC power flow.